Numerical Weather Prediction: East Asian Perspectives (Springer Atmospheric Sciences) 3031405668, 9783031405662

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Springer Atmospheric Sciences

Seon Ki Park   Editor

Numerical Weather Prediction: East Asian Perspectives

Springer Atmospheric Sciences

The Springer Atmospheric Sciences series seeks to publish a broad portfolio of scientific books, aiming at researchers, students, and everyone interested in this interdisciplinary field. The series includes peer-reviewed monographs, edited volumes, textbooks, and conference proceedings. It covers the entire area of atmospheric sciences including, but not limited to, Meteorology, Climatology, Atmospheric Chemistry and Physics, Aeronomy, Planetary Science, and related subjects.

Seon Ki Park Editor

Numerical Weather Prediction: East Asian Perspectives

Editor Seon Ki Park Department of Climate and Energy System Engineering Ewha Womans University Seoul, Korea (Republic of)

ISSN 2194-5217 ISSN 2194-5225 (electronic) Springer Atmospheric Sciences ISBN 978-3-031-40566-2 ISBN 978-3-031-40567-9 (eBook) https://doi.org/10.1007/978-3-031-40567-9 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

To the Pioneers of NWP in East Asia: Dong-Kyou Lee, Zhenchao Gu, Yoshimitsu Ogura, and Ching-Yen Tsay

Preface

Numerical weather prediction (NWP) is a cutting-edge technique that can calculate and forecast the weather objectively using computational resources. It is considered one of the most significant human inventions in history. In an era of changing climate, NWP plays a critical role in modern society to save assets and human lives from catastrophic weather and climate events. The fundamental concept of NWP was elucidated about 120 years ago by Vilhelm Bjerknes through his seminal 1904 paper,1 which addressed how future atmospheric states can be predicted based on physical laws, with given initial conditions. Lewis Fry Richardson’s attempt to put Bjerknes’ idea of numerical forecasting into practice failed, as he detailed in his 1922 book2 ; his dream came true in 1950 when Julius Charney, Ragnar Fjørtof, and John von Neumann published a groundbreaking study3 based on their forecast results using the first (filtered) weather model on ENIAC,4 the first general-purpose electronic computer. The first operational NWP was conducted in Sweden in December 1954, followed by the USA in May 1955 and by Japan in June 1960 (first operational trial in 1959). East Asian scientists also performed crucial roles in the development and advancement of NWP. Inspired by Charney et al. (1950), Prof. Shigekata Syono and his student Kanzaburo Gambo at the University of Tokyo (UTokyo) immediately began working on it. Later, as noted in John Lewis’ 1993 paper,5 a group of Prof. Gambo’s students moved to the USA and took positions at various institutions, making colossal 1

Bjerknes V (1904) Das Problem der Wettervorhersage betrachtet vom Standpunkt der Mechanik und Physik (The problem of weather prediction, considered from the viewpoints of mechanics). Meteorol Z 21:1–7 (translated and edited in 2009 by Volken E and Brönnimann S in Meteorol Z 18:663–667). 2 Richardson LF (1922) Weather prediction by numerical process. Cambridge University Press, London. 3 Charney JG, Fjørtof R, von Neumann J (1950) Numerical integration of the barotropic vorticity equation. Tellus 2:237–254. 4 Electronic Numerical Integrator And Computer. 5 Lewis JM (1003) Meteorologists from the University of Tokyo: Their exodus to the United States following World War II. Bull Am Meteorol Soc 74:1351–1360. vii

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accomplishments in NWP that inspired other scientists in East Asia to become pioneers in this field. In this book, East Asian scientists who are junior to the NWP pioneers from Korea, China, Japan, and Taiwan present some of their recent contributions to the field. The book contains 21 chapters, which are topically divided into five categories. Part I begins with chapters on operational NWP systems, both historical background and current status, in China (Zhang et al.; Chen et al.) and Korea (Lee et al.; Kwon). Part II collects chapters on parameterizations and optimization: Song-You Hong, the creator of a widely used planetary boundary layer scheme, serves as the lead author of a chapter on vertical turbulence mixing in atmospheric models; Park et al. introduce new parameterization schemes for carbon allocations and snow surface albedo over the vegetated land surfaces; Yoon et al. conduct parameter uncertainty reduction via combinational optimizations. Part III consists of five chapters on data assimilation of remotely sensed (RS) data, including weather radar (Chung et al.), satellite (GeoHIS; Han et al.) and multiscale RS data (Min et al.), and of precipitation features (Otsuka et al.); additionally, model error reduction using covariance methods in an ensemble data assimilation system is presented (Lim and Park). Part IV contains chapters on precipitation systems: Hong and Kim investigate the characteristic mechanism of heavy rainfalls over East Asia through numerical modeling; Takemi discusses predictability of mesoscale precipitation systems in moist environments; Wang et al. present an example of numerical quantitative precipitation forecast in Taiwan. Part V focuses on numerical forecasting of high-impact weather (HIW) events: The conditional nonlinear optimal perturbations method is applied to ensemble forecasting (Duan et al.) and targeting observation (Qin et al.); forecasts of HIW systems in East Asia (Cha and Yoon) and Japan (Saito et al., focusing on high-performance computing) are provided; Tsuboki discusses the use of the CReSS model in high-resolution simulations of tropical cyclones and mesoscale convective systems; Takamata et al. present simulation results of a typhoon-induced decrease in lake water level. This book is dedicated to the East Asian pioneers who have made monumental contributions to NWP: Prof. Dong-Kyou Lee (Korea), Prof. Zhenchao Gu (China), Prof. Yoshimitsu Ogura (Japan), and Dr. Ching-Yen Tsay (Taiwan). Prof. Dong-Kyou Lee is an NWP pioneer who has made outstanding contributions to the advancement of atmospheric sciences in Korea. He graduated from Seoul National University (SNU) and received his MS and Ph.D. in Meteorology from the University of Wisconsin-Madison in the USA. Returning to Korea, he taught for 28 years at SNU’s Department of Atmospheric Sciences, producing many outstanding students in the areas of numerical modeling/prediction for heavy rainfall, typhoon, Changma, and regional climate. In the mid-1980s, he spearheaded the development of operational numerical weather prediction at the Korea Meteorological Administration (KMA). He was the president of the Korean Meteorological Society (1998–2000) and the Asia Oceania Geosciences Society (2008–2010). Following his retirement from SNU, he continued to contribute to operational NWP advancements as the Director General of the KMA Numerical Modeling Center (2015–2019).

Preface

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Prof. Zhenchao Gu (1920–1976) was awarded the Chinese government scholarship in 1947 to study in Sweden, where he earned a Ph.D. in Meteorology from the Stockholm University, under the supervision of internationally renowned meteorologist Carl-Gustaf Rossby. He had positions as a professor at the Institute of Geophysics and the director of the Institute of Atmospheric Physics, both of the Chinese Academy of Sciences. From the mid-1950s to the mid-1960s, he established the research fields of NWP, cloud physics and weather modification, lightning physics, atmospheric turbulence, and atmospheric sounding and observing in China. He was a pioneer of the atmospheric science research in China, and he was instrumental in promoting the establishment of Chinese numerical weather forecast operations and research work. Prof. Yoshimitsu Ogura (1922–2022) received his Ph.D. in 1954 from UTokyo, where he had graduated and joined the faculty in 1944. His research focused on homogeneous isotropic turbulence; in 1955, he received the first Meteorological Society of Japan (MSJ) Award for his work on atmospheric turbulence. He then moved to Johns Hopkins University and to the Massachusetts Institute of Technology where he collaborated with Prof. Jule Charney on NWP. He returned to Japan in 1964 to become a professor at the UTokyo Ocean Research Institute, where he also served as the director from 1965 to 1967. In 1969, he was invited by the University of Illinois Urbana-Champaign (UIUC) to establish the Laboratory for Atmospheric Research, which later became the Department of Atmospheric Sciences in 1982. He served as the department head until 1985. After retiring from the UIUC in 1988, he returned to Japan and continued research and education: He wrote a number of meteorological textbooks in Japanese, which inspired many young scientists in Japan to study general meteorology, atmospheric dynamics, mesoscale meteorology, and weather and climate. In recognition of his contributions to dynamic meteorology research and meteorology education, he received the MSJ’s Fujiwara Award in 1980 and was made an honorary member in 1998. His innovative work on constructing the governing equations for convective motion at various height scales served as the foundation for convective-scale numerical models to study thunderstorms and mesoscale convective systems and paved the way for the advancement of non-hydrostatic cloud models, which are now widely employed as a regional-scale NWP model at operational centers. Dr. Ching-Yen Tsay served as a professor at the National Taiwan University (1974–1989) and as the Director General of the Central Weather Bureau (CWB) in Taiwan (1989–1994). He modernized the CWB and instituted NWP during his stay there. Following that, he held a number of significant positions in Taiwan, including the Director General of the Civil Aviation Administration (1994–1996), the Deputy Chair of the National Science Council (1996–2000), the Minister without Portfolio of the Executive Yuan (2000–2004), and the Chairman of the Board of Directors of the Industrial Technology Research Institute, among others.

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Individual researchers and graduate students will benefit from this book as a resource for recent scientific achievements in NWP made by East Asian scientists and their international colleagues. Seoul, Republic of Korea February 2023

Seon Ki Park

Contents

Part I 1

2

3

4

Operational Prediction Systems

History and Status of Atmospheric Dynamical Core Model Development in China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yi Zhang, Jian Li, He Zhang, Xiaohan Li, Li Dong, Xinyao Rong, Chun Zhao, Xindong Peng, and Yiming Wang Development of Operational NWP in Korea: Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Woo-Jin Lee, Rae-Seol Park, In-Hyuk Kwon, Adam Clayton, Junghan Kim, and In-Jin Choi Development of the RMAPS-STv2.0 Hourly Rapid Updated Catch-up Cycling Assimilation and Forecast System . . . . . . . . . . . . . . Min Chen, Bing Lu, Jiqin Zhong, Yang Yang, Jin Feng, Wenxue Tong, Shuting Zhang, Cheng Wang, and Xiang-Yu Huang

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The Operational Run of the Newly Developed KIM and Update Efforts at Korea Meteorological Administration . . . . . . 105 Young Cheol Kwon

Part II

Physical Parameterization and Optimization

5

Vertical Turbulent Mixing in Atmospheric Models . . . . . . . . . . . . . . . 127 Song-You Hong, Hyeyum Hailey Shin, Jian-Wen Bao, and Jimy Dudhia

6

Novel Physical Parameterizations in Vegetated Land Surface Processes for Carbon Allocations and Snow-Covered Surface Albedo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Seon Ki Park, Hyeon-Ju Gim, and Sojung Park

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Contents

Reducing Model Uncertainty in Physical Parameterizations: Combinational Optimizations Using Genetic Algorithm . . . . . . . . . . . 179 Ji Won Yoon, Sujeong Lim, and Seon Ki Park

Part III Data Assimilation 8

Assimilation of Geostationary Hyperspectral Infrared Sounders (GeoHIS): Progresses and Perspectives . . . . . . . . . . . . . . . . . 205 Wei Han, Ruoying Yin, Jun Li, Xueshun Shen, Hao Wang, Jincheng Wang, Yongzhu Liu, and Di Di

9

Evaluating the Assimilation of Observable and Retrievable Weather Radar Information for Quantitative Precipitation Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Kao-Shen Chung, Chih-Chien Tsai, Chieh-Ying Ke, Phuong-Nghi Do, and Yu-Chieng Liou

10 Assimilation of Multiscale Remote Sensing Data to Improve Mesoscale Precipitation Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Ki-Hong Min, Miranti Indri Hastuti, Ji-Won Lee, Jeong-Ho Bae, Jae-Geun Lee, and Yushin Kim 11 Assimilating Precipitation Features Based on the Fractions Skill Score: An Idealized Study with an Intermediate AGCM . . . . . . 283 Shigenori Otsuka, Taeka Awazu, Christian A. Welzbacher, Roland Potthast, and Takemasa Miyoshi 12 Model Error Representations Using the Covariance Inflation Methods in Ensemble Data Assimilation System . . . . . . . . . . . . . . . . . . 295 Sujeong Lim and Seon Ki Park Part IV Precipitation Systems: Mechanism and Forecast 13 Heavy Rainfall Mechanism Over East Asia: Numerical Modeling Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Song-You Hong and Jung-Eun Esther Kim 14 Analysis and Predictability of Mesoscale Precipitating Systems in Moist Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Tetsuya Takemi 15 Quantitative Precipitation Forecasts Using Numerical Models: The Example of Taiwan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Chung-Chieh Wang, Shin-Hau Chen, Pi-Yu Chuang, and Chih-Sheng Chang

Contents

Part V

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High-Impact Weather Prediction

16 Analysis and Forecasting of High-Impact Weather Systems in East Asia Using Numerical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Dong-Hyun Cha and Donghyuck Yoon 17 Conditional Nonlinear Optimal Perturbation: Applications to Ensemble Forecasting of High-Impact Weather Systems . . . . . . . . 441 Wansuo Duan, Lichao Yang, Zhizhen Xu, and Jing Chen 18 Forecast and Numerical Simulation Studies on Meso/ Micro-scale High-Impact Weathers Using High-Performance Computing in Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 Kazuo Saito, Takuya Kawabata, Hiromu Seko, Takemasa Miyoshi, Le Duc, Tsutao Oizumi, Masaru Kunii, Guixing Chen, Kosuke Ito, Junshi Ito, Sho Yokota, Wataru Mashiko, Kenichiro Kobayashi, Shin Fukui, Eigo Tochimoto, Arata Amemiya, Yasumitsu Maejima, Takumi Honda, Hiroshi Niino, and Masaki Satoh 19 High-Resolution Simulations of Tropical Cyclones and Mesoscale Convective Systems Using the CReSS Model . . . . . . . 483 Kazuhisa Tsuboki 20 Applications of Conditional Nonlinear Optimal Perturbations to Targeting Observation of Tropical Cyclones . . . . . . . . . . . . . . . . . . . 535 Xiaohao Qin, Mu Mu, Feifan Zhou, Boyu Chen, and Jie Feng 21 Simulating Rapid Water Level Decrease of Lake Biwa Due to Typhoon Jebi (2018) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 Kohei Takatama, John C. Wells, Yusuke Uchiyama, and Takemasa Miyoshi Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

Contributors

Arata Amemiya Advanced Institute of Computer Science, RIKEN, Kobe, Japan Taeka Awazu Center for Computational Science, RIKEN, Kobe, Japan; Now at: Kanden Systems Inc., Osaka, Japan Jeong-Ho Bae National Typhoon Center, Korea Meteorological Administration, Seogwipo, South Korea Jian-Wen Bao NOAA/ESRL/PSL, Boulder, CO, USA Dong-Hyun Cha Department of Civil, Urban, Earth, and Environmental Engineering, Ulsan National Institute of Science and Technology, Ulsan, Korea Chih-Sheng Chang Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Boyu Chen Weather Forecasting Office, National Meteorological Center, China Meteorological Administration, Beijing, China Guixing Chen Sun Yat-Sen University, Guangzhou, China Jing Chen CMA Earth System Modeling and Prediction Centre, Beijing, China Min Chen Institute of Urban Meteorology, CMA, Beijing, China Shin-Hau Chen Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan In-Jin Choi Korea Institute of Atmospheric Prediction Systems, Seoul, Republic of Korea Pi-Yu Chuang Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Kao-Shen Chung Department of Atmospheric Sciences, National Central University, Taoyuan City, Taiwan

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Contributors

Adam Clayton Korea Institute of Atmospheric Prediction Systems, Seoul, Republic of Korea Di Di Nanjing University of Information Science and Technology, Nanjing, China Phuong-Nghi Do Scripps Institution of Oceanography, University of California, San Diego, CA, USA Li Dong State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China; College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China Wansuo Duan LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China Le Duc Institute of Engineering Innovation, University of Tokyo, Tokyo, Japan Jimy Dudhia NCAR, Boulder, CO, USA Jie Feng Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China Jin Feng Institute of Urban Meteorology, CMA, Beijing, China Shin Fukui Meteorological Research Institute, Tsukuba, Japan Hyeon-Ju Gim Korea Institute of Atmospheric Prediction Systems, Dongjak-gu, Seoul, Republic of Korea Wei Han CMA Earth System Modeling and Prediction Centre (CEMC), Beijing, China Miranti Indri Hastuti Agency for Meteorology, Climatology, and Geophysics of the Republic of Indonesia, Beringin, Deli Serdang, Indonesia Takumi Honda Hokkaido University, Sapporo, Japan Song-You Hong University of Colorado/CIRES and NOAA/ESRL/PSL, Boulder, CO, USA Xiang-Yu Huang Institute of Urban Meteorology, CMA, Beijing, China Junshi Ito Tohoku University, Sendai, Japan Kosuke Ito University of the Ryukyus, Okinawa, Japan Takuya Kawabata Meteorological Research Institute, Tsukuba, Japan Chieh-Ying Ke Department of Atmospheric Sciences, National Central University, Taoyuan City, Taiwan Jung-Eun Esther Kim Center for Climate Environment Change Prediction Research, Ewha Womans University, Seoul, Republic of Korea

Contributors

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Junghan Kim Korea Institute of Atmospheric Prediction Systems, Seoul, Republic of Korea Yushin Kim Department of Meteorology, University of Oklahoma, Norman, OK, USA Kenichiro Kobayashi Kobe University, Kobe, Japan Masaru Kunii Japan Meteorological Agency, Tokyo, Japan In-Hyuk Kwon Korea Institute of Atmospheric Prediction Systems, Seoul, Republic of Korea Young Cheol Kwon Numerical Modeling Center, Korea Meteorological Administration, Daejeon, Republic of Korea Jae-Geun Lee Republic of Korea Air Force, Yechon, South Korea Ji-Won Lee Department of Atmospheric Sciences, Kyungpook National University, Daegu, South Korea Woo-Jin Lee Korea Institute of Atmospheric Prediction Systems, Seoul, Republic of Korea Jian Li State Key Laboratory of Severe Weather (LASW), Chinese Academy of Meteorological Sciences, Beijing, China Jun Li National Satellite Meteorology Center (NSMC), Beijing, China Xiaohan Li State Key Laboratory of Severe Weather (LASW), Chinese Academy of Meteorological Sciences, Beijing, China; 2035 Future Laboratory, PIESAT Information Technology Co., Ltd., Beijing, China Sujeong Lim Center for Climate/Environment Change Prediction Research, Ewha Womans University, Seoul, Republic of Korea Yu-Chieng Liou Department of Atmospheric Sciences, National Central University, Taoyuan City, Taiwan Yongzhu Liu CMA Earth System Modeling and Prediction Centre (CEMC), Beijing, China Bing Lu Institute of Urban Meteorology, CMA, Beijing, China Yasumitsu Maejima Advanced Institute of Computer Science, RIKEN, Kobe, Japan Wataru Mashiko Meteorological Research Institute, Tsukuba, Japan Ki-Hong Min Department of Atmospheric Sciences and Center for Atmospheric Research, Kyungpook National University, Daegu, South Korea Takemasa Miyoshi Center for Computational Science, RIKEN, Kobe, Japan; Cluster for Pioneering Research, RIKEN, Kobe, Japan;

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Contributors

Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Kobe, Japan; University of Maryland, College Park, Maryland, USA; Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan; Advanced Institute of Computer Science, RIKEN, Kobe, Japan Mu Mu Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China Hiroshi Niino Atmosphere and Ocean Research Institute, University of Tokyo, Chiba, Japan Tsutao Oizumi Meteorological Research Institute, Tsukuba, Japan Shigenori Otsuka Center for Computational Science, RIKEN, Kobe, Japan; Cluster for Pioneering Research, RIKEN, Kobe, Japan; Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Kobe, Japan Rae-Seol Park Korea Institute of Atmospheric Prediction Systems, Seoul, Republic of Korea Seon Ki Park Department of Climate and Energy Systems Engineering, Ewha Womans University, Seodaemun-gu, Seoul, Republic of Korea Sojung Park Department of Climate and Energy Systems Engineering, Ewha Womans University, Seodaemun-gu, Seoul, Republic of Korea; Now at Clean Air Center, Korea Institute of Science and Technology (KIST), Seongbuk-gu, Seoul, Republic of Korea Xindong Peng State Key Laboratory of Severe Weather (LASW), Chinese Academy of Meteorological Sciences, Beijing, China; CMA Earth System Modeling and Prediction Center (CEMC), China Meteorological Administration, Beijing, China Roland Potthast Deutscher Wetterdienst, Division Meteorological Analysis and Modeling, Offenbach am Main, Germany; University of Reading, Reading, UK Xiaohao Qin State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China Xinyao Rong State Key Laboratory of Severe Weather (LASW), Chinese Academy of Meteorological Sciences, Beijing, China; CMA Earth System Modeling and Prediction Center (CEMC), China Meteorological Administration, Beijing, China Kazuo Saito Atmosphere and Ocean Research Institute, University of Tokyo, Chiba, Japan

Contributors

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Masaki Satoh Atmosphere and Ocean Research Institute, University of Tokyo, Chiba, Japan Hiromu Seko Meteorological Research Institute, Tsukuba, Japan Xueshun Shen CMA Earth System Modeling and Prediction Centre (CEMC), Beijing, China Hyeyum Hailey Shin NCAR, Boulder, CO, USA Kohei Takatama RIKEN Center for Computational Science, Kobe, Japan Tetsuya Takemi Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan Eigo Tochimoto Meteorological Research Institute, Tsukuba, Japan Wenxue Tong Institute of Urban Meteorology, CMA, Beijing, China Chih-Chien Tsai National Science and Technology Center for Disaster Reduction, New Taipei City, Taiwan Kazuhisa Tsuboki Institute for Space-Earth Environmental Research (ISEE), Nagoya University, Nagoya, Japan; Typhoon Science and Technology Research Center (TRC), Yokohama National University, Yokohama, Japan Yusuke Uchiyama Department of Civil Engineering, Kobe University, Kobe, Japan Cheng Wang Institute of Urban Meteorology, CMA, Beijing, China Chung-Chieh Wang Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan Hao Wang CMA Earth System Modeling and Prediction Centre (CEMC), Beijing, China Jincheng Wang CMA Earth System Modeling and Prediction Centre (CEMC), Beijing, China Yiming Wang 2035 Future Laboratory, PIESAT Information Technology Co., Ltd., Beijing, China John C. Wells Department of Civil and Environmental Engineering, Ritsumeikan University, Kusatsu, Japan Christian A. Welzbacher Deutscher Wetterdienst, Department on Numerical Modeling, Offenbach am Main, Germany Zhizhen Xu CMA Earth System Modeling and Prediction Centre, Beijing, China Lichao Yang College of Resource Environment and Tourism, Capital Normal University, Beijing, China Yang Yang Institute of Urban Meteorology, CMA, Beijing, China

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Contributors

Ruoying Yin CMA Earth System Modeling and Prediction Centre (CEMC), Beijing, China Sho Yokota Japan Meteorological Agency, Tokyo, Japan Donghyuck Yoon Department of Civil, Urban, Earth, and Environmental Engineering, Ulsan National Institute of Science and Technology, Ulsan, Korea; Program in Atmospheric and Oceanic Sciences, Princeton University, New Jersey, USA Ji Won Yoon Severe Storm Research Center, Ewha Womans University, Seoul, Republic of Korea He Zhang International Center for Climate and Environment Sciences (ICCES), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China; Earth System Numerical Simulation Science Center, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China Shuting Zhang Institute of Urban Meteorology, CMA, Beijing, China Yi Zhang State Key Laboratory of Severe Weather (LASW), Chinese Academy of Meteorological Sciences, Beijing, China; 2035 Future Laboratory, PIESAT Information Technology Co., Ltd., Beijing, China; Beijing Research Institute, Nanjing University of Information Science and Technology, Beijing, China Chun Zhao School of Earth and Space Sciences, University of Science and Technology of China, Hefei, China Jiqin Zhong Institute of Urban Meteorology, CMA, Beijing, China Feifan Zhou Key Laboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

Part I

Operational Prediction Systems

Chapter 1

History and Status of Atmospheric Dynamical Core Model Development in China Yi Zhang, Jian Li, He Zhang, Xiaohan Li, Li Dong, Xinyao Rong, Chun Zhao, Xindong Peng, and Yiming Wang

Abstract This chapter reviews the history and status of dynamical core model development efforts in China. In summary, the entire chain of model development, from basic guiding principles and algorithm design through to model implementation and evaluation, is fully covered by the Chinese modeling community. Ten modern global models that have contributed to dynamical core development are described in detail. Different modeling groups have made different choices and implemented various Y. Zhang · J. Li · X. Li · X. Rong · X. Peng State Key Laboratory of Severe Weather (LASW), Chinese Academy of Meteorological Sciences, Beijing, China e-mail: [email protected] X. Li e-mail: [email protected] X. Rong e-mail: [email protected] X. Peng e-mail: [email protected] Y. Zhang (B) · X. Li · Y. Wang 2035 Future Laboratory, PIESAT Information Technology Co., Ltd., Beijing, China e-mail: [email protected] Y. Wang e-mail: [email protected] Y. Zhang Beijing Research Institute, Nanjing University of Information Science and Technology, Beijing, China H. Zhang International Center for Climate and Environment Sciences (ICCES), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China Earth System Numerical Simulation Science Center, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China H. Zhang e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_1

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strategies for model development according to their specific objectives and areas of expertise. It is argued here that the process of model development should, in addition to improving model performance, continuously boost productivity in both the industrial and academic sectors. Three major trends (higher model resolution, earth system approach, unified weather, and climate modeling) that may affect the design and development of dynamical cores are identified in the summary section. Keyword Chinese model development

1.1 Introduction Global atmospheric models used for NWP (all abbreviations are defined in Tables 1.1 and 1.2) and climate modeling simulate the interactions among numerous complex nonlinear processes. The dynamical core is responsible for simulating the resolvedscale fluid dynamical, thermodynamic, and material transport processes (Williamson 2007). It can be regarded as a simplified three-dimensional atmospheric model that does not include diabatic processes, friction, material sources/sinks, and interactions with the underlying surface. The dynamical core1 was the first creation after the birth of atmospheric modeling. Its evolution closely follows the history of numerical atmospheric modeling (Randall et al. 2018). The development of a new dynamical core typically starts with shallow-water (wave) equations. This set of equations consists of a momentum equation and a mass continuity equation that predicts fluid depth (Vallis 2017). Physically, the shallowwater equations represent a hydrostatic, incompressible fluid of constant density on L. Dong State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China e-mail: [email protected] College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China X. Rong · X. Peng CMA Earth System Modeling and Prediction Center (CEMC), China Meteorological Administration, Beijing, China C. Zhao School of Earth and Space Sciences, University of Science and Technology of China, Hefei, China e-mail: [email protected] 1

Because the creation of a dynamical core is for practical weather and climate simulations, it would be of less interest to discuss the dynamical core independent from its host model. Thus, the terms “dynamical core” and “model” are loosely interchangeable in this chapter.

1 History and Status of Atmospheric Dynamical Core Model …

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Table 1.1 A list of the abbreviated and expanded names of models discussed in Sect. 1.3 Abbreviated model name

Full model name

BCC-AGCM

Beijing Climate Center-Atmospheric General Circulation Model

CAMS-CSM

Chinese Academy of Meteorological Science Climate System Model

FAMIL

Finite-volume Atmospheric Model of the Institute of atmospheric physics/LASG

GAMIL

Grid-point Atmospheric Model of the Institute of atmospheric physics/LASG

GRAPES

Global/Regional Assimilation PrEdiction System

GRIST

Global-Regional Integrated forecast SysTem

iAMAS

integrated Atmospheric Model Across Scales

IAP-AGCM

Institute of Atmospheric Physics-Atmospheric General Circulation Model

MCV

Multi-moment Constrained finite Volume

SAMIL

Spectral transform Atmospheric Model of the Institute of atmospheric physics/LASG

YUNMA

Yin-yang-grid UNified Model for the Atmosphere

the surface of a sphere. This can be justified when the horizontal scale of the fluid is much greater than the fluid depth. Mathematically, discretizing the shallow-water equations requires overcoming the major challenges associated with the horizontal discretization of a three-dimensional model. These challenges include, for example, designing horizontal grid, the numerical construction of the transport operator, the Coriolis term, and the explicit diffusion operators. These challenges are related to the specific forms of the equations (e.g., Arakawa and Lamb 1981; Lin and Rood 1997; Ringler et al. 2010). Williamson et al. (1992) have provided a collection of useful test cases for guiding the development of shallow-water models. A three-dimensional dry dynamical core can be developed based on the discretization method of the shallow-water equations, but the solved equations represent different physical meanings. At this stage, there are also many important design choices that may affect the behavior of the final model, including the choice of continuous equations (shallow or deep atmosphere, hydrostatic or nonhydrostatic), the vertical discretization and the vertical coordinate system. By incorporating the moisture transport equation, a moist dynamical core can be established. A moist dynamical core is a useful testing scenario with which to examine the behavior of a model under simplified physics forcing, representing the nonlinear interactions between wave dynamics, the transport of moisture species, and diabatic forcing (e.g., Thatcher and Jablonowski 2016). When one considers all of these factors, the problem of physics–dynamics coupling further occurs and poses a major challenge for model development (Gross et al. 2018). In general, faithfully mimicking the physical principles of the continuous system and obtaining an acceptable level of

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Table 1.2 A list of abbreviations and acronyms used in this paper Abbreviation/acronym

Full name

AMIP

Atmospheric Model Intercomparison Project

AMR

Adaptive Mesh Refinement

AREM

Advanced Regional Eta Model

CAM

Community Atmosphere Model

CAMS

Chinese Academy of Meteorological Sciences

CAS

Chinese Academy of Sciences

CFL

Courant–Friedrichs–Lewy

CMA

China Meteorological Administration

CMIP

Coupled Model Intercomparison Project

CPS

Climate Prediction System

CREM

Climate version of advanced Regional Eta Model

DCMIP

Dynamical Core Model Intercomparison Project

DYAMOND

DYnamics of the Atmospheric general circulation Modeled On Nonhydrostatic Domains

ECHAM

European Center for medium-range weather forecast HAMburg

ESM

Earth System Model

FFT

Fast Fourier Transform

GCR

Generalized Conjugate Residual

GFS

Global Forecast System

HEVI

Horizontally Explicit Vertically Implicit

IAP

Institute of Atmospheric Physics

LASG

Laboratory of numerical modeling for Atmospheric Sciences and Geophysical fluid dynamics

MPI

Message Passing Interface

NCAR

National Center for Atmospheric Research

NCEP

National Center for Environmental Prediction

NWP

Numerical Weather Prediction

PIO

Parallel I/O

PRM

Piecewise Rational Method

SISL

Semi-Implicit Semi-Lagrangian

TSPAS

Two-step Shape-Preserving Advection Scheme

computational efficiency are two important aspects of developing a dynamical core. The DCMIP test case suites provide many useful experimental protocols to guide the development and assessment of dynamical cores (Ullrich et al. 2017). While the development of dynamical core models in the international scientific community has a long and well-documented history, model development efforts in China have received less attention and are not as widely known in the broader

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scientific community. In this chapter, the authors present an overview of the history and status of contributions to atmospheric dynamical core model development from the Chinese modeling community. A more comprehensive review of recent progress in numerical atmospheric modeling in China is provided in a recent article by Yu et al. (2019). Some earlier reviews more specifically related to operational NWP include articles by Xue (2004), Xue and Liu (2007), and Shen et al. (2020). The remainder of this chapter is organized as follows: Sect. 1.2 describes the early works, most of which were done before the 1990s, Sect. 1.3 describes more recent model development works (i.e., in the modern era), and Sect. 1.4 provides a summary and outlook.

1.2 Early Works The early works began in the quasi-geostrophic era. Shortly after the founding of the People’s Republic of China in 1949, Liao (1956) and Gu et al. (1957) made 24- and 48-h weather forecasts using the “graphical method” (Fjørtoft 1952). They reported that the Fjørtoft quasi-geostrophic two-layer model produced errors when forecasting blocking highs because it failed to account for divergence at 500 hPa. They proposed the use of a three-layer model to calculate the geopotential height at 500 hPa. In low latitudes, the geostrophic relationship is replaced by the windpressure balance equation, as suggested by Charney (1955). Liao and Chow (1962) introduced several generalized approaches to solving the balance equation using iterative methods. These early “theoretical” models focused on the circulation over a period of a few days; they do not consider the effects of phase change of moisture or diabatic heating, and thus they cannot produce precipitation. While these early models are far from dynamical cores in the modern sense, they mark the beginning of the pursuit of NWP by Chinese scientists. With the development of computers and an increase in the availability of observational data, numerical methods more akin to those used by today’s numerical models have been refined incrementally. Chou et al. (1963) proposed a method for the solution of barotropic equations in a spherical coordinate system. Zeng (1963) suggested that the accuracy of the model solutions could be enhanced by subtracting an atmospheric temperature reference profile. This approach has become widely used in dynamical cores developed in China later (e.g., Zhang and Liang 1989; Yu 1989; Zhang 1990; Wang et al. 2004; Zhang et al. 2012). Zeng and Zhang (1987) proposed a discretization approach that is able to conserve the available energy with a reference background state removed. During this period, the study of dynamical cores focused largely on methods of maintaining long-term integration. This work provided motivation for further studies on the discretization of energy conservation (e.g., Zhang 1982) and the relationship between diffusion processes and computational instability (e.g., Ji 1986).

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Shortly after the “cultural revolution” of China, Zeng (1979) published a book “The Mathematical and Physical Basis of Numerical Weather Prediction,” in which the approach of implementing mathematical discretization methods in atmospheric modeling was systematically described. Emphasis was paid to specifically focus on formulating physically based numerical approaches that closely resemble the continuous system (e.g., conservation). This design philosophy for the dynamical core is closely aligned with the “mimetic” methods, which are widely accepted by the applied mathematical area today (Arakawa 1966; Lipnikov et al. 2014). Zeng and his colleagues developed China’s first global general circulation model, which is now known as IAP-AGCM (see Sect. 1.3.7 for details). Because global modeling in the 1980s–1990s operated at very coarse resolutions (of the order of 5°), it was hoped that higher resolution can be used for local weather prediction. Thanks to the development of limited-area modeling techniques, some of the features of IAP-AGCM were able to be used for experimental regional weather prediction. Based on discretization methods used in IAP-AGCM, Yu (1989) developed a limited-area E-grid eta-coordinate atmospheric model that is now known as AREM (Yu 1995). As suggested by the presence of “eta” in its name, AREM uses a “step-topography” approach for the representation of surface elevation (Mesinger and Veljovic 2017). This regional model has been widely used for regional weather forecasting applications in China (Yu and Xu 2004). A climate extension of AREM, known as CREM, has been developed by Shi et al. (2009). In addition to the grid-point method, at the end of the 1970s Chinese scientists successfully solved the barotropic vorticity equation using a semi-spectral method. This simplified system was subsequently used for operational forecasting from 1972 to 1973. In 1974, a three-layer quasi-geostrophic spectral model of the Northern Hemisphere was developed at the CAMS. This model was used in a small number of numerical weather forecast experiments (Zheng 1979). It adopts a special discretization strategy for the nonlinear term, in which a fully spectral treatment is used for the zonal direction while a quasi-spectral method is used for the meridional direction. This discretization algorithm is fundamentally different from the well-known interaction coefficients method (Silberman 1954) and the transform method (Orszag 1970). In this algorithm, the spectral coefficients of the nonlinear term are calculated in Fourier space, while for the interaction coefficients and spectral transform methods, the spectral coefficients are calculated in Legendre and Gaussian space, respectively. In 1976, this method was expanded to a seven-layer primitive-equation model for the Northern Hemisphere and applied to case studies. During the 1980s, it was further expanded, producing a global seven-layer model as well as a regional refinement of the hemisphere model (Zhao and Zheng 1988; Zheng 1989). The early numerical models also considered the influence of topography and sub-grid diabatic heating effects such as radiation and phase change of moisture. For instance, Chen (1964) added the dynamical effects of topography and land–sea distribution and the thermal effects of radiation, turbulence, and condensation to the two-layer quasi-geostrophic model. This model was numerically integrated with a computer using the fourth-order Runge–Kutta method, and it was used to explore weather forecasting on longer time scales. Zhu et al. (1980) focused on models with

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realistic topography and diabatic processes including radiation, boundary turbulence, and large-scale condensation. They developed a primitive-equation hemispherical model with three vertical levels and tested the model with 48-h forecasting. Zhu et al. (1983) improved this model with a modified sigma coordinate system that is similar to a hybrid coordinate system.

1.3 Modern Era Over the past three decades, model development in China has made important progress. In this section, a summary of the major developments in dynamical core modeling from different modeling groups is listed in alphabetical order by model name. These models include traditional spectral transform dynamical cores, finitedifference dynamical cores on regular latitude–longitude grids, and recent finitevolume dynamical cores built upon quasi-uniform and/or general unstructured grids. Some models have been used for weather prediction (e.g., GRAPES), while some models have been used for climate simulations (e.g., BCC-AGCM, CAMS-CSM, FAMIL, GAMIL, IAP-AGCM, SAMIL). Table 1.3 summarizes the major features of each model. A summary of their key discretization methods is given in Table 1.4. From these tables, we may see a transition that, for models that were started to develop since 2010, quasi-uniform grids (e.g., cubed-sphere, icosahedron, Yin-Yang) become more popularly used. Such a transition closely follows the development trend of high-performance computational devices.

1.3.1 BCC-AGCM BCC-AGCM was developed at the National Climate Center of the CMA for the purpose of global climate modeling (Wu et al. 2008a, b). It was originally developed as a branch of NCAR-CAM3 (Collins et al. 2006), with a significant amount of effort devoted to developing the dynamical and physical components. This kind of branching model development strategy is common in the modeling community. The dynamical core was built on the basis of the Eulerian spectral transform core of CAM3 by introducing reference stratified atmospheric temperature and reference surface pressure into the governing equations (Wu et al. 2008a, b), with the aim of improving calculations of pressure gradient force and surface pressure and temperature gradients. The results showed that the BCC-AGCM climate simulations outperformed CAM3 simulations (Wu et al. 2008a, b). Some recent improvements to this dynamical core include adapting it to higher resolutions for climate modeling (e.g., T266, T382), and the use of spatially varying divergence damping operators to improve the simulation of atmospheric temperature in the stratosphere (Wu et al. 2021). BCC-AGCM was used in CMIP5 and CMIP6 and is currently in use as a model component of CMA-CPS.

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Table 1.3 A list of the major model features, including major organization of model development, starting year of development, governing equations, typical horizontal resolutions, and major references Model

Major organization of model development

Starting year Governing of equations development

Typical global Major references horizontal resolution

BCC-AGCM Beijing Climate Center

2005

Primitive equations

30–110 km

Wu et al. (2008a, b, 2021)

CAMS-CSM

CAMS

2009

Primitive equations

25–110 km

Rong et al. (2018)

FAMIL

LASG

2010

Primitive equations

25–100 km

Zhou et al. (2015)

GAMIL

LASG

2003

Primitive equations

25–200 km

Wang et al. (2004), Li et al. (2020b)

GRAPES

NWP center at CMA

1999

Fully 12.5–50 km compressible Euler equations

Chen et al. (2008), Yang et al. (2008), Shen et al. (2020)

GRIST

CAMS, PIESAT

2017

Primitive 3.75–120 km equations/ fully compressible Euler equations

Zhang et al. (2019, 2020a)

iAMAS

University of 2020 Science and Technology of China

Fully 3–120 km compressible Euler equations

Gu et al. (2022)

IAP-AGCM

IAP

1981

Primitive equations

Zhang et al. (2012), Zhang et al. (2020b)

MCV

NWP center at CMA

2012

Fully 100 km/under compressible testing Euler equations

Li et al. (2020a, c, d), Chen et al. (2022)

SAMIL

LASG

1995

Primitive equations

160 km

Wu et al. (1996)

YUNMA

CAMS

2012

Fully 12.5 km compressible Euler equations

Li et al. (2015b), Li and Peng (2018), Chen et al. (2023)

25–140 km

Note that because some models (e.g., GRAPES) are used for weather prediction, and some models (e.g., BCC-AGCM, CAMS-CSM, FAMIL, GAMIL, IAP-AGCM, SAMIL) are used for climate simulations, the typical horizontal resolution has different implications and does not mean a limit of the model

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Table 1.4 A list of the major discretization methods used by each dynamical core Model

Spatial discretization and horizontal grid Temporal discretization

BCC-AGCM

Spectral transform, Gaussian grid

Eulerian, semi-implicit

CAMS-CSM

Spectral transform, Gaussian grid

Eulerian, semi-implicit

FAMIL

Finite volume, Arakawa-D cubed-sphere Eulerian/vertically Lagrangian, grid forward–backward

GAMIL

Finite difference, Arakawa-C regular latitude–longitude grid

Eulerian, predictor corrector

GRAPES

Finite difference, Arakawa-C regular latitude–longitude grid

Semi-Lagrangian, semi-implicit

GRIST

Finite volume, Arakawa-C icosahedral hexagonal grid

Eulerian, forward–backward, semi-implicit

iAMAS

Finite volume, Arakawa-C icosahedral hexagonal grid

Eulerian, split-explicit

IAP-AGCM

Finite difference, Arakawa-C regular latitude–longitude grid

Eulerian, predictor corrector

MCV

Multi-moment finite volume, Collocated Eulerian, horizontally explicit, cubed-sphere grid vertically implicit

SAMIL

Spectral transform, Gaussian grid

Eulerian, semi-implicit

YUNMA

Finite difference, Arakawa-C Yin-Yang grid

Semi-Lagrangian, semi-implicit

1.3.2 CAMS-CSM CAMS-CSM uses the ECHAM5 atmospheric model, which was developed at the Max Planck Institute for Meteorology (Roeckner et al. 2003). Its dynamical core also inherited the spectral transform core of ECHAM5, which can be traced back to the spectral transform core used at ECMWF. A major distinction of the CAMS-CSM dynamical core is the introduction of TSPAS (Yu 1994) to solve the moisture tracer transport equation (Rong et al. 2018). The novel aspect of this version of TSPAS is the use of a zonal leaping-point finite-difference operator for high latitudes, to avoid the timestep restriction resulting from very small grid spacing (Zhang et al. 2013). A motivation for using TSPAS instead of the original transport scheme of ECHAM5 was avoiding the overestimated precipitation rates at the southern slope of the Tibetan Plateau. Introducing TSPAS largely alleviates this bias. This is because TSPAS restricts the multi-grid transport of water vapor over the southern slope of the Tibetan Plateau, which leads to a more realistic representation of the condensation–advection problem compared with other higher-order or semi-Lagrangian-style transport methods. This model behavior is rather similar to that reported by Yu et al. (2015), although the host models are different. A more detailed analysis of the sensitivity of the condensation–advection problem to different transport methods at the southern slope of the Tibetan Plateau is given by Zhang et al. (2021; see also Sect. 1.3.5 for more details). CAMS-CSM is a model in CMIP6.

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1.3.3 GAMIL GAMIL is the only Chinese global atmospheric model that has been used in all three of the most recent CMIP phases (CMIP3, CMIP5, and CMIP6). Its dynamical core was developed based on a combination of the ideas used in the IAP dynamical core (see Sect. 1.3.7) and several novel numerical methods (Wang et al. 2004), including an implicit solver for zonal external gravity waves and an explicit time integration scheme for achieving quadratic conservation. In the meridional direction, a weighted equal-area mesh was designed to further increase stability when computations include polar regions. The main achievement of GAMIL is its spatiotemporal discretization, which conserves both linear and quadratic integral invariants, enabling the exact conservation of global available energy (i.e., sum of kinetic energy, the available potential energy, and the available surface potential energy). The first iteration of GAMIL (i.e., GAMIL1) combined its dynamical core with the physics suite of NCAR CAM2. From GAMIL1 to GAMIL2, development efforts were mostly focused on model physics (Li et al. 2013b). During this period, Zhang et al. (2008) examined a consistency issue with the GAMIL transport scheme concerning chemical species transport. They suggested that an inconsistency between the transport scheme and the discrete continuity equation may have led to spurious sources and sinks. From GAMIL2 to GAMIL3, work on developing the dynamical core resulted in the adjustment of the weight used in the area-weighted meridional grids to adapt to higher model resolutions, and several bug fixes in the moisture transport module. This corrected transport scheme led to a more balanced global average water budget. Additionally, an improved parallel implementation of the model code was achieved by considering two-dimensional domain decomposition and hybrid MPI–OpenMP parallelization (Liu et al. 2014). These efforts helped to improve computational efficiency. In recent years, the GAMIL group has sought newer numerical strategies with which to advance their approach to high-resolution modeling. First, the equation set was changed to a vector-invariant form to address a pole noise problem that was solved by Li et al. (2020). Because a part of the nonlinear momentum advection is divided and merged into the “nonlinear” Coriolis term (i.e., the sum of the quasi-linear Coriolis force term, and the rotational part of the nonlinear velocity transport term as represented by the cross product of the vertical relative vorticity and horizontal velocity vector), no time-splitting technique was applied. The advection scheme was also changed to a finite-volume scheme (Lin and Rood 1996). Second, a Gaussian convolution filter was applied to several key variables for the calculation of dynamical tendencies. The filter width varies continuously from the pole to the equator in accordance with the CFL condition (Courant et al. 1928), so that the effective zonal grid scale in the polar region is increased, improving stability. With the use of convolution techniques, the amount of data and frequency of halo exchanges were reduced (in contrast to the typical approach of using a FFT filter for high latitudes), so that the scalability of this new latitude–longitude dynamical core was largely improved. The explicit time step was increased significantly, such that a value of

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60 s is possible at a horizontal resolution of 0.25°. Additionally, the horizontal resolution can be changed flexibly according to the application. Global 0.05° resolution simulations with a time step size of 10 s were tested using 6000 CPU cores. Since the algorithms are very succinct and the rectangular grid is memory-access friendly, the computational efficiency may be comparable to that of other dynamical cores built on quasi-uniform grids after thorough optimization of parallel implementation. This new GAMIL dynamical core is still being developed intensively.

1.3.4 GRAPES In the 1990s, the operational weather forecast system at the CMA was still ported from external sources. It was realized that this arrangement lacked the versatility and sustainability required for continuous model development/improvement because the local scientists and engineers did not fully understand the ported model and were therefore unable to make scientific or technical improvements. This issue was considered a major hindrance to the continued improvement of operational NWP performance in China. In view of this difficulty, the CMA created the “GRAPES project” in 2000. The project aimed to develop a locally constructed NWP system. GRAPES was also originally intended to be used in climate modeling applications, but it was ultimately only used for short-term and medium-range weather forecasting. This limitation partly motivated the creation of BCC-AGCM, which was developed during the period 2005–2008. GRAPES was designed to be used for both global and limited-area applications, while the global and limited-area versions are separate. This issue partly motivated the development of YUNMA (see Sect. 1.3.10). Many scientists and engineers have been involved in the development and improvement of GRAPES over the last two decades. It forms the basis of the current operational global and limited-area weather forecast systems of the CMA (i.e., CMA-GFS and CMA-Meso). The GRAPES dynamical core is based on fully compressible shallow-atmosphere nonhydrostatic equations (Chen et al. 2008; Yang et al. 2008; Shen et al. 2020). The dry dynamical core is solved using a two-time-level SISL (Robert 1982) method on an Arakawa-C grid, which is widely used in global operational weather models (e.g., Davies et al. 2005). A height-based terrain-following vertical coordinate system is used, with a Charney–Phillips-style arrangement of variables. A non-centered finite-difference scheme (Semazzi et al. 1995) is used for SISL discretization. A three-dimensional vector SISL scheme based on a latitude–longitude grid (Qian et al. 1998) is used to discretize the momentum equations. The resultant elliptic equation is solved using the GCR iteration method with an incomplete lower–upper factorization to speed up the convergence of iteration. In its recent configuration, the model has 87 vertical levels with a top at 63 km for operational applications. The semi-Lagrangian method solves the material time derivative equation by tracking the fluid trajectory backwards. It can maintain numerical stability when relatively large Courant numbers are involved, though this stability comes at the

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cost of being non-conservative. The spherical departure point is calculated based on the iterative approach that searches for the midpoint at the half-time level (Ritchie and Beaudoin 1994). The departure point is limited to within the outermost halo boundaries to avoid multi-time data exchange during the parallel computation. In the classic semi-Lagrangian approach, the Lagrange advection velocity and nonlinear terms are calculated using temporal extrapolation. This may result in computational instability and even integration interruption in areas with sharp gradients, such as the westerly jet. Following the ENDGame dynamical core (Wood et al. 2014), Zhang et al. (2022a) adopted a predictor–corrector method to reduce the impact of temporal extrapolation, achieving quasi-second-order precision for temporal discretization. For tracer transport, GRAPES addresses the grid-scale advection of six-class hydrometeors (i.e., water vapor, rain droplets, cloud droplets, cloud ice, snow, and graupel). Both mixing ratio and number concentration are advected. To avoid the problem of negative water vapor in the numerical integration, a positive-definite PRM (Xiao and Peng 2004) was adopted to calculate the advection of water substances, due to its excellent monotonicity and shape-preserving properties. A dimensional splitting method is used to solve the three-dimensional problem based on the onedimensional PRM algorithm. In the SISL approach, a linearization procedure is required to generate linear terms (containing fast processes such as gravity waves) that are solved implicitly. The prognostic variables in the linear term are divided into a time-independent reference state and a small perturbation that varies with time. The earlier version of GRAPES used a one-dimensional reference state based on global mean temperature for an easier formulation. This dimensionless reference temperature can lead to large regional perturbations, thus reducing the accuracy of spatial discretization. Hence, a hydrostatic three-dimensional reference state derived from the climate mean value is used in the current version of the operational model to reduce the perturbation terms (Su et al. 2018). Changes in the reference state led to different coefficients of the elliptic equation but did not affect the GCR iteration solver. Several real-world forecast experiments have demonstrated that the three-dimensional reference state ameliorates the biases in predicted tropospheric height and temperature and reduces energy dissipation at upper levels.

1.3.5 GRIST GRIST is a unified weather–climate model system. It was created in response to a broad requirement for and calls to develop, unified weather and climate modeling in China. This “unification” process was pursued following two routes: (i) maximizing the possibility of constructing weather and climate models using a single model framework and dynamical core; (ii) maximizing the possibility of using a unified model formulation which requires minimal application-specific changes for weather-to-climate forecast applications that are relevant to most operational business demands. These two principles motivated the design of the GRIST dynamical

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core framework. Three aspects of GRIST are detailed below, including the general design, the dynamical core solver technique, and the physics–dynamics coupling and model applications. General design. Global weather and climate modeling applications still differ significantly today in terms of their spatial and temporal scales. The global weather prediction industry will continue to pursue increasing resolution, down to the kilometer scale (Bauer et al. 2021). Conventional long-term global climate modeling of multiple centuries will also be needed in the foreseeable future (Eyring et al. 2016). Appeals have been made for a thorough unification of weather and climate modeling using the kilometer-scale global models for all possible time scales (cf., Palmer 2020), but many difficulties remain unresolved in the pursuit of this goal. To maintain a sustainable model development environment that considers both present and future, the design of GRIST follows an application-driven route. This is reflected in several technical aspects of the model system. First, the dynamical core is designed to be able to switch between the hydrostatic and nonhydrostatic core in a single integration flow. This is especially valuable for coarse-grid (e.g., > 10 km) applications where the use of a nonhydrostatic set of equations hardly justifies its cost. Second, because atmosphere model physics codes typically have a long lifecycle and are often tuned for applications at different scales, GRIST is designed to be able to use different model physics suites that were originally obtained from different weather and climate modeling communities. Thus, the original application scenario of each physics suite is inherited, providing a practical starting point that can boost further development and knowledge transfer across different physics suites. Third, GRIST is designed to be free from dependency on existing, more comprehensive modeling frameworks or coupling systems. This helps to speed up the iterative development cycle and allows a greater degree of flexibility in enhancing its core function for atmospheric modeling applications. Ocean–atmosphere coupling is achieved using a third-party coupler. Dynamical core solver technique. The dynamical core (Zhang et al. 2019, 2020a) solves the primitive equations that are conventionally used for global modeling (Kasahara 1974). It has a runtime option to allow the vertical acceleration term (dw/dt, where w is height-based vertical velocity, and t is time). When the vertical acceleration term is restored, the nonhydrostatic core is able to maintain the hydrostatic balance at coarse grid spacing, and its ability to do so has been verified. The implication of this is that the prognostic equation dw/dt = F (F represents the net effect between vertical pressure gradient force and gravitational force) must create little to no acceleration at coarse grid spacings. For long-term climate modeling applications, a hydrostatic core will continue to work well because solving a nonhydrostatic set of equations should physically reproduce the hydrostatic flow. Model development experience suggests that even in real-world modeling applications with complex physics–dynamics interactions and land–sea contrast, the nonhydrostatic GRIST model produces solutions at the hydrostatic scale that are reasonably consistent with those of its hydrostatic counterpart. Figure 1.1 shows the 10-day mean precipitation rates for a weather forecast case from hydrostatic and nonhydrostatic

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model simulations. The resolution is 15 km, with 61 vertical layers and a model top at 2.25 hPa. These two models generate closely comparable simulations. This implies that the nonhydrostatic core, with its additional numerical discretization and physical modes (e.g., vertical acoustic wave), can faithfully reproduce a more simplified hydrostatic core. With all other things being equal, the nonhydrostatic core also adds ~ 30–35% more wall-clock time relative to the hydrostatic core.

Fig. 1.1 Mean precipitation rates (mm day−1 ) for a 10-day period from 15–25 June 2021 from a Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG), version 06 satellite data and b, c medium-range weather forecast experiments produced by the GRIST hydrostatic model (b) and nonhydrostatic model (c). The horizontal resolution is ~ 0.125° (15 km), with 60 vertical layers under a model top at 2.25 hPa

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The vertical discretization is formulated using a layer-averaged mass-based approach, whereby all coordinate metric terms in the governing equations are first transformed into a physical definition of layer thickness (see Zhang et al. 2019). This transforms both the advection and pressure gradient terms into a control volume formulation. With properly formulated pressure gradient algorithms, consistency between the advection and pressure-gradient terms is guaranteed. This consistency has been verified using a nonhydrostatic mountain wave test (e.g., Zhang et al. 2019). A layer-averaged approach also naturally demands a proper relation between the horizontal and vertical pressure gradient terms, by recognizing that the generalized horizontal pressure gradient term for a control volume is related to the vertical acceleration. For the most dynamical core extension, a dry-air-mass-based hybrid vertical coordinate system is used (Zhang et al. 2020a). This ensures that the dynamical core exactly conserves the dry air mass for a moist atmosphere without having to add a fixer. Horizontally, GRIST is developed on a fully unstructured mesh, which has the potential to represent arbitrarily shaped polygonal grids. The unstructured-grid modeling approach is widely used in today’s dynamical cores (see e.g., Ullrich et al. 2017); it should be noted, however, that they are not equivalent to quasi-uniform grids. Figure 1.2 shows two examples of typical unstructured-grid definitions; one grid is derived from an icosahedron, and the other is derived from a cube. Flexibility in the choice of the grid structure also allows GRIST to switch between uniform-resolution and variable-resolution meshes (Zhou et al. 2020). The horizontal numerical operators adopt the “hexagonal-C” grid approach (Thuburn et al. 2009; Ringler et al. 2010; Zhang 2018; Wang et al. 2019). In theoretical studies and simple-model experiments, the hexagonal-C grid has been found to support an excellent dispersion relation for gravity waves, as its superior isotropy leads to a good mathematical representation of the divergence and gradient operators (Niˇckovi´c et al. 2002; Thuburn 2008). Multiple scalar transport methods are also available (e.g., Skamarock and Gassmann 2011; Miura and Skamarock 2013; Zhang et al. 2017b; Zhang 2018). Zhang et al. (2021) recently described a comparison between these different numerical methods and assessed the ability of each method to deal with the condensation–advection issue near a steep slope. They showed that at the southern slope of the Tibetan Plateau, higher-order upwind-biased transport schemes are more likely to suffer from poorly modeled condensation–advection processes, because of their excessive use of the remote upwind cells at the upwind slope. A recent improvement to the passive transport module incorporates an adaptively implicit vertical moist transport scheme to enhance model stability (Li and Zhang 2022). The time integration approach is based on a combination of an inner forward– backward, semi-implicit (for a nonhydrostatic core only) integration and an outer predictor–corrector cycle. All advection terms are evaluated and marched in time in the forward step, which ensures the consistency of all mass-related transport terms (e.g., potential temperature, vorticity). For the nonhydrostatic core, the dynamical integration does not split the acoustic integration from other processes. All prognostic variables are stepped forward in their primitive forms.

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Fig. 1.2 An illustration of an unstructured mesh with two specific examples. a A grid based on a subdivided icosahedron, and b a grid based on a subdivided cube. The black lines form the “primal” cell, which is the major control volume for numerical discretization; the blue lines form the “dual” cell, which is the control volume associated with each vertex of the primal cell; the red dot indicates the intersecting point between primal- and dual-cell edges. In a hexagonal C-grid arrangement, the mass point is defined at the center of the primal cell, the normal velocity is defined at the red edge point, and the vorticity is defined at the center of the dual cell. Note that both icosahedral grid and cubed-sphere grid may also be arranged in a (semi) structured-grid approach (i.e., each grid cell can be indicated by a pair of two indices (i, j) in the memory), but different data structures are required to represent them (e.g., an icosahedral grid has ten rhombi while a cubed-sphere grid has six square faces). An unstructured approach can utilize a common data structure to represent these different grids

Physics–dynamics coupling and model applications. Zhang et al. (2020a) described how the general workflow for physics–dynamics coupling in the model system was established. They have also studied the behavior of the model using a simple physics suite. Two separate real physics suites have recently been coupled to the GRIST dynamical core (Zhang et al. 2021; Li et al. 2022). Both configurations have been tested using AMIP experiments, and the simulations are promising. While physics–dynamics coupling may sound like simply putting two components together, a number of issues must be treated carefully and may require scientific exploration. For example, pressure can have different meanings in model dynamics and physics (e.g., air pressure, mass pressure, moist or dry pressure), and using the appropriate “pressure” in the appropriate place in the model is important. In addition, certain physics suites conserve their own definitions of “total energy” (e.g., Williamson et al. 2015), which need to be carefully combined with different dynamical equation sets. Furthermore, the moist transport module and the dry dynamical core should be coupled in a mass-consistent manner by first accumulating and averaging the mass flux during the dry dynamical integration; this time-mean mass flux is used for passive tracer transport (e.g., water vapor) (Zhang et al. 2020a).

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A hexagonal-C grid model has better isotropy, but its overly high edge-to-cell ratio (3:1) also leads to several difficulties. Although the artificial computational mode caused by this issue can be well controlled (e.g., Zhang 2018), it still results in a higher computational burden (e.g., compared with a quadrilateral or triangular grid, with all other things being equal) because the edge-based computational patterns (e.g., flux divergence and gradient operators) dominate a C-grid model. That said, compared with modern global models, the computational efficiency of GRIST is competitive. Some earlier tests of its parallel computing infrastructure have been documented by Liu et al. (2020). Since then, a significant amount of work has been devoted to improving both the parallel efficiency and the algorithm implementation. This includes the use of an offline mesh partition to avoid a long waiting time due to online domain decomposition, which is beneficial for global kilometer-scale modeling. The large-scale parallel capability of GRIST was recently tested for 10,000–30,000 CPU cores, and the results were promising. GRIST’s customized group I/O function (Liu et al. 2020) is a natural fit for the massively parallel computer. GRIST has been used in the global storm-resolving model intercomparison project DYnamics of the Atmospheric general circulation Modeled On Nonhydrostatic Domains (DYAMOND; Stevens et al. 2019; https://www.esiwace.eu/ser vices/dyamond-initiative/services-dyamond-winter). The DYAMOND experiment (5 km, nonhydrostatic) uses 1600 CPU cores with a throughput of ~ 2.1 simulated days per day. Higher-resolution (3.75 km) sensitivity tests have been performed to examine the behavior of the model, particularly its self-consistency and convergent behavior (Zhang et al. 2022b). The pursuit of global kilometer-scale modeling using GRIST will continue, using both its uniform-resolution and variable-resolution configurations.

1.3.6 iAMAS The iAMAS model is established on the Sunway supercomputer with heterogeneous cores for environmental prediction (Gu et al. 2022), which includes sophisticated physical and chemical processes for global kilometer-scale simulations. Its dynamical core is based on the Model for Prediction Across Scale (Skamarock et al. 2012), a height-based split-explicit unstructured-grid nonhydrostatic model. The model code was reconstructed and adapted for the Sunway computer. A global 3-km atmospheric simulation with online interactive aerosol feedbacks was achieved. The model was scaled to 39,000,000 processor cores and achieved 0.82 simulated day per hour with routine I/O (Hao et al. 2022). Several challenging computational issues related to global kilometer-scale simulations were overcome, which are described as follows. I/O redesign. High-resolution simulations typically require many processes to achieve a desirable computational speed but performing I/O with many processes may increase the wall clock time significantly. The PIO library is a popular choice to provide a possible solution to alleviate the file-system burden due to intensive I/

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O. With PIO, a small number of processes is selected manually for handling data I/ O, while the other processes access the required data from the I/O processes via MPI communication instead of directly reading from or writing to the hard disk. This is called a “N-M-1” mode, where M processes are selected as I/O processes among all N processes. These M processes read or write one file at the same time. When the data amount becomes overly huge such as those in global kilometer-scale simulations, a dilemma occurs. M cannot be set to a small number due to the memory limitation, but it can also not be a very large number because too many processes accessing the same file at the same time will cause the I/O contention problem. Therefore, a new I/O framework called Fragmented PIO (F-PIO) is designed, which simultaneously reading or writing multiple files. This framework turns the I/ O pattern into “N-M × S-M” mode. In this mode, M communicators are generated instead of one communicator in PIO. M × S processes are manually selected as the I/ O processes to read or write M files at the same time, where S processes read or write only one file and do not interact with other groups of I/O processes. Therefore, the original single large input or output file is divided into M small files. In addition, data required by each process are stored only in one file. They are not needed to access other files during I/O. With the F-PIO method, inputting or outputting file at each time only stores the variable values on the cells, edges, or vertices of the unstructured mesh that are assigned to the corresponding process and its communication domain. The F-PIO method greatly reduces the I/O time for global kilometer-scale modeling. It solves the I/O bottleneck and significantly improves the parallel scalability. Tracer transport redesign. Tracer transport is the most time-consuming procedure of iAMAS because the number of aerosol-related tracers is 123. Most time is spent for exchanging data at the halo region. The loop bodies of the dynamical transport procedures are embedded with neighboring communications when the processes deliver a small amount of data to other processes. This computational feature occurs frequently during the model integration and thus leads to a lot of overheads. To reduce the overhead of the dynamical core, the multiple communications from all loop steps of all tracer species are aggregated into a single communication to fully utilize the communication bandwidth. The entire loop of the tracer species is decomposed into three parts: pre-communication, communication, and post-communication. The results of pre-communication computation are saved for the post-communication part. More importantly, this code redesign aggregates the pre- and post-communication computations to ensure that enough computational tasks can be loaded onto the slave cores of Sunway, which makes them computationally intensive and thus significantly increases the speedup ratio with the large-size computing system. Thread-level optimization. A compilation-guidance optimization is done for the code with a simple computational pattern in the dynamical core using the SWACC compiler based on the OpenACC 2.0 standard. This optimization method enables the distribution of computational tasks of the mesh cells to the slave cores of Sunway to achieve the thread-level parallelism.

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Data-level optimization. After completing the thread-level parallelization, datalevel parallelization for computational kernels in the dynamic core is further performed by manually vectorizing the loop of a vertical layer, because the computational and memory-access patterns among different computing procedures of the dynamic core are roughly the same, with the most inner loop iterating over the vertical layer.

1.3.7 IAP-AGCM Dynamical core design at the IAP, CAS began in the 1960s. Qingcun Zeng proposed several finite-difference schemes for the primitive equations, which guaranteed computational stability. These schemes were preliminarily applied to short-term weather forecasting in a two-level regional atmosphere model (Zeng 1961). At that time, the nonlinear instability in the computation of primitive equations posed a significant problem. Lorenz (1960) pointed out that the conservation of energy is a sufficient condition for computational stability. During the 1960s, several energyconservative schemes were proposed, such as the Lilly (1965) scheme and Arakawa (1966) scheme, which were able to improve the stability of the computation of primitive equations. However, computational instability sometimes still occurs when using these schemes. Zeng and Ji (1981) pointed out that any numerical scheme for a one-dimensional advective equation or the vorticity equation of two-dimensional non-divergent flow that does not exactly conserve or dissipate the energy always has some special solutions that result in computational instability. These unstable solutions cannot be excluded from the instantaneously energy-conservative schemes such as the Lilly scheme and the Arakawa scheme if the leapfrog difference is used in time integration. Therefore, Zeng et al. (1982) designed a time–space difference scheme conserving exactly the total energy for any initial conditions via the subtraction of a standard atmosphere and IAP transformation of variables. This time–space difference scheme was subsequently extended from Cartesian coordinates to spherical coordinates by Zeng and Zhang (1987). The accumulated experiences of dynamical core modeling described here culminated in the IAP atmospheric general circulation model version 1.0 (IAP-AGCM 1.0), which was the first operational model to incorporate these design features. The model featured a horizontal resolution of 4° (latitude) × 5° (longitude) and was developed through team efforts (Liang 1986; Zeng et al. 1989). Since there were only two vertical levels in IAP-AGCM 1.0 and the model top was 200 hPa, IAP-AGCM 2.0 was developed with a nine-level 10-hPa model top to better reproduce the behavior of the troposphere–lower stratosphere system (Zhang 1990; Liang 1996). The major change to the dynamical core of IAP-AGCM 2.0 was the use of a cubic splinefitting technique to construct the standard atmosphere. Both IAP-AGCM 1.0 and IAP-AGCM 2.0 were used in phases I and II of the AMIP experiment.

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To increase the model resolution in order to represent the forcing of complex topography and land–sea distribution, IAP-AGCM 3.0 was developed (Zuo et al. 2003). IAP-AGCM 3.0 includes 21 vertical levels, and its horizontal resolution is 2° × 2.5°. The nonlinear iterative time integration method was introduced into IAPAGCM 3.0 in place of the leapfrog scheme (Zuo et al. 2004). Furthermore, IAPAGCM 3.0 was able to benefit from parallel computing via the OpenMP technique. With the rapid development of computing technology, the programming structure and software framework of IAP-AGCM 3.0 were regarded as obsolete, and thus a radical change was required. The development of the fourth-generation model, IAP-AGCM 4.0 (Zhang et al. 2009), was based on the model framework of the widely used NCAR-CAM3.1. Major new features of the IAP-AGCM 4.0 dynamical core included a flexible leaping-point scheme, a time-splitting method, and a twodimensional parallel-decomposition algorithm. Moreover, the horizontal resolution of IAP-AGCM 4.0 was increased to 1.4° × 1.4°, with 26 vertical levels and a model top at 2.2 hPa. The latest version, IAP-AGCM 5.0, was released in 2020 as part of the CAS Earth System Model version 2.0 (CAS-ESM 2.0; Zhang et al. 2020b). In previous versions of IAP-AGCM, a Fourier filter was applied to damp the high-frequency waves in the high latitudes. However, the global data communication in the FFT algorithm imposed a serious limitation on the parallel scalability. Thus, an adaptive leap-format difference was implemented instead of the FFT filter in IAP-AGCM 5.0, to achieve higher parallel efficiency with three-dimensional decomposition (Cao et al. 2020). There are several choices of both horizontal resolution and the number of vertical levels in IAP-AGCM 5.0. The horizontal resolutions include 1.4° × 1.4°, 0.5° × 0.5°, and 0.23° × 0.31°. For the vertical resolution, both 35 levels with a top at 2.2 hPa and 69 levels with a top at 0.01 hPa can be used. Under the trend of developing higher-resolution climate models that may require more computing resources, the developers of IAP-AGCM have identified two possible ways to further improve the dynamical core of IAP-AGCM. The first is a further improvement based on the current finite-difference dynamical core, for example, the application of an implicit or semi-implicit scheme to use a large time step. The second involves designing a new dynamical core code to benefit from the powerful computing power of GPUs. Both methods represent considerable challenges that will require significant research effort. The novel features of IAP-AGCM’s dynamical core are summarized below. Subtraction of the standard atmospheric stratification. The subtraction of the standard atmospheric stratification is a method proposed by Zeng and Zhang (1982) to reduce truncation errors, especially over regions of high terrain such as the Tibetan Plateau. A model’s standard atmosphere is characterized by two functions, T˜ ( p) and ϕ( ˜ p), which are the basic vertical distributions of temperature and geopotential height, respectively. A flat sea surface is assumed and a hydrostatic balance is established. For the standard version of IAP-AGCM, the temperature profile reaches

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60 km by using the US standard Atmosphere, 1976 as a reference and a spline-fitting method (Zhang 1990). For the high-top version of IAP-AGCM, the temperature profile extends to 120 km, and some smoothing modifications have been made using the cubic B-spline method and the cubic Akima-spline method (Chai et al. 2021). The “IAP transform”. In the IAP transform, proposed by Zeng and Zhang (1982), the prognostic variables are atmospheric state variables weighted by the square root of the surface pressure, so that the numerical scheme conserves total available energy instead of total energy. The total available energy consists of kinetic energy defined by transformed zonal wind and meridional wind, available potential energy defined by transformed temperature, and available surface potential energy defined by perturbed surface pressure. Nonlinear iterative time integration method. The nonlinear iterative time integration method was proposed by Qingcun Zeng and was implemented into IAP-AGCM by Zuo et al. (2004) with three iterative steps. The first step of this method is a forward difference, the second step is a backward difference, and the final step is a center difference. The effect of this method is similar to that of the semi-implicit method, but it is much easier to implement. Time-splitting method. A time-splitting method based on work by Zeng et al. (1982) was implemented in IAP-AGCM 4.0 by Zhang et al. (2009). The primitive equations can be divided into inertia–gravity wave terms and advection terms. The inertia– gravity wave terms are quasi-linear and describe the adaptation process, which is fast, while the advection terms describe the evolution process, which is slow and is dominated by advection. The time scale of the evolution process is about ten times longer than that of the adaptation process. Therefore, the time-splitting method was designed to integrate the two processes separately with different time steps to save calculation time. Since the total available energy is conserved in both the adaptation process and the evolution process, at each step of the time-splitting method, the total available energy is instantaneously conserved. Adaptive leap-format difference scheme. One critical problem of a finite-difference scheme based on a regular latitude–longitude grid is that the zonal grid size shrinks quickly with increasing latitude, resulting in a small-time step due to the CFL condition. If the time step is larger than the threshold value determined by the CFL condition, the shortest waves will lead to an instability. Therefore, FFT filtering is applied at high latitudes to damp the amplitude of short waves and make the time step larger. However, FFT filtering is a scheme with global dependency, which incurs high communication and computation overheads and results in a scaling bottleneck. Cao et al. (2020) proposed a new leap-format finite-difference scheme with adaptive wider intervals; this local filter is able to maintain computational stability with a large time step. In this scheme, every zonal interval in the higher latitudes is automatically adjusted to the equivalent physical size of a mid-latitude (45°) reference value. The effect of this new scheme is similar to that of FFT filtering. With this adaptive leap-format difference scheme, the communication overhead of the AGCM is significantly reduced and a good load balance is achieved. Moreover, the new scheme

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is parallelized with a shifting communication scheme in the three-dimensionaldecomposition dynamical core, which achieves higher parallel scalability than the original parallel scheme based on the two-dimensional decomposition.

1.3.8 MCV Dynamical Core MCV is a numerical method that was originally developed in the field of computational fluid dynamics. It was used for solving geophysical fluid dynamics problems. This approach defines different types of “moment” (i.e., point value, volume integrated value, and derivative value) (Yabe et al. 2001) as either model variables (Xiao et al. 2006) or constraint conditions (Ii and Xiao 2007; Xiao et al. 2013) to derive the evolution equations. With a new requirement for NWP models to produce more detailed operational products, and the need to make adaptations for massively parallel computers, the MCV method was adopted by the operational NWP center of the CMA2 in 2012 to develop a new atmospheric model dynamical core. This “MCV dynamical core” had several new features: a high numerical convergence rate, material conservation, high scalability, and mesh adaptivity. Because of its spectral-like properties, the MCV dynamical core is more accurate than a traditional finite-volume model in terms of the numerical convergence rate. It also facilitated the efficient usage of new supercomputers due to the decrease in data communication among the nodes (Zhang et al. 2017a). Since the birth of the MCV method, it has been used to develop global shallowwater models (Chen and Xiao 2008; Li et al. 2008; Chen et al. 2014; Li et al. 2015a) on three quasi-uniform spherical grids, including the icosahedral–hexagonal grid, the cubed-sphere grid, and the Yin-Yang grid. It has also been used to construct a two-dimensional compressible nonhydrostatic solver for simulating idealized atmospheric flow (Li et al. 2013a), and it was further extended to three-dimensional space in the Cartesian coordinate system (Qin et al. 2019). The research studies cited here demonstrate the potential of the MCV method in the development of a new dynamical core. The MCV approach was also used in the development of the AMR shallowwater model (Chen et al. 2011). These results suggest that the AMR technique is able to achieve a comparable level of numerical accuracy with a reduced computational cost compared with the uniform high-resolution models. For the tracer transport module, where positivity is highly desirable, a nonoscillatory MCV global transport model on a cubed-sphere grid with a WENO slope limiter (Tang et al. 2018) was developed. A non-negativity correction for the MCV transport model with a WENO limiter (Li et al. 2020a, d) has also been developed. These efforts to implement the MCV approach in the development of a new nonhydrostatic dynamical core have been reviewed by Li et al. (2020a, d). 2

This operational center was reorganized and renamed the CMA Earth System Modeling and Prediction Center (CEMC) on 30th September 2021.

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More recently, a compressible nonhydrostatic atmospheric dynamical core on a cubed sphere has been built (Chen et al. 2022). A three-point MCV scheme is used for the horizontal discretization, and a conservative finite-difference scheme is used to solve the vertical flux-form equations. An optional fourth-order MCV scheme can also be used in the vertical direction, such that a fourth-order convergence rate can be achieved (Chen et al. 2020). However, this approach was abandoned due to a coupling problem with the physics suite (see details in Chen et al. 2022). For optimal model performance with massively parallel clusters, and to avoid the timestep restriction resulting from a very large ratio between the horizontal and vertical grid intervals, the HEVI approach is used. A regional/global unified nonhydrostatic atmospheric model in which this MCV dynamical core is coupled with a model physics suite originally ported from NCEPGFS is currently under development. The C-coupler was used for the physics– dynamics coupling of this model (Liu et al. 2018). The resultant global nonhydrostatic model has been used to perform several real-time forecast runs at a horizontal resolution of 1° with 60 vertical layers. The preliminary results at this coarse resolution show that the 500 hPa anomaly correlation coefficient of the MCV model is better than that of CMA-GFS and is competitive with NCEP-GFS.

1.3.9 SAMIL/FAMIL SAMIL was originally developed from the Australian spectral model at an R15L9 resolution (Wu et al. 1996). Since then, efforts have been made to reduce the truncation error and pressure gradient force error using the reference atmosphere algorithm of Zeng (1963). The results of studies of the model have shown that this scheme helps to reduce errors in the model around several major mountains. The model was later upgraded to a higher R42L26 resolution (Wang et al. 2005a, b), with its original sigma coordinate system upgraded to a hybrid sigma-pressure coordinate system (Wang et al. 2005a, b). The model code has also been restructured to increase its modularity and standardization. A relatively recent development includes the use of a flux-form semi-Lagrangian transport method (Lin and Rood 1996) in place of its original spectral transform transport advection operator (Wang et al. 2013) to increase its shape-preserving ability for moisture transport. FAMIL is a successor to the SAMIL model. It was developed by combining the finite-volume cubed-sphere (FV3 ) dynamical core (Lin 2004; Putman and Lin 2007) with the physics suite of SAMIL (Zhou et al. 2015). The dynamical core inherits most of the features of the widely used FV3 . An excellent aspect of FAMIL is its parallel scaling and I/O performance, which can scale to tens of thousands CPU cores (Zhou et al. 2012; Li et al. 2017). The CMIP5 and CMIP6 projects made use of SAMIL and FAMIL, respectively.

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1.3.10 YUNMA Around 2010, it was recognized that the use of GRAPES for higher-resolution simulations would be hindered by the “polar problem,” that is, the convergence of meridians in the polar regions. For a SISL model that has a very large stability tolerance, the polar problem still matters because it severely degrades computational performance. Too many grid points in the polar region cause a large increase in the amount of time required for the GCR to solve the elliptic equation. Although the limitedarea and global versions of GRAPES were developed separately at the CMA, a truly unified global/regional model that shares the same code is desirable. Therefore, the global–regional unified YUNMA dynamical core was developed for global and limited-area high-resolution NWPs, with flexible coordinate rotation and nesting on a quasi-uniform Yin-Yang grid. It can be also configured as a limited-area model for polar regions without singularities. YUNMA was developed using largely the same numerical algorithms as GRAPES. The Yin-Yang grid is a combination of two identical regular latitude–longitude grids with some overlapping regions (Kageyama and Sato 2004; Fig. 1.3). In the Yin-Yang grid, the coordinate for each component zone is orthogonal, without singularities. In the standard configuration, the Yang zone coincides exactly with the lowlatitude part of the latitude–longitude grid, and the Yin zone is rotated to be supplementary to the Yang zone. An advantage of the Yin-Yang grid model is that it can largely inherit the simple geometry of its regular latitude–longitude grid counterpart. Fig. 1.3 An illustration of the Yin-Yang grid, with the red mesh denoting the Yang part and blue the Yin part. The black lines represent the regular latitude–longitude grid

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The governing equations are solved with the same two-time-level SISL method as GRAPES. Because of the arbitrarily rotated coordinate system, a three-dimensional Coriolis force term has been used, leading to a small modification of the original GRAPES dynamical core (Li et al. 2015b). Bicubic Lagrangian interpolation is used to provide Dirichlet-type boundary conditions between the sub-domains for the GCR solver (Li et al. 2015b; Li and Peng 2018). Because the semi-Lagrangian transport of GRAPES does not conserve first-order integral invariants such as mass, a global mass fixer is used to conserve the total air mass at every time step. A fourth-order horizontal divergence damping (Whitehead et al. 2011) was added to the momentum equations to dissipate artificial high-frequency waves. In addition to the global model configuration, YUNMA can be configured as a limited-area model for any region on the globe (Chen et al. 2023). The generation of the limited-area grid is straightforward because it can be configured as a part of, or as an extended area of, the Yin-Yang grid. Multi-level nesting for highresolution modeling is available for both the global and regional configurations. Code sharing between the Yin and Yang components and the nesting regions facilitates easy maintenance and upgrades of the model. The nested grids are rectangular and are aligned in parallel with the horizontal coarse grid. Bicubic Lagrangian interpolation and temporal linear interpolation are used to specify lateral boundary conditions for the prognostic variables in the nested grid. This limited-area model version has recently been examined with idealized test cases and will be subjected to more realistic atmospheric simulations, such as tropical cyclones.

1.4 Summary In this chapter, an overview of the history and status of dynamical core model development in China has been presented. Although model development began in China a little later than in the international community, the entire chain of dynamical core development, from basic guiding principles and algorithm design through to model implementation and evaluation, has been fully covered. Different modeling groups have made different choices in terms of model design and development strategies, based on their own motivations, ideas, target applications, and areas of understanding. Some groups decided to develop models based on existing models, and some groups developed their models from scratch. Important things to consider are the extent to which the developed models can be continuously improved, their simulation results better understood, their development cycles and organization restructured to accommodate different application trends, and their model development processes continuously pushed forward in a sustainable and efficient manner. In short, model development should boost productivity in both the industrial and academic sectors. Doing so needs a deep and comprehensive understanding of model development and numerical modeling. Looking to the future, three major trends that may affect the design and development of dynamical core models are summarized as follows.

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Higher model resolution. Atmospheric models greatly benefit from increases in resolution. Global storm-resolving models are now much more popular than they were a decade ago (Stevens et al. 2019; https://www.esiwace.eu/services/dyamondinitiative/services-dyamond-winter). The NWP industry will continue to benefit from increasing resolution as this allows fine-scale weather details such as severe convective storms to be resolved more accurately. To accommodate higher-resolution global modeling, much more attention must be devoted to the dynamical core than to conventional model development efforts related to coarse-resolution global modeling. In that arena, improving the dynamical core is typically viewed as playing a minor role in model improvement (e.g., the philosophy outlined by Schmidt et al. 2006), and the primary expectation of the dynamical core is that it works reliably. For kilometer-scale modeling, the role of resolved model convection represented by dynamics–microphysics interactions competes with or outweighs the role of underresolved model convection represented by cumulus parameterization (e.g., Zhang et al. 2022b). Fully understanding the model dynamics and its interaction with other model physics components is a prerequisite to improving the model performance. In addition, a nonhydrostatic compressible solver is desirable for global kilometer-scale applications, although the DYAMOND project already has two models that side aside this theoretical requirement. Enhancing computational performance is important when pursuing increased model resolution, which also leads to fast turnover and iterations of the model development–application cycle. Explicit and Eulerian-style horizontal computational patterns are generally preferred over SISL-style computational patterns. Earth system approach. From an Earth system modeling perspective, the atmosphere interacts with other components in the system. This implies that to better simulate atmospheric processes, a comprehensive Earth system modeling approach is useful because many processes can affect the behavior of the atmosphere. While this approach is currently quite common in the global climate modeling community, the NWP industry conventionally mainly focuses on the atmosphere itself. To move forward, atmospheric forecasting should be replaced by forecasting of the atmospheric component of the Earth system; this approach has already been adopted by some leading operational NWP centers. Doing so implies that the robustness and stability of the dynamical core must meet the demands of dealing with a variety of environments and forcings. Consistency between dynamics and physics is also important (e.g., energy), otherwise the desired robustness may degrade. Unified weather and climate modeling. Although weather and climate models differ significantly in terms of their application scenarios and optimal design choices, it is a general hope that these two applications of atmospheric modeling can be unified as much as possible. Pursuing high-resolution modeling and comprehensive Earth system modeling are two mutually complementary routes. Recent progress in modeling techniques motivates the pursuit of an even more ambitious goal: global kilometer-scale climate simulations on the time scale of decades or even centuries (Slingo et al. 2022; Hewitt et al. 2022), in which weather and climate modeling would be truly unified. This general trend is worthy of continued research efforts.

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Unlike model physics that has higher scale and application dependencies, a unified model framework and dynamical core can be more easily achieved. Achieving this unification will not only streamline model development processes (e.g., code development, maintenance, workflow, staff management) and negate the requirement for additional repetitive work, but it will also improve cooperation between the weather and climate modeling communities. A dynamical core must therefore be capable of performing well, in both physical and computational aspects, at a broad range of spatial and temporal scales. Acknowledgements Dr. Xingliang Li is thanked for drafting the description of the MCV dynamical core. Drs. Tongwen Wu and Qing Bao are thanked for useful discussions on BCC-AGCM and SAMIL/FAMIL. This manuscript was supported the Open Research Program of the State Key Laboratory of Severe Weather (2023LASW-A02).

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Zhang H, Zhang M, Jin J et al (2020b) Description and climate simulation performance of CASESM version 2. J Adv Model Earth Syst 12(12):e2020MS002210. http://doi.org/10.1029/202 0MS002210 Zhang Y, Yu R, Li J et al (2021) AMIP simulations of a global model for unified weather-climate forecast: understanding precipitation characteristics and sensitivity over East Asia. J Adv Model Earth Syst 13(11):e2021MS002592. http://doi.org/10.1029/2021MS002592 Zhang H, Shen X, Su Y (2022a) A semi-implicit semi-Lagrangian time integration schemes with a predictor and a corrector and their applications in CMA-GFS. Acta Meteorol Sin 80(2):280–288 (in Chinese). http://doi.org/10.11676/qxxb2022.021 Zhang Y, Li X, Liu Z et al (2022b) Resolution sensitivity of the GRIST nonhydrostatic model from 120 to 5 km (3.75 km) during the DYAMOND winter. Earth Space Sci 9(9):e2022EA002401. http://doi.org/10.1029/2022EA002401 Zhao Q, Zheng Q (1988) The application of seven-level primitive equation spectral model to numerical forecasts for a limited area. J Appl Meteor Sci 3:17–24 Zheng Q (1979) A northern-hemisphere three-layer quasi-geostropic spectral model. Acta Meteorol Sin 37:36–43 (in Chinese) Zheng Q (1989) Experiments on the 30-day long-range numerical weather prediction in a seven-level spectral model. J Appl Meteor Sci 4:234–246 Zhou L-J, Liu Y-M, Bao Q et al (2012) Computational performance of the high-resolution atmospheric model FAMIL. Atmos Oceanic Sci Lett 5(5):355–359. https://doi.org/10.1080/167 42834.2012.11447024 Zhou L, Bao Q, Liu Y et al (2015) Global energy and water balance: characteristics from finitevolume atmospheric model of the IAP/LASG (FAMIL1). J Adv Model Earth Syst 7(1):1–20. https://doi.org/10.1002/2014MS000349 Zhou Y, Zhang Y, Li J et al (2020) Configuration and evaluation of a global unstructured mesh model based on the variable-resolution approach. Geosci Model Dev 1–25. https://doi.org/10. 5194/gmd-2020-150 Zhu B, Chen J, Zhang X et al (1980) A primitive equation numerical model including orography and non-adiabatic heating. Acta Meteorol Sin (2):130–141. http://doi.org/10.11676/qxxb1980.016 Zhu B, Chen J, Zhang D et al (1983) A 5-layer primitive equatiion model in a modified σ-coordinates. Acta Meteorol Sin (2):167–182. http://doi.org/10.11676/qxxb1983.019 Zuo R, Zhang M, Zhang D et al (2003) The designing and testing on the dynamic framework of IAP21L AGCM. The study on the dynamic theory, model and prediction of climate system. China Meteorological Press, pp 37–49 Zuo R, Zhang M, Zhang D et al (2004) Designing and climatic numerical modeling of 21-level AGCM (IAP AGCM-III) Part I. Dynamical framework. Chin J Atmos Sci 28(5):659–674

Chapter 2

Development of Operational NWP in Korea: Historical Perspective Woo-Jin Lee, Rae-Seol Park, In-Hyuk Kwon, Adam Clayton, Junghan Kim, and In-Jin Choi

Abstract Over the past 30 years, Numerical Weather Prediction (NWP) in Korea has advanced rapidly due to collaborative efforts between the science community and the operational modeling center, along with improved scientific understanding and the growth of information technology infrastructure, which enables provision of reliable and seamless forecast services 10 days ahead and beyond. This article gives a brief overview of the evolution, latest developments, and future directions of operational NWP in Korea. Keywords Spectral element · 4DEnVar · LETKF · Extended range · Earth system

2.1 Introduction Daily weather forecasting has been advancing with the progress in Numerical Weather Prediction (NWP). Models provide quantitative guidance on various timescales to support forecasts and warnings of high-impact weather at meteorological centers and decision-making in weather-sensitive business sectors. With the W.-J. Lee (B) · R.-S. Park · I.-H. Kwon · A. Clayton · J. Kim · I.-J. Choi Korea Institute of Atmospheric Prediction Systems, Park Square 4F, 35 Boramae-ro 5-gil, Dongjak-gu, Seoul 07071, Republic of Korea e-mail: [email protected] R.-S. Park e-mail: [email protected] I.-H. Kwon e-mail: [email protected] A. Clayton e-mail: [email protected] J. Kim e-mail: [email protected] I.-J. Choi e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_2

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ever-increasing model resolution and more and more sophisticated physics, NWP models have become an indispensable tool to meet the needs of a society requesting fine-scale weather details with longer and longer lead times. Korea is affected by the various severe weather phenomena typical of mid-latitude nations, such as heavy rain and tropical cyclones, snow storms, severe thunderstorms with violent winds, hail and lightning, dust storms, and temperature extremes. The rugged orography and densely populated cities, particularly near shorelines, add complexity and challenges to modelers and forecasters trying to protecting its people and economic activities from meteorological stresses and extremes. The Korean peninsula sits at the entrance of the Pacific storm track where baroclinic processes are very active. Baroclinic waves are frequently spawned and move downstream across the nation, often developing into bomb storms. Located on the eastern rim of the Asian continent, between the Tibetan Plateau and the Pacific Ocean, Korea is subject to the monsoon, with distinct weather regimes between summer and winter (Ludlum 1950; Lee 2010). In summer, southerly winds bring heavy rainfall and tropical cyclones modulated by the Madden Julian Oscillation (MJO) activity along with hot and humid air. In winter, northerly winds bring occasional cold surge outbreaks and snow storms, which are sometimes anchored by a blocking high near the Kamchatka peninsula. As in many Asian countries operational model development in Korea only started in the late 80s, even though forecasters began to produce forecasts from foreign NWP products a decade or two earlier. Thirty years later, Korea now runs a domestically developed global model and data assimilation (DA) system 4 times daily to predict the state of atmosphere 10 days ahead, which can be accessed by users through various forms of interactive devices to generate visual charts and probabilistic guidance. The performance of the model is within the range of the medium group of major international global models, as illustrated in a companion article in this book (Kwon 2023). This article provides a review of the status and prospects of operational NWP development in Korea. A brief history of operational NWP development is presented in Sect. 2.2. The salient features of the model and data assimilation are described in Sects. 2.3 and 2.4, respectively. Finally, future prospects are discussed in Sect. 2.5.

2.2 Historical Background Early Development NWP science in Korea has been slowly evolving through atmospheric research since the late 1970s. Simplified filtered equation models based on quasi-geostrophic theory were first developed to diagnose or simulate large-scale atmospheric processes. Around the mid-80s, foreign primitive equation models were introduced to the Korea Meteorological Administration (KMA) and universities. These models were

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primarily used for research, including simulations of cyclone development and heavy rainfall along monsoon fronts in Asia. Despite initial simulation results, which indicated a potential value for weather forecasting, a model would not be fully applied to operational NWP for another decade. Making a community model operational requires enormous effort to expand pre- and post-processing, data assimilation, workflow sequences, monitoring, and diagnostic tools. Optimization and parallelization are crucial to ensure that there is enough computing power to meet the timeline of the weather forecasting business. Operational Infrastructure Operation of an NWP system requires both technological infrastructure and personnel with domain knowledge and expertise. The technological infrastructure was gradually built up during 1980 to 1990. The transmission of observations through global telecommunication systems was automated first, followed by printed weather maps without human intervention. Pre- and post-processing of the NWP system, including statistical interpretation of the model’s output, was implemented on a mainframe computer, while the mesoscale model (MM4) from the National Center for Atmospheric Research was operating on a remote supercomputer through a batch process. The knowledge gained from the early development provided a strong foundation for running a fully operational NWP system and to apply the results to weather forecasting. In 1990, a new department dedicated to the development and operation of NWP was formally established under KMA with about 20 staff members. KMA’s first supercomputer was installed in 1999, giving the ability to run a global model and data assimilation system in real time. Regular upgrades to the supercomputer occurred every five years. The peak performance after the fifth upgrade period reached 51 Peta Flops, which correlates to two hundred thousand times faster than the first version. Building Expertise Turning to 2000, regional community models have been widely used in academic circles for case simulations and sensitivity experiments to understand physical mechanisms, extending to the downscaling of climate change scenarios. Others have applied Earth system models to climate change studies with various modified physical parameterizations. In parallel with applying the models for research, there were also active developments in physical parameterizations and dynamical cores (for instance Hong et al. 2013; Cheong 2006). Physics options, including the Yonsei University (YSU) planetary boundary layer (PBL) scheme, and convective gravity wave drag parameterization were plugged into community models for international use (Lee and Hong 2005; Chun et al. 2008). More details on academic research activities are found in the review article Lee et al. (2023). Research in model development and applications significantly helped build expertise in numerical modeling, which worked as a fundamental human resource later to develop an in-house model. In the operational center at KMA, the global spectral model of the Japan Meteorological Agency (GSM JMA) and the community mesoscale model were implemented and used operationally until both were replaced by the unified model (UM)

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of the UK Met Office in 2010. An optimal interpolation scheme was implemented first and then replaced by variational data assimilation schemes—3DVar and 4DVar. Direct assimilation of satellite radiances was made available along with the variational data assimilation framework. As the quality of the initial analyses improved, so did the global model performance. The global model provided reliable background and lateral boundary conditions for regional community model runs. The quality of the weather charts improved as well, and forecasters were able to add minor modifications creating finer scales, including frontal positions. A detailed history of operational NWP at KMA is summarized in the historical review published by the Korea Institute of Atmospheric Predictions (KIAPS 2011). Ensembles of model runs made it possible to produce a probabilistic forecast of weather elements, such as precipitation and temperature at a medium range. The ensemble perturbations were first generated by a combination of time-lagged ensembles and fast-growing modes and then replaced by ensemble transform Kalman filter (ETKF) perturbations along with the UM. The updated model output statistics (MOS) were used to interpret high-resolution regional model predictions, which supported the hourly digital forecast database on a village scale. Operation of global and regional models, data assimilation, and ensemble systems requires handling of a huge amount of observations and interim numerical products associated with pre-processing, quality control, data processing, post-processing, and customization to support diverse user needs. To meet with the ever-increasing workload, the organization size for operational NWP has expanded triple fold, with specialized subdivisions for models, data assimilation, and operations, respectively. Various interface tools were developed to help forecasters interpret NWP guidance. Model Development Project KMA regularly provided research funding for short-term NWP projects, mostly for the duration of 2–5 years, with steadily increasing funding since the mid-2000s. Even though the subjects were diverse due to the interest and specialty of the project awardees, they pivoted the technology from research into operations. Expertise gained through academic research along with the operational experience at KMA provided a strong framework for a more strategic and coherent research program and resulted in the initiation of a 9-year NWP development project (2011–2019). The Korea Development Institute estimated the monetary value of the project in terms of the unit increment of heavy rainfall warning lead time. The total benefits were valued conservatively at about 71 million USD, which would increase further if indirect benefits were included (Lee 2013). KIAPS was established in 2011 to carry out a research program under the commission of KMA, meeting KMA’s priorities in contributing to Korea’s NWP capability. The Numerical Modeling Center (NMC) at KMA is responsible for the operation of the model and data assimilation system developed at KIAPS. Thus, NMC informs KIAPS about operational needs and provides general directions, and KIAPS in turn provides model and data assimilation codes that meet these operational requirements. Experimental evaluation of the developed code is conducted at KIAPS, and operational evaluation and stability tests are carried out at NMC.

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During the project period, KIAPS developed a non-hydrostatic global model called Korea Integrated Model (KIM) using a spectral element dynamical core on a cubed-sphere grid and a hybrid-4DEnVar data assimilation system incorporating LETKF ensemble perturbations. A brief history of the model development is summarized in KIAPS (2020). The KIM runs 4 times a day with 12-day forecasts at 00 and 12 UTC and 3-day forecasts at 06 and 18 UTC. The latest model performance is comparable to that of some of the major global modeling centers. More details on model performance and subsequent improvements are described in Kwon (2023). Comprehensive reviews of the KIM dynamical core, data assimilation, and operational system, with supporting experimental results, are found in Hong et al. (2018), Kwon et al. (2018), and Kim et al. (2018), respectively. The following two sections describe the major features therein, with the updates representing the current configuration of the operational NWP.

2.3 Model Dynamical Core Terrain-Following Coordinate The KIM is based on the non-hydrostatic primitive equations on hydrostatic pressure (or mass) coordinates (Laprise 1992; Skamarock et al. 2021). The governing equations are formulated on a hybrid vertical coordinate denoted by η ∈ [0, 1], using dry hydrostatic pressure (Choi and Hong 2016). pd = [η − B(η)][ p0 − pt ] + B(η)[ ps − pt ] + pt ,

(2.3.1)

where pd is the hydrostatic pressure of dry air and B(η) is the relative weighting of the terrain-following coordinate versus the normalized pressure coordinate, designed to closely represent the rugged surface features, while the topographical influence is effectively attenuated in the free atmosphere. ps , pt , and p0 are the hydrostatic surface pressure of dry air, the top-level pressure, and a reference sea level pressure, respectively. The current KIM version has 91 vertical levels. Governing Equations The flux form variables are introduced as: ˙ θ, q∗ , c∗ ) (V , W, Ω, ϴ, Q ∗ , C∗ ) ≡ μd (v, w, η,

(2.3.2)

with μd ≡

∂ pd , ∂η

(2.3.3)

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where μd is the mass of the dry air per unit area and unit column. v ≡ (u, v) and w are the velocities in the horizontal and vertical directions, respectively, η˙ ≡ dη is the dt contravariant vertical velocity, θ is the potential temperature, q∗ are the mixing ratios for water vapor and four hydrometeors (cloud, ice, rain, snow), and c∗ is concentrate for cloudiness. Using the flux form variables in Eq. 2.3.2 and perturbed variables (Klemp et al. 2007), the moist Euler equations on the sphere can be written as ] [ ] [ ∂(Ωv) ∂V ˆ = − ζ k × V + μd ∇ K − + v∇ · V ∂t ∂η [ )] ( ' ( ) α ∂p μd ∇ϕ ' + αd ∇ p ' + αd' ∇ p + ∇ϕ − μ'd − αd ∂η ] [ ] [ Wv + FV − f kˆ × V − eW iˆ + (2.3.4) a [ ] ∂(Ωw) ∂W = − ∇ · (V w) + ∂t ∂η ) ] [( )( ' ∂p α ' − μd (qv + qc + qi + qr + qs ) − μd +g αd ∂η ] [ v·V + FW + eU + (2.3.5) a [ ] ∂(Ωθ ) ∂ϴ = − ∇ · (V θ ) + + Fϴ (2.3.6) ∂t ∂η [ ] ∂ϕ g 1 ∂ϕ ' V · ∇ϕ + Ω =− + W (2.3.7) ∂t μd ∂η μd [ ] ∂Ω ∂μ'd =− ∇·V + (2.3.8) ∂t ∂η [ ] ∂ Q∗ ∂(Ωq∗ ) = − ∇ · (V q∗ ) + + FQ ∗ (2.3.9) ∂t ∂η [ ] ∂C∗ ∂(ΩC∗ ) = − ∇ · (V C∗ ) + + FC∗ , (2.3.10) ∂t ∂η where ∇ is horizontal gradient on η surface. αd is the specific volume (or inverse density) of the dry air and α is the specific volume of the moist air, i.e., α = αd (1 + qv + qc + qi + qr + qs )−1 , where qv , qc , qi , qr , qs are mixing ratios for water vapor, cloud water and ice, rain, and snow, respectively. f = 2Ωe sin φ is the Coriolis parameter, ϕ is the geopotential, and φ is the latitude. Ωe is the angular rotation rate of the Earth. K = |v|2 /2 is the horizontal kinetic energy. iˆ and kˆ are unit vectors in

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longitudinal and vertical directions, respectively. ∇ × v = ζ kˆ is the vertical component of relative vorticity. Fs represent external forcing terms from sub-grid-scale physical processes. It is noted that the curvature terms with the mean Earth radius a and e = 2Ωe cos φ near the end of the momentum equations Eqs. 2.3.4–2.3.5 come from the Coriolis force and horizontal advection on the spherical surface. The change in horizontal grid distance as a function of height above the surface is not taken into account. The perturbations p ' , ϕ ' , αd' , μ'd are departures from the hydrostatically balanced reference state and defined as p = pd + p ' , ϕ = ϕ + ϕ ' , αd = αd + αd' , μd = μd + μ'd , respectively. The reference state variables denoted by overbars satisfy the governing equations for every atmosphere column at rest, which varies in both horizontal and vertical direction. The perturbed form of the equations is advantageous to reduce numerical errors in the pressure gradient in Eq. 2.3.4 and buoyance calculations in Eq. 2.3.5 along with rugged orography (Klemp et al. 2007; Skamarock et al. 2021). The perturbed specific volume for dry air αd' is diagnostically determined from the definition of dry hydrostatic vertical coordinate, i.e., ∂ϕ ' = −μd αd' − αd μ'd . ∂η

(2.3.11)

Lastly, the full pressure p is diagnostically obtained from the equation of state. ( p = p0

R d θm p0 αd

) ccp v

,

(2.3.12)

( ( ) ) where θm = θ 1 + RRvd qv ≈ θ (1 + 1.61qv ) is a modified potential temperature, with specific heat for constant pressure cp = cv + Rd , gas constant for dry air Rd , and specific heat for constant volume cv . The flux form is not applied to the advection terms in the momentum equation Eq. 2.3.4 and mass continuity Eq. 2.3.7. The advection terms in Eqs. 2.3.4–2.3.6 and 2.3.8–2.3.10 are written in vector invariant form to facilitate coordinate transformation from the spherical coordinate to the local coordinate on the cubed-sphere. In passing, the second term in the right of Eq. 2.3.4 represents the vertical advection term. The explicit prognostic variables are V , W , ϴ, ϕ ' , μ'd , Q ∗ , and C∗ , while Ω, αd' , and α are diagnostically derived. While total mass conservation is separated into a dry air mass part in Eq. 2.3.8 and a hydrometeor part in Eq. 2.3.9, the coupling of dry air mass to the prognostic variables is retained throughout the governing equations. It is noted that the dry surface pressure is derived from the surface pressure by subtracting the moisture contribution in the post-processing stage of data assimilation. Spectral Element Solver Considering the scalability in a distributed computing environment, and load balancing over Polar Regions, KIAPS applies the spectral element method (SEM) on a cubed-sphere in line with the CAM-SE numerics (Dennis et al. 2011). The numeric

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solver for the non-hydrostatic governing equations, Eqs. 2.3.4–2.3.10, is based on the spectral element method (SEM) for horizontal discretization and the finite difference method for vertical discretization (Choi et al. 2014; Choi and Hong 2016), with a time-split RK3 integration scheme to march forward in time (Klemp et al. 2007). The SEM allows solution of the differential operations in a local element with a small communication stencil (Kelly and Geraldo 2012). The state variable χ in a non-overlapping rectangular element Ae on the sphere is approximated by Nth-order Lagrange polynomials corresponding to the Gauss–Lobatto–Legendre (GLL) grid points inside Ae . χ (λ, φ, η, t) =

+1)2 (N∑

L n (λ, φ)χ (λn , φn , η, t),

(2.3.13)

n=1

where (λn , φn ) represents (N + 1)2 GLL grid points in the element Ae on the spherical coordinate (λ, φ). λ and φ denote longitude and latitude, respectively. L n represents the two-dimensional tensor product of the Nth-order Lagrange polynomials. Currently, N is set to 2, and a single cube panel is divided into 360 × 360 elements, equivalent to 12 km resolution. To evaluate differential operations on χ, the operator and χ are expressed in terms of the local Cartesian coordinate systems associated with the central angles (α, β) on the cubed-sphere. The cubed-sphere grid is constructed by the equiangular gnomonic projection of cube panels onto the spherical surface (Nair et al. 2009). The derivatives are calculated on the cubed-sphere and restored back to the corresponding GLL grid points on the physical spherical coordinate. The non-differential operations in Eqs. 2.3.4–2.3.10 are computed directly at GLL grid points where the nodal basis functions are defined. A global solution satisfying C 0 continuity at the boundaries between neighboring elements is obtained by assembling local solutions, known as direct stiffness summation (Fig. 2.1). To achieve efficient parallelism and load balance, the algorithm called spacefilling curves, as used in CAM-SE, is applied for the domain decomposition of spectral elements, so that blocks of computational grid elements are almost equally allocated to each process (Nair et al. 2009). As a result, the KIM shows good parallel scalability up to 69,696 CPU cores for 12 km resolution on a Cray XC40 with peak performance of 2.9 Peta Flops (Kim et al. 2018). On KMA’s latest operational supercomputer—a ThinkSystem SD650 V2 with peak performance of 50.99 Peta Flops—a 10-day simulation is performed within 100 min with 17,280 CPU cores. The state variables are staggered in the vertical direction following the Lorenz convention (Choi et al. 2014). The third-order upwind biased discretization is employed for the flux form of the vertical advection term, and a centered difference scheme is used for other vertical differential terms. Once transformed to a system of ordinary differential equations, they are marched forward using the time-split RK3 integration scheme (Klemp et al. 2007). The equations are split into two parts, and different time steps are used for each part: short time steps for the fast-moving acoustic wave part and large time steps for the remaining

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Fig. 2.1 Structure of the cubed-sphere grid: a A rotated cubed-sphere grid in which Korea is located at the center of cube face 1. The grid points of the cubed-sphere were generated by projecting Earth’s surface to a circumscribed cube surface. b Face numbers and element indices of the cubed-sphere grid. The figure is redrawn from Kim et al. (2018)

of slowly moving parts (Skamarock and Klemp 2008). A semi-implicit scheme is used for the vertical advection term in the fast-moving part for numerical stability. The explicit time integration scheme facilitates elementwise parallelism along with the SEM. While the SEM on the cubed-sphere grid has advantages in terms of high scalability and an elegant solution for the polar singularity, it also has some disadvantages. Numerical noise associated with Gibbs phenomena is unavoidable in the SEM approach. In addition, the conservation property at element level is not strictly controlled, while the global conservation property is satisfied. The non-orthogonality along the edges of cubed-sphere surfaces can yield grid-imprinting noise. A fourthorder filter and divergence damping with coefficient 0.1 have been introduced to suppress the numerical noise and high-frequency sound waves. Physics The sub-grid-scale processes are parameterized to mimic the collective effect of small-scale motions onto resolved grid-scale state. (F V , FW , FΩ , Fϴ , FQ ∗ , FC∗ ) in Eqs. 2.3.4–2.3.7, 2.3.9 and 2.3.10 represent various sources including sub-grid-scale forcing: radiative fluxes, deep and shallow convection, planetary boundary layer turbulence, precipitation-cloud physics, gravity waves, and small-scale diffusion. Radiation The G-packed McICA is derived from the rapid radiative transfer model for GCMs (RRTMG, Iacono et al. 2008). The scheme has been revised to improve the computational efficiency, giving a 20% saving of CPU time. The backscattering properties of cloud particles, depending on size, are adjusted based on global model simulation (Baek 2017). In order to consider the direct aerosol feedback on radiation, detailed

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aerosol information based on aerosol climatology and global chemistry model simulation is utilized (Choi et al. 2019). In addition, the sub-grid-scale cloud information is also directly used in the radiation process for simulation of the precise cloud radiative forcing (Bae and Park 2019). Convection The simple Arakawa–Schubert (SAS) convection scheme, based on single bulk entraining and detraining plumes (Grell 1993), has been revised in several ways in reference to large eddy simulation (LES) experiments (Han et al. 2020): a trigger condition dependent on the lower-level relative humidity and vertical motion (Hong and Pan 1998), an entrainment rate increasing with humidity (Han and Pan 2011), a convective adjustment depending on daily variation of boundary layer height (Bechtold et al. 2008), and an autoconversion rate decreasing for high-level clouds (Han et al. 2016). Initially, the shallow convection parameterization was derived from Tiedtke (1989) with revisions to the eddy diffusivity and triggering function (Hong and Jang 2018), but this has recently been replaced by the SAS scheme for consistency with the deep convection parameterization, with a few modifications to parameters and conditions. Boundary Layer and Surface Process The non-local K-profile boundary layer scheme (Hong et al. 2006) was revised to add turbulent mixing near capping inversions enhanced by radiative cooling on the top of clouds (Lee et al. 2018). The main parameters in the scheme are adjusted with reference to LES simulations (Noh et al. 2003). The eddy flux varies with the unit grid interval for local and non-local mixing separately in the gray zone (Shin and Hong 2015). Surface fluxes are based on the Monin–Obukhov similarity scheme with the turbulent-orographic form drag (Koo et al. 2018). The land surface model (LSM) is derived from Noah 3.0 (Ek et al. 2003; Chen and Dudhia 2000) with revisions to snow physics and form drag (Koo et al. 2017; Kim et al. 2019). The soil moisture is updated using an ensemble Kalman filter (EnKF) to assimilate ASCAT soil moisture observations from MetOp-A and MetOp-B. IMS snow cover observations are used to correct first-guess snow fields. Precipitation-Cloud Physics The cloud and precipitation microphysics scheme, derived from the WRF single moment five-class microphysics scheme (WSM5), has been revised to reflect warm rain process during the rainy season (Bae et al. 2019; Song and Sohn 2018; Song et al. 2017; Lim and Hong 2010). The effective radii of cloud water, rain, ice, and snow have been adjusted to consider the radiation feedback. The spatial variation of cloud in model grid is considered in cloud condensation and evaporation processes, including accretion rate of cloud water and autoconversion rate of cloud water to rain, via application of the partial cloudiness (Kim and Hong 2018) derived from the prognostic cloud fraction scheme, which has been developed to take into account sub-grid-scale convection (Park et al. 2016).

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Gravity Wave Drag The gravity wave drag (GWD) parameterization over mountainous regions includes low-level wave breaking and flow breaking, considering orographic anisotropy (Choi and Hong 2015) and turbulent-scale orography (Koo et al. 2018). GWD from convective sources has been parameterized to represent spatiotemporal variations and nonlinearity, three-dimensional ray-based propagation, convection moving speed, and wave propagation direction (Choi et al. 2018; Chun et al. 2008). Non-orographic GWD has been extended to incorporate gravity wave sources from jet-front system (Richter et al. 2010). Gray Zone The cloud base mass flux and detrainment rate has been tuned to decrease with the grid spacing (Kwon and Hong 2017; Lim et al. 2014). Both non-local and local vertical transports in convective boundary layers vary with the grid spacing (Shin and Hong 2014) (Table 2.1).

2.4 Data Assimilation The KIM NWP system includes two main atmospheric data assimilation systems—a locally developed hybrid-4DEnVar data assimilation system for deterministic analyses (Kwon et al. 2018) and an adopted local ensemble transform Kalman filter (LETKF) system for updating ensemble perturbations (Hunt et al. 2007; Shin et al. 2016, 2018). Both systems ingest pre-processed observations produced by the KIAPS Package for Observation Processing (KPOP; Kang et al. 2018). The three systems are described below, focusing mainly on the hybrid-4DEnVar system. In this section, we describe the version of the KIM hybrid-4DEnVar system that became operational at KMA on December 29, 2021. This is still the operational version at the time of writing (October 2022). General Variational Formalism In variational data assimilation systems using four-dimensional (4D) trajectories— the evolution of three-dimensional ( ) (3D) states during a time window—we aim to minimize a penalty function J δx of the general form )T ( ) ( ) 1 1( o y − y R−1 yo − y J δx = δx T B −1 δx + 2 2

(2.4.1)

with a nonlinear forecast model M, ignoring model errors, such that x = M(x).

(2.4.2)

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Table 2.1 Summary of the KIM physics packages Physics

Remarks

Radiation

Derived from RRTMG (Iacono et al. 2008) of Baek (2017) WRF, but with a newly developed unified radiation Baek and Bae package including two-stream approximation (2018) Bae and Park (2019)

References

Land surface layer

Derived from Noah 3.0 (Ek et al. 2003; Chen and Dudhia 2000), but with revised snow physics and form drag

Koo et al. (2017) Kim et al. (2019)

Boundary layer

Derived from the YSU PBL (Hong et al. 2006; Hong 2010) of WRF, but with the inclusion of scale-aware functions and stratocumulus mixing. Near surface, Monin–Obukhov similarity but with the inclusion of turbulent-orographic form drag

Shin and Hong (2015) Lee et al. (2018) Koo et al. (2018)

Deep convection

Derived from the GFS scheme, but with improved Han et al. (2016) cloud microphysics and the inclusion of Kwon and Hong scale-aware functions (2017) Han et al. (2019)

Shallow convection

Derived from the GFS scheme, but with the inclusion of scale-aware functions and bug fixes

Orographic gravity wave drag

Derived from Kim and Arakawa (1995) and Hong Choi and Hong et al. (2008), but with the inclusion of orography (2015) blocking and anisotropy of mountains Koo et al. (2018)

Non-orographic gravity wave drag

A newly developed source-based spectral non-orographic scheme based on Choi and Chun (2011) and Richter et al. (2010)

Choi et al. (2018)

Cloud microphysics

Derived from WSM5 (Hong et al. 2004) of WRF, but with the inclusion of cloud properties in the radiation package and use of partial cloudiness in the microphysics

Bae et al. (2016) Kim and Hong (2018)

Cloudiness

A newly developed prognostic cloudiness package Park et al. (2016) based on the Tiedtke prognostic cloudiness scheme (Tiedtke 1993)

Han et al. (2016)

The underlines refer to 4D vectors and operators, and x is the 3D state vector at the initial time. M symbolically represents the governing equations in Eqs. 2.3.4–2.3.10 for the evolution of the atmospheric state x. δx is a 4D increment to the background trajectory: δx = x − x b . B is an estimate of the 4D background error covariance for the background trajectory x b , giving a Gaussian probability distribution function for the 4D increment δx. yo is a vector containing observation values within the data assimilation window, and y is the model equivalent of yo . R is the observation error covariance, which should include both instrument and representativity errors. y is calculated from the incremented background states using an observation operator H : ( ) y = H x b + δx .

(2.4.3)

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H typically includes temporal and spatial interpolation of model variables to the observation locations and potentially nonlinear transformations from model variables to the observed quantities. For example, for satellite radiance observations, H includes nonlinear radiative transfer calculations. The analysis increment δx is determined by minimizing the penalty function measuring the distances from the background and the observations. To reduce computational costs and allow use of efficient minimization methods, we adopted the incremental approach of Courtier et al. (1994), where analysis increments are calculated on a potentially lower-resolution grid, and the observation operator H is linearized to produce an exactly quadratic penalty function. Under this formulation, the penalty function J becomes )T ( ) )T ( ) 1( o ( ) 1( y − y R−1 yo − y , (2.4.4) J δw = δw − δwg B −1 δw − δwg + 2 2 where δw is a 4D increment on the analysis grid and δwg is the difference between the latest “guess” and background states on the analysis grid, so that δw − δwg is the total difference from the guess state. 4D analysis states w are connected to 4D model states x by a potentially nonlinear operator S, which typically includes spatial interpolations and may include transformations to a different set of variables: ( ) w=S x .

(2.4.5)

( ) y = H x g + Hδw,

(2.4.6)

y is linearized as follows:

( ) where H is the Jacobian of H evaluated at wg = S x g . The superscript g indicates that x g is the latest 4D guess analysis. This formulation supports an “outer loop” strategy in which H is recalculated at the beginning of each outer loop against the latest guess analysis. This reduces linearization errors as the guess converges on the optimal analysis. An inner loop is then focused on minimizing J against a fixed guess. The J of Eq. 2.4.4 is exactly quadratic, so it is possible to use efficient minimization algorithms. The KIM hybrid4DEnVar system uses a conjugate-gradient solver (Song and Kwon 2015). The outer loop approach also supports gradual increases in analysis resolution or accuracy between outer loops, which can reduce overall computational costs. The KIM hybrid-4DEnVar system is mostly conformant with this standard formulation, but Eq. 2.4.6 is replaced by ( ) y = H wg + Hδw,

(2.4.7)

where the nonlinear observation operator H is applied to wg rather than x g . This change was made for practical reasons but degrades the quality of the analysis. We are now working on an upgrade that will allow us to use the standard formulation

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without compromise. As discussed below, we also reduce the truncations of spectral transforms between outer loops, to further reduce the overall computational cost. In the current operational version, the horizontal grid point spacings of the cubed-sphere analysis and model grids are approximately 32 and 12 km, respectively. Climatological Covariance and Variable Transformation The hybrid-4DEnVar background error covariance is essentially a weighted sum of a climatological background error covariance B c and an ensemble-based background error covariance B e . To improve the conditioning of the minimization problem, B c is implement via its square-root U, i.e., B c = U U T . Its design is based on a 3D transform T that transforms climatologically typical background error vectors to a set of scalar variables that are approximately uncorrelated and have unit variance. T is broken down into a sequence of three transforms: T = T v T h T p.

(2.4.8)

Here, T p is a parameter transform that transforms increments to the main model variables (zonal and meridional winds, temperature, surface pressure, and water vapor mixing ratio) to a set of “control variable” fields that are approximately uncorrelated (stream function, unbalanced velocity potential, unbalanced temperature, unbalanced surface pressure, and pseudo-relative humidity). Pseudo-relative humidity is defined by scaling the mixing ratio by the background saturation mixing ratio (Dee and da Silva 2003). Unbalanced variables are obtained via balanced counterparts, which are derived from stream function increments via linear regression (Song et al. 2017). T h transforms the analysis grid control variable fields to spectral space, and T v transforms the resulting model-level spectral coefficients to spectral coefficients of vertical eigenmodes, which are calculated via a standard eigen-decomposition method. U is built from approximate inverses of the above transforms: U = U pU hU v,

(2.4.9)

where U v is the approximate inverse of T v , U h the approximate inverse of T h , and U p the approximate inverse of T p , but includes a copy to all increment times, hence the underline. Thus, U defines a 3DVar-like covariance that takes no account of the time correlations between background errors within the analysis window (Song and Kwon 2015). The statistical parameters required for the definition of B c are generated using the so-called NMC method of Parrish and Derber (1992), by processing a large sample of differences between T + 48 and T + 24-h, T + 36 and T + 24-h, and T + 24 and T + 12-h forecasts, as described in section 2b of Kwon et al. (2018). Generation of Ensemble Perturbations In hybrid-4DEnVar, time correlations are provided only by the ensemble covariance, which is based on 4D ensemble forecasts x ek , where k is the ensemble member index.

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Ensemble states are required at each analysis increment time. In the current hybrid4DEnVar system, there are 50 ensemble members and seven increment times within the data assimilation window, one hour apart. We require the ensemble forecasts to be on the analysis grid, so we transform them using a counterpart S e of the S used for deterministic model states in Eq. 2.4.5: ( ) wek = S e x ek

(2.4.10)

( ) x ek = M e x ek + F ek ,

(2.4.11)

with

where x ek is the 3D state vector for the kth ensemble perturbation at the initial time. The ensemble states x ek are generated by an LETKF-based ensemble. The LETKF control variables include zonal wind, meridional wind, temperature, and specific humidity. For conventional data, the basic localization scales—defined as the separations at which the localization functions reach zero—are 1800 km in the horizontal direction and 0.2 pressure scale heights (i.e., 0.2 ln( p) units) in the vertical direction. The analysis ensemble perturbations are re-centered on the analysis of the KIM hybrid-4DEnVar system, forming initial ensemble states x ek . The perturbations are inflated using relaxation-to-prior perturbations (RTPP) (Whitaker and Hamill 2012) and additive inflation with randomly sampled differences between 6- and 12-h forecasts to control filter divergence. Usually, the M e in Eq. 2.4.11 for the propagation of ensemble states has a lower resolution than the original nonlinear model M for economy. Currently, M e runs with a lower resolution of 32 km. F ek is a stochastic forcing to simulate model uncertainty, using both stochastic perturbations of parameterization tendencies (SPPT) and stochastically perturbed parameterizations (SPP). Hybrid-4DEnVar Ensemble Covariance To form the 4D ensemble covariance within our hybrid-4DEnVar system, we define a rectangular matrix W whose columns are scaled differences between the 4D ensemble forecasts wek and the 4D background wb . we1 − wb , we2 − wb , . . . , weK − wb , √ K ) ( = w1 ' , w2 ' , . . . , w K '

W=

(2.4.12)

where K is the number of ensemble members. The “raw” ensemble covariance P e is then given by P e = W W T.

(2.4.13)

Note that we are using the 4D background wb rather the 4D ensemble mean we to define the ensemble perturbations. We intend to review this choice in 2023.

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Spatial localization is required to reduce the impact of sampling error in P e . This is done by applying a three-dimension localization matrix L to P e : B e = P e ◦ I L,

(2.4.14)

where ◦ denotes an element-by-element (Schur) product, I is an operator that copies a 3D state to all increment times, and B e is the final ensemble-based background error covariance. Similar to the construction of the climatological covariance, L is defined via a square root U α which transforms from vectors v α of uncorrelated variables with unit variance to 3D scalar fields α: α = U α vα .

(2.4.15)

U α is broken down into vertical and horizontal localization transforms U αh and

U αv :

U α = U αh U αv .

(2.4.16)

The vertical transform U αv uses eigen-decomposition to implement a vertical localization covariance, and U αh uses spectral decomposition to implement a homogeneous and isotropic Gaussian covariance with a specified scale (Kleist and Ide 2015). The vertical and horizontal localizations are separable—for example, the same vertical localization is applied to all horizontal scales. Thus, the order of U αh and U αv in Eq. 2.4.16 has no effect on results. We have now defined two four-dimensional covariances—a climatological covariance B c = U U T and an ensemble-based background error covariance B e = W W T ◦ I U α U αT . Multi-resolution Minimization We may now reformulate the penalty function J in terms of a control vector v for the climatological increments and control vectors v α1 , v α2 , . . . , v αK for a series of localization fields α k —one for each ensemble member: K ∑ ) 1 ( 1 αT α v v J v, v α1 , v α2 , . . . , v αK = v T v + 2 2 k k k=1 )T ( ) 1( o y − y R−1 yo − y + 2

(2.4.17)

with α k = U α v αk . It is noted that the same α k field is used for all the variables, which leads to inter-variable correlations being retained (Clayton et al. 2013). Hybridization of the climatological and ensemble-based covariances is achieved by introducing 3D weights β c and β e into the definition of the transform between the control vectors and the increments, as elaborated in Park and Zupanski (2022). In the current KIM hybrid-4DEnVar system, the definition is as follows.

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Table 2.2 Triangular spectral truncations for the static covariance B c and the ensemble localization covariance L as a function of the outer loop number. The ensemble localization scales are also gradually reduced Outer loop number

B c truncation

L truncation

Localization scale (km)

1

42

10

1728

2

85

15

1249

3

170

20

882

4

170

40

447

K ) ∑ ( [ ( )] δw = U p β c ◦ U h U v v + I β e ◦ U α v αk ◦ wk ' .

(2.4.18)

k=1

The covariance weightings are the squares of β c and β e . Assuming B c and B e have similar variance, the total variance is therefore approximately conserved if the squares of β c and β e sum to unity, so we currently enforce this as a constraint. The weights vary with latitude and model level. In the troposphere, the weighting given to B e is 45% at the poles, smoothly increasing to 70% at the equator. The B e percentage gradually reduces above the troposphere to 19% or less at the top of the model. Minimization of the penalty function J defined by Eq. 2.4.17 is currently divided between four outer loops. To reduce computational costs, the spectral truncations of the horizontal and vertical transforms—U h , U v , U αh and U αv —are gradually relaxed between outer loops (Song et al. 2017, 2018). In the current operational system, the truncations are as given in Table 2.2. We see that the horizontal localization scale for the ensemble covariance is also gradually reduced. The vertical localization scale is not changed—a fixed scale of 0.4 pressure scale heights is used for all outer loops.1 Incremental Analysis Update Hybrid-4DEnVar analysis increments are added to the model via a conventional Incremental Analysis Update (IAU) scheme. The fourth and therefore central total analysis increment is remapped onto the model grid and then processed slightly as described in section 2a of Kwon et al. (2018). The resulting increment state is then gradually added to the model during the first six hours of the forecast, using a weighting function based on a Dolph filter (Lynch 1997). We are currently looking to replace this “3DIAU” scheme with a “4DIAU” scheme which makes use of analysis increments distributed through the analysis window.

1

Horizontal and vertical localization scales are specified here as “Daley” length scales )] [ (page ( 110 of Daley 1991). We use approximately Gaussian localization functions μ(z) = exp −z 2 / 2L 2 . In this case, the Daley length scale is equal to L.

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Observation Preprocessing The KPOP has been established to provide quality-controlled real-time observations for DA systems (Kang et al. 2018). Currently, KPOP is capable of processing various observation types, including synoptic and aircraft observations, satellitebased microwave and infrared radiances, satellite retrieved winds, GNSS radio occultation (GPSRO), and tropical cyclone bogus observations. Table 2.3 shows the main observation types and instruments supported by KPOP for global data assimilation. The functions of KPOP include handling data encoding and decoding, quality control, cloud screening, bias correction, and thinning for conventional and radiance observations. The bias coefficients vary with the background and quality-controlled observations are selected through consecutive examination of observation increments. Variational bias correction (VarBC) is used for the quality control of AMSU-A, MHS, ATMS, IASI, and CrIS observations and will be extended to other satellite observation types and channels.

2.5 Entering Second Phase Development Developing a state-of-the-art numerical model and DA system for both weather and climate prediction is a tremendous challenge that requires a coordinated and integrated management of operations, research, and infrastructure. This becomes a more difficult challenge because of increasing resolution, lead time, components of the Earth’s system, data volume, and the size of ensembles. The unified modeling approach is well recognized in the modeling community worldwide as a solution to meet this challenge. For instance, the UK Met Office took a seamless approach using the UM modeling framework (Brown et al. 2012). NCEP is moving forward toward a unified forecasting system, UFS (Bernardet et al. 2017). While KIM supports medium-range weather forecasting, KMA uses a UM-based coupled climate model for seasonal forecasting and climate change studies. It is expensive to operate and maintain both numerical prediction systems simultaneously. The improvement of one system is not easily transferred to the other system. To meet the complexity in a multi-model and multi-disciplinary environment with the constraints of available resources, the strategy for model development at KIAPS is built on a holistic approach, covering various temporal and spatial scales in a unified modeling framework. The probabilistic concept based on ensemble manipulation is central for both data assimilation and seamless prediction. Considering the limited human resources and expertise available at KIAPS, significant focus is placed on a few strategic targets for development, while adopting readily available Earth system model components. The second phase of the KIAPS project, which started in September 2020, will span a 7-year period until the end of 2026. The project aims at developing a highresolution model and data assimilation system, including land, ocean, sea ice, and

2 Development of Operational NWP in Korea: Historical Perspective Table 2.3 Observations processed in KPOP as of 2022 Type Conventional

Satellite-based wind

GNSS

Observations

Remark

SONDE

TEMP, PILOT, DROP, WINPRO, DESCENT

T, u, v, q

SURFACE

LNDSYN, SHIP, BUOY(B), METAR

T, u, v, q, RH, Psfc

AIRCRAFT

AMDAR, AIREP

T, u, v

Mode-S

u, v Korean peninsular

AMV

MeteoSat-8/11, GOES-16, Himawari, GK-2A, NOAA-18/19, Aqua, Dual-MetOp, (LEOGEO)

Ocean/land

SCATWIND

MetOp-B/C

u, v

ALADIN

Aeolus (HLSO)

Wind, ocean/land

GPSRO

COSMIC, COSMIC2, GRAS, SAC-C, PAZ, GRACE-A/B/C, TerraSAR-X, CORISS, TANDEM-X, FY-3C/D, KOMPSAT-5

GrndGNSS

Zenith Total Delay (ZTD) China, EU, Japan, Korea

Bogus

TC-BOGUS

RSMC Tokyo Typhoon report

Pressure

Radar

RADAR

Dual polarization radial velocity and reflectivity

By 2025 (plan)

Ozone

OZONE

AURA, NOAA-19/20

Micro wave radiance

AMSU-A

NOAA-15/18/19, MetOp-B/C

Ch5-14, ocean

MHS

NOAA-18/19, MetOp-B/ C

Ch4-5, ocean

ATMS

NPP, NOAA-20

Ch6-11, 18-20, ocean

AMSR2

GCOM-W1

Ch7-11, ocean

SAPHIR

Megha-Tropiques (M-T)

Ch1-6, ocean

SSMIS

F17/18

Ch2, 4-7, ocean

MWHS2

FY-3C

Ch11-15, ocean

GMI

GPM

Ch4-7, 9, ocean

IASI

MetOp-B/C

91 channels, ocean/land

CrIS

NPP, NOAA-20

28 channels, ocean

CSR

GK-2A, GOES, MSG, Himawari-8

Ch8-10, ocean/land

GIIRS

FY-4A

Tested only

Infrared radiance Geostationary

55

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atmospheric chemistry components. This will give the ability to forecast both shortterm high-impact weather and extended-range climate anomalies a month in advance, modulated by low-frequency oscillations such as blocking and the MJO (Table 2.4). High-Resolution Dynamical Core As a natural extension of the cubed-sphere dynamical core, variable-resolution numerics will be developed first, and then scale-aware physics will be incorporated to properly represent various spatial scales across the global domain. The hybrid sigma pressure coordinate will be revised to employ scale-dependent vertical decay of underlying terrain features, particularly for small-scale variations decaying efficiently with height (Schar et al. 2002; Choi and Klemp 2021). The Schmidt transformation will be applied to systematically shrink grid distances as the target region is approached, while the built-in SEM dynamical core will be applied to the deformed grid system. The grid spacing will be narrowed down to 1–3 km in the finest mesh area, which is comparable to individual deep convective clouds and boundary layer heights. To avoid errors re-entering from the coarse mesh region, the variable-resolution dynamical core will only be safely used for shortrange predictions in a time frame of less than 48 h. A limited-area version of the dynamical core with one-way nesting will also be developed and compared with the variable-resolution core in terms of accuracy, stability, flexibility, and economy. Physics The sub-grid-scale physics depends on the grid spacing (e.g., Kwon and Hong 2017; Shin and Hong 2015). Sensitivity experiments will be conducted with varying resolution to determine parameters for gray-zone physics, including convection, boundary layer turbulence, and gravity wave drag, maintaining the physical consistency with special attention to cloud-radiation feedback (Bae and Park 2019). Microphysics will be improved to explicitly control both the number and mass of cloud particles and to introduce nucleation processes using prognostic aerosol distributions. The WRF Table 2.4 Evolution of KIAPS projects First phase (2011–2019)

Second phase (2020.9–2026)

Lead time

10 days Initial value dominant

30 days Initial and boundary values Extensive use of ensembles

Atmospheric model

Cubed-sphere Spectral element method Equiangular numeric and physics

Cubed-sphere Spectral element method Variable grid numeric and physics

Boundary models

Land surface 1D mixed layer ocean

Land surface and rivers Ocean circulation and sea ice Aerosols

Coupled assimilation

Atmosphere

Atmosphere Land surface Ocean and sea ice

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chemistry modules, with limited hygroscopic types of aerosols, will interface with the double moment microphysics to simulate the aerosol indirect feedback by predicted aerosol (or cloud condensation nuclei) information and cloud-number concentration (Kang et al. 2019). Storm-Scale Data Assimilation We will use an LETKF-based system to assimilate data into the high-resolution model. There is no immediate plan to combine this system with a high-resolution 4DEnVar-based system. The LETKF will assimilate dual-polarized radar reflectivity and Doppler wind observations, along with geostationary satellite observations, including atmospheric motion vectors and radiances. Cloud properties will be included in the control variables of the LETKF to distribute radar reflectivity increments to other model state variables. Satellite radiance assimilation will be extended to cover cloudy sky and channels sensitive to surface and stratospheric ozone, benchmarking recent success at ECMWF and other centers (ECMWF 2017). The observation operators will be updated to use the latest radiative transfer model (RTTOV) versions to simulate radiative transfer in cloudy skies. While utilizing the inflation measures inherent in the LETKF to alleviate filter divergence, additional stochastic forcing will be introduced to enhance the ensemble spread with an enlarged sample space. Toward Extended-Range Prediction Initial focus is on coupling the KIM atmospheric driver with the various Earth system components, along with building expertise on data assimilation and longterm ensemble simulation to improve the predictive skill of the bias-corrected system on a 30-day timescale. Considering familiarity and practicability, the selected Earth system components include the Noah-MP LSM, the Kama-Flood river discharge model, the NEMO/SI3 ocean/sea ice model, the WW3 wave model, and the GEOSCHEM chemical model. The Model Coupling Toolkit (MCT) supports the data exchange between the atmospheric driver and Earth system components. The soil moisture updates based on the EnKF with Noah LSM will be replaced by an LETKF using the Noah-MP LSM. Regarding the ocean data assimilation, weakly coupled assimilation will be examined first, and we will then proceed toward quasi-strong coupled assimilation with the use of cross-domain error covariances. An intermediate step would be to develop a quasi-strongly coupled assimilation system by keeping the atmospheric data assimilation system in its current state, but updating the ocean analysis using both atmosphere and ocean observations, as in Sluka et al. (2016). Operational Support As the complexity of the system increases, it becomes more challenging to monitor the model performance and diagnose model error sources. Following the hierarchical system development (HSD) approach, KIAPS will establish a test guideline from small elements such as individual single column physics, then progressively

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combines elements with increased coupling between Earth system components and evaluation steps (Ek et al. 2019). To monitor observation sensitivity, a prototype ensemble-based forecast sensitivity to observations (EFSO) system has been developed in KIAPS and applied to a stand-alone LETKF cycling system. This will be extended further to estimate observation impacts when using hybrid-4DEnVar. The computation load is expected to increase by a factor of four from project phase I to phase II. The parallelization and optimization of numerical algorithms and I/O will be a continuous task to meet the strict operation timeline. In parallel, data-driven machine learning technologies will be explored to improve flexibility and efficiency of the operational NWP, focusing on the bias correction and quality control of observations, emulation of sub-physical process, and real-time image processing for now casting. Acknowledgements The authors wish to thank the reviewer for the valuable comments which is very helpful to improve the manuscript and to go over future direction for development. This work was carried out through the R&D project on the development of a next-generation NWP system of the KIAPS funded by KMA 2020-02212.

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Chapter 3

Development of the RMAPS-STv2.0 Hourly Rapid Updated Catch-up Cycling Assimilation and Forecast System Min Chen, Bing Lu, Jiqin Zhong, Yang Yang, Jin Feng, Wenxue Tong, Shuting Zhang, Cheng Wang, and Xiang-Yu Huang

Abstract The key technical features of RMAPS-STv2.0, the Hourly Rapid Catch-up Cycling Assimilation and Forecast System, are introduced in detail. The initialization approach used by the system, known as incremental analysis update (IAU), successfully suppresses the initial noise accumulation issue. The two coupling components, such as cycle analysis and forecast updates with the implementations of data with different cut-off times, run in turn within each hourly cycling to meet the high demands raised by the nowcasting and short-term forecast service by taking into full consideration the actual truncated time of all kinds of observations’ arrival. The dynamic constraint of the global model’s large-scale field on the growth of

M. Chen (B) · B. Lu · J. Zhong · Y. Yang · J. Feng · W. Tong · S. Zhang · C. Wang · X.-Y. Huang Institute of Urban Meteorology, CMA, Beijing 100089, China e-mail: [email protected] B. Lu e-mail: [email protected] J. Zhong e-mail: [email protected] Y. Yang e-mail: [email protected] J. Feng e-mail: [email protected] W. Tong e-mail: [email protected] S. Zhang e-mail: [email protected] C. Wang e-mail: [email protected] X.-Y. Huang e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_3

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the regional model’s small- and medium-scale thermal dynamic field is realized through the application of the dynamic forecast hybrid scheme to the assimilated background field, and the deformation of the large-scale prediction field brought on by the accumulation of the rapid update cycle prediction errors is effectively suppressed. To prevent the continual accumulation of water vapor, the national-wide mosaic radar reflectivity is only assimilated during the forecast update stage. The optimization of the radar assimilation background field error variance and length scale technique successfully encouraged the use of the radar assimilation effect. Additionally, the application of national wind profile radar observation data in real time is accomplished. A series of optimization of physical parameterization schemes have been performed. The cloud radiative forcing scheme, planetary boundary layer, and surface-layer scheme have all been optimized to address the systematic bias in diurnal 2m temperature and humidity. The updates of vegetation coverage and soil type with Noah’s new soil hydraulics parameter table also contribute to the better balance of the surface energy budget and the energy transfer between the ground and the atmosphere in the model. Additionally, a scale-aware cumulus convection parameterization scheme is implemented to the system to enhance the precipitation forecast performance of the cumulus scheme and reduce overprediction errors for light precipitation. Keywords Rapid updated cycling · Radar data assimilation · Initialization · Scale-aware cumulus parameterization · Forecast performance optimization

List of Acronyms Name 3DVAR ACM2 ARW BNU BST CMA CPS DB ECMWF ETS FAO GNSS GTS IAU IRMCD IUM LHF

Description Three-dimensional Variational DA Asymmetrical Convective Model version 2 Advanced Research Model Beijing Normal University Beijing Standard Time China Meteorology Administration Cumulus Parameterization Scheme Dynamic Blending European Center for Medium-Range Weather Forecasts Equitable Skill Score The Food and Agriculture Organization Global Navigation Satellite System Global Telecommunication System Incremental Analysis Updates Iterated Reweighted Minimum Covariance Determinant Institute of Urban Meteorology Latent Heating Flux

3 Development of the RMAPS-STv2.0 Hourly Rapid Updated …

LSM MODIS Noah OMB PBL RMAPS RMSE RRTMG SHF SL TS WRF WRFDA YSU ZTD

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Land Surface Model Moderate Resolution Imaging Spectroradiometer NOAA/NCEP–Oregon State University–Air Force Research Laboratory–NOAA/Office of Hydrology land surface model Observation-background deviation (OMB) Planetary Boundary Layer Rapid Refresh Multiscale Analysis and Prediction System Root Mean Square Error Rapid Radiative Transfer Model for General circulation model applications Sensible Heating Flux Surface Layer Threat Score Weather Research and Forecasting Model WRF model’s Community Variational/Ensemble Data Assimilation System Yonsei University PBL Scheme Zenith Total Delay

3.1 Overview of the IUM Hourly Forecasting System In 2016, the Institute of Urban Meteorology of the China Meteorology Administration (IUM/CMA) developed and put the Rapid Refresh Multiscale Analysis and Prediction System (RMAPS) into operation, which consists of five offline, one-way nested components (Liang et al. 2018). One component is short-term, whose version 1.0 (RMAPS-STv1.0) was a 3-h update cycling forecasting system developed based on the Advanced Research version of the WRF (WRF-ARW, version v3.8.1; Skamarock et al. 2008) and WRFDA (version v3.8; Barker et al. 2012) and has been operational since June 2017 (Xie et al. 2019; Wang et al. 2020). After years of research and development, assimilation technologies for densely deployed and multi-source conventional and remote sensing observations have been developed. In addition, key physical processes associated with surface and precipitation forecasting as well as fundamental static dataset updates have been gradually optimized and incorporated into the model system. Simultaneously, in order to improve the numerical weather prediction support capability for short-term forecast and warning, a series of related technology research and development was conducted and eventually integrated with the purpose of suppressing high-frequency noise and imbalance in the initial field, as well as the rapid growth of the model prediction error. The entire technical scheme is now fully integrated. Based on version 1.0, the version 2.0 prediction system is iteratively developed and updated. This chapter describes

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the hourly forecast system frameworks, such as the incremental analysis updating initialization scheme, the rapid catch-up cycling strategy, and the dynamic blending of large-scale global forecast fields, as well as the most recent data assimilation updates, including national radar reflectivity mosaic data and wind profile radar assimilation technology. In addition, the optimization of key physical processes associated with surface and precipitation forecasting is discussed. Based on WRFv4.1.2 and WRFDAv4.1.2, RMAPS-STv2.0 is a regional rapid updated cycling assimilation and short-time forecast system, which provides shortterm operational forecasts over mesoscale limited-area domains (horizontal resolution of 9 km) covering the Chinese territory and a one-way nested 3 km domain centered in the northern part of China (Fig. 3.1). The configurations, including the major attributes, physics package and data assimilation of the RMAPS-STv2.0 are summarized in Table 3.1. Table 3.1 lists major attributes of the current configuration of the RMAPS-STv2.0.

D01

D02

Fig. 3.1 Forecast domains of RMAPS-STv2.0 system (D01: 9 km, D02: 3 km)

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Table 3.1 System settings of RMAPS-STv2.0 System configuration

Model and version

WRF/ARWv4.1.2

Domain center

110E,35N

Grid points

D01: 649 × 500; D02: 550 × 424

Grid distance

D01:9 km; D02:3 km

Vertical layers/model top

59/10 hPa

Update interval

1h

Lateral boundary

ECMWF-IFS 12UTC-0.125°×0.125°

Forecast length

24h/96 h [initiating from 08,20 BST (Beijing Standard Time)]

Physics package Radiation

Data assimilation

RRTMG (v3.6) (Iacono et al. 2008)

PBL

YSU

Cumulus

New Tiedtke (only in 9 km domain)

Microphysics

Thompson

Land surface model

Noah

Data assimilation system

WRFDAv4.1.2

DA method

3DVAR

Control variables

u, v, T, pseudo relative humidity, surface pressure

Assimilated types of observations

Surface, Radiosondes, Pilot, AMDAR, Wind Profiler, GNSS/ZTD, Doppler Radar reflectivity, and radial wind

Initialization

IAU

3.2 The Operational Framework of the Hourly Updated Forecast System The hourly rapid updated cycle and forecast system frequently encounters the following issues during real-time daily operations: First, the background field for the rapid updated cycle assimilation is derived from the 1-h forecast from the previous cycle. In general, after one hour of integration, the model cannot reach the ideal balance state, resulting in more high-frequency noise and a rapid accumulation of prediction errors after multiple cycles, both of which have a negative impact on the current cycle’s assimilation and prediction, as well as subsequent cycles. Second, it is critical to incorporate as many available observations as possible into the model and accurately depict the atmospheric characteristics during the initial phase in order to meet the demands of short-term forecasting and nowcasting. To complete the model forecast, the hourly cycling forecast must be launched as soon as possible. Different types of high-frequency observation data, on the other hand, frequently have distinct cut-off times. As a result of the updated cycle’s quick start, the observations valid at the start of each hourly cycling run typically have too short cut-off times, and the

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amount of data that can be used in the assimilation is relatively limited, which cannot guarantee the quality of the analysis field after assimilation. To address the practical issues raised by the above update cycle prediction, an incremental analysis update initialization method and a quick catch-up cycle technique for data assimilation are developed.

3.2.1 Incremental Analysis Updated Initialization Scheme Bloom et al. (1996) established the Incremental Analysis Updates (IAU) initialization method, which is now widely used in meteorology and oceanography. The IAU method works on the principle of gradually incorporating the analysis increment formed by data assimilation into the model integration process as the forcing term in the time window centered on the assimilation time, rather than adding it all at once at the analysis time, to effectively control the false high-frequency noise caused by data assimilation and the initial imbalances between the wind and air pressure field, hydrometeors and dynamic field, and so on. The model’s spin-up/spin-down time is also shortened. For any prognostic variable , the tendency equation in the initialization time window can be written in the following form: ∂φ ∂t

n

=

n

∂φ ∂t

+ dynamics

∂φ ∂t

n

+ λ(t) physics

δφana tc

(3.1)

tc

λ(t)dt = 1, λ(t) ≥ 0

(3.2)

0

That is, the time tendency ∂φ ∂t ∂φ ∂t

n dynamics n physics

∂φ ∂t

n

is divided into three parts: dynamic tendency

reflecting the adiabatic and dynamic framework, physical tendency

reflecting physical processes, such as wet physics, boundary layer, radi-

ation, and land surface, and the analysis tendency λ(t) δφana , which is the timetc distributed analysis increments in the time window period. Where λ(t) denotes the time weight coefficient, which is derived from the digital filter cut-off time and the IAU time window. Chen et al. (2023) developed a WRF model incremental analysis updated initialization approach, which calculates the forecast increments from (t) to (t + t) with the following form: φ(t +

t)IAU = φ(t +

t) + λ(t)δφana

(3.3)

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Fig. 3.2 Precipitation forecast scores. a CSI and b BIAS in the hourly updated cycling experiments from May 8 to August 31, 2019. It was quoted from Chen et al. (2023)

In Eq. (3.3), φ denotes the prognostic variables of the WRF model, such as horizontal wind component, potential temperature, dry air disturbance pressure, water vapor mixing ratio, and hydrometeors, the analysis increments of which can be generated through data assimilation. In many IAU applications, the inverse of the integral time step in the time window is used as the value of the time weight coefficient λ(t), to achieve uniform distribution of the analysis increment in the time window. Chen et al. (2023) used the Dolph-Chebyshev window (Lynch 1997) filter to generate time weight coefficients. A series of hourly cycling experiments revealed that using IAU as an initialization method resulted in a more stable precipitation rate generated during model integration than using no initialization method. In terms of initial noise and spin-up/spin-down control of the hydrometeors’ initial value, reasonable and optimal results were obtained. The IAU effectively corrected the precipitation overprediction caused by the spin-up process, according to a detailed hourly precipitation and radar reflectivity forecast comparison. During the three-month period, the precipitation forecast scores derived from the two real-time hourly updated cycling forecasts demonstrated that the IAU scheme has a positive impact on all precipitation thresholds and forecasting leading time (Fig. 3.2). As a result, IAU is used as the initialization scheme in the RMAPS-STv2.0 system, and the time window for the incremental update of the analysis is set to 2 h. In other words, after data assimilation in each hour update cycle, the analysis increments from t = −1 h to t = 1 h were integrated using the time weight ratio generated by the Dolph-Chebyshev Window filter, and the normal prediction was made after t = 1 h.

3.2.2 Fast Catch-up Cycling Strategy A fast-updating catch-up cycle strategy is developed in the RMAPS-STv2.0 to account for differences in the cut-off time of the actual arrival of all types of observation data and to ensure their full and efficient utilization.

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Within the IUM/CMA operational environment, the GTS data valid at each punctual hourly time has four cut-off times: 13, 37, 66, and 93 min after the hour. Assuming that the data arrival rate is 100% when the time lag of the hour T is T + 93 min (which is too late to start the cycling), radiosonde observation has the lowest data arrival rate, 86.34%, at T + 66 min. Other data arrival rates, such as aircraft, ships, national and regional automatic weather stations, surface observation, and so on, exceed 90% (Fig. 3.3). The hourly cycle start time of assimilating the GTS data should be set at 66 min after the hour to ensure that more complete GTS observation data can be used for assimilation. The assimilation of rapidly arriving real-time observations, such as radar and automatic weather station observations, which are typically collected within 15 min, is critical to the application value of a fast update cycle forecast system. As a result, the RMAPS-STv2.0 is designed with a two-part operational framework for the hourly catch-up cycle. Part I is the cycle analysis, which begins at T + 70 min after the hour of T and assimilates observation data valid at T with a cut-off time of T + 66 min, allowing for enough important observations, such as radiosonde, to be used in each cycle to ensure that a lack of observation data does not significantly impact the basic assimilation quality valid at T. The assimilating background field for the current forecast cycle and the following catch-up cycle is then generated using a one-hour forecast. Part II refers to a forecast update. Radar and AWS observations with a cut-off time of 15 min are assimilated against the background generated in Part I. A variety of processes, such as 24-h forecasting, post-processing, and product distribution, are carried out on this basis. Figure 3.4 depicts the timeline of the entire catch-up cycle. Part I, cycle analysis beginning at T, completes the assimilation run and 1-h forecast in 8 min. That is, at T + 78 min, the forecast valid at T + 1 can be obtained, against which Part II, the so-called forecast update, will begin, including assimilation of the quick arrival radar data valid at T + 1 and forecast of the next 24 h. Part II

Arrival rate of GTS observations at different cut-off times 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% AMDAR t+13 min

PILOT t+37 min

BUOY t+66 min

t+92 min

RGWST

RNWST

SHIP

SOUND

Data Type

Fig. 3.3 Data arrival reporting of various GTS observations at different cut-off times

SYNOP

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Fig. 3.4 The running timeline of the hourly catch-up cycle

should take about 24 min, according to the wall clock. Furthermore, real-time forecast products initiated at T + 1 h can arrive at the forecaster’s desktop and be displayed on the web page at T + 102 min, implying a 42-min lag time. Overall, the process considers the timeliness of short-term forecasting requirements as well as the number of assimilated observations. It also avoids the issue of forecast error rapidly increasing due to the hourly continuous assimilation of radar data, which better meets the operational needs of the hourly rapid update cycle and is expected to achieve comparable forecast performance with the 3-h rapid update cycle. The hourly rapid update catch-up cycle process described above was completed with careful planning on the IUM/CMA’s high-performance computer, and real-time operation began on June 17, 2021. This is the basic operation framework for the RMAPS-STv2.0.

3.2.3 The Flow of the Hourly Rapid Updated Cycling Forecasting System The hourly rapid update catch-up cycling system, RMAPS-STv2.0, includes one cold start, 24 cycling analyses, and 24 forecast runs per day. Cold start runs at 02BST, driven by 6-h ECMWF global forecasts that initiate at 20BST the night before. Cycling analysis runs are the procedures for assimilating observations with long cutoff times (such as radiosondes) and 1-h forecasts to provide the 1-st guess field for the current forecast update and the subsequent analysis cycle, which are typically scheduled to begin at T + 70 min. The updated forecast runs represent the procedures

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for performing fast arrival data assimilation and forecasting for the next 24 h. The operational cycling process of the RMAPS-STv2.0 is displayed in Fig. 3.5.

Fig. 3.5 Cycle analysis and update forecast flow of the RMAPS-STv2.0 system. The number in the black box in the inner circle is the start time of the cycle analysis, and the black dotted line indicates the start time of the cycle analysis. The blue box indicates the starting time of the update forecast and the blue dashed line indicates the starting time of the update forecast. The solid red line indicates the running time indicated by the arrow and the one-hour forecast of the running time indicated by the arrow tail as the background field

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3.3 Data Assimilation of Hourly Observations The RMAPS-STv2.0 employs the 3DVAR method to assimilate conventional surface, radiosonde, automatic weather station, pilot measurement, aircraft report, wind profiler radar, GNSS/ZTD, weather radar reflectivity mosaic, and radial wind observation data (Fig. 3.6). The main differences in data assimilation between RMAPSSTv1.0 and v2.0 are the implementation of national radar reflectivity mosaic and wind profile observations data assimilation. A dynamic blending scheme for background field assimilation is also developed to effectively suppress large-scale field deformation caused by forecast error accumulation during continuous cycling runs.

3.3.1 Dynamic Blending Scheme Systematic errors of initial fields accumulate significantly with rapid updated cycles due to a lack of effective observation correction in the data sparse area and the impacts of lateral boundary to large-scale synoptic systems. Global forecasts combined with

Fig. 3.6 Assimilated observations of the RMAPS-STv2.0 system. a SYNOP (red), TEMP (blue), AMDAR (green), BUOY (orange), and SHIP (pink), b ground-based GNSS/ZTD, c weather radar, d wind profiler radar

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regional model forecasts are used to reduce large-scale systematic errors in the initial fields (Wang et al. 2014; Hsiao et al. 2015). The scheme gradually replaces the longwave component of the background field above a predefined wavenumber with the global model forecast, while retaining the small- and medium-scale detailed features produced by the previous cycle’s regional model forecast. Cut-off wavenumber refers to the predefined wavenumber. The dynamic blend (DB) scheme is implemented in RMAPS-STv2.0, which calculates time-varying cut-off wavenumbers based on the distribution of error spectra in the global and regional models (Feng et al. 2020, 2021, Luo et al. 2022). Experiments with the RMAPS-STv1.0 show that this scheme can effectively reduce both the initial and forecast errors in meteorological variables and precipitation. The scheme in RMAPS-STv2.0 blended the previous cycle’s regional model forecasts with the counterpart from the global model to form the new initial background fields. The global model’s large-scale fields can constrain the development of thermodynamic fields in the regional model. The DB scheme bases on the 6-order tangent low-pass filter. Using a filter with a given cut-off wavenumber, a variable can be divided into large-scale and small-scale parts. The blended field is then obtained by adding the large-scale component of the global model and the small-scale component of the regional model. For a variable X , forecasts from the global and regional model are X g and X r , respectively. And the blended fields X b can be expressed as: Xg =

f (k; kc )xg (k) + k

Xr =

f (k; kc )xr (k) + k

Xb =

[1 − f (k; kc )]xg (k)

(3.4)

[1 − f (k; kc )]xr (k)

(3.5)

[1 − f (k; kc )]xr (k)

(3.6)

k

k

f (k; kc )xg (k) + k

k

where kc is the cut-off wavenumber and f represents the filter, which is defined as: f (k; kc ) = 1 + tan−6

kc π N

tan6

kπ N

−1

(3.7)

The cut-off wavenumber is calculated in two steps. The first seeks to regulate the quality of large-scale fields extracted from the global model. Because the forecast error of the global model increases with decreasing scale, DB computes the global model’s forecast error spectra against the reanalysis, and then retains the large-scale part as a candidate for blending based on a predefined error tolerance. The second step aims to control the development of the regional model’s small-scale system. In the regional model, DB keeps small-scale kinetic energy error residuals for smallscale system development. The final cut-off wavenumber is determined by selecting the smaller of the two wavenumbers calculated from the two steps respectively.

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Fig. 3.7 Upper-air temperature, specific humidity and wind speed scores from 12UTC in January 2019 (black line: CTL, red line: DB)

RMAPS-STv2.0 implements DB scheme to generate the corrected background of the hourly analysis cycle. Then, using the corrected background, perform data assimilation. The January and July 2019 results show that the DB scheme improves forecast performance for surface variables. Each upper-air variable’s forecast error, particularly the wind field, is reduced (Fig. 3.7). And the threat scores for precipitation forecasts have increased significantly, and the bias score is close to one. The DB scheme performed better in forecasts beginning at 12 UTC than forecasts beginning at 00 UTC, indicating that the scheme can effectively control the accumulated errors caused by the continuous updating cycle while maintaining the regional model’s stability.

3.3.2 National Radar Reflectivity Mosaic Data Assimilation The real-time assimilation of reflectivity mosaic data from China’s 224 Doppler weather radars is a significant update of the RMAPS-STv2.0 system. Figure 3.6c depicts the distribution of the radar network, which consists of various types of radars such as SA, SB, SC, CB, CC, and CD.

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A series of quality control and processing routines are performed on radar base data prior to data assimilation, including abnormal data identification, noise removal, outlier removal, gap-filling, removal of clutter echo, feature clutter elimination, superrefraction clutter removal, rejection of sea echo recognition, blocking beam compensation, clear clutter removal, and radial velocity dealiasing. The radar data is delayed by 13 min. To assimilate the national-wide radar reflectivity mosaic data, the indirect scheme (Wang et al. 2013; Fan et al. 2013) is used. Using the following relationship, reflectivity mosaic data are first classified based on background temperature and then transformed into proxy observations of various mixing ratios of hydrometeors (rain, snow, and graupel, for example). Tb > 5 ◦ C ⎨ Z (qr ) Z e = Z (qs ) + Z (qh ) Tb < −5 ◦ C ⎩ α Z (qr ) + (1 − α)[Z (qs ) + Z (qh )] −5 ◦ C < Tb < 5 ◦ C Z (qr ) = 3.63 × 109 (ρqr )1.75 Z (qs ) = 9.80 × 108 (ρqs )1.75 Z (qh ) = 4.33 × 1010 (ρqrh )1.75 Furthermore, if the radar reflectivity exceeds a certain threshold (set at 30 dBZ) and is located above the lift condensation height, the cloud is considered saturated, implying that the relative humidity is 100%. At this point, the estimated saturated water vapor mixing ratio can be calculated and assimilated as a proxy observation using the linear observation operator shown below. dqv ≈ c1

c2 T ε exp p T + c3

· dr h + c4 · qv · dT.

2 c3 where c4 = (Tc+c 2 , ε = 0.622, c1 = 6.112, c2 = 17.67, c3 = 243.5. 3) It can be found that dqv , the increment of water vapor is calculated by the increment of relative humidity dr h and the increment of temperature dT . The observation error of water vapor in the RMAPS-STv2.0 system is specified as 20% of the saturated water vapor value. The results of the RMAPS-STv1.0 operational forecast performance show that the continuous cycling assimilation of radar reflectivity mosaic data frequently results in the accumulation of extra water vapor and precipitation overprediction. The radar observation assimilation strategy was modified in two ways to address the aforementioned issues. On the one hand, as shown in Table 3.2, radar reflectivity mosaic data is only used in forecast update steps to avoid positive excess water vapor accumulation due to continuous cycling assimilation.

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Table 3.2 Radar data assimilation strategy Experiment ID

Cycling assimilation or not

Scaling factors of the background error covariance in radar data assimilation

RadarC

Yes, radar data consecutively assimilated in the cycling analysis stage

Var_length = 2 Scaling_length = 0.5

RadarS

No, radar data only assimilated in the update forecast stage

Var_length = 1.0 Scaling_length = 0.25

Second, for radar assimilation, the adjusted background error covariance and length scaling factors are used. The background error variance scale (var scaling) during radar assimilation is adjusted from 0.5 to 1 based on the results of a series of single-point and parallel radar data assimilation experiments. To increase the localized impact of radar observation in the analysis, the eigenvector length scale (length scaling) was changed from 0.5 to 0.25. Using the radar assimilation test results from 09UTC on June 4, 2019 as an example, the 3-h accumulated precipitation forecasts from RadarC at 0–3 h and 3– 6 h were distributed in Guangdong, Guangxi, Yunnan, and other regions (Fig. 3.8). However, RadarS experiments significantly reduced the areas of false alarms and the intensity of precipitation. Overall, RadarS forecasts precipitation more accurately than RadarC and gets closer to precipitation observations. From June to August 2019, two retrospective parallel experiments of the RMAPSSTv2.0 system’s hourly update cycle were carried out using the two radar assimilation

Fig. 3.8 3-h accumulated precipitation valid at 09-12UTC June 4, 2019, a observation and the 0–3 h forecasts from b RadarC and c RadarS experiments initiating from 09UTC June 4, 2019. d–f same as (a)–(c), but for the 3-h accumulated precipitation valid at 12-15UTC June 4, 2019. e, f are the 3–6 h forecasts

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Fig. 3.9 Verification scores of 3-h accumulative precipitation forecasts of RMAPS-STv2.0 against rain gauge observations in the 9 km domain from June to August 2019, a TS, b BIAS (Pink: RadarC; Blue: RadarS)

schemes described above. According to the scores of the 3-h accumulated precipitation forecasted over the 9 km domain verified against rain gauge observations, using the adjusted radar assimilation scheme significantly improved the threat skill score (TS) of the precipitation with all thresholds during the 24-h forecasting period (Fig. 3.9). Specifically, during the 0–12 h forecast period, the BIAS score of precipitation with all thresholds was greatly reduced, approaching 1, indicating that the use of the RadarS scheme can effectively suppress the phenomenon of overprediction caused by the original scheme.

3.3.3 Assimilation of National Wind Profiler Observation As a significant update, the national-wide wind profiler radar observation data (Fig. 3.6d) has been formally incorporated into the operational application in the RMAPS-STv2.0 system.

3 Development of the RMAPS-STv2.0 Hourly Rapid Updated … Observation Input (Original Wind Profiler Observations)

The Background Counterpart Value corresponding to the Observation

QC1: Blacklisting

Samples Accumulation for Both Observations and Backgrounds

QC2: Removing the Outliers Identified by the IRMCD Method Profiler Observations)

79 Pre-processing (OMB Calculation by Rejecting Obsolete Observations)

Observation Output (Quality-controlled Wind Profiler Observations)

Fig. 3.10 Quality control process of wind profile observation data

For data assimilation, a two-step dynamic quality control procedure for wind profiler observations was developed (Zhang et al. 2017). The first step (QC1) is blacklisting, which involves calculating and comparing the correlation coefficient between observed and background wind profiles time series station by station. Stations with correlation coefficients less than the critical correlation threshold are considered lowquality and are immediately added to the blacklist. The iterated reweighted minimum covariance determinant (IRMCD) method is used to remove outliers in the second step (QC2). That is, for profiler radars that have passed the QC1, an IRMCD outlier discrimination is performed on the U/V components’ observation-background deviation (OMB) dataset. This step effectively removes the U/V component outliers, and the remaining OMB of the wind profiler is observed to meet the Gaussian distribution required by data assimilation. Figure 3.10 depicts the specific quality control process. In real-time quality control, the blacklisting and IRMCD-based outlier detection steps are both dynamic processes that change over time. To ensure that its OMB sample dataset only contains observations from the last three months, each wind profiler radar can implement the process of adding new samples and withdrawing old samples. Overall, the blacklisting step (QC1) can dynamically reflect the most recent quality of each wind profiler station. In order for the IRMCD method to be effective and statistically significant, the total sample size must meet certain requirements. Wind profiler stations that are clearly uncorrelated with the background will be eliminated in QC1, while wind profiler observations that passed QC1 but have outliers in their OMB will be eliminated in QC2. As shown in Fig. 3.11, the time series of the profiler observation number and passing rate at each QC step from 10 June to 31 July 2018 indicate that in general, except for only a few missing data, approximately 3000+ wind profiler records are collected in every 3-h time slot, among which the passing rate of QC1 is approximately 90%, i.e., 10–15 profiler stations are entirely removed due to their poor correlation with the model background. And the actual assimilation absorption rate of wind profiler data reaches 98% after two-step quality control, indicating that the quality control has essentially achieved the expected effect (Figure omitted). The assimilation of wind profiler observations is found to have a continuous and stable positive effect on upper-air wind forecasting performance in the 9 km domain but has no effect on upper-air temperature and humidity elements (Figure omitted).

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Fig. 3.11 The profiler observation numbers and their passing rates (%) of two-step quality control during 0600 UTC 10 Jun–2100 UTC 31 Jul 2018

In the wind profiler observation convective scale assimilation scheme proposed by Wang et al. (2020), U/V is used as the control variable instead of the conventional stream function and unbalanced velocity potential. In areas with densely distributed wind profiler and radar radial wind observations, such as the 3 km domain of the RMAPS-ST v2.0 system covering North China, the strategy of simultaneously assimilating wind profiler and radar radial wind observations outperforms. In other words, conventional GTS data are assimilated first, and their analysis serves as the first guess field against which wind profile observations and radar observations (radial wind and reflectivity) are assimilated simultaneously (Wang et al. 2022). More importantly, it has been demonstrated that this strategy is capable of better realizing the mutual constraint of the two types of wind observation data, as well as having better forecasting performance.

3.4 Optimization of Physical Parameterization Schemes 3.4.1 Radiation, Planetary Boundary and Surface-Layer Physics Forecasts of surface weather (for example, 2 m temperature, 2 m humidity, and 10 m wind) have a direct impact on people’s lives, agricultural production, and the ecological environment. The diurnal variation of air temperature, as well as the daily maximum and minimum temperatures, have gotten a lot of attention. In general, the lowest layer temperature, surface temperature, and surface heat flux of the model are used together to diagnose 2 m air temperature. It is the end result of the balance of the surface energy budget and the energy transformation between the earth and the atmosphere.

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Fig. 3.12 2 m temperature bias over the 9 km domain valid at 17:00 BST. a January 2017, b July 2017, c 2 m specific humidity bias over the 9 km domain valid at 17:00 BST, d–f similar to (a)–(c), but for the 3 km domain

The RMAPS-STv1.0 surface temperature and humidity forecast have obvious seasonal forecast error, which is especially noticeable in the warm season when the 2 m temperature forecast is obviously higher and the 2 m humidity forecast is drier in the afternoon in the North China Plain, and the same forecast error is also found, but to a lesser extent, in the mountainous area (Fig. 3.12). The 2 m temperature in the mountains of north China has a cold bias during the day and a warm bias at night during the winter. This type of forecast systematic error is most likely to occur in the Yangtze River’s north from the 9 km domain of the RMAPS-STv2.0. A series of sensitive experiments also show that the forecast bias has nothing to do with the initial model values, data assimilation, or model resolution. These systematic forecasting errors are thought to be related to physical processes in models and land surface processes.

Cloud Radiative Forcing Scheme Cloud feedback would continue to be a significant contributor to numerical weather forecast uncertainty. The forecasted 2 m temperature is influenced by the surface energy budget. As a result, the effect of clouds on radiation is proportional to the 2 m temperature forecast error.

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In WRF’s radiation process, there are three cloud cover diagnosis schemes. ICLOUD = 1 is the scheme developed by Xu and Randall (1996), which was adopted in RMAPS-ST v1.0 system. Cloud fraction CF = RH0.25 1 − exp(arg) , where arg = max −6.9, −

max

100Q c −10 10 , rqs

− Qv

,

ICLOUD = 2 is a simple diagnostic in which the cloud cover is defined as 1 when the cloud water content exceeds a predefined threshold and 0 otherwise. ICLOUD = 3 is called Sundqvist (Sundqvist et al. 1989; Mocko and Cotton 1995) scheme, which is based on the empirical correlation between relative humidity and model resolution (dx) CF = 1.0 −

0.5

1 − RH 1 − RH00

.

where RH00 = 0.781 + RH00 = 0.831 +

1 35.0 + 0.5 ∗ d x 3

0.5

1 70.0 + 0.5 ∗ d x 3

for land surface and 0.5

for water body.

The surface received 30% more downward shortwave radiation in RMAPSSTv1.0 than in daytime observations (Fig. 3.13a). The overall excessive downward shortwave radiation has been cut in half after changing the cloud cover diagnosis scheme (ICLOUD) from 1 to 3, but it is still 15% higher than observations. Raoyang (ID: 54606), a station with significant and representative surface temperature and humidity forecasted bias, is chosen to investigate how the cloud radiation scheme affects the radiation budget, 2 m temperature forecasts, and humidity forecasts. A small but still over-predicted downward shortwave radiation bias can be found during 7th–July 14, 2017 with a small total amount of clouds. Both cloud radiation schemes have comparable performance. However, ICLOUD = 1 forecasted significantly higher downward shortwave radiation and a warm bias for the period 20th–July 29, 2017. The peak value and overprediction of downward shortwave radiation during the daytime are reduced after adjusting to ICLOUD = 3, and the corresponding 2 m temperature forecast bias is also improved.

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Fig. 3.13 The forecasted surface received downward shortwave (a, b) and net total radiation (c, d) (unit: 106 J), a, c from ICLOUD = 1 (RMAPS-STv1.0) and b, d from ICLOUD = 3 scheme. The numbers represent the forecasted bias at every station. Black triangle is RaoYang (station ID: 54606)

In general, the two cloud radiation schemes perform similarly when there is less cloud cover, but when there is precipitation or cloud cover, the ICLOUD = 3 scheme forecasts less downward shortwave and net total radiation, resulting in a slightly improved warm bias of 2 m temperature (Fig. 3.14). Cloud cover forecasts with ICLOUD = 3 show an increase in the lower atmosphere above the boundary layer during the day (3–12 h, 27–36 h) and in the middle and upper atmosphere during the night (15–24 h) (Fig. 3.15). As a result, the amount of shortwave radiation reaching the ground decreases significantly, lowering atmospheric temperature and increasing atmospheric humidity (Yang et al. 2020).

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Fig. 3.14 Time series diagram of site 54606 in July 2017. 24-h forecasts with 3-h intervals starting at 08:00BST each day. a 2 m temperature forecast deviation (blue line: operation, icloud1; Red line: icloud3), the corresponding dots in the figure represent precipitation (≥ 1 mm/3 h), black is the site observation, blue is the operational forecast, and red is the icloud3 test forecast. b 2 m specific humidity forecast deviation; c downward shortwave radiation forecast deviation; d net total radiation forecast deviation; e observations of low cloud cover (black dots) and high cloud cover (green dots)

Adjustment of the Planetary Boundary Layer and Surface-Layer Scheme It is discovered in the summer of North China that the ACM2 used by the RMAPSSTv1.0 system is warmer and drier than other boundary layer schemes. As a result, the ACM2 scheme is replaced with the YSU boundary layer scheme, which produces more accurate surface forecasts. The surface-layer (SL) scheme, which provides the energy exchange coefficient for the boundary layer, also has a greater impact on

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Fig. 3.15 The 48-h time series of the station (ID: 54606): a domain-average cloud cover profiler forecasted by RMAPS-STv1.0 and b changes in domain-average cloud cover with ICLOUD = 1 switched to ICLOUD = 3

predictions of temperature and humidity profiles in the boundary layer, according to sensitivity tests. The heat exchange coefficient (C h ) is calculated using the modified MM5, which is the YSU PBL scheme’s default surface-layer scheme. ku ∗

Ch = ln

ρcp ku ∗ z cs

+

z zl

− ψh

z L

+ ψh

zl L

,

According to Chen and Zhang (2009) research, the above formula commonly underestimated and overestimated the C h of forest and grassland, respectively. Later they modified the calculation of the thermal roughness and the heat exchange coefficient is determined as follows: ku ∗

Ch = ln

z z 0t

− ψh

z L

+ ψh

z 0t L

,

The thermal roughness z 0t is calculated as (Zilitinkevich 1995) z 0t = z 0m exp −kCzil Re , Czil typically accepts a fixed value of 0.1. In order to fully account for the effect of vegetation height on heat roughness and energy exchange coefficient, Czil is fitted by the height of the vegetation in Chen and Zhang (2009): Czil = 10(−0.4h) ,

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Fig. 3.16 Surface heat exchange coefficient Ch (in log10 ). a RMAPS-STv1.0 operational system, b adjusted Ch , and c the distribution of land use categories in the 3 km domain area

Ch can be calculated using two different surface-layer schemes, and Fig. 3.16 illustrates how they differ. After adjusting the PBL and SL schemes, as shown in Fig. 3.17, the distribution of both surface sensible and latent heating changes, resulting in significant changes in the forecasted temperature and humidity profiles in the boundary layer (Fig. 3.18) and the prediction of 2 m temperature and specific humidity, alleviating the problem of dry bias of ground humidity in North China to some extent.

Update of Vegetation Coverage Dataset Currently, most numerical models, including WRF, use multi-year averaged monthly vegetation cover data. Vegetation cover data for the RMAPS-STv1.0 system were created in 1995 using the MODIS dataset (MODIS1995), which represented global vegetation cover with coarse resolution from 1989 to 1993. The WRF website introduced a new set of vegetation datasets based on MODIS remote sensing observation data from 2002 to 2011 (MODIS2013) in 2013. Figure 3.19 depicts the differences

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Fig. 3.17 For July 2017, the effects of updated schemes of the near layer and boundary layer on a sensible surface heat ( unit: W m−2 ); b the influence of latent heat flux (unit: W m−2 ); c the 2 m temperature forecast (unit: °C); d the 2 m specific humidity forecast (unit: g/kg)

Fig. 3.18 a Temperature forecast difference and b specific humidity forecast difference at site 54606 after updating the surface-layer and PBL scheme

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Fig. 3.19 Distribution of vegetation cover in July, a from 1990 to 1995, b from 2002 to 2010; c the difference between them in the 3 km domain

in vegetation cover across Greater East Asia in July, as well as the differences in North China. Overall, MODIS2013 vegetation cover is slightly higher in Southern China but significantly lower in Southwest and Northeast China than MODIS1995. The difference in vegetation coverage between the two datasets in the D02 forecast area is depicted in Fig. 3.19c, with MODIS2013 having greater coverage in farmland and grassland and significantly less coverage in forests and other land-use attribute areas. MODIS2013 vegetation coverage is approximately 20% larger in the southeast area of D02, where corresponds to the area with significantly higher 2 m temperature forecast. Latent heating flux dominates land-air coupling in the North China Plain during the warm season (figures omitted). Figure 3.20 shows that when the new vegetation dataset was used, the upward sensible heating flux decreased while the upward latent heating flux increased in the farmland area. The sensible and latent heating fluxes calculated by the land surface process are forcing terms of the model’s boundary layer physical processes, influencing low-level temperature and humidity forecasts. The warm bias of the 2 m temperature forecast is significantly weakened in the afternoon (17 BST), and some local 2 m temperatures can be reduced by 1 degree. The dry bias of the 2 m humidity forecast is also reduced, and some local forecasts rise by 1 g/ kg. The surface sensible heating flux decreasing (increasing), surface latent heating flux decreasing (increasing), 2 m temperatures decreasing (increasing), and 2 m specific humidity increasing (decreasing) during the afternoon are consistent with the increase (reduction) of vegetation coverage brought in by the new vegetation dataset and change in an almost linear relationship, similar to Miller et al. (2006). Experiments demonstrate the significance of accurately reflecting surface features.

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Fig. 3.20 Effects of the new vegetation data on a surface sensible heat flux (unit: W m−2 ); b latent heat flux (unit: W m−2 ); c 2 m temperature forecast (unit: °C); d 2 m specific humidity forecast (unit: g/kg) in July 2017

Update of Soil Type and Noah’s Soil Hydraulics Parameter Table The default soil texture data out of United Nations over the entire globe (with 5 min resolution) in WRF is from FAO. Shangguan et al. (2013) established a soil composition map of China with a resolution of 30'' based on raw observations, and subsequently Shangguan et al. (2014) constructed a global dataset of soil texture by integrating the soil texture data in different regions and countries. The WRF website now releases the Beijing Normal University (BNU) soil map, whose higher resolution represents a significant improvement over the previous default dataset. The soil hydraulic parameters can also influence soil temperature and moisture in an LSM. A more recent soil parameter lookup table may be desirable to investigate, as these Noah LSM parameters have not been updated in many years. Kishné et al. (2017) revised the default soil hydrological parameter table in the Noah scheme based on 6749 samples of soil physical properties in Texas and the surrounding area and discovered that the field water content and water content of wilting point in

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Fig. 3.21 The soil types of the top layer from a the default soil type dataset in WRF, b Beijing Normal University soil type dataset. The covered area is the 9 km domain, and the black box in North China represents the 3 km domain

Noah’s default soil parameters were underestimated. As a result, additional revisions to Noah’s default soil parameter table were made through observations. The default soil texture dataset might not accurately represent the extremely detailed soil features found outside of the United States (Gao et al. 2008). In this study, the standard soil texture dataset for Noah LSM is substituted by the Chinese 30arc-second-resolution soil texture dataset created by BNU (Shangguan et al. 2014). The BNU soil texture fields and the default soil texture are both displayed in the 9 km domain in Fig. 3.21. The BNU soil maps exhibit more spatial variation than the default soil map, as can be seen. Large area with soil texture of clay loam in the default soil map, where many stations have noticeable dry Q2 bias, is replaced by the BNU soil map’s loam. Kishné et al. (2017) show the differences between WRF’s default soil parameter lookup table and their revised lookup table. The revised soil hydraulic parameter table, in comparison to the default soil hydraulic parameter table, allows for a wider range of moisture availability among different soil textures. More water in the soil is transported to the atmosphere via evaporation and transpiration following the update of the soil map and soil hydrological parameters, resulting in a decrease in soil moisture and temperature. As a result, SHF and LH during the land surface process increase during the day, while SHF transported from the land surface to the atmosphere decreases as LH increases. T2 falls while Q2 rises, helping to correct the operational forecast’s near-surface warm and dry biases (Fig. 3.22).

Comprehensive Optimization Performance Figure 3.23, like Fig. 3.12, shows the forecast errors at the surface level for both domains with all of the above physical schemes combined during the month of July

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Fig. 3.22 In July 2017, the effect of the new soil map and hydrological parameter table on a the surface sensible heat flux (unit: W m−2 ), b the latent heating flux (unit: W m−2 ), c 2 m temperature (unit: °C), and d 2 m specific humidity forecast (unit: g/kg)

2017. Regardless of whether the domain is 9 km or 3 km, it is clear that the new scheme can successfully address the warm and dry surface forecast bias in North China all day. In North China, the results from both domains are comparable. It should be noted that the new scheme has amplified the cold-wet bias in several parts of southern China. The 48-h forecast bias and the RMSE against observations were computed for the 2017 warm season, which lasted from April 1 to August 31, 2017 (Fig. 3.24). Surface temperature and humidity forecasts improved with each scheme individually, but their combined results improved the most. When compared to the operational prediction, the average forecast bias and RMSE of 2 m temperature in 3 km region of North China are reduced by 73% and 13%, respectively. Furthermore, the results of 2 m specific humidity are reduced by 61% and 18%, respectively.

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Fig. 3.23 The forecast error of a, c 2 m temperature and b, d specific humidity, where a, b and c, d represents the results from 9 and 3 km domain, respectively. The stations with black circles represent those have passed the student’s t 95% confidence test

Fig. 3.24 The average bias and RMSE scores of all experiments for a 2 m temperature and b 2 m specific humidity from April 1 to August 31, 2017

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3.4.2 Precipitating Cumulus and Shallow Convection Processes According to the RMAPS-STv1.0 verification scores from June to August of 2019, the system has a problem with too much weak precipitation and too little largemagnitude precipitation. In this section, a scale-aware cumulus convection parameterization scheme is introduced to improve the precipitation forecast of the cumulus scheme, thereby optimizing the errors of the RMAPS-precipitation STv1.0.

Optimization of Scale-Aware Cumulus Convection Parameterization Scheme When the model’s resolution is high enough (for example, less than 4 km) and the grid spacing is less than or close to the size of the convection system, it is generally accepted that the model can explicitly describe some convective processes without requiring a cumulus parameterization scheme (Arakawa et al. 2016). A cumulus parameterization scheme is typically required to describe the sub-grid process when the grid distance exceeds 10 km. Convective parameterization schemes’ “gray zone” refers to the range of model resolutions where some theoretical presumptions of convective parameterization schemes are no longer valid and the model and can only partially resolve convective processes (Kuell et al. 2007; Hong and Dudhia 2012; Kishné et al. 2017). To ensure that the parameterization assumption is reasonable, a scale threshold separating the resolvable scale from the parameterized scale must be defined. The resolution of RMAPS-STv1.0’s outer domain is 9 km, which is insufficient to explicitly and completely identify various convective processes occurring in the atmosphere. As a result, the scale-aware cumulus convection parameterization scheme is more reasonable than the conventional cumulus convection parameterization scheme. (Yang et al. 2021) present detailed results using different cumulus parameterization schemes based on RMAPS-STv1.0. The scare awareness is optimized to improve the new Tiedtke convective parameterization scheme used in the RMAPS-STv1.0. The following are the key differences between the new Tiedtke scheme and its scale-aware counterpart: (1) grid distance-dependent convective adjustment time; (2) grid distance-dependent cloud water conversion rate, and (3) when the model layer is saturated, middle layer convection will not be triggered. This scheme has been made public (Wang 2022, https://www2.mmm.ucar.edu/wrf/ users/workshops/WS2018/oral_presentations/6.5%20PDF). The spatial distribution of sub-grid cumulus and grid-resolved microphysical process precipitation, as well as their contributions to total precipitation, is depicted in Fig. 3.25. In the experiment using the original version of the new Tiedtke convective scheme, total precipitation is dominated by sub-grid cumulus precipitation, particularly over southern and northeast China, as well as over oceans. In the experiment of scale-aware version, however, microphysical processes are primarily responsible

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for precipitation over land, including Sichuan, northeast China, and the southern slope of the Tibetan Plateau, while cumulus convective precipitation is primarily responsible for precipitation over the South China Sea and the northern Indian Ocean. The scale-aware new Tiedtke scheme outperforms in predicting the spatial distribution characteristics of precipitation. By computing the TS and BIAS scores of 3-h accumulated precipitation scores at various magnitudes, the effects of the new Tiedtke convective parameterization scheme (nTiedtke) and its scale-aware version (scale-aware nTiedtke) on precipitation are further investigated. Both groups of tests, as shown in Fig. 3.26, overestimated precipitation by 0.1 mm, especially during the day. The scale-aware nTiedtke reduces false alarms and contributes to an increase in the TS score for 0.1 mm of precipitation. The bias scores of 0.3-0.5 for 25 mm/3 h for the nTiedtke scheme indicated that the operation model frequently failed to forecast strong precipitation above the 25 mm/3 h threshold, whereas the scale-aware version significantly improved its BIAS score, thereby improving the TS score throughout the day. According to the 24-h BIAS score, which is closer to 1, the scale-aware nTiedtke scheme is useful for reducing false alarms of small-magnitude precipitation (Fig. 3.27) and has higher TS scores than the original new Tiedtke scheme for precipitation ranging from 0.1 mm/ 3 h to 25 mm/3 h. Total rain

CP rain

MP rain

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 3.25 The June–August 2019 averaged 24-h accumulated precipitation forecast a total, b from cumulus parameterization, and c from microphysics parameterization. d–f similar to (a–c) but from the experiments with scale-aware new Tiedtke scheme (unit: mm)

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Fig. 3.26 TS (left column) and BIAS (right column) scores of a, e 0.1 mm, b, f 5.0 mm, c, g 10.0 mm, and d, h 25.0 mm precipitation on a 3-h basis averaged during June to August 2019

Optimization of the Shallow Convection Process The new Tiedtke cumulus convection parameterization scheme includes parameterizations for both deep and shallow convections, based on cumulus cloud thickness, with deep (shallow) convection being thicker (thinner) than 200 hPa. Shallow convective clouds are more widely spread horizontally than deep convective clouds, grow vertically less quickly, and have small inner-cloud mass fluxes that are insufficient to produce heavy precipitation. These clouds have less thermal and dynamic influence on their surroundings than deep convective clouds, but they can produce light rains, which distinguishes the new Tiedtke from other shallow convection schemes. After reviewing batch test results, it was discovered that the RMAPS-STv1.0 has a large area of false alarms for small amounts of precipitation when convections are relatively weak. As a result, the processes of shallow convection were tuned and analyzed using various methods based on the scale-aware new Tiedtke convective

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Fig. 3.27 The forecast performance diagram of 24-h accumulated precipitation averaged during June to August 2019

parameter scheme, such as changing the shallow convection threshold, the shallow convection closure condition, and the conversion coefficient of cloud water and rainwater in shallow convection. Turning off shallow convection has the greatest effect, according to numerical tests. The results of the batch tests are shown below. The spatial distribution of the 24-h accumulated precipitation forecasts beginning at 08:00 on July 14, 2020 is displayed in Fig. 3.28. Small-amount precipitation is significantly false-alarmed in Southern China (bottom left) in the experiment with the shallow convection scheme turned on, particularly in the Guangdong-Guangxi region. In the cumulus scheme, turning off the shallow convective process reduces the range of predicted small precipitation, leading to the closer spatial distribution of precipitation to the observation (lower right). The case shows that the over-forecasted small-magnitude precipitation can be improved by turning off the shallow convective process in the cumulus convection parameterization scheme. Figure 3.29 compares the TS and BIAS scores of batch runs performed from June to August 2019 using the scale-aware new Tiedtke cumulus convective parameterization with shallow convection (Shallow off) disabled to the original version

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Fig. 3.28 The 24-h accumulated precipitation during 08 BST 14–15 July, 2020. a Observation, b forecasted with the scale-aware new Tiedtke cumulus scheme and c same as (b) but turned off the shallow convection

(OPER20). Turning off the shallow convection process in the convection scheme reduced false alarms and improved the TS score of small precipitation (0.1 mm/3 h and 1 mm/3 h), particularly the 0.1 mm/3 h threshold.

3.5 Verification For the period July 1 to October 31, 2020, the real-time precipitation forecasts of the RMAPS-STv1.0 and v2.0 systems were evaluated and compared. The hourly rainfall observations come from approximately 11,000 automatic weather stations spread across China. Figure 3.30 depicts the distribution of stations. For runs beginning at 08BST, RMAPS-STv2.0 significantly improved forecasting accuracy during the first nine hours for the 0.1 mm/3 h and 1 mm/3 h thresholds (Fig. 3.31a, b), and the performance of the two systems was essentially equivalent for longer forecast leading time. The forecast advantage of RMAPS-STv2.0 was

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(a)

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Fig. 3.29 a Threat score and b BIAS score of the 24-h accumulated precipitation forecasts averaged during June–August 2019 with scale-aware new Tiedtke scheme, where green represents the scaleaware new Tiedtke convective parameterization scheme, and red represents the experiment switching off shallow convection process in scale-aware new Tiedtke scheme

Fig. 3.30 Distribution of about 11,000 national weather stations across the China, with terrain height filled in color in the figure

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mostly maintained during the first six hours and even shorter leading time for thresholds greater than 5 mm/3 h (Fig. 3.31d, e). Nonetheless, the verification results for the forecast beginning at 20BST revealed that RMAPS-STv2.0’s forecasting performance in the 9 km domain was significantly improved in the 3–24 h forecast time compared to RMAPS-STv1.0 (figures omitted). The results of the ETS score averaged across the country for 6-h accumulated precipitation forecasts during the same period show that the forecasting performance of RMAPS-STv2.0 was significantly improved for all thresholds and leading time for the runs beginning at 20BST (Fig. 3.32). In the 9 km forecast score, the RMAPSSTv2.0 outperforms the RMAPS-STv1.0 due to a higher success rate or fewer false alarms. For the D02 domain, the ETS scores of 3-h accumulated precipitation forecasted by RMAPS-STv2.0 and v1.0 beginning at 08BST were comparable to those forecasted in the D01 domain (Figures omitted). However, for the forecasts beginning at 20BST, the forecasting skill of RMAPS-STv2.0 with leading time of 3–24 h was significantly better than that of RMAPS-STv1.0 for thresholds of 10 mm/3 h and less. However, for both the 9 km and 3 km domains, RMAPS-STv2.0 outperforms

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Fig. 3.32 ETS scores of 6-hour accumulative precipitation forecasts beginning at 20BST of RMAPS-STv1.0 and 2.0 systems in the 9km domain from July to August 2020. a 0.1 mm, b 1 mm, c 5 mm, d 10 mm, e 25 mm, f 50 mm

RMAPS-STv1.0 primarily in terms of thresholds of 25 mm/3 h and 50 mm/3 h with leading time of 15–24 h (Fig. 3.33). Similarly, the 6-h accumulated precipitation in D02 forecasted by RMAPS-STv2.0 beginning at 20BST was significantly better for all thresholds than forecasts beginning at 08BST (Fig. 3.34).

3.6 Summary In this chapter, the key technical characteristics of RMAPS-STv2.0 system, which is an operational hourly rapid updated cycling analysis and short-term forecast system, are addressed as follows: 1. To address the noise balance issue of the hourly rapid update cycle, a WRF-based incremental analysis update initialization scheme is developed and successfully implemented. The hourly catch-up cycle operation framework is created to realize the full and efficient utilization of various observation data. It consists of two

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Fig. 3.33 ETS score of 3-h accumulative precipitation forecasts beginning at 20BST of RMAPSSTv1.0 and 2.0 systems in the 3km domain from July to August 2020. a 0.1 mm, b 1 mm, c 5 mm, d 10 mm, e 25 mm, and f 50 mm

coupling parts: cycle analysis and forecast update. The difference in cut-off time from real-time data collection is fully considered when designing the RMAPSSTv2.0 system’s operation process. 2. A dynamic blending scheme is developed and applied to the RMAPS-STv2.0 system to better exert dynamic constraint of the large-scale forecasts from the global model on the development of the regional model’s small-scale thermal field. The national radar reflectivity mosaic observation products are effectively assimilated with the optimized variance and length scales of the background error covariance. The RMAPS-STv2.0 system successfully assimilates national wind profile data by constructing a two-step quality control scheme based on the IRMCD scheme. 3. The issue of the significant systematic warmer and drier forecast bias in the RMAPS-STv1.0 during the warm season was investigated, beginning with the balance of the surface shortwave radiation budget and the energy distribution and transmission during the land-air coupling process. The systematic errors of

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Fig. 3.34 ETS scores of 6-hour accumulative precipitation forecasts beginning at 20BST of RMAPS-STv1.0 and 2.0 systems in the 3km domain from July to August 2020. a 0.1 mm, b 1 mm, c 5 mm, d 10 mm, e 25 mm, f 50 mm

land surface prediction were effectively reduced by integrating four comprehensive optimized schemes, including changing to a new cloud radiation scheme, modifying the land-air energy exchange coefficient in the surface-layer scheme, updates of the latest vegetation cover and soil type datasets. 4. The scale-aware cumulus convection parameterization scheme is used to address the issue that the RMAPS-STv1.0 tends to over-forecast weak precipitation and under-forecast heavy precipitation. The precipitation forecast performance score improves significantly after optimization. Furthermore, turning off the shallow convection process in the cumulus scheme effectively resolves the issue of overprediction of small magnitude precipitation.

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Chapter 4

The Operational Run of the Newly Developed KIM and Update Efforts at Korea Meteorological Administration Young Cheol Kwon

Abstract Korean Institute of Atmospheric Prediction Systems (KIAPS) successfully developed the next-generation global model (KIM; Korean Integrated Model) at 2019 by nine-year national project (2011~2019). After being refined several components suitable to the operational environment, the KIM has been the operational global model of Korea Meteorological Administration (KMA) since April 2020. Because the performance of the initial version of KIM is 2% behind the existing operational global model (2019 version of United Kingdom Meteorological Office—Unified Model; KMA-UM) in terms of 500 hPa anomaly correlation coefficient (ACC) over northern hemisphere, KMA continues struggling to improve the accuracy of KIM. The efforts consist of addition of new observation data to data assimilation (DA) system, especially satellite data, introduction of new DA techniques, such as variational bias correction (VARBC), and update of physics packages based on diagnostics of model output compared to observation or analysis data. Among the updates, one of the most impactful upgrades will be described in this chapter. In addition, outstanding issues related to the future plans will also be discussed. Keywords KIM · Pole · Cold-bias · Forecast bust

4.1 Operational Launch of Korean Integrated Model (KIM) After successful development of KIM at Korean Institute of Atmospheric Prediction Systems (KIAPS), the Korean Meteorological Administration (KMA) has started running KIM with operation basis since late April 2020. As configured at KIAPS, the operational KIM consists of the horizontal resolution of 12km, and 91 vertical levels with model top of p = 0.1Pa (h ~ 80km). The horizontal discretization is spectral Y. C. Kwon (B) Numerical Modeling Center, Korea Meteorological Administration, Daejeon 35208, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_4

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element method over cubed sphere projections (Hong et al. 2018 and references therein). The KIM is running four times a day at 00, 06, 12 and 18UTC with making 144-hour forecast at 00, 12 UTC and 87hour predication at 06, 18UTC. The flowchart of KIM with cut-off time of data collection and model runtime is shown at Fig. 4.1 for 00UTC, and other three times are operating similar time schedules. Currently, three downstream models are running derived by KIM forcing, which are Asian Dust Aerosol Model (ADAM), Wave-Watch III and RDAPS-KIM (Regional Data Assimilation and Prediction System). The detailed descriptions of the downstream model are omitted because names of the downstream models are self-explanatory and detailed documentations of these models are beyond the scope of this book. In addition to deterministic KIM, the ensemble of KIM is also conducted for the purpose of 1) data assimilation and 2) providing forecast uncertainty information. The number of KIM ensemble member is 51, and horizontal resolution is 32km. The initial perturbations are made by the method of Relaxation to Previous Spread (RTPS, Whitaker and Hanmill 2012), and physics and dynamic tendencies are stochastically perturbed during the model run as well. The spread of the KIM ensemble is used for estimating background error for data assimilation. Various products from KIM and KIM ensemble are provided to weather forecasters of KMA in order to help predicting weather over Korean Peninsula. The traditional surface and upper level weather maps (sea level pressure, precipitation, 500 hPa

Fig. 4.1 Flowchart of KIM operational system including downstream models. The time shown at the bottom of the boxes denoted starting and ending time of each module in terms of UTC. The time sequence is denoted for 00UTC simulation

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vorticity and geopotential height, 200 hPa wind fields and so on) and other supplementary graphics (vertical-temporal evolutions of wind, cloud amount, temperature, rainfall amount at a certain city) are produced. Some examples are shown in Fig. 4.2. This chapter consists of an example of KIM physics update which had shown most improvement and future plans with corresponding outstanding issues.

4.2 Updates of KIM Since KIM became operational at KMA, Numerical Modeling Center (NMC) has updated KIM twice a year. The brief descriptions of each upgrades and their improvement rates in percentage are summarized in Table 4.1. The addition of observation data, mainly satellite data and assimilation methods, is refined regarding the data assimilation system. Also, the resolution of the ensemble model for data assimilation became finer from 50 to 324km in order to reduce the discrepancy between deterministic forecast and assimilation models. At the early stage of the physics updates, the sensitive physics parameters are optimized by the generic algorithm (Jang et al. 2020). After optimizing the parameters, KIM physics are updated by identifying the weakness of KIM via diagnostics of model initial and forecast fields (update 3.6a and beyond). In fact, v3.6a was one of the success procedures of KIM updates in KIM’s short life, so it is worth to describe in this book. In the following, the processes of diagnostics and updates of 3.6a will be described in detail. Figure 4.3 is the time series of the 500 hPa geopotential root mean square errors (RMSE) over northern hemisphere for KIM, KMA-UM and IFS from August 1 to 31, 2020. While the daily errors of all three models vary, the magnitude of fluctuation of errors is the largest in KIM. Sudden jump of RMSE of KIM is noticeable at the date of August 16. This kind of sudden increase of error is not uncommon in NWP models, and it is known as a dropout case. Many research and operational groups have been aware of the dropout cases and their detrimental effect on average model performances. Therefore, identifying the source of dropout cases and fixing the problem are critical to improve the forecast accuracy of NWP models. In order to separate the cause of the August 16 dropout case, the initial data swap experiment is conducted—KIM simulation initialized with the UM analysis data (EXP1 hereafter). If EXP1 produces smaller error than KIM and similar magnitude to KMA-UM, it can be assumed that the initial data might be the main reason of deteriorated KIM forecast of August 16. Figure 4.4 shows the 500 hPa GPH RMS errors of KIM, KMA-UM and EXP1 verified against IFS analysis from t = 0 hr to t = 120 hr. As expected from Fig. 4.3, the model error grows faster with time in KIM compared to KMA-UM, and the differences are getting larger with simulation time. Despite spin-up at the initial state due to balance problem, the GPH errors of the EXP1 converge to those of KMA-UM with time, and the error magnitude of two experiments becomes similar at t = 120 hr. Therefore, the initial data quality of

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Fig. 4.2 Some examples of graphic output of KIM, a mean sea level pressure and accumulated precipitation, b 500 hPa geopotential height and relative vorticity, c, d as in (a, b) but over northern hemisphere, e as in (a) except over Korean Peninsula, and f meteogram

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Table 4.1 List of KIM updates and their impact. The positive values mean improvement rate in percentage while negative values denote degradation Update Date

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Five-day forecast error, positive value means improvement in percentage

Fig. 4.3 Time series of 5-day forecast RMS errors of 500 hPa GPH of KIM (green line), KMA-UM (blue line) and IFS (magenta line) over northern hemisphere from August 1 to August 31, 2020

KIM is somehow responsible for this dropout case, although it remains to be seen whether data assimilation or model itself is the source of the problem. In order to investigate the differences of KIM and KMA-UM initial conditions, both initial fields are compared to IFS analysis. After examining many aspects of data, it is found that the cold bias at the high-latitude, low-levels region is one of the most prominent features of KIM analysis compared to KMA-UM analysis field (Fig. 4.5). However, it cannot be 100% sure that the cold bias seen in Fig. 4.5 is the actual cause of error growth of KIM. Therefore, an additional experiment, EXP2, is designed to confirm whether the high latitude cold bias identified in KIM analysis is the real source of the forecast error in the dropout case. The initial data of EXP2 is constructed by mixture of two analysis data which are KMA-UM analysis data for north of 60° N and KIM analysis data for the rest of globe (south of 50° N) as shown in Fig. 4.6. In order to minimize the discontinuity of border along two different analysis data, linear weighted of two analysis data are assigned between 50 and 60° N. For example, the weight of KMA-UM analysis at 60° N is 1.0, and that of KIM analysis at 50° N is 1.0, while the weight at 55° N is 0.5 for both analysis data.

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Fig. 4.4 Time series RMS error of 500 hPa GPH over northern hemisphere of KIM (green line), KMA-UM (blue line) and EXP1 (black line) verified against IFS analysis from t = 0 hr to t = 120 hr

Fig. 4.5 Height-latitude cross sections of temperature difference against IFS analysis, a KIM initial condition and b KMA-UM initial condition

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Figure 4.7 shows the temporal evolution of EXP2 errors denoted in the red line, and the errors of EXP2 are very close to those of EXP1 with slight differences around initial time and after t = 80 hr. Because the performance of the EXP2 is similar to the performance to that of KMA-UM, the source of the error of the dropout case should be the KIM cold bias at the low-level, high latitude region. The initial data (or analysis) of NWP model is obtained by adding observation data to model first guess fields which are usually t = + 06-hr forecast of a model. Because model 6-hour forecast fields usually have some degree of error, calibrations should be made by available observation data with a data assimilation system. Therefore, the initial data errors (or departure from IFS analysis defined in this case) of the KIM could result from either first guess caused by model physics or calibration of model bias by the data assimilation system. In order to quantify the low-level temperature cold bias of KIM analysis at high latitude area, the time evolutions of area averaged

Fig. 4.6 New initial condition made by combining KIM and KMA-UM analysis fields. The north of 60° N is from KMA-UM and the rest of globe if from KIM

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Fig. 4.7 As in Fig. 4.2 except adding EXP2 (red line) which is blending of KIM and KMA-UM initial field

temperature north of 60° N at 850 hPa of KMA-UM and EXP1 are plotted (Fig. 4.8). Although the two simulations are done with the same initial condition (UM analysis), the 850 hPa temperature of EXP1 becomes colder with forecast time larger than that of KMA-UM. Although both simulation results show the cold bias, the tendency of cold bias from EXP1 (about − 1.5 °C) is much larger than that of UM simulation, leveling off with the maximum cold bias of 0.7 °C at t = 120h. Therefore, Fig. 4.8 indicates that the physics of KIM is also responsible for larger cold bias at the low level in the high latitude area. The analysis increments are the amount of the corrections to the first guess data (+6hr forecast of KIM in this case) by assimilation of observation data. When first guess bias (model bias) is large, analysis increment should also be big but with opposite sign to cancel the bias. Because of the bigger temperature bias of KIM than that of KMA-UM, the KIM’s analysis increments are expected to be larger than UM’s analysis increment. Figure 4.9 compares the bias of the 925 hPa temperature analysis of KIM with respect to IFS analysis and corresponding analysis increments. As seen in Fig. 4.9, the cold bias of KIM analysis exists over most of North Pole area, but there is not enough positive analysis increment to make appropriate correction. UM physics produces less cold analysis bias compared to KIM according to Fig. 4.8; UM analysis increments are bigger than KIM analysis increments. Considering Figs. 4.8 and 4.9, KIM physics tends to make colder at low-level, high latitude region more than UM; KIM data assimilation is less effective to correct this bias than UM assimilation as well. The dropout case in this case is caused by the low-level cold bias over high latitude, and it is found that KIM physics is responsible for cold bias and KIM DA is not properly correct for the bias. Therefore, the efforts should be made to reduce the bias in both physics and data assimilation aspects to reduce the cold bias at

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Fig. 4.8 Time series of the magnitude of 850 hPa temperature bias compare to the IFS analysis averaged over 60° N to North Pole. The green bars are for EXP1, while blue bars represent KMA-UM

Fig. 4.9 925 hPa temperature analysis increment for a KIM and b KMA-UM

the low-level polar region. Many updates are implemented to KIM version 3.6a which became operational at April 20, 2021, but two modifications most directly reducing the cold bias are described below. One change is that in-house developed snow cover assimilation system is introduced to remove the dependency of the 6hourly snow cover initial data from National Weather Service (NWS), USA. The observation data used in the new snow cover assimilation is interactive multi-sensor

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Fig. 4.10 Vertical cross section of temperature difference, a between the original snow cover assimilation scheme and the newly implemented snow cover assimilation scheme and b caused by fixing the sea ice initialization method at t = 120 hr

snow and ice mapping system (IMS), which is composite of various satellite observations. IMS data is prepared and distributed by National Environmental Satellite, Data and Information Service of National Oceanic and Atmospheric Administration (NESDIS/NOAA). The vertical cross section of zonal mean temperature difference between original and new snow cover assimilation (Fig. 4.10a) indicates that the newly implemented assimilation scheme alleviates the polar low-level bias about 10.3%. Another modification is fixing bugs related to sea ice distributions of KIM. Although the initial sea ice extension is designated by satellite analysis (OSTIA; Operational Sea Surface Temperature and Sea Ice Analysis) in daily basis, surface albedo and surface roughness are not properly updated since the first operation date (2020. 04. 28 00UTC). Therefore, the sea ice area shrinks with solar zenith angle decreases with summer season approaches, but the surface albedo and roughness do not reflect change of season. The net effect of fixing this error reduces the bias as expected but not completely. Figure 4.10b is the vertical cross section of this effect. According to hindcast results with V3.6a, the polar cold bias becomes much weaker (Fig. 4.11), which may lead to reduce the 500 hPa RMS error in the previous version. While aforementioned two modifications may not be 100% responsible to cold bias reduction, we believe that the collective effects of V3.6a updates contribute the improvement of the bias with nonlinear interactions with model integration. The quantitative assessment of each and every update to model performance improvement is beyond the scope of this book. The time series of 500 hPa geopotential height and 850 hPa temperature RMS error of V3.6 and V3.6a are shown in Fig. 4.12 from July 1 to July 31, 2020. As can be seen, the improvement is not confined in specific period of time but rather uniformly over all test periods, which may indicate the upgrades are quite substantial. Considering the cold bias of KIM found in this study, it might be reasonable to assume that there is a relationship between the magnitude of the cold bias and KIM’s RMS error. Figure 4.13 is the cold bias magnitude averaged over 60–90°

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Fig. 4.11 Cross section of temperature difference of KIM V3.6a and KIM V3.6 analysis against IFS analysis

N denoted with bars and KIM’s 500 hPa GPH RMS error with line at t = 120 hr. Figure 4.13 shows that there is no clear relationship between the two values with correlation coefficient of 0.25. This is quite unexpected, but it might be attributed to the sensitivity of initial condition known as the butterfly effect. The initial error growth could amplify quickly with time in a certain condition, whereas the initial error could decay in other condition. This is just our assumption at this stage which is yet to be proven. Another interesting feature is that low-level cold bias over polar region in KIM is prominent only over sea ice and snow over land. Comparing vertical temperature soundings of KIM and KMA-UM, two profiles are similar over ocean and land with no ice or snow, while over the sea point covered by ice (sea ice area) and land covered by snow, the temperatures of KIM at the lower level are colder than those of KMA-UM (not shown). These features could be a clue that surface-air interaction over snow/ice regions in KIM has problems. We are currently investigating surface flux-related variables over sea and ice such as thermal/momentum roughness length, frictional velocity and other surface layer physics. Hopefully, some of the unanswered questions will be resolved in the newer version of KIM and report the results in near future.

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Fig. 4.12 Time series of a 500 hPa geopotential height and b 850 hPa temperature RMS error of V3.6 and V3.6a from July 1 to July 31, 2020. V3.6 is denoted by green line, while V3.6a is represented by red line

4.3 Outstanding Issues and Future Plan Although KIM has been updated several times since its operational launch on April 2020, Numerical Modeling Center of KMA continues to struggle to improve the performance of KIM. In this section, the areas we identified as issues and corresponding future plan will be described. When the dropout case of August 2020 is analyzed to investigate the source of the growing errors of KIM, the cold bias over polar region in KIM initial condition is identified as a main reason. Whether this cold bias exists over all four seasons or just summertime temporary phenomenon, daily time series of temperature bias against IFS analysis over whole year of 2021 are plotted at the several vertical levels

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Fig. 4.13 Time series of 500 hPa geopotential height RMS error of KIM over northern hemisphere at t = 120 hr (magenta line) and temperature difference of KIM analysis against IFS analysis (blue bar)

(Fig. 4.14). There are two notable features in Fig. 4.14. One is temperature bias of KIM over high latitude which is not always negative all year around, but the sign of the bias changes with season. Interestingly enough, temperature bias show wave number two undulation annually—cold bias occurs in summer and winter while warm bias in spring and autumn. Annual wave number two oscillation may not be directly related to natural causes but rather more complicated internal variability. We have been looking into the possible mechanisms of annual wave number two temperature bias but not reached the conclusive result yet. The relatively steady state of sea ice in winter and summer and the rapid melting and freezing of spring and autumn might be the probable cause we assume at this stage. We believe that the coupling to the realistic sea ice model could be one of the solutions of this problem. The other feature of Fig. 4.14 is that the amplitude of temperature bias is the largest at the lower levels and the amplitude seems to decrease with height. While

Fig. 4.14 Daily time series of temperature bias of KIM against IFS analysis at 925 hPa (blue line), 850 hPa (green line), 700 hPa (yellow line) and 600 hPa (red line) levels, start at January 1 to December 31, 2021. The values are averaged from 70° N to North Pole

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the wavy patterns of annual temperature bias are maximum at p = 925 hPa (blue line), the undulation became almost disappears at p = 600 hPa (red line). This heightdependent temperature bias may implicate that the source of the cold bias is surface rather than upper- or mid-levels. Therefore, the initial efforts are put to revise surface temperature, such as usage of analyzed sea surface temperature instead constant value of − 1.8 °C where sub-grid sea ice exists. In addition, albedo over sea ice is modified to be the function of solar zenith angle, and surface roughness of sea ice is updated by recent study (Andreas et al. 2010). Although the sea ice surface temperature became warmer with aforementioned efforts, the reduction of low-level cold bias only lasts for one or two days. After few days, the warming trend due to revised surface temperature vanishes and even became colder after 3 or 4 days of forecast. Our diagnostics indicate that the main cause of the stronger low-level cold bias in the revised version is forming more low-level cloud resulted from warmer surface, which leads more long wave radiation cooling (not shown). Further development is ongoing combining the refinement of cloud-radiation interactions on top of surface temperature updates. Beside polar cold bias, persistent surface warm bias is identified over Siberian area as seen in Fig. 4.15a. With combination of polar cold bias, Siberian warm bias would cause strong polar jet due to the large meridional temperature bias (thermal wind relationship). Our preliminary analysis indicates that KIM’s drier soil moisture than ERA5 is one of the responsible factors as seen in Fig. 4.15c. Therefore, the land surface data assimilation and land surface physics are examined to produce more realistic wet soil moisture fields in KIM. The last issue we are investigating is to refine data assimilation scheme in order to correct model errors properly around polar regions. In the long-term plan, more sophisticated sea ice model will be introduced, and low-level microwave satellite data should be assimilated over sea ice areas with all sky assimilation capability. In the meantime, it is identified that ensemble spread of KIM at the low-level of North and South Pole is much smaller than they should be (Fig. 4.16). As mentioned in the previous chapter, KIM data assimilation uses 4DEnVAR, which means background

Fig. 4.15 Temperature bias of the 6-hr forecast KIM over North Pole region against IFS analysis, a at surface and b at 950 hPa initialized at 00UTC July 30, 2021. Global soil moisture bias is shown at c at the corresponding time

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Fig. 4.16 Zonal mean of KIM temperature error (a) versus KIM ensemble temperature spread (b) at t = 6 hr

errors are calculated from both ensemble spread and climatological method. If the ensemble spread is smaller than model error, the background error for data assimilation will be underestimated. Therefore, the data assimilation assumes the background errors at polar low level are smaller, which lead less impact of observation data because model error there is thought to be small. In order to proper calibration over pole area, the ensemble spread in these regions should become realistic, and itis under investigation, we hope this issue will be resolved soon.

4.4 The Performance of KIM In this section, the KIM performance will be shown. Because KIM has been running operationally less than three years, it should be noted that the results are preliminary and the verification is done for the year 2021. The evaluation of KIM performance is conducted over northern hemisphere and Korean Peninsula. The RMSE of 500 hPa geopotential height is the most widely used variable as model accuracy. Figure 4.17 is the monthly RMSE of 500 hPa geopotential height over the northern hemisphere from August 2020 to December 2021 for KIM and KMA-UM. The RMSE of KIM (red line) is 2–8m larger than that of KMA-UM before April 2021, while the RMSEs of KIM and KMA-UM are comparable after April 2021. The improvement of KIM shown in Fig. 4.17 is the results of update 3.6a as described before. As many modelers have known, we learnt a lesson again that the identifying model weakness through detailed diagnostics and fixing the problems are the best way to improve the model accuracy. Things which weather forecasters at KMA care are not northern hemisphere skill but rather predictability over Korean Peninsula, especially extreme weather events, such as torrential rain, typhoon, heat wave and other life-threatening weather phenomena. Table 4.2 shows the accuracy of rain and typhoon forecast of KIM and KMA-UM of 2021. The rainfall forecast skills in terms of ACC and POD during Korean summer, so-called Changma, of KIM and KMA-UM are comparable on 2021. Also, intensity and track prediction skills on two typhoons which impact Korean Peninsula, Omais (12) and Chantu (14), KIM is better for Omais and KMA-UM is

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Fig. 4.17 Monthly averaged root mean square error of 500 hPa geopotential height over northern hemisphere at t = +120 hr. Red line is for KIM, and blue line is for KMA-UM

better for Chantu. As in RMSE of 500 hPa geopotential height over northern hemisphere, KIM’s prediction skill over Korean Peninsular is comparable to KMA-UM’s skill. ACC =

H +C H + M + F +C

POD =

H H+M

Forecast Observation

Rain

No rain

Rain

H

M

No rain

F

C

Table 4.2 Precipitation skills of KIM and KMA-UM for 2021 Korean summer monsoon season a), and tack and intensity forecast errors of KIM and KMA-UM for two typhoons, which impact Korea in 2021. Rainfall verification is done for 12-hour accumulated rain amount at t 72 hr. The track and intensity of hurricanes are also verified at t = 72 hr a)

ACC

KIM

0.68

0.83

KMA-UM

0.60

0.86

b)

OMAIS (12) Track

KIM KMA-UM

POD

CHANTHU (14) Intensity

Track

Intensity

97.4

6.3

284.5

25.1

306.4

8.9

264.2

13.7

Bold characters denote the superior performance

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There are eight countries and one institute which report their 500 hPa RMSE at t = + 120 hr over norther hemisphere to World Meteorological Organization (WMO). They are European Center for Medium-Range Weather Forecast (ECMWF), UK, Germany, Canada, USA, Japan, Russia, China, and recently joined Korea. Among nine of them, the accuracy of KIM is ranked sixth right above Japan and right below USA in terms of 2021 annual mean RMSE of 500 hPa geopotential height at t = + 120 hr. However, all the models are constantly updated, so the current ranking is not much meaningful. However, we believe that KIM’s operational launch is quite successful considering short time developmental period and short history of operational run. With dedicated researchers in Numerical Modeling Center of KMA, KIM’s future will be bright. Version

Components

3.5a (‘20.6.)

[Model physics] • (radiation) Modification to avoid “divide by zero” error, Time error Fix for solar radiation • (ocean mixed layer) Daily initial data of ocean mixed layer depth and mean temperature • (deep convection) Optimization of empirical parameters

3.6 [Model physics] (‘20.10.) • (surface) Bug fix in sea ice initialization • (laud) Modification of in-land water process [Data Assimilation] • (observation) (new conventional) Domestic radiosonde descent data (new satellite) GK-2AAMV& CSR; KOMPSAT-5, FY-3C/D GNSS-RO • (preprocessing) (thinning, blacklist) Improvement of aircraft data (observation error) Improvement of AMV and GNSS-RO (bias correction) improvement of microwave radiance • (hybrid data assimilation) (background error) New background error and tuning (VarBC) Expansion of satellite data (2→5 types) • (laud data assimilation/ensemble) Data assimilation of soil moisture. SST perturbation

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Version Components 3.6a [Model physics] (‘21.4.) • (radiation) Bug fix in effective radius of snow and spectral band of shortwave • (surface) Optimization of empirical parameters associated with turbulent-scale orography Bug fix in wind speed calculation at the lowest model level Initialization of emissivity and roughness length in the ocean and sea ice regions • (ocean mixed layer) Optimization of empirical parameters associated with diurnal variation of SST • (deep convection) Modification of conversion parameter determining the fraction of condensate converted to precipitation. Reducing mass flux at cloud base • (boundary layer) Optimization of thermal-background mixing coefficient, removal of turbulent transport of rain, snow, ozone, cloud fraction, modification of bulk Richardson number calculation • (microphysics) Improvement of the relation equation between terminal velocity and drop size, bug fix in Gamma function [Data Assimilation] • (preprocessing) (observation error) Improvement of tropical AMV observation (bias correction) Improvement of microwave radiance • (hybrid data assimilation) (background error) Tuning of the error • (land data assimilation) Improving the initialization of snow using the snow-covered satellite data

Version

Components

3.7 [Model physics] (‘21.12.) • (deep convection) Recovery of mass flux at cloud base • (microphysics) Improvement of ice properties [Data Assimilation] • (observation) (new satellite) Metop-C AMSU-A, Metop-C MHS, NOAA-20 ATMS; Himawari-8, MSG-1/4 CSR; COSMIC GNSS-RO, Aeolus ALADIN wind data • (satellite) Expanding the ATMS water vapor channel • (preprocessing) (RTTOV) 10.2 → 12.3 update (thinning, blacklist) Improvement of GK-2A • (hybrid data assimilation) (resolution) Increase from 50 to 32km (background error) New background error and optimization • (land data assimilation/ensemble) Improvement of the initialization of snow for ensemble/AMSR2 data assimilation and removal of upper damping

References Andreas E, Horst T, Grachev A et al (2010) Parametrizing turbulent exchange over summer sea ice and the marginal ice zone. Q J R Meteorol Soc 136:927–947 Hong S-Y, Kwon YC, Kim T-H et al (2018) The Korean Integrated Model (KIM) system for global weather forecasting. Asia Pac J Atmos Sci 54:267–292

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Jang J-Y, Lee YH, Lee H-J et al (2020) The improvement of summer season precipitation predictability by optimizing the parameters in cumulus parameterization using micro-genetic algorithm. Atmos 30:225–346 (in Korean with English abstract) Whitaker JS, Hamill TM (2012) Evaluating methods to account for system errors in ensemble data assimilation. Mon Weather Rev 140:3078–3089

Part II

Physical Parameterization and Optimization

Chapter 5

Vertical Turbulent Mixing in Atmospheric Models Song-You Hong, Hyeyum Hailey Shin, Jian-Wen Bao, and Jimy Dudhia

Abstract This chapter begins by providing a brief historical review of the vertical turbulent mixing schemes, followed by an overall concept of representing vertical turbulent mixing processes in atmospheric models and their classification. Then, the evolutionary features of the so-called YonSei—University (YSU) scheme are described from the 1990s to the present, focusing on its development strategy for atmospheric phenomena from the planetary scale to the sub-kilometer scale. Limitations in existing schemes and directions for future refinements are given. A comprehensive description of the concept for various vertical turbulent mixing schemes is available in (Stensrud in Parameterization schemes: keys to understanding numerical weather prediction models. Cambridge University Press, Cambridge, 2007). Keywords Turbulent mixing · Planetary boundary layer (PBL) · YSU scheme · Gray-zone PBL · Physical parameterization

5.1 Historical Overview The earliest generation of atmospheric models had so-called bulk planetary boundary-layer (PBL) schemes and poor vertical resolutions, with only one or two levels in the lowest kilometer. Simple bulk formulas related the lowest levels to S.-Y. Hong (B) University of Colorado/CIRES and NOAA/ESRL/PSL, Boulder, CO, USA e-mail: [email protected] H. H. Shin · J. Dudhia NCAR, Boulder, CO, USA e-mail: [email protected] J. Dudhia e-mail: [email protected] J.-W. Bao NOAA/ESRL/PSL, Boulder, CO, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_5

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surface fluxes via the bulk Richardson number. Later as the surface layer became resolvable with a thin ~ 100-m model layer, similarity theory became relevant, and much observation work in that area could be leveraged to give more physically based surface fluxes of heat and momentum. Current PBL schemes are mostly based on similarity assumptions to connect the lowest layer to the surface. In the 1970s and 1980s, turbulence modeling increasingly turned to so-called higher-order closure, inspired by the seminal paper on the hierarchy of turbulence closures by Mellor and Yamada (1974). Computational power was increasing rapidly in the 1970s, so there was a general belief that the number of prognostic equations for turbulence statistics could be increased, thereby pushing uncertain closure assumptions to second-order [e.g., turbulence kinetic energy (TKE)] and/or even higher moments, where they would either be simplified or at least not be so critical. For example, such a scheme was adopted for the regional Eta model at the US National Meteorological Center (NMC) [currently, National Centers for Environmental Prediction (NCEP)] (Janji´c 1990) based on the ideas of Mellor and Yamada (1982). Together with a diagnosed vertical turbulence length scale, TKE can be used to compute the vertical diffusion coefficients or vertical eddy diffusivities, K. A prognostic TKE approach can be applied to the whole atmospheric column, handling elevated turbulence in the free atmosphere (FA) as well as the atmospheric boundarylayer (ABL) turbulence, while maintaining a memory of the turbulence even after surface forcing ceases. Another trend in the 1990s among the K-diffusion (or eddy diffusivity) schemes was the increasing use of enhanced K-profile methods (similar to O’Brien 1970) along with a nonlocal or countergradient term in the vertical heat transport (similar to Deardorff 1972). The ideas of Troen and Mahrt (1986) helped to quantify these terms as a function of surface heat flux, surface layer stability, and an ABL depth defined in terms of a bulk Richardson number. Holtslag and Boville (1993) applied this approach to replace the local K-diffusion scheme in the US National Center for Atmospheric Research (NCAR) Community Climate Model, second version (CCM2). Hong and Pan (1996) similarly replaced a local K-diffusion scheme in the US NCEP global numerical weather prediction (NWP) model, Medium-Range Forecast (MRF), with one that includes a countergradient term and enhanced K-profile. Another form of nonlocal mixing following the ideas of Blackadar (1979) was adopted by Zhang and Anthes (1982) in their high-resolution PBL used in the Penn State Mesoscale Model 4th Generation (MM4) model. This method persists in the asymmetric convection model (ACM) of Pleim (2007) and includes an entrainment layer. This effort can be regarded as an early precursor to mass-flux approaches by directly mixing the surface layer with higher PBL levels due to subgrid thermals to and from the surface layer. In the 2000s, the eddy-diffusivity mass-flux (EDMF) approach started to be used in NWP models. This method combines local methods for vertical diffusion, either TKE-based or diagnostic-K-based, with a mass-flux treatment of convective ABL (CBL) thermals using a one-dimensional plume model with a nonlocal mass flux between the surface and the thermal top (Soares et al. 2004). The European Centre for Medium-Range Weather Forecasts (ECMWF) model switched the vertical turbulent

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mixing scheme in their operational NW model from a local-K scheme to a cubic Kprofile scheme, similar to those mentioned earlier with enhanced values in the middle of the ABL (e.g., Troen and Mahrt 1986; Holtslag and Boville 1993; Hong and Pan 1996), plus a separate mass-flux term represented by an entraining and detraining plume transporting the surface air upward (Siebesma et al. 2007). Following a related but different approach, the US NCAR Community Atmosphere Model version 4 (CAM4) adopted Bretherton and Park’s (2009) CAM University of Washington (UW) ABL scheme, which included a diagnostic TKE and a generalized vertical turbulence term with the use of moist-conserved variables (i.e., total specific humidity and liquidice static energy) that allow deeper moist and dry layers to mix. The CAM4 physics also separately considers vertical turbulence mixing in shallow clouds (Park and Bretherton 2009) and includes top-down mixing. Since 2000, the YSU ABL scheme (Hong et al. 2006), commonly used in the Weather Research and Forecasting (WRF) model simulations, added explicit entrainment to the medium-range forecast (MRF) ABL countergradient scheme modifying the K-profile to stop at the top of the neutral layer and adding a term proportional to surface buoyancy flux in an entrainment layer above. Meanwhile, the National Oceanic and Atmospheric Administration (NOAA)’s operational regional NWP models—i.e., rapid refresh models [RAP, High-Resolution Rapid Refresh (HRRR)]—switched to another Mellor–Yamada-based TKE scheme with more sophisticated length scales (Nakanishi and Niino 2006). Since 2010, the YSU ABL scheme was further developed to include a top-down enhanced mixing profile driven by radiative cooling at the cloud top (Wilson and Fovell 2018); the NOAA’s RAP and HRRR models have been enhancing their Nakanishi–Niino TKE scheme to include an EDMF nonlocal part and shallow convection (Olson et al. 2019). The NCEP Global Forecast System (GFS) (formerly MRF) ABL scheme has replaced their nonlocal turbulence mixing from a purely countergradient term to a hybrid countergradient and mass-flux terms based on the ABL instability (Han et al. 2016). At present, mesoscale numerical models at high resolutions (i.e., horizontal grid spacing on the order of a few kilometers) produce realistic but only partially resolved convective rolls and cells in the ABL to make up for the “lost” transport if no subgrid scale turbulent mixing scheme is used. Properly representing the vertical turbulence mixing processes in the ABL in a model grid mesh with horizontal spacings in the ABL–LES “gray zone” or Wyngaard’s (2004) “Terra Incognita”—where the turbulence in the ABL is partially resolved (e.g., sub-kilometer-scale horizontal spacing for CBL)—remains an active area of research, and several investigators are using LES (e.g., Honnert et al. 2011, 2016; Beare 2014; Shin and Hong 2013, 2015; Shin and Dudhia 2016; Zhou et al. 2017, 2018). Further details in the review of ABL schemes are given in LeMone et al. (2020, AMS, monograph).

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5.2 Concept and Classification Consider a prognostic water vapor (q) equation in Eq. (5.1). The local change of q can be written as ∂ρuq ∂ρvq ∂ρwq ∂ρq =− − − + ρ E − ρC, ∂t ∂x ∂y ∂z

(5.1)

where ρ is the density of air, u, v, and w are the wind components in x-, y-, and z-directions in the Cartesian coordinates. E and C stand for evaporation and condensation due to diabatic processes, respectively. In atmospheric models, a value at a specific location can be represented by the sum of grid-mean and subgrid-scale (SGS) perturbation, for example, u = u + u ' , and q = q + q ' (Fig. 5.1). Here, it is important to note that the model predicts u and q, and the major issue lies in the fact that how to represent the second-order terms that consists of u ' and q ' in terms of the first-order mean variables, u and q. A standard approach to obtain the SGS properties is to utilize the so-called, Reynolds averaging. By applying the rule of the Reynolds average, such as q ' = 0, u ' q = 0, u q = u q, Eq. (5.1) can be written as

(5.2)

In Eq. (5.2), the grid-resolvable advection, denoted as ➀, is represented by model dynamics processes, and the last two terms by moist processes. The remaining issue is how to represent the SGS or turbulent scale processes in ➁. By assuming the horizontal homogeneity in the ABL—i.e., ∂/∂z ≫ ∂/∂x and ∂/∂z ≫ ∂/∂y—the turbulent 'q' , becomes the major SGS contribution to the term in the vertical direction, ∂ρw ∂z moisture transport. 'q' In the zeroth-order closure scheme, the effect of turbulent transport, ∂ρw , can ∂z be neglected as Fig. 5.1 Schematic of grid-mean (a) and subgrid-scale (SGS) perturbation (a ' ) properties over the model grid. The red box indicates the area of a prognostic variable at a grid point in atmospheric models

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−ρw ' q ' = constant,

(5.3)

A more physically based representation includes the vertical turbulent flux is proportional to the vertical gradient of grid-mean values, which can be written as −ρw ' q ' = K

∂q . ∂z

(5.4)

This formula includes the proportionality function, K, vertical diffusivity (or exchange coefficient), leading to the first-order closure: i.e., parameterizing the second-order moments on the left-hand side (lhs) using the first- and zero-order moments on the right-hand side (rhs). The next complex level is to predict the turbulent flux as in Eq. (5.1), ∂ρwq = ∂t ∂ρuwq − ∂ x + · · · . Then, as in Eq. (5.2), the application of Reynolds averaging leads to the relationship,

∂ρw ' q ' ∂t

=

∂ρw ' w ' q ' . ∂z

Consequently, the rhs term can be written

−ρw ' w ' q ' = K '

∂ρw ' q ' , ∂z

(5.5)

where K' is the exchange coefficient resulting from the second-order closure and parameterizing the third-order moments on the lhs using the second- or lowerorder moments on the rhs. With this hierarchy of the approximations, the degree of complexity in parameterizing turbulent transport can be classified. The seminar article by Mellor and Yamada (1974) provides the details on the derivation of turbulent kinetic equations. In a well-mixed layer in the daytime, multiscale turbulent eddies coexist. Vertical velocities within thermals can reach 5 m s−1 , although values of 1–2 m s−1 are more common (Stull 1988). Larger eddies with coherent updrafts are regarded to transport atmospheric properties throughout the ABL (i.e., nonlocal plumes), whereas smaller eddies are regarded to mix the atmospheric properties locally, and their formulations can be expressed as L NL w ' c' = Fwc + Fwc

(5.6)

and its schematic is given in Fig. 5.2. In Eq. (5.6), c refers to model prognostic variables: e.g., u, v, θ, and q, which refer to zonal and meridional wind components, potential temperature and moisture, respectively: The first term on the rhs describes the local (L) transport by small eddies, whereas the second term for the nonlocal (NL) transport by large eddies. In Fig. 5.2, the surface layer is characterized by a superadiabatic lapse rate, while the entrainment zone on top is stably stratified. zi is the mixed layer depth that is diagnosed as the vertical level of the minimum heat flux. Given the vertical profiles of potential temperatures and heat flux, one can tell that the upper part of the mixed layer is slightly stable, whereas it is unstable in its below. This indicates a countergradient mixing in the upper part of the mixed layer since

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Fig. 5.2 (left) Schematic of the nonlocal thermals and local eddies, as well as (right) the potential temperature and heat flux profiles of the convective boundary layer. From Zhou et al. (2018). ©American Geophysical Unison. Used with permission

upward heat flux appears in thermally stabilized layers. This locally countergradient fluxes are associated with nonlocal thermals that span the depth of the mixed layer (left of Fig. 5.2). The nonlocal term can be parameterized as a mass-flux term or a countergradient gamma term (γc ) which is an addition to the local transport. More details on NL transport term is provided in Sect. 2.2. The vertical turbulence mixing scheme can be classified as a local versus nonlocal diffusion approach and further by the following 4 categories.

5.2.1 Local Diffusion (Louis 1979) The local diffusion scheme, the so-called local-K approach (Louis 1979), ∂ ∂c ∂c ∂ = (−w ' c' ) = kc , ∂t ∂z ∂z ∂z

(5.7)

had been utilized for the entire atmosphere at NCEP GFS prior to the MRF PBL. In this scheme, the vertical diffusivity coefficients for momentum and mass (u, v, θ, q) are represented by | | | ∂U | | K m,t = l 2 f m,t (Rig)|| ∂z |

(5.8)

in terms of the length (l), the stability functions ( f m,t (Rig)), and the vertical | mixing | |, where U is the horizontal wind speed). wind shear (| ∂U ∂z

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The stability functions, f m,t , are represented in terms of the local gradient Richardson number ∂θv /∂ z (Rig = g/T |∂U/∂z| 2 , where g is the gravitational constant and θ v is the virtual potential temperature) at a given level. The mixing length scale, l, is given by 1 1 1 = + , l kz λ0

(5.9)

where k is the von Karman constant (=0.4), z is the height from the surface, and λ0 is the asymptotic length scale. λ0 can be a constant or a function of vertical grid spacing as in WRF.

5.2.2 Nonlocal Diffusion with Countergradient Term (Troen and Mahrt 1986) According to Deardorff (1972), Troen and Mahrt (1986), and Hong and Pan (1996), the turbulence diffusion equations for prognostic variables (c; u, v, θ, q) can be expressed by ∂c ∂ ∂c ∂ = (−w ' c' ) = − γc Kc ∂t ∂z ∂z ∂z

,

(5.10)

where K c is the eddy-diffusivity coefficient and γc is a correction to the local gradient which incorporates the contribution of the large-scale eddies to the total flux. This correction applies to θ and q in Troen and Mahrt (1986) and Hong and Pan (1996) within the mixed boundary layer. In the daytime mixed layer, the momentum diffusivity is formulated as K zm = kws z(1 −

z p ) , h

(5.11)

where p is the profile shape exponent taken to be 2. h is the height of the PBL. The mixed layer velocity scale is represented as ws = u ∗ φm−1 ,

(5.12)

where u ∗ is the surface frictional velocity scale, and φm is the wind profile function evaluated at the top of the surface layer. The countergradient terms for θ and q are given by γc = b

(w ' c' )0 , ws

(5.13)

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where (w ' c' )0 is the corresponding surface flux for θ and q, and b is a coefficient of proportionality. In order to satisfy the compatibility between the surface layer top and the bottom of the PBL, the identical profile functions to those in surface layer physics are used. The boundary-layer height is given by h = Ribcr

θva |U (h)|2 , g(θv (h) − θs )

(5.14)

where Ribcr is the critical Bulk Richardson number, U(h) is the horizontal wind speed at h, θva is the virtual potential temperature at the lowest model level. θv (h) is the virtual potential temperature at h, and θs is the appropriate temperature near the surface. The virtual potential temperature near the surface is defined as θs = θva + θT = b

(w ' θv' )0 , ws h

(5.15)

where θT is the scaled virtual potential temperature excess near the surface. The eddy diffusivity for temperature and moisture (K zt = K zm Pr −1 ) is computed from K zm in (5.11) by using the relationship of the Prandtl number (Pr), which is given by Pr =

φt 0.1h , + bk φm h

(5.16)

where Pr is a constant within whole mixed boundary layer. In addition to the inclusion of the nonlocal gamma term in Eq. (5.10), another main ingredient of the Troen and Mahrt concept is the height of ABL, h, which locates the top of entrainment layer by adding thermal excess and by using the critical Ri greater than 0 (Fig. 5.3). Thus, this approach represents the downward mixing in the entrainment layer implicitly by locating h above the minimum flux level.

5.2.3 Nonlocal Diffusion with Eddy Mass-Flux Term (Siebesma et al. 2007) This approach utilizes a plume model to represent the strong updrafts. Instead of K c γc in Eq. (5.10), a mass-flux term, M(cu − c), where cu is c of the strong updrafts, is introduced, and expressed as ∂c ∂c ∂ ∂ −kc = (−w ' c' ) = − + M(cu − c) ∂t ∂z ∂z ∂z

(5.17)

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Fig. 5.3 Schematic of the Troen and Mahrt nonlocal scheme. The left panel shows a parabolic shape of diffusion coefficients in Eq. (5.11) with p = 2, and the right panel describes the definition of ABL height, h, due to the contribution of the thermal excess in Eq. (5.15) and the Ribcr with 0.5. θ vh is virtual potential temperature at h, and θ va and θ s are as defined in Eq. (5.11)

The mass-flux, M = au wu , where au is a fractional area of the strong updrafts in the model grid box under consideration, is directly proportional to wu since au is constant by definition. The updraft velocity wu can be obtained by ∂w 2 1 (1 − 2μ) u = −bu εwu2 + B, 2 ∂z

(5.18)

where μ and bu are proportionality factors, ε the fractional entrainment rate, and B the buoyancy term. This approach is an advanced, as compared to the Troen and Mahrt approach, since it utilizes a convective plume model with entrainment and detrainment processes. By the comparison of the countergradient term in Troen and Mahrt (1986) and the mass-flux term in Siebesma et al. (2007), one can tell that the nonlocal transport term with gamma and mass flux contributes to the total flux in the same way as stabilizing the column (Fig. 5.4). It is also seen that the ED-CG model gives a stable potential temperature profile in the upper half of the boundary layer. In contrast, the ED-MF model reproduces the well-mixed ABL, which is consistent with the LES results. Siebesma et al. (2007) explained that this over-stabilization in the ED-CG approach is due to the countergradient term always being positive, which reduces the top-entrainment flux. Consequently, the BL height of the countergradient experiment is slow compared to the EDMF approach. This behavior of the ED-CG experiment is contradictory to the study of Hong and Pan (1996), with a deeper ABL depth with the countergradient nonlocal mixing over the profile with a local diffusion only. The stabilized profile in the upper part of ABL is an intrinsic nature of the Troen and Mahrt approach, but the behavior of the scheme in specific models depends upon how it is configured.

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Fig. 5.4 a Time evolution of the inversion height for the three different approaches with local diffusion (ED), eddy mass flux (ED-MF), eddy countergradient term (ED-CG) along with LES results as a reference. b The mean potential temperature profiles after 10 h of simulation. From (Siebesma et al.2007). ©American Meteorological Society. Used with permission

5.2.4 TKE (Turbulent Kinetic Energy) Diffusion (Mellor and Yamada 1982) The TKE scheme predicts the turbulent kinetic energy, u i u j , as a prognostic variable, which can be written as, ∂u i u j ∂u i u j ∂ 1 + uj ··· , =− ui u j uk + ∂t ∂x j ∂ xk ρ

(5.19)

where i, j, and k denote the vector index to x-, y-, and z-directions in Cartesian coordinates. The expressions for the eddy diffusivities K are complex and include terms related to the environmental wind shear and stability, but can be represented in conceptual form as K z = L(u i u j )1/2 ,

(5.20)

where L is again one of the empirical length scales. It is noted that the lower order TKE scheme, such as the MYJ scheme, is essentially a local mixing concept since the tendency is computed using the local scheme with the K z diffusivity that was calculated in the TKE equations. The MYNN scheme uses higher-order terms to represent the countergradient term.

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5.3 Evolution of a Nonlocal Diffusion Scheme (MRF-YSU-ShinHong-3DTKE Schemes) This section provides a hierarchy of a nonlocal diffusion scheme since MRF PBL scheme, as summarized in Table 5.1.

5.3.1 Medium-Range Forecast Model (MRF) Scheme Prior to 1996 at NCEP, there was no explicit planetary boundary layer (PBL) parameterization—diffusivity coefficients were parameterized as functions of the local Richardson number (Eq. (5.1)). Thus, the local-K approach (by Louis 1979) is used for both boundary layer and free atmosphere. This scheme has been widely used because it is computationally inexpensive and produces reasonable results under typical free convection regimes. However, the scheme cannot handle conditions when the atmosphere is well mixed because of the countergradient fluxes; i.e., there is active turbulent mixing in the ABL that occurs against the local gradient of meteorological variables, while Eq. (5.7) computes vertical mixing as 0 when the ABL is well mixed, and therefore, there is no local gradient. Thus, the method is not well-behaved for unstable conditions. For the above reasons, Hong and Pan (1996) adapted the Troen and Mahrt concept. The strategy is to add the nonlocal features to the Louis-type local scheme and considers the fundamental differences between the local and nonlocal schemes. By examining the impact of parameters in the scheme, the countergradient term is found to be responsible for the well-mixed PBL structure. Other parameters, such as shape parameters, are found to be of a similar impact as described in Troen and Mahrt. θT Table 5.1 Evolution of a nonlocal vertical diffusion scheme Scheme

Date

Description

MRF

1995

Operational at NCEP GFS model (Hong and Pan 1996)

1996

Implemented onto Mesoscale Model 5th generation (MM5)

2004

First implementation in WRF (Hong et al. 2006)

2008

Enhanced stable layer mixing (Hong 2010)

2009

Implicit momentum forcing for numerical stability

2010

Revised ws computation in stable boundary layer

2011

Revised thermal excess term (Shin et al. 2012)

2012

Revised Prandtl number for free convection

2015

Top-down mixing (Wilson and Fovell 2018)

Shin-Hong

2015

First implementation in WRF (Shin and Hong 2015)

3DTKE

2019

First implementation in WRF (Zhang et al. 2018)

YSU

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sometimes could become too large when the surface wind is very weak, resulting in unrealistically large h. This large h due to unrealistic θT does not harm the results because the diffusivity coefficients are usually very small in these situations, but it is not desirable for diagnostic purposes. For this reason, a maximum limit of θT as 3 K is applied. In implementing the Troen and Mahrt nonlocal concept onto the MRF model, it was found that the determination of the boundary-layer height, h, turns out to be a crucial factor. In the MRF PBL, h is obtained iteratively (see Fig. 5.3). First, h is estimated by Eq. (5.14) without considering the thermal excess, θT . This estimated h is utilized to compute the mixed layer velocity, ws Eq. (5.12). Using ws and θT in Eq. (5.15), h is enhanced. With the enhanced h and ws , K zm , is obtained by Eq. (5.11), and K zt by Eq. (5.16). The countergradient correction terms for θ and q in Eq. (5.10) are also obtained by Eq. (5.13). In order to avoid the dependency of vertical grid spacings, h is determined by comparing the Rib at a level with the Ribcr by increasing the level from the 2nd model level in its above. h is finalized at the level of Rib = Ribcr by applying a liner interpolation with respect to z. The main concept of Troen and Mahrt is the addition of nonlocal terms. One can tell that the magnitude of nonlocal mixing is a multiple product, γ K . By applying the derivative to Eq. (5.11) with respect to z, one can tell that the maximum value of this quantity locates at 1/3 h. In the local scheme, the mixed layer should stay unstable in order to transport heat upward, whereas the nonlocal term cools the layer below 1/3 h and heats the column in its above, which consequently results in the mixed layer to be neutral or weakly stable in the upper part of the mixed layer. Unlike a negligible impact of the PBL height that was determined by the critical Ri (Ribcr ) for dry conditions (Troen and Mahrt 1986), this parameter is found to play a crucial role in organizing the precipitating convection (Fig. 5.5). The impact of Ribcr on precipitation forecasts was found to be significant on heavy rain case for 15–17 May 1995. Less effective mixing with lower PBL height (due to lower Ribcr ) most likely leads to similar precipitation as a local scheme. However, a nonlocal PBL scheme experiment with larger Ribcr (Ribcr = 0.75) shows more effective mixing and gives a boundary-layer structure that is favorable for precipitating convection, leading to more organized precipitation. This behavior is most likely due to the fact that simulated precipitating convection is more sensitive to the boundary-layer structure when the PBL collapses than when it develops. This finding could be generalized if buoyancy-driven local convection typically occurs in the late afternoon or evening. A scientific milestone of the Hong and Pan study is their finding that efforts to improve the surface and PBL formulation are as important as efforts to improve the precipitation physics in atmospheric models and should be a prerequisite to realizing better precipitation forecasts. The MRF PBL scheme became operational in NCEP in October 1995 and was implemented in the Pennsylvania State University (PSU)/ National Center for Atmospheric Research (NCAR) Mesoscale Model 5 (MM5) in 1996.

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Fig. 5.5 Convective (shaded areas) and large-scale (dotted lines) rainfall (mm) ending at 1200 UTC 17 May 1995 for, a the local and nonlocal experiments with, b Ribcr = 0.25, c Ribcr = 0.50, and d Ribcr = 0.75. From Hong and Pan (1996). ©American Meteorological Society. Used with permission

5.3.2 YSU Scheme In the late 1990s, it was reported that the MRF PBL scheme tended to overmix in general. This behavior was detrimental to the accurate prediction of air pollutants in the Community Multiscale Air Quality Modeling System (CMAQ) when the meteorological input data was obtained from GFS (1999, personal communication with Dr. D. Byun). Also, excessive mixing accompanying too dryness and heating was reported by the evaluation of MM5 forecasts. These behaviors were also known to NCEP, but the scheme remained unchanged since a weakened mixing by reducing the Ribcr in the MRF PBL scheme tends to deteriorate the precipitation forecasts. It was found that the overall excessive mixing in the MRF PBL is mainly due to the uncertainty in the Troen and Mahrt concept. As seen below, the MRF PBL scheme represents the entrainment of the free tropospheric air into the mixed layer underlying it by locating the ABL height above the minimum flux level. In other words, the entrainment layer is located below h, and the vertical mixing using Eq. (5.10) is applied from the surface to h (see Fig. 5.3). The thermal excess term in Eq. (5.15) can be as large as 2 ~ 3 K in clear-sky conditions, and the corresponding excess due to Ribcr = 0.5 can be as large as 3 K when wind speed is 15 m s−1 . The resulting thermal excess greater than 5 K tends to locate the PBL height unphysically higher

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level (see Fig. 5.3). This behavior is often observed when winds are strong, for example, hurricane predictions. To overcome inherent deficiencies in the Troen and Mahrt concept, Noh et al. (2003) derived a new formula for entertainment from the LES model. The modifications in Noh et al. (2003) involve three parts. First, the heat flux from the entrainment at the inversion layer is incorporated into the heat and momentum profiles, and it is used to predict the growth of the PBL directly. Second, profiles of the velocity scale and the Prandtl number in the PBL are proposed, in contrast to the constant values used in the TM model. Finally, the nonlocal mixing of momentum was included. The new PBL model demonstrated the improved predictability of the PBL height and more realistic profiles of potential temperature and velocity as compared to the Troen and Mahrt. They also found that explicit representation of the entrainment rate is the most critical among the three modifications, which is expressed as

(5.21)

The new scheme was found to be promising in LES vertical resolution (about 20 m); however, it is not straightforward to implement it in an NWP model having a coarser vertical resolution (a few 10–100 m with height). For instance, vertical grid spacing ranges 100 ~ 300 m in the PBL in the daytime, a precise estimate of h and is a crucial component. Also, entrainment depth (typically a few 10 m) needs to be accurately represented by the grid-point values of models at coarse vertical resolution. This numerical discretization took more than a year. After early release of the YSU scheme in 2003, about three years were taken to adjust the package to be balanced with other part of physical processes (Fig. 5.6). The paper of Hong et al. (2006) on the final version of the YSU scheme was submitted in early 2006. In the early version of YSU PBL, the characteristic behavior over the MRF PBL was clearly demonstrated in the clear-sky turbulence region (Fig. 5.7). A typical sounding from Tennessee shows a significant difference in the PBL depth in this case. Overall cooling and moistening of YSU over MRF indicate the accurate representation of the entrainment processes in Noh et al. (2003). This difference is more exaggerated here than in most other situations, but it shows that the shallower moister PBL produced by the YSU scheme has more CAPE than the deeper and drier PBL produced by the MRF scheme. A major challenge that the early version of the YSU scheme faced lies in the fact that the scheme tends to produce spurious light precipitation and less-organized strong convection. By refining some aspects of the formulation, for example, entrainment fluxes, the scheme showed an overall improvement in precipitation forecasts. A large region of significantly higher CAPE in Fig. 5.7 is due to the reduced entrainment of dry air into the PBL during the morning hours, which is a direct result of the entrainment parameterization of the YSU PBL, as seen from the idealized

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Fig. 5.6 Schematic of YSU PBL development

Fig. 5.7 Simulated sounding near Nashville, TN, obtained from the experiments with the YSU (left), MRF (middle) PBL, and the observed (right) at 1800 UTC 10 Nov 2002. The number on the lower left corner indicates the level of inversion layer, which is 870 mb, 865 mb, and 720 mb, respectively

experiments in the previous section. The MRF PBL is particularly active in this case because of a strong 20 m s−1 southwesterly flow just above the boundary layer. This leads to a decrease in the PBL’s Rib used to compute the boundary layer height, enhancing the entrainment above the inversion layer. In the YSU PBL scheme, the shear only contributes in a secondary way to enhance entrainment, which is governed

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Fig. 5.8 Composite maximum reflectivity (dBZ) at 1800 UTC 10 November (upper) and 0000 UTC 11 November (lower) from the YSU (left) and MRF (middle) experiments and the corresponding observations (right)

mainly by the magnitude of the surface fluxes and thus does not maximize until later in the day. Despite the higher CAPE with the YSU PBL compared with the MRF PBL, the radar reflectivity showed the weakening of convection in the prefrontal region. Examining the frontal and prefrontal areas can better explain the reason. It is seen that the light precipitation in front of intense convection is better captured by the YSU PBL than the MRF PBL. In the area of intense convection, the model underestimated the precipitation amount irrespective of the choice of the PBL scheme. Still, the YSU PBL scheme better captured the time variation of the precipitation associated with late afternoon convection after 2100 UTC on 10 November 2002 (Fig. 5.8). The different impacts can be attributed to the differences in the synoptic environment associated with the formation of convection. Upward motion prevails within the entire troposphere, and cloud tops reach the tropopause, whereas the downward motion is dominant above the PBL ahead of a front. Ice microphysics is the critical mechanism, whereas warm clouds are prevalent in the prefrontal region. This indicates that, in contrast to the prefrontal area, the PBL processes play a secondary role in the intense convection region. Because of the weakened mixing in the YSU PBL, the PBL clouds are weakened before 2100 UTC on 10 November, but with a negligible difference. Because the synoptic environment associated with frontal convection is strong, the difference in the PBL mixing does not influence the overall evolution of daytime convection. The enhanced convection in the late afternoon in the case of the YSU PBL is due to the moister boundary layer below clouds, which reduces the evaporation of falling precipitation. The resulting overall impact is that

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the boundary layer from the YSU PBL scheme remains less diluted by entrainment, leaving more fuel for severe convection when the front triggers it (see Hong et al. (2006) for details). In addition to the dependency of PBL processes on the synoptic environment concerning precipitating mechanisms, an essential lesson in Hong et al. (2006) is that PBL processes play a critical role not only in modulating convection triggering but also in providing PBL structure directly affecting cloud microphysical processes when they fall near the surface. After the YSU scheme was officially announced to the WRF community in early 2000, some systematic biases were reported. One is an underestimate of the chemical species over cold-water bodies (Kim et al. 2008, WRF workshop). Another is underestimating PBL heights at nighttime (2006, F. Zhang, personal communication). He noticed that the nocturnal PBL heights in WRF using the YSU scheme are nearly constant between 0 and 20 m. Lidar data from the recent Mexico City field campaign reveal nocturnal PBL heights vary between 20 and 500 m, with strong winds corresponding to large PBL heights. Cold and wet biases were reported at nighttime in the real-time operation of WRF over East Asia at Seoul National University. These systematic biases were regarded as due to insufficient mixing in the stable boundary layer, to which no attention was paid. The stable boundary layer was formulated as a local mixing in the MRF and YSU PBL schemes. Based on an observational analysis of stable boundary conditions (Vickers and Mahrt 2004), Hong (2010) formulated a new stable boundary-layer scheme by elevating the mixing height when winds are strong. The main idea is the same as in the Troen and Mahrt in the sense that h is determined by Ribcr , which can be expressed as Ribcr = 0.16 10−7 Ro

−0.18

,

(5.22)

where Ro = U10 /( f z 0 ) as in Vickers and Mahrt 2004. This formula is only valid when z0 is a molecular roughness length over oceans. Over land, a theoretical value for turbulent activity (= 0.25) is employed. Aside from the improvement of cold and wet biases by enhanced mixing in stable conditions, Hong (2010) demonstrated that the interaction of stable boundary layer and precipitation processes improves the summer monsoon precipitation climatology (Fig. 5.9). Compared to the CTL simulation results, the SBL experiment displaces the monsoonal rainfall southward, increasing rainfall amounts in Central China, Korea, and Japan. The results with the new SBL scheme demonstrate that modulating the subcloud structure with enhanced vertical mixing improves the simulated monsoon climatology by displacing the monsoonal precipitation southward. The behavior of northward displacement of simulated precipitation over East Asia in summer has been a systematic error in other regional climate models (Fu et al. 2005; Park et al. 2008). Some studies focused on the convective parameterization scheme to resolve this issue, but these biases remained unchanged irrespective of the selected scheme. Hong (2010) demonstrated that together with the local effects

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of the enhanced SBL mixing that warms and dries the boundary layer, the dynamical feedback accompanying strengthened moisture convergence results in enhanced precipitation southward toward what was observed. Hong (2010) further suggests that care should be taken in interpreting the results with the vertical diffusion package with some modifications since the boundary-layer structure significantly influences the simulated climate through interaction with other physical processes in weather and climate models, which is important for further improvement of existing schemes and developing a new parameterization method. Related to this issue, Kim and Hong (2009) confirmed that the new SBL scheme designed in this study plays a critical role in representing proper interaction between the BL and gravity-wave drag processes in a version of the NCEP global model, which leads to a significant improvement of seasonal climatology in terms of zonal wind and temperature.

Fig. 5.9 Monthly accumulated precipitation (mm) for July 2006 from the, a TMPA observation, experiments with stable boundary-layer scheme in, b Hong et al. (2006) (CTL), c Hong (2010) (SBL), and d their differences

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In 2010, too strong surface wind biases from the use of this scheme were reported by the WRF community. This behavior was found to be associated with the too strong nighttime mixing by this PBL scheme. In collaboration with Peggy LeMone at NCAR, the mixed layer velocity scale—ws = u ∗ φm−1 , Eq. (5.12)—was revised with φm = 1 + 5z/L; with this revision, ϕ m is computed as a function of z, whereas the original formulation of ϕ m in Hong et al. (2006) is computed at a fixed height, i.e., the surface layer height at z = z1 (lowest model level). By implementing the height dependency of ϕ m into the scheme, the vertical mixing is reduced with height, alleviating the excessive nighttime mixing. Figure 5.10 demonstrates the temporal evolution of wind speed for the changes in WRF versions. WRF 3.2 is the same as in Hong (2010). WRF 3.4 with the revision in Pr, which affects the daytime mixing. WRF 3.4.1 reflects the above revision. The revised ws enhances the nighttime LLJ by increasing the vertical gradient of wind speed. It is due to smaller eddy diffusivities in the nighttime boundary layer and, consequently, lower and stronger LLJs. As a result, related overestimation problems for near-surface temperature and wind speeds appear to be resolved, and the nighttime minimum near-surface O3 concentrations are better captured (Hu et al. 2013). Various evaluation testbeds have been applied in developing/revising the YSU PBL scheme. First, a theoretical concept is derived based on evaluations of the WRF community and the scheme developer. In the case of YSU PBL, a new formula based on an updated LES is the core part (Noh et al. 2003). Numerical discretization considering the characteristics of NWP and climate models should be followed,

Fig. 5.10 Wind speed from observation (upper left) WRF version 3.2 (lower left), 3.4 (upper right), and 3.4.1 (lower right)

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assuring that the discretized scheme coupled with simple physics in atmospheric models reproduces the same behavior in LES studies. Second, evaluate the revisions in full physics models. Since evaluation results are combined products between PBL and all other physical processes, care should be taken in interpreting results. Process study for each component of the revised scheme needs to be followed. Considering the interaction with other physical processes as in nature, refinement and/or reformulation should be followed. Finally, the revised scheme should positively impact the short-medium-long-range forecasts with the forecast skill score. For instance, WRF and other global and regional models, such as GRIMs, were utilized to evaluate the performance of the new scheme (e.g., Byun and Hong 2004). Another example is the interaction between the orography-induced gravity-wave drag and boundary-layer processes in a global atmospheric model (e.g., Kim and Hong 2009). They showed that stable boundary is limited in the lower troposphere, but it enables the significant modulation of planetary-scale waves in the stratosphere through the upward propagation of gravity waves that originated near the surface.

5.3.3 Shin-Hong PBL Scheme In the summer of 2010, scientists from operational and research institutes in Korea, Japan, France, England, Finland, and the USA met to discuss recent developments in the parameterizations of physical processes for next-generation, high-resolution numerical weather prediction (NWP) models. The meeting summaries are provided by Hong and Dudhia (2012). The main topic of the workshop focused on future problems in physics parameterizations as NWP models go to finer horizontal model resolutions where there exist “gray zones” in which the explicit model dynamics is capable of partially resolving features that are entirely parameterized at coarser resolutions, e.g., deep and shallow moist convection, and turbulence in the PBL, particularly in the convective PBL (CBL). In the gray zone of an atmospheric process, model grid spacing (Δ) is comparable to the process’s characteristic scale (l) to be parameterized, i.e., Δ ~ l. For example, the gray zone of the CBL and shallow cumulus convection is approximately 0.1–1 km (Honnert et al. 2011; Dorrestijn et al. 2013; Shin et al. 2013). The gray zone scale decreases to 10–100 m (Honnert et al. 2020) in the neutral ABL (NBL) as l decreases with the absence of buoyancy to generate thermally driven turbulence. It may be a decade before the NBL gray-zone issues must be addressed. Hereafter, discussions focus on the CBL gray zone. One-dimensional (1D) PBL schemes are adequate at grid sizes above a few kilometers where no CBL turbulence eddies are resolved (Δ >> l). However, in the CBL “gray zone” (Δ ~ l), new types of PBL parameterizations are needed to adjust the amount of parameterized SGS turbulence in response to the partially resolved turbulence. There was also discussion about extending the use of three-dimensional (3-D) SGS models in large-eddy simulation (LES) to the PBL gray zone (as used for many years in cloud-resolving models at grid spacings of 0.1–1 km). At LES grid sizes—for example, grid sizes of 100 m or smaller for the CBL—it is considered

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that the model dynamics explicitly resolve nonlocal vertical transport by coherent and well-organized large eddies, i.e., ➀ on the rhs of Eq. (5.2). All SGS turbulence is assumed locally isotropic. All SGS mixing can be represented by 3D local mixing with LES SGS models. LES SGS turbulence models work well in the inertial subrange, but their assumptions break down in the gray zone. This challenge in numerical modeling of turbulence, where Δ and l are of the same order is well-documented in the pioneering study by Wyngaard (2004). To develop a new SGS parameterization for the CBL gray zone, an investigation of how the characteristics of the SGS turbulence to be parameterized change with model grid spacing must take precedence. Honnert et al. (2011) (hereafter, HMC11) proposed an original method to quantify the amount of the SGS vertical turbulent fluxes and TKE, using LES results of different types of CBLs (i.e., free convection, shear- and buoyancy-driven, and cloud-topped CBLs). They applied a simple spatial filtering to the LES results for the spatial filter size (that represents Δ) ranging between their LES grid spacing (ΔLES) and LES domain size (D). Shin and Hong (2013) (hereafter, SH13) further extended the LES study of HMC11 by implementing the effects of CBL stability into the grid-size dependency functions. They computed the grid-size dependencies of SGS nonlocal and local vertical transports in CBLs at gray-zone resolutions, using a 25-m-resolution WRFLES as the benchmark. They produced reference data for gray-zone grid spacing by spatially filtering the benchmark LES (Fig. 5.11). In their analysis, the amount of SGS vertical transport could be partitioned at each grid (Δ), along with the scale dependency of the total (nonlocal plus local) SGS transport. This is consistent with the key finding of Honnert et al. (2011), who revealed that the inclusion of the mass-flux term is more important than the formulation of eddy diffusivity in determining the grid-size dependency of the parameterized transport in the gray zone. SH13 further decomposed turbulent vertical mixing into two components—nonlocal mixing and local mixing—and examined the grid-size dependency functions of these two components separately. They found that the nonlocal mixing component is more sensitive to the CBL stability, and the amount of the nonlocal transport is larger than the local part. SH13 also demonstrated that the effects of CBL stability need to be considered in developing a new gray-zone CBL parameterization by implementing the stability effects into the nonlocal mixing term. Based on the conceptual derivation by SH13, Shin and Hong (2015) (hereafter, SH15) proposed a new PBL parameterization that replaces the CBL mixing algorithm of the YSU PBL scheme with an LES-informed scale-adaptive vertical mixing algorithm. First, nonlocal transport by large eddies and local transport by remaining smaller eddies are separately parameterized. Second, the SGS nonlocal transport is newly formulated by replacing the countergradient and the explicit entrainment terms of the YSU PBL scheme with an LES-fitted nonlocal mixing profile. The nonlocal mixing profile is multiplied by a grid-size dependency function, and the impact of CBL stability is implemented into the grid-size-dependent function. Finally, the SGS local transport is formulated by multiplying a grid-size dependency function by the K-profile diffusivity of the YSU PBL scheme. This new scheme is called as ShinHong PBL scheme. SH15 demonstrated that the new scheme increases the resolved

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Fig. 5.11 a Two-dimensional energy spectra at z/zi = 0.5, normalized by total TKE. b Ratio of resolved (red) and subgrid-scale (blue) TKE to total TKE as functions of dimensionless grid size (Δ/zi ): for cases BT (buoyancy-driven and organized thermals; thick solid), BF (buoyancy-driven and wind forced; thick dotted), SW (weak shear-driven; thick dotted-dashed), and SS (strong sheardriven; thin solid). From Shin and Hong (2013). ©American Meteorological Society. Used with permission

energy, which is toward the reference spectra in sub-kilometer resolutions. The new algorithm produces mean temperature profiles closer to the LES results than the YSU scheme. Between the two most significant modifications from the YSU PBL scheme (a change in the total nonlocal transport profile and inclusion of the scale dependency), the improvement in the mean profiles is mainly due to the revised total nonlocal transport profile fit to the LES data. The grid-size dependency functions help the resolved motions and resolved transport profiles improve via accurately computing the SGS transport profiles at different resolutions.

5.3.4 3D TKE-Based Scale-Aware Scheme (3D TKE, Zhang et al. 2018) To address the requirement for the gray-zone issue, a scale-adaptive parameterization scheme of 3D turbulent mixing based on the whole 3D TKE prognostics equation has been developed to represent turbulent mixing on subgrid scales in the gray zone (Zhang et al. 2018). In this scheme, the TKE-based parameterization scheme for turbulent mixing commonly used for LES is revised to be suitable for resolutions typically used in a mesoscale model. In particular, this scheme provides a pathway to consider all the components of the Reynolds-stress tensor in a coherent, more general framework, making it feasible to replace conventional 1D PBL schemes with the scale-adaptive 3D TKE-based scheme. In convective boundary layer (CBL), coherent structures due to the buoyancy dominate the vertical turbulent flux in a nonlocal way (Shin and Hong 2013; Hellsten and Zilitinkevich 2013). The flux productions can be expressed by conventional

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eddy-diffusivity models including the nonlocal effects as follows: u i' u 'j = − K iMj

∂u j ∂u i + ∂x j ∂ xi

u i' θ ' = −K iHj

+ δi3 u i' u 'j

NL

,

NL ∂θ + δi3 u i' θ ' , ∂x j

(5.23)

(5.24)

where superscripts M, H, and NL indicate momentum, heat, and nonlocal, respectively. That is, both subgrid-scale stress and heat flux can be decomposed into two components: the local flux due to the gradient of mean fields and the nonlocal flux due to the buoyant-production terms. Note that the nonlocal terms are only retained in the vertical because they are directly related to the buoyancy-driven transport. A pragmatic approach based on Shin and Hong 2013 for the transition of vertical turbulent mixing across the gray zone is adopted in this scheme. That is, the heat flux for particular grid size Δ can be divided into the local and nonlocal components: Δ

Δ w ' θ ' = −K Hv

∂θ Δ,NL Δ,L Δ,NL + w' θ ' = w' θ ' + w' θ ' , ∂z

(5.25)

where the superscript L and NL refer to local and nonlocal, respectively. The subscript v refers/to vertical. The nonlocal flux term is multiplied by the partition function PNL (Δ z i ) shown in Fig. 5.11 as follows: w' θ '

Δ,NL

= w' θ '

NL

/ PNL (Δ z i ),

(5.26)

NL

where w ' θ ' the nonlocal heat flux at the mesoscale. The vertical eddy diffusivity is formulated as K HΔv = L Δ e1/ 2 for Δ, the corresponding local heat flux is expressed as w' θ '

Δ,L

= −K HΔv

∂θ ∂z

Δ

Δ

= −L Δ e1/ 2

∂θ . ∂z

(5.27)

The length scale L Δ is obtained by blending the LES length scale L LES = ck1lLES and the/ mesoscale length scale L Meso = ck2 lMeso using the partition function PNL (Δ z i ), where ck1 and ck2 are dimensionless constants, / / L Δ = PNL (Δ z i )L Meso + 1 − PNL (Δ z i ) L LES .

(5.28)

Note that the dimensionless constants ck1 and ck2 are different at LES and mesoscale limits. The transition of horizontal diffusion across the gray zone is introduced as follows: / / K h = PN L (Δx z i )K D + 1 − PN L (Δx z i ) K T ,

(5.29)

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where K D is the horizontal diffusivity based on the deformation (i.e., Smagorinskytype formula), K T is the horizontal diffusivity based on the TKE. And cs and ck are dimensionless constants. In the development of the scheme, specific attention was given to the determinations of nonlocal heat/momentum flux and the master mixing length for vertical mixing. A series of dry convective boundary layer (CBL) idealized simulations were also carried out by Zhang et al. (2018) to compare the scheme’s performance with the conventional treatment of subgrid mixing using the ARW-WRF-LES dataset, highlighting the importance of including the nonlocal component for vertical turbulent mixing in this new scheme. The improvements of the new scheme over the conventional treatment of subgrid mixing across the gray zone were also in these idealized simulations. Results from real-case simulations also showed the feasibility of using this new scheme in a mesoscale model in place of the conventional treatment of turbulent mixing on subgrid scales. As compared to the Shin-Hong scheme in the previous subsection, the new scheme is advanced since it bridges the numerical dissipation and turbulence properties explicitly via 3D TKE. The conventional approach such as YSU scheme underestimates the resolved kinetic energy when grid spacing is smaller than a few kilometers and deficiency becomes substantial at sub-kilometers (Fig. 5.12). Shin-Hong scheme represents the gray zone by empirical function that is derived from the filtered LES data. Thus, this scheme implicitly represents the isotropic turbulence at LES scales. Meanwhile, the 3D-TKE scheme (Zhang et al. (2018)) represents the transition from isotropic to anisotropic eddies using a predicted 3D TKE in an explicit manner. Both schemes commonly utilize the same nonlocal transport terms and a similar scaleaware functionality. Further research is required to elucidate the turbulent properties at LES or higher resolutions. It should be noted that adequately representing horizontal turbulent mixing in the gray zone remains a research subject. Some horizontal turbulent mixing schemes are implemented in global and mesoscale models primarily for numerical purposes, e.g., to remove small-scale noise with wavelengths of 2–4 times the grid intervals (Xue 2000; Knievel et al. 2007; Langhans et al. 2012). Others are intended to mimic unresolved subgrid-scale mixing processes following Smagorinsky (1963). Recently, more and more studies addressed the importance of horizontal turbulent mixing in more realistic cases to evaluate and quantify horizontal turbulent mixing (Bryan and Rotunno 2009; Rotunno and Bryan 2012; Bryan 2012; Machado and Chaboureau 2015). Honnert (2016) calculated the horizontal mixing length from LES of neutral and convective cases in the gray zone resolutions.

5.4 Future Directions In conclusion, there has been a general trend from very simple dry local mixing approaches in earlier models to ABL schemes that represent nonlocal transport by thermals, cloud effects, top-down mixing, etc., thus including the full spectrum of

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Fig. 5.12 A schematic of the turbulent kinetic energy spectra in the convective boundary layer. Its density is depicted as a function of wave number K and of the corresponding length scale L = 2π /K. k t and k d represent the turbulence length scale and dissipation scale, respectively. Thick lines with arrows indicate the scale for a specific scheme to be eligible explicitly. An open arrow in Shin-Hong scheme represents a range of implicit coupling with numerical dissipation

ABL types within a single parameterization scheme and enabling improvements in representing the evolution of low cloud cover. The idea that ABL schemes should be unified with shallow cumulus schemes has been gaining popularity with the concept of top-down radiatively driven mixing that influences boundary layer growth and shallow cloud development. There are further ambitious efforts to extend this to deep convection (e.g., Park 2014), but deep convection contains net diabatic and internal dynamical effects that are not representable by simple transport or reversible thermodynamics, and it is debatable whether this can be unified with the more reversible and mixing-like processes of shallow convection and PBL schemes. As the resolution of NWP models approaches sub-kilometer scales, threedimensional mixing becomes more relevant, and some new gray-zone approaches transition to fully three-dimensional large-eddy schemes that do not require nonlocal vertical mixing as boundary-layer eddies resolve by the dynamics. Consistent treatment of horizontal and vertical turbulent mixing is still one of the challenging problems in atmospheric model development for gray-zone resolution simulations. There is no converging theory for quantifying the intensity of horizontal mixing. Few observations are available to constrain the quantitative aspects of the parameterization (e.g., the horizontal mixing length). However, as an example, Hanley et al. (2015) investigated the sensitivity of the storm morphology and statistical properties to horizontal mixing. They evaluated it against rainfall measurements of a radar network. Nevertheless, since horizontal turbulent mixing is dynamically coupled with vertical

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mixing across the gray zone, future development of vertical turbulent mixing parameterization on subgrid scales should consider the physical consistency between the vertical and horizontal mixing for atmospheric simulations at gray-zone resolutions. Even as the convective boundary layer becomes better represented at higher resolutions, challenges remain with the stable boundary and complex environments (terrain, urban, forests) that will still require subgrid parameterizations using knowledge of heterogeneity with grid cells. Acknowledgements The authors wish to acknowledge collaborations with Hua-Lu Pan, Yign Noh, Xu Zhang, Baode Chen, and Evelyn Grell. Comments on the manuscript from anonymous reviewers should be acknowledged.

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Chapter 6

Novel Physical Parameterizations in Vegetated Land Surface Processes for Carbon Allocations and Snow-Covered Surface Albedo Seon Ki Park, Hyeon-Ju Gim, and Sojung Park Abstract Vegetation growth/decay is important in land surface modeling to represent fluxes of surface energy and mass as well as surface albedo. This chapter introduces two new parameterization schemes, implemented in the Noah land surface model with multiple parameterization options (Noah-MP), to improve the vegetationrelated physical processes: the allocation of assimilated carbon to plant parts and the snow-covered surface albedo. The new carbon allocation scheme is supplemented with additional biophysical processes linked to variations in photosynthesis, which are assessed against tower measurements from forest sites in Korea. Leaf area index (LAI), gross primary production (GPP), ecosystem respiration (ER), and latent heat flux were better represented by the augmented Noah-MP—particularly when simulating the amplitudes and phase shift timing in the LAI seasonal cycle and the amount of GPP and ER in the growing season. In line with those from satellite observations, the temporal variations of LAI, GPP, and net primary production (NPP) in East Asia are also well simulated. Parameterization of the snow-covered surface albedo is highly uncertain because it is dependent on many factors, including the characteristic land cover and canopy density and structure. In East Asia, the Noah-MP has a large positive bias in the winter surface albedo under snow-covered conditions because it tends to produce too low values of LAI and stem area index (SAI) for nearly all vegetation types—primarily due to an incompetent representation of vegetation effect and hence photosynthetic activeness. Through the newly developed parameters—the S. K. Park (B) · S. Park Department of Climate and Energy Systems Engineering, Ewha Womans University, 52 Ewhayeoda -gil, Seodaemun-gu, Seoul 03760, Republic of Korea e-mail: [email protected] S. Park e-mail: [email protected] H.-J. Gim Korea Institute of Atmospheric Prediction Systems, Boramae-ro 5-gil, Dongjak-gu, Seoul 07071, Republic of Korea e-mail: [email protected] S. Park Now at Clean Air Center, Korea Institute of Science and Technology (KIST), 5 Hwarang-ro 14-gil, Seongbuk-gu, Seoul 02792, Republic of Korea © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_6

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leaf index (LI) and the stem index (SI), the new snow albedo scheme properly managed the effect of vegetation structure on the snow-covered surface albedo, leading to a notable improvement of the Noah-MP in simulating the winter surface albedo. Keywords Physical parameterization · Land surface model · Vegetation · Carbon allocation · Snow surface albedo

6.1 Introduction Land surface models (LSMs), represented by a bunch of parameterized physical processes, calculate the energy and water budgets in the atmosphere-land surface system (e.g., Cassardo et al. 2009; Park et al. 2017; Cassardo et al. 2018; Park et al. 2018). They also serve as the bottom condition of numerical weather/climate prediction models; thus, the land surface processes exert strong impacts on the weather/climate variations in numerical models through land-atmosphere interactions. Among the various components in LSMs, vegetation plays crucial roles in the exchange of energy and water (e.g., Duveiller et al. 2018; Cui et al. 2022; Oehri et al. 2022) and that of carbon via its allocation to vegetation parts (e.g., Lacointe 2000; Litton et al. 2007; Guillemot et al. 2015; Haverd et al. 2016; Xia et al. 2017) at the atmosphere-land surface boundary in association with vegetation physiology and structure and the photosynthesis process. The LSMs include biophysical processes that can improve the prediction of vegetation features—including seasonal changes in photosynthetic ability (Muraoka et al. 2010; Mengoli et al. 2022) and its variations among leaves (Bonan et al. 2011) and in the canopy-soil processes (Haverd et al. 2016), and the effect of nutrients limitation on vegetation growth (Thornton and Zimmermann 2007; Fisher et al. 2012)—which consequently affect the energy/water/carbon cycle. Several studies addressed that further improvement in vegetation dynamics should be made, in particular with regard to the regional-scale seasonality and long-term vegetation changes (e.g., Purves and Pacala 2008; Liang and Schwartz 2009; Richardson et al. 2012; Franklin et al. 2020). Carbon allocation is a crucial component of vegetation dynamics in terms of the following processes: atmospheric carbon assimilation via photosynthesis; partitioning of the photosynthetic assimilates to vegetation parts; and the carbon remaining time in vegetation before its release to the atmosphere (Ceballos-Núñez et al. 2020). Allocation of assimilated carbon among vegetation parts plays critical roles to determine the seasonal/long-term changes in vegetation amount and carbon exchanges over the land surface (De Kauwe et al. 2014; Ise et al. 2010; Fatichi et al. 2019). Ambiguity and difficulty in representing carbon allocation in LSMs have impeded its modeling effort (Friedlingstein et al. 1999; Franklin et al. 2012; Ceballos-Núñez et al. 2020). Among the widely used allocation schemes, the fixed allocation (FA) scheme has been adopted by many LSMs—see the list of models that employ the FA scheme in Gim et al. (2017): the FA scheme is well validated for a stationary forest (Franklin et al. 2012); however, it regards the assimilated carbon fraction as constant, thus hardly describing the seasonal variation of the carbon allocation ratio among vegeta-

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tion parts, which can bring about erroneous simulations of the vegetation properties (De Kauwe et al. 2014). In contrast, the allometric scaling (AS) scheme evaluates the carbon allocation ratio with respect to the vegetation part’s relative/absolute mass (Dickinson et al. 1998). Here, the allocation ratio is subject to the prescribed allometric ratio between vegetation parts; thus, in spring, high carbon amount can be allocated to leaves via the AS scheme, as in the nature (Steinaker and Wilson 2008). For a temperate forest, however, the prescribed leaf mass was set too high in the AS scheme; thus, allocation of the assimilated carbon to leaves goes on throughout the entire growing season, whereas the leaves cannot get to the prescribed mass. In reality, the carbon allocation to leaves reduces down tremendously in the later half of summer in a temperate climate (Steinaker and Wilson 2008). Snow surface albedo is another crucial factor in evaluating the energy budget in LSMs, but its parameterization is still obscure because vegetation effects are not properly taken into account. Vegetation impinges upon snow cover and albedo in the following ways: (1) snow depth can be modified by the canopy interception of snow; (2) vegetation has a higher roughness than bare soil, resulting in a lower total albedo over vegetation; and (3) heat flux can be altered by vegetation due to temperature difference from bare soil. Vegetation height also affects the surface albedo. With the same snow amount, total albedo over forests is much lower than that over short vegetation: The tree tops can be covered by snow though the snow accumulation is lower than the tree tops; however, the shading effect remains at nonzero solar zenith angle (SZ). A tree also emits its own radiation downward, altering the longwave radiation component of the energy budget. Satellite and in situ observations have evidenced that snow surface albedo is strongly related to snow cover over different vegetation types (Henderson-Sellers and Wilson 1983; Jin et al. 2002). The snow-covered albedos over forest type generally show lower maximum than those over non-forest types due to the shading effect on snow cover by the canopy density and structure (Gao et al. 2005). The patterns of land cover types typically determine the spatial distribution of albedo (Betts and Ball 1997; Jin et al. 2002); however, LSMs that use inadequate vegetation parameters or ignore the impact of vegetation on snow albedo do not detect any appreciable variations in snow-covered albedo over various land surfaces. Among the 10 BOREAS1 sites, Betts and Ball (1997) demonstrated that the followings in winter: two grass sites had the highest albedo (.∼0.7–0.8 with snow cover); the aspen site had a much lower albedo (.∼ 0.21); and the seven conifer sites had the lowest average albedo (.∼ 0.15 with snow on the ground under the canopy) (see Fig. 6.1a). Snow cover fraction is also important for estimating surface albedo because most numerical models parameterize albedo under snow conditions using separate treatments for snow-free versus snow-covered surfaces that are weighted by snow cover fraction (Gao et al. 2005; Qu and Hall 2007). Figure 6.1b depicts that albedo is more sensitive to snow cover fraction in grassland than in evergreen needleleaf forest due to 1

Boreal Ecosystem-Atmosphere Study; https://data.eol.ucar.edu/project/BOREAS EcosystemAtmosphere Study.

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Fig. 6.1 Variations in surface albedos: a Daily average albedo for 10 BOREAS mesonet sites for 1994, showing two grass sites, the aspen site, and an average of the seven conifer sites. From Betts and Ball (1997). .©1997 American Geophysical Union. Used with permission; b shortwave white-sky albedos extracted from global high-quality retrievals in the Moderate Resolution Imaging Spectroradiometer (MODIS) Climate Modeling Grid (CMG) albedo product during 2001, at a resolution of 0.05.◦ pixel, as a function of snow fractions. From Gao et al. (2005). .©2005 American Geophysical Union. Used with permission

canopy masking of snow (Gao et al. 2005). Some climate models, however, continue to use unrealistic vegetation parameters or distributions (Essery 2013); thus, a better understanding of snow and radiation interactions with forest canopies is essential. In this study, we present two recent efforts to incorporate vegetation effects in the physical parameterizations of the Noah LSM with multiple parameterization options (Noah-MP) (Niu et al. 2011): (1) to develop a carbon allocation scheme for temperate forests by modifying the original AS scheme for more realistic partitioning of the assimilated carbon to leaves and other plant parts (Gim et al. 2017); and (2) to improve the snow-covered surface albedo scheme by parameterizing nonphotosynthetic vegetation structures in winter (Park and Park 2016).

6.2 Model and Data Description We employ the Noah-MP, having 12 different scheme set options of multifarious physical processes, to create the two parameterization schemes. According to Niu et al. (2011), the Noah-MP, which simulates land surface processes with atmospheric forcing in offline mode, outperforms the Noah LSM version 3.0 in terms of surface fluxes, skin temperature, snow, and runoff.

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6.2.1 Carbon Allocation Experiments Vegetation dynamics in LSMs are represented by the leaf mass changes, which are controlled by photosynthesis, carbon allocation to leaves, and other factors. In NoahMP, photosynthesis is simulated with a two-big-leaf model that separately considers the sunlit leaves and the shaded leaves (de Pury and Farquhar 1997): photosynthesis in the former is limited by intercellular CO.2 concentration while that in the latter is limited by insolation. Photosynthesis here is linked to evapotranspiration via stomata conductance using a Ball-Berry-type stomatal resistance scheme (Ball et al. 1987; Collatz et al. 1992; Sellers et al. 1996). In Noah-MP, plant respiration consists of two functions: maintenance and growth. Maintenance respiration for leaves has an empirical connection with nitrogen concentration and temperature via the Q.10 temperature coefficient2 (Dickinson et al. 1998; Ryan 1991), whereas that for other plant parts is related to temperature and carbon mass. Growth respiration is viewed as a ratio of the carbon accumulation to new growth that is assigned to be an empirical constant (Poorter and Villar 1997). The leaf death is associated with soil temperature and moisture. Other leaf loss processes are obtained by turnover rate (Dickinson et al. 1998). Allocation of the assimilated carbon is given to four plant parts in Noah-MP— leaves, stems, woods, and fine roots; the allocation fractions are determined by the AS allocation scheme (Dickinson et al. 1998; Gulden et al. 2007). Stems are nonwoody parts of plants with no photosynthesis, whereas woods include coarse roots. The assimilated carbon fraction .(Fl ) is given by [ .

Fl = exp

] ) L ( 1 − eαL − Fs , 100

(6.1)

where . L is leaf area index (LAI), . Fs = L/10 is the carbon allocation ratio to stem, and .α = 0.75. For the evergreen broadleaf type, .α = 0.50 (Yang et al. 2011). The assimilated carbon fraction is constantly allocated to leaves and stems until . L hits 6 (Gulden et al. 2007). After being allocated to leaves and stems, the remaining carbon is distributed to woods and fine roots. The fraction of fine root allocation .(Fr ) is determined as follows: ] [ Cr 1 , exp −βrw . Fr = (6.2) β Cw where .Cr and .Cw are carbon biomass of fine roots and woods, respectively; .rw is the approximate ratio of wood carbon to fine root carbon; and .β = 0.9 is an adjustable constant (Dickinson et al. 1998). The ratio.Cr /Cw is compelled to approach.rw , which is set to 30 for forests and 3 for shrubs. We conducted three experiments: (1) Experiment ORI uses the original NoahMP; (2) Experiment VEA appends three biological schemes related to vegetation 2

Q.10 indicates the rate of a reaction change by a 10.◦ C temperature rise.

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seasonality, i.e., the vegetation phenology, the leaf aging effect, and the vertical profile of photosynthetic capacity, to the original Noah-MP; and (3) Experiment ALL implements the new carbon allocation scheme into the VEA version of NoahMP with a modified parameter related to allocation [see Appendix A in Gim et al. (2017)]. For these experiments, we have set the model spin-up time to more than 50 years for each site by cyclically repeating model runs; for example, for the site with a 5 year measurement, we repeated a 5 year model run for 11 times sequentially, and the model output of the last 5 years is used for the assessment. For the model assessments, we used observational data from two tower measurement sites (Gim et al. 2017): Gwangneung Deciduous Forest (GNDec) and Gwangneung Coniferous Forest (GNCon), which are located in the mid-western part of the Korean Peninsula and are apart by .∼1.2 km, thus sharing the same regional climate (Ryu et al. 2014).

6.2.2 Snow-Covered Surface Albedo Experiments For the study on snow-covered surface albedo, we employed the default options that were verified for global river basins (Yang et al. 2011) and further selected the following options: (1) the dynamic vegetation to assess the minimum leaf and stem area indices; (2) the Biosphere-Atmosphere Transfer Scheme (BATS) (Dickinson et al. 1993) for snow surface albedo; and (3) the Canadian Land Surface Scheme (CLASS) (Verseghy 1991; Verseghy et al. 1993) with new vegetation parameters for testing model performance of albedo. In terms of the albedo options, the CLASS simply computes the overall snow albedo depending on fresh snow albedo and snow age, whereas the BATS calculates snow albedo for direct and diffuse radiation in visible and near-infrared broadband accounting for several additional parameters such as grain size growth, impurity, and especially SZ (Niu et al. 2011). The Noah-MP tends to overestimate the snow-covered albedos over all vegetation types in winter, compared to the MODIS3 observation, with little difference between forest and short vegetation (Park and Park 2016). This is mainly because the original scheme uses LAI and stem area index (SAI), which are not able to quantify leaves and stems representing the forest masking in winter. In the Noah-MP, LAI and SAI are computed as LAI = max (Al · m l , 0.05) , SAI = max (As · m s , 0.01) ,

.

(6.3) (6.4)

where . Al and . As are the area of leaf and stem per unit mass (in m.2 g.−1 ), respectively; and .m l and .m s are the mass of leaf and stem per unit area (in g m.−2 ), respectively. The values 0.05 and 0.01 (in m.2 m.−2 ) represent the default values of minimum LAI (i.e., LAI.min ) and minimum SAI (i.e., SAI.min ), respectively, for all vegetation types. 3

https://modis.gsfc.nasa.gov/.

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In most of the winter period, both LAI and SAI stay at their minimum values. It is reported that the model uncertainty in quantifying LAI and SAI leads to discrepancies in winter albedo between LSMs and the MODIS observations; furthermore, in the albedo parameterization, LAI and SAI may not be treated the same way because green leaves and stems have different single-scattering albedo (Tian et al. 2004). The computational domain covers 4000 km by 4000 km in the East Asia region (105–145.◦ E, 20–60.◦ N), with a grid size of .∼30 km. We minimize the effect of snow cover change by averaging the MODIS white-sky albedo over dominating vegetation type in each area during wintertime (i.e., 273–129 Julian days) in total shortwave broadband for 10 years (2001–2010) with a 100% snow cover fraction. We conduct the model simulation for the period of 2001–2010, starting on 0000 UTC 1 June, by initializing soil temperature, soil moisture, and snow cover with a spin-up period of 6 months. In order to drive the Noah-MP, we employ the GLDAS4 data in the years 2001– 2010, using eight atmospheric forcing fields—surface pressure, downward shortwave and longwave radiation, precipitation, and the near-surface variables of air temperature, specific humidity, and zonal and meridional wind—from the combined data sets of NOAA5 /GDAS6 atmospheric analysis field, spatially and temporally disaggregated NOAA/CMAP7 fields, and observation-based downward shortwave and longwave radiation fields derived using the USAFWA8 /AGRMET9 method. The land use/cover data are from the yearly MODIS land cover and land use data within the IGBP10 global vegetation classification scheme, modified to fit into the USGS11 land cover classification (27 types). The MODIS albedo product (MCD43C3), evaluated every 16 d, is used for validation: we use total shortwave broadband for white-sky albedo and quality flags, which include the percentage of snow and the percentage contribution of fine-resolution data.

4

Global Land Data Assimilation System (Rodell et al. 2004); https://ldas.gsfc.nasa.gov/gldas Land Data Assimilation System. 5 National Oceanic and Atmospheric Administration. 6 Global Data Assimilation System; https://www.ncei.noaa.gov/products/weather-climate-models/ global-data-assimilation. 7 Climate Prediction Center Merged Analysis of Precipitation; https://psl.noaa.gov/data/gridded/ data.cmap.html. 8 U.S. Air Force Weather Agency. 9 AGRicultural METeorology Modeling System (Eylander et al. 2022). 10 International Geosphere-Biosphere Programme. 11 U.S. Geological Survey; https://www.usgs.gov/programs/gap-analysis-project/science/landcover-data-overview.

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6.3 Development of Parameterization Schemes The original AS scheme has a fixed and high upper limit of LAI and results in an overestimation of leaf allocation for the entire growing season in temperate forests. In order to have appropriate seasonal changes in the carbon allocation in temperate forests, we modified the original AS scheme (Gim et al. 2017). Non-photosynthetic vegetation structures—essential for simulating the wintertime surface albedo through shadowing—are not parameterized at all in the original Noah-MP; thus, it is deficient in simulating the snow-covered surface albedo. Surface albedo in Noah-MP depends on the photosynthetically active LAI and SAI; however, in winter, photosynthetically active leaves and stems are absent, causing LAI and SAI to be set to their minimum values, which brings about large positive bias errors of surface albedo. We improved the snow-covered surface albedo in Noah-MP using a new, simple, and effective parameterization of vegetation parameters (Park and Park 2016).

6.3.1 Carbon Allocation Parameterization In this new scheme, we contrived a way to determine an adequate upper limit of LAI for each grid—equivalent to the estimated annual net primary production (NPP) of leaves; thus, the annual NPP of leaves are mostly used for the leaf growth in early growing season until LAI reaches the upper limit, after which the leaf allocation is reduced and used only for maintenance respiration and compensation of leaf losses, reflecting the observational aspects of spring-dominant leaf growth (Steinaker and Wilson 2008). The annual leaf NPP is estimated using the climatology of annual NPP of entire plants and the reported ratio of annual NPP of leaves to that of entire plants (Wolf et al. 2011). In Noah-MP, a stem is defined as an above-ground nonwoody, nonleaf biomass incompetent to do photosynthesis (Niu et al. 2011). Leaf stalks would be considered as the stem part in Noah-MP if we regard them as nonleaf and nonwoody; however, this stem part is usually not measured in the field experiments, and hence, no observational study on the allometric growth of this stem part exists. This prevented us from determining the coefficient of this stem in the new allocation scheme. Therefore, in Noah-MP, we used only the carbon storage of three plant parts—leaves, fine roots, and wood—as in BATS (Dickinson et al. 1998). The new allocation scheme explicitly represents the upper limit of LAI (. L max ) as follows: [ )] 10L 1 ( L 1 − e max . . Fl = exp (6.5) 104 Here, . Fl decreases as LAI increases in spring, and it approximates zero as LAI approaches . L max . Compared to the original AS scheme (6.1), . Fl shows a steeper reduction with an increase of LAI, thus holding a large value until LAI reaches . L max . In (6.5), . L max is forced to be reduced after summer solstice as

6 Novel Physical Parameterizations in Vegetated Land Surface Processes ... .

L max = L 1 (1 − a (D − Dss )) , for D > Dss ,

165

(6.6)

where .a = 0.5/180, . D is the day of year of a given time step, and . Dss is the summer solstice day of year. Here, . L 1 is given by L 1 = L 2 − bL 32

(6.7)

L 2 = Nc γl Al Sl ,

(6.8)

.

with .

where .b = 4 × 10−3 , . Nc is the climatology of annual NPP for the entire plant, .γl the ratio of leaf NPP to total NPP, . Al specific leaf area (i.e., the leaf area per unit mass), and . Sl the lifespan of leaves (in year). . Sl is assumed to be 1 for deciduous forests, 5 for evergreen forests, and 1.3 for mixed forests; .γl is set to 0.2 following the value of mature forest (Wolf et al. 2011); . Nc is updated every 1 January by averaging . Nc and annual NPP of the entire plant from the previous year. We also developed a new scheme for the carbon allocation to fine roots, following the observation (Steinaker and Wilson 2008) that the main period of carbon allocation to leaves is preceded by that to fine roots; thus, the fine root allocation occurs in the early and middle summer. We modify (6.2) so that the fine roots grow as the springtime leaf growth terminates till they meet the amount of estimated annual NPP of fine roots as )] [ ( c2 M r , . Fr = (1 − Fl ) exp c1 1 − e Nc γr Sr (6.9) where .c1 = 0.01, .c2 = 5.7, . Mr is the carbon mass of fine roots, .γr = 0.25, following (Wolf et al. 2011), is the ratio of annual NPP of fine root to that of total plant, and . Sr = 0.2 is the lifespan of fine roots (in year). In (6.9), fine root mass is forced to reach the values equivalent to the estimated annual fine root growth multiplied by its lifespan. The remaining assimilated carbon, after allocation to leaves and fine roots, is transferred to woods (Gim et al. 2017). We further adopted three essential biological processes from the CLM version 4.5 (Oleson et al. 2013), which are related to the seasonal-scale vegetation dynamics: (1) the exact period of the growing season is determined by the function of heat accumulation and day length, for describing phenology and phenological carbon transport; (2) the leaf aging effect on photosynthesis is considered, noting that photosynthetic capacity varies with phenological states of leaves (e.g., leaf emergence, maturity, and senescence); and (3) the vertical profile of photosynthetic capacity is represented by an exponentially reducing function against an increase of LAI accumulation from top of tree. More details of these enhancements to biological processes are referred to Appendix A in Gim et al. (2017).

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Table 6.1 Monthly mean SAI in Noah-MP in 2001–2010 for deciduous broadleaf forest (DecB), deciduous needleleaf forest (DecN), evergreen needleleaf forest (EverN), and mixed forest (Mix). The highest SAI values for different forest types are shown in bold Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

DecB

0.009

0.009

0.009

0.009

0.015

0.080

0.140

0.151

0.120

0.064

0.021

0.011

DecN

0.012

0.009

0.009

0.009

0.016

0.047

0.181

0.268

0.252

0.146

0.056

0.022

EverN

0.009

0.009

0.009

0.009

0.009

0.017

0.068

0.091

0.067

0.025

0.010

0.010

Mix

0.010

0.010

0.010

0.010

0.016

0.051

0.130

0.158

0.128

0.069

0.025

0.011

6.3.2 Snow-Covered Surface Albedo Parameterization The LAI values calculated from Noah-MP exhibit a seasonal cycle and are much lower than the reference values (Asner et al. 2003) for all vegetation types in winter, as depicted in Park and Park (2016) (see Fig. 6.3 therein). Table 6.1 shows that the modelcomputed SAI values for the four forest types—deciduous broadleaf (DecB), deciduous needleleaf (DecN), evergreen needleleaf (EverN), and mixed forest (Mix)—have large seasonal variations: for all forest types, the highest values occur in summer, especially in August, whereas the lowest values occur in winter. This evidences that the seasonal variations are related to photosynthesis and its corresponding leaf/stem mass variations. In August, DecN showed the highest SAI while EverN showed the lowest SAI values. For calculating the winter surface albedo, however, vegetation structure plays more important role. In Noah-MP, the values of canopy gap probability—the chance that a photon penetrates through the vegetation without being intercepted by any crowns (Niu and Yang 2004)—for direct and diffuse beam are determined by the options for twostream radiation transfer. The modified two-stream approximation (MTS), i.e., the first option of the two-stream radiation transfer scheme, explicitly includes the threedimensional structure of the vegetation canopy by calculating the total canopy gap probability for direct beam, .Prdtc , which is equal to the sum of the between-crown gap probability, .Prdbc , and the within-crown gap probability, .Prdwc : here, .Prdbc is a function of crown geometric properties and SZ, whereas .Prdwc is parameterized on the basis of a modified version of Beer’s law. They are formulated as follows: [

] −ρc π R 2 = exp , cos θ ' [ ] ) ( −0.5Fa Hd d d Prwc = 1 − Prbc exp , cos θ ) ( Prdtc = min 1 − f gv , Prdbc + Prdwc , d .Prbc

(6.10) (6.11) (6.12)

where .ρc is the crown density (stems; in m.−2 ), . R is the horizontal crown radius, .θ is the SZ, .θ ' = tan−1 [(r/R) tan θ ], and .r is the vertical crown radius. . Fa is the foliage area volume density (in m.−1 ) and is equal to LSAI./( 43 π R 2 rρt ), where LSAI is the

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effective leaf and stem area index, through which the effect of clumping of needles into shoots is included (Niu and Yang 2004). . Hd is the crown depth, and . f gv is the green vegetation fraction, ranging from 0 to 1. Therefore, if we apply new leaf index (LI) and stem index (SI), the canopy gap probability changes because LSAI changes. Total albedo by vegetation and ground, .αtot , is evaluated as { α

. tot

=

( ) αdc 1 − Prdtc + αds Prdtc (for direct beam) ( ) , αic 1 − Pribc + αis Pribc (for diffuse beam)

(6.13)

where .αdc and .αds are the direct albedo of the canopy and the underlying surface, respectively, and .αic and .αis are the diffuse albedo of the canopy and the underlying i is the between-crown gap probability for diffuse radiation, surface, respectively. . Pbc which is set to 0.05. Details of the canopy albedo parameterization are referred to Sellers (1985). Based on (6.13) and the fact that snow albedo over a vegetated surface is lower than that over bare soil, total albedo over the four forest types typically decreases with increasing SI (Park and Park 2016). Albedo has different patterns for different SZ at a constant SI: as SZ gets higher, albedo reduces at low SI while increasing at high SI. At low SI, albedo is largest with smallest shadow area of the underlying snow-covered surface, or at local noon [see Fig. 5 in Park and Park (2016)]. In Noah-MP, the model-calculated LAI.min is greatly underestimated for all forest types during winter, compared to the reference value of LAI.min (Asner et al. 2003) because LAI and SAI are both related to photosynthetic activity in the model; SAI.min is even lower than LAI.min . These uncertainties arise from the model deficiency to account for non-photosynthetic process when defining LAI. The observed LAI includes all leaves, regardless of their photosynthetic capacity, and thus is greater than the model’s. Indeed, the structure and density of all leaves and stems exert impacts on albedo. Thus, it is crucial to appropriately incorporate the vegetation effect into parameterization of the snow-covered surface albedo. In the new scheme, we introduce two new parameters in Noah-MP—LI and SI: the former represents the sum of LAIs from photosynthetic leaves and nonphotosynthetic leaves while the latter represents the sum of SAIs from photosynthetic stems and non-photosynthetic stems. In order to draw a realistic SI effect, we assigned the reference LAI.min values to LI for the four forest types (DecB, DecN, EverN, and Mix), following Asner et al. (2003). For each of the four forest types, the default values for LAI.min and SAI.min in Noah-MP are set to 0.05 and 0.01, respectively. The LI values (i.e., the reference values of LAI.min ) are set to 0.6 for DecB and 0.5 for the other forest types. Since it is assumed that trees are mature and the growing season is over (i.e., winter), SI has no seasonal cycle. The bias errors of winter surface albedo decrease as SI increases for the four forest types [see Fig. 6 in Park and Park (2016)]; the optimized SI values are 1.30 for DecB, 1.50 for DecN, 2.30 for EverN, and 2.00 for Mix, respectively.

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6.4 Validation Results 6.4.1 Carbon Allocation We validated the model results using two tower measurements in South Korea— GNDec and GNCon. Each flux tower site collects data on surface air temperature, wind, radiation, humidity, precipitation, and fluxes. The latent heat flux (LH) and CO.2 flux data are obtained from the eddy covariance flux measurements, which are properly corrected using the KoFlux data processing protocol (Hong et al. 2009). Gim et al. (2017) provides more details on the nighttime CO.2 flux correction and its partitioning into gross primary production (GPP) and ecosystem respiration (ER). The LAI is measured from the flux towers equipped with the plant canopy analyzers at 10 points within the GNDec footprint and 7 points within the GNCon footprint. Model results of LAI, GPP, ER, and LH are compared to the site-measured values to validate the parameterization scheme.

Validation Against Tower Measurements We represent the validation results at GNDec (i.e., a DecB type) and GNCon (i.e., an EverN type). Figure 6.2 compares the model results of three experiments (ORI, VEA, and ALL) for LAI, GPP, ER, and LH to the observed values at the two sites—GNDec (left panels) and GNCon (right panels). The GNDec site (a DecB type) showed distinct seasonal changes in all the variables, though ER depicted a relatively weaker seasonality with smaller magnitude in summer (Fig. 6.2e). In winter, the observed LAIs are zero at GNDec (Fig. 6.2a); however, the observed GPP has some values (Fig. 6.2c)—due to the instrument-related measurement error (Burba et al. 2008; Saigusa et al. 2013); thus, the winter GPP values are excluded from model validation. In autumn, both LH and GPP fall off a few weeks earlier than LAI, implying that the photosynthetic activity primarily controls the seasonal changes in LH (Fig. 6.2g). The ORI experiment at GNDec also demonstrates distinct seasonal variations in all the variables; however, the LAIs of the growing season are notably lower than the observed ones, and their senescence in the decaying season depicts unreasonably slower progress than observations. The lack of explicit processes of phenological leaf falling in ORI contributes to the slow fall-off of leaves in winter. Because of the longer-lasting large LAI in autumn, the model-evaluated GPP and ER in the growing season last longer than observations. The obvious overestimation of LH in early spring is attributed to the deficiency in the model’s ground evaporation processes. The VEA experiment, supplemented with three biophysical processes related to vegetation seasonality, partially solves problems in ORI. The LAI in VEA during the transition from the growing season to the dormancy period matches well the observation, while that during the growing season is still far lower than the observed one. The VEA largely reduces the autumnal GPP overestimations in ORI, resulting

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Fig. 6.2 Observations (OBS) and three model simulations (ORI, VEA, and ALL) during 2006– 2010 at GNDec (left panels) and GNCon (right panels): a and b LAI; c and d GPP; e and f ER; and g and h LH. For the LAI observations, the average and standard deviation are represented by circles and vertical bars, respectively. Modified from Gim et al. (2017). .©2017 Authors. Distributed under the CC BY-NC-ND 4.0 License

in reduction of ER during the growing season with lower maintenance and growth respiration; meanwhile, VEA slightly decreases LH in the growing season. In ALL, where the new allocation scheme is added to VEA, the LAI amplitudes are much larger than those from VEA and match well the observations (Fig. 6.2a). The phenology scheme in ALL detects the green-up time and transfers the stored carbons to leaves, describing well the abrupt leaf increases at the beginning of the growing season and representing better LAI curve in early spring. The GPP values of ALL are slightly larger than those of VEA during the growing season (Fig. 6.2c); the winter GPP values, having noticeable measurement error, are theoretically reasonable (nearly zero) in VEA and ALL. The ER values in ALL are lower (higher) in the growing (dormant) season than those in VEA (Fig. 6.2e); the overestimation of LH is also lessened in ALL (Fig. 6.2g). For the GNCon site (an EverN type), seasonal cycles are also notable in the observations of the four variables (Fig. 6.2; right panels). The large observed range of LAI may have been affected by the deciduous trees outside the coniferous forest due to high installation of instrument (Fig. 6.2b). The observed GPP values in winter (Fig. 6.2d) are assumed to be unrealistic due to the instrumental error in low temperature.

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At GNCon, the ORI experiment significantly underestimates the annual average values of both LAI and GPP (Figs. 6.2b and d, respectively). During winter, LAI becomes almost null because of the cold stress on the leaves. The ER values are generally underestimated throughout the seasons (Fig. 6.2f); the LH values are lower than the observations, especially during the late growing season (Fig. 6.2h). The VEA experiment further underestimates LAI, GPP, and ER because the model has less photosynthetic capacity in spring and autumn. The LH values from VEA and ALL are quite close to each other. The ALL experiment simulates LAI similar to the observations. Although the GPP and ER are underestimated in ALL, they show better agreement in the amplitudes and the growing season lengths, compared to ORI and VEA. The LH values are similar to those from ORI and VEA. Overall, the ALL experiment outperforms the ORI and VEA experiments in both types of forests—DecB (GNDec) and EverN (GNCon); VEA is superior to ORI but inferior to ALL. It is notable that LAIs from ALL are much larger than those from VEA at both GNDec (Fig. 6.2a) and GNCon (Fig. 6.2b). In terms of GPPs, however, ALL simulates similar to VEA at GNDec (Fig. 6.2c), whereas the former is much larger than the latter at GNCon (Fig. 6.2d). This implies that GPP is not sensitive to LAI in ALL, especially over a DecB forest, primarily due to the excessive difference of photosynthetic activity between the upper and bottom part of canopy. In ALL and VEA, the sunlit (shaded) leaf fraction decreases (increases) exponentially as the accumulated LAI becomes larger at the canopy top—allowing only limited diffuse insolation to the shaded leaves at the bottom part of canopy. In an EverN forest, this effect is not apparent because the enlargement of LAI at the canopy top is not substantial.

Validation Against Satellite Retrievals We also have assessed the new allocation scheme in a regional domain of East Asia by comparing LAI, GPP, and NPP from the three experiments (i.e., ORI, VEA, and ALL) with those from the satellite retrievals. For this purpose, we coupled the original and the augmented versions of Noah-MP to the Weather Research and Forecasting (WRF) model and had run the coupled system over the East Asia domain with boundary conditions from the NCEP12 -DOE13 AMIP14 Reanalysis (R-2) dataset (Kanamitsu et al. 2002) for the period of 2000–2004. For the model’s land cover type, we adopted the MODIS land cover-type data. We also obtained the satellite retrievals of annual LAI, GPP, and NPP from the MODIS land products website (https://lpdaac.usgs.gov/) and compared them with the model results. Figure 6.3 depicts seasonal variations in LAI, GPP, and NPP as represented by the time series of domain-averaged values at 32–44.◦ N latitudes in East Asia. The seasonal oscillations in the MODIS retrievals (OBS) are distinct for the three variables. During 12

National Centers for Environmental Prediction; https://www.weather.gov/ncep/ Department. of Energy; https://www.energy.gov/. 14 Atmospheric Model Intercomparison Project; https://pcmdi.llnl.gov/mips/amip/amip.html-II. 13

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Fig. 6.3 Domain-averaged values of a LAI, b GPP, and c NPP from the MODIS retrievals (OBS), and the experiments of ORI, VEA, and ALL for the East Asia region between 32.◦ N and 44.◦ N. From Gim et al. (2017). .©2017 Authors. Distributed under the CC BY-NC-ND 4.0 License.

the growing season, ORI simulates noticeably lower values of LAI and NPP than OBS while producing GPP fairly well. In VEA, the three variables are generally underestimated: the near-null LAI of VEA in winter is caused by the phenological leaf falling process, through which a significant fraction of leaf mass is transferred to the litter carbon pool when the scheme detects the onset of dormancy season. In ALL, the LAI magnitudes match the MODIS retrievals well; however, the annual averaged LAI is overestimated due to the longer growing season. This implies that a revision of the scheme, which incorporates the detection of dormancy season’s onset, can enhance the model performance in simulating the LAI’s seasonal change (Gim et al. 2017). The GPP and NPP values from ALL generally agree well with the MODIS retrievals, but they are greatly inflated in mid-summer when East Asia is influenced by the summer monsoon.

6.4.2 Snow-Covered Surface Albedo The model performance with the new scheme, employing LI and SI, has been evaluated by calculating the root mean square errors (RMSEs) of albedo against the MODIS observation (see Fig. 6.4): the albedo RMSEs, simulated with the observed LAI and the prescribed monthly SAI, are also shown (square symbols). For the

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Fig. 6.4 Comparison of RMSE values of albedo with the original minimum value of LAI and SAI (dashed lines) versus new LI and SI (solid lines) versus observed LAI and prescribed SAI (square symbols) for three radiation options for a BATS and b CLASS radiation schemes. OPT_RAD1 is MTS, OPT_RAD2 is two-stream radiation option with no canopy gap, and OPT_RAD3 is the scheme that calculates the gap from vegetation fraction. From Park and Park (2016)..©2016 Authors. Distributed under the CC BY 3.0 License.

observed LAI, we used the AVHRR15 GIMSS16 LAI3g data (available from https:// daac.ornl.gov/VEGETATION/guides/Mean_Seasonal_LAI.html) and took an average for winter during 2001–2010 for each vegetation type within the domain of 40–60.◦ N and 105–145.◦ E. As SAI is not observed, we took the prescribed monthly SAI value in Noah-MP for each vegetation type. Even with the observed vegetation parameters, the RMSEs in simulated albedo are still remarkable. With the new scheme, Noah-MP’s performance in calculating surface albedo has remarkably improved—the RMSE has been dropped by .∼69%. Despite using the MTS to optimize SI, Fig. 6.4 demonstrates how the parameterization impacts albedo 15

Advanced Very High Resolution Radiometer; https://www.earthdata.nasa.gov/sensors/avhrr. Global Inventory Modeling and Mapping Studies. https://csdms.colorado.edu/wiki/Data: GIMMS.

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when using alternative options. The RMSEs for all two-stream radiation transfer and snow surface albedo schemes—the BATS (Fig. 6.4a) and the CLASS (Fig. 6.4b)—are reduced by .∼70% on average. As shown in Fig. 6.4, the Noah-MP has three radiation options for calculating energy fluxes: (1) the MTS, which is used for the parameterization in this study and computes canopy gaps from SZ and three-dimensional structure (OPT_RAD1); (2) the two-stream radiation option with no canopy gap, in which leaves are evenly distributed within the grid cell with a full vegetation cover (OPT_RAD2); and (3) the tile approach—calculating energy fluxes separately in vegetated fraction and bare fraction and then summing them up with weights by fraction (OPT_RAD3). When compared to the other options, the optimal LI and SI from the MTS had the similar improvement effect on albedo. The RMSEs with the original LAI.min and SAI.min values increase up until mid-winter (e.g., the 17th Julian day) and then decrease. Snow cover and forest masking exert strong impact on albedo during the winter (Essery et al. 2009; Bonan 2008; Brovkin et al. 2013). The Noah-MP significantly overestimates albedo by underestimating vegetation parameters (i.e., LAI and SAI) and overestimating snow cover fraction. By employing the new parameterization scheme that takes into account all of the forest structure effect with realistic values, this error is remarkably decreased in the model results.

6.5 Conclusions It is critical to adequately reflect vegetation aspects in land surface models for a more accurate representation of energy, water, and carbon exchanges over the vegetated land surface. This chapter introduces new parameterization schemes in the vegetation-related land surface processes, with a focus on carbon allocations and snow-covered surface albedo. These schemes are implemented in the Noah land surface model with multiple parameterization options (Noah-MP) model and validated against the flux tower measurements and/or the satellite (MODIS) observations. The first scheme involves allocating assimilated carbon to the plant parts, including leaves, fine roots, and wood (Gim et al. 2017). This new scheme is created by modifying the allometric scaling scheme (Dickinson et al. 1998) and taking into account an empirical ratio of the plant parts’ annual net primary productions (NPPs). In order to calculate the fraction of assimilated carbon into leaves, we adjusted the upper limit of the leaf area index (LAI) value, which is equivalent to the estimated NPP of leaves; thus, LAI is compelled to reach the upper limit in the spring, after which the leaf carbon allocation decreases to be used for maintenance respiration and compensation of leaf losses. We further adjusted the fraction of assimilated carbon into fine roots so that they grow after the springtime leaf growth is finished and continues to grow until they reach the estimated annual NPP of fine roots. The new allocation scheme is implemented into the Noah-MP, which is supplemented by other biophysical processes, including the phenology, the leaf aging effect, and the vertical profile of photosynthetic capacity within canopy; its performance

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is evaluated by comparing simulation results of LAIs, gross primary productions (GPPs), NPPs, ecosystem respirations (ERs), and latent heat fluxes (LHs) to their corresponding observations. In the LAI simulations, the seasonal cycle amplitudes for both the deciduous broadleaf forests (DecB) and evergreen needleleaf forests (EverN) are prominently improved. Other augmented biophysical processes also improved LAI, GPP, and ER in terms of the timing and the pattern of phase changes between the growing and dormant seasons, particularly in DecB. The model augmentation just slightly improves LH. In a regional comparison over East Asia, the LAI seasonal cycle amplitudes from the new allocation scheme matched well those from the MODIS retrievals; however, the growing seasons of simulated LAI lasted longer in autumn, leading to an overestimation of annual LAI, primarily due to the late termination of growing season in the augmented model. The GPP and NPP values agreed well with the MODIS retrievals. The second scheme addresses the vegetation effect on the snow-covered surface albedo. Snow cover causes a significant variation in surface albedo in winter; however, in the forest regions, the snow-covered albedo remains low for two reasons: (1) when snow covers a forest canopy, the incident radiation is diffused rather than reflected due to irregular surfaces; (2) vegetation shields the snow-covered surfaces. Furthermore, the forest cover effect becomes dominant in regions with average winter (December-January-February) temperatures above.−1◦ C, which speeds up snowmelt due to an increase in longwave radiation; thus, a forest cover reduces snow duration by 1–2 weeks compared to adjacent open areas (Lundquist et al. 2013). A strong positive feedback is produced as a result of this effect, which further lowers surface albedo and increases the amount radiation absorbed by the ground (Qu and Hall 2007). Thus, accurate albedo calculation is very crucial in the land surface processes. Through satellite observations, we addressed the noticeable relationship between vegetation types and snow-covered surface albedo. Nonetheless, in Noah-MP and many other land surface models, surface albedo is calculated without properly accounting for vegetation effects. We introduced new parameters—leaf index (LI) and stem index (SI)—to apply the vegetation effect on snow-covered albedo. We concentrated on the SI effect because stems are more important than leaves in the winter albedo. Calculation of albedo in Noah-MP has notably improved with the new parameterization for all radiation options and snow surface albedo schemes; however, improving albedo accuracy is limited by changing only vegetation indices. It is essential to further evaluate the other parameters, including snow cover fraction and fresh snow albedo, which have not been assessed with observations. Acknowledgements This work is supported by an NRF grant funded by the Korean government (MSIT) (grant no. NRF-2021R1A2C1095535) and by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (grant no. 2018R1A6A1A08025520).

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Chapter 7

Reducing Model Uncertainty in Physical Parameterizations: Combinational Optimizations Using Genetic Algorithm Ji Won Yoon, Sujeong Lim, and Seon Ki Park

Abstract The numerical weather prediction skills are strongly affected by the uncertainties in parameterizations of subgrid-scale physical processes and by the undetermined parameters. Recently, various artificial intelligence algorithms have been used to reduce these uncertainties. In particular, the genetic algorithm (GA), including micro-GA, has been extensively applied in hydrology and meteorology. This chapter introduces two recent studies on scheme- and parameter-based optimization using micro-GA. First, scheme-based optimization is conducted to find the optimal combination of four physical parameterization schemes associated with the sea breeze circulation, which includes the planetary boundary layer, land surface, shortwave radiation, and longwave radiation, in the Weather Research and Forecasting (WRF) model. Second, parameter-based optimization is performed to seek the optimal values of six parameters in the snow-related processes—snow cover fraction, snow albedo, and snow depth—of the Noah land surface model (LSM) for South Korea. In both applications, the optimal scheme combination and the optimally-estimated parameters, obtained through the coupled system of micro-GA and the WRF model or the Noah LSM improved the forecasting skill by reducing model uncertainties related to physical parameterizations. Keywords Genetic algorithm · Optimal scheme combination · Parameter estimation · Weather Research and Forecasting (WRF) model · Land surface model Ji Won Yoon and Sujeong Lim equally contributed to this work as co-first authors. J. W. Yoon Severe Storm Research Center, Ewha Womans University, Seoul 03760, Republic of Korea e-mail: [email protected] S. Lim Center for Climate/Environment Change Prediction Research, Ewha Womans University, Seoul 03760, Republic of Korea e-mail: [email protected] S. K. Park (B) Department of Climate and Energy System Engineering, Ewha Womans University, Seoul 03760, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_7

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7.1 Introduction The numerical weather prediction (NWP) models have uncertainties due to parameterizations of subgrid-scale physical processes and undetermined parameters, which reduces the accuracy of model forecasts. Therefore, it is essential to optimize the scheme combination or parameters of the physical parameterization process based on observations. In general, numerical sensitivity analysis is widely used for the optimization of numerical models to offer model responses to various parameterization schemes or parameters (Quan et al. 2016; Zhang et al. 2017; Gbode et al. 2019; Rodrigo et al. 2018; Shirai et al. 2022; Zaidi et al. 2022); however, it cannot ensure the best solutions for precise model forecasts. Furthermore, many of these sensitivity studies were constrained to conducting experiments with only a few physical parameterization schemes or parameters because of computing resource constraints. Recently, to address these challenges, the genetic algorithm (GA), an optimization method based on artificial intelligence, has been extensively employed in optimization problems in hydrology and meteorology: an efficient GA method, called the micro-GA (Krishnakumar 1990), has been preferably used. Lee et al. (2006) applied GA to an NWP model for the first time in meteorology. They successfully estimated the optimal values of both physical and computational parameters in a cumulus parameterization scheme in the fifth-generation Pennsylvania State University (PSU)/National Center for Atmospheric Research (NCAR) Mesoscale Model (MM5) (Grell et al. 1994) to improve the prediction performance of quantitative precipitation forecast (QPF) in a heavy rainfall case over South Korea (SK). Yu et al. (2013) optimized two physical parameters related to convection in a cumulus parameterization scheme of the Weather Research and Forecasting (WRF) model using the micro-GA and improved the QPF of Typhoon Rusa (2002) over SK. A series of pioneering works was done by Hong et al. (2014, 2015), using the micro-GA, to seek an optimal option set of the Noah land surface model (LSM) with multiple physics options (Noah-MP), which brought about the best forecasts of evapotranspiration and runoff over the Han River basin in SK (Hong et al. 2014) and four different regions having different climatic characteristics in East Asia (Hong et al. 2015). This coupled system of micro-GA and Noah-MP (say, the Noah-MP-.μGA system) could diagnose the performance of each implemented scheme and the interrelationships with the other schemes. By extending these scheme-based optimization studies, Park and Park (2021) developed the WRF-.μGA optimization system to find the optimal scheme set among the cumulus (CU), microphysics (MP), and planetary boundary layer (PBL) parameterizations in WRF for improving the QPF skill in a heavy rainfall event over the central-eastern coast of SK. Noting that SK is surrounded by three seas and is constantly affected by sea breezes, Yoon et al. (2021) also used the WRF-.μGA system to find optimal scheme set for accurate simulations of the sea breeze circulation over the central-eastern coast of SK. Most recently, Lim et al. (2022) found the optimal values for various snow-related parameters of Noah LSM in SK, by developing the coupled Noah LSM-.μGA system.

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In this chapter, we introduce the latest studies of the scheme- and parameter-based optimization in meteorology and hydrology by applying the micro-GA. Section 7.2 explains the basic concept of micro-GA. Sections 7.3 and 7.4 introduce the schemebased optimization study applied to the sea breeze in WRF and the parameter-based optimization study for the snow-related processes in the Noah LSM, respectively. Conclusions are given in Sect. 7.5.

7.2 Micro-genetic Algorithm John Holland developed the GA, a global optimization algorithm, in the 1970s (Holland 1973, 1975), based on Charles Darwin’s theory of natural evolution. The algorithm involves three critical optimization operators: selection, crossover, and mutation. The selection operator chooses random mates, corresponding to the parents, for crossover through a shuffling process. The crossover operator generates new offspring using the genetic information of two parents. The mutation operator alters part of the offspring’s genes to maintain genetic diversity. Individuals can diversify and converge more quickly to a global optimum using these operators, avoiding a local optimum. The generations continue to evolve until the best solution or maximum generation is obtained. Although the GA requires significant computing resources, the micro-GA effectively reduces the required resources by using re-initialization as an alternative to mutation, with a smaller population size (Krishnakumar 1990).

7.3 Scheme-Based Optimization: Sea Breeze Sea breeze is a localized atmospheric circulation that occurs due to differences in heating between land and sea surfaces in coastal regions. This phenomenon notably impacts local weather and meteorological conditions, as it carries moist and cool air inland and often results in coastal thunderstorms (Bhate et al. 2016). It significantly influences the dispersion of atmospheric pollutants at low levels by altering wind patterns and boundary layer structures (Lee and Han 1992; Salvador et al. 2016a). Since the sea breeze impacts precipitation, humidity, temperature, and air pollution over coastal areas, an accurate prediction of the sea breeze is essential. Sea breezes from three directions continuously influence SK (see Fig. 7.1a) (Nam et al. 2014; Park and Chae 2018; Lim and Lee 2019). Yeongdong, located on the northeastern coast of SK, has a long and narrow coastline surrounded by the East Sea/Sea of Japan (ESJ) to the east and steep mountains to the west (see Fig. 7.1b). This area suffers various and complicated weather patterns caused by a combination of factors such as the geography of the region, the structure of the coastline, sea breezes, and synoptic systems. These conditions can become particularly challenging when the Kor’easterlies (Park and Park 2020)—the low-level winds blowing from the ESJ toward the land—are strengthened by certain synoptic conditions (Lee and Lee

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Fig. 7.1 a Model domain with triple nesting including different horizontal resolutions, namely 9 km (d01), 3 km (d02), and 1 km (d03), and b locations of the observational stations in d03. GangNeung (GN; in red) is used only to select sea breeze cases. The actual location of the buoy station (red point inside the dotted box) is (37.54.◦ N, 130.0.◦ E), i.e., out of domain d03. The wind profiler radar is located at BukGangNeung (BGN). Other observational stations (e.g., AWS) are identified by abbreviations such as CheongHo (CH), YangYang (YY), JuMunjin (JM), GangMun (GM), Gangneung-Seongsan (GS), OkGye (OG), SamCheok (SC), and GungChon (GC). The color bar represents the terrain height (in m)

2003; Park and Lee 2007; Lee and Kim 2008; Nam et al. 2014; Tsai et al. 2018; Park and Park 2020). A climatological investigation of sea breezes in Yeongdong (Tsai et al. 2018) showed noticeable sea breezes on 268 days in April–June from 2009 to 2018. Thus, sea breezes exert a significant influence on the local weather conditions in Yeongdong by influencing temperature, humidity, and wind, among other weather elements. Accordingly, various studies are required to enhance the accuracy of numerical simulations of sea breezes in Yeongdong. Many sensitivity tests have recently been performed using mesoscale models to investigate the forecasting skill of different schemes in particular physical processes, such as CU, land surface, or PBL, in sea breeze circulations. However, the majority of sensitivity studies were limited to experiments involving a small number of schemes. This constraint arose from the limited computational resources required to identify the optimal scheme for enhancing sea breeze predictions (Srinivas et al. 2007; Steele et al. 2013; Salvador et al. 2016a, b; Hock and Pu 2017; Reddy et al. 2020). To overcome the limitations of previous sensitivity studies, we developed an optimization system by coupling WRF with micro-GA. The system was used to identify the optimal set of physical parameterization schemes to enhance the precision of the sea breeze circulation in the Yeongdong region, SK, specifically focusing on the weather elements near the surface and winds within PBL in the mountainous coastal area.

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7.3.1 Methodology Data and Sea Breeze Cases We employed data collected at 8 Automatic Weather Stations (AWS) and 1 Wind Profiler Radar (WPR) provided by the Korea Meteorological Administration (KMA) near the coast of Yeongdong for optimization and validation (see Fig. 7.1b). The data were recorded at hourly intervals. The meteorological variables for optimization and verification include temperature and relative humidity at the height of 2 m and wind speed and direction at 10 m, which were collected from the AWSs, and the vertical wind profile, which was obtained from the WPR. For selecting the sea breeze cases, we employed the method of Hwang et al. (2020), using temperature, precipitation, wind direction, and sea level pressure at GN and a buoy station over the sea. We selected sea breeze cases for this study based on data from the April–June period between 2016 and 2021, with the smallest monthly precipitation and the most notable contrast in surface temperature between land and sea. The following cases were chosen for this study: April 16, 2018, April 12, 2019, and May 3, 2019, for optimization, and April 17, 2018, April 11, 2020, and April 15, 2021, for validation.

WRF Physical Parameterization Schemes The accuracy of numerical simulations for sea breezes relies on the representation of subgrid-scale physical phenomena in the model, including PBL, land surface, radiation physics, etc. (Srinivas et al. 2007; Steele et al. 2013; Salvador et al. 2016a, b; Reddy et al. 2020). The interaction between the lower atmosphere and the sea/land surface is crucial to the sea breezes system. In order to identify the optimal combination of physical parameterization schemes that can precisely represent sea breezes, we chose eighteen schemes from four categories of physical processes in WRF. They include eight PBL, four land surfaces, three shortwave radiation, and three longwave radiation schemes. Based on the PBL sensitivity studies, we selected one or two surface layer schemes associated with each PBL scheme (Banks et al. 2015, 2016; Avolio et al. 2017). The PBL scheme divides into nonlocal closure and local closure schemes. The non-local closure schemes are YonSei University (YSU) (Hong et al. 2006), Asymmetrical Convective Model version 2 (ACM2) (Pleim 2007), and Total Energy-Mass Flux (TEMF) scheme (Angevine and Mauritsen 2010). The local closure schemes are Mellor–Yamada–Janjic (MYJ) (Janji´c 2002), Quasi-Normal Scale Elimination (QNSE) (Sukoriansky et al. 2005), Mellor–Yamada–Nakanishi–Niino level-2.5 (MYNN2) (Nakanishi and Niino 2006), Bougeault–Lacarrere (BouLac) (Bougeault and Lacarrere 1989; Martilli et al. 2002), and University of Washington (UW) (Bretherton and Park 2009; Hurrell et al. 2013) scheme. The LSM candidates include the 5-layer thermal diffusion (TD) (Dudhia 1996), Rapid Update Cycle (RUC) (Benjamin et al. 2004; Smirnova et al. 2016), Noah (Chen and Dudhia 2001; Ek et al. 2003), and Noah-MP scheme (Niu et al. 2011). The shortwave radiation schemes are Dudhia (1989), NCAR Community Atmospheric

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Model (CAM) (Collins et al. 2004), and Rapid Radiative Transfer Model for General circulation models (RRMTG) (Iacono et al. 2008) scheme. The longwave radiation schemes are Rapid Radiative Transfer Model (RRTM) (Iacono et al. 2008), CAM (Collins et al. 2004), and RRMTG (Iacono et al. 2008) scheme. WRF-.µGA System and Fitness Function We developed the WRF-.μGA system by coupling the micro-GA algorithm and WRF to obtain an optimal scheme set for the sea breeze. The system optimized three sea breeze cases simultaneously, adequately performing model optimization of schemes for the sea breeze. The algorithm flow chart illustrates the representation of the WRF-.μGA system—see Fig. 7.3 in Yoon et al. (2021). The system consists of several steps: (1) When the WRF-.μGA system initializes, the micro-GA generates a random population of chromosomes composed of binary code, with each chromosome representing a combination of physical parameterization schemes; (2) The WRF model runs with a modified namelist file, using each scheme combination; (3) The model’s output is evaluated against observational data using a fitness function, and the selected scheme combination via selection is passed down to the offspring using the crossover mechanism; (4) If the desired level of convergence, such as the nominal convergence, is achieved, the system randomly generates new individuals through re-initialization, excluding the elite (e.g., best individual); (5) This process continues until the maximum number of generations is reached. In GA optimization, the fitness function plays a crucial role in determining how close the problem is to achieve the optimal solution. Therefore, it should be defined appropriately according to the optimization goal. The normalized root-mean-square error (NRMSE; . E NR ) is selected as the fitness function for this study because it can be used to assess variables on different scales. Our optimization focuses on predicting sea breezes, so we build the fitness function around surface meteorological variables and vertical wind profiles, which are important for predicting sea breezes. The fitness function, . f , is defined as follows (Yoon et al. 2021): .

NR NR f = E sfc + E upper

(7.1)

NR NR where . E sfc and . E upper are defined, respectively, as .

NR NR NR NR E sfc = E TNR + E RH + E WS + E WD 2m 2m 10m 10m

(7.2)

for the surface variables, as represented by the subscript .sfc, and .

NR NR NR E upper = E WS + E WD

(7.3)

for the upper-level (vertical) wind profile, as described by the subscript .upper. Subscripts .T2m , .RH2m , .WS10m , and .WD10m represent 2 m temperature, 2 m relative

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humidity, 10 m wind speed, and 10 m wind direction, respectively; subscripts .WS and .WD mean the wind speed and direction at upper levels, respectively. The NRMSE, . E NR , can be computed by normalizing the root-mean-square error (RMSE; . E R ) with the standard deviation of observations (.σ ) as .

E NR =

ER , σ

(7.4)

R where the RMSEs for the surface variables (i.e., . E sfc ) and the upper-level wind R variables (i.e., . E upper ) are given by

.

R E sfc

and .

R E upper

[ | S ∑ K ∑ T | 1 ∑ =| (Fkst − Okst )2 Nkst k=1 s=1 t=1 [ | K ∑ L T ∑ | 1 ∑ =| (Fktl − Oktl )2 , Nktl k=1 t=1 l=1

(7.5)

(7.6)

respectively, for the given forecasts .(F) and observations .(O). Here, . K , . S, .T , and . L represent the number of sea breeze cases, observational stations, observations with an interval of 1 h, and model vertical levels below 1 km, respectively; . N represents the total number of observations with . Nkst = K × S × T and . Nktl = K × T × L. It should be noted that a smaller fitness function value indicates a higher performance. Additionally, the RMSE for the wind direction was calculated using the method by Jiménez et al. (2012).

7.3.2 Experimental Designs WRF Model Setup In this study, we used version 4.1.5 of WRF. The horizontal domain was set up with three nested domains (Fig. 7.1), each with resolutions of 9, 3, and 1 km, along with 45 vertical levels in the eta vertical coordinate system. The initial and boundary conditions are obtained from the 6 h global final analysis (FNL) data at.0.25◦ × 0.25◦ grids produced by the National Center for Environmental Prediction (NCEP) Global Forecast System (GFS). The model is started at 0300 LST (1800 UTC), and the simulations are conducted for 18 h in each sea breeze case. The first 6 h is the spinup time, followed by an 11 h search period for the optimal scheme set for the sea breeze. The physics schemes except for schemes for optimizing are the Kain–Fritsch (KF) convective scheme (Kain 2004) and the WRF Double Moment 5-class (WDM5) (Lim and Hong 2010) scheme. The land data employed the 15 s Moderate Resolution

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Imaging Spectroradiometer (MODIS) with the International Geosphere-Biosphere Program (IGBP) modified 21 categories. In all cases, the simulations were started at 1800 UTC.

Optimization The optimization results in micro-GA are highly dependent on the evolutionary generation and population size. The selection of the evolutionary generation as 100 and the population size as 5 in this study follows the approach of Yu et al. (2013) and Zhu et al. (2019), which are widely accepted values for micro-GA optimization. To ensure genetic diversity, the uniform crossover technique with a rate of 0.5 is employed. To determine the optimal scheme set, we conducted the WRF-.μGA system on the three cases simultaneously: April 16, 2018, April 12, 2019, and May 3, 2019. Our optimization efforts focused on the sea breeze circulation, and we specifically targeted the period from 0900 LST (0000 UTC) to 1900 LST (1000 UTC). This time frame corresponds to the typical onset of the sea breeze until the initiation of the land breeze in the GN area.

7.3.3 Results Optimal Combination The optimization results indicated that the fitness function reached its minimum value in the .25th generation—see Fig. 7.3 in Yoon et al. (2021). The optimal scheme set included the MYNN2 PBL, Noah-MP land surface, RRTMG shortwave radiation, and RRTMG longwave radiation schemes. The theoretical supports of this result are as follows: (1) The Noah-MP enables a more precise representation of land surface processes, inducing more reliable simulations of sea breeze and boundary layer features in coastal regions (Reddy et al. 2020; Rajeswari et al. 2020); (2) The MYNN2 has demonstrated enhanced accuracy in reproducing the structure of the PBL in coastal areas (Lombardo and Colle 2013; Tyagi et al. 2018; Hariprasad et al. 2014).

Validation We chose three sea breeze cases, namely April 17, 2018, April 11, 2020, and April 15, 2021, for validation. The validation period spanned 11 h with 1-hour intervals, starting from the initiation of the sea breeze until the beginning of the land breeze, which aligns with the optimization period. During the validation, we compared the model outputs with observational data for surface meteorological variables such as . T2m , .RH2m , .WS10m , and .WD10m as well as vertical wind profile variables. To assess the performance, we compared the optimal combination of physical parameteriza-

7 Reducing Model Uncertainty in Physical Parameterizations … Table 7.1 List of the experiments PBL scheme Land surface scheme

187

Shortwave radiation scheme

Longwave radiation scheme

References

– Rajeswari et al. (2020) Dewi et al. (2019) Salvador et al. (2016b) Papanastasiou et al. (2010)

OPTM EXP1

MYNN2 YSU

Noah-MP Noah-MP

RRTMG Dudhia

RRTMG RRTM

EXP2

YSU

Noah

Dudhia

RRTM

EXP3

MYJ

Noah

Dudhia

RRTM

EXP4

MYJ

TD

Dudhia

RRTM

c 2021 Authors. Distributed under CC BY 4.0 License From Yoon et al. (2021). ◯

tion schemes obtained from our study with commonly used scheme sets in numerical simulations of sea breeze research (Salvador et al. 2016a; Rajeswari et al. 2020; Dewi et al. 2019; Papanastasiou et al. 2010). The combinations of physical parameterization schemes used in the comparison experiments (e.g., EXP1–EXP4), including the optimal scheme set (e.g., OPTM), are presented in Table 7.1. We used Eqs. (7.1)– (7.3) to assess the forecast skills of various combinations of physical parameterization schemes concerning all variables, surface meteorological variables, and PBL winds, respectively. The OPTM performed best in all variables (Fig. 7.2a) and surface variables (Fig. 7.2b), followed by EXP1. In terms of the vertical wind variables (Fig. 7.2c), the best performance differed for each sea breeze case, with EXP1 and EXP2 outperforming OPTM on April 11, 2020, and April 15, 2021, respectively. Overall, OPTM showed the best performance in simulating sea breeze circulations. Compared to EXP4, the improvement rates in terms of NRMSE .(E NR ) were the largest for OPTM as follows: 29.% for all variables on April 11, 2020 (see Fig. 7.2a); 38.% for the surface meteorological variables on April 15, 2021 (see Fig. 7.2b); and 24.% for the vertical wind profile variables on April 11, 2020 (see Fig. 7.2c). Both OPTM and EXP1 indicated good forecast skills because of the influence of NoahMP, known for its accurate representation of the PBL height and heat flux during the development of a shallow, unstable boundary layer near the coast in sea breeze conditions (Jain 2015).

Sensitivity Analysis The transfer of heat and moisture at the surface, along with their mixing by turbulent eddies and subsidence, plays a crucial role in the formation and expansion of PBL (Yerramilli et al. 2010; Jain 2015). The sea breeze can cause significant changes to land surface fluxes by bringing in cold and moist air through advection, thus ultimately impacting the development of the boundary layer (Miao et al. 2009);

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Fig. 7.2 Comparison between optimized and non-optimized experiments using NRMSE.(E NR ) for a all variables according to Eq. (7.1), b surface variables based on Eq. (7.2), and c winds at specific vertical levels as per Eq. (7.3), on April 17, 2018, April 11, 2020, and April 15, 2021, respectively

it causes weakening of the convection structure and decrease in temperature, consequently inhibiting PBL growth. Thus, we conducted a sensitivity analysis on the vertical wind structure of the sea breeze and the PBL height at GN, a representative area of Yeongdong, using the optimal scheme set and the other schemes sets. Figure 7.3 shows time variation of the vertical wind structure and PBL height for the experiments, including OPTM and EXP1–EXP4 on April 15, 2021. In the OPTM, the PBL height initially increased in the morning due to solar radiation and peaked at 1100 LST (Fig. 7.3a). After that, as the sea breeze strengthened, the PBL height decreased. Particularly, the PBL height appeared to be the lowest at 1400–1500 LST (0500–0600 UTC) and then slightly increased again. This feature is strongly linked to the sea breeze circulation, which was the strongest at 1400–1500 LST and then decreased slightly, influencing the PBL height variation. Both OPTM and EXP1 employ the Noah-MP scheme and exhibit similar characteristics regarding the PBL height and horizontal wind vector. This is expected as LSM calculates the heat and moisture fluxes for land, which serve as lower boundary conditions for vertical transport in the PBL. However, in EXP1, the peak of the PBL height appeared at 1200 LST (0300 UTC), which was 1 h later than in OPTM (Fig. 7.3b). This delay was mainly due to the different physical parameterization schemes used, other than LSM, which affected the development of the sea breeze (see Table 7.1). In EXP2, the PBL height peak occurred at 1200 LST, similar to EXP1 (Fig. 7.3c). The only difference between these two experiments is the LSM, with EXP2 using the Noah

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Fig. 7.3 Time variation of PBL height (black line), horizontal wind speed (shading), and vector (arrow) on April 15, 2021. a OPTM, b EXP1, c EXP2, d EXP3, and e EXP4. From Yoon et al. c 2021 Authors. Distributed under CC BY 4.0 License (2021). ◯

LSM. Both EXP2 and EXP3 share the same parameterization schemes except for the PBL scheme—YSU for EXP2 and MYJ for EXP3 (see Table 7.1)—which led to unrealistic PBL characteristics in EXP3 (Fig. 7.3d). The only difference between EXP4 and EXP3 is the LSM, i.e., 5-Layer scheme in EXP4 and Noah LSM in EXP3, but EXP4 showed much more unrealistic PBL evolution than EXP3 (Fig. 7.3e). Overall, the PBL structure and evolution were better with the optimized combination of physical parametrization schemes than with other combinations.

7.3.4 Summary Our aim is to enhance the accuracy of sea breeze prediction along the eastern coast of Yeongdong in SK. To achieve this, we employed the micro-GA, a global optimization algorithm, to identify the optimal set of physical parameterization schemes in WRF. We developed the WRF-.μGA system and performed it to find the optimal set of physical parameterization schemes for sea breeze circulation over the central-eastern coast of SK. We choose nine observational stations for optimization and validation in the Yeongdong coastal region of SK. The fitness function consisted of NRMSEs for the surface variables (.T2m , .RH2m , .WS10m , and .WD10m ) and the upper-level wind variables (.WS and .WD). The optimal scheme set, including the MYNN2 (PBL),

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Noah-MP (land surface), and RRTMG (shortwave and longwave radiation), was identified using the WRF-.μGA system. We compared optimized and non-optimized experiments. The results showed that WRF performed best when using the optimal schemes set (OPTM) for sea breeze circulation in the coastal region. Additionally, we discovered that the combination of YSU, Noah-MP, Dudhia, and RRTM schemes exhibited similar performance. YSU and MYNN2 schemes effectively captured the structure of PBL in coastal regions and the characteristics of sea breezes, respectively. Furthermore, the Noah-MP scheme is widely recognized as the optimal land surface scheme for accurately simulating the circulation of sea breezes. The sensitivity experiments showed that the optimized combination of parameterization schemes improved the PBL structure and evolution features. This optimal scheme set obtained through the WRF-.μGA system can provide a more accurate analysis of the dynamical and thermodynamical features of sea breeze. Therefore, this optimal scheme set can provide valuable insights into meteorological phenomena and local circulations in coastal regions, including precipitation patterns, low-level air convergence, and the distribution of atmospheric pollutants.

7.4 Parameter-Based Optimization: Snow LSMs generally have empirical parameters, which introduce uncertainty into the model’s results. The empirical parameters sometimes require modification when they apply to different locations because these parameters usually reflect the local characteristics where the empirical relations developed. This study seeks the optimal snow-related parameters over SK, where heavy snowfall events occur in the winter. Snow processes in LSMs include the snow cover fraction, snow albedo, and snow depth. The optimization is conducted using the micro-GA and in situ and satellite observations for the snow depth, snow cover fraction, and snow albedo. To find the optimal regional parameters using the single-column model (e.g., Noah LSM), we selected representative stations over SK to cover various land cover types. Then, we identify which snow-related parameters can be optimized and suggest the optimal parameters using the micro-GA over SK.

7.4.1 Methodology Snow-Related Parameters in Noah LSM The Noah LSM uses a single layer to simulate the snow processes (Sultana et al. 2014; Ek et al. 2003; Jonas et al. 2009). It describes heat exchanges between the snow and the atmosphere, as well as snow accumulation, sublimation, and melting (Suzuki and Zupanski 2018). The snow processes and related parameters in Noah LSM are listed below.

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Fractional snow cover (FSC;.σs ) is a function of snow water equivalent (SWE;.Ws ) (Livneh et al. 2010), and it varies non-linearly following the empirical snow depletion curves of Anderson (1973): σ = 1 − e−Ps W + W e−Ps .

(7.7)

. s

Here, . Ps is the distribution shape parameter with a control value of 2.6 and .W = Ws /Wmax , where.Wmax is the.Ws threshold at which snow cover is 100%. FSC contains two uncertain parameters—. Ps and.Wmax . First parameter,. Ps has a positive correlation with snow cover, and the second parameter,.Wmax has a negative correlation with snow cover, and it is more sensitive compared to . Ps (Lim et al. 2022). .Wmax especially depends on the land cover types (LCTs), and it is provided as a lookup table. For instance, .Wmax has the highest value in forests due to the irregular geometry of the cover of forests (Livneh et al. 2010; Wang and Zeng 2010). Therefore, we will estimate the optimal . Ps and .Wmax suited to SK in the assigned range (Table 7.2). Snow albedo (SA; .αs ) is the proportion of incident radiation reflected by the snowpack and is important for determining surface-energy balance, especially during snow melting (Warren and Wiscombe 1980; Warren 1982). Surface albedo (.α) reflects the patchiness effect due to an accumulation or diminution of snow, which consists of snow-covered surface albedo (.αs ) and snow-free surface albedo (.α0 ) as α = α0 + σs (αs − α0 ).

(7.8)

.

SA is high over fresh snow and decreases depending on the ablation and accumulation periods. SA is determined by the fresh SA (.αmax ), the number of days since the previous snowfall (.t), and the albedo-decay rates (. A and . B) as B

α = αmax At ,

(7.9)

. s

Table 7.2 List of optimized snow-related parameters in FSC, SA, and SD Variable Snow parameter LCTs Min/control/Max Optimized value FSC

. Ps . Wmax

SA

.αmax,CofE .C

SD

. P1 . P2

– DBF MF WS CL UB – – – –

2.0/2.6/4.0 0.01/0.08/2.00 0.01/0.08/2.00 0.01/0.03/2.00 0.01/0.04/2.00 0.01/0.04/2.00 0.10/0.85/1.00 0.1/0.5/1.0 0.00/0.05/0.10 0.0002/0.0017/0.003

2.7097 0.1632 0.0529 0.0406 0.0406 0.0284 0.7387 0.5355 0.0698 0.0002

The ranges employed in the optimization process are minimum (Min), control, and maximum (Max). c 2022 Authors. Distributed under CC BY 4.0 License From Lim et al. (2022). ◯

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where the control values for the empirical parameters A and B are, respectively, 0.94 and 0.58 during the accumulation phase. By adding the satellite-based maximum SA (.αmax,sat ) (Robinson and Kukla 1985) and applying adjustment to a maximum SA (.αmax,CofE ) (USACE 1956; Livneh et al. 2010), spatial variation in SA is taken into account in .αmax as α

= αmax,sat + C(αmax,CofE − αmax,sat ),

. max

(7.10)

where .C is a proportionality coefficient with a control value of 0.5. All things considered, we have selected two empirical parameters—.αmax,CofE and .C—positive to SA to optimize in SK in the assigned range (Table 7.2). Snow depth (SD) is evaluated as the ratio of .Ws to snow density (.μs ), i.e., .Ws /μs (Gotleib 1980; Koren et al. 1999). When temperature is less than .0 .◦ C, several processes (e.g., compression and melting of snow) (Koren et al. 1999) determine .μs (Koren et al. 1999). The fresh snow density (.μs,fresh ) is affected by 2 m air temperature (.Tair ) (Gotleib 1980) as μs,fresh = P1 + P2 (Tair + 15)1.5 ,

.

(7.11)

where . P1 = 0.05 g cm.−3 and . P2 = 0.0017 g cm.−3 .◦ C.−1 . .μs,fresh is 0.05 g cm.−3 if ◦ . Tair is less than .− 15 . C; otherwise, it tends to rise as . Tair rises. Therefore, we will seek optimal values of . P1 and . P2 . Since .μs is inversely proportional to SD, both parameters have negative correlations with SD. Coupled System of Noah LSM and Micro-GA (Noah LSM-.µGA) The Noah LSM-.μGA coupled system optimizes snow-related parameters via the following procedures (see Fig. 7.2 in Lim et al. (2022)): (1) Micro-GA randomly initializes the snow parameter combinations; (2) Micro-GA modifies parameter-related files in the Noah LSM and produces forcing data for each station; (3) The five populations, with the different snow parameters, parallelly run the Noah LSM; (4) A fitness function is used to compare each Noah LSM result to the observation; (5) Micro-GA chooses the best fitness by comparing a number of populations through the tournament selection; (6) The uniform crossover produces new combinations for the next generation; (7) When the convergence condition arrives, all populations aside from the best one denoted by elitism randomly re-initialize; and (8) Micro-GA repeats these steps until the required number of iterations converges to a global maximum of the fitness function. We suggest the RMSE, . E R (x), for all snow variables as an evaluation index to assess the improvement of snow prediction skills, including FSC, SA, and SD, as follows: / )2 ∑N ( ˆ i − xi i=1 x R , (7.12) . E (x) = N

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where .xˆ is the model results from Noah LSM and .x is the corresponding observations, respectively, for the three snow variables—FSC, SA, and SD; . N is the total number of observation times with a time index .i. The number of observations varies according to the observational types: the Automated Synoptic Observing System (ASOS) produces hourly data for SD, while the MODerate resolution Imaging Spectroradiometer (MODIS), a sensor onboard the polar orbiting satellite Terra, produces daily data for FSC and SA. Note that Noah LSM simulations are carried out at the ASOS location, and the MODIS data uses the value that is closest to the ASOS location. Next, we compare the RMSEs from the model results using optimized and nonoptimized (i.e., control) parameters to get the improvement ratio, .r (x), as r (x) =

.

R R E CP (x) − E OP (x) R E CP (x)

(7.13)

where subscripts .CP and .OP represent control parameters and optimal parameters, respectively. We average the improvement ratios for the FSC, SA, and SD to define the fitness function, . f (x), as

.

f (x) =

M ∑ r (x) j q j j=1

M

(7.14)

where . M is the number of stations and .q is a quality control flag (QCF), which can be either zero or one. For example, QCF has a zero value when the snow events are not simulated after optimization and the number of snow observations is less than two. In order to prevent the degradation of performance by optimization, we additionally double (7.14). Finally, by defining a normalized fitness function, . f n (x) in the range .[− 1, 1], as f (FSC) + f (SA) + f (SD) , . f n (x) = (7.15) 3 the micro-GA eventually finds the maximum fitness.

7.4.2 Experimental Design To obtain the optimal snow-related parameters in SK, we have selected representative stations with respect to LCTs—deciduous broadleaf forest (DBF), mixed forest (MF), woody savanna (WS), cropland (CL), and urban and built-up lands (UB)— considering the sufficient observation (Fig. 7.4). Experiments were conducted from 0000 UTC 1 May 2009 to 2300 UTC 30 April 2018, and the spin-up period was from May to October in the first year.

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First, we optimized snow-related parameters within the Noah LSM-.μGA coupled system using the recommended settings for micro-GA (e.g., five population, uniform crossover, and elitism) (Carroll 1996; Yu et al. 2013; Yoon et al. 2021). The two optimization experiments are as follows: (1) OP5, which optimized five snow parameters (. Ps , .αmax,CofE , .C, . P1 , and . P2 ); and (2) OPW, which optimized only .Wmax that varies depending on the LCTs. Since OP5 optimized more parameters, we performed an optimization in the larger generations (e.g., 200) with smaller number of stations (i.e., ten stations; two stations per LCT) (see Fig. 7.4a). On the other hand, OPW optimized .Wmax with twenty-five stations (i.e., five stations per LCT) in fewer generations (i.e., five stations per LCT) (see Fig. 7.4b).

Fig. 7.4 Map of station locations in each experiment: a OP5 and b OPW, CTL, VF5 and VF6. Five LCTs are colored black in DBF, blue in MF, green in WS, yellow in CL, and red in UB. The abbreviations for stations are as follows: Ulleungdo (UL), Taebaek (TB), Inje (IJ), Chupungnyeong (CP), Youngwol (YW) for DBF; Bongwha (BW), Hapcheon (HP), Hongcheon (HC), Miryang (MY), Gumi (GM) for MF; Imsil (IS), Andong (AD), Boeun (BE), Uljin (UJ), and Bukgangneong (NG) for WS; Buan (BA), Icheon (IN), Haenam (HN), Boryeong (BR), Jeongeup (JE) for CL; Gwangju (GJ), Seoul (SL), Daejeon (DJ), Suwon (SW), Incheon (IC) for UB. From Lim et al. c 2022 Authors. Distributed under CC BY 4.0 License (2022). ◯

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Second, we verified the optimized performance in terms of snow prediction skills by comparing the model results using optimized snow parameters and non-optimized snow parameters for the twenty-five observation stations via the following experiments: (1) CTL using control parameters without optimization; and (2) VF5 using the five optimized parameters obtained from OP5; and (3) VF6 using the six optimized parameters obtained from both OP5 and OPW (see Fig. 7.4b).

7.4.3 Results Optimization suggested optimal snow-related parameters specialized in SK (Table 7.2). OP5 converged at 160th generation producing five optimal snow-related parameters (. Ps , .αmax,CofE , .C, . P1 , and . P2 ) during the 200 generation. On the other hand, OPW for DBF, MF, WS, CL, and UB converged at 3rd, 70th, 7th, 7th, and 12th generation, respectively, producing optimal .Wmax during the 100 generation. Since OPW only optimized .Wmax according to the LCTs, it converged quickly to find the optimal parameters. The first parameter related to FSC, . Ps , was increased, which resulted in an increase of FSC. The second parameter, .Wmax , was optimized depending on each LCT. The .Wmax in DBF and WS was increased, while the .Wmax in MF and UB was decreased. In the case of CL, the optimized value is similar to the control value. The third parameter related to SA, .αmax,CofE , was decreased to reduce an overestimated SA. The fourth parameter, .C, already was an optimal control value. The fifth parameter, . P1 , was increased, resulting in a decrease in SD. On the other hand, the last parameter, . P2 , was decreased, leading to an increase in SD. We further investigated how the optimized snow-related parameters affect to snow prediction in terms of RMSE, mean bias (MB), and coefficient of determination (. R 2 ) in verification experiments (e.g., CTL, VF5, and VF6) (Table 7.3). We explained those results in terms of the improvement ratio from CTRL to VF5 and VF6. In VF5, new five parameters resulted in an improvement of RMSE for FSC, SA and SD by 0.7.%, 5.4.% and 13.7.%, respectively. Since .Wmax was not yet optimized, the RMSE of FSC was relatively weak (e.g., 0.7.%). In terms of MB, SA and SD solved the bias problems by 26.9.% and 35.9.%, respectively. Lastly, . R 2 was solely meaningful in SD with values greater than 0.8, and SD showed positive impacts by 1.5.% from the optimized parameters. Because FSC and SA had relatively less observations due to coarse resolution in satellite, they had small . R 2 . We additionally optimized .Wmax depending on LCT (OPW) and VF6 showed further improvement in SA and SD as well as FSC. As a result, an improvement of RMSE for FSC, SA, and SD was 3.3, 6.2, and 17.0.%, respectively. However, MB for FSC still strengthened from 9.1 to 11.9.% in VF6: some DBF stations had a larger negative bias, thus it contributed to strengthening MB in FSC. As for the SA and SD, VF6 enhanced the improvement ratio of MB by 4.1.% and 4.3.%, respectively. In terms of . R 2 , it was still only meaningful in SD, and it showed a 3.0.% improvement. Figure 7.5 is the time series of snow variables in the observations and the model simulations (CTL vs. VF6) for DBF, represented by UL. It explains how the six

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Table 7.3 The RMSE, MB, . R 2 of snow variables from CTL to VF5, and VF6 over the twenty-five stations Experiment CTL VF5 VF6 Variables FSC SA SD FSC SA SD FSC SA SD RMSE MB R.2

0.249 0.132 9.094 0.247 0.125 7.847 0.124 0.125 7.547 0.0408 .−4.39 .−0.145 0.0298 .−2.81 .−0.149 0.0281 .−2.45 0.257 0.281 0.808 0.265 0.276 0.821 0.277 0.274 0.834

.−0.133

optimized snow-related parameters changed the snow variables. FSC was hard to distinguish certain bias patterns in CTL (black dots), but VF6 (red dots) made it closer to observation (gray dots) (Fig. 7.5a). The overestimated SA in CTL has reduced in VF6 (Fig. 7.5b) and the underestimated SD in CTL has increased in VF6 (Fig. 7.5c).

7.4.4 Summary Six parameters of the FSC, SA, and SD equations suitable for SK were optimized using the coupled system of micro-GA and Noah LSM. The optimized snow-related parameters led to an improvement in RMSEs. SD showed the greatest improvement since it uses in situ observation to optimize, whereas FSD and SA use satellite observation with coarse spatiotemporal resolution, which results in fewer improvements; thus, the only underestimated SD and overestimated SA have been alleviated. It is noted that the parameter estimation using the micro-GA is effective in Noah LSM and generates remarkable improvements in snow processes in SK.

7.5 Conclusions The numerical weather prediction (NWP) models have inherent uncertainties related to the parameterizations of subgrid-scale physical processes and various parameters therein. Therefore, various artificial intelligence algorithms have recently been used to improve forecast skills by reducing model uncertainty. In particular, the genetic algorithm (GA), including the micro-GA, has been extensively used in hydrology and meteorology. This chapter introduced two recent studies that applied the micro-GA to optimization problems in a weather model and a land surface model, respectively. First, a scheme-based optimization was applied to seek the optimal combination of the four physical parameterization schemes related to the local sea breeze circulations, including planetary boundary layer, land surface, shortwave radiation, and longwave radiation, in the Weather Research and Forecasting (WRF) model. The

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Fig. 7.5 Time series of a FSC, b SA, and c SD (in cm) for DBF (e.g., UL) from May 2009 to April 2018. Observations are in gray dots, and model results are in black dots for CTL and in red dots for c 2022 Authors. Distributed under CC BY 4.0 License VF6. From Lim et al. (2022). ◯

optimal scheme set, obtained through the WRF-.μGA system, included the MYNN2 for PBL, Noah-MP for land surface, RRTMG for shortwave radiation, and RRTMG for longwave radiation. The overall performance of WRF, employing the optimized set, was superior to other possible combinations of parameterization schemes in simulating the sea breeze circulations over the given local region. Second, a parameter-based optimization was conducted to obtain the optimal values of six parameters in the snow-related processes—fractional snow cover (FSC), snow albedo (SA), and snow depth (SD)—of the Noah land surface model (LSM) over SK, by developing the Noah LSM-.μGA system. The optimized snow-related parameters led to an improvement in RMSEs by 3.3%, 6.2%, and 17.0% for FSC, SA, and SD, respectively. We address that the micro-GA, an efficient artificial intelligence-based optimization algorithm, can be adopted for various optimization problems in meteorology and

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hydrology and other disciplines to reduce the model uncertainty related to physical parameterizations. We demonstrated that the optimization systems (i.e., numerical models coupled with the micro-GA) can find an optimal set among a bunch of choices on the parameterization schemes and can estimate the optimal values of parameters in each scheme that are under prespecified ranges. These studies can pave a way to ultimate superparameterization through the sequential optimization by combining the search for the optimal scheme set and the optimal parameter estimation (Park 2022). Acknowledgements This work is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1A6A1A08025520) and by the NRF grant funded by the Korea government (MSIT) (NRF-2021R1A2C1095535).

References Anderson E (1973) National weather service river forecast system: snow accumulation and ablation model. US Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service Angevine HJ, Mauritsen T (2010) Performance of an eddy diffusivity-mass flux scheme for shallow cumulus boundary layers. Mon Weather Rev 138:2895–2912 Avolio E, Federico S, Miglietta MM et al (2017) Sensitivity analysis of WRF model PBL schemes in simulating boundary-layer variables in southern Italy: an experimental campaign. Atmos Res 192:58–71 Banks RF, Tiana-Alsina J, Rocadenbosch F et al (2015) Performance evaluation of the boundarylayer height from lidar and the weather research and forecasting model at an urban coastal site in the north-east Iberian Peninsula. Bound Layer Meteorol 157:265–292 Banks RF, Tiana-Alsina J, Baldasano JM et al (2016) Sensitivity of boundary-layer variables to PBL schemes in the WRF model based on surface meteorological observations, lidar, and radiosondes during the HygrA-CD campaign. Atmos Res 176:185–201 Benjamin SG, Grell GA, Brown JM et al (2004) Mesoscale weather prediction with the RUC hybrid isentropic-terrain-following coordinate model. Mon Weather Rev 132:473–494 Bhate J, Kesarkar AP, Karipot A et al (2016) A sea breeze induced thunderstorm over an inland station over Indian South Peninsula—a case study. J Atmos Sol Terr Phys 148:96–111 Bougeault P, Lacarrere P (1989) Parameterization of orography-induced turbulence in a mesobetascale model. Mon Weather Rev 117:1872–1890 Bretherton CS, Park S (2009) A new moist turbulence parameterization in the community atmosphere model. J Clim 22:3422–3448 Carroll D (1996) Genetic algorithms and optimizing chemical oxygen-iodine lasers. Dev Theoret Appl Mech 18:411–424 Chen F, Dudhia J (2001) Coupling an advanced land surface-hydrology model with the Penn StateNCAR MM5 modeling system. Part I: model implementation and sensitivity. Mon Weather Rev 129:569–585 Collins WD, Rasch PJ, Boville BA et al (2004) Description of the NCAR community atmosphere model (CAM 3.0). NCAR technical note, NCAR/TN-464+STR; technical report. NCAR, Boulder, CO Dewi DPR, Fatmasari D, Gustari I (2019) Simulation of sea breeze events in gulf of Jakarta under different synoptic condition: an application of WRF model. IOP Conf Ser Earth Environ Sci. In:

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Koren V, Schaake J, Mitchell K et al (1999) A parameterization of snowpack and frozen ground intended for NCEP weather and climate models. J Geophys Res Atmos 104:19569–19585 Krishnakumar K (1990) Micro-genetic algorithms for stationary and non-stationary function optimization. In: Intelligent control and adaptive systems, vol 1196. Proceedings of SPIE, 1989 symposium on visual communications, image processing, and intelligent robotics systems, Philadelphia, PA, 1–3 Nov 1989. International Society for Optical Engineering, Bellingham, WA, pp 289–296 Lee DI, Han YH (1992) Vertical distribution of aerosol concentrations in the boundary layer observed by a tethered balloon: part II: distributions of aerosol concentrations in relation to the sea breeze front. J Korean Meteor Soc 28:497–507 Lee JG, Kim YJ (2008) A numerical simulation study using WRF of a heavy snowfall event in the Yeongdong coastal area in relation to the northeasterly. Atmosphere 18:339–354 (in Korean with English abstract) Lee JG, Lee JS (2003) A numerical study of Yeongdong heavy snowfall events associated with easterly. J Korean Meteor Soc 39:475–490 (in Korean with English abstract) Lee YH, Park SK, Chang DE (2006) Parameter estimation using the genetic algorithm and its impact on quantitative precipitation forecast. Ann Geophys 24:3185–3189 Lim S, Gim HJ, Lee E et al (2022) Optimization of snow-related parameters in the Noah land surface model (v3.4.1) using a micro-genetic algorithm (v1.7a). Geosci Model Dev 15:8541–8559 Lim KSS, Hong SY (2010) Development of an effective double-moment cloud microphysics scheme with prognostic Cloud Condensation Nuclei (CCN) for weather and climate models. Mon Weather Rev 138:1587–1612 Lim HJ, Lee YH (2019) Characteristics of sea breezes at coastal area in Boseong. Atmosphere 29:41–51 (in Korean with English abstract) Livneh B, Xia Y, Mitchell K et al (2010) Noah LSM snow model diagnostics and enhancements. J Hydrometeorol 11:721–738 Lombardo K, Colle BA (2013) Processes controlling the structure and longevity of two quasi-linear convective systems crossing the southern New England coast. Mon Weather Rev 141:3710–3734 Martilli A, Clappier A, Rotach MW (2002) An urban surface exchange parameterisation for mesoscale models. Bound Layer Meteorol 104:261–304 Miao JF, Wyser K, Chen D et al (2009) Impacts of boundary layer turbulence and land surface process parameterizations on simulated sea breeze characteristics. Ann Geophys 27:2303–2320 Nakanishi M, Niino H (2006) An improved Mellor–Yamada level-3 model: its numerical stability and application to a regional prediction of advection fog. Bound Layer Meteorol 119:397–407 Nam HG, Kim BG, Han SO et al (2014) Characteristics of easterly-induced snowfall in Yeongdong and its relationship to air-sea temperature difference. Asia Pac J Atmos Sci 50:541–552 Niu GY, Yang ZL, Mitchell KE et al (2011) The community Noah land surface model with multiparameterization options (Noah-MP): 1. Model description and evaluation with local-scale measurements. J Geophys Res Atmos 116:D12109. https://doi.org/10.1029/2010JD015139 Papanastasiou DK, Melas D, Lissaridis I (2010) Study of wind field under sea breeze conditions; an application of WRF model. Atmos Res 98:102–117 Park MS, Chae JH (2018) Features of sea-land-breeze circulation over the Seoul metropolitan area. Geosci Lett 5:28. https://doi.org/10.1186/s40562-018-0127-6 Park SK, Lee E (2007) Synoptic features of orographically enhanced heavy rainfall on the east coast of Korea associated with Typhoon Rusa (2002). Geophys Res Lett 34:L02803. https://doi.org/ 10.1029/2006GL028592 Park SK, Park S (2020) On a flood-producing coastal mesoscale convective storm associated with the Kor’easterlies: multi-data analyses using remote sensing, in-situ observations and storm-scale model simulations. Remote Sens 12:1532. https://doi.org/10.3390/rs12091532 Park S, Park SK (2021) A micro-genetic algorithm (GA v1.7.1 a) for combinatorial optimization of physics parameterizations in the weather research and forecasting model (v4.0.3) for quantitative precipitation forecast in Korea. Geosci Model Dev 14:6241–6255

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Part III

Data Assimilation

Chapter 8

Assimilation of Geostationary Hyperspectral Infrared Sounders (GeoHIS): Progresses and Perspectives Wei Han, Ruoying Yin, Jun Li, Xueshun Shen, Hao Wang, Jincheng Wang, Yongzhu Liu, and Di Di

Abstract Continuous atmospheric temperature and moisture profiles can be measured by high-temporal geostationary hyperspectral infrared sounder (GeoHIS) radiance observations, which could capture the temporal and spatial variability for high-impact weather or rapidly changing weather events. On December 10, 2016, China’s FengYun-4A satellite (FY-4A) was successfully launched into geostationary orbit. The Geostationary Interferometric Infrared Sounder (GIIRS) onboard FY-4A usher in a new era in Earth observation system. It provides the first time-continuous observations of upwelling thermal infrared with high-spectral resolution. Since December 2018, a subset of GIIRS longwave temperature sounding channels has been assimilated into CMA-GFS (Global Numerical Weather Prediction System of China Meteorological Administration), improving forecasts over East Asia, particularly for high-impact weather forecasts including Typhoons, cold air outbreaks, and W. Han (B) · R. Yin · X. Shen · H. Wang · J. Wang · Y. Liu CMA Earth System Modeling and Prediction Centre (CEMC), Beijing, China e-mail: [email protected] R. Yin e-mail: [email protected] X. Shen e-mail: [email protected] H. Wang e-mail: [email protected] J. Wang e-mail: [email protected] Y. Liu e-mail: [email protected] J. Li National Satellite Meteorology Center (NSMC), Beijing, China D. Di Nanjing University of Information Science and Technology, Nanjing, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_8

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rainstorms. This paper will discuss the recent progress, current major challenges of GeoHIS assimilation based on the evaluation and assimilation of the real GeoHIS data from GIIRS. Keywords Targeted observing · Geostationary hyperspectral infrared sounders · Data assimilation · Typhoon forecasts · Fengyun satellites

8.1 Background Many thousands of channels are present in hyperspectral infrared (IR) sounders, which together offer excellent vertical resolution and the capacity to precisely monitor temperature and humidity profiles (Smith et al. 2009, 2021; Okamoto et al. 2020; Han et al. 2021). However, the temporal coverage of polar hyperspectral IR sounders is inadequate, which limits their ability to analyze and predict rapid changing weather events. High-temporal geostationary hyperspectral IR sounder (GeoHIS) radiance measurements can continuously detect atmospheric temperature and humidity and can capture the temporal and spatial variability of high-impact weather or rapid evolving weather systems. In 2019, the WMO 2040 vision for the space-based component of the Integrated Global Observing System (WIGOS) for the operational geostationary satellite constellation included GeoHIS (WMO 2020). On December 10, 2016, China’s FengYun-4A satellite (FY-4A) was successfully launched into geostationary orbit. The Geostationary Interferometric Infrared Sounder (GIIRS) onboard FY-4A usher in a new era in Earth observation system. It provides the first time-continuous observations of upwelling thermal infrared with high-spectral resolution (Yang et al. 2017). FengYun-4B satellite (FY-4B) was launched on June 3, 2021, and it also carries GIIRS, which is currently the second GeoHIS in orbit internationally. Except for GIIRS, the Infrared Sounder (IRS), as a part of Meteosat Third Generation (MTG3), is an operational advanced GeoHIS that is being developed by EUMETSAT for the Exploitation of Meteorological Satellites in the mid-2020s. JMA also has begun to discuss the follow-up plans for the operational geostationary (GEO) satellites Himawari-8 and Himawari-9, which are scheduled to operate until 2029. Based on the real GeoHIS data from GIIRS, this paper will discuss the recent progress, current major challenges of GeoHIS assimilation.

8.2 Progresses of GeoHIS Assimilation GIIRS onboard FY-4A and FY-4B is the only GeoHIS currently in orbit, while EUMETSAT will have IRS in GEO orbit in 2024 time frame and NOAA is planning to have GEO-XO satellite with hyperspectral IR sounder around 2035 (see Fig. 8.1).

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Fig. 8.1 Preliminary GEO-XO constellation concept. From NOAA (2023)

This section will discuss the most recent GeoHIS assimilation progress based on the assessment and assimilation of the actual observation data from GIIRS.

8.2.1 The Evaluation of FY-4A GIIRS FY-4A’s GIIRS is the first hyperspectral IR sounder on board a GEO weather satellite. Statistical evaluation of the departures of GIIRS observations from CMA-GFS (Global Numerical Weather Prediction System of China Meteorological Administration) shows that the mean biases for most longwave infrared (LWIR) channels are within ± 2 K after quality control and within ± 0.02 K after bias correction except for the contaminated channels (Yin et al. 2020). Figure 8.2 shows the bias characteristics for the GIIRS LWIR channels 2–120 on August 2017 after quality control (QC). Except for the contaminated channels (LWIR channels 38–64), the noise level (magenta line) of GIIRS LWIR channels 2–120 is generally below 0.1 K@300 K and the standard deviation (STD) (error bar) is around 0.02 K. Overall, the observation minus background (O–B) mean biases (green curve) and STD (red curve) of the contaminated channels are larger than the other channels, the maximum values of these channels potentially reaching − 8 K and 5 K, respectively. For the upper troposphere channels (channels 2–20), the O–B mean biases vary from − 1.5 to 0 K and the STD is less than 1 K. The O–B mean biases of the middle tropospheric channels (channels 21–30) are between − 2.5 and 2 K with large fluctuation, and the STD is about 1 K, which is relatively stable. However, there is a large fluctuation (between − 3 and 2 K) in the O–B bias of the

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Fig. 8.2 Biases for GIIRS LWIR channels 2–120. From Yin et al. (2020). © 2020 John Wiley and Sons. Used with permission

channels in the lower troposphere (channels 71–90), and the STD is about 1 K. For surface channels 91–120, the O–B mean biases are generally between ± 1.5 K, but the STD is larger, varying between 1 and 1.5 K. The latitudinal dependences of mean biases and STD are obvious due to the FOVs array observation mode, and the biases and STD of GIIRS for longwave sounding channels have fields of view (FOVs) dependencies that are smaller near the center of the FOVs and become larger to the north/south ends with maximum values in the 32nd and 96th FOVs (with channel 6 as an example, as shown in Fig. 8.3).

8.2.2 Impact of Assimilating High-Temporal Resolution FY-4A GIIRS on Typhoon On July 10, 2018, targeted observations over a period of 36 h were made for Typhoon Maria (2018) using FY-4A GIIRS with a high-temporal resolution of 15 min. Based on this case, Yin et al. (2021) compared the impact of different observation frequencies and showed the added value of high-temporal-resolution GeoHIS. The variation in the background field (black line), as seen in Fig. 8.4, is significant during the assimilation period. Therefore, in order to modify the initial field, the model requires adequate information regarding the variation in atmospheric structure over both time and space (Schmit et al. 2009). The TC diurnal variation may be associated with changes in typhoon structure and intensity, according to studies (Dunion et al. 2014; Tang and Zhang 2016), which also suggests that continuous atmospheric information is crucial for typhoon forecasts. However, the temporal variation in GIIRS observations is much less for GIIRS assimilation with a lower-temporal resolution (Fig. 8.4a), which does not meet the background field’s requirements for temporal variation. With increasing temporal resolution, the temporal fluctuations in the observed BTs fluctuate noticeably more. The GIIRS observed BTs change widely

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Fig. 8.3 Temporal variations (a), spatial distributions (biases in b, STD in c) and FOVs dependences of the biases (d) and noise NeDT (e) for channel 6. From Yin et al. (2020). © 2020 John Wiley and Sons. Used with permission

with measurements made every 15 min for assimilation (Fig. 8.4d), suggesting that GIIRS does collect more precise temporal and spatial temperature and humidity structure data. As a result, it can satisfy the need for background field alteration and so enhance the analysis field. We compare track forecasts after GIIRS assimilation to the CTRL, it is evident that the GIIRS assimilation brings the forecasts closer to the Best Track (as shown in Fig. 8.5). The track forecasts are improved quite significantly as track errors are

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Fig. 8.4 Averaging over the whole GIIRS measured region, the black line depicts the simulated BTs from background field in channel 100. The four GIIRS trials are represented as a, b, c, and d in that order (3 h, 1 h, 30 min, and 15 min). From Yin et al. (2021). © 2021 John Wiley and Sons. Used with permission

reduced by 43% (15 min), 40% (30 min), 28% (1 h), and 18% (3 h) from 0000 UTC on 10 July 2018, respectively. As a result of the tremendous information about the atmospheric structure and superior initial fields for the model forecast, GIIRS assimilation with higher-temporal resolution shows better track forecast than experiments with lower-temporal resolution.

8.2.3 Impacts of GIIRS Water Vapor Channels Assimilation On July 20, 2021, a record-breaking heavy rainstorm struck China’s Henan Province. The high-temporal resolution FY-4A GIIRS water vapor (WV) channel data is assimilated in the high-resolution CMA-MESO (Mesoscale Weather Numerical Forecast System of China Meteorological Administration) in Yin et al. (2022) study to examine the effects of the GIIRS data assimilation on model analysis and forecasts of this rainfall event. The vertical cross-sections of the water vapor flux along 34.71° N in the 24 and 32 h forecast fields, initialized from 0000 UTC on July 19, 2021, are shown in Fig. 8.6. Figure 8.6b demonstrates that the GIIRS experiment’s water vapor flux was moist

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Fig. 8.5 36 h/30 h track forecast for Typhoon Maria from 0000 UTC (top)/0600 UTC (bottom) on July 10th, 2018. The Best Track, CTRL, 15 min, 30 min, 1 h, and 3 h are represented by the colors black, blue, red, green, cyan, and magenta, respectively. From Yin et al. (2021). © 2021 John Wiley and Sons. Used with permission

and deep at 900 hPa near Zhengzhou. The differences between the two experiments demonstrate that, with GIIRS assimilation, the WV flux in Henan Province (113°– 115° E) grew obviously (Fig. 8.6c). This creates an appropriate water vapor environment for an intense precipitation event to occur on July 20 in Henan. Meanwhile, the excessive hourly rainfall (201.9 mm) at Zhengzhou at that time was consistent with the noticeable wet layer that was seen near Zhengzhou in the GIIRS experiment (Fig. 8.6e), which reached from the ground to around 600 hPa. Figure 8.6f demonstrates that the WV flux clearly increased after the assimilation of the GIIRS WV channels. The wet layer in Henan, particularly in Zhengzhou, grew thicker and deeper, stretching to more than 500 hPa, which was favorable to improve the precipitation forecast. The model WV analysis might be improved by the GIIRS WV radiance assimilation, which would then alter the distributions of hydrometeors and the wind field, ultimately leading to an improved precipitation forecast. The location error of the maximum 24 h accumulated precipitation forecast is improved by 77.45% with the GIIRS WV data assimilation for the cold-start experiment at 0000 UTC on July 19, 2021, and by about 60.52% for the warm-start experiment at 0600 UTC on July 19,

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Fig. 8.6 Vertical cross sections along 34.71° N of water vapor flux (kg m−1 s−1 ) of GIIRS experiment (b), CTRL experiment (a), and their differences (c) at 0000 UTC on July 20, 2021 (24 h forecast initialized from 0000 UTC on July 19, 2021). d–f The same as a–c, but for 0800 UTC on July 20, 2021 (32 h forecast). Zhengzhou station is indicated by the black arrow. From Yin et al. (2022). © 2022 Authors. Distributed under CC BY 4.0

2021 (Fig. 8.7). Additionally, the GIIRS assimilation experiment displays an area of very heavy rainfall (above 250 mm/24 h) around Zhengzhou station that is closer to the observed extreme precipitation than the CTRL experiment. This study illustrates the potential benefits of using observation from GeoHIS into the early warning and forecasting of extreme weather.

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Fig. 8.7 Predicted 24 h accumulated precipitation from 0000 UTC on July 20, 2021 to 0000 UTC on July 21, 2021 (shading; mm) by the CTRL (a) and GIIRS (b) experiments from the cold-start at 0000 UTC on July 19, 2021, and from the warm-start at 0600 UTC on July 19, 2021 (c, d). The center of the heaviest precipitation is represented by the black dot. e The 24 h total observation precipitation. From Yin et al. (2022). © 2022 Authors. Distributed under CC BY 4.0

8.3 How to Best Use the High-Temporal GeoHIS in NWP The high-temporal resolution of GeoHIS is its main benefit. Both an opportunity and a challenge exist in determining how to employ the GeoHIS high-temporal and high-spectral observations in data assimilation. The 4DVAR is still one of the most advanced data assimilation methodologies for the use of temporal near-continuous observations, both theoretically and practically (Lean et al. 2021), despite significant advancements in data assimilation methodologies over the past 20 years, such as some recent techniques based on machine learning. There is an obvious benefit to producing

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analyses and predictions utilizing the high-temporal observations for regional NWP systems that are designed to forecast sub-synoptic and mesoscale characteristics with correspondingly short predictability time scales. These typically employ hourly cycling data assimilation systems with a 1 h assimilation window (Smith et al. 2020) demonstrating that the addition of GeoHIS (i.e., FY-4A GIIRS) to the combined polar hyperspectral and GEO multispectral satellite data used to initialize the numerical forecast model with hourly assimilation cycle improves hazardous precipitation forecasts. This enhancement is due to the inclusion of vertical soundings with hyperspectral resolution rather than only multispectral resolution in the gaps in space and time between the polar hyperspectral data. When high-spatial-resolution and hightemporal-resolution hyperspectral sounding instruments are carried on the upcoming worldwide system of GEO satellites, improvements in global hazardous weather forecasting can be anticipated.

8.4 Summary and Discussion GeoHIS provides new information and added value for nowcasting and NWP forecasting. As the precursor data of the future global GeoHIS observing system, GIIRS measurements from Chinese FengYun-4A and FengYun-4B provide unique opportunity on understanding the impact of geostationary sounding information on NWP, the LWIR measurements have been successfully assimilated in the CMA operational NWP system (CMA-GFS), and improvements are found on predicting high-impact weather events such as tropical cyclones and cold waves. GIIRS middle wave (MW) measurements are being evaluated and positive impact on precipitation forecasts is found; they will also be operationally assimilated in CMA-GFS soon. GIIRS provides flexible observing mode for targeted observations, which provides more frequent observations specifically for the weather-sensitive region where the highimpact weather usually occurs. Those targeted observations provide unique value for improving the monitoring, simulating, and predicting severe weather from the current numerical weather models. It has been demonstrated using the CMA-GFS that higher-temporal resolution provides better positive impact on tropical cyclone forecasts, which confirms the importance of high-temporal resolution soundings from geostationary orbit. The high-temporal resolution is not only valuable for the assimilation, but also is important for improving derived products such as fourdimensional horizontal winds (Ma et al. 2021). For example, winds from 15 min GIIRS measurements are better than those from the 30 min GIIRS measurements. For successful assimilation of GIIRS data, understanding the sources of observation errors and quality control of the data is extremely important, the detector array-dependent observation errors need to be well quantified. Both spectral and radiometric calibration uncertainties need to be carefully understood and considered in the assimilation system. Improving calibration remains challenge and needs to be further investigated, especially for the middle wave band. There are also other significant topics for future work, one task is to assimilate the data under cloudy skies. While

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direct assimilation of cloudy radiances requires accurate radiative transfer model, assimilation of cloud-cleared radiances (CCRs) from partially cloud-filled FOVs is an effective approach, the CCRs can be derived through combining GIIRS with collocated high spatial resolution data from imager (AGRI) onboard the same platform (Li et al. 2022). Another important topic is the assimilation of dynamic information from GIIRS, with both thermodynamic information from GIIRS assimilated, the added value of dynamic information (e.g., four-dimensional horizontal winds) needs to be studied and understood, especially for predicting the high-impact weather events. Assimilation of GIIRS data in high-resolution regional numerical model has been started, more efforts are needed to realize the benefits of high-temporal resolution GeoHIS in regional NWP for rapid changing weather forecasting, through 3DVAR, 4DVAR, or other assimilation approaches, the representative errors of GIIRS for regional NWP should be investigated before assimilation. In addition, using large angle data can further benefit the NWP applications, which remains a challenge for study. In summary, GIIRS provided very valuable data for NWP applications and demonstrations before other international GeoHIS (e.g., MTG-IRS is to be launched in 2024time frame, and hyperspectral IR sounders are planned for Himawari-8/-9 follow-on satellite in 2029 time frame and GEO-XO sounder satellite in 2035 time frame). Acknowledgements This work was supported by the National Natural Science Foundation of China (42075155, 42205158, and U2142201).

References Dunion JP, Thorncroft CD, Velden CS (2014) The tropical cyclone diurnal cycle of mature hurricanes. Mon Weather Rev 142:3900–3919. https://doi.org/10.1175/MWR-D-13-00191.1 Han W, Knuteson R, Li J et al (2021) Assimilation of geostationary hyperspectral infrared sounders (GeoHIS): opportunities and challenges. JCSDA Q Newsl 69:1–11. https://doi.org/10.25923/ KZKY-4383 Lean P, Hólm EV, Bonavita M et al (2021) Continuous data assimilation for global numerical weather prediction. Q J R Meteorol Soc 147:273–288. https://doi.org/10.1002/qj.3917 Li J, Geer AJ, Okamoto K et al (2022) Satellite all-sky infrared radiance assimilation: recent progress and future perspectives. Adv Atmos Sci 39:9–21. https://doi.org/10.1007/s00376-021-1088-9 Ma Z, Li J, Han W et al (2021) Four-dimensional wind fields from geostationary hyperspectral infrared sounder radiance measurements with high temporal resolution. Geophys Res Lett 48:e2021GL093794. https://doi.org/10.1029/2021GL09379 NOAA (2023) GEO-XO | NOAA National Environmental Satellite, Data, and Information Service (NESDIS). https://www.nesdis.noaa.gov/GEO-XO. Accessed 8 Feb 2023 Okamoto K, Owada H, Fujita T (2020) Assessment of the potential impact of a hyperspectral infrared sounder on the Himawari follow-on geostationary satellite. SOLA 16:162–168. https:// doi.org/10.2151/sola.2020-028 Schmit TJ, Li J, Ackerman SA et al (2009) High-spectral- and high-temporal-resolution infrared measurements from geostationary orbit. J Atmos Ocean Technol 26(11):2273–2292. https://doi. org/10.1175/2009jtecha1248.1

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Smith WL, Revercomb H, Bingham G et al (2009) Technical note: evolution, current capabilities, and future advance in satellite nadir viewing ultra-spectral IR sounding of the lower atmosphere. Atmos Chem Phys 9:5563–5574. https://doi.org/10.5194/acp-9-5563-2009 Smith WL, Zhang Q, Shao M et al (2020) Improved severe weather forecasts using LEO and GEO satellite soundings. J Atmos Ocean Technol 37:1203–1218. https://doi.org/10.1175/JTECH-D19-0158.1 Smith WL, Revercomb H, Weisz E et al (2021) Hyperspectral satellite radiance atmospheric profile information content and its dependence on spectrometer technology. IEEE J Sel Top Appl Earth Obs Remote Sens 14:4720–4736. https://doi.org/10.1109/JSTARS.2021.3073482 Tang X, Zhang F (2016) Impacts of the diurnal radiation cycle on the formation, intensity, and structure of Hurricane Edouard (2014). J Atmos Sci 73(7):2871–2892. https://doi.org/10.1175/ JAS-D-15-0283.1 WMO (2020) Vision for the WMO integrated global observing system in 2040. https://public.wmo. int/en/resources/library/vision-wmo-integrated-global-observing-system-2040. Accessed 8 Feb 2023 Yang J, Zhang Z, Wei C et al (2017) Introducing the new generation of Chinese geostationary weather satellites—FengYun-4 (FY-4). Bull Amer Meteor Soc 98(8):1637–1658. https://doi. org/10.1175/BAMS-D-16-0065.1 Yin R, Han W, Gao Z et al (2020) The evaluation of FY4A’s geostationary interferometric infrared sounder (GIIRS) long-wave temperature sounding channels using the GRAPES global 4D-Var. Q J R Meteorol Soc 146(728):1459–1476. https://doi.org/10.1002/qj.3746 Yin R, Han W, Gao Z et al (2021) Impact of high temporal resolution FY-4A geostationary interferometric infrared sounder (GIIRS) radiance measurements on Typhoon forecasts: Maria (2018) case with GRAPES global 4D-Var assimilation system. Geophys Res Lett 48(15):e2021GL093672. https://doi.org/10.1029/2021GL093672 Yin R, Han W, Wang H et al (2022) Impacts of FY-4A GIIRS water vapor channels data assimilation on the forecast of “21·7” extreme rainstorm in Henan, China with CMA-MESO. Remote Sens 14(22):5710. https://doi.org/10.3390/rs14225710

Chapter 9

Evaluating the Assimilation of Observable and Retrievable Weather Radar Information for Quantitative Precipitation Forecasts Kao-Shen Chung, Chih-Chien Tsai, Chieh-Ying Ke, Phuong-Nghi Do, and Yu-Chieng Liou

Abstract By using an ensemble data assimilation system, this chapter reviews the impact of assimilating observable and retrievable ground-based scanning weather radar information. Pseudo-observations of temperature, humidity, and dualpolarimetric parameters are assimilated in addition to radial velocity and reflectivity. Instead of assimilating the information inside the weather system, retrieved moisture information surrounding precipitation systems could be further obtained by collocated dual-wavelength radars. Via the studies of idealized and different high-impact weather cases, analyses and quantitative precipitation forecasts are examined and validated. Keywords Radar observations · Mesoscale meteorology · Thermodynamic retrievals · Cloud microphysics · Quantitative precipitation forecast

K.-S. Chung (B) · C.-Y. Ke · Y.-C. Liou Department of Atmospheric Sciences, National Central University, Taoyuan City, Taiwan e-mail: [email protected] C.-Y. Ke e-mail: [email protected] Y.-C. Liou e-mail: [email protected] C.-C. Tsai National Science and Technology Center for Disaster Reduction, New Taipei City 23143, Taiwan P.-N. Do Scripps Institution of Oceanography, University of California, San Diego, CA, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_9

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9.1 Introduction Among modern meteorological instruments, weather radars provide the most complete three-dimensional observation information on precipitation systems at high spatial and temporal resolution. Radial velocity (Vr ) comprises the projections of three-dimensional wind velocities and hydrometeor terminal velocity on the radial direction. Reflectivity (Z H ) and dual-polarimetric variables reflect various microphysical properties of hydrometeors, including the size, shape, orientation, and number concentration (Zrnic and Ryzhkov 1999). Therefore, assimilating these radar observations into numerical weather prediction (NWP) models have been a mainstream method for decades to analyze and predict the dynamical and cloud microphysical states of severe weather systems at convective scales and consequently to improve quantitative precipitation forecasts (QPFs) (e.g., Sun 2005; Xiao and Sun 2007; Jung et al. 2008; Zhang et al. 2009; Li et al. 2012). Although radar data assimilation has shown some improvement in quantitative precipitation forecasts (QPFs), it has been observed that the impact of assimilating traditional radar observations, such as V r and Z H , is limited. In a study conducted by Ge et al. (2013) using a three-dimensional variational (3DVar) system and observing system simulation experiments (OSSEs), it was found that dynamic variables such as horizontal wind play a major role in analyzing storm structure at convective scales. Additionally, the study showed that thermodynamic variables, such as temperature and humidity, are more effective than hydrometeor variables in reconstructing severe storms. This is because hydrometeors are primarily lagging indicators of thermodynamic processes and can rapidly evaporate or precipitate without supporting wind, temperature, and humidity conditions. Various studies have investigated the assimilation of thermodynamic information in addition to radar data. For instance, Wattrelot et al. (2014) assimilated retrieved humidity profiles and radar data using a 1D + 3DVar assimilation method and demonstrated improvements in analysis and shortterm forecasts. Kerr et al. (2015) evaluated the effect of assimilating both retrieved cloud-top temperature from satellite data and radar observations, while Caumont et al. (2016) assimilated retrieved temperature and humidity profiles from groundbased microwave radiometers. In another study, Sun et al. (2020) assimilated rainfall estimated from radar and surface observations and showed the important role of assimilating rainfall in correcting moisture and temperature. However, despite these efforts, the improvement in quantitative precipitation forecast by assimilating traditional radar observations, such as radial velocity and reflectivity, is limited. Recent studies have explored alternative strategies to modify humidity or temperature or both, including the use of vertical integrated liquid water content or differential reflectivity columns (Carlin et al. 2017; Lai et al. 2019), which have demonstrated significant utility in predicting high-impact weather events. However, Fabry and Meunier (2020) have noted that utilizing radar data assimilation for temperature and humidity modification is challenging. While radar assimilation does lead to notable corrections in precipitation and wind components, unobserved variables such as temperature and humidity are only minimally updated from the background.

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The aforementioned studies proved the positive impact of assimilating temperature and/or humidity information on QPFs. However, the spatial distribution of the assimilated temperature data were either 1D or two-dimension (2D), and the utilized moisture data were only available inside precipitation systems. On the other hand, a minor variation in environmental humidity can result in significant changes in the rain pattern and intensity (Fabry and Meunier 2020). The information on moisture surrounding the convection system is crucial for forecasting storm initiation. Based on these reasons, our studies utilize a developed radar data assimilation system that couples the Weather Research and Forecasting (WRF; Skamarock et al. 2021) model with the local ensemble transform Kalman filter (LETKF; Hunt et al. 2007), named the WRF-LETKF radar assimilation system (WLRAS; Tsai et al. 2014), and expand its observation operators for more observable or retrievable weather information (You et al. 2020; Tsai and Chung 2020; Do et al. 2022; Ke et al. 2022). The purpose is to, under the same assimilation infrastructure, evaluate the different benefits from different weather information to convective-scale analyses and short-term forecasts, especially the challenging QPFs. In the next section, the WLRAS system, observation operators, and retrieval algorithms for pseudo-observation fields are introduced. Section 9.3 presents the impact of assimilating additional information observed or retrieved from scanning radars. Section 9.4 summarizes the findings in this study.

9.2 Methodology 9.2.1 WRF-LETKF Radar Assimilation System (WLRAS) The WRF model is a world-famous regional NWP model developed by the National Center for Atmospheric Research and used by many research and operational agencies. The governing equations are compressible and nonhydrostatic in a terrainfollowing coordinate system, and a rich collection of sophisticated dynamical and physical schemes are available. The prognostic variables contain three-dimensional wind velocities, perturbation moist potential temperature, perturbation geopotential, perturbation dry air surface pressure, and optional scalar variables, such as the mixing ratios of water vapor and different hydrometeor species. LETKF is an advanced data assimilation scheme developed by the University of Maryland (Ott et al. 2004) and complete derivation can be found in Hunt et al. (2007). It belongs to the family of ensemble Kalman filters (EnKFs; Evensen 1994; Bishop et al. 2001; Anderson 2001; Whitaker and Hamill 2002), which analyze an ensemble that estimates the mean and uncertainty of the model state, and to the branch of deterministic EnKFs, which do not need to perturb observations during the assimilation process. At an LETKF analysis step, the ensemble mean increment and ensemble perturbations of the prognostic variables at each model grid point are calculated from the linear combination of background perturbations as

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xa = xb + Xb w,

(9.1)

Xa = Xb W,

(9.2)

where x is the ensemble mean, X is the ensemble perturbations, subscripts b and a denote background and analysis, respectively, w and W are the weighting coefficient vector and matrix, derived as w = P˜ a YbT R−1 yo − yb , W = (K − 1)P˜ a

1/2

(9.3)

,

(9.4)

and P˜ a is the analysis error covariance matrix in ensemble space, derived as P˜ a = (K − 1)I/ρ + YbT R−1 Yb

]−1

,

(9.5)

where yo is the assimilated observations near the model grid point, yb and Yb are the background ensemble mean and perturbations in observation space, respectively, R is the observation error covariance matrix, I is the identity matrix, K is the ensemble size, ρ is the multiplicative covariance inflation factor. There are several advantages of the LETKF data assimilation scheme. Firstly, the flow-dependent, ensemble-based background error statistics of LETKF make this scheme comparable to the four-dimensional variational (4DVar; Le Dimet and Talagrand 1986) scheme and better than 3DVar in analysis accuracy. Secondly, unlike 4DVar that requires coding tangent linear and adjoint models, it is easier to adapt LETKF to different NWP models because this scheme only handles the inputs and outputs of NWP models, treated as black boxes. Thirdly, the NWP model and observation operator can be fully nonlinear in LETKF to account for the nonlinearities of atmospheric processes. Lastly, the analysis of every prognostic variable (row in Eqs. 9.1 and 9.2) at every model grid point can be parallelly processed, and therefore various inflation and localization techniques acting on the covariances between prognostic and observation variables are available, such as adaptive inflation (Miyoshi 2011), variable localization (Kang et al. 2011), and mixed localization (Tsai et al. 2014). Coupling the WRF model with LETKF, Tsai et al. (2014) coded WLRAS along with its observation operators for Vr and Z H under single-moment cloud microphysics and validated its capability to improve short-term QPFs. Since then, the authors have continued to expand its observation operators for dual-polarimetric radar variables, including Z H , differential reflectivity (Z DR ), and specific differential phase (K DP ) under multi-moment cloud microphysics, and for thermodynamic variables, including temperature (T ) and water vapor mixing ratio (qv ). All the observation operators and utilized retrieval algorithms for thermodynamic variables are

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described in the following sections, prior to the experimental results of the follow-up studies in Sect. 9.3.

9.2.2 Observation Operators Radial Velocity In terms of Vr , the observation operator is described as Vr = [u(x − xi ) + v(y − yi ) + (w − vt )(z − z i )] x 2 + y 2 + z 2

−1/2

,

(9.6)

where x, y, and z are the Cartesian coordinates with the origin at the radar site, x i , yi , and zi are the coordinates of the target (hydrometeors), u, v, and w are the zonal, meridional, and vertical winds, respectively. The terminal velocity vt can be computed by assuming a Marshall–Palmer drop size distribution (Marshall and Palmer 1948) as follows: vt = 5.40( p0 / p)0.4 (ρa qr )0.125

(9.7)

where p0 and p denote the surface pressure and base-state pressure, respectively, ρa is the air density, qr is the rain mixing ratio.

Reflectivity Under Single-Moment Cloud Microphysics The Z H observation operator is subject to the size distributions of rain, snow, graupel, and/or hail assumed by the cloud microphysical parameterization scheme. When the single-moment, three-ice Goddard Cumulus Ensemble (GCE; Tao et al. 2003) scheme is in use, the reflectivity factor (Z ) is calculated by summing the components contributed from rain (Z r ), wet snow (Z ws ), dry snow (Z ds ), and graupel (Z g ) as Z = Z r + Z ws + Z ds + Z g ,

(9.8)

where the components can be derived as Z r = 3.63 × 109 (ρa qr )1.75 ,

(9.9)

Z ws = 1.21 × 1011 (ρa qs )1.75 if T > 0 ◦ C,

(9.10)

Z ds = 2.79 × 108 (ρa qs )1.75 if T ≤ 0 ◦ C,

(9.11)

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Z g = 1.12 × 109 ρa qg

1.75

,

(9.12)

where qr , qs , and qg are the mixing ratios of rain, snow, and graupel, respectively.

Reflectivity, Differential Reflectivity, and Specific Differential Phase Under Multi-moment Cloud Microphysics To make WLRAS further compatible with dual-polarimetric radar variables and various multi-moment cloud microphysical parameterization schemes, the Z H , Z DR , and K DP observation operators developed by Jung et al. (2008) are incorporated. For every hydrometeor species, including mixed-phase species generated via a melting ice model, the reflectivity factors at horizontal and vertical polarizations (Z h and Z v ) and K DP can be derived as +μ+1 [ ] 2βaμ+4 6ρa q 4λ4 N0 (2βa + μ + 1) Aαa2 + Bαb2 + 2Cαa αb , Zh = π N0 (μ + 4)ρ π 4 |K w |2 (9.13) +μ+1 [ ] 2βbμ+4 6ρa q 4λ4 N0 (2βb + μ + 1) Bαa2 + Aαb2 + 2Cαa αb , Zv = π N0 (μ + 4)ρ π 4 |K w |2 (9.14) ⎫ ⎧ βa +μ+1 μ+4 ⎪ ⎪ 6ρa q ⎬ 180λN0 Ck ⎨ αa (βa + μ + 1) π N0 (μ+4)ρ K DP = , (9.15) βb +μ+1 ⎪ ⎪ μ+4 π 6ρa q ⎭ ⎩ − α (β + μ + 1) b b π N0 (μ+4)ρ

where λ is the radar wavelength, K w is the dielectric constant of water, q is the hydrometeor mixing ratio, ρ is the hydrometeor density, N0 and μ are respectively the intercept and shape parameters of the gamma hydrometeor size distribution, α and β are respectively the constant and exponent of the fitted power-law functions for simulated backscattering amplitudes, a and b respectively denote horizontal and vertical axes, A, B, and C are coefficients accounting for the canting behavior of falling hydrometeors. By summing up the contributions from all the hydrometeor species, the total Z H , Z DR , and K DP are calculated as Z H = 10 log10

Z h,x ,

(9.16)

Z h,x , Z v,x

(9.17)

x

Z DR = 10 log10

x x

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K DP =

K DP,x ,

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(9.18)

x

where x is the type of hydrometeor, x can be rain, snow, graupel, or hail.

9.2.3 Retrieval Algorithms for Pseudo-Observation Fields Terrain-Permitting Thermodynamic Retrieval Scheme (TPTRS) The 3D thermodynamic variables (T and qv ) inside a precipitation system can be obtained from the Terrain-Permitting Thermodynamic Retrieval Scheme (TPTRS) by using three-dimensional (3D) wind fields at two successive (e.g., 15 min interval) moments. Three fundamental equations of motion are used in the algorithm to derive thermodynamic fields (Liou et al. 2003), including moisture-related contributions: ] [ ∂π ' 1 ∂u + V · ∇u − f v + turb(u) = − ≡−F θv0 ∂t ∂x [ ] 1 ∂v ∂π ' + V · ∇v + f u + turb(v) = − ≡ −G θv0 ∂t ∂y [ ] ∂π ' θ' 1 ∂w + V · ∇w + turb(w) + gqr = − +g c ≡−H θv0 ∂t ∂z θv0 θ0 u

∂θ ' ∂θ ' ∂θ0 ∂θc' +v c +w c +w +S=0 ∂x ∂y ∂z ∂z

(9.19) (9.20) (9.21) (9.22)

where f is the Coriolis parameter, g is the gravitational acceleration, qr is rain mixing ratio, which can be estimated by radar reflectivity, turb(…) is a subgrid-scale turbulence parameterization operator that can be parameterized using a simple firstorder closure scheme, a normalized pressure (π ) is obtained (Exner function), and it is defined as π = Cp

P Poo

R Cp

(9.23)

Here, θ v is the virtual potential temperature, P is the air pressure, Poo is the reference pressure of 1000 hPa, R is the gas constant for dry air, and C p is the specific heat capacity at constant pressure. The θ vo term denotes the basic state of the virtual potential temperature. The S term represents the total effect of various processes such as temporal variation, diffusion, and source/sink through microphysical processes (Liou 2001). In this study, the S term is considered as a retrievable parameter and no additional parameterizations are applied.

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Furthermore, the contributions of vapor, cloud, and rainwater are included to estimate the buoyancy force. The virtual potential temperature (θvir ) and virtual cloud potential temperature perturbation (θc ; Roux 1985) are defined by θvir = θ (1 + 0.61qv )

(9.24)

θc' = θ ' + 0.61qv' − qc θ0

(9.25)

where θ0 is potential temperature, qv' (unit: g kg−1 ) is the perturbation of the water vapor mixing ratio based on its basic statistics, qc (unit: g kg−1 ) is the cloud water mixing ratio. The moisture adjustment method used in this study is based on the approach proposed by Liou et al. (2014), which involves iterative techniques for adjusting temperature and moisture fields. Specifically, the temperature is transformed into virtual cloud potential temperature (θ vc ) using Eq. (9.25). This thermodynamic field is then derived from the temperature perturbation field, while the cloud water mixing ratio is determined from the model. The dew-point temperature (Td ) is calculated using the reversed surface water vapor mixing ratio and pressure: Td =

B ln(Aε/qv P)sfc

(9.26)

A = 2.533 × 108 kPa

(9.27)

B = 5.417 × 103 K

(9.28)

ε = 0.622

(9.29)

qv = qv' + qv0 .

(9.30)

When Z H values exceed 10 dBZ, the corresponding grid points are considered to be saturated. The water vapor mixing ratio is calculated for these points, and the basic state water vapor mixing ratio is subtracted from it, resulting in a new qv' . This value is then used in Eq. (9.25) to obtain a new potential temperature perturbation field (θ ' ). The difference between the newly obtained and previously obtained water vapor perturbation and potential temperature perturbation fields is calculated. If this difference is below the threshold value, the iterative water vapor adjustment procedure is terminated, resulting in a new qv' and θ ' . For the temperature field, the threshold is set at 5 × 10−5 , whereas for the water vapor mixing ratio, the threshold is 5 × 10−2 .

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Retrieving Humidity from Dual-Wavelength Radar Observations In this study, the difference in atmospheric attenuation between radar observations of two different wavelengths is utilized to estimate the mean water vapor content (Ellis and Vivekanandan 2010). The Ka-band attenuation, with a shorter wavelength (8 mm), has a much stronger dependence on water vapor compared to the S-band (10 cm). The Ka-band Z H value is subtracted from the S-band Z H at the end of the radar ray segments, and combined with the range to obtain the Ka-band total atmospheric attenuation through a cloud- and precipitation-free atmosphere. Liebe’s microwave propagation model is used to define the water vapor density on several ray segments based on the relation between humidity and attenuation. The retrieved water vapor density is assigned to the height of the midpoint of the ray segment. The mixing ratio of water vapor (qv ) was estimated using the retrieved water vapor density (ρw ) from S- and Ka-band dual-wavelength (S-PolKa) and sounding data near the radar site. To calculate the density of dry air, the temperature (T ) and pressure of dry air (P) were obtained by subtracting the actual vapor pressure from the total air pressure, as follows: ρd =

P RT

(9.31)

where R is the ideal gas constant that equals 287.05 J (kg K)−1 . Then, qv can be obtained as follows: qv =

ρw ρd

(9.32)

9.3 Impact of Assimilating Observable and Retrievable Weather Radar Data 9.3.1 Assimilation of Retrieved Temperature and Humidity This study investigates the effect on analyses and forecasts of assimilating highdensity thermodynamic variables in addition to radar observations in a frontal system. A mesoscale convective system event accompanied by a frontal system resulted in total accumulated rainfall of more than 400 mm within 10 h, leading to flooding in northern Taiwan on June 11, 2012. We perform OSSEs to investigate the impact of assimilating weather radar data (RCWF at 121.77° E, 25.07° N and NCU-CPol at 121.18° E, 24.97° N) with additional thermodynamic variables (T and qv ) from two sources: the truth and TPTRS (Liou et al. 2019). For the OSSE, ERA-interim reanalysis data with a higher resolution of 0.75° × 0.75° are utilized as the reference to run the model. The final operational global

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analysis (FNL) data with a resolution of 1° × 1° from the National Centers for Environmental Prediction (NCEP) at 0000 UTC 11 June 2012 is employed for all the experimental simulations. By this time, the rainband in the reference data has already reached northern Taiwan, while in the control run initialized by NCEP (Fig. 9.1b), the rainband is still over the ocean. The simulated observations are generated based on the truth, while considering the uncertainty of the observations. The true states are randomly perturbed according to prescribed observation errors, which are 5 dBZ for Z H and 3 m/s for Vr as in Tsai et al. (2014), and 0.8 K for temperature (T ) and 0.8 g kg−1 for water vapor mixing ratio (qv ). Radar observation data of Z H and Vr from two radars in northern Taiwan are obtained up to a range of 230 km (180 km) from the RCWF (NCU-CPOL) site every 15 min on nine plan position indicator (PPI) elevations between 0.5° and 19.5°. To reduce the simulated observation count, the superobbing method (Alpert and Kumar 2007; Lindskog et al. 2004) is applied in this study. The results of the temperature (T ) retrieved by TPTRS show that the root mean square error (RMSE) in T is less than 0.5 K, and the bias is positive, indicating that the retrieved T is slightly warmer than the true T. The retrieved water vapor mixing

Fig. 9.1 a Improvement in spatial correlation coefficient of microphysical variables as compared to Exp. 5 (ZVr). Qg , Qs , and Qr refer to the mixing ratio of graupel, snow, and rain; b, c Fractions Skill Score (FSS) of b 1 h and c 3 h rainfall accumulation from 1400 UTC by deviation distance 24 km

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ratio (qv ) results suggest that the overall performance is slightly wetter than the true qv , with a correlation of 0.99 and an error of 0.56 g kg−1 . These experiments assume that the basic state (i.e., background fields) of T and qv is error-free, and the source of the error is from the perturbations of thermodynamic variables. The observation errors of the retrieved T and qv are set at 0.8 K and 0.8 g kg−1 , respectively, which are slightly larger than the root mean square error of the retrieved T and qv . The assimilation experiments in this study are divided into three sets. The first and second sets aim to investigate the added value of assimilating 3D thermodynamic fields in the severe weather system without any bias. Therefore, T and qv observations are obtained from the precipitation area in the experiments, and the observation operator maps the true state of T and qv on the model grid to the observation space. We define the relative spatial correlation coefficient (RSCC) using the following equation: RSCC =

SCCexp − SCCZVr × 100% SCCZVr

(9.33)

If RSCC is positive, the experiment represents positive improvement compared to ZVr. The results reveal that all the hydrometeor variables improve by approximately 10% when the assimilation period is extended (Fig. 9.1a). Assimilating T leads to additional improvements above freezing for qg and qs . However, when qv is assimilated with Vr and Z H , qr , qg , and qs improve by more than 20%. In particular, qr exhibits a more than 40% improvement when assimilated with qv (ZVrQv and ZVrTQv). Thus, radar data assimilation with additional thermodynamic variables improve the hydrometeor structure. Temperature assimilation has a positive impact on cold particle structure, and qv information affects rainwater directly. The skill scores obtained from the OSSEs (Fig. 9.1b, c) show that only the assimilation of radar data for 1 h fails to achieve a high score (scores for Z, V r , and ZVr are less than 0.5). The forecast score for ZVr2h is higher than that for ZVr, as more radar data are assimilated. The forecast skill score for ZVrT is similar to that for ZVr2h, indicating that adding 3D temperature assimilation improves the performance of radar data assimilation for short-term rainfall forecasting, and reduces the assimilation period from 2 to 1 h. The results of the OSSEs in which qv is assimilated indicate that a wetter qv field could greatly improve the rainfall forecast score in the 1–3 h QPF. This finding highlights the importance of qv in prolonging the rainfall forecast results in the frontal event examined in this study. In the final set, to mimic bias that could exist in observations retrieved from remote sensing, a retrieved 3D T and qv information with warm and wet bias is assimilated (ZVrTR, ZVrQvR, and ZVrTQvR). Figure 9.2a–c present the low-level convergence fields in the final analysis. The convergence of ZVrTR reveals comparable intensity as ZVrT and better than ZVr2h (figure not shown). Z H (Fig. 9.2d) shows a strong convective area at 1 km height as in ZVrT and the truth in northern Taiwan but does not completely reveal the line-shaped convective rainband. In ZVrQvR, the convergence (Fig. 9.2b) is weaker than ZVrTR (Fig. 9.2a). The Z H (Fig. 9.2e) shows a part of the line-shaped convective rainband in northern Taiwan. In ZVrTQvR, the

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range of convergence (Fig. 9.2c) is wider than in ZVrTR and ZVrQvR. In addition, the simulated Z H in Fig. 9.2f shows that the analysis could better represent the lineshaped area as the truth. The optimal results for convergence and Z H among the three experiments are those in which the retrieved T and qv information is assimilated with radar data by ZVrTQvR. Figure 9.2g–i depict the cross-section of vertical velocity and T fields. In the experiment that assimilates retrieved T with radar only (ZVrTR, Fig. 9.2g), the upward motion is stronger compared to ZVrQvR and ZVrTQvR. Moreover, the T perturbation exhibits a warm core at the mid-level similar to the truth, but the cold pool at the low level is limited compared to the truth and ZVrT, because retrieved T shows a warm bias. Assimilating qv only (ZVrQvR, Fig. 9.2h) weakens the warm core and upward motion at the mid-level compared to ZVrTR. However, the T perturbation exhibits a better distribution of the cold pool at the low level compared to ZVrQv

Fig. 9.2 Final analysis fields of Exps. ZVrTR (a, d, g), ZVrQvR (b, e, h), and ZVrTQvR (c, f, i) at 1400 UTC. a–c The low-level convergence field (shaded, units: 10−4 s−1 ) and wind vectors are shown at 1 km height; d–f reflectivity field on 2.5 km height; g–i vertical velocity (shaded) and potential temperature perturbation (contours, solid lines are positive values while dashed line are negative values with contours of − 1.5, − 1.2, − 0.5, 1.0, 3.0, 5.0 K) shown on vertical cross-sections as in Fig. 9.1a

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(see Fig. 13 in Ke et al. 2022). The optimal T perturbation results from ZVrTQvR (Fig. 9.2i). The results reveal that the cold pool and the warm area are close to the truth via assimilating qv and T , respectively. Moreover, assimilating retrieved T has a greater impact on the dynamic field than qv assimilation. Overall, the results demonstrate that assimilating retrieved T and qv together has a positive impact on the low-level dynamic convergence, strengthening the intensity of the cold pool near the surface and reproducing a warm core in the stratiform region of the severe weather system. The impact of assimilating retrieved thermodynamic information on QPF is examined by initializing the model from the ensemble mean of analysis. Among the experiments, ZVrTR (Fig. 9.3d) produced a local maximum rainfall of over 50 mm in the 3 h total accumulated rainfall forecast. Despite the warm bias in the retrieved T field compared to the truth, ZVrTR outperformed ZVr2h (Fig. 9.3c) in predicting the local maximum of heavy rainfall with a shorter data assimilation period (1 h). In ZVrQvR, more precipitation occurred in the first hour (not shown), but the 3 h forecast precipitation amount (Fig. 9.3e) was less than the truth and ZVrQv. The optimal result was obtained from ZVrTQvR (Fig. 9.3f), which revealed a well line-shaped pattern and coverage of rainfall accumulation over northern Taiwan, similar to the truth. Moreover, the amount of precipitation was closer to the truth (Fig. 9.3a). This feasibility study shows that assimilating the retrieved T has more impact to improve the QPF than assimilating retrieved qv . This is because a better cold pool and warm core are reproduced in the analysis when assimilating retrieved T . In addition, (a) Truth

(b) ZVr

(c) ZVr2h

(d) ZVrTR

(e) ZVrQvR

(f) ZVrTQvR

Fig. 9.3 Rainfall accumulation in northern Taiwan in d03 from 1400 to 1700 UTC for experiments a truth; b ZVr; c ZVr2h; d ZVrTR; e ZVrQvR; f ZVrTQvR

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when both retrieved T and qv information is assimilated, the result can still improve the QPF and outperform ZVr2h.

9.3.2 Assimilation of S-PolKa–Retrieved Water Vapor This section examined the effect of assimilating S-PolKa–retrieved water vapor with Z H and V r data for convective-scale weather systems. Two organized heavy rainfall events (18 and 16 October 2011) and a scattered convection event (12 October 2011) from the Dynamics of the Madden–Julian Oscillation (DYNAMO) field campaign were selected for analysis. The data for assimilation included the quality-controlled Z H and V r from the NCAR S-Pol located at Addu Atoll and the water vapor mixing ratio (Qv ) estimated from the S-PolKa–retrieved water vapor density and sounding data in the Maldives. Because of the close distance between each Qv location, two approaches were applied to thinning Qv . In the first method, all Qv observations were combined and averaged to obtain one Qv profile. The location of averaged Qv profile is at the mean latitude and longitude of all observational points. In the second method, the Qv observations were separated into four quadrants (northeast, southeast, southwest, and northwest of the radar site). In each quadrant, an averaged Qv profile was computed. In this study, WLRAS (Tsai et al. 2014) was employed to assimilate data in two hours. To investigate the benefit of assimilating additional SPolKa–retrieved Qv , three experiments were conducted. Experiment ZVr assimilated only Z and V r but in experiment ZVrQv_a and ZVrQv_4q, the extra S-PolKa– retrieved Qv was assimilated with Z and V r . One averaged Qv profile and fourquadrant Qv profiles were utilized in ZVrQv_a and ZVrQv_4q, respectively. Based on the characteristics of the retrieved moisture data which was only available in the nonprecipitation area, experiments Qv_ZVr_a and Qv_ZVr_4q were performed to investigate the assimilation strategy for the retrieved water vapor information. These two experiments solely assimilated water vapor data in the first hour and Z and V r observation in the second hour; Qv_ZVr_a and Qv_ZVr_4q used one averaged Qv profile and four-quadrant Qv profiles, respectively. To examine the impact of assimilating extra S-PolKa retrieved Qv , the Qv increment of experiments ZVr, ZVrQv_a, and ZVrQv_4q at 1 km in the first cycle was analyzed in Fig. 9.4. In all three cases, the assimilation of retrieved Qv had the capability of modifying the moisture in nonprecipiation areas near S-PolKa location with the more notable adjustment appeared in the experiment utilizing four-quadrant Qv profiles. The Qv modification in ZVrQv_a and ZVrQv_4q were verified to be more precise than those in ZVr (the values in black boxes in Fig. 9.4). Additionally, assimilating four-quadrant Qv profiles generated the optimal correction of moisture field. For a more extensive comparison, the analysis of Z H , V r , and Qv in the final cycle of all experiments are evaluated by calculating their RMSEs. The results revealed that the assimilation of additional S-PolKa–retrieved Qv (either one averaged Qv profile or four-quadrant Qv profiles) resulted in lower RMSEs of Z, V r , and Qv

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Fig. 9.4 The Qv analysis increment at 1 km at the first cycle for the a–c first case, d–f second case, and g–i third case. The increments are from experiment (left) ZVr, (center) ZVrQv_a, and (right) ZVrQv_4q. The encircled black cross indicates the S-PolKa location. The numbers in the black boxes denote the root mean square errors (RMSEs) of Qv compared with the S-PolKa–retrieved Qv observation. This figure is reproduced from Fig. 6 in Do et al. (2022)

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than the experiments assimilating only Z H and V r for all three cases. Furthermore, the strategy assimilating only Qv in nonprecipitation areas in the first hour of the assimilation period had the outperformed analyses of Z, V r , and Qv compared with assimilating all data over the entire 2 h. To further investigate the benefit of assimilating extra retrieved Qv information, the second case was selected to examine the 3 h accumulated rainfall (Fig. 9.5). All experiments could forecast heavy rainfall but the main rainband moved faster than the observation, leading to the underestimation to the southwest and overestimation to the southeast of the domain. Compared with the experiment assimilating only Z H and V r (Fig. 9.5b), the additional assimilation of S-PolKa retrieved Qv during 2 h (i.e., ZVrQv_a and ZVrQv_4q) resulted in a closer short-term forecast to observation (Fig. 9.5c, e). Both underestimations to the southwest and overestimation to the southeast of the domain were less in ZVrQv_a and ZVrQv_4q than those in ZVr. The optimal QPF was yielded in the experiments assimilating only Qv in the first hour of the assimilation period (i.e., Qv_ZVr_a and Qv_ZVr_4q; Fig. 9.5d, f). The overprediction in the southeast domain was most alleviated in these two experiments. Additionally, the intensity of the main rainband was most enhanced. The improvement of the short-term forecast obtained by the assimilation of additional Qv information was more comprehensively proved when examining QPF quantitatively. Figure 9.6 demonstrates the Fractions Skill Score (FSS) of accumulated rainfall from 1 to 4 h averaged over the three cases. Among all experiments, Qv_ ZVr_4q had the most notable enhancement during the 2–4 h forecast for most of the thresholds. For the rest of the four experiments, compared with assimilating only Z H and V r , higher FSS occurred in the experiments assimilating additional retrieved Qv information. Furthermore, the FSS indicated that the assimilation of four-quadrant Qv profiles provided more benefit for QPF than the assimilation of one averaged Qv profile. Overall, the moisture information in the nonprecipitation areas retrieved by the S-PolKa is crucial for further enhancing the analysis and forecast of convective weather systems. However, the retrieved Qv is unavailable when the convective system totally covers the radar location. Moreover, the retrieved humidity was located within 25 km of the radar center, which limited the range of moisture adjustment. In other words, assimilating S-PolKa-retrieved Qv could modify the moisture nearby the radar location.

9.3.3 Verification of Model Simulation by Dual-Pol Parameters The case of a meso-scale convective system (MCS) during Southwest Monsoon Experiment intensive observing period 8 (SoWMEX-IOP8) in 2008 is used to examine and validate the performance of numerical simulation before investigating the impact of assimilating dual-pol data. On June 14, 2008, a squall line system’s

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Fig. 9.5 Accumulated 3 h rainfall from 0200 to 0500 UTC Oct 16, 2011 for the second case. a Observation, b ZVr, c ZVrQv_a, d Qv_ZVr_a, e ZVrQv_4q, and f Qv_ZVr_4q. The encircled black cross represents the S-PolKa location. Adopted from Fig. 12 in Do et al. (2022)

evolution is depicted in Fig. 9.7. At 0930 UTC, the NCAR S-POL captured three squall line systems (A, B, and C in Fig. 9.7a), with squall line A landing and causing rainfall in southern Taiwan. Meanwhile, squall lines B and C were developing and heading toward Taiwan. These squall line systems affected southern Taiwan, resulting in a six-hour duration of exceptionally heavy rainfall.

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Fig. 9.6 The FSS score of a 1, b 2, c 3, and d 4 h accumulated rainfall. Scores are averaged across the three cases. Adopted from Fig. 14 in Do et al. (2022)

When examining the dual-pol observation operator, Contoured Frequency by Altitude Diagram (CFAD) in Fig. 9.8 shows the results of a sensitivity test for the adjustment of the total number concentration; Fig. 9.8a–c display the minimum total number concentration at 10 m−3 , 100 m−3 , and 1000 m−3 , respectively. If mixedphase hydrometeors are present, it is necessary to convert a fraction of the total number concentration. The conversion proportion equals the mixing ratio conversion fraction that is determined using coexisting hydrometeors. However, the total number concentration of mixed-phase hydrometeors is only derived from the total number concentration of snow or hail species. It is suggested that to obtain a smoother and closer structure of simulated bright band level as observed radar data, it is suggested to setup the threshold to exclude total number concentration smaller than 100 m−3 of model grid point in mixing-phase area parameters for maritime precipitation. Furthermore, the evaluation of assimilating radial wind and reflectivity is extended to the GCE and Morrison microphysics schemes in comparison to the model simulation using dual-polarimetric variables. Both squall lines exhibit strong reflectivity, up to 45–50 dBZ, and broad stratiform regions are dispersed to the west of the primary convection area. Additionally, the simulation utilizing the GCE scheme displays a

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Fig. 9.7 Evolution of squall line systems on June 14, 2008, observed by the S-band dualpolarimetric radar (S-POL) reflectivity (1.1° PPI): a 0930 UTC, b 1000 UTC, c 1030 UTC, and d 1100 UTC. The red rectangle is the selected data area of the CFAD in Figs. 9.8 and 9.9

clearer structure of the squall line than the simulation using the Morrison scheme. This information can be found in Fig. 7 of You et al. (2020) and is not shown here. In order to statistically evaluate the model’s performance, CFADs are generated to display the characteristics of the model simulation and observations. The data coverage for the selected CFAD is indicated by red boxes in Fig. 9.7d (S-POL observation) and the Analysis field (not shown, see Fig. 7 in You et al. 2020). Figure 9.9 illustrates the S-POL CFAD of Z H (Fig. 9.9a), Z DR (Fig. 9.9b), and K DP (Fig. 9.9c) at 1100 UTC on June 14, 2008. The CFADs show the radar variables at 1100 UTC

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Fig. 9.8 CFAD results of sensitivity tests on the number concentration of mixed-phase hydrometeor filtering. The filter threshold at each grid point is less than a 10 m−3 , b 100 m−3 , and c 1000 m−3 . The selected data area is shown as a red box in Fig. 9.7d

on June 14, 2008, for experiments that assimilate radial wind and reflectivity using different microphysics schemes. It should be noted that the CFAD for Z DR and K DP is only displayed below 6 km Above Sea Level (ASL) due to complex cold rain processes, which make it challenging for the observation operator to simulate higher-level values. The reflectivity ranges from 21 to 37 dBZ, with a maximum of around 48 dBZ. High reflectivity probability is higher at 5 km ASL, indicating the bright band is near that height. In the upper layer, the echo is sustained within 10–20 dBZ. The post-DA Z H CFADs (Fig. 9.9d, g) indicate that the 25th, 50th, and 75th percentiles are similar to observations, although both schemes slightly underestimate the 50th and 75th percentiles. The model enhances the bright band structure at 5 km ASL and increases the probability of mixed-phase hydrometeors. In the mid-level (5– 9 km), the GCE scheme overestimates Z H by approximately 5 dBZ (Fig. 9.9a) and the Morrison scheme by around 10 dBZ (Fig. 9.9g). Both schemes produce relatively reliable analysis fields in this study, indicating that the thermodynamic fields match the observations after DA. However, the estimated probabilities of Z H in the higher atmosphere (above 9 km) are underestimated by approximately 10 dBZ. The concentration of reflectivity is primarily found between 21 and 37 dBZ, with a maximum of 48 dBZ. The bright band structure is located near 5 km ASL, as indicated by a higher probability of high reflectivity in this region. Echoes in the upper layer are generally maintained within 10–20 dBZ. After DA, the Z H CFADs (Fig. 9.9d, g) indicate that the 25th, 50th, and 75th percentiles are generally in agreement with the observations, although slightly underestimated in some cases. Additionally, the bright band structure at 5 km ASL is enhanced in the model, indicating the presence of mixed-phase hydrometeors. However, in the mid-level (5–9 km), the GCE scheme overestimates Z H by approximately 5 dBZ (Fig. 9.9a) and the Morrison scheme by 10 dBZ (Fig. 9.9g). At higher altitudes (above 9 km), the estimated probabilities of Z H are around 10 dBZ, which is underestimated compared to the observations. Despite these discrepancies, both schemes exhibit relatively reliable analysis fields, suggesting that the thermodynamic fields match the observations after DA. The Z DR CFAD in S-POL (Fig. 9.9b) indicates that the raindrops tend to be spherical with a 50th percentile at approximately 0.5 dB in the warm cloud region.

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Fig. 9.9 CFADs of S-POL observations at 1100 UTC on June 14, 2008: a reflectivity, b differential reflectivity, and c specific differential phase; d–f are reflectivity, differential reflectivity, and specific differential phase, respectively, in the GCE scheme; g–i are the same as d–f but for the Morrison scheme

The maximum Z DR is around 1.5 dB, which, along with the Z H values, suggests the presence of small but highly concentrated raindrops. However, in the Z DR CFADs (Fig. 9.9e, h), both schemes overestimate Z DR after DA. In the GCE scheme (Fig. 9.9e), the mixing ratio increases during DA cycles, causing an overall increase in raindrop size and Z DR . In the Morrison scheme (Fig. 9.9h), both the mixing ratio and total number concentration contribute to the increase in Z DR . Moreover, the default setting of the dual-pol observation operator may cause overestimation of Z DR due to the assumption of elliptical and large raindrops based on observations in the contiguous United States. This difference in cloud microphysics and DSD characteristics between the United States and Taiwan is reflected in the S-POL Z DR CFAD (Fig. 9.9e).

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In relation to the K DP CFAD in S-POL (shown in Fig. 9.9c), about half of the data falls within the range of 0.1° km−1 , while the 75th percentile is approximately 0.2° km−1 . Although K DP can be used as a proxy for liquid water content, it is not very sensitive in the low rainfall rate region of S-band radar, such as the stratiform area. In terms of the K DP CFAD analyses (shown in Fig. 9.9f, i), the DA system captures the occurrence of high K DP , but the 75th percentile remains below 0.05° km−1 . Overall, the reflectivity structures in the GCE and Morrison schemes were similar and resembled the S-POL CFAD. However, both schemes overestimated Z DR compared to the observations, especially the Morrison scheme. The investigation into the total number concentration increment further revealed that assimilating radial wind and reflectivity data only resulted in slight modifications to the number concentration.

9.3.4 Assimilation of Dual-Pol Parameters Typhoon Soudelor was chosen as the case study due to its significant observations by the RCWF radar after its polarimetric upgrade, and the availability of valuable data before the radar was damaged. This tropical cyclone reached tropical storm intensity on July 30, 2015, rapidly intensified to Category 5 with a minimum central pressure of 900 hPa and 10 min maximum sustained winds of 59.7 m s−1 on August 3, and eventually made landfall on the eastern coast of Taiwan at Category 3 intensity on August 7–8. During the hours surrounding landfall, strong gusts and rainbands north of the typhoon center severely impacted northern Taiwan (Fig. 9.10a), resulting in significant damage to the RCWF radar when its radome and antenna were blown away. At 2000 UTC 7 August, Typhoon Soudelor’s eye was located 110 km south of the RCWF radar (Fig. 9.10a). The northern semicircle of the typhoon, also known as the dangerous semicircle, comprised several massive rainbands with Z H exceeding 50 dBZ. In contrast, fewer rainbands were visible and only near the eye in the southern semicircle, and the innermost one had a notable amount of large raindrops distinguished by high Z DR and K DP values, which reached 2.7 dB and 1.8° km−1 , respectively (Fig. 9.10b, c). Z DR and K DP values inside the northern huge rainbands were lower over the ocean but increased over the land, especially K DP , indicating that orographic lifting influenced rainbands moving toward terrain and resulted in more intense convection and precipitation. Within a range of 170 km, ρHV values were primarily greater than 0.98 but decreased beyond (Fig. 9.10d). A set of experiments were conducted to examine the impact of polarimetric radar data assimilation on QPFs, as shown in Table 9.1. The experiments are denoted by uppercase V, Z, D, and K, which represent assimilating Vr , Z H , Z DR , and K DP , respectively. The NoDA experiment serves as the control, where only a cold-start simulation initialized with the NCEP Global Forecast System (GFS) 0.25° forecast at 1200 UTC 7 August is performed. The simulation’s first eight and final six hours (from 2000 UTC 7 August to 0200 UTC 8 August) are considered the model spin-up period and benchmark forecast, respectively. The experiments that assimilate RCWF observations with the LETKF scheme, using a 40-member ensemble

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Fig. 9.10 The a Z H , b Z DR , c K DP , and d ρHV PPI observations of the RCWF radar at a 0.5° elevation angle at 2000 UTC 7 August. The dot in panel a is the location of the RCWF radar. The dashed circle in panel d is a range of 170 km

perturbed around the NoDA initial condition via the random-cv facility of the WRF 3DVar system, are denoted by DA. During the initial ensemble’s 6 h spin-up period and nine assimilation cycles at a 15 min interval, radar data assimilation only takes place in the fine grid, with the analysis increments fed back to the coarse grid through two-way interaction. The analysis ensemble mean is then used to generate the 6 h deterministic forecast. Table 9.1 The list of the experiments in the study of assimilating dual-pol

Name

Assimilated radar variables

NoDA

None

VZ

Vr and Z H

VD

Vr and Z DR

VK

Vr and K DP

VZD

Vr , Z H , and Z DR

VZK

Vr , Z H , and K DP

VZDK

Vr , Z H , Z DR , and K DP

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Figure 9.11 illustrates a comparison between predicted rainfall and observed rainfall interpolated from more than 750 surface rain gauges to the fine grid points for the first three hours, second three hours, and total six hours of deterministic forecasts in experiments NoDA, VZ, VD, and VK. The black rectangle highlights areas A–C for easier visual comparison. During the first three hours, the patterns of areas A–C in the three DA experiments are more similar to the observations than in NoDA. Outside the rectangle, the observed 3 h rainfall is generally lower than 50 mm (in blue), while NoDA and VD have more areas with higher rainfall (in green and yellow) than VZ and VK. During the second three hours, all the NoDA and DA experiments show similar underestimates in areas A–C and overestimates in area D, indicating that the positive effect of radar data assimilation on QPFs can last up to three hours in this study. As for the total 6 h accumulations, the improved pattern of areas A–C is diluted but still distinguishable in the three DA experiments. Figure 9.12 displays a comparison of the root mean square error (RMSE), spatial correlation coefficient (SCC), and equitable threat score (ETS) on a threshold of 15 mm for the predicted hourly rainfall on land within the 230 km maximum unambiguous range during 2000 UTC 7 August–0200 UTC 8 August in two groups of experiments. The first group’s ranking order from best to worst during the first three hours is VK, VZ, V, VD, and NoDA. The order is the same as the order from lowest to highest q_r, indicating a high dependence of QPFs on rainwater analyses for this typhoon case. The second group’s ranking order from best to worst is VZK, VZDK, VZD, VZ, and NoDA, suggesting that further QPF improvement is still achievable by the additional assimilation of polarimetric variables, especially K DP , when Vr and Z H are already assimilated. During the total six hours, the DA experiments perform better than NoDA in terms of RMSE and ETS but show mixed results in SCC. Overall, the assimilation of polarimetric radar variables significantly improves QPFs during the first three hours and has potential for further improvement.

9.4 Summary and Future Work By using ensemble data assimilation system, this chapter reviewed the impact of assimilating retrieved 3D thermodynamic fields (temperature and humidity), humidity profiles, dual-polarimetric parameters with doppler wind, and reflectivity from ground-based weather radar. With different high-impact weather events, the results of analysis and very short-term forecast are demonstrated and verified by available data near surface. Here are the summary of the findings: • In the OSSEs, providing additional information regarding the temperature and/ or humidity fields in the multiscale precipitation system is able to shorten the assimilation period. Furthermore, it was observed that the assimilation of additional thermodynamic variables had a greater impact on improving the vertical motion and temperature structures in the stratiform areas than the assimilation of additional cycles of radial wind and reflectivity data. The improvements in

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Fig. 9.11 The Z H , Z DR , and K DP CAPPI fields at a 3.5 km altitude at 2000 UTC 7 August for the a–c RCWF radar observations, d–f NoDA forecast, g–i VZ analysis ensemble mean, j–l VD analysis ensemble mean, and m–o VK analysis ensemble mean. The green circle is the maximum unambiguous range of the RCWF radar. The black rectangle highlights areas A–C for easier visual comparison

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Fig. 9.12 The a, b RMSE, c, d SCC, and e, f ETS on a threshold of 15 mm for the predicted hourly rainfall on land within the 230 km maximum unambiguous range during 2000 UTC 7 August–0200 UTC 8 August in two groups of experiments

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the stratiform region, in turn, had a positive influence on the hydrometeor variables, which were found to be closely linked to the vertical temperature structure. The results of QPF showed that assimilating thermodynamic variables improved 0–3 h short-term forecast in heavy rainfall event compared to only assimilating radial wind and reflectivity. In addition, assimilating humidity information alone yielded a stronger QPF performance than assimilating the 3D temperature field alone. When 3D thermodynamic fields were retrieved and provided to be assimilated with radial wind and reflectivity, the additional temperature information produced strong convection as the truth state at the final analysis and reduced the assimilation period to improve the QPF skill score. In the retrieved temperature and water vapor assimilation experiment, the 3 h heavy rainfall accumulation was closer to the truth state than that of the other experiments. The S-PolKa–retrieved humidity was available nearby the precipitation system which may represent the environmental moisture conditions. It was useful to assimilate the humidity profile earlier than radar observations (radial wind V r and reflectivity Z H ). The qualitative and quantitative evaluation for the short-term forecasts demonstrated that additionally assimilating the moisture information with radar data could further improve the QPF up to 3 h forecast lead time compared with assimilating only the Z H and V r . Furthermore, assimilating humidity profiles in different directions could capture the variation of environmental moisture and obtain a better analysis compared to one average profile to represent the humidity profile nearby the precipitation system. As dual-pol parameters highly depend on the size distributions of various hydrometeor species, multi-moment cloud microphysical schemes with adjustable total number concentrations are more appropriate for dual-pol radar data assimilation than single-moment ones. However, excessively low total number concentrations may lead to unrealistically high dual-pol parameter values, which often occur in the melting ice model that generates mixed-phase hydrometeors and bright band signatures near the melting layer. Therefore, applying a lower threshold to the total number concentrations of mixed-phase hydrometeors is found necessary in the melting ice model. The evaluation of cloud microphysics illustrated that total number concentration can be modified slightly when assimilating radial wind and reflectivity The study of typhoon event showed that further QPF improvement can be achieved when dual-polarimetric parameters were assimilated, especially K DP , on top of Vr and Z H .

Although ensemble-based data assimilation system could modify different model variables via background error covariance, our studies revealed the positive effects of assimilating thermodynamics and microphysics information with radar data. Besides, weather radar is able to retrieve useful information which is not observed directly. For future work, the impact of assimilating the following data can be further investigated: (1) radar-derived refractivity which provides high-density moisture data near the surface; (2) MicroPulse differential absorption lidar (MPD) which provides humidity

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profile. In addition, information on satellite, lidar, and surface should be integrated and assimilated all together, so the optimal mesoscale analysis can be obtained, and the improvement of the short-term forecast can be achieved.

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Chapter 10

Assimilation of Multiscale Remote Sensing Data to Improve Mesoscale Precipitation Forecasting Ki-Hong Min, Miranti Indri Hastuti, Ji-Won Lee, Jeong-Ho Bae, Jae-Geun Lee, and Yushin Kim

Abstract This chapter summarizes research related to data assimilation of remote sensing data with focus on ground-based weather radar. Radar data assimilation has its limits and advantages. Radar can provide information of hydrometeors and winds by observing the three-dimensional distribution of rainfall, intensity, and the movement of precipitation systems. However, estimated in-cloud water vapor amount tends to overpredict the amount of rainfall at the early hours of model forecast. To overcome the limitations in the initial condition of the atmosphere, multiscale remote sensing data ranging from satellite and Global Positioning System (GPS) to radar is utilized to improve mesoscale precipitation forecasting. This study showcases that humidity errors can be reduced by assimilating satellite all-sky radiances and GPS Radio Occultation (GPSRO) refractivity to enhance the moisture analysis during K.-H. Min (B) Department of Atmospheric Sciences and Center for Atmospheric Research, Kyungpook National University, Daegu, South Korea e-mail: [email protected] M. I. Hastuti Agency for Meteorology, Climatology, and Geophysics of the Republic of Indonesia, Jl. Tengku Heran, Beringin, Deli Serdang, Indonesia e-mail: [email protected] J.-W. Lee Department of Atmospheric Sciences, Kyungpook National University, Daegu, South Korea e-mail: [email protected] J.-H. Bae National Typhoon Center, Korea Meteorological Administration, Seogwipo, South Korea e-mail: [email protected] J.-G. Lee Republic of Korea Air Force, Yechon, South Korea e-mail: [email protected] Y. Kim Department of Meteorology, University of Oklahoma, Norman, OK, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_10

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the cycling period. The assimilation of satellite Atmospheric Motion Vectors (AMVs) can further improve wind fields of atmospheric dynamics driving the moisture field, which in turn increases the accuracy of the moisture convergence and fluxes at the center of convection. As a result, the timing and intensity accuracy of heavy rainfall are improved and the hourly forecast errors are reduced. Keywords Data assimilation · Radar · All-sky radiance · AMV · Rainfall forecast

10.1 Introduction With increasing computing power, the resolutions of Numerical Weather Prediction (NWP) models are increasing, depicting finer-scale mesoscale features. The transition to higher resolution NWP models has the potential for resolving 100 m scale convection and accurately predicting forecasts of intense and damaging rainfall. However, solely increasing NWP model resolution does not ensure accurate prediction. The routine assimilation of various meteorological data is key to establishing the accuracy of NWP, allowing the variables of the NWP model to align with the real-world weather observations. Radar reflectivity sensors have been widely used to provide high-resolution precipitation hydrometeors in clouds, with Doppler radar radial velocity providing motion information. Xiao et al. (2005) assimilated Doppler radar radial velocity using a radial velocity observation operator with the inclusion of rainwater terminal velocity and estimated the vertical velocity increment based on the dynamic balance of the Richardson equation (Sun and Crook 1997, 1998). Results showed reasonable wind and vertical velocity analysis, thus improving rainband movement and intensity prediction. Reflectivity from radar observation provides cloud property information of precipitating areas. Gao and Stensrud (2012) introduced a radar reflectivity operator that uses the model background temperature from the NWP model to divide hydrometeors species (snow, graupel, and hail), which results in improved shortrange forecasts. Furthermore, Wang et al. (2013) introduced the in-cloud humidity with radar reflectivity assumption, wherein the environment is saturated in the presence of radar reflectivity higher than a certain threshold. The assimilation of the water vapor from radar can provide humid environment for maintaining convection. However, many studies show that this assumption is rudimentary and overpredicts water vapor content and rainfall at the early hours of prediction (Lee et al. 2020a, b; Bae and Min 2022). Overcoming these problems is crucial since the environment of storms is interrelated to the moisture and thermodynamic condition of the atmosphere, which significantly impacts the generation or dissipation of storms (Lee and Min 2019; Lee et al. 2022). Research to alleviate the extra water vapor and spurious precipitation from radar was investigated but the uncertainty in drying the precipitation environment remains (Gao et al. 2018). Recent studies have proved the assimilation of humidity observations such as satellite or Global Positioning System (GPS) together with wind and hydrometeors from radar and have improved moisture

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fields and the initiation of forecast storms (Pan et al. 2018; Yang et al. 2020). Furthermore, satellite and GPS assimilation has the potential to improve the limitation of radars in providing information prior to the formation of precipitation particles. Global Positioning System Radio Occultation (GPSRO) observations provide water vapor information for use in NWP with high vertical resolutions and accuracy. GPSRO data can retrieve a variety of data that can be used in NWP systems (e.g., refractivity, bending angle, and derived moisture and temperature). The assimilation of refractivity shows a good compromise as compared to the assimilation of bending angles or derived temperature and moisture (Kuo et al. 2000). Chen et al. (2009) employed the local and nonlocal refractivity observation operator for GPSRO refractivity data assimilation, which produced similar analysis increments and improved the detoured track of Typhoon Kaemy that struck Taiwan. Ha et al. (2014) investigated the impact of GPSRO refractivity using a local refractivity operator and corrected moisture variable in the lower troposphere level and modified wind variable through the dynamic process, improving the maximum precipitation forecasts and threat scores. Cheng et al. (2018) showed that the assimilation of GPSRO refractivity alone enhances both the 24 and 48 h regional rainfall forecasts, while that of GPSRO refractivity and conventional observations enhanced the 48 h forecast of light and heavy rain. Kunii et al. (2012) demonstrated that the addition of GPSRO refractivity into the assimilation of conventional, radar, and satellite observations improves accuracy and intensity forecasts. However, the GPSRO measurements usually have low spatiotemporal resolution, because they are random and occurrence are limited. Therefore, assimilating other potential water vapor observations from satellite alongside the GPSRO observations will assist in water vapor distribution. Satellite uses infrared (IR) channels to observe the brightness temperature (BT; determined as “radiance”), which provide continuous atmospheric state information about water vapor, temperature, winds, and cloud properties for the NWP using the Radiative Transfer Model (RTM) as the observation operator (King et al. 2003). Satellite observations have better spatial and temporal coverage where radar are not available, such as over oceans and in clear skies. Okamoto et al. (2019) and Xu et al. (2021) investigated the performance of assimilating all-sky radiance and showed the enhancement of hydrometeor and water vapor field and improved the accuracy of location and rainfall intensity. Zhang et al. (2019) assimilated hydrometeor and wind information from radar observations along with the all-sky satellite radiance values, demonstrating that all-sky satellite data increased warning leading times and improved the accuracy of mesocyclone track, improving the accuracy and longer lead times of the mesocyclone. Wang et al. (2020) obtained simultaneous satellite and radar data, establishing that satellite data assimilation enhanced the large-scale temperature and moisture variable, while the addition to radar data assimilation enhanced wind field and hydrometeors in the precipitation area. These improvements caused the assimilation to spin up faster, strengthening the rainfall initial field. Jones et al. (2020) combined radar and conventional observations data together with all-sky satellite radiances, providing improved analysis and forecasts of storm environments.

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The storm morphology and evolution within NWP are sensitive to the wind fields. The satellite derived winds or Atmospheric Motion Vectors (AMVs) offer tropospheric wind with high spatial and temporal coverage that radar radial velocity or conventional data cannot observe. AMVs are mainly used to identify synoptic scale airflows, but AMVs can also be used to identify mesoscale winds induced by convective clouds (Bedka and Mecikalski 2005). It is important for the mesoscale flow fields to be resolved for high-impact convective-scale forecasts events (Wu et al. 2014). Otsuka et al. (2015) showed the assimilation of AMVs enhanced the initial wind fields at the upper-level and low-level convergence around the front, causing a positive impact on the timing and intensity of heavy rainfall. Kim and Kim (2018) discussed the potential benefits of AMVs over East Asia, and the resulting Himawari AMVs reduced the forecast errors. This chapter describes how the accuracy of radar data assimilation can be improved using additional remote sensing data. The impact of GPSRO refractivity and satellite all-sky radiances in improving the water vapor fields and satellite AMVs in updating the real-world atmosphere flows are investigated when combined with radar data. The contributions are assessed based on summertime precipitation forecast using Weather Research and Forecasting Three-Dimensional Variational Data Assimilation (WRF 3DVAR) system. Section 10.2 describes the details of experimental method, data, and design. Sections 10.3 and 10.4 analyzes the increments and water vapor dynamics in the initial condition, as well as result of the forecast rainfall and verification statistics. Section 10.5 summarizes and concludes the study and discusses future research.

10.2 Methodology 10.2.1 Weather Research and Forecasting 3DVAR Data Assimilation System The WRF data assimilation system (WRFDA) with Three-Dimensional Variational Data Assimilation (3DVAR) framework was utilized on this study (Barker et al. 2004, 2012). The 3DVAR system produces multivariate incremental analysis for relative humidity, temperature, pressure, and wind through an incremental formulation. The incremental cost function J(x) is minimized for calculating the analysis state x (Ide et al. 1997). J (x) = Jb (x) + Jo (x) =

1 (x − xb )T B −1 (x − xb ) 2

1 + (y0 − H (x))T R −1 (y − H (x)) 2

(10.1)

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Jo (x) and Jb (x) are the cost functions obtained from the observations and background, respectively. The x, xb , y0 , B, H, and R are the analysis field, first guess, observation, background error (BE) covariance matrix, nonlinear observation operator, and observation error covariance matrix, respectively. The BE covariance matrix was produced by using 12 and 24 h forecasts during summer season from August 1 to September 30, 2020, based on the National Meteorological Center (NMC) method (Parrish and Derber 1992).

10.2.2 Satellite Radiances Observation Operator Radiance observation operator is required to calculate simulated radiance data from the model state vector. Community Radiative Transfer Model (CRTM) from the United States Joint Center for Satellite Data Assimilation (JCSDA) was used as the radiance observation operator (Han et al. 2006). CRTM contains various modules: gaseous transmittance model, surface emission and reflection model, cloud and aerosol scattering model, and radiative transfer solver. The variational bias correction (VarBC) was performed when assimilating radiance data (Derber and Wu 1998; Dee and Uppala 2009; Liu et al. 2012; Zhu et al. 2014). The radiance observation error can be defined as standard deviation of observationminus-background departure (OMB) that can be described by cloud parameter (CA ). CA formulation developed by Okamoto et al. (2014) can be written as: CA =

(|B − Bclr | + |O − Bclr |) , 2

(10.2)

where O, B, and Bclr are radiance observation, simulated all-sky radiance, and simulated clear-sky radiance, respectively. In this study, all-sky radiance observation error was estimated using a pre-calculated look-up table (LUT) approach based on cloud situation using CA (Geer and Bauer 2011; Okamoto et al. 2014). CA and the standard deviation of OMB statistics were calculated during August 2020 every six hours. CA was split into bins of 1 K, and standard deviation of OMB was computed for each CA bins. The observation error was produced by fitting CA bins and the standard deviation of OMB using polynomial regression, which is written as: y = ax + bx 2 + cx 3 + d x 4 + ex 5 + f,

(10.3)

where y, as the polynomial fit, represents the observation error, x is cloud parameter (CA ), and a–f are coefficients of the polynomial fit. Before reaching a maximum STD of the OMB value, observation error follows these polynomial fit values and the rest remain constant with the highest value of polynomial fit.

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10.2.3 GPSRO Refractivity Observation Operator GPS radio occultation technique utilizes GPS radio signals received from low-Earth orbit (LEO) satellites for measuring amplitude and phase of the signals. These measurements, together with the precise knowledge of the position and velocity of the LEO and GPS satellites and the assumption of spherically symmetric refractive, compute the vertical profiles of ray bending angle and retrieve the atmospheric refractivity (N) through the able transform method (Phinney and Anderson 1968). After the ionospheric effect is removed in the neutral atmosphere, the equation of refractivity (N) as a function of water vapor pressure e (hPa), temperature T (K), and pressure p (hPa) and can be expressed as follows (Smith and Weintraub 1953): N = 77.6

e p + 3.73 × 105 2 . T T

(10.4)

To assimilate refractivity, the model variable of temperature, pressure, and water vapor field was interpolated into GPSRO observations locations.

10.3 Data and Experimental Setup 10.3.1 Observation Data Radar reflectivity and radial velocity were obtained from the Korea Meteorological Administration (KMA) S-band radars (Fig. 10.1a). Radar data was quality controlled using the Kyungpook National University (KNU) fuzzy logic algorithm (Ye et al. 2015), which removes the anomalous propagation (AP) and non-precipitating areas of electromagnetic waves. The procedure included the quality check on plan position indicator (PPI), before converting to constant altitude PPI (CAPPI). The radar data was interpolated onto the same resolution and size of NWP domain. Therefore, the resolution of radar data for domain 2 was 3 km and for domain 1 was 1 km. The vertical resolutions for radar data were set to 200 m. The satellite observation used in this study were obtained from the GK-2A geostationary satellite. In this study, channels 8–10 (6.3, 6.9, and 7.3 μm) are used for all-sky radiance observation. Those bands are the water vapor wavelengths that are sensitive to the water vapor in the middle to upper troposphere (Di et al. 2016; Lee et al. 2020a, b). The GPSRO is a limb measurement that is based on Snell’s law of refraction. GPSRO soundings data were obtained from various missions: the Constellation Observing System for Meteorology, Ionosphere and Climate 2 (COSMIC 2), Meteorological operational satellite-A (Metop-A), Metop-B, Metop-C, PAZ (Spain peace satellite), Terra Synthetic Aperture Radar X (TerraSAR-X, TSX) and TSX add-on for Digital Elevation Measurements (TDX), and KOMPSAT 5 (Korea Multi-Purpose

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Fig. 10.1 Distribution of observation data for a radar observations and b AWS, wind profiler, and radiosonde observations

Satellite 5) in wetPf2 (atmospheric occultation profile with moisture information 2) format, which consists of the refractivity associated with the location point (longitude, latitude) and the height of tangent point. The GK2A AMVs are defined as the output of the atmospheric movement obtained by tracking clouds or water vapor fields with satellites. To calculate the motion vectors, consecutive three images are typically used in time series. AMVs used in this study were from channels shortwave IR (SWIR) (3.8 μm), water vapor (WV) (6.3, 6.9, and 7.3 μm), IR (10.5 and 11.2 μm), with observation errors of 3.26, 4.62, 3.86, 4.94, 4.29, and 4.32 m s−1 , respectively. The AMVs were quality checked before being input into the 3DVAR data assimilation. Only AMVs with a quality indicator (QI) above 0.85 were assimilated. For horizontal resolutions, the AMVs GK-2A had resolutions 32 × 32 km. The radiosonde, wind profiler, and Automatic Weather Station (AWS) observation data obtained from stations operated by the KMA (Fig. 10.1b). AWS precipitation data were interpolated into the same resolution and domain size of model grid.

10.3.2 Event Overviews Four cases of heavy rainfall over South Korea during summer were chosen to study the impact of multiscale data assimilation into NWP model forecasts. The four characteristics of selected cases: the mesoscale precipitation induced by Changma front (Case 1), convective systems along Changma front (Case 2), Mesoscale Convective Systems (MCS) along Changma front (Case 3), and convective band (Case 4), together with the forecast period are shown in Table 10.1. For Cases related to Changma front, Cases 1 and 2 predicted the short period time (9 and 12 h), but Case 3 predicted the long period time (27 h). Case 4 predicted short time (6 h) rainfall

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for convective band case. In Case 1 at 0000 UTC on August 9, 2020, the Changma front propagated from southwest to northeast, and a large amount of water vapor was brought by the low-level jet (purple zones) (Fig. 10.2a). Changma front caused heavy rainfall, recording 53.0 mm of hourly rainfall in Osan, Gyeonggi-do Province (Fig. 10.2e). The accumulation of 9 h of rainfall reached 107.32 mm located in Pogog-eup, Gyeonggi-do Province. In Case 2, at 0000 UTC on August 15, 2020, it can be seen an extended westward of high pressure over North Pacific and an extended westward of low pressure over Northeast China, inducing Changma front approached eastward over South Korea (Fig. 10.2b). The hourly rainfall peaked 44.0 mm in Gangnam, Gyeonggi-do Province at 2200 UTC August 15, 2020 (Fig. 10.2f). The 12 h precipitation peak reached 114.80 mm in Hoengseong Gyeonggi-do Province. In Case 3 at 1200 UTC on August 2, 2020, the low pressure over Northwest China approached the southeast region and met the high pressure from North Pacific, causing the Changma front (Fig. 10.2c). The MCS occurred near the front that was initiated by the low-level jet (Fig. 10.2c). Along the low-level jet, MCS propagated from north to south, causing heavy rainfall over Gangwon-do, Gyeonggi-do, Chungcheongnam-do, and Chungcheongbuk-do. The hourly precipitation reached 50.0 mm in Baekhak-myeon, Gyeonggi-do Province at 0700 UTC August 2, 2020 (Fig. 10.2g). The accumulation of 27 h rainfall reached 294.64 mm located in Gyeonggi-do Province. On July 11, 2021 (Case 4), low pressure approached from East China and high pressure approached over North Pacific (Fig. 10.2d). In Case 4, the synoptic factor was weak because it was caused by the local convective systems over Gyeonggido Province. This convective system caused the peak hourly precipitation 52.5 mm at 0700 UTC July 11, 2020 (Fig. 10.2h), and the 12 h precipitation peak reached 72.87 mm in Buknae Gyeonggi-do Province. Table 10.1 List of the four cases Period

Characteristics

Case 1

August 8, 2020 at 2100 UTC–August 9, 2020 at 0600 UTC

Changma front

Case 2

August 14, 2020 at 1800 UTC–August 15, 2020 at 0600 UTC

Convective system along Changma front

Case 3

August 2, 2020 at 0300 UTC–August 3, 2020 at 0600 UTC

MCS inducing by Changma front

Case 4

July 11, 2021 at 0600 UTC–July 11, 2021 at 1200 UTC

Convective band

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Fig. 10.2 a–d Synthesis weather chart and e–h radar reflectivity of 1.5 km for Case 1, Case 2, Case 3, and Case 4, respectively

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10.3.3 Experimental Setup and Design The NWP model to conduct the experiments was constructed using WRF. The WRF model offers an open-source code, flexible, and wide range of meteorological applications. WRF features a compressible and non-hydrostatic with a mass coordinate system (Skamarock et al. 2021). For every case, the WRF model used three nesting domains (D01, D02, and D03) with the resolution of 9 km, 3 km, and 1 km, respectively (Fig. 10.3). The vertical level has 60 η model layers with the highest level was 50 hPa. The initial and boundary conditions used the NCEP/FNL (National Centers for Environmental Prediction/ Final Analysis) with a resolution of 1° × 1° developed by the National Centers for Environmental Prediction/National Centers for Atmospheric Research (NCEP/ NCAR). In the WRF forecast simulations, Kain–Fritsch Scheme was applied for domains 1 and 2 (Kain and Fritsch 1993). For all domains, the WRF Double Moment 6 class (WDM6) scheme (Lim and Hong 2010), Unified Noah land surface model (Tewari et al. 2004), the YSU scheme (Hong et al. 2006), and the Rapid Radiative Transfer Model (RRTM) longwave–Dudhia shortwave schemes (Dudhia 1989), were employed for cloud microphysics, land surface, planetary boundary layer, and the atmospheric radiation process, respectively. All model parameterizations and vertical levels were same in each domain configurations. To understand and analyze the strengths and limitations of each moisture information data types (radar, satellite, and GPSRO) and AMVs, the sequence of the four experiments (CTRL, RQV, GPS + ASR, and GPS + ASR + AMV) was confirmed (Table 10.2), and the increment analyses and prediction from each experiment were then compared with available observations. CTRL experiment assimilates AWS, radiosonde, wind profiler, and radar measurements. RQV, GPS + ASR, and GPS + ASR + AMV were identical to CTRL, except RQV additionally assimilated the incloud water vapor from radar reflectivity, GPS + ASR was identical to RQV with the addition of GPSRO refractivity and satellite all-sky radiances assimilation, and GPS + ASR + AMV was identical to GPS + ASR and combined with the assimilation of AMVs. All assimilation experiments were conducted with continuous cycling in

Fig. 10.3 Model domain and nesting configurations for a Case 1 and Case 2, b Case 3, and c Case 4, respectively

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Table 10.2 Cases selected for numerical experiments and their storm characteristics Data

CTRL

RQV

GPS + ASR

GPS + ASR + AMV

AWS

O

O

O

O

Radiosonde

O

O

O

O

Wind profiler

O

O

O

O

Radar radial velocity

O

O

O

O

Radar reflectivity (hydrometeors)

O

O

O

O

Radar reflectivity (water vapor)

–

O

–

–

GPS refractivity

–

–

O

O

Satellite all-sky radiance

–

–

O

O

Satellite AMV

–

–

–

O

The names for the DA experiments are control (CTRL), radar reflectivity with water vapor operator (RQV), GPS with satellite all-sky radiance (GPS + ASR), and GPS + ASR with AMV, respectively

a 30 min window during a 3 h period. Satellite all-sky radiances and GPSRO refractivity were assimilated into D01, D02, and D03. This method allows more data to be assimilated and may improve the synoptic scale analysis. AWS, radar, wind profiler, and radiosonde were assimilated into D02 and D03.

10.3.4 Verification Method This study selected a couple of verification statistics to objectively evaluate the performance of forecast models. AWSs observation were utilized for the verification. The quantitative verification was performed using Bias and Root Mean Square Error (RMSE) metrics, which can be defined based on the following equations: Bias =

RMSE =

1 N 1 N

N

(Pi − Oi )

(10.5)

(Pi − Oi )2 ,

(10.6)

i=1 N

i=1

where N represent the total number of data, Pi represent the prediction, and Oi represent the observation. Bias describes whether the forecast models are underpredict (BIAS < 0) or overpredict (BIAS > 0) events. RMSE determines the standard deviation of the forecast errors. The verification of precipitation occurrences can be verified using four categories (Hits, False Alarms, Misses, and Correct Negatives), which are shown by contingency table. The accuracy (AC) describes the quantity of correct forecast, as defined in Eq. (10.7). The value of one is the perfect score.

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Accuracy =

Hits + Correct Negatives Total

(10.7)

The critical measure index (CSI) determines the ratio of correct predictions. The ratio of prediction gets higher when hits occur, but gets lower when misses and false alarms. The best CSI score is one. CSI =

Hits Hits + Misses + False Alarms

(10.8)

The equitable threat score (ETS) is comparable with CSI, but ETS also considers the random chance of hits. The ETS perfect score is one. (Hits + Misses)(Hits + False Alarms) Total

(10.9)

Hits − Hitsrandom . Hits + Misses + False Alarms − Hitsrandom

(10.10)

Hitsrandom = ETS =

To objectively evaluate the precipitation pattern, the pattern correlation (PC) was performed. PC can be expressed in Eq. (10.11): Rpatt_cor =

N i=1

X obs,i − X obs X pred,i X pred , σobs σpred

(10.11)

where N is the number of data, X obs and X obs are the precipitation observation and the mean of precipitation observation, respectively. X pred and X pred are the precipitation forecast and the mean of precipitation forecast, respectively. σobs and σpred are the standard deviation of precipitation observation and forecast, respectively. The highest accuracy is one.

10.4 Results 10.4.1 Analysis Increment on Initial Fields To improve the fidelity of numerical model simulations, the initial analysis fields should represent similarity to the real world. Thus, the contribution of each simulation on improving the rainfall forecast can be established by analyzing the increment on initial fields. Water vapor content enhancement is associated with changes in the thermodynamic process that may contribute to wind field changes. Also, changes in dynamic winds primarily should result from changes in the pressure fields. Thus, understanding that the wind, pressure, and temperature fields are modified in the initial field through each simulation is crucial. The horizontal and vertical increments

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were analyzed at the end of the cycling assimilation window for evaluating the impact of each simulation. Figures 10.6, 10.7, 10.8, and 10.9 show the increment of water vapor mixing ratio (g kg−1 ) overlaid by wind (m s−1 ) at 850 hPa, perturbation pressure (hPa) overlaid by geopotential height (m) at 850 hPa, and vertical (A–B line) perturbation temperature (K) overlaid by wind (u, w × 5 m s−1 ) for Cases 1, 2, 3, and 4, respectively. In Case 1, the BT observation from the satellite showed convective elements over the east of Yellow Sea denoted by BT < 220 K, associated with moister atmospheric conditions (Fig. 10.4a). RQV showed a strong magnitude of positive water vapor mixing ratio in the larger areas over the east of Yellow Sea at approximately 4.5 g kg−1 (Fig. 10.5a). Such an increment may cause overprediction of rainfall. GPS + ASR also increased the water vapor mixing ratio at approximately 4.5 g kg−1 in smaller areas compared to RQV (Fig. 10.5b). GPS + ASR + AMV showed similarity with GPS + ASR on the increment of water vapor mixing ratio over the convective area (Fig. 10.5c), as was indicated by small differences in water vapor content between GPS + ASR + AMV and GPS + ASR (Fig. 10.5d). Clearly, the positive water vapor increment in RQV, GPS + ASR, and GPS + ASR + AMV was associated with the increased of blowing wind from northwest to Yellow Sea at approximately 2 m s−1 , 2 m s−1 , and 4.5 m s−1 , respectively, enhancing the convergence (Fig. 10.5a–c). This result mainly caused by the intensified low-pressure regions over the eastern of Yellow Sea (Fig. 10.5e–g). However, there was a slight gradient of perturbation pressure in GPS + ASR at approximately 35.8° N 124° E before reaching the convection area (Fig. 10.5f). This increment changed the wind direction moving from northwesterly to easterly and weakened the convergence over the convection area (Fig. 10.5b). GPS + ASR + AMV showed the most intensification of low perturbation pressure over the convection area at approximately 4.5 hPa (Fig. 10.5g), increasing wind convergence (Fig. 10.5c). In addition, the highest gradient of geopotential height in GPS + ASR + AMV was mostly observed in the northwest, with strong northwesterly winds that bring relatively dry air (Fig. 10.5g). Hence, there was little enhancement of water vapor content in GPS + ASR + AMV compared to GPS + ASR, resulting in similar water vapor increment as mentioned above (Fig. 10.5d). The strong increase of water vapor on experiment RQV as mentioned above (Fig. 10.5a), resulted in the release of more latent heat, as indicated by deep perturbation temperature centered at 500–200 hPa (Fig. 10.5i). RQV generated a higher scale of strong perturbation temperature, by approximately 4.5 K, than CTRL, indicating a moister area (Fig. 10.5i). GPS + ASR produced a warm core over the convective area for approximately 3 K centered at 500–200 hPa, with a smaller scale and magnitude than RQV (Fig. 10.5j). Along the deep perturbation area, the updraft wind increased. GPS + ASR + AMV produced more wind convergence of 1.5 m s−1 at approximately 35.8° N 124° E than GPS + ASR, which indicates stronger updraft motion than GPS + ASR (Fig. 10.5k, l). Thus, the condensation of water vapor in GPS + ASR + AMV was accelerated, releasing more latent heat that indicates that perturbation temperature increments were higher by 2 K centered at 500–200 hPa as compared to GPS + ASR (Fig. 10.5l).

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Fig. 10.4 Brightness temperature (K) from channel water vapor 6.9 μm at the last data assimilation time of a Case 1, b Case 2, c Case 3, and d Case 4

Fig. 10.5 Increment of a–d water vapor mixing ratio (g kg−1 ) and wind vectors (u, v m s−1 ) at 850 hPa, e–h perturbation pressure (hPa) and geopotential height (solid lines, m) at 850 hPa, and i–l vertical structures of perturbation temperature (K) and wind vectors (u, w × 5 m s−1 ) from RQV-CTRL, GPS + ASR-CTRL, GPS + ASR + AMV-CTRL, and GPS + ASR + AMV-GPS + ASR at the last data assimilation time for Case 1

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In Case 2, the satellite water vapor image showed BT lower than 220 K over the Yellow Sea at approximately 36° N 122° E and 36.6° N 124° E, indicating convective clouds (Fig. 10.4b). These convective systems were caused by the Changma Front that propagated from the West to East. RQV increased water vapor mixing ratio for approximately 4 g kg−1 over only one convective area (36.6° N 124° E) (Fig. 10.6a). In addition, RQV also increased water vapor mixing ratio at approximately 2 g kg−1 over Gyeonggi Province and extended to the Yellow Sea (37.3° N 125.8° E) (Fig. 10.6a). GPS + ASR exhibited the enhancement of water vapor fields for approximately 3 g kg−1 over the two locations of the convective systems as shown by satellite observations (Fig. 10.6b). Compared to GPS + ASR, GPS + ASR + AMV showed similarities on the water vapor increments for horizontal structures, except at 36.6° N 124° E (Fig. 10.6c, d). There was a noticeable increase of water vapor at approximately 1.5 g kg−1 as compared to GPS + ASR + AMV (Fig. 10.6d). Over the convective area, RQV, GPS + ASR, and GPS + ASR + AMV enhanced the wind convergence at approximately 2.5 m s−1 , 3.5 m s−1 , and 4.5 m s−1 , respectively (Fig. 10.6a–c). This result is associated with the strengthened of low perturbation pressure over 36.6° N 124° E at approximately 3, 3.5, and 4.5 hPa, respectively (Fig. 10.6e–g). In addition, GPS + ASR and GPS + ASR + AMV also enlarged the low perturbation pressure area at around 36.0° N 122° E at approximately 2.5 and 3.5 hPa, respectively (Fig. 10.6f, g). The above results suggest that GPS + ASR + AMV exhibited the strongest low pressure at the two main convection areas indicating air convergence (Fig. 10.6g). The intensified winds convergence are mainly from the Yellow Sea, bringing relatively moist air; hence, GPS + ASR + AMV has more water vapor as compared to GPS + ASR (Fig. 10.6d). In vertical structures, the perturbation temperature (± 4.5 K) increment was clearly seen in RQV at approximately 36.6° N 124° E centered at 500–200 hPa (Fig. 10.6i). These results suggest that RQV released more latent heat due to the condensation of water vapor, creating the warm core (Fig. 10.6i). GPS + ASR also produced the positive increment of perturbation temperature (4.5 K) but only centered at 400–200 hPa, indicating that the warm core in RQV was deeper than GPS + ASR (Fig. 10.6j). The warm core was associated with the increased updraft. GPS + ASR + AMV produced more convergence than GPS + ASR at approximately 36.6° N 124° E, enhancing updraft motion and accelerating water vapor condensation (Fig. 10.6k, l). Thus, GPS + ASR + AMV released more latent heat and showed stronger perturbation temperature at 1.0 K than GPS + ASR at the convergence region (Fig. 10.6k). In addition, more positive temperature perturbation increments at approximately 37.6° N 127° E at surface to 800 hPa in RQV than other simulations were observed, increasing winds toward the northeast (Fig. 10.6i). This resulted in precipitation being shifted to northeast in RQV. In Case 3, observed MCS in BT (Fig. 10.4c) approached from the north of Yellow Sea toward the Korean Peninsula during Changma front and convective elements in the precipitation area developed on the border of Gyeonggi and Gangwon Province. From Fig. 10.7, it can be inferred that RQV, GPS + ASR, and GPS + ASR + AMV produced positive water vapor mixing ratio of approximately 5 g kg−1 and 0.8 g kg−1 over the MCS and precipitation area, respectively, compared to CTRL (Fig. 10.7a–c).

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Fig. 10.6 Increment of a–d water vapor mixing ratio (g kg−1 ) and wind vectors (u, v m s−1 ) at 850 hPa, e–h perturbation pressure (hPa) and geopotential height (solid lines, m) at 850 hPa, and i–l vertical structures of perturbation temperature (K) and wind vectors (u, w × 5 m s−1 ) from RQV-CTRL, GPS + ASR-CTRL, GPS + ASR + AMV-CTRL, and GPS + ASR + AMV-GPS + ASR at the last data assimilation time for Case 2

However, the coverage of positive water vapor increment area (5 g kg−1 ) in GPS + ASR was observed to be smaller than that in RQV (Fig. 10.7a, b). Meanwhile, GPS + ASR + AMV increased water vapor over the MCS area at 0.5 g kg−1 , as compared to GPS + ASR (Fig. 10.7d). The positive water vapor mixing ratio increments in RQV, GPS + ASR, and GPS + ASR + AMV associated with the wind convergence at approximately 6 m s−1 , 3 m s−1 , and 5 m s−1 , respectively (Fig. 10.7a–c). These results interrelated with the intensified of low perturbation pressure over MCS area in RQV, GPS + ASR, and GPS + ASR + AMV, with slightly different magnitude and distribution (Fig. 10.7e–g). RQV produced strong low pressure than GPS + ASR and GPS + ASR + AMV over 37.8° N 124.3° E at approximately 5 hPa (Fig. 10.7e), while the other area increased at approximately 3 hPa (Fig. 10.7f,

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g). Such an increment caused stronger wind convergence. GPS + ASR increased the low perturbation pressure at approximately 2.5 hPa over most of MCS area (Fig. 10.7f), while GPS + ASR + AMV clearly intensified at approximately 4.5 hPa (Fig. 10.7g). This convergence mainly came from Yellow Sea which brings moist air; hence, there was the increased of water vapor mixing ratio over the MCS area in GPS + ASR + AMV as compared to GPS + ASR (Fig. 10.7d). In addition, GPS + ASR + AMV produced the strongest westerly trough, extending to the precipitation area, increasing wind toward the precipitation area that brings moist air from MCS (Fig. 10.7h). This result may present the distribution of rainfall in larger coverage in the precipitation area. RQV increased perturbation temperature by approximately ≥ 4.5 K over the core of MCS area (approximately 37.3° N 124.5° E) centered at 300– 250 hPa as compared to CTRL (Fig. 10.7i). GPS + ASR exhibited higher perturbation temperature than CTRL for approximately 3 K and updraft for approximately 1 m s−1 over the MCS area centered at 500–200 hPa level, with a clearly shallower warm core than RQV (Fig. 10.7j). GPS + ASR + AMV increased the perturbation temperature more than GPS + ASR by approximately 3 K and 0.5 K at 800–500 hPa and 500– 200 hPa, respectively (Fig. 10.7k, l). These results were also associated with increased updraft by approximately 3 m s−1 , indicating that GPS + ASR + AMV produced a stronger convection of MCS than GPS + ASR (Fig. 10.7l). In Case 4, satellite water vapor image showed convective band centered between Gyeonggi and Gangwon Provinces (approximately 37.5° N 128° E) denoted by BT < 220 K (Fig. 10.4d). From Fig. 10.8, it can be inferred that RQV produced a larger coverage of water vapor content of approximately 5 g kg−1 as compared with CTRL experiment (Fig. 10.8a). Such an increment may produce a strong convective band. GPS + ASR increased the water vapor mixing ratio centered between Gyeonggi and Gangwon Provinces, which was much closer to the BT observations (Fig. 10.8b). GPS + ASR and GPS + ASR + AMV have similar water vapor content as indicated by small differences (Fig. 10.8c, d). RQV, GPS + ASR, and GPS + ASR + AMV clearly increased the low perturbation pressure over the precipitation area at approximately 5, 3, and 3 hPa, respectively (Fig. 10.8e–g); hence, intensifying the wind convergence around the precipitation area at approximately 5 m s−1 (Figs. 10.8a and 10.9c). In addition, RQV produced the coverage of low perturbation pressure extremely larger (Fig. 10.8e), causing wind convergence immensely strengthened (Fig. 10.8a), as compared to GPS + ASR and GPS + ASR + AMV. GPS + ASR and GPS + ASR + AMV produced similar distributions of low perturbation pressure and wind convergence (Fig. 10.8f, g), except the increment of low perturbation pressure in GPS + ASR + AMV is higher at approximately 0.5 hPa over 36.2° N 128.5° E, inducing the northwesterly trough toward the convective area (Fig. 10.8h). This result promoted stronger wind (0.5 m s−1 ) from southwest which slightly enhanced wind convergence over the precipitation area in GPS + ASR + AMV (Fig. 10.8d). The increased water vapor and wind convergence in RQV caused a strong updraft which accelerated the condensation of water vapor, creating deep warm core on the upper level of approximately 5 K centered at 300 hPa (Fig. 10.8i). This result suggested the development of deep convection. GPS + ASR also produced a deep warm core at the upper level, but in a smaller scale and at a lower magnitude for only 3 K (Fig. 10.8j).

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Fig. 10.7 Increment of a–d water vapor mixing ratio (g kg−1 ) and wind vectors (u, v m s−1 ) at 850 hPa, e–h perturbation pressure (hPa) and geopotential height (solid lines, m) at 850 hPa, and i–l vertical structures of perturbation temperature (K) and wind vectors (u, w × 5 m s−1 ) from RQV-CTRL, GPS + ASR-CTRL, GPS + ASR + AMV-CTRL, and GPS + ASR + AMV-GPS + ASR at the last data assimilation time for Case 3

GPS + ASR + AMV showed similarity to GPS + ASR (Fig. 10.8j, k), except for the warm core in GPS + ASR + AMV, which was slightly stronger by ± 0.5 K at approximately 37.0° N 128.0° E (Fig. 10.8l).

10.4.2 Analysis of Water Vapor and Dynamical Processes To better understand the water vapor distribution and dynamics after using the modified variables in the initial fields, several kinds of weather charts are displayed for

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Fig. 10.8 Increment of a–d water vapor mixing ratio (g kg−1 ) and wind vectors (u, v m s−1 ) at 850 hPa, e–h perturbation pressure (hPa) and geopotential height (solid lines, m) at 850 hPa, and i–l vertical structures of perturbation temperature (K) and wind vectors (u, w × 5 m s−1 ) from RQV-CTRL, GPS + ASR-CTRL, GPS + ASR + AMV-CTRL, and GPS + ASR + AMV-GPS + ASR at the last data assimilation time for Case 4

each simulation. Moisture convergence and flux represent the moisture process associated with precipitation. This study derived the water vapor convergence (∇ · q U ) and water vapor flux (q U ), which indicates that the magnitude and direction of water vapor maintains rainfall. Positive vertical velocity denotes rising motion associated with precipitation. Figures 10.9 and 10.10 show water vapor convergence (g kg−1 s−1 ) overlaid by water vapor flux (g kg−1 m s−1 ) vectors at 850 hPa and vertical velocity (hPa h−1 ) overlaid with wind (m s−1 ) at 700 hPa. In Case 1, at 850 hPa, the converging water vapor in the eastern region of the Yellow Sea and water vapor flux toward the precipitation area (Chungcheongnamdo and Gyeonggi Province) were generated in all experiments (Fig. 10.9a–d). CTRL slightly captured water vapor convergence (− 60 ×10−6 g kg−1 s−1 ) in the eastern

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Fig. 10.9 Water vapor convergence (shaded; g kg−1 s−1 ) and flux (vectors; g kg−1 m s−1 ) at 850 hPa from CTRL, RQV, GPS + ASR, and GPS + ASR + AMV at the last data assimilation time for a–d Case 1, e–h Case 2, i–l Case 3, m–p Case 4

region of the Yellow Sea and flux (325 g kg−1 m s−1 ) toward the precipitation area (Fig. 10.9a). RQV showed stronger and wider coverage of water vapor convergence (− 90 × 10−6 g kg−1 s−1 ) in the Yellow Sea and flux (480 g kg−1 m s−1 ) toward precipitation area than in other simulations (Fig. 10.9b). This is mainly caused by excessive water vapor on the initial field as mentioned above (Fig. 10.5a). GPS + ASR exhibited moisture convergence (− 75 g kg−1 m s−1 ) in the Yellow Sea and flux (450 g kg−1 m s−1 ) toward the precipitation area in lower intensity and narrower scale than RQV (Fig. 10.9c). Lastly, GPS + ASR + AMV evidently intensified the

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Fig. 10.10 Vertical velocity (hPa h−1 ) and horizontal wind (m s−1 ) at 700 hPa from CTRL, RQV, GPS + ASR, and GPS + ASR + AMV at the last data assimilation time for a–d Case 1, e–h Case 2, i–l Case 3, m–p Case 4

water vapor convergence to a greater extent than GPS + ASR by approximately − 90 × 10−6 g kg−1 s−1 , but the coverage was smaller than RQV (Fig. 10.9d). Water vapor flux in GPS + ASR + AMV was of a similar magnitude as compared to GPS + ASR by approximately 450 g kg−1 m s−1 , but the coverage in GPS + ASR + AMV was smaller than GPS + ASR (Fig. 10.9c, d). These results suggest that GPS + ASR + AMV had the optimal amount of moisture convergence and flux, leading

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to more accurate rainfall in terms of intensity and coverage. At 700 hPa, CTRL exhibited weaker vertical velocity by approximately − 50 hPa h−1 as compared to other simulations over the convergence area (eastern Yellow Sea) (Fig. 10.10a). RQV, GPS + ASR, and GPS + ASR + AMV enhanced vertical velocity above − 75 hPa h−1 over the eastern region of the Yellow Sea, as expected with the enhancement of convergence at 850 hPa (Fig. 10.10b–d). However, RQV produced strong vertical velocity (≥ − 75 hPa h−1 ) in a larger scale than GPS + ASR and GPS + ASR + AMV, extending to Chungcheongnam-do Province (Fig. 10.10b–d). Over the inland South Korea (near the northern Gyeonggi-do area), only GPS + ASR + AMV exhibited vertical velocity of approximately − 65 hPa h−1 , suggesting that only GPS + ASR + AMV may be capable of capturing significant rainfall over the northern Gyeonggi-do area (Fig. 10.10d). In Case 2, at 850 hPa, CTRL failed to generate the convergence over the convective area as there was no wind convergence enhancement (Fig. 10.9e). Meanwhile, water vapor convergence (− 90 × 10−6 g kg−1 s−1 ) and flux (280 g kg−1 m s−1 ) over the main convective area (approximately 36.6° N 124° E) were evidently observed in RQV, GPS + ASR, and GPS + ASR + AMV, with the largest scale in GPS + ASR + AMV (Fig. 10.9f–h). GPS + ASR and GPS + ASR + AMV also showed convergence over the other convective areas (36° N 122° E) (Fig. 10.9g, h). In addition, over inland Gyeonggi and Gangwon Province (precipitation area), the magnitude of water vapor flux in RQV was higher by approximately 100 g kg−1 m s−1 as compared to other simulations (Fig. 10.9f). This result suggests that RQV may produce intense rainfall at the earlier forecast hours. Moreover, the direction of water vapor flux in RQV was slightly turned toward northeast, which does not enhance the propagated West–East direction of Changma front (Fig. 10.9f). At 700 hPa, it can be inferred that CTRL exhibited almost zero vertical velocity than other simulations over convective area (approximately 36.6° N 124° E) (Fig. 10.10e), associated with zero convergence at 850 hPa (Fig. 10.9e). RQV, GPS + ASR, and GPS + ASR + AMV generated a vertical velocity of approximately ≥ − 60 hPa h−1 in the convective area (36.6° N 124° E) (Fig. 10.10f–h), as expected with strong convergence at 850 hPa (Fig. 10.9e– h). Moreover, GPS + ASR and GPS + ASR + AMV produced a vertical velocity of − 40 hPa h−1 and − 45 hPa h−1 at 36° N 122° E, respectively (Fig. 10.10g, h). This result suggests that GPS + ASR + AMV enhanced convective system development along the Changma front (Fig. 10.10h). In Case 3, at 850 hPa, water vapor convergence was evidently seen over the MCS and precipitation area in all experiments (Fig. 10.9i–l). However, only RQV, GPS + ASR, and GPS + ASR + AMV were able to intensify the water vapor convergence by approximately − 90 × 10−6 g kg−1 s−1 at the center of MCS (Fig. 10.9j–l). Due to increased water vapor convergence, moisture flux was also increased by approximately 350 g kg−1 m s−1 (Fig. 10.9j–l). Over the precipitation area, water vapor convergence and flux were also intensified in RQV, GPS + ASR, and GPS + ASR + AMV, with differences in scale or magnitude (Fig. 10.9j–l). RQV mainly generated water vapor convergence (≥ − 75 × 10−6 g kg−1 s−1 ) extended more to Gangwon Province or larger scale than GPS + ASR or GPS + ASR + AMV (Fig. 10.9j). Meanwhile, GPS + ASR and GPS + ASR + AMV mainly produced

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water vapor convergence (≤ − 75 × 10−6 g kg−1 s−1 ) in the precipitation area, but the coverage of water vapor convergence in GPS + ASR + AMV was larger than that in GPS + ASR (Fig. 10.9k, l). The water vapor flux toward the precipitation area in RQV was also larger by approximately 270 g kg−1 m s−1 (Fig. 10.9j). Meanwhile, GPS + ASR and GPS + ASR + AMV produced water vapor flux of approximately 230 g kg−1 m s−1 and 250 g kg−1 m s−1 , respectively (Fig. 10.9k, l). At 700 hPa, it can be observed that CTRL exhibited a very weak vertical velocity as compared to other simulations in the MCS and precipitation area (Fig. 10.10i), and associated weak enhancement of convergence at 850 hPa (Fig. 10.9i). RQV, GPS + ASR, and GPS + ASR + AMV generated strong vertical velocity stronger than − 75 hPa h−1 in the MCS area (Fig. 10.10j–l), as expected with the convergence enhancement at 850 hPa (Fig. 10.9j–l). However, GPS + ASR mainly produced strong vertical velocity in a smaller scale than RQV and GPS + ASR + AMV (Fig. 10.10k). Over the precipitation area, RQV, GPS + ASR, and GPS + ASR + AMV exhibited strong vertical velocity (≥ − 75 hPa h−1 ) (Fig. 10.10j–l), but RQV had a larger scale than other simulations (Fig. 10.10j). In addition, GPS + ASR + AMV mainly produced vertical velocity (≤ − 75 hPa h−1 ) in increased coverage of precipitation area than RQV or GPS + ASR (Fig. 10.10l). In Case 4, at 850 hPa, it can be inferred that CTRL generated a weak water vapor convergence and flux over the precipitation area (Northeastern Chungcheongbuk-do) (Fig. 10.9m). Thus, CTRL was unable to produce any precipitation. RQV showed the strongest water vapor convergence of approximately − 90 × 10−6 g kg−1 s−1 over the precipitation area associated with water vapor flux of approximately 150 g kg−1 m s−1 , which may result in the overestimation of rainfall (Fig. 10.9n). GPS + ASR produced a weaker water vapor convergence (− 75 × 10−6 g kg−1 s−1 ) and flux (125 g kg−1 m s−1 ) as compared to RQV (Fig. 10.9o). GPS + ASR + AMV was similar to GPS + ASR, but the water vapor convergence was slightly intensified at the precipitation area by approximately − 85 × 10−6 g kg−1 s−1 (Fig. 10.9p). At 700 hPa, it can be seen that CTRL exhibited very weak vertical velocity as compared to other simulations in the precipitation area (Fig. 10.10m), associated with weak convergence at 850 hPa (Fig. 10.9m). RQV generated the strongest vertical velocity of approximately − 57 hPa h−1 (with a maximum of − 70 hPa h−1 ) in the precipitation area (Fig. 10.10n), as expected with strong convergence at the lower level (Fig. 10.9n). GPS + ASR and GPS + ASR + AMV produced a vertical velocity of approximately − 32 and − 37 hPa h−1 , suggesting that GPS + ASR + AMV enhanced convective band development more as compared to GPS + ASR; hence, increased accuracy in predicting maximum precipitation.

10.4.3 Qualitative Forecast Evaluation The distribution cumulative rainfall forecasts from each simulation were displayed with AWS observation data. Figure 10.11 shows the cumulative rainfall generated by CTRL, RQV, GPS + ASR, and GPS + ASR + AMV for Cases 1, 2, 3, and

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4 forecast period, respectively. For Case 1, the AWS observation shows an intense northeast-shifted rainband and two maximum precipitation areas marked by A and B in Fig. 10.5 with the maximum precipitation reaching 120 mm (Fig. 10.11a). CTRL predicted a small amount precipitation and missed the intense rainfall over locations A and B (Fig. 10.11b). CTRL assimilated no moisture information, causing no water to precipitate out of the air that will occur as rain. Meanwhile, RQV produced a stronger and broader northeast-shifted rainband with the maximum precipitation reaching 200 mm over location A, but it did not predict any rainfall over location B (Fig. 10.11c). GPS + ASR overpredicted rainfall by approximately 30 mm in the northeast-shifted rainband as compared to AWS, but it slightly improved intense rainfall by approximately 30 mm over location B as compared to RQV (Fig. 10.11d). The last experiment, GPS + ASR + AMV, captured a northeast-shifted rainband similar to that in GPS + ASR, but it reduced the overestimation in some areas along the band (Fig. 10.11e). Additionally, GPS + ASR + AMV captured a maximum precipitation of approximately 110 mm in location B similar to the AWS observations (Fig. 10.11e). For Case 2, AWS observations produced an east-shifted rainband with a maximum precipitation reaching 120 mm over location A (Fig. 10.11f). CTRL captured a weak and broken east-shifted rainband and missed the intense rainfall over location A (Fig. 10.11g). Meanwhile, RQV generated the east-shifted precipitation well, but RQV missed the intense rainfall in location A and generated false alarms in the north and southwest of location A (Fig. 10.11h). GPS + ASR generated the east-shifted rainband and the maximum precipitation of location A (Fig. 10.11i). However, the east-shifted rainfall was narrower compared to AWS observation, causing underprediction in some areas (Fig. 10.11i). In addition, the maximum precipitation in GPS + ASR exceeded 120 mm, which was evidently overestimated as compared to AWS (Fig. 10.11i). Meanwhile, GPS + ASR + AMV produced the east-shifted rainfall well and broader than that of GPS + ASR while capturing the maximum precipitation of the location A; however, the intensity of maximum precipitation overestimated the AWS (≥ 120 mm) (Fig. 10.11j). Overall, GPS + ASR + AMV was the closest to the AWS observation compared to the other simulations. For Case 3, AWS mainly observed intense rainfall which exceeded 200 mm over locations A and B (Fig. 10.11k). Evidently, CTRL did not generate rainfall for both locations A and B (Fig. 10.11l). RQV generated rainfall over location A with a maximum precipitation of 200 mm (Fig. 10.11m). However, the rainband was centered further north, causing the scale of rainfall on the location A to be smaller than AWS (Fig. 10.11m). RQV also generated rainfall further north of location B (Fig. 10.11m). Contrarily, GPS + ASR slightly generated the rainfall centered further south compared to RQV, which covered rainfall area of location A better than RQV (Fig. 10.11n). However, GPS + ASR underpredicted the intensity of rainfall over location A (≥ 200 mm) (Fig. 10.11n). For location B, GPS + ASR slightly captured rainfall of approximately 70 mm and clearly underestimated the AWS observations, though it reduced the underprediction by approximately 30 mm compared to that in RQV (Fig. 10.11n). Meanwhile, GPS + ASR + AMV showed larger scale of rainfall with higher intensity (≥ 200 mm) in location A than the other simulations which

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Fig. 10.11 Cumulative precipitation (mm) distribution from AWS, CTRL, RQV, GPS + ASR, and GPS + ASR + AMV for a–e Case 1, f–j Case 2, k–o Case 3, and p–t Case 4 forecast period of D03

has better agreement with AWS observations (Fig. 10.11o). Moreover, GPS + ASR + AMV also captured rainfall with intensities greater than 70 mm over location B, which is a higher intensity than other simulations and closer to AWS observations (Fig. 10.11o). A convective band occurred in Case 4, which caused rainfall along the Chungcheongbuk-do Province and in some parts of Gyeongsangbuk-do Province observed by AWS observation, with a maximum precipitation of 70 mm (Fig. 10.11p). Evidently, CTRL missed the main convective band rainfall in Chungcheongbukdo Province and overestimated small precipitation (30 mm) in Gyeongsangbukdo Province (Fig. 10.11q). Meanwhile, RQV produced a strong precipitation band (≥ 120 mm), but the rainband was further north of Chungcheongbuk-do

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Province (Fig. 10.11r). This strong rainband caused overprediction in some areas of Gangwon Province and missed rainfall in some areas of Chungcheongbuk-do Province (Fig. 10.11r). The overestimation in Gyeongsangbuk-do Province also remained in RQV, with larger coverage than CTRL (Fig. 10.11r). GPS + ASR captured the rainband further south to Chungcheongbuk-do Province as compared to RQV (Fig. 10.11s). The intensity of rainfall in GPS + ASR was mainly 70 mm (with the maximum exceeding 70 mm) and was slightly overestimated as compared to AWS (Fig. 10.11s). GPS + ASR + AMV also generated a precipitation similar to GPS + ASR, which may be caused by the inclusion of AMV into the assimilation which does not significantly influence the convective band case (Fig. 10.11t). However, the rainfall distribution in GPS + ASR + AMV was slightly larger than GPS + ASR, with the maximum precipitation only reaching 70 mm closer to the AWS (Fig. 10.11t).

10.4.4 Model Verification Quantitative verification was performed on hourly rainfall for evaluating the forecast leading time. Figure 10.12 and Table 10.3 show the calculation of quantitative error (RMSE and BIAS) and categorical rainfall smaller than 0.1 mm (AC and CSI) using the forecast models and AWS data of every 1 h forecast for Cases 1, 2, 3, and 4, respectively. The influence distance of AWS in South Korea was effectively 10 km × 10 km. Thus, the precipitation from the models of domain 3 averaged nine grid points as compared to AWS. For Case 1 (Fig. 10.12a, b), due to rainfall underprediction, CTRL showed the lowest AC and CSI in terms of rainfall classification because CTRL missed the rainfall at all the forecast times. RQV increased the AC and CSI score by approximately 45% only during the first 6 h compared to CTRL and had the worst AC and CSI scores relative to other experiments. Both AC and CSI scores of GPS + ASR also showed an increased (35%) as compared to CTRL until the 6th hour, but at later hours both scores were reduced. GPS + ASR + AMV increased the scores lower than RQV during the first 5 h because rainfall classification only determines precipitation larger than 0.1 mm but it does not determine the extent of overestimation. Overall, GPS + ASR + AMV showed the highest AC and CSI at the most of forecast times than other experiments, especially near the forecast completion. For Case 2 (Fig. 10.12c, d), the RQV increased the AC and CSI scores by approximately 40% as compared to CTRL until the 5th hour, before continuing to decrease and possessing a lower score as compared to CTRL. GPS + ASR improved AC and CSI score by approximately 60% throughout the times than CTRL, except at 6th hour because there were many false alarms occurring. Meanwhile, GPS + ASR + AMV increased the scores by approximately 65% during the first 9 h and 20% after 9 h.

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For Case 3 (Fig. 10.12e, f), due to the underestimation, CTRL’s AC and CSI scores were very low because of the missed rainfall. The RQV showed an improvement of AC and CSI by approximately 40% during the first 15 h, but continued to decrease after the 15th hour. The improvement of AC and CSI scores in GPS + ASR was not higher than RQV, but GPS + ASR persisted the improvement for a longer period. GPS + ASR + AMV improved by 18% as compared to GPS + ASR at most forecast times, except at approximately the 12th–15th hours because of the prediction of more false alarms as compared to GPS + ASR during these hours. In general, GPS + ASR + AMV increased statistics scores for longer forecast times than other simulations. For Case 4 (Fig. 10.12g, h), CTRL produced the lowest AC and CSI scores for most of the forecast times. RQV improved the AC score by 10% as compared to CTRL during the first 2 h, before the decreasing. RQV mostly increased the CSI scope by 60% CSI as compared to CTRL, except for the 3rd and 6th hours. Considering AC score, GPS + ASR and GPS + ASR + AMV increased 5% and 7% as compared to CTRL during the first 3 h, respectively. Considering the CSI score, GPS + ASR and GPS + ASR + AMV increased 50% and 58% as compared to CTRL throughout the forecast times, respectively. Overall, the best improvements were observed in GPS + ASR + AMV (Fig. 10.12). The cumulative rainfall forecasts were also verified with AWS observation data through quantitative error (RMSE and BIAS), classification rainfall occurrences (> 0.1 mm) (Accuracy and CSI), and pattern correlation method. Table 10.3 shows quantitative verification of cumulative rainfall for Cases 1, 2, 3, and 4, as well as average of all cases. For Case 1 (Table 10.3), RQV increased RMSE by approximately 35% compared to that for CTRL. This error was mainly caused by the overestimation indicated by BIAS 20.17 mm. Meanwhile, GPS + ASR showed a decreased RMSE by approximately 3% as compared to CTRL, with the BIAS of 9.5 mm indicating decreased overestimation by approximately 52% compared to RQV. GPS + ASR + AMV decreased more RMSE by approximately 12% as compared to CTRL, and BIAS error by approximately 55% as compared to RQV. Considering category classification, the scores of all experiments were mostly comparable to CTRL. However, the best performances were achieved by GPS + ASR + AMV with an increased score of 2% for AC and CSI as compared to CTRL. Pattern correlation indicates that RQV has the worst correlation due to the excessive overestimation, making it less correlated to AWS observation. Meanwhile, GPS + ASR + AMV produced the best correlation with an increase of approximately 50% compared to that of CTRL because it captured the two locations of maximum rainfall. For Case 2 (Table 10.3), compared to CTRL, all experiments show reduction of RMSE or BIAS error. RQV, GPS + ASR, and GPS + ASR + AMV decreased RMSE by approximately 32%, 17%, 45%, and 46%, respectively. RQV showed 72% reduction of BIAS, though the BIAS of 3.44 mm indicates overestimation. Moreover, GPS + ASR and GPS + ASR + AMV decreased BIAS error by approximately 90% and 95%, respectively. However, GPS + ASR slightly underestimated (− 1.7), while GPS + ASR + AMV slightly overestimated (0.55). AC and CSI scores also exhibited an improvement in all experiments compared to that of CTRL. GPS + ASR and GPS + ASR + AMV produced the best performances with AC and CSI score

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Fig. 10.12 Hourly categorical statistics verification of Cases 1, 2, 3, and 4 forecast period for CTRL, RQV, GPS + ASR, and GPS + ASR + AMV

improvements of 11% and 20%, respectively. This could primarily be attributed to the correction of maximum precipitation location. Pattern correlation (PC) shows increased correlation on all experiments as compared to CTRL. RQV, GPS + ASR, and GPS + ASR + AMV produced comparable correlation with 71%, 74%, and 74.5% improvement, respectively. For Case 3 (Table 10.3), RQV, GPS + ASR, and GPS + ASR + AMV reduced RMSE by approximately 30%, 34%, and 38%, respectively. Additionally, BIAS error indicates that RQV, GPS + ASR, and GPS + ASR + AMV reduced the underestimation by approximately 57%, 87%, and 89%, respectively. Considering the rainfall occurrences, AC and CSI scores possess comparable values between the assimilation experiments. RQV, GPS + ASR, and GPS + ASR + AMV produced approximately 0.9%, 2.2%, and 4.4% improvement in AC score, and approximately 0.24%, 4.35%,

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Table 10.3 Quantitative verification of cumulative rainfall from CTRL, RQV, GPS + ASR, and GPS + ASR + AMV against AWS observation for Cases 1, 2, 3, and 4, respectively, and average of all cases Case 1

Case 2

Case 3

Case 4

Average

Experiment

RMSE (mm)

BIAS (mm)

AC

CSI

PC

CTRL

31.57

− 10.94

0.81

0.88

0.4

RQV

48.28

20.17

0.86

0.92

0.3

GPS + ASR

30.43

9.5

0.88

0.94

0.61

GPS + ASR + AMV

27.86

9

0.89

0.96

0.64

CTRL

28.62

− 11.97

0.76

0.69

0.21

RQV

19.95

3.44

0.81

0.82

0.73

GPS + ASR

15.21

− 1.7

0.83

0.8

0.82

GPS + ASR + AMV

15.2

0.55

0.85

0.84

0.83

CTRL

52.05

− 19.29

0.80

0.827

0.51

RQV

36.06

− 8.68

0.81

0.829

0.76

GPS + ASR

34.3

− 2.42

0.82

0.863

0.8

GPS + ASR + AMV

32.21

− 2.04

0.83

0.858

0.82

CTRL

10.81

− 1.66

0.63

0.28

0.27

RQV

10.79

2.18

0.73

0.51

0.52

GPS + ASR

8.8

1.29

0.77

0.52

0.51

GPS + ASR + AMV

8.68

1.09

0.77

0.53

0.53

CTRL

30.48

− 10.96

0.75

0.67

0.34

RQV

28.77

4.27

0.80

0.77

0.57

GPS + ASR

22.18

2.16

0.81

0.78

0.68

GPS + ASR + AMV

20.98

2.15

0.83

0.79

0.71

and 3.74% improvement in CSI score as compared to CTRL. PC score reveals that GPS + ASR + AMV produced the best score with an increased value of 60% compared to CTRL. Meanwhile, RQV and GPS + ASR increased by approximately 49% and 56%, respectively. Considering Case 4 (Table 10.3), RQV produced only a 0.18% reduction in RMSE as compared to CTRL. Additionally, RQV generated a BIAS of 2.18 mm, indicating an overestimation. GPS + ASR and GPS + ASR + AMV show a comparable reduction of 18 and 19% for RMSE, and 22 and 34% for BIAS error. GPS + ASR and GPS + ASR + AMV generated a similar AC and CSI scores. Both improved the AC and CSI scores by 22 and 86%, respectively, compared to that of CTRL. RQV, GPS + ASR, and GPS + ASR + AMV improved PC by 82, 88, and 96% when correlated to AWS observations. From the average of quantitative verification from all cases (Table 10.3), the lowest RMSE and BIAS error was achieved by GPS + ASR + AMV, followed by GPS + ASR, RQV, and CTRL experiments. The value of reduction percentage of RMSE and BIAS error in GPS + ASR + AMV reached 31 and 80% compared to CTRL. In

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Fig. 10.13 Average of hourly ETS of all cases for CTRL, RQV, GPS + ASR, and GPS + ASR + AMV

categorical quantitative, GPS + ASR + AMV performed the best, with an AC and CSI increase of 10 and 16%, respectively. PC also established that GPS + ASR + AMV was the most correlated to AWS by approximately 71%. To further investigate the impact of assimilation experiments on rainfall forecasts, the ETS was calculated using the simulation forecast fields and AWS observations as the function of rainfall threshold per hour (mm) (Fig. 10.13). Four rainfall thresholds light rain (0.1 mm ≤ R ≤ 3 mm), moderate rain (3 mm ≤ R ≤ 15 mm), heavy rain (15 mm ≤ R ≤ 30 mm), and very heavy rain (R ≥ 30 mm) were used. The ETS of the four cases was averaged. Compared to CTRL, RQV, GPS + ASR, and GPS + ASR + AMV improved the ETS by 38%, 50%, and 59% for the light rain, respectively. For moderate rain, GPS + ASR + AMV showed the highest accuracy with a 62% improvement in ETS compared to that of CTRL; however, RQV and GPS + ASR only produced improvements of 28% and 44%, respectively. RQV, GPS + ASR, and GPS + ASR + AMV increased the heavy rain ETS by approximately 28%, 63%, and 53%, respectively. For the very heavy rain threshold, ETS showed a small value because the occurrence of very heavy rainfall was rare. The enhancement by assimilation experiments was also small, and RQV, GPS + ASR, and GPS + ASR + AMV produced a similar 23% increase of the ETS compared to that of CTRL. Overall, it can be inferred that the improvement in experiment assimilations primarily corresponded to light and moderate rain, with GPS + ASR + AMV showing the best improvement.

10.4.5 Comparison of Forecast Variables The vertical profile of water vapor mixing ratio (g kg−1 ), temperature (°C), wind (m s−1 ), and geopotential height (m) were verified using radiosonde observations for

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Fig. 10.14 Average of bias vertical profiles of CTRL (black), RQV (green), GPS + ASR (blue), and GPS + ASR + AMV (red) against radiosondes for a water vapor mixing ratio (Qv, g kg−1 ), b temperature (°C), c wind (m s−1 ), and d geopotential height (GPH, m)

each case. The time and location of verification were selected based on the available data and proximity to the precipitation area during the forecast period of each case. There were 12 radiosonde observations validated during the events and the vertical biases were averaged using these 12 radiosonde observations. For Q variables (Fig. 10.14a), it was evident that water vapor mixing ratio of CTRL underestimated the radiosonde observations at all levels. RQV reduced the underestimation in CTRL from 925 to 400 hPa, and overestimation from 925 to 600 hPa; however, underestimation was reduced from 600 to 400 hPa. Above 400 hPa, RQV had increased underestimation as compared to CTRL. This result showed that RQV was incapable of maintaining high water vapor bias during the forecast, leading to frequent rainfall underestimation at the end of forecast hours. GPS + ASR and GPS + ASR + AMV reduced the underestimation of water vapor mixing ratio from CTRL at all levels, without producing overestimation as large as in RQV from 925 to 600 hPa. The near-zero value of bias was mostly achieved by GPS + ASR + AMV at all levels. For T variables (Fig. 10.14b), CTRL showed warm bias below 400 hPa and above 300 hPa, but cold bias was between 400 and 300 hPa. All the experiments reduced the warm bias from 900 to 500 hPa and cold bias from 400 to 300 hPa. GPS + ASR + AMV showed the most reduction in BIAS as compared to CTRL. For wind variables (Fig. 10.14c), CTRL produced a negative BIAS below 500 hPa, and a positive BIAS above 500 hPa. At below 500 hPa, RQV, GPS + ASR, and GPS + ASR + AMV showed reduction of negative BIAS of wind as compared to CTRL. Meanwhile, above 500 hPa, only GPS + ASR and GPS + ASR + AMV were capable of reducing the positive BIAS of wind. In general, a near-zero BIAS value was mostly produced by GPS + ASR + AMV. For geopotential height (GPH)

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variables (Fig. 10.14d), CTRL showed positive BIAS at all levels. RQV, GPS + ASR, and GPS + ASR + AMV reduced the positive BIAS of CTRL at all levels. However, GPS + ASR + AMV substantially showed the lowest BIAS at all levels as compared to other simulations.

10.5 Summary and Conclusions The performance of 3DVAR assimilation with GPSRO refractivity, all-sky radiance, and AMV assimilation was investigated based on four heavy rainfall events during summertime in South Korea. Three cases included rainfall associated with Changma front with different forecast periods and one case included convective rainfall. These cases were selected because they facilitate better understanding on the impact of assimilating different atmospheric motions from meso- (short- and long-term periods) to convective scales. To establish the contribution of each simulation in generating rainfall forecasts, the increments on the initial field were analyzed. It was observed that assimilating derived-water vapor from radar (RQV) exhibited extra and spurious water vapor content, while the combination of GPSRO refractivity and all-sky radiances (GPS + ASR and GPS + ASR + AMV) assimilation was able to enhance water vapor content appropriately for extreme rainfall associated with Changma front and convective cases. The additional AMVs in GPS + ASR + AMV drive significant changes in winds, interrelated to the pressure fields. These changes in winds were mainly associated with enhanced wind convergence and low pressure. However, the assimilation of AMVs has a minor impact on convective-scale storm rainfall. Due to the adjustment of water vapor mixing ratio and wind convergence in GPS + ASR + AMV, the intensity and acceleration of water vapor condensation were increased, resulting in deep warming increments because of latent heat released from condensation. Finally, GPS + ASR + AMV produced more dynamically and thermodynamically consistent analysis increments on the initial fields. From the weather chart analysis, the geopotential height at 850 hPa demonstrated that GPS + ASR + AMV strengthened low pressure or trough over the convective area in all cases due to improved pressure fields. The correction of water vapor and winds in GPS + ASR + AMV was attributed to the intensified water vapor convergence and flux in proper magnitude, leading to an improved accuracy of intensity and location of heavy rainfall. Considering rainfall forecasts, RQV generally overestimated rainfall during the first 4 h either on mesoscale or local scale. GPS + ASR and GPS + ASR + AMV mainly reduced the overestimation in RQV and underestimation in CTRL by assimilating water vapor information from GPSRO refractivity and satellite all-sky radiances. However, only GPS + ASR + AMV frequently sustained heavy rainfall with an increasing lead-time compared to other simulations, especially for rainfall associated with Changma front. The errors were reduced by approximately 35%, and the accuracy score was improved by approximately 25% for most of forecast times

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compared to CTRL. The qualitative and quantitative accumulated rainfall verification reveals that GPS + ASR + AMV had a better agreement on both rainfall and intensity compared to other simulations for meso- and convective scales. The error reduction can be up to 31% for RMSE and 80% for BIAS, while the improvement of skill scores can be up to 10% for AC, 16% for CSI, and 53% for PC compared to CTRL. Particularly, ETS indicates that GPS + ASR + AMV has the best ability in predicting light and moderate rainfall. The calculation of vertical profile bias against radiosonde data shows GPS + ASR + AMV has the greatest improvement in water vapor mixing ratio, temperature, wind, and geopotential height fields as compared to other simulations at most levels. It should be noted that the 3DVAR technique was used for data assimilation in this study. However, 3DVAR is limited by issues, such as the use of static background error covariances, making it impractical for manifesting the flow-dependent feature of the atmosphere. The ensemble-based assimilation method is known to provide flowdependent background error covariances. Additionally, the Adaptive Observation Error Inflation (AOEI) method, which utilizes the ensemble-based data assimilation framework, is expected to enhance the assimilation of all-sky radiances. Further, only water vapor channels were used to assimilate the all-sky radiances. Assimilating other surface infrared channels will pose various challenges and requires a careful treatment of surface emissivity. Moreover, the assimilation of satellite allsky radiance was performed on multiple domains, which may cause a data overlap. Methods to effectively and simultaneously assimilate all-sky radiance, radar, and other observations data need to be investigated further. Acknowledgements The contents herein are reproduced from Miranti Indri Hastuti’s master’s thesis. The work reflects many years of cumulated study results contributed by the coauthors of Ji-Won Lee, Jeong-Ho Bae, Jae-Geun Lee, and Yushin Kim.

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Chapter 11

Assimilating Precipitation Features Based on the Fractions Skill Score: An Idealized Study with an Intermediate AGCM Shigenori Otsuka, Taeka Awazu, Christian A. Welzbacher, Roland Potthast, and Takemasa Miyoshi Abstract Advanced observation techniques such as radars and satellites provide spatial patterns of precipitation areas on regional scales and global scales. Although information on the spatial structure is potentially useful for better prediction of precipitation, precipitation observation has nonlinear processes and non-Gaussian distributions; therefore, improving numerical weather predictions by assimilating precipitation observations is known to be difficult. This paper proposes a novel approach for precipitation data assimilation: assimilating features based on the fractions skill score. In an idealized experimental design with an intermediate atmospheric general circulation model and the local ensemble transform Kalman filter, assimilating the fraction observations helped improve the meteorological fields consistently. Forecast experiments showed that the proposed method improved the forecast accuracy.

S. Otsuka (B) · T. Awazu · T. Miyoshi Center for Computational Science, RIKEN, Kobe, Japan e-mail: [email protected] S. Otsuka · T. Miyoshi Cluster for Pioneering Research, RIKEN, Kobe, Japan Interdisciplinary Theoretical and Mathematical Sciences Program, RIKEN, Kobe, Japan T. Awazu Now at: Kanden Systems Inc., Osaka, Japan C. A. Welzbacher Deutscher Wetterdienst, Department on Numerical Modeling, Frankfurter Str. 135, 63067 Offenbach am Main, Germany R. Potthast Deutscher Wetterdienst, Division Meteorological Analysis and Modeling, Frankfurter Str. 135, 63067 Offenbach am Main, Germany University of Reading, Reading, UK T. Miyoshi University of Maryland, College Park, Maryland, USA Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_11

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Keywords Data assimilation · Ensemble Kalman filter · SPEEDY-LETKF · Fractions skill score · Non-Gaussian

11.1 Introduction Precipitation is an important factor in the meteorological observation. Recent advances in precipitation observation techniques include advanced meteorological satellites and precipitation radars; they provide spatial patterns of precipitation areas. Although the spatial pattern provides more information on physics behind than conventional single-point observations such as rain gauge observations do, traditional approaches of data assimilation in meteorology do not fully take advantage of the spatial information. Most data assimilation methods for high-dimensional systems such as the ensemble Kalman filter (EnKF; Evensen 1994) assume linear processes and/or Gaussian error distributions, but precipitation observation has nonlinearity and non-Gaussian distributions, leading to difficulties in precipitation data assimilation. Reduction of non-Gaussianity in the error statistics of precipitation requires an ultra-rapid update system with dense observations (Ruiz et al. 2021). Hence, considering the spatial structures of precipitation areas explicitly in data assimilation can be a promising alternative. In verification of precipitation forecasts, there are several methods to evaluate spatial patterns of precipitation areas (e.g., Davis et al. 2006; Wernli et al. 2008; Lack et al. 2010; Awazu et al. 2019). Once a difference between observed and predicted precipitation patterns is quantified, data assimilation can use it. Regarding the non-Gaussian problem, Lien et al. (2013) proposed a novel approach to assimilate precipitation by the Gaussian transformation (GT); at first, probability density functions (PDFs) of precipitation are computed empirically using observed and model-simulated precipitation for the past 10 years. Then, precipitation data are transformed to Gaussian-distributed values by the PDF. Lien et al. (2013) and follow-on studies (Lien et al. 2016a, b; Kotsuki et al. 2017) succeeded in improving model variables by assimilating satellite-based precipitation observations. However, GT requires a history of model simulations and observations; the system tends to become complex. This study proposes a simpler yet promising approach to assimilate spatial patterns of precipitation observed by satellites or radars: assimilating fractions of precipitation area, inspired by the fractions skill score (Roberts and Lean 2008). Assimilating spatial structure is an emerging field in data assimilation; Li et al. (2017) presented a method to assimilate shapes of oil spills into an oceanic model. Among various shape features, calculating fractions of a given condition is one of the simplest approaches. The computation of fraction consists of two operations: thresholding a value, and averaging the error of the thresholded value. A scientific question here is whether thresholding and averaging help increase the Gaussianity of error distributions. This paper presents idealized data assimilation experiments using the fractions of precipitation area with an intermediate atmospheric general circulation model and EnKF.

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This paper is organized as follows: Section 11.2 describes the methodology, Sect. 11.3 presents the experimental design, Sect. 11.4 presents the results, and Sect. 11.5 provides discussion. Finally, conclusions are drawn in Sect. 11.6.

11.2 Methodology 11.2.1 Fraction of Precipitation Areas This study proposes data assimilation by fractions of precipitation areas. Within .nby-.n grid points centered at the analysis point, the number of grid points exceeding a given threshold of precipitation is assumed as the “observation”. Here, .n is the side length of a target square, and the count is divided by .n 2 to obtain a fraction. Figure 11.1 (left) shows an example of fraction observation in the case of side length .n = 5; the fraction becomes .6/(5 × 5), and this value is assigned to the central grid point (red square) of the target area (orange square). The length parameter .n should be an odd number for the symmetry. In the case of .n = 1, the fraction observation becomes an integer of 1 or 0, indicating existence or non-existence of precipitation above the given threshold. Figure 11.1 (right) shows examples of real precipitation patterns. As the side length .n increases, the distribution becomes smoother. This observation model will be applied to observed and simulated precipitation fields.

Fig. 11.1 (Left) A schematic showing a fraction observation of precipitation areas. In this case, the fraction is .6/25 and assigned to the central grid (red square) of the orange square area. (Right) Examples of raw precipitation (a), fraction observations for rain rate greater than 0.7 mm (6 h).−1 with the side lengths 1 (b), 3 (c), and 5 (d)

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Fig. 11.2 The spatial distribution of radiosonde-like locations

11.2.2 Model and Assimilation Method This study uses the Simplified Parameterizations, primitivE-Equation Dynamics (SPEEDY)-Local Ensemble Transform Kalman Filter (LETKF) system (Miyoshi 2005). The SPEEDY (Molteni 2003) is a simplified atmospheric general circulation model that runs at the T30-L7 resolution, corresponding to .96 × 48 grid points and 7 levels. SPEEDY has five state variables: the zonal (.U ) and meridional (.V ) wind, temperature (.T ), specific humidity (. Q), and surface pressure (.Ps). Additionally, it has a diagnostic variable of previous 6-h accumulated precipitation (. R). Data assimilation is performed by the LETKF (Hunt et al. 2007), which is a specific algorithm of EnKF. In the LETKF, this study uses a Gaussian weighting function for the covariance localization and the Relaxation to Prior Spread (RTPS; Whitaker and Hamill 2012) as the covariance inflation method. In this study, the ensemble size is set to 20.

11.2.3 Synthetic Observations After one-year spin-up of SPEEDY from an arbitrary date 0000 UTC 1 January 1981, the following 13-month run is used as the nature run. Following Kondo and Miyoshi (2016), synthetic observations are generated by adding independent, Gaussian-distributed random numbers to the nature run data with the standard deviations of 1 m s.−1 , 1 m s.−1 , 1 K, 1.0 g kg.−1 , and 1 hPa for .U , .V , .T , . Q, and .Ps, respectively, every six hours at the 416 radiosonde-like locations (Fig. 11.2). Variables except .Ps are observed at each model level. . Q observations are generated only from the lowest level to the fourth model level. Synthetic observations of six-hour accumulated precipitation . R o are generated at all the model horizontal grid points by the following equation under the assumption

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that the probability of rain is skewed in the real world: .

) ( )] [ ( R o = exp ln R t + R0 + N 0, ϵ 2 − R0 )[ ( ) ] ( = R t + R t + R0 exp N 0, ϵ 2 − 1 ,

(11.1)

) ( where. R t represents precipitation in the nature run,. N 0, ϵ 2 represents independent, Gaussian-distributed random numbers with the mean 0 and the standard deviation .ϵ, and .ϵ is set to 0.5. At a fixed . R t , the median of the error distribution is zero, and the expected error becomes )[ ( ( ) ] = R t + R0 exp ϵ 2 /2 − 1 > 0,

.

(11.2)

where. represents the expectation. The constant. R0 controls the noise level over the clear sky region; the current experiments adopt . R0 = 0.5 mm (6 h).−1 . A relatively large . R0 is used to highlight the differences among different assimilation algorithms. Fraction observations will be generated by applying the observation operator to these synthetic six-hour accumulated precipitation observations. Following Lien et al. (2016b), fraction and precipitation observations are treated as in-situ data at 850 hPa. LETKF uses the “true” observation error standard deviations for .U , .V , .T , . Q, and .Ps in the current experiments. Under the assumption that the functional form of the true observation error for . R is unknown, the observation error standard deviation .ϵr of the conventional assimilation of raw . R in LETKF is set by the following equation: ( ) ϵ = β · max R o , Rmin ,

. r

(11.3)

where . Rmin is fixed at 0.1 mm (6 h).−1 , and the ratio .β will be tuned manually. The observation error standard deviations of the fraction observations (denoted as .ϵn , .n = 1, 3, 5) will be tuned manually. The observation error covariance matrix is assumed to be diagonal.

11.3 Experimental Design In this paper, we compare the experiments assimilating precipitation as the fraction observations, assimilating raw precipitation . R o , and without precipitation observation. The control run (CTRL) assimilates the radiosonde observations of .U , .V , .T , . Q, and .Ps from January 1, 1982 to March 31, 1983 using the SPEEDY-LETKF system. The 13-month experiments to assimilate precipitation start on March 1, 1982 after the two-month spin-up of CTRL with radiosonde observations. The proposed method has six parameters: the horizontal and vertical length scales of the localization for precipitation (.σPH and .σPV , respectively), relaxation parameter .α of RTPS, precipitation threshold . Rc and the side length .n for the fraction computation, and observation error standard deviation .ϵn . In this study, . Rc is fixed at

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Table 11.1 The horizontal and vertical covariance localization length scales denoted by the standard deviations of the Gaussian weighting functions, .α of the RTPS, and observation error parameters .ϵn or .β in each experiment Horizontal (km) Vertical .α .ϵn , .β CTRL FRAC_1 FRAC_3 FRAC_5 PREC

Radiosonde obs. Radiosonde obs. Fraction obs. Radiosonde obs. Fraction obs. Radiosonde obs. Fraction obs. Radiosonde obs. Precipitation obs.

800 800 800 800 800 800 800 800 200

0.3 .ln p 0.3 .ln p 0.3 .ln p 0.3 .ln p 0.3 .ln p 0.3 .ln p 0.4 .ln p 0.3 .ln p 0.1 .ln p

0.6 0.7 0.6 0.6 0.6

– – 0.7 – 0.6 – 0.7 – 0.8

0.7 mm (6 h).−1 according to preliminary experiments. A dependence on the threshold is a future research topic. The side length for the fraction computation is .n = 1, 3, or 5 grid points; these experiments are referred to as FRAC_.n. The experiment to assimilate raw six-hour accumulated precipitation . R o with the conventional method is referred to as PREC. The parameter tuning was conducted with the following values; .σPH = 200, 400, 600, 800, or 1000 km, .σPV = 0.05, 0.1, 0.2, 0.3, or 0.4 .ln p, .α = 0.5, 0.6, 0.7, or 0.8, .ϵn = 0.4, 0.5, 0.6, 0.7, 0.8, or 0.9 for FRAC_.n, and .β = 0.4, 0.5, 0.6, 0.7, or 0.8 for PREC. Here, .ln p represents the natural logarithm of pressure in Pa. In total, 2300 experiments were performed. Table 11.1 summarizes manually-tuned parameters. If the first-guess spread of fraction or accumulated precipitation is zero at an analysis point, LETKF cannot assimilate fraction observations or accumulated precipitation observations. Therefore, the criterion for the fraction assimilation or precipitation assimilation in this study is that the ensemble spread of fraction or precipitation is not zero; that is, at least one member needs to have non-zero fraction in the case of FRAC_.n, or precipitation greater than 0.1 mm (6 h).−1 in the case of PREC. Although Lien et al. (2013) show that increasing the minimum number of precipitating members increases the analysis accuracy, this study investigates the loosest condition, one member. Sensitivity to the choice of minimum number of precipitating members in the case of FRAC_.n will be a future research topic.

11.4 Results The fraction observations improved the analysis root mean squared errors (RMSEs) of five model state variables and the threat score of precipitation, as well as the fractions skill scores. Table 11.2 shows the analysis RMSEs of state variables, the threat scores for . R ≥ 0.5 mm (6 h).−1 , and the fractions skill scores for . R ≥ 0.7 mm (6 h).−1

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Table 11.2 The analysis RMSEs of .U at the 4th model level (.Lev = 4) (m s.−1 ), .V at .Lev = 4 (m s.−1 ), .T at .Lev = 2 (K), . Q at .Lev = 1 (g kg.−1 ), and .Ps (hPa), the analysis threat scores for . R ≥ 0.5 mm (6 h).−1 , and the analysis fractions skill scores for . R ≥ 0.7 mm (6 h).−1 with the box sizes of .1 × 1, .3 × 3, and .5 × 5, averaged over the period from 1 March 1982 to 31 March 1983 RMSE

Threat score

Fractions skill score .1 × 1

.3 × 3

.5 × 5

0.753

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0.817

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0.665

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FRAC_3_u

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FRAC_5_u

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PREC_u

0.947

0.923

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0.805

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0.669

0.824

.U

.V

.T

.Q

.Ps

CTRL

1.031

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FRAC_1

0.811

0.801

0.278

0.159

FRAC_3

0.860

0.846

0.286

FRAC_5

0.908

0.889

PREC

0.928

FRAC_1_u

Fig. 11.3 Globally-averaged analysis RMSEs of . Q at the lowest level for CTRL (black), FRAC_1 (red), FRAC_3 (green), FRAC_5 (blue), and PREC (orange)

averaged over the period from March 1, 1982 to March 31, 1983. The experiment FRAC_1 shows the greatest improvement in RMSEs of all the variables among all the five experiments, indicating that thresholding the precipitation is beneficial. The mean RMSEs increase as the side length .n increases. PREC did not improve the RMSEs much, whereas FRAC_1 improved all the variables, indicating that simple information such as existence or non-existence of precipitation was effective for this experimental setting. Although FRAC_1 resulted in the highest threat score, precipitation areas and locations were similar among FRAC_1, FRAC_3, and FRAC_5. The fractions skill scores improved the most in FRAC_3 at all the scales from .1 × 1 to .5 × 5 despite the fact that FRAC_3 was designed to optimize the fractions skill score for .3 × 3.

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Fig. 11.4 Globally-averaged RMSEs of . Q at the lowest level for analysis (solid) and 10-day deterministic forecasts from analysis ensemble means (dotted) of CTRL (black), FRAC_1 (red), and PREC (green)

Figure 11.3 shows the time series of analysis RMSEs of . Q at the lowest level from March 1, 1982 to March 31, 1983. The experiment FRAC_1 showed the highest improvement. CTRL showed a large temporal variability of RMSE, whereas the experiments FRAC_.n, assimilating the fraction observations, showed smaller variability; the fraction observations successfully suppressed abrupt changes of performance. PREC sometimes degraded the analysis RMSE. Although experiments FRAC_.n improve the analyses, improving forecasts requires consistency between different model prognostic variables. Therefore, a series of 10-day deterministic forecasts was performed from the analyses by CTRL, FRAC_1, and PREC initialized at 0000 UTC on 8, 18, and August 28, 1982. Figure 11.4 shows the forecast RMSEs of . Q at the lowest level. FRAC_1 outperforms CTRL and PREC for these three initial conditions, indicating that assimilation of the fraction observations updates the model state variables consistently. Although the analysis RMSE of PREC is similar to that of CTRL, the forecast RMSE gradually approaches that of FRAC_1 as the forecast time increases, indicating that PREC can also extract meaningful information from observations.

11.5 Discussion The comparison between FRAC_1 and PREC implies that conversion to bi-level data simply helps (Table 11.2); this may be related to the fact that a binomial distribution can be approximated by a Gaussian, and also the fact that the thresholding reduces the effect from noise over the clear sky regions. According to the central limit theorem, increasing the side length .n will help improve Gaussianity of the fraction observation error distributions. Figures 11.5a–d show the histograms of observation-minus-firstguess for observations of fraction with .n = 1, 3, and 5, and those of raw . R at 00 UTC

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Fig. 11.5 The histograms of observation-minus-first-guess (O.−B) of fraction observations for = 0.7 mm (6 h).−1 with the side length a, e 1, b, f 3, and c, g 5, and d, h 6-h accumulated precipitation observations for a–d the original observations . Ro and e–h unbiased observations . R˜ o . Black curves show the Gaussian distributions estimated from the means and standard deviations of O.−B. Dashed lines represent the means. Computed for 20 ensemble members at 0000 UTC March 1, 1982

. Rc

March 1, 1982. Compared to the observations of raw precipitation . R (Fig. 11.5d), fraction observations (Fig. 11.5a–c) better fit the Gaussian distributions shown by the black curves. However, the comparison among FRAC_1, FRAC_3, and FRAC_5 indicates that the use of wider area does not necessarily improve the analysis accuracy (Fig. 11.3) despite better Gaussianity in FRAC_3 and FRAC_5 (Fig. 11.5a–c). Possible mechanisms to make FRAC_1 the best include loss of information by spatial averaging, biases in the observations, the observation error variance, and correlated observation errors. As shown in Eq. (11.2), rain observations . R o are positively biased due to the skewed error distribution; this type of bias may also exist in the real world as a result of non-Gaussian error statistics. However, the analysis accuracy may be degraded by violating the assumption in EnKF that the errors are unbiased. Therefore, the following form is investigated additionally to obtain unbiased errors: .

)[ ( ) ( ( )] R˜ o = R t + R t + R0 exp N 0, ϵ 2 − exp ϵ 2 /2 ,

(11.4)

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where .< R˜ o − R t > = 0 at a fixed . R t . As shown in Fig. 11.5e–h, the biases are largely reduced when compared to Fig. 11.5a–d. Experiments with this unbiased observation dataset are denoted as FRAC_.n_u and PREC_u. The same tuning parameters as those of FRAC_.n and PREC are used. The bottom half of Table 11.2 shows the scores for FRAC_.n_u and PREC_u. All the experiments show improvements relative to CTRL except the RMSE of .T for PREC_u. However, the experiments FRAC_.n_u show degradation compared to FRAC_.n. In contrast, PREC_u shows better scores in .T , . Q, the threat scores, and the fractions skill scores than PREC, and .U , . V , and .Ps are degraded in PREC_u. In summary, PREC better fits observed precipitation by removing the observation bias, whereas the experiments FRAC_.n do not; fraction observations seem to contribute better when the median of the error distribution for raw precipitation observations is zero. Here, directly comparing FRAC_.n_u with PREC_u may not be fair because the parameters are not tuned for the experiments with . R˜ o . The errors of the neighboring fraction observations may be correlated if they share the same grid points in the computation of fraction. This will negatively impact the analysis accuracy if a diagonal observation error covariance matrix is assumed. However, the experiments above did not take account of this fact. Appropriate treatment of correlated observation errors such as thinning of spatially-dense observations (e.g., Kotsuki et al. 2017) and explicitly considering off-diagonal elements of the observation error covariance (e.g., Miyoshi et al. 2013; Terasaki and Miyoshi 2014) may help. In the current experiments, the ensemble size, the observation error standard deviation, the criterion on the minimum number of precipitating members, and the assimilation interval are fixed to focus on the feasibility of the proposed method. The advantage of the proposed method may depend on these parameters; further investigations are needed to clarify the sensitivity to these parameters.

11.6 Conclusion This paper proposed an alternative approach to assimilate precipitation into an atmospheric model: assimilating the fractions of precipitation areas. As a proof of concept, idealized experiments with the SPEEDY-LETKF were performed. The fraction was obtained by the count of the precipitation grid points divided by the total number of grid points in the target square determined by the side length parameter. Under the perfect model assumption, experiments to assimilate the fractions with the side length of 1, 3, and 5 were performed. For comparison, an experiment to assimilate precipitation observations with the conventional method, and the control experiment without precipitation observations were conducted. Radiosonde observations were assimilated in all the experiments. The proposed method succeeded in improving the analysis RMSEs of the state variables and the threat scores of precipitation, as well as the fractions skill scores of precipitation. The fraction observations with the side length of 1 improved the

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analysis RMSEs most. The fraction observations with the side length 3 and 5 also improved the analyses. However, assimilating precipitation observations with the conventional method did not improve the analysis RMSEs as much as assimilating the fraction observations. Forecasts from the analyses that assimilated the fractions outperformed those of the control experiments without assimilating precipitation. From the results above, the analysis and forecast RMSEs were improved by the fraction observations, indicating that the fraction observation was effective under the idealized conditions. Several issues need to be addressed when it is applied to real cases. Although the proposed method uses only a single threshold for precipitation, the use of multiple levels may further strengthen the current approach in real cases. The spatial scale of fraction computation was fixed in space and time. However, the optimal value may also vary, potentially also depending on the used threshold. Finally, the proposed method has a potential in wider applications; not only the atmospheric applications, but also various geophysical applications, and any applications assimilating image data may obtain benefits from the proposed method. Acknowledgements We thank Dr. Keiichi Kondo for his enormous advice about the SPEEDYLETKF system. We also thank the members of Data Assimilation Research Team, RIKEN Center for Computational Science for their help.This work was partly supported by JST CREST grant JPMJCR1312 and the JAXA Precipitation Measuring Mission. The figures were partly produced by the GFD-Dennou Library.

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Lien GY, Kalnay E, Miyoshi T (2013) Effective assimilation of global precipitation: simulation experiments. Tellus A 65:19915. https://doi.org/10.3402/tellusa.v65i0.19915 Lien GY, Kalnay E, Miyoshi T, Huffman GJ (2016a) Statistical properties of global precipitation in the NCEP GFS model and TMPA observations for data assimilation. Mon Wea Rev 144:663–679. https://doi.org/10.1175/MWR-D-15-0150.1 Lien GY, Miyoshi T, Kalnay E (2016b) Assimilation of TRMM multisatellite precipitation analysis with a low-resolution NCEP global forecast system. Mon Wea Rev 144:643–661. https://doi.org/ 10.1175/MWR-D-15-0149.1 Miyoshi T (2005) Ensemble Kalman filter experiments with a primitive-equation global model. Ph.D. thesis. University of Maryland, College Park Miyoshi T, Kalnay E, Li H (2013) Estimating and including observation-error correlations in data assimilation. Inv Prob Sci Eng 21:387–398. https://doi.org/10.1080/17415977.2012.712527 Molteni F (2003) Atmospheric simulations using a GCM with simplified physical parametrizations. I: model climatology and variability in multi-decadal experiments. Clim Dyn 20:175–191. https:// doi.org/10.1007/s00382-002-0268-2 Roberts NM, Lean HW (2008) Scale-selective verification of rainfall accumulations from highresolution forecasts of convective events. Mon Wea Rev 136:78–97. https://doi.org/10.1175/ 2007MWR2123.1 Ruiz J, Lien GY, Kondo K, Otsuka S, Miyoshi T (2021) Reduced non-Gaussianity by 30 s rapid update in convective-scale numerical weather prediction. Nonlinear Process Geophys 28:615– 626. https://doi.org/10.5194/npg-28-615-2021 Terasaki K, Miyoshi T (2014) Data assimilation with error-correlated and non-orthogonal observations: experiments with the Lorenz-96 model. SOLA 10:210–213. https://doi.org/10.2151/sola. 2014-044 Wernli H, Paulat M, Hagen M, Frei C (2008) SAL-a novel quality measure for the verification of quantitative precipitation forecasts. Mon Wea Rev 136:4470–4487. https://doi.org/10.1175/ 2008MWR2415.1 Whitaker JS, Hamill TM (2012) Evaluating methods to account for system errors in ensemble data assimilation. Mon Wea Rev 140:3078–3089. https://doi.org/10.1175/MWR-D-11-00276.1

Chapter 12

Model Error Representations Using the Covariance Inflation Methods in Ensemble Data Assimilation System Sujeong Lim and Seon Ki Park

Abstract Ensemble data assimilation estimates the initial conditions and the flowdependent background error covariance using observations and ensemble forecasts. The ensemble background error covariance represents the model uncertainty, but it is usually underestimated due to insufficient ensemble size and model errors. Consequently, analysis overtrusts the model forecasts and ignores observations. To solve this problem, we implemented the stochastically perturbed hybrid tendencies scheme to the local ensemble transform Kalman filter in a global numerical weather prediction model—the Korean Integrated Model. It describes the model uncertainties from the computational representations of underlying partial differential equations and the imperfect physical parameterizations, simultaneously. As a result, the new stochastic perturbation scheme leads to an increase in ensemble spread and a decrease in the ensemble mean error, especially in the troposphere. Keywords Ensemble data assimilation · Background error covariance · Model uncertainty · Inflation methods · Stochastic perturbations

12.1 Introduction The ensemble data assimilation (EDA) system produces the uncertainties in initial conditions (ICs) and model forecasts. An ensemble of analyses, computing the flow-dependent background error covariance (BEC), improves the assimilation of observations (Palmer et al. 2009). The EDA system often generates underestimated BEC due to the limited ensemble size and model errors (Miyoshi 2011; Kotsuki et al. S. Lim Center for Climate/Environment Change Prediction Research, Ewha Womans University, Seoul 03760, Republic of Korea e-mail: [email protected] S. K. Park (B) Department of Climate and Energy System Engineering, Ewha Womans University, Seoul 03760, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_12

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2017). Therefore, covariance inflation (CI) methods that artificially increase the error covariance (Luo and Hoteit 2013) are required to prevent the filter divergence whose analyses diverge from the real state (Houtekamer and Mitchell 1998; Lim et al. 2020). The CI methods in the EDA system have two approaches with respect to the prior (i.e., background) and posterior (i.e., analysis) (Duc et al. 2020): the prior CI methods inflate BEC, and then it is digested into the EDA system to determine the analysis mean and analysis error covariance while the posterior CI methods use BEC in the DA process, and the resulting analysis error covariance is inflated. In detail, the prior CI methods indirectly inflate the analysis error covariance by inflating BEC. For example, multiplicative inflation (e.g., Anderson and Anderson 1999) multiplies BEC (.Pb ) with an inflation factor (.γ ). It increases the amplitude of the error covariance without modifying the structure as follows: Pb inf = γ Pb ,

.

(12.1)

where.Pb inf is the inflated BEC and.γ is larger than 1. Next, additive inflation adds the perturbation samples with zero mean from a given model error distribution to analysis ensemble members (e.g., Mitchell and Houtekamer 2000; Whitaker and Hamill 2012). It helps to depict the heterogeneous model uncertainties to analysis perturbations. Last, stochastic perturbation methods estimate the model uncertainties due to the imperfect processes (e.g., Buizza et al. 1999; Shutts 2005; Berner et al. 2009) such as the dynamical and physical approximations: the stochastically perturbed parameterization tendency (SPPT) scheme assumes uncertainty in the parameterized physical tendency (Palmer et al. 2009); the stochastically perturbed dynamical tendency (SPDT) scheme assumes uncertainty in the dynamical tendency (Koo and Hong 2014); and the stochastic kinetic energy backscatter (SKEB) scheme assumes uncertainty from the unresolved scale interactions of NWP model (Shutts 2005). It is known that they are effective in increasing ensemble spread and improving probability skills (Leutbecher et al. 2017). Previous studies simulated the SPPT and stochastic backscatter (SPBS) schemes to investigate the impacts of model uncertainty on the EDA system (Isaksen et al. 2010). Results showed that the SPPT scheme increased the ensemble spread of temperature at the top of the planetary boundary layer (PBL) and wind in the tropics near 700 hPa, whereas SPBS increased the ensemble spread of wind in the PBL. Therefore, it is recommended to use a combination of stochastic perturbation schemes in the EDA system because they complement each other by expressing different model uncertainties. As for the posterior CI methods, it directly inflates the analysis error covariance including the following methods. First, relaxation-to-prior perturbation (RTPP; Zhang et al. 2004) inflates the analysis perturbations (.Xa ) with relaxation factor (.α) as follows: a Xinf = (1 − α)Xa + αXb ,

.

(12.2)

a where .Xinf is the inflated analysis perturbations, .Xb is the forecast perturbations, and .α approaches 1.0. It relaxes the posterior perturbations back toward the prior per-

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turbations. Second, relaxation-to-prior spread (RTPS; Whitaker and Hamill 2012) inflates the analysis ensemble standard deviation (spread), and thus, it relaxes the ensemble standard deviation back to the prior by multiplication as below: ( ( b )) σ a .Xinf = 1+α − 1 Xa , (12.3) σa where .σ b and .σ a are the prior and posterior ensemble standard deviation at each analysis grid point. Note that RTPP works on large-scale processes and RTPS works on small-scale processes (Bowler et al. 2017; Duc et al. 2020). Last, adaptive inflation adaptively estimates the multiplicative inflation parameters (.α) using the posterior innovation statistics (Ying and Zhang 2015). In this study, we focused on the stochastic perturbation method, which is one of the prior CI methods, to account for the model uncertainties in the EDA system. We assume that the model uncertainties come from dynamical and physical tendencies and have implemented the stochastic perturbation hybrid tendencies scheme to a global numerical weather prediction model (Lim et al. 2020). We anticipate that this new stochastic perturbation scheme increases the ensemble spread and reduces the ensemble mean error by solving the underestimated BEC problems. Section 12.2 presents the methodology, and the experimental design is described in Sect. 12.3. Sections 12.4 and 12.5 provide the results and discussion and conclusion, respectively.

12.2 Methodology 12.2.1 Forecast Model and Ensemble Data Assimilation System We used the Korean Integrated Model (KIM) (Hong et al. 2018; Kim et al. 2021), which is an operational global atmospheric model at the Korea Meteorological Administration (KMA) since April 2020. It consists of a spectral-element nonhydrostatic dynamical core on a cubed sphere and advanced physics parameterization packages (see Hong et al. 2018). The ensemble forecast implemented to the EDA system has a 50 km horizontal resolution and 91 vertical levels up to 0.01 hPa in the hybrid sigma-pressure vertical coordinate. For the EDA system, we used the four-dimensional local ensemble transform Kalman filter (4D-LETKF) system (Hunt et al. 2007; Liu et al. 2008; Shin et al. 2016). The 4D-LETKF system finds the ensembles of analysis obtained by assimilating the observations within a local region (Hunt et al. 2007; Shin et al. 2016, 2018). Control variables are the zonal wind, meridional wind, potential temperature, humidity mixing ratio, and surface pressure. The initial 50 ensemble members are produced by modifying the analysis with the lagged forecast differences. Assimilated observations

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are sonde, surface, aircraft, Global Positioning System-Radio Occultation (GPS-RO), Infrared Atmospheric Sounding Interferometer (IASI), Advanced Microwave Sounding Unit-A (AMSU-A), Cross-track Infrared Sounder (CrIS), Microwave Humidity Sounder (MHS), Advanced Technology Microwave Sounder (ATMS), and Atmospheric Motion Vector (AMV) (Kang et al. 2018).

12.2.2 Stochastic Perturbation Hybrid Tendencies Scheme We simultaneously perturb dynamical and physical tendencies and define it as the stochastic perturbation hybrid tendencies (SPHT) scheme (i.e., SPDT + SPPT) (Lim et al. 2020). The dynamical tendency is related to the explicitly resolved dynamics and horizontal diffusion, and the physical tendency is related to the physical parameterization schemes. As a result, the SPHT scheme accounts for model uncertainties associated with computational representations of the underlying partial differential equations and imperfect physical parameterizations. In the SPHT scheme, the dynamical and physical tendencies are perturbed using the randomly generated multiplicative perturbation at each model time step and grid point, i.e., ( n) ∂x n∗ n .x = x + (1 + μr ) ∆t, (12.4) ∂t dyn (

and .

x n+1 = x n∗ + (1 + μr )

∂ x n∗ ∂t

) ∆t,

(12.5)

phy

( ) ( ) where . ∂∂tx dyn and . ∂∂tx phy are the dynamical and physical tendencies, respectively, .n is time step, .t is time, and .∗ is provisional solution of the dynamical process; η−1 .μ ∈ {0, 1} represents the vertical tapering function (.e ) in the generalized vertical coordinate (.η), and .r is the random forcing. Note that the model variable (.x) consists of temperature and humidity mixing ratio only. Since the physics and dynamics in KIM are coupled by a time-splitting method, this approach differs from the method of perturbing total model tendency. The random forcing determining the perturbations depends on the following tuning parameters: (1) the horizontal correlation length scale (. L) determines how much perturbed errors propagate in a horizontal direction; (2) the de-correlation time scale (.τ ) determines how long the perturbed errors will be sustained; (3) the standard deviation of perturbation (.σ ) controls the amplitudes of random forcing; and (4) the tapering function (.μ) determines whether the error would exponentially decrease by tapering to zero in the lowermost and the uppermost vertical layers or remain the same to avoid numerical instability. If the SPPT and SPDT schemes use the same random forcing, the latter produces larger perturbations; thus, we have designed the SPDT scheme to use smaller .σ in order to suppress spurious instability (Koo and Hong 2014).

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Table 12.1 List of random forcing tuning parameters used in the SPDT and SPPT schemes, respectively Length scale Time scale Standard Tapering function (. L; in km) (.τ ; in s) deviation (.σ ) (.μ) SPDT SPPT

500 500

10,800 21,600

0.5 1.0

On Off

12.3 Experimental Design We performed two sets of EDA runs to assess the SPHT scheme: (1) CTRL is the control EDA runs without any stochastic perturbation schemes, and (2) STOC runs the SPHT scheme in EDA runs. The random forcing tuning parameters used in the SPHT scheme are listed in Table 12.1. The experiments started at 12:00 UTC on 22 June 2018 and ended at 12:00 UTC on 7 July 2018. We specified the first 78 h as a spin-up period, and each cycle produced 6 h forecasts to generate ensemble BEC. To prevent the filter divergence, the two experiments included the localization and posterior CI methods. Regarding the covariance localization in LETKF, the horizontal localization is given by a Gaussian-like piecewise fifth-order rational function (Gaspari and Cohn 1999; Miyoshi 2011) and varies from 660 to 1800 km in radius of influence depending on vertical levels (Kleist and Ide 2015). The vertical localization differs as to the observation/type: the conventional data are defined by a

Gaussian-like rational function as 2. 10 .σ where .σv depends on pressure (. p) (e.g., 3 v .σv is .0.2 ln( p) for wind and surface pressure and .0.1 ln( p) for mass variables), and the radiance data are defined by the gradient of transmittance of the measured radiance (Thépaut 2003). Regarding the posterior CI methods, both experiments used the additive inflation and the RTPS with the relaxation parameter of 0.95.

12.4 Results We examined how ensembles in CTRL describe the model uncertainty by comparing the ensemble spread and ensemble mean error. Here, we defined the ensemble mean error as the root-mean-squared error (RMSE) of the ensemble mean against the Integrated Forecast System (IFS) analysis produced by the European Centre for MediumRange Weather Forecasts (ECMWF). IFS has a 25 km resolution with 25 pressure levels from 1000 to 1 hPa, and we assumed it as a true state. Figure 12.1 shows the zonally averaged ensemble spread and ensemble mean error to diagnose the current ensemble status. The ensemble spread is expected to be similar to the ensemble mean error in terms of magnitude and patterns. For temperature (Fig. 12.1a and d), the underestimated ensemble spread is found in the lower troposphere (e.g., below 700 hPa) and the stratosphere. For specific humidity (Fig. 12.1b and e), the underestimation is

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Fig. 12.1 Zonal mean ensemble spread (top panels) and ensemble mean error (bottom panels) for a, d temperature (in K), b, e specific humidity (in g kg.−1 ), and c, f zonal wind (m s.−1 ) in CTRL. Background (i.e., 6 h forecasts) is averaged from 1800 UTC 25 June 2018 to 1800 UTC 7 July 2018, excluding the spin-up period (first 78 h of the experiment time)

founded in the tropics and mid-latitudes below 700 hPa. For zonal wind (Fig. 12.1c and f), the ensemble spread already described the model uncertainty, but the underestimation also remained in Antarctica and most of the stratosphere. Overall, the model uncertainties in the troposphere, especially below 700 hPa, were not depicted in CTRL experiments. Although available large ensemble members (i.e., 50 ensemble members), localization methods, and posterior CI methods (e.g., additive inflation and RTPS) tried to describe the model uncertainty, they were insufficient, especially for temperature and specific humidity. Therefore, an additional CI method is necessary to increase the ensemble spread in the lower troposphere to produce the desirable ensembles in EDA cycles. Next, we examine if the SPHT scheme as a prior CI method can increase the ensemble spread in the EDA system. Figure 12.2 shows the globally averaged vertical profiles of the difference between STOC and CTRL for temperature, specific humidity, and zonal wind. The ensemble spread of ICs in the initial cycle was identical, but they were increased as the forecast times. The main difference was founded below 700 hPa, and the strongest amplitude is near 950–925 hPa. The tapering function in the SPHT scheme reduces perturbation in the lowermost and uppermost layers to secure stability. We did not perturb zonal wind as did in temperature and specific humidity, but ensemble spread of zonal wind was indirectly increased. Similarly, the stratosphere (e.g., from 10 to 1 hPa) showed an increased ensemble spread due to propagation from the perturbations in other layers. We investigated the time series of globally averaged ensemble spread and ensemble mean error to assess the SPHT scheme (Fig. 12.3). Compared to CTRL, STOC increases the ensemble spread and decreases ensemble mean error for temperature,

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Fig. 12.2 Differences of the ensemble spread between STOC and CTRL (i.e., STOC-CTRL) in the globally averaged vertical profiles of a temperature (T; in K), b specific humidity (Q; in g kg.−1 ), and c zonal wind (U; in m s.−1 ) for forecast times of + 3 h (blue), + 6 h (green), and + 9 h (red) from the initial time (+ 0 h; black dots) at 1200 UTC 22 June 2018. Variations in the ensemble spread c reflect the effect of the new SPHT scheme. ◯2020 Authors. Distributed under CC BY 4.0 License

Fig. 12.3 Time series of the globally averaged ensemble spread (dotted line) and the ensemble mean error (solid line) in the prior for CTRL (blue line) and STOC (orange line). a is temperature (in K), b is specific humidity (in g kg.−1 ), and c is zonal wind (in m s.−1 ). The x-axis is the analysis time with 6 h assimilation window

specific humidity, and zonal wind. As a result, the prior CI method using the SPHT scheme successfully increased the ensemble spread by 3.7%, 3.9%, and 2.3% for temperature, specific humidity, and zonal wind, respectively, and decreased the ensemble mean error by 1.1%, 0.9%, and 0.6%, respectively. To summarize, the notable improvements occurred in temperature, and they were effective in the tropics below 700 hPa. In detail, the SPPT scheme mainly works in the overall ensemble spread except for the southern hemisphere, and the SPDT scheme weakly compensates for the unresolved ensemble spread in the southern hemisphere (not shown). But, the underestimated ensemble BEC still remained in the near-surface atmosphere (not shown).

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12.5 Discussion and Conclusions Model uncertainties can be addressed by the stochastic perturbation schemes. Before taking this approach, it is recommended to examine where the underestimated ensembles occurred within the current status, because it helps to determine which stochastic perturbation system is suitable to compensate for the underestimating the ensemble spread. Our current experiment showed underestimation in ensemble spread for temperature and specific humidity in most of the troposphere, especially below 700 hPa. To solve this problem, we implemented the stochastic perturbation hybrid tendencies (SPHT) scheme that perturbs both dynamical and physical tendencies as the prior covariance inflation method. It simultaneously explains uncertainties that come from the computational representations of underlying partial differential equations and the imperfect physical parameterizations. As a result, most underestimated ensemble spread in the troposphere was alleviated. However, the near-surface uncertainties over the land are still unresolved due to uncertain interaction between the land and atmosphere. In particular, land surface models (LSMs) contain heterogeneous land cover and soil texture, which is hard to capture in coarser model resolution. Since the parameters and parameterization schemes in LSMs contribute to the model uncertainties (Liu et al. 2023), the parameters or soil variable (e.g., soil temperature or soil moisture) can be perturbed to solve the near-surface uncertainty (MacLeod et al. 2016; Draper 2021). Because the atmosphere and the land surface have different scales and the ensemble dispersion is sensitive to perturbation, the random forcing tuning parameters should be carefully determined to generate adequate perturbations in LSMs (Bouttier et al. 2012; Lupo et al. 2020). Therefore, as a further study, the stochastic perturbation scheme in LSM can be used to improve the model uncertainty for near-surface variables and atmospheric variables below PBL through the heat flux changes. Acknowledgements This work is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1A6A1A08025520) and by the NRF grant funded by the Korean government (MSIT) (NRF-2021R1A2C1095535).

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Part IV

Precipitation Systems: Mechanism and Forecast

Chapter 13

Heavy Rainfall Mechanism Over East Asia: Numerical Modeling Perspective Song-You Hong and Jung-Eun Esther Kim

Abstract This chapter begins by providing a brief historical review of heavy rainfall studies over East Asia, centered at the Korean peninsula, using numerical atmospheric models. A special attention is given to the uniqueness in mechanisms causing heavy rainfall in that region, as compared to studies over geographically different regions such as the Great Plains in United States. Early mesoscale modeling studies before 1990s over Korea and US are reviewed, focusing on the model’s ability to reproduce heavy rainfall. In the early 2000s, as the reanalysis data is available, a long-lasting argument on considerably different sensitivities to precipitation physics algorithms in both regions was able to be clarified, along with the analyses of unique synoptic-scale features causing heavy rainfall over East Asia. In the early 2010s, uniqueness in heavy rainfall system in terms of internal structure was visualized by analyzing satellite observations. Observational evidence with dominant warm-type rain over Korea, as compared to conventional cold-type rain in US, rectifies speculations that have been experienced in modeling communities since mid-1980s. By virtue of partitioning precipitation into two portions of sub-grid scale due to cumulus parameterization scheme and grid scale due to microphysics scheme in numerical models, changes in heavy rainfall mechanisms under global warming are presented. Future efforts on the research on the numerical weather forecasts over East Asia are suggested. Keywords Heavy rainfall · Precipitation physics · Cumulus parameterization scheme · Numerical weather prediction (NWP)

This study focuses on heavy rainfall over Korea since numerical modeling and observational studies that can be directly compared to the findings in US are available in the region. It is also noted that the Korean peninsula is geographically located at the center of East Asia. S.-Y. Hong (B) University of Colorado/CIRES and NOAA/ESRL/PSL, Boulder, CO, USA e-mail: [email protected] J.-E. E. Kim Center for Climate Environment Change Prediction Research, Ewha Womans University, Seoul, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_13

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13.1 Background Heavy rainfall events in East Asia are typically accompanied by long quasi-stationary summer monsoon frontal circulations (Changma front in Korea, the Mei-Yu front in China and the Baiu front in Japan). Intense rainfall is usually associated with the motions of scale interactions between planetary, synoptic, and mesoscales. Readers are referred to a review of the East-Asian summer monsoon circulation by Ninomiya and Akiyama (1992). Recent decadal enhancement of the heavy rainfall over East Asia was reported (Takahashi and Fujinami 2021). Disastrous rainfall is associated directly or indirectly with typhoons. In this chapter, studies are limited to heavy rainfall over Korea that are not directly influenced by typhoons. The number of heavy rainfall exceeding 150 mm/12 h was about 5 per year during the period of 1980–1990 (Lee et al. 1998). By classifying heavy precipitation systems over the Korean peninsula from 2000 to 2006 (Lee and Kim 2007), the most dominant type of about 47% is cloud clusters with an oval-shape area of low cloud-top temperature, whereas isolated storms and squall lines share about 12% and 7%, respectively. Over US, research on mesoscale convective systems (MCSs) causing severe weathers has been dated back to mid-1950s, through the analyses of observational data (Fig. 13.1). This early conceptual model has been updated by using field campaigns using increasingly sophisticated radars, better aircraft instrumentation, and satellite instruments, especially satellite-borne radars (Houze 2018). When cumulonimbus clouds develop into a single entity with precipitation covering a horizontal scale of hundreds of kilometers, they are called MCSs. MCSs generate severe weather events and flooding, produce cirriform anvil clouds, accompanied by cold-pool induced meso-highs and meso-lows in the trailing stratiform regions. The dynamics and thermodynamic characteristics of a severe weather event were clarified by organized field campaigns such as the Severe Environmental Storms and Mesoscale Experiment (SESAME, https://www.eol.ucar.edu/field_projects/sesame) to learn more about the structure, meso-synoptic processes, and dynamics of severe convective mesoscale systems. As deeper understanding of internal structure of MCSs from field campaigns was achieved and mesoscale numerical models were being developed in the early 1980s (Anthes 1983), it became feasible for researchers to challenge in the reproducibility of observed phenomena. Zhang and Fritsch (1986) first attempted to reproduce the mesoscale features that are responsible for the heavy rainfall event over Pennsylvania, so-called 1977 Johnstown flood, and their results were greatly encouraging. Their results imply that quantitative precipitation forecasts can be plausible with a standard rawinsonde dataset in numerical prediction models. From a research point of view, successful simulation of mesoscale-β scale phenomena can be used as a comprehensive tool in identifying the rainfall mechanism and associated mesoscale features such as meso-high, meso-low, and trailing stratiform rain. Their researches were extended to the intense squall line case over the Great Plains in June 1985

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Fig. 13.1 Schematic section through a squall line. From Fujita (1955)

(Zhang et al. 1989). Their results confirmed that the surface wake low in Fig. 13.1 develops as a consequence of adiabatic warming and drying behind the descending rea inflow. Over East Asia, researchers have tried to simulate three-dimensional mesoscale evolution of MCSs embedded within summer monsoonal fronts over East Asia (Ninomiya et al. 1984; Kuo et al. 1988; Nagata and Ogura 1991), but they realized that model formulation is quite difficult to achieve the quantitative precipitation forecast. Unlike the successful simulation studies on mesoscale convection over the United States by Zhang and Fritsch (1986) and Zhang et al. (1989), there have been no successful attempts at reproducing meso-β scale structure of convective systems embedded within East-Asian summer monsoons using real data. Note that early case studies by Ninomiya et al. (1984), Kuo et al. (1988), and Nagata and Ogura (1991) are considered as meso-α scale phenomena in an aspect of its observed dynamic characteristics or related model formulation. Since the purpose of this chapter is to isolate uniqueness in heavy rainfall mechanisms over East Asia, as compared to those in US, we refrain from overviewing numerical modeling studies using other models than Mesoscale Model 4th generation (MM4, Anthes et al. 1987). It is rational to practice the predictability of heavy rainfall over East Asia following the same setup of MM4 over US, as done by Zhang and Fritsch (1986). In mid-1980s, D. K. Lee of Seoul National University adopted the MM4 to apply for the simulation of mesoscale phenomena over East Asia. Unlike the successful simulation of intense heavy rainfall over US, the model with a full physics as in the Zhang and Fritsch failed to reproduce the observed rainfall, indicating different aspects in mechanisms. The successful simulation was achieved when the cumulus parameterization scheme (CPS) to be responsible for convectively unstable layers was removed (Lee and Hong 1989; Hong 1992), which is contrary to the argument

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of Zhang et al. (1988). Zhang et al. (1988) demonstrated that the CPS plays a critical role in preventing a delay of initiation of convective updrafts, and in the generation of numerical point storms due to ill-posed feedback between low-level convergence, upper- to mid-level heating, and upper-level divergence. Even though there was a speculation on the unique mechanism that is associated with a stationary monsoonal front over East Asia, it was not possible to justify the hypothesis due to lack of observations. It is noted that heavy rainfall develops over the oceans in East Asia, where in-situ observations are unavailable. Despite uncertainty in understanding the internal structure of heavy rainfall and lacking to support for the model setup, the MM4 without the CPS has been operational at KMA since 1990. The following section describes the early numerical modeling studies using MM4 in both US and Korea. In Sect. 13.3, the uniqueness of heavy rainfall mechanisms over Korea has been explored by modeling experiments, the analysis of a synoptic climatology, and observational evidence from satellite data. In Sect. 13.4, the changes in mechanism under the global warming are presented by analyzing the reanalysis data (Hersbach et al. 2020), focusing on the portions of sub-grid scale due to a CPS and grid scale due to a microphysics parameterization scheme (MPS) in precipitation. Future efforts on the research on the numerical weather forecasts over East Asia are given in the final section.

13.2 Early Numerical Modeling Studies Using MM4 a. Mesoscale Simulations Over US Pioneered by Da-Lin Zhang’s research on numerical simulation of MCSs over US, meteorological communities got excited to see a hope in that quantitative precipitation forecasts could be achieved by a mesoscale model with conventional observations. Zhang and Fritsch (1986) modified the MM4 to simulate the mesoscale structure and evolution of convectively driven weather systems. The horizontal resolution at a 25 km grid is nested by a 75 km grid. The cumulus parameterization schemes are employed for both grids, with the Anthes-Kuo scheme (Anthes et al. 1987) and the Fritsch–Chappell scheme (Fritsch and Chappell 1980) for 75 km and 25 km grids, respectively. The Fritsch–Chappell scheme was significantly modified to resolve convective updrafts and downdrafts of convective cells. The modified MM4 was able to predict the size, propagation rate, and orientation of the mesoscale components that were observed in the mid-Atlantic states. The simulated evolution includes the planetary boundary layer, cold-pool outflow boundaries, and surface pressure perturbations, such as mesoscale lows and highs (Fig. 13.2). Although it is a single case study, their results suggest that significant improvements in warm-season quantitative precipitation forecast might be possible in operational centers. Da-Lin Zhang’s group further extended the modeling study to the case of an intense squall line during June 10–11, 1985, Preliminary Regional Experiment for Storm scale Operational and Research Meteorology (PRE-STORM) over the Great Plains

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Fig. 13.2 a Mesoscale analysis for 1800 UTC July 1977. Heavy dashed lines indicate troughs. Cold and Warm frontal symbols alternated with double dots indicate most-downdraft outflow boundaries. The light shading denotes the level-1 radar echoes. b the corresponding 6 h forecast from MM4, with analysis of sea-level pressure (solid lines, mb) and surface temperature (dashed lines, °C). From Zhang and Fritsch (1986). ©American Meteorological Society. Used with permission

of US. As in the similar model setup of Zhang and Fritsch (1986), Zhang et al. (1989) successfully reproduced many observed meso-β scale features that are analyzed from the high-resolution network data. These include the generation of areas of deep convection at the model initial time, the development of several convective bands, the rapid intensification, and rapid dissipation processes of the squall lines as it entered and moved out of the network. Movement of a squall line was remarkably simulated (Fig. 13.3). The generation of a pre-squall meso-low, a squall-induced meso-high and a wake low as well as corresponding surface convergence-divergence flow structure, the development of rear-inflow jet, and the leading convective rainfall followed by a transition zone and trailing stratiform precipitation (Fig. 13.4). They confirmed that the wake low develops hydrostatically as a consequence of adiabatic warming by descending flow behind the squall line with the rear-inflow jet. By analyzing the simulated results, they found that the squall line was initialized as a surface front moved into a convectively unstable environment. The rapid evolution of the squall line most likely results from variations in the convective environment into which the system was propagating. The interaction of the low-level wind shear with the convectively generated cod pool provides an additional mechanism for explaining the initial rapid intensification process. By conducting precipitation physics sensitivity experiments, Zhang and Gao (1989) discovered that the generation of the descending air inflow and the surface and mid-level pressure perturbations are found to be most sensitive to the parameterized moist downdrafts in the cumulus parameterization scheme, and hydrostatic water loading, evaporative cooling and ice microphysics.

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Fig. 13.3 Comparison of a the observed hourly position of the squall line to b the simulated over the period 0100 and 0900 UTC June 1985. From Zhang et al. (1989). ©American Meteorological Society. Used with permission

Fig. 13.4 Comparison of the time series of a the observed pressure, rainfall, and horizontal wind at the observed station to b the simulated. From Zhang et al. (1989). ©American Meteorological Society. Used with permission

The results from Zhang et al. (1989) indicate that the meso-β scale structure and evolution of MCSs under certain synoptic-scale environmental conditions can be well simulated using the standard network observations if compatible grid resolution, reasonable model physics and initial conditions are utilized. They discovered that descending area inflow is a product of the dynamic response to the latent-coolinginduced circulation.

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b. Mesoscale Simulations Over Korea Numerical simulations using MM4 were initiated in mid-1980s in Korea. The first trial was to simulate disastrous heavy rainfall in Seoul, for the period of August 30–September 1, 1984 (Lee and Hong 1989). With a 2.5 × 2.5 gridded data as initial and boundary conditions, the MM4 reproduced the observed heavy rainfall that elongated from South China to the Korean peninsula. This rainfall was organized within an autumnal monsoonal front, whereas abundant moisture and heat were transported from a dissipating typhoon in South China (Park et al. 1986). The scale of observed precipitation is analyzed as a meso-α scale phenomena, as the event was well simulated at an 80 km grid. Another disastrous heavy rainfall event was recorded at central Korea on July 20–21, 1987 (Fig. 13.5). The maximum rainfall amount at Puyeo was over 700 mm, causing the deaths of 149 people, and property damage of about 300 million US dollars. Such devastation has motivated Korean meteorologists to understand its mechanism and attempt to predict the rainfall amount quantitatively in numerical models. Synoptic-scale and mesoscale analysis revealed that heavy rainfall is established as upper-level baroclinicity to the northwestern side of the Korean Peninsula, resulting from the southeasterly movement of a deep midlatitude trough from the northwest, which is intensified. Analysis of surface observations, satellite images, and radar echoes indicated that the dynamic scale associated with this heavy precipitation is clearly meso-β scale, exhibiting features such as a meso-high and a multicellular behavior of convective cells embedded within a monsoonal front. A pre-frontal mesolow (upper left of Fig. 13.5) and meso-highs in the dissipating stage of heavy rainfall (upper right of Fig. 13.5) were commonly seen in US (Fig. 13.2), but meso-lows in relation to trailing stratiform precipitation in US were not analyzed. Hong (1992) attempted to reproduce the 1987 meso-β scale heavy rainfall in Fig. 13.5, using MM4. A nested grid system with a fine-mesh grid at a 20 km is employed, together with modifications made to surface layer, PBL, and horizontal diffusion processes. This model setup complies with the studies of Zhang and Fritsch (1986) and Zhang et al. (1989) in the previous subsection, but exclusion of a cumulus parameterization scheme. The model fairly well reproduced the distribution of rainfall with two maxima (Fig. 13.6). The predicted maximum rainfall amounts for two maxima are 186 mm and 147 mm, whereas the corresponding observed values are 441 mm and 160 mm, respectively. The amount of area-averaged precipitation is comparable for both the simulation and observation, which are 6.3 mm h−1 and 7.7 mm h−1 , respectively. Excessive amount of precipitation in the case of exclusion no-CPS indicated by Zhang et al. (1988) is unseen. The spin-up problem that was indicated by Zhang et al. (1988) is not distinct. With the inclusion of the Anthes-Kuo CPS, the distribution of precipitation was not organized, with a displacement of the major precipitation area to the south of the observed, along with its maximum at about 110 mm (figures not shown). Note that the Anthes-Kuo scheme is the only CPS option in the public version of MM4 before 1990.

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Fig. 13.5 Surface charts at 0000 UTC 22 (upper left) and 0600 UTC (upper right) July 1987. Red lines indicate the dew point temperature at 23 °C. Visible satellite image at 1800 UTC July 21, 1987 (lower left) and hourly precipitation at Puyeo from 0000 UTC 21 to 1200 UTC July 22, 1987 (lower right)

The hourly time series of the simulated rainfall at Puyeo confirms that the model could reproduce the timing and intensity of each convective cell associated with multicellular behavior (Fig. 13.7). It is particularly noteworthy that the model could simulate the three major convective cells at 1700, 2000 UTC 21 and 0000 UTC 22, which are comparable to what was observed. The increase of pressure in the dissipating stage of major rainfall at around 0000 UTC July 22, 1987 (24 forecast hours) is distinct, indicating a meso-high that is induced by evaporative cooling of falling raindrops, although the increasing trend is in part due to cold advection north of the precipitation area. Surface patterns including cold pools and meso-highs were identified by horizontal plots (figures not shown). By analyzing the cross-sections of temperature, moisture, horizontal winds, vertical velocity, and horizontal divergence in details, a warm core generated by latent heat release in the middle atmosphere and a cold core in the low atmosphere,

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Fig. 13.6 (Left) Simulated precipitation amount for 12 h ending at 2200 UTC July 1987 and (right) the corresponding observation

Fig. 13.7 Time series of the 1 hourly rainfall amount (left) and sea-level pressure (right) at Puyeo from the simulated (CTL) and observed (OBS)

and convergence and divergence associated with evolution of each convective cell were identified. As the convective activity is weakened, mesoscale downdrafts and divergence in the lower atmosphere are intensified. These dynamic characteristics including generation of a warm core and a cold core, and mesoscale updrafts and downdrafts are comparable to those of MCSs in US. In other words, multi-cell convective cells and its mechanisms with cold-pool forcing (Rotunno et al. 1988) are confirmed. On the other hand, the model does not simulate a wake low that is formed by adiabatic warming by the rear-inflow low-level jet at the back edge of stratiform rainfall of the squall line or MCC in the United States, where it has been observed and simulated by several authors (Johnson and Hamilton 1988; Zhang and Gao 1989). This is presumably inferred from the dynamic characteristics of convective cell for

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this case, which there exists dominant cold advection from northwest to southeast at the back edge of rain band, and there is not clear distinct convective rain portion from stratiform rain portion in the rain band, which is unlikely in a moving convective cell of MCC or squall line in US. Hong (1992) conducted sensitivity experiments by excluding ice physics, melting, sublimation, freezing, and evaporation terms in MPS. The results follow the study of Zhang et al. (1989), in which a CPS is employed. The experiment excluding evaporation of raindrops did not reproduce multicellular features in Fig. 13.7. Ice microphysics is found to be responsible for suppressing a numerical point storm in this case, which is realized as common problems over US when CPS scheme is excluded (Zhang et al. 1988). In other words, in the sensitivity experiments excluding either ice physics or evaporation of raindrops simulated low-pressures over the heavy rainfall area rather than a meso-high associated with cold downdrafts which appear in the observation and the control simulation. Further, in spite of enhanced rainfall, the intensity of mesoscale circulation such as vertical velocity and low-level convergences was significantly weakened when evaporation is taken out. c. Speculation From the MM4 experiments over US and Korea in previous subsections, we found that the model can reproduce observed precipitation to some extent, and associated changes in temperature and pressure. Meso-β scale features such as meso-highs that are generated by evaporative cooling of falling raindrops are commonly appear in both continents. However, wake lows that are generated by rear-inflow jet over US are unseen over Korea. Distinction of trailing stratiform precipitation and convective precipitation at the leading edge of a squall line is not visible over Korea. The major difference in model setup is the exclusion of CPS over Korea. The CISKlike (Conditional Instability of the Second Kind) numerical instability causing a numerical point storm and serious delay of initiation of convection with MPS only over US (Zhang et al. 1988) was not noticed over Korea. The model setup without the usage of CPS over Korea is contrary to previous modeling studies for the convective systems in the Central Great Plains of US (e.g., Zhang and Fritsch 1986; Molinari and Dudek 1986). Over the convective systems over US, the role of parameterized convection is critical to the success of simulations of mesoscale features as well as precipitation. Without the parameterized convection, a bull’s eye pattern of excessive precipitation was reported. However, such a serious problem has not been reported in numerical modeling studies of heavy rainfall over Korea. It is surmised that high relative humidity of over than 95% in the vicinity of the Changma front can induce the air column to be favorable for grid-scale saturation. In other words, the air column prior to the onset of rainfall, and during heavy rainfall, is more adiabatically neutral and nearly saturated up to the midtropospheric level, resulting in a smaller amount of CAPE. In this case, existing cumulus parameterization schemes could negatively impact the simulation of rainfall amount.

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Despite the limitation of a case study, there was a speculation in which the mechanism for heavy rainfall and associated mesoscale features could differ over geographically different regions. Further investigation was hindered, which is mainly due to the fact that the same quality of initial data over the globe had been unavailable until mid-1990s.

13.3 Uniqueness in Heavy Rainfall Mechanisms Over East Asia As the National Centers for Environmental Prediction (NCEP)/NCAR reanalysis data (Kalnay et al. 1996) was available to meteorological communities in the late 1990s, research using regional numerical models was able to be accelerated. Also, models have been developed with advanced physics package in 1990s. The NCAR Mesoscale Model 5th generation (MM5) and the NCEP Regional Spectral Model (RSM) (Juang et al. 1997) are examples, and Weather Research and Forecasting models (WRF; Skamarock et al. 2005) models in the early 2000s. Readers are referred to Dudhia (2014) for a history of mesoscale model development since 1970s. Thus, systematic numerical experiments to elucidate the heavy rainfall mechanisms over the geographically different regions became to be feasible by investigating the predictability of rainfall. This section focuses on the studies of Hong (2004) for numerical simulations and Sohn et al. (2013) for observational evidence. a. RSM simulation Hong (2004) attempted to identify potential differences in mechanisms responsible for heavy rainfall over Korea and the central US through a series of numerical experiments. A case of heavy rainfall over Korea and another over the US is simulated using the NCEP RSM. An identical model system for the two heavy rainfall events was set up with a 25-km grid spacing, except for the longitudinal difference between Korea and the US. The initial and boundary data are derived from the NCEP/NCAR reanalysis. The CPS scheme of Hong and Pan (1998), the so-called Simplified Arakawa-Schubert (SAS) scheme is employed. Diagnostic or simplified ice-microphysics schemes are employed for MPS, as described in Hong et al. (1998). The experiment with CPS and prognostic MPS showed the best performance in terms of correlation coefficients, bias, and maximum amount (see Hong (2004) for details). In Fig. 13.8, it is seen that CPS only experiment reasonably reproduces the distribution of observed precipitation over US, but with apparent underestimation of precipitation core over Kansas. However, the same experiment did not simulate the major precipitation band over Korea. The maximum amount of 59 mm is far less than that in observed at 371 mm. Meanwhile, the experiment with MPS only showed a bull’s eye over the Great Plains of US. The maximum amount is exaggerated by a factor of 10. These numerical point storms are sporadic over the model domain. However, the same experiment reproduces the heavy precipitation band over the

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Fig. 13.8 24-h accumulated observed precipitation over US, valid at 1200 UTC 16 May 1995 (upper left), and over Korea, valid at 0000 UTC July 15, 2001 (lower left). The corresponding simulated precipitation with the CPS only (middle column), and MPS only (right column). Numbers at the upper right comers of each panel indicate the maximum amount

Korean peninsula with success. The maximum of 271 mm is still less than what was observed. Overall, the above results are consistent with previous findings in mesoscale simulation over the US (Zhang et al. 1988, 1989), in that either grid-resolvable precipitation physics via MPS alone, or a combination of parameterized convection via CPS and diagnostic explicit cloud schemes for grid-resolvable precipitation physics, induces a runaway type of positive feedback among latent heat release, larger-scale moisture convergence, and the surface pressure fall. In contrast to the US case, the bull’s eye-like excessive precipitation is not visible when the parameterized convection for sub-grid-scale precipitation processes is taken out. This finding over Korea assures us to convince the heavy rainfall mechanism in July 1987 with MM4 (Hong 1992), which was discussed in the previous subsection. b. Synoptic characteristics Substantially different sensitivity that was shown in the previous subsection implies that the significant CAPE and strong synoptic environment are pronounced in the US and Korea cases, respectively. Ninomiya and Akiyama (1979) also pointed out the differences between the stratification of the heavy rain event over Japan and the US. By virtue of the reanalysis data (Kalnay et al. 1996), this assumption can be elucidated (Fig. 13.9). It is evident that the summertime climatology over the Korean region, compared to that in US, is characterized by a stronger baroclinicity. The atmosphere over the Korean region is identified as thermodynamically neutral against large CAPE in the US region, along with moister environment than in the US.

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Fig. 13.9 Vertical profiles of a horizontal wind speed (m s−1 ), and b moist static energy (× 10–3 kJ kg−1 , without cross symbols) and saturated moist static energy (× 10–3 J kg−1 , with cross symbols), averaged over the Korean region (30–45° N, 120–135° E) (solid line) and the US region (30–45° N, 100–85° W) (dotted line) for May–August climatology during 1979–2002. Adopted from Hong (2004)

The above comparison indicates that synoptic environments over East Asia are favorable for the grid-resolvable precipitation algorithm to initiate precipitation by making the atmosphere supersaturated in dynamically strong meteorological conditions. c. Observational evidence Despite the significant advances in mesoscale modeling with improved physics package (e.g., WRF model) in 2000s and understanding uniqueness in synoptic environments causing heavy rainfall over the geographically different regions, fundamental differences in heavy rainfall formation have been unknown until the satellite data are employed to visualize the internal cloud-microphysical structure of convective systems (Sohn et al. 2013). Tropical Rainfall Measuring Mission (TRMM) measurements over Korea and US demonstrated that storm height for the light rain exhibit similar features in Korea and US-OK, but storm heights over US-OK shift rapidly to higher altitude with intensified rain rates (Fig. 13.10). In particular, the peak shown at around 5 km for light rain is shifted quickly to much higher altitudes when rain intensity become stronger. In contrast, the peak shown in the Korean case is

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much less variable; the peak for the light rain at 5 km moves slightly to 7–8 km for the other three classes. Higher cloud top indicates more ice water over US-OK, whereas the heavy rainfall mechanism over the Korean peninsula is closely associated with warmer clouds whose storm heights are located at lower altitudes. Sohn et al. (2013) argued that the growing processes in the lower troposphere should be closely associated with strong water vapor convergence over the Korean peninsula, which is caused by large-scale environmental conditions and appears to represent an important physical mechanism necessary to produce heavy rainfall from low level. During summer, the intensifying North Pacific high leads to a pressure distribution that helps transport water vapor from the South and East China Sea to the Korean peninsula along the periphery of the high, establishing an atmospheric

Fig. 13.10 PDFs of storm height (km) classified by four rain-rate (RR) intensities: a RR < 10 mm h−1 , b 10 < RR < 20 mm h−1 , c 20 < RR < 40 mm h−1 , and d RR > 40 mm h−1 . Black and red lines represent Korea and US-OK, respectively. From Sohn et al. (2013). ©American Meteorological Society. Used with permission

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river–like water vapor transport channel across the Korean peninsula area. This argument complies with the analyses in the previous subsection, in that warm and moist layer up to the freezing level with a relatively weak CAPE under strongly baroclinic environments. This finding of Sohn et al. (2013) provides a hint on why significantly different sensitivities exist for case studies over Korea and US. The main ingredient of CPS is to stabilize the air column when air is convectively unstable. Given the entrainment and detrainment rates, the convective updraft plume re-distributes the heat and moisture from the surface to cloud top. Here cloud top is determined by the equilibrium level or higher in case of the inclusion over overshooting. The cloud top from a climatology over US in Fig. 13.9 (center panel) could be as high as 15 km, as confirmed in the observation (Fig. 13.10). This issue will be further discussed in the final section. Song and Sohn (2015) extended the observational study of heavy rainfall over East Asia for the period of 2002–2011 (Fig. 13.11). By applying the K-means clustering method, two types of heavy rainfall are classified: type 1 (cold type) characterized by high storm height and abundant ice water under convectively unstable conditions, developing mostly over inland China; and type 2 (warm type) associated with a lower storm height and lower ice water content, developing mostly over the ocean. Type 1 indicates a well-developed deep convective system with large reflectivity near the surface and a high vertical extent (upper panels of Fig. 13.11). The geographical distribution for type 1 shows that it occurs mainly over inland China and has a much smaller frequency over the ocean. The warm-type process (Type 2, lower panels of Fig. 13.11) appears to link the low-level moisture convergence area to the vertically aligned divergence area formed over the jet stream level, pushing air upward under moist-adiabatically near-neutral conditions and thus yields heavy rainfall, as seen in Fig. 13.9. As warm-type heavy rainfall persists longer, it is considered to be more responsible for flood events occurring over the Korean peninsula. This finding confirms the previous observation study (Lee and Kim 2007), in which cloud cluster type is the most dominant over Korea. The negative role of CPS and relatively insignificant effect of ice microphysics in simulating heavy rainfall over Korea that were discussed in previous sections is also elucidated.

13.4 Changes in Mechanisms Under Global Warming a. Convective rain ratio (CRR) Precipitation is usually classified into convective and stratiform types according to their genesis and characteristics. In reality, however, revealing the type of precipitation is still challenging (Houze 1997). It requires to adopt the criteria for stipulating the precipitation types by analyzing additional observed variables (Yang et al. 2013; Ahmed and Schumacher 2015), their spatiotemporal structures (Ruiz-Leo et al. 2013;

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Fig. 13.11 (Left) Vertical structure and (right) occurrence frequency distribution of the heavy rain types classified by K-means clustering analysis. The percentage in the (left) represents the percentage occurrence of the corresponding type. From Song and Sohn (2015). ©American Meteorological Society. Used with permission

Han et al. 2016), or morphological cloud types (Ye et al. 2016; Chernokulsky et al. 2019). Furthermore, convective and stratiform precipitation affect each other and synchronize in many cases. In a model world, precipitation partitioning is straightforward. Modeled precipitation is separated into two distinct types, i.e., convective precipitation versus largescale precipitation. The activation of convective precipitation in the model, which is implicitly represented through the CPS, is responsible for the removal of convectively available potential energy (CAPE). In contrast, the formation of grid-resolvable precipitation (so-called non-convective precipitation) within the model is due to the removal of supersaturated water vapor associated with large-scale instability through the MPS (Hong and Pan 1998). By taking this convenient aspect of the modeled precipitation, it can be assumed that the relative proportion of convective precipitation to total precipitation (convective precipitation plus non-convective precipitation) is roughly equivalent to the contribution of convective instability to precipitation in the real atmosphere. Therefore, the percentage ratio of convective precipitation to total precipitation (hereafter, convective rain ratio or CRR) can be defined as a proxy measure to quantify the majority of precipitation mechanisms (Kim 2010). With regard to discriminating a

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dominant mechanism causing precipitation, the use of the two types of precipitation is more reliable than certain convective parameters such as CAPE and CIN, of which observed data are spatially and temporally limited. Here the two types of precipitation are taken from the European Centre for Medium-Range Weather Forecasts (ECMWF) global reanalysis (ERA) version 5 (Hersbach et al. 2020). We obtained the dataset at 0.25° horizontal resolution but bilinearly interpolated it to 1.5° resolution. There are important advantages in employing the reanalysis data for the CRR calculation. One is that the reanalysis might be close to a real world by adopting a data assimilation scheme ingesting all available observations. The long-term integration of the model could be contaminated by the model’s inherent uncertainties. Another benefit from the reanalysis is its internal consistency throughout the period of the reanalysis by generating precipitation with a freezing (unchanging) version of a model system. The summer climatology of the CRR over East Asia (20–60° N, 90–150° E) and US (20–60° N, 120–60° W) for the recent 42 years (1979–2020) are compared in Fig. 13.12. Note that the summer period is June–July–August (JJA) for East Asia and May–June–July (MJJ) for US. In East Asia, the CRR tends to decrease toward higher latitudes (Fig. 13.12a). Particularly noteworthy is the fact that the values in Korean Peninsula, Japan, and surrounding oceans are much smaller than other areas, which is less than 50%. It indicates that precipitation in East Asia is mainly dynamically driven in East Asia rather than thermodynamically driven. Meanwhile, in US, convective precipitation prevails in most areas (Fig. 13.12b). In other words, the majority of precipitation in US could be driven convectively, despite the equal latitudinal location to East Asia. This contrasting feature of the CRR in the two regions confirms the uniqueness in rainfall mechanism, which is consistent with the modeling and observational results described above in Sects. 13.2 and 13.3.

Fig. 13.12 Spatial distribution of the climatological convective rain ratio (CRR, %) over a East Asia during June–August and b US during May–July for the years of 1979–2020. The regions where the amount of annual precipitation is exceeding 2 mm day−1 are only shaded. The gray contour designates JJA-mean (MJJ-mean) total precipitation with the interval of 3 mm day−1 (2 mm day−1 ) for East Asia (US)

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b. Changes in CRR As the global warming has been underway, the increase in mean precipitation and extreme precipitation via increasing evaporation and strengthening atmospheric circulations is expected (Trenberth et al. 2003; Cahynová and Huth 2010). In particular, convective precipitation may be largely influenced by rising temperature according to Clausius–Clapeyron hypothesis (Alexander et al. 2006; Berg et al. 2013). Thus, many studies have focused on understanding the changes in global and regional precipitation and their variabilities (Wang and Ding 2006; Held and Soden 2006; Feng et al. 2019). However, the global warming response to the precipitation mechanism has not been comprehensively addressed yet, since the precipitation-triggered mechanism varies across the region. The use of the CRR facilitates to quantitatively estimate of the contribution of precipitation mechanisms closely connected with internal precipitation dynamics. The increase in convective precipitation is largely associated with the enhanced convective instability via local instability. Meanwhile, the changes in large-scale precipitation are due mainly to changes in dynamic processes such as baroclinic instability. Therefore, the trend in the CRR can provide insight for intensification or decline in precipitation processes. Although the amount of convective precipitation depends on a specific cumulus parameterization scheme, its relative trend may provide reliable results considering that the ratio is based on precipitation amount in the one reanalysis dataset. Recognizing that the CRR decreases as the resolution increases, the CRR is meaningful unless the model resolution reaches cloud-resolving scale. The monotonic tendency of the CRR over the 42 years (1979–2020) is shown in Fig. 13.13 (left panel), by performing the Mann–Kendall test over East Asia and US (Mann 1945; Kendall 1955). The result demonstrates that East Asia has experienced the general increase in the CRR, whereas US has undergone a decrease in the CRR. It indicates that local instability became crucial to the formation of precipitation in recent decades over East Asia, while precipitation in US is not directly influenced by local instability in recent decades. The temporal trend of the CRR over each region is presented by the area-averaged CRR for the summer season (right panel in Fig. 13.13). It can be seen that East Asia has a small variability of the CRR and the modest increase in tendency. The trend is 0.37% per decade over land. In the whole region including ocean, the trend falls to 0.12% per decade, which is not significant. In contrast, the trend in US is more pronounced in comparison to East Asia. The tendency is − 1.46% and − 1% per decade for the land-only and whole regions, respectively, suggesting overall significant changes in US. Although the trends for the spatial average are promising, the trend at the local scale is not homogeneous and statistically significant, especially for East Asia. Nevertheless, the trend analysis strongly supports that the global warming has led to the changes in major mechanism generating precipitation. In contrast to the overall increasing trend before 2000, the larger inter-annual variation of the CRR indicates more diverse types of heavy rainfall over East Asia in recent decades. Through the same analysis using the Japanese 55year Reanalysis (JRA-55; Kobayashi et al. 2015) dataset of about 1.25° horizontal

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Fig. 13.13 Linear trend in convective rain ratio (CRR, %) over a East Asia for JJA and b US for MJJ for the years of 1979–2020. The regions, where the amount of annual precipitation is exceeding 2 mm day−1 , are only calculated (left panel). The right panel exhibits the year-to-year variability of the area-averaged CRR (black and gray lines) and its 15-year running mean (red and orange lines) for each region. The solid (dashed) line designates the value for land only (both land and ocean)

resolution, we confirmed that the CRR distribution and its local trends in the JRA-55 follow those in ERA5 (not shown). It indicates that the overall conclusion is quite robust regardless of the resolution and modeling system including physics schemes and data assimilation. c. Implications Despite the rapid progress in numerical modeling skill, predicting precipitation is still exacting. In addition, it is widely accepted that climate change may make more vulnerable to perfect forecasting due to the severity of extreme weather events and the shift of mean climate state. Regarding precipitation modeling, the modulation in the atmospheric internal dynamics such as precipitation mechanisms may change the hydrological predictability. Considering that convective precipitation is parameterized, and the CPS does not explicitly resolve the convective cloud, the region with the increase in the CRR may have more uncertainty in simulating precipitation. It implies that much more caution should be needed on reliable precipitation prediction in a warmer world.

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13.5 Future Directions A hypothesis on different heavy rainfall mechanism over Korea from that in US was suggested by attempting to reproduce the heavy rainfall and associated with mesoscale phenomena in numerical modeling studies. Considerably different sensitivities of simulated results to moist physics parameterizations in models over both regions indicate unique features of convective systems over Korea under synoptically strong environments. More than two decades have passed to understand the heavy rainfall mechanism embedded within East-Asian summer monsoon until observed structure of convective cells is visualized. In research communities, case studies have been focused on the severe weather events causing disastrous damage in life and economy. In US, the squall line-type MCS have been paid attention, whereas cloud cluster-type convective storms are the main subject in research communities over Korea. Obviously, in real world various types of precipitation coexist over geographically different regions. Even in US, as in the typical profile for heavy rainfall over Korea, moist-adiabatically absolutely unstable layer has been often observed (Bryan and Fritsch 2000). Deep convection over US is initiated when the warm and moist air near the surface is penetrated across the capping inversion up to the tropopause, which complies with an essential concept of the cumulus parameterization. Meanwhile, heavy rainfall over Korea is initiated by synoptic-scale forcing within a couplet of upper- and lowerlevel jets, exerting uplift of low-level near-saturated air (center and right panels of Fig. 13.9). In this environment, the effective triggering of the CPS could stabilize the column by consuming moisture in the lower troposphere, which consequently suppress the development of precipitating convection. Unless the precise configuration of coupling between the CPS and MPS is modeled, the MPS only has a potential to resolve the convective cell over Korea. Lower cloud top by the MPS than CPS in physics algorithms (Fig. 13.14) complies with the observational evidence in Figs. 13.10 and 13.11. As the quality of initial conditions is improved, along with the advances in representing precipitation convection in numerical models, the skill of quantitative precipitation forecasts is continuously being improved, although the progress is plodding. It is out of question to include the CPS in NWP models, even at 1 km, as suggested by Kwon and Hong (2017). A key issue is to represent sub-grid cloud scale motions by removing instability, dropping some precipitation immediately, and changing the air column to make the MPS to generate hydrometeors and additional precipitation (upper-left panel of Fig. 13.14). Too effective stabilization by the CPS would result in suppressing subsequent development of convective cells by the MPS, whereas inactivation of the CPS where it should be would result in displacement of location of cells to the place where air column is supersaturated by grid-scale motions. By analyzing the observed internal features of convective cells, efforts need to be given to correct coupling of the CPS and MPS.

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Fig. 13.14 Schematic of the conceptual role of the CPS and MPS and their coupling for convectively unstable (left) and stable (right) conditions. The gray tones in the cloud in the upper left panel denote the absence of a cloud in the model, while in the other panels indicate that the model predicts clouds. Adopted from COMET. The source of this material is the COMET® Website at http://meted.ucar. edu/ of the University Corporation for Atmospheric Research (UCAR), sponsored in part through cooperative agreement(s) with the National Oceanic and Atmospheric Administration (NOAA), US Department of Commerce (DOC). ©1997–2023 University Corporation for Atmospheric Research. All Rights Reserved

It has shown that the mechanism is changing under global warming. East Asia is characterized by less convectively unstable region over the globe, which means a strong synoptic environment. Convective instability increases until 2000, accompanied by enhanced inter-annual variability. This indicates that prevailing largescale features change with global warming. Incorporating the change in large-scale circulations into the parameterization of precipitation physics needs to be pursued. Acknowledgements The authors wish to acknowledge long-term discussion on this subject with Dong-Kyou Lee, Tae-Young Lee, and Byung-Ju Sohn. Comments on the manuscript from Jian-Wen Bao, Jimy Dudhia, and Saymin Hong should be acknowledged.

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Chapter 14

Analysis and Predictability of Mesoscale Precipitating Systems in Moist Environments Tetsuya Takemi

Abstract The environment for the development of mesoscale precipitating systems in East Asia during the summer monsoon season is characterized by warm and humid conditions. Moist conditions provide a unique feature for the development of mesoscale precipitating systems. In this chapter, the morphology and predictability of mesoscale precipitating systems in moist environments are described through a comparison with those that occur in drier environments in midlatitude, continental regions. The role of moisture fluctuations in the free troposphere in characterizing and controlling mesoscale precipitating systems is a topic of specific focus. The predictability of deep moist convection is examined through a case study for a thunderstorm development over a mountain topography. It is argued that the moisture variability is essentially important in understanding the predictability of deep convection affected by topography. In moist environments, the humidity fluctuation is a key to characterize and determine the feature of mesoscale precipitating systems and their predictability. Keywords Mesoscale convective systems · Precipitation · Moist convection · Static stability · Predictability

14.1 Introduction Precipitating cloud systems develop under the influences of synoptic-scale disturbances such as tropical and extra-tropical cyclones, monsoon depressions, and fronts as well as under synoptically undisturbed conditions including the effects of locally induced circulations. Precipitating cloud systems cause both convective and stratiform rainfalls and are organized at mesoscales and even at synoptic-scales. Among such precipitating cloud systems, mesoscale convective systems (MCSs) have been investigated in a large number of observational, analytical, and numerical studies. T. Takemi (B) Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_14

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Such a large number of studies on MCSs are mostly attributable to MCSs sometimes spawning severe weather hazards such as strong winds and heavy rainfalls that have high societal impacts. Another possible reason is that robust structural and evolutionary characteristics are found in MCSs, especially squall lines. Because of either densely distributed observations conducted operationally in extended regions or abundant/intensive observations from specially coordinated field campaigns, MCSs that occur in North American continental regions and in the tropical oceanic regions have been focused on. In a large number of observational, analytical, and numerical studies on MCSs in such regions, the processes and mechanisms for the generation and development of MCSs were investigated from a dynamical and a thermodynamic point of views. From a dynamical viewpoint, the vertical shear of horizontal winds plays a significant role in determining the longevity and organization mode of MCSs. Weisman and Klemp (1982) clearly demonstrated how the vertical shear determines the organization mode of thunderstorms. They used the bulk Richardson number (BRN), which is the ratio of convective available potential energy (CAPE) against the magnitude of the difference in the horizontal wind vectors within a certain depth (e.g., from the surface to the 6-km height), to distinguish the organization mode: supercell storms for a smaller BRN (≤ 30–50) and multicell storms for a larger RBN (≥ 30–50). From observational analyses, LeMone et al. (1998) showed that the shape of squall lines depends on the magnitudes of low-level and middle-level vertical shears, and Parker and Johnson (2000) demonstrated that the magnitude and direction of the tropospheric vertical shear affect the shape and evolution of squall lines with stratiform precipitation. The role of the vertical shear in determining the mode of squall lines with stratiform precipitation as well as the supercell mode was clearly summarized in French and Parker (2008). From numerical and theoretical studies, it is recognized that the counterbalance and interaction between the low-level vertical shear and the evaporatively generated cold-air pool determine the intensity and longevity of squall lines (Rotunno et al. 1988; Weisman 1992; Weisman and Rotunno 2004). Especially, the theoretical framework put forth by Rotunno et al. (1988) is known as the RKW theory. Robe and Emanuel (2001) showed that the organized morphology and dynamics of the simulated squall lines under radiative–convective equilibrium states can be well explained by the RKW theory. The vertical shear also affects the temporal change of cell regeneration at the leading edge of multicellular convective storms and their life cycles (Fovell and Ogura 1989; Fovell and Dailey 1995; Fovell and Tan 1998). In this way, the role of vertical shear in determining the organization mode and longevity of MCSs has been well established. The importance of the vertical shear becomes more significant when well-defined cold pool develops. From a thermodynamic perspective, moist processes generate latent heating, which induces buoyant forcing and hence vertical motion. The magnitudes of buoyancy and vertical motion depend on a tropospheric stability condition. If the condition is more unstable, the convective updraft becomes stronger (Weisman and Klemp 1982). The degree of instability can be diagnosed through a number of indices including CAPE, which are useful in characterizing the stability conditions for the occurrence of severe storms in the middle plains of the continental USA (Bluestein

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and Jain 1985), afternoon thunderstorms in Florida (Fuelberg and Biggar 1994), and also convective events in a subtropical area in the western North Pacific (Wang et al. 1990). Compared with the above-mentioned studies, studies on MCSs in East Asia were not sufficiently conducted, although there were some international field campaigns and related analytical and numerical studies conducted in regions of South China Sea (Lau et al. 2000; Ding and Liu 2001; Johnson et al. 2005), East China Sea (Moteki et al. 2004a; b), and the continental areas of China (e.g., Ding et al. 2001; Uyeda et al. 2001; Shinoda et al. 2005; Yamada et al. 2007). In East Asia including both the landmass and the ocean, the ocean covers a wide area. Thus, the air-sea interaction is one of the key factors in characterizing MCSs and their environmental properties in East Asia, understanding the roles of air-sea interaction processes, especially in conditions of mei-yu/baiu/Changma fronts and tropical cyclones (typhoons), is critically important. There are some observational studies of air-sea interaction over the open ocean around East Asia (Mitsuta and Fujitani 1974; Fujitani 1981; Tsukamoto et al. 1990); however, observations in the open ocean are not easily conducted and the observational capacity is limited, especially in cases of precipitation events. The East Asian region which has a vast area of open oceans faces a challenge in obtaining observational evidence and conducting analytical and numerical studies of MCSs in the region. In addition, rainfalls are generated not only by MCSs but also by stratiform-type precipitating systems. Long-duration rainfall from a stratiform-type system can at times lead to a significant accumulated amount and cause disastrous flooding, inundation, and landslides. From the viewpoint of precipitation phenomena, it is important to not limit our focus to MCSs but to extend our focus to examine precipitating cloud systems in general. Furthermore, under wet conditions as frequently seen in East Asia, cold pool may be very weak or not develop, and hence, the role of the vertical shear will be a minor contributing factor or will not clearly appear. Therefore, stability conditions will be more dominating in determining the MCSs. In this chapter, we describe the morphology and environmental properties of mesoscale precipitating systems that occur in East Asia. Special attention is devoted to those that develop in warm seasons when the environments are characterized by very wet conditions. Investigations from modeling and data analysis on mesoscale precipitating systems are described. A predictability issue is discussed particularly for intrinsic predictability of precipitating convection.

14.2 Convective Updraft in Different Stability Conditions The formation of precipitating clouds is initiated from a cloud-scale or a meso-γ-scale upward motion. Upward motion is generated by external forcing such as thunderstorm gust fronts, sea breeze fronts, cold fronts, topography, thermal convection

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due to surface solar heating, and upper-level divergence and/or low-level convergence associated with surface low pressure systems. In stably stratified environments, upward motion leads to low-level clouds or stratiform clouds with shallow depths. In this case, cloud-layer depths are determined by cloud microphysical and radiative processes (Stevens et al. 2005; van Zanten and Stevens 2005; Wood 2012). By contrast, under unstable conditions, upward motion is strongly regulated by the degree of static stability. Here we focus on the characteristics of upward motion due to instability, i.e., convective updraft, which is an important ingredient for the development and evolution of precipitating clouds. The difference in the strength of convective updrafts between tropical and midlatitude thunderstorms was recognized by an earlier study of Ziper and LeMone (1980). They showed that the updrafts within convective cores observed during the field campaign of the Global Atmospheric Research Program’s (GARP) Atlantic Tropical Experiment (GATE) which was conducted in the tropical Atlantic Ocean are significantly weaker than those seen in midlatitude, continental thunderstorms measured in the Thunderstorm Project in Florida, and Ohio in the USA (Byers and Braham 1949). Similar features for the difference in the vertical velocity between the tropical oceanic and the midlatitude continental regions were found in other studies (Jorgensen and LeMone 1989; Lucas et al. 1994a; Igau et al. 1999). The strength of updraft velocity can be assessed, at least qualitatively, in terms of the degree of convective instability. The convective instability is quantified with the use of CAPE. Starting with the vertical momentum equation for inviscid motion: T' dw =B=g v, dt Tv where w is vertical velocity, B is buoyancy, g is the gravitational acceleration constant, and T v and Tv' are the ambient and perturbation virtual temperatures, respectively. Rearranging and integrating this equation from the level of free convection (LFC) to the level of neutral buoyancy (LNB) lead to: LNB {

1 dw2 dz = 2 dz

LFC

LNB { T' g v dz. Tv

LFC

Recognizing that the right-hand side is equal to CAPE and assuming that w(z = LFC) = 0, we can obtain the vertical velocity at LNB as: 1 2 || w z=LNB = CAPE, 2 and hence, wmax =

√ 2CAPE,

(14.1)

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where wmax denotes the maximum updraft speed that would be achievable at LNB. Therefore, the updraft strength can be diagnosed in terms of the CAPE magnitude. Jorgensen and LeMone (1989) compared the strength of maximum updraft for cumulonimbus clouds in the tropical oceanic, subtropical oceanic, and midlatitude continental regions as well as in hurricane and tornadic-storm environments and demonstrated that the updraft strength can be well scaled with the CAPE value. Updrafts are stronger in tornadic and midlatitude environments that have a larger CAPE than in tropical/subtropical and hurricane environments having a smaller CAPE. Qualitatively, the updraft strength can be assessed by diagnosing an environmental CAPE value based on Eq. (14.1). From a quantitative perspective, Eq. (14.1) neglects the pressure gradient force and turbulent mixing and thus should be regarded as a general guide to compare the updraft strength under different CAPE conditions. An illustrative thought on this point was put forth by Lucas et al. (1994a, b). By examining the vertical change of excess temperature for an air parcel from the ambient environment, Lucas et al. (1994a) noted that the area of the positive excess temperature is “skinny” over the ocean but is “fat” over the continental region of the USA. The skinny profile suggests that the smaller buoyancy for a lifted air parcel over the ocean is easily diluted with the environment through mixing when compared with a larger buoyancy over the continent. In other words, updraft air parcels in continental convective clouds will be less diluted with their environments and can be more accelerated by the positive buoyancy than the air parcels in oceanic convection. A more precise assessment of updraft acceleration has been investigated (Powell 2022). These studies emphasize that the temperature lapse rate affects the magnitude of buoyancy and, hence, the strength of convective updrafts, leading to a control in the resulting rainfall intensity. It is also suggested that mesoscale precipitating systems organized from an individual convective cloud will be affected by a change in the temperature lapse rate. For example, Xu and Randall (2001) showed that the largest difference between the tropical and midlatitude convection is seen for the strongest vertical velocity that largely depends on thermal buoyancy and water loading. McCaul et al. (2005) demonstrated that stronger updrafts in cooler environments are due to larger positive buoyancy from fusion processes that start at lower altitudes than in warmer environments. By keeping CAPE unchanged in various tropospheric temperatures, James et al. (2006) further indicated the convective clouds in warmer, moister environments, which are effective in reducing the evaporation rate, generate weaker cold pools, which determines the three-dimensional structure of convective lines. By conducting numerical experiments, Houston and Niyogi (2007) examined the influence of the temperature lapse rate above LFC on the development of cumulus convection and showed that stronger convection is produced under conditions with a larger temperature lapse rate. Based on these studies, which emphasized the importance of the stability condition in terms of the temperature lapse rate, Takemi (2007a, b; 2010) investigated the effects of the change in the tropospheric temperature lapse rate on the structure and development of MCSs (particularly squall lines) by conducting numerical experiments under idealized environmental conditions. In determining the temperature

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lapse rate, they used the analytical function for a storm environment proposed in Weisman and Klemp (1982) and changed the temperature at the tropopause height to obtain a number of different tropospheric lapse rates. The analytical function of the temperature profile proposed in Weisman and Klemp (1982) is θ (z) = θ0 + (θtr − θ0 )

( ) 54 z z tr

,

(14.2)

where θ is potential temperature, with θ0 (fixed at 300 K) and θtr denoting the values at the surface and at the tropopause height z tr (set to 12 km), respectively. In Weisman and Klemp (1982), θtr is set to be 343 K, which is intended to represent a typical environment for convective storms over the plains of the USA. In Takemi (2007a) and his following studies, the θtr value is set to be either 343, 348, 353, or 358 K to examine the effects of stability changes on MCS development. A lower value of θtr represents a midlatitude, continental environment, whereas a higher value of θtr mimics a tropical, oceanic environment. For reference, the lapse rate of the US Standard Atmosphere corresponds to the profile intermediate between θtr values of 348 and 353 K. Under this setting, a difference in the temperature lapse rate leads to a difference in the vertical distribution of buoyancy for a surface-based air parcel lifted adiabatically. Through setting a different θtr value, the tropospheric temperature lapse rate can be systematically examined. But at the same time, a different θtr value results in a difference in the value of CAPE, if only the temperature lapse rate is changed. Thus, one may argue that the sensitivity to the temperature lapse rate cannot be separated from the sensitivity to CAPE. For example, a lower θtr value indicates a smaller CAPE. This is attributed to the buoyancy becoming smaller in the case of a lower θtr . According to Eq. (14.1), the updraft becomes weaker when θtr is lower, which appears to be an obvious result. Therefore, Takemi (2007b, 2010) further examined conditions having different temperature lapse rates with a similar amount of CAPE by changing the low-level water vapor content. Theoretically, the maximum updraft achievable in convective cores is unchanged if CAPE is the same, even among the different lapse rate cases, which is guided from Eq. (14.1). The vertical profiles of the temporal mean and maximum updrafts as well as the fractional areas of stronger updrafts within the simulated squall lines are demonstrated in Fig. 14.1. The results from the simulations with CAPE of 1700 J kg−1 are shown here. With the increase in the θtr value, both the mean and maximum updrafts become weaker and the areal extent of stronger updrafts becomes substantially smaller. This result clearly indicates that the updraft strength is sensitive to the temperature lapse rate. Because the amount of CAPE is the same, the change in the lapse rate corresponds to a difference in the vertical distribution of buoyancy assessed for a surface-based air parcel, which results in different vertical acceleration due to the buoyancy. With a larger θtr value (i.e., a smaller temperature lapse rate), the magnitude of buoyancy at a certain level decreases. A smaller buoyancy leads to a weaker updraft and, as mentioned by Lucas et al. (1994b), provides a situation more susceptible to mixing and entrainment, indicating that the lifted air parcels are more

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Fig. 14.1 Vertical profile of a the temporal mean (solid lines) and maximum (dashed lines) updrafts and b the fractional area of updrafts with a speed greater than or equal to 1 m s−1 within the simulated squall lines under conditions of different θtr values but with the same amount of CAPE (= 1700 J kg−1 ). The last two digits (i.e., 43, 48, 53, and 58) in the experimental name denote the θtr value of 343, 348, 353, and 358 K, respectively. Modified from Takemi (2007b). ©2007 America Geophysical Union. Used with permission

diluted with the environment. This feature is reflected in the vertical distribution of stronger updraft areas (Fig. 14.1b); a smaller area of stronger updrafts suggests that vigorous updrafts are strongly diluted. Takemi (2007a) proposed that the temperature lapse rate in the convectively unstable layer (which basically corresponds to the lower-to-the middle troposphere) well explains the relationship between the squall-line intensity and the stability condition. This lapse rate is written as: emin ))−T (z=z(θemax )) ┌ = − T (z=z(θ , z(θemin )−z(θemax )

(14.3)

where T is temperature and z(θemin ) and z(θemax ) are the heights having the minimum and maximum equivalent potential temperatures, respectively. Note that both θemin and θemax appear within the convectively unstable layer which is below z(θemin ). With Eq. (14.3), the lapse rate in the convectively unstable layer is quantified. Takemi (2007b) found that the rainfall amount generated by MCSs scaled well with the lapse rate defined by Eq. (14.3). Furthermore, the vertical distribution of CAPE for each air parcel that originated at a different height was shown to strongly depend on the temperature lapse rate (Takemi 2010). In the environment with a smaller lapse rate, the depth having a substantial amount of CAPE becomes shallower even though the CAPE value for the surface-based air parcel is not changed. If the depth having some CAPE values becomes deeper, air parcels not only at the lowest level but also at elevated levels in the lower troposphere will contribute to the upward motion, which is beneficial for the development of MCSs. The importance of the vertical distribution of CAPE in developing MCSs was emphasized by Takemi and Satomura (2000) who investigated the mechanism for the maintenance of squall lines in a dry environment.

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From a number of sensitivity experiments, Takemi (2010) found that the difference in the buoyancy profile under different temperature lapse rates can be interpreted as the difference in the vertical distribution of CAPE for surface-based and elevated air parcels. The vertical distribution of CAPE was also recognized to play a key role in the development of nocturnal convective systems (Parker 2008). Although the impact of the tropospheric temperature lapse rate on the development of MCSs was clearly demonstrated, the analytical function represented by Eq. (14.2) cannot properly reproduce the lapse rate of the tropical, oceanic environment. Specifically, the lapse rate in the lower to middle troposphere represented by Eq. (14.2) is larger than the tropical lapse rate actually observed in, for example, the tropical western Pacific (Trier et al. 1996; Yoneyama 2003; Takemi et al. 2004). Because the buoyancy profile is sensitive to the tropospheric lapse rate, the use of an actual sounding in a tropical, oceanic region will be more realistic and, hence, more appropriate. Therefore, Takemi (2014a) used the sounding data of Trier et al. (1996) for a squall-line environment in the tropical western Pacific to represent a tropical, oceanic condition as well as the original analytical sounding of Weisman and Klemp (1982) for a midlatitude, continental condition. Based on the analysis of Takemi (2010), another midlatitude-type profile having a CAPE distribution similar to that of the tropical condition was examined by decreasing the moisture content in the lower troposphere from the Weisman and Klemp sounding. Again, the strength and areal extent of updrafts within the simulated squall lines were shown to depend critically on the tropospheric temperature lapse rate. The importance of the vertical buoyancy profile, and hence the CAPE profile, in characterizing the updraft and precipitation features under different thermodynamic conditions was also confirmed. Specifically, the precipitation amount generated by the simulated squall line increases with increasing the depth of the layer having a significant amount of CAPE. It should be noted here that the system-scale mean precipitation and the pointwise maximum precipitation respond differently to the temperature lapse rate (Takemi 2007b, 2010, 2014a). With a decrease in the lapse rate, the mean precipitation also decreases, whereas the maximum precipitation increases (Fig. 14.2). Such different responses to the lapse rate are attributed to the negative effects of dilution of convective cores with the environment. In the temporal mean sense, the updraft cores are more negatively affected by the environmental dilution, especially when the updrafts are weaker and smaller. Weaker updrafts, which are observed in the tropical environment, lead to a weaker convective system as a whole and, hence, to a smaller amount of total precipitation. In other words, the total amount of precipitation is strongly controlled by the degree of organization and intensification of a convective system as a whole. On the other hand, the instantaneous maxima of precipitation intensity are not directly related to the organization of a convective system as a whole but are dependent on the intensity of individual convective cells. The rainfall amount from an individual cell is considered to depend on the total moisture content, i.e., precipitable water vapor, at local scales. Such local-scale abundant moisture leads to an increase of the maximum precipitation within the precipitating system. The tropical, oceanic environment examined by Takemi (2014a) is characterized by a very humid condition whose lapse rate is close to moist adiabatic. The relative

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Fig. 14.2 Mean (symbols) and standard deviation (error bars) from the time series of a the area-mean precipitation intensity and b the area-maximum precipitation intensity in the simulated squall lines under a weak-shear condition in different stability cases. Modified from Takemi (2010). ©2010 Elsevier. Used with permission

humidity for this tropical environment is greater than 90% from the surface up to a height of about 7 km. Therefore, the characteristics of updraft and precipitation as revealed in the tropical condition can be regarded as the baseline features for understanding the morphology and environmental properties of mesoscale precipitating systems in very humid conditions. Takemi (2014a) also examined the sensitivity of the simulated squall lines under various stability conditions to the initialization method by using either a warm thermal or a cold pool as the initial perturbation to trigger convection. A pronounced sensitivity to the initial perturbation was observed in the cases under the midlatitudetype, drier condition. This sharp difference arises because the drier environment is detrimental to the development of convective clouds especially at their early stage. Once convection sufficiently develops, squall lines evolve in a spontaneous manner through producing cold pools and regenerating new convective cells according to the RKW theory (Rotunno et al. 1988). However, if the initial convection does not gain sufficient intensity to trigger a spontaneous mechanism, a squall-line system does not develop. In contrast, under conditions with higher relative humidity, a detrimental effect does not operate, and therefore, convective clouds favorably develop throughout their lifetimes, which are relatively insensitive to the initial perturbation. This analysis of the sensitivity to the idealized initialization method clearly indicates that diagnosing environmental thermodynamic conditions provides a basis to explain

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the structure and intensity of MCSs at their mature stage. In contrast, an environmental diagnosis alone is not sufficient for predicting the initiation of MCSs from an undisturbed state. From a predictability point of view, the result implies that the dependence on the initial perturbation should be carefully investigated. An important point that should be emphasized from a series of the abovementioned studies is that the tropospheric temperature lapse rate itself should carefully be examined in order to understand the generation and intensification of upward motion and resulting convective clouds. The lapse rate determines the vertical distribution of buoyancy for an air parcel lifted from a low level, which is directly related to the magnitude of upward motion. The lapse rate affects the magnitudes of various environmental indices. For example, an environment with a large lapse rate leads to a larger buoyancy at each height level, resulting in a larger value of CAPE which is the vertical integrated amount of buoyancy. In other words, environmental indices somehow take into account the magnitude of the temperature lapse rate. In order to assess the magnitude of updraft more exactly, the contribution of vertical pressure gradient should be included (Das 1979; Rotunno and Klemp 1982; Davies-Jones 2002; Doswell and Markowski 2004; Parker 2010). In addition, entrainment and mixing processes that dilute buoyant parcels affect the updraft strength (Romps and Kuang 2010; Yeo and Romps 2013; Romps 2014). Incorporating these processes enables to more precisely quantify and predict the upward motion field in convectively unstable environments. Despite these improvements for quantitative diagnosis of convective updrafts, the temperature lapse rate, i.e., the shape of the temperature profile, is a primary factor in determining the magnitude of buoyancy. Therefore, it is important to diagnose the fine-scale structures of temperature in the vertical direction, which will affect the strength of updrafts and hence the development of convective clouds.

14.3 Morphology and Environmental Properties of Mesoscale Precipitating Systems The morphology and environmental properties of MCSs have been widely investigated in the literature. State-of-the-art knowledge on MCSs is thoroughly described in a number of textbooks on mesoscale meteorology (e.g., Lin 2007; Markowski and Richardson 2010; Cotton et al. 2011; Trapp 2013; Houze 2014). Although there are abundant observational and numerical studies on MCSs, as mentioned in Sect. 14.1, much attention has been devoted to cases that occurred over continental regions and during special field projects over tropical oceanic regions. In contrast, fewer studies have been conducted for cases occurring in East Asia. In addition, recognizing that precipitation consists mainly of convective types and stratiform types, we do not limit our focus to MCSs. This section therefore overviews mesoscale precipitating systems in moist environments, focusing on those occurring in East Asia during warm seasons. Some recent extreme rainfall events are described here.

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The vertical profile of moisture is known to strongly affect the development and evolution of cumulus convection in a moist environment such as the tropical oceanic region. The vertical development of tropical cumulus clouds is strongly limited by the tropospheric dryness above the boundary layer (Brown and Zhang 1997) and by the stable layer due to cloud detrainment at a middle level (Zuidema 1998). Under such influences, tropical cumulus convection exhibits trimodal characteristics: cumulus, cumulus congestus, and cumulonimbus (Johnson et al. 1999; Takayabu et al. 2010). Numerical modeling studies demonstrated that the middle-level stable layer, together with dry-air entrainment, regulates the vertical development of cumulus clouds (Redelsperger et al. 2002) and that dry conditions in the middle and upper troposphere inhibit the development of deep convection (Ridout 2002; Derbyshire et al. 2004). Takemi et al. (2004) investigated the effects of the depth of a humid layer (conversely, the depth of a dry layer) on the vertical evolution of cumulus convection by conducting observational data analysis and performing idealized numerical experiments. In their numerical experiments, environmental relative humidity was systematically changed. They indicated that the vertical extent of cumulus convection is highly sensitive to the humidity at the middle-to-upper levels. In addition, moistening of the free troposphere because of cloud detrainment by congestus clouds was shown to play a key role in the development of deep tropospheric convection; this moistening process by congestus clouds is known as congestus preconditioning (Waite and Khouider 2010). The effect of tropospheric moisture on tropical convection development was further investigated in observational and modeling studies of real cases (Powell and Houze 2013; Hagos et al. 2014; Bellenger et al. 2015; Ruppert and Johnson 2015; Takemi 2015; Zermeno-Dias et al. 2015; Sakaeda et al. 2018; Powell 2019). Free-tropospheric moisture influences were also investigated for MCSs. From the analysis of observational data, LeMone et al. (1998) suggested that low relative humidity between the top of the boundary layer and the 500-hPa level shortens the lifetimes of slow-moving squall lines (Barnes and Sieckman 1984). Numerical experiments indicated that the squall-line properties vary drastically with changes in the free-tropospheric humidity and the shear profiles (Lucas et al. 2000; Takemi 2006, 2007a). The outcomes of these studies that demonstrated the role of tropospheric moisture in determining the mode of tropical convection and the structure and intensity of MCSs should help us understand the morphology and mechanisms of MCSs or, in general, mesoscale precipitating systems under moist conditions. In the followings, we describe the morphology and environmental properties of mesoscale precipitating systems in moist environments, which are aimed at those occurring in East Asia during the monsoon (mei-yu/baiu/Changma) season. The observational network of weather radars is useful for capturing and monitoring the development and evolution of MCSs and precipitating clouds over an extended area. The temporally long and spatially wide coverage of the radar observations enables to reveal climatological characteristics of mesoscale precipitating systems. A pioneering work of Bluestein and Jain (1985) identified four typical modes of squall lines over the central plains of the USA. Wide varieties of squall lines

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were further demonstrated in subsequent studies (e.g., Houze et al. 1990; Parker and Johnson 2000; Pettet and Johnson 2003; James et al. 2005; Schumacher and Johnson 2005). The recent development of an operational radar network in China has enabled such climatological studies. Meng et al. (2013) used two-year radar data to identify three patterns of structural evolution of squall lines in east China and found that the squall lines in east China tend to form in a moister environment (which possesses a larger amount of precipitable water vapor) with weaker vertical shear than squall lines in the USA, such as those described in Bluestein and Jain (1985). They also found that the largest instability and the most humid environment are seen in squall lines with leading stratiform regions in east China, in contrast to the case in the USA, where trailing-stratiform-type squall lines display the most unstable and humid conditions. The dominance of the leading-stratiform-type squall line in China may be due to the influence of synoptic-scale flow patterns such as troughs and cyclonic circulation at upper levels. An advantage of the network of ground-based radars is its wide coverage over land, which is suitable to capture the initiation, development, and dissipation processes of mesoscale precipitating systems. In other words, the size of the land somewhat limits the monitoring of such whole processes. Nevertheless, long-term accumulation of radar data is still useful in conducting climatological studies of mesoscale precipitating systems. Climatological analysis of convective systems over Japan was first conducted by Unuma and Takemi (2016a) who examined the composites of operational weather radars throughout the Japanese main islands. Despite an anticipated limitation of the spatial coverage over the Japanese land area, a long-term dataset covering 8 years enabled the detection of robust features of mesoscale precipitating systems during warm seasons (i.e., from May to October). Stationary and slow-moving systems, termed quasi-stationary convective clusters (QSCCs), were specifically chosen. An automated detection algorithm which was originally developed by Shimizu and Uyeda (2012) to identify individual convective cells was used to extract QSCCs. To diagnose the environmental conditions for the occurrence of mesoscale precipitating systems, upper-air sounding data observed at nearby stations were used. The typical horizontal scale of QSCCs is about 20 km, indicating that they are meso-β-scale phenomena. A comparison of the environmental conditions between the QSCC and no-rain cases indicated that the relative humidity at low and middle levels controls the development of QSCCs; specifically, the QSCCs favorably occur under conditions of higher humidity not only in the lower layer but also in the middle troposphere. Unuma and Takemi (2016a) suggested that the middle-tropospheric moistening before the convection development plays an important role in generating QSCCs. Unuma and Takemi (2016b) further investigated the morphology of QSCCs by distinguishing elongated and circular modes. The shapes of a QSCC detected by Unuma and Takemi (2016a) were fitted with an ellipse; after the fitting, the central position, orientation, and the lengths of the major and minor axis of the fitted ellipse were derived. Then, an aspect ratio was obtained by calculating the ratio of the length of major to minor axis. Finally, the elongated mode was defined as having its

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Fig. 14.3 Spatial distribution of the linear-shaped QSCC fraction (in %) among the total occurrence of QSCCs over the main islands of Japan. The percentage is assessed in terms of the QSCC occurrence in each 50 km2 area. The locations with no color marks indicate the areas where no QSCCs are detected. From Unuma and Takemi (2016b). ©2016 The Meteorological Society of Japan. Used with permission

aspect ratio of 1.4 or greater in accordance with the studies by Maddox (1980) and Yang et al. (2015). Figure 14.3 shows the spatial distribution of the percentage of the occurrence of the elongated mode against the total number of QSCC occurrence evaluated within each 50 km by 50 km area. The distribution indicates that most QSCCs take a linear shape throughout the areas where they frequently occur. The analysis of the precipitation characteristics during the QSCC events showed that the degree of instability better explains the system-mean precipitation intensity than shear-related parameters (Unuma and Takemi 2016a). Among the stability indices examined, CAPE, the temperature lapse rate in the lower to middle troposphere [similar to Eq. (14.3)], and the Showalter stability index indicate higher correlations with precipitation intensity. This observational evidence is consistent with and thus appears to support the numerical analysis from the idealized simulations (Fig. 2a). Interestingly, precipitable water vapor does not correlate well with the precipitation intensity. Rather, the precipitable water content seems to provide some threshold for whether QSCCs occur. On the other hand, compared with the stability indices, shear-related parameters describe the precipitation area relatively well because vertical shear is a key factor for the organization mode and morphology of MCSs and precipitating systems (Weisman and Klemp 1982; Thorpe et al. 1982; Rotunno et al. 1988; LeMone et al. 1998; Parker and Johnson 2000; Weisman and Rotunno 2004; French and Parker 2008) and, thus, for determining the horizontal extent of system-generated precipitation. Stationary precipitating systems sometimes spawn heavy rainfall and resultant disastrous phenomena such as flooding, inundation, and landslides. Forecasting quantitatively high-impact rainfall events is scientifically challenging and societally

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important. Therefore, the mechanisms and prediction of such stationary systems have received more attention not only from a research point of view but also from an operational forecasting point of view. Quasi-stationary MCSs can exist throughout the world, and those occurring in the contiguous USA were investigated by Schumacher and Johnson (2005, 2006, 2008, 2009). In general, the middle-to-upper troposphere over a midlatitude, continental region is not humid; therefore, low-level moisture is expected to play a role in controlling the development of MCSs. Schumacher (2015) and Schumacher and Peters (2017) emphasized that small changes in lowlevel moisture strongly affect the rainfall generated by warm-season midlatitude MCSs. As described in Sect. 14.2, a midlatitude squall line that develops in the drier free troposphere is more sensitive to an initial perturbation than its tropical counterpart (Takemi 2014a). Such a feature of a midlatitude squall line may be a factor that affects the sharp sensitivity of squall lines to low-level moisture perturbations, as found in Schumacher (2015) and Schumacher and Peters (2017). On the other hand, the environment for MCSs and mesoscale precipitating systems in the warm season in East Asia is very moist. According to the idealized modeling analyses described in Sect. 14.2, the effects of highly moist conditions on mesoscale precipitating systems can differ from those identified for midlatitude systems. As demonstrated by Unuma and Takemi (2016a), moisture contents in the middle troposphere (above the 3-km height) significantly contribute to the total column moisture (i.e., precipitable water vapor content) in the QSCC occurrences, while the contributions of the low-level moisture content to the total column moisture do not change between the QSCC and no-rain cases. Based on the observational and numerical studies, middle-level moisture is considered to be critically important for environmental control of mesoscale precipitating systems under very humid conditions. A comparison of the environmental conditions for linear-shaped and circularshaped QSCCs (Unuma and Takemi 2016b) shows that CAPE and shear-related parameters are statistically significant in distinguishing the difference in the environmental conditions. A non-dimensional parameter that combines CAPE and vertical shear, i.e., the bulk Richardson number (BRN), also substantially separates the environmental difference; BRN for the linear-shaped QSCCs is 32.8, which is significantly lower than that for the circular QSCCs, and is comparable to the value for the back-building squall lines in the USA (Bluestein and Jain 1985). Considering that most QSCCs take a linear shape (Fig. 14.3), a mechanism for generating linearshaped QSCCs is suggested to be a back-building process. As a case study, Kato and Goda (2001) clearly demonstrated that a back-building mechanism played a role in maintaining the stationary rainband which produced a significant amount of rainfall in northern Japan in 1998. Statistical analysis of the environmental properties for precipitating events was extended to afternoon local-scale precipitation under synoptically undisturbed conditions in summer. Diagnosing the environmental properties for such afternoon rainfalls over the Kanto Plains area (i.e., in the Tokyo metropolitan area), Japan with the use of the Japan Meteorological Agency’s operational MesoScale Model (MSM) analysis data, Nomura and Takemi (2011) revealed that colder temperatures at middle levels

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Fig. 14.4 Spatial distribution of KI for the occurrence/non-occurrence of local-scale rainfalls over the Kanto Plains, Japan, at 0900 JST under summertime, synoptically undisturbed conditions. Mean KI values for (left) no-rain cases, (middle) rain cases, and (right) strong-rain cases

and higher relative humidity at low-to-middle levels significantly contribute to the generation of afternoon precipitation events in the area. Because of this significant difference between the rain and no-rain occurrences, the K index (KI) (George 1960) was found to clearly describe and explain the environmental difference. The KI is defined as: KI = T850 − T500 + Td850 − (T700 − Td700 ),

(14.4)

where T850 , T700 , and T500 are the temperatures at the 850-, 700-, and 500-hPa level, respectively, and Td850 and Td700 are the dew-point temperatures at the 850and 700-hPa level, respectively. From this definition, KI incorporates the low-tomiddle temperature lapse rate and the humidity at low and middle levels. Figure 14.4 compares the spatial patterns of KI in the cases of no-rain, rain (at least 1 mm h−1 rainfall at any raingauge station within the area), and strong-rain (rainfall greater than or equal to 10 mm h−1 at any raingauge stations within the area) over the Kanto Plains at 0900 Japan Standard Time (JST, UTC plus 9 h) in summer. It is seen that KI becomes larger with a stronger rainfall. A similar statistical analysis with the use of the operational MSM analysis data was used to diagnose the environmental properties of afternoon rainfalls under summertime, synoptically undisturbed conditions for cases in the Nobi Plains, corresponding to the Nagoya metropolitan area, Japan (Takemi 2014b). KI was found to be a proper index to distinguish the conditions between the rain and no-rain cases; in particular, higher moisture was preferentially observed in the rain cases than in the no-rain cases. In this way, the environmental condition for the development of afternoon rainfalls in situations without any major synoptic-scale external forcings (such as tropical cyclones, baiu fronts, and warm/cold fronts) is characterized by a sufficient amount of moisture, which is significantly large as compared with the no-rain cases. This property is similar to that found for the QSCC occurrence (Unuma and Takemi 2016a). Thus, the importance of middle-level moisture in generating afternoon thunderstorms and quasi-stationary precipitating systems should be emphasized.

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The research progress in and current understanding of stationary precipitating systems over Japan have recently been reviewed by Kato (2020). In Kato (2020), special focus was placed on quasi-stationary band-shaped precipitation systems that produced concentrated areas of heavy rainfalls (i.e., a total rainfall of 200 mm or greater). Such a stationary precipitating system forms a linear-shaped precipitation area. The linear-shaped precipitation area defined operationally by the Japan Meteorological Agency refers to a banded rainfall area with a length of 50–300 km and a width of 20–50 km, generated by successive development of convective cells within similar areas. The definitions of these spatial scales are set by the Japan Meteorological Agency based on the analyses on the past events (Kato 2020) in order to automatically identify threatening heavy rainfall events and to promptly issue alerts and warnings to the public. Hirockawa et al. (2020) and Hirockawa and Kato (2021) developed an automated algorithm to objectively detect localized heavy rainfall areas. Such a method should be useful to conduct statistical analysis and reveal climatological features of heavy-rain-producing systems. Major processes for the formation of such linear precipitation area are a brokenline type and a back-building type similar to those identified for squall lines in the USA (Bluestein and Jain 1985). Kato (2020) listed six conditions favorable for the generation of a linear-shaped precipitation area: that is, a larger amount of moisture flux at the 500-m height; a short LFC distance for an air parcel that originated at the 500-m height; a higher relative humidity at the 700- and 500-hPa levels; higher storm-relative helicity; a larger upward velocity at the 700-hPa level; and a higher LNB for a parcel at the 500-m height. A short displacement distance of an air parcel to LFC was found to be a favorable condition for maintaining squall lines in dry environments (Takemi and Satomura 2000) (see Fig. 14.5 for a schematic). Because of low relative humidity, LFC for a surface-based air parcel is generally quite high. High LFC is consistent with the formation of an extremely deep, mixed layer which has a depth of greater than 4 km (Takemi and Satomura 2000). Thus, surface-based air parcels [denoted as “CAPE > 0, d(LFC) ≫ 1” in Fig. 14.5) will not easily be raised to LCL and LFC. Instead, air parcels located in the upper part of the deep mixed layer (denoted as “CAPE > 0, d(LFC) « 1” in Fig. 14.5) are easily raised to LFC with the forcing of the gust front, because of a short distance to LFC. A pressure gradient force (denoted as “PGF” in Fig. 14.5) induced by the local-scale high (denoted as “H” in Fig. 14.5) just in front of the gust front provides upward acceleration. Although a dry condition and a deep mixed layer are commonly seen in other midlatitude, continental regions such as the continental are of the USA, the mixed layers in dry environments such as desert regions are extremely deep (Gamo 1996). In such dry conditions, air parcels in the upper part of the mixed layer primarily contribute to the generation of deep convection and squall lines. Therefore, the mechanism described here and schematically shown in Fig. 14.5 is a unique feature for the maintenance of squall lines and MCSs. A point which should be emphasized is that the lifting of elevated air parcels having short distance to their LFCs is a key to understand the processes for the intensification and maintenance of MCSs.

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Fig. 14.5 Schematic depicting the maintenance mechanism for squall lines in dry environments proposed by Takemi and Satomura (2000). dLFC denotes the vertical distance between the originating level and LFC

It is interesting to note that this short displacement toward LFC has been identified as an important factor for forming mesoscale precipitating systems also in moist environments. We also note the importance of moisture at middle levels. Operational identification and diagnosis of heavy-rain-producing stationary precipitating systems have been implemented and are continuously being improved at the Japan Meteorological Agency. Climatological studies of linear-shaped precipitation areas were further conducted for cases that occur in East Asia. Goto and Satoh (2022) indicated that those stationary precipitating systems contribute significantly to the total rainfall amount in western Japan, the Nansei Islands, and the East China Sea. In the 2010s, a number of extreme rainfall events occurred and spawned severe disasters in Japan. In early July 2017, in particular, a heavy rainfall event occurred in northern Kyushu Island, with a total daily rainfall greater than 600 mm in a localized area (Kato et al. 2018; Takemi 2018). This event spawned flooding and landslides in a concentrated region, thereby having significant societal impacts. One year later, in early July 2018, heavy rainfalls developed across wide areas over the Japanese islands, particularly in the western and central parts of Japan, and flooding, inundation, and landsides caused a large number of human losses and devastating damages to social infrastructures, agriculture, economic activities, etc. In response to these extreme events, numerous studies have been conducted. A part of the outcomes from such studies was briefly summarized in Takemi (2021). In the followings, the analyses of the events that occurred in July of 2017 and 2018 are described.

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Takemi (2018) conducted convection-resolving simulations of a linear-shaped stationary MCS, resolved at a horizontal grid spacing of 167 m, which produced the heavy rainfall in northern Kyushu in early July 2017. In these 167-m mesh simulations, the model topography was generated with the use of a high-resolution digital elevation model (DEM) dataset having a 50-m resolution to precisely reproduce complex features of the topography in the region. The representation of complex terrain was shown to be critically important in reproducing the stationarity of the linear-shaped convective systems and in quantitatively reproducing the resulting heavy rainfall in convection-resolving simulations. Figure 14.6 indicates that decreasing the horizontal grid spacing from 167 to 500 m, 1.5, and 4.5 km results in poor representation of the spatially concentrated nature because of to the linear-shaped stationary MCS. The case with the highest resolution quantitatively reproduced the observed rainfall. It was further shown that the use of a coarserresolution DEM dataset to create model topography results in a smaller amount of total rainfall (i.e., approximately 2/3) than when the higher-resolution DEM data are used, even with the same grid spacing for the atmosphere. As Yoshizaki et al. (2000) showed that even small and low mountains are able to generate an organized rainband under a moist convectively unstable condition, the present analysis emphasizes a possible role of variable terrain features in developing stationary MCSs and hence leading to a concentrated area of rainfall. The heavy rainfall event that occurred in July 2018 had also high impacts on the society. The year 2018 in Japan was marked not only by this July heavy rainfall event but also by subsequent extreme hot weather (Imada et al. 2019; Nishi and Kusaka 2019) and a number of extreme typhoon landfalls (Takemi et al. 2019). Actually, extreme weather in summer 2018 was a global phenomenon; heat waves and/or extreme rainfalls developed almost simultaneously in regions of the Northern Hemisphere in summer. The large-scale atmospheric conditions for the extreme rainfall and heat wave in July 2018 in Japan were investigated by Shimpo et al. (2019), who documented that the extreme rainfall was caused by persistent moist airflows and baiu frontal ascent, whereas the heat wave was due to the enhancement of both the surface-level North Pacific Subtropical High and the upper-level Tibetan High. From a mesoscale point of view, Takemi and Unuma (2019) documented the environmental properties of the heavy rainfall event in July 2018 in Japan by comparing them with those identified for the warm-season QSCCs. They suggested that high relative humidity in the middle layer contributes to the occurrence of the heavy rainfall through minimizing negative effects of environmental mixing on in-cloud air parcels and through decreasing vertical displacements to reach LFC, similar to the process proposed by Takemi and Satomura (2000). Further investigations (Unuma and Takemi 2021) indicated the importance of the middle-level relative humidity in characterizing the environmental properties of mesoscale precipitating systems in the heavy rainfall events in July of 2017 and 2018. Tsuji et al. (2020) showed that the environment for the July 2018 heavy rainfall was more humid than that for the July 2017 case, although both were basically moister than the climatology. They also indicated that the 2017 and 2018 cases were characterized as, respectively, the

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Fig. 14.6 Accumulated rainfall from 0300 JST 5 July to 0900 JST 7 July in 2017, as simulated with a horizontal grid spacing of (upper left) 167 m, (upper right) 500 m, (lower left) 1.5 km, and (lower right) 4.5 km

extreme rainfall events and the extremely tall convection events, which were categorized by Hamada et al. (2015) and Hamada and Takayabu (2018). In addition to the moisture condition, a dynamical forcing is also required to generate larger-scale upward motion to provide a favorable condition for triggering the development of mesoscale precipitating systems (Yokoyama et al. 2020). Figure 14.7 summarizes the conceptual model for the development of the heavy rainfalls in July of 2017 and 2018. The stability condition is shown to be more unstable in the 2017 case than in the 2018 case; thus, under the sufficiently unstable condition in 2017 deep convection favorably develops. On the other hand, the environmental condition in the 2018 case is more stable and moister than that in 2017. In addition, in 2018, a deep

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Fig. 14.7 Conceptual models for the development of a the 2018 heavy rainfall and b the 2017 heavy rainfall. From Tsuji et al. (2020). ©2020 The Author(s). Published by the Meteorological Society of Japan under a Creative Commons Attribution 4.0 International (CC BY 4.0) license

trough develops and hence induces dynamical ascent. Under the very moist condition in 2018, such dynamically induced ascent can easily lead to the development of precipitating clouds. The moist conditions seen in the heavy rainfall events as described above can lead to an environment that satisfies the criteria for moist absolute instability (Bryan and Fritsch 2000). Moist absolute instability is one of the stability states and is a state where the temperature lapse rate is greater than the moist-adiabat and the relative humidity is 100%. Specifically, the temperature lapse rate γ = γs satisfies the equation as follows: γs > ┌m ,

(14.5)

where γs denotes the saturated temperature lapse rate and ┌m is the moist-adiabatic lapse rate. This unstable layer denoted in Eq. (14.5) is referred to as a moist absolutely unstable layer (MAUL) and is found within or nearby MCSs (Bryan and Fritsch 2000). A schematic for the presence of such a saturated unstable layer was noted in Kingsmill and Houze (1999) who investigated the internal structure of tropical squall lines. MAULs are shown to play a role in activating convective roll circulations within squall lines (Bryan et al. 2007). Because a very moist condition may not appear frequently over the continental regions, the condition of MAUL may not easily be satisfied. In contrast, the environmental condition during the warm season in East Asia is characterized with high relative humidity. Therefore, it is possible that MAUL may appear more frequently than expected. Motivated by these studies, Takemi and Unuma (2020) demonstrated the presence of deep MAULs, some having a depth greater than 2 km, within spiral rainbands of

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Typhoon Hagibis (2019) (Fig. 14.8). During this event, several observation sites observed record-breaking heavy rainfalls, with one site recording a daily rainfall of 922.5 mm, which broke the observed record in Japan. The whole troposphere was shown to be almost saturated, and the column total water vapor content was extremely high. Although the tropospheric stability is characterized with a moderate value of CAPE and a nearly moist-adiabatic lapse rate, moist absolute instability, abundant moisture, and high humidity jointly play a key role in increasing the potential for generating heavy rainfalls. Tsuji et al. (2021) investigated the role of freetropospheric moisture convergence in the occurrence of summertime heavy rainfalls in western Japan by statistical analyzing cases between 2006 and 2020 and found that the free-tropospheric moisture convergence that occurs before the rainfall develops leads to atmospheric moistening and to the formation of an environmental condition favorable for heavy-rain-producing MCSs. MAUL was found to increase the rainfall peaks during the events. It is considered that MAUL is more commonly seen in moister environments than in drier environments, because the relative humidity condition for MAUL will not be easily achieved. In this sense, the very humid condition as frequently seen in the environment of East Asia, particularly during the monsoon season, will be favorable in forming MAUL. Further studies are required to reveal the characteristics and processes of the MAUL formation, mechanisms how MAULs contribute to organizing MCSs and/or mesoscale precipitating systems, and the relationship of MAUL with extreme rainfalls. Fig. 14.8 Depth (km) of MAUL at 1200 JST 12 October 2019 during the northward translation of Typhoon Hagibis (2019). From Takemi and Unuma (2020). ©2020 The Author(s). Published by the Meteorological Society of Japan under a Creative Commons Attribution 4.0 International (CC BY 4.0) license

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Because the presence of MAUL critically depends on the relative humidity, the formation of MAUL will require the transport of humid airmass, like the case seen in the heavy rainfall event in July 2018 (Sekizawa et al. 2019; Takemura et al. 2019). In other words, the moisture variability is fundamentally important in forming a very humid condition and a very unstable condition like MAUL and finally causing extremely heavy rainfalls in the monsoon period in East Asia highly. Such a high sensitivity to the moisture profile is recognized for the development of convective clouds and convective mode (such as cumulus, congestus, and cumulonimbus) (Brown and Zhang 1997; Redelsperger et al. 2002; Ridout 2002; Derbyshire et al. 2004; Takemi et al. 2004). In this regard, the generation and evolution of moist convection and mesoscale precipitating systems have similarity with those of tropical convection in which the fluctuation and variability of moisture play a key environmental control.

14.4 Predictability Accurate and reliable weather prediction is required in order to mitigate and prevent disasters resulting from extreme weather phenomena. Achieving a convectionresolving numerical weather prediction (NWP) technique is a realistic goal, not a dream, in the meteorological community. In a theoretical study on predictability, Lorenz (1969a) indicated that depending on the characteristic scale of flow that consists of many scales of motion, there is a corresponding intrinsic predictability range. Corresponding to the shape of the energy spectra (i.e., spectral slope), the predictability is regarded as bounded for the k −5/3 spectra (where k is wavelength) and is infinite for the k −3 spectra (Lorenz 1969a; Lilly 1990). Observational evidence demonstrated that large-scale motion has a k −3 spectrum and mesoscale motion has a k −5/3 spectrum (Nastrom and Gage 1985). Rotunno and Snyder (2008) extended the Lorenz (1969a) model to demonstrate unlimited and limited predictability for flows with a k −3 spectrum and a k −5/3 spectrum, respectively. Hohenegger and Schär (2007) investigated the predictability of synoptic-scale and mesoscale phenomena by comparing medium-range synopticscale and short-range cloud-resolving simulations and suggested that a given scale inherent in the atmospheric processes should have an intrinsic predictability rather than independent from initial uncertainties. Although the theoretical background and practical approach for the synoptic-scale predictability seem to be sound and established (see a review by Yoden 2007), the predictability of cloud-resolving (or convection-permitting) scales is an active research area from both scientific and practical viewpoints. Note that the numerical simulation and prediction with a resolution at 1 km or a few are regarded as being in a cloud-permitting or convection-permitting range (Zhang et al. 2007; Romine et al. 2014; Prein et al. 2017; Takayabu et al. 2022). Leith (1971) examined the atmospheric predictability from a theoretical viewpoint of two-dimensional turbulence which has a characteristic sharp spectral shape and pointed out that the numerical model investigation of the atmospheric predictability

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can be conducted if the model has a sufficient resolution that is capable of capturing an observed spectra of eddy kinetic energy. Skamarock (2004) demonstrated that the simulated kinetic energy spectra from 4-km grid spacing forecasts well capture the observed spectra having the k −5/3 spectral slope at mesoscales. The k −5/3 slope was also found at mesoscales in global model simulations (Terasaki et al. 2009; Skamarock et al. 2014). These results strongly support the basis of the mesoscale predictability investigations with NWP models. Skamarock (2004) also indicated that there is an effective model resolution that corresponds to the wavelength at which a model spectrum starts to rapidly decay compared with the observed spectrum. Rapid decay of the spectrum in numerical simulations is due to numerical filtering inherent in the numerical schemes and/or artificially implemented to mitigate numerical instabilities (Takemi and Rotunno 2003). Actually, because of the presence of numerical filtering and mixing in NWP models, the k −5/3 spectral slope is not able to be properly represented in numerical simulations having a grid spacing on the order of 1 km (Takemi and Rotunno 2003). In addition, the turbulence mixing parameterization based on the Smagorinsky (1963) scheme has an effect equivalent to a Gaussiantype filtering in the spectral space; hence, the power spectrum at the shortest scales simulated in NWP models sharply decreases (i.e., sharper than the k −5/3 slope) by the modeling design (Pope 2000; Takemi and Rotunno 2003). By conducting idealized numerical simulations of squall lines, Bryan et al. (2003) demonstrated that a minimum grid spacing on the order of 100 m is required in simulating convective motion and MCSs in order for the eddy viscosity parameterizations to adequately perform for their modeling design. Bryan (2005) also showed that an effective resolution for properly capturing convective-scale processes is approximately six times the horizontal grid spacing. Although the scale at which the k −5/3 spectral slope appears to depend on the scale at which energy from synoptic and/or larger-scale disturbances is ingested, representing the k −5/3 spectral slope is considered to be a key to understanding the inherent predictability in convection-resolving simulations. Fan et al. (2022) indicated that deep moist convection plays an important role in energizing the mesoscale in the upper troposphere and representing a shallow slope near – 5/3 of the kinetic energy spectra. In general, two types of predictability are recognized: practical predictability and intrinsic predictability. Practical predictability is defined as “the ability to predict based on the procedures that are currently available”, and intrinsic predictability as “the extent to which prediction is possible if an optimum procedure is used in the presence of infinitesimal initial errors” (Lorenz 1969b; Zhang et al. 2006; Melhauser and Zhang 2012). Practical predictability has been actively investigated through examinations of uncertainties in model parameterizations and initial conditions, while intrinsic predictability has been a fundamental issue in predictability research and was focused on for severe storms/tornadoes (Park 1999; Melhauser and Zhang 2012; Zhang et al. 2016; Markowski 2020) and MCSs (Durran and Weyn 2016; Weyn and Durran 2017). Severe and tornadic thunderstorms have distinct signatures; they are therefore considered to be useful cases to explore the predictability issue. However, the environments for such thunderstorms are characterized by drier conditions, corresponding to midlatitude, continental type thunderstorms. The

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intrinsic predictability of deep moist convection in humid environments such as those in the summer monsoon season in East Asia should be explored. As Takemi (2014a) demonstrated that tropical, oceanic MCSs are less sensitive to the initialization than midlatitude, continental MCSs in idealized numerical experiments, intrinsic predictability will be an important issue in forecasting mesoscale precipitating systems in humid conditions. In humid conditions, there is no preference in the location of precipitating cloud development, if the conditions including the ground surface are spatially uniform, because boundary-layer fluctuations may reach lifting condensation level (LCL) and LFC stochastically to lead to cloud development. In other words, minor fluctuations of temperature and/or water vapor in the lower troposphere may determine a favorable location of cloud condensation and eventually deep moist convection. Such minor fluctuations will be within the range of observational errors and/or will appear in places where no observation data are available. Therefore, it is expected that the forecast errors in predicting moist convection and thunderstorms grow very quickly and hence the predictability of thunderstorm development is quite low. On the other hand, if there is any inhomogeneity in the ground surface and topography, the development of clouds may be regulated by topographic features and geographical locations. Topography provides an external forcing to generate precipitating clouds and seems to be quite effective in generating clouds. With this consideration, the influence of topography on the predictability of precipitating clouds has been investigated in the literature. Recent studies investigated the impact of topography on the predictability of thunderstorms (Bachmann et al. 2019, 2020). Bachmann et al. (2019) investigated how radar data assimilation and topography affect the forecast skill of deep convection development in idealized numerical simulations and indicated that the topography plays a role in organizing the precipitation field, especially when no radar data are assimilated. They suggested that topographic forcing can correct potential errors included in initial conditions and thereby provide a source of predictability to a development of deep convection. Bachmann et al. (2020) extended their study for a real case of thunderstorm development over mountains to investigate the practical predictability limits and found increased predictability in the presence of topography. On the other hand, the intrinsic predictability of thunderstorm development over topography has not been investigated in detail. Wu and Takemi (2021) investigated the influence of topography on the initial error growth associated with moist convection by conducting identical twin experiments with or without topography with the use of the Weather Research and Forecasting (WRF) model (Skamarock et al. 2019) in an idealized configuration. A sounding at a single observation site, the Shionomisaki site in Japan, on a summer day under a weakly sheared environment (which suggests that the mesoscale organization factor is low) was used to create horizontally homogeneous base state. Wu and Takemi (2021) found that deep moist convection develops earlier and organizes to a larger size in the experiment with topography than without topography. The initial error growth was diagnosed in terms of the moist difference total energy (MDTE), which was an extended version of difference total energy

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(Zhang et al. 2003) incorporating moist process. MDTE is computed with the equation that appears in the moist total energy norm used by Ehrendorfer et al. (1999) and is defined as: [ ( ' )2 ] c p '2 ps 1 '2 L 2v '2 '2 MDTE = qv + RTr , (14.6) u +v + T + 2 Tr c p Tr Pr where u ' , v' , T ' , qv' , and ps' are the differences of the westerly wind component, the southerly wind component, temperature, water vapor mixing ratio, and surface pressure, respectively, between the identical twin experiments; Tr and Pr are the reference temperature (270 K) and the reference pressure (1000 hPa), respectively; c p , L v , and R are the specific heat capacity at constant pressure (1004.9 J kg−1 K−1 ), the latent heat of condensation (2.5104 × 106 J kg−1 ), and the specific gas constant of dry air (287.04 J kg−1 K−1 ), respectively. Figure 14.9 shows the MDTE values with respect to the size of convective cloud areas in the experiments with topography (denoted as TOPO) and without topography (denoted as FLAT). The MDTE here is assessed in terms of the vertical mass-weighted average and is computed either as the mean at the detected cloud grids having the ten largest MDTE values or as the mean at all the cloud grid points. The detected cloud area in the largest range is larger in TOPO than in FLAT, indicating that topography influences the organization of convective clouds toward a larger scale. The initial development of convective clouds at smaller scales (i.e., smaller than about 10 km) is also observed to start earlier with smaller MDTE in TOPO than in FLAT. This is due to a result in TOPO indicating preferred locations of convective cloud development over the mountain, irrespective of the twin experiments. In other words, the error growth is smaller in the presence of topography, suggesting potentially a higher predictability. Topography forces upward motion and, in humid conditions, the lifted air parcels will easily reach LCL and LFC. As described in Sect. 14.3, a short distance between LFC and the originating height of an air parcel (d(LFC) denoted in Fig. 14.5) is favorable for the development of deep convection. Under humid conditions, such a short distance can easily be achieved. Besides, mountain topography raises the baseline height of surface air parcels, which also contribute to shorten the distance of d(LFC). This process seems to play a key mechanism for generating deep moist convection preferentially over the mountain (Wu and Takemi 2023). The mechanism here further suggests that humidity and moisture variabilities are essential in determining the favorable location of deep convection and hence the predictability. As given in the concluding remark at the end of Sect. 14.3, the moisture variability again is essentially important in understanding the predictability of deep convection affected by topography. In real situations, the presence of complex and complicated topography is considered to locally affect momentum and heat transfers and to influence the boundarylayer circulations that would lead to the development of clouds. In dry environments which can be seen in midlatitude, continental regions, LCL and LFC are extremely

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Fig. 14.9 MDTE against convective cloud size for the mean at cloud grid points having the ten largest MDTE in the experiment a without topography (denoted as FLAT), b with topography (TOPO) and for the mean at all the cloud grid points in the experiment, c without topography, and d with topography. Each point represents a detected cloud area at a time represented by color marks. From Wu and Takemi (2021). ©2021 The Author(s). Published by the Meteorological Society of Japan under a Creative Commons Attribution 4.0 International (CC BY 4.0) license

high (e.g., Takemi and Satomura 2000; Nakamae and Takemi 2022), and boundarylayer air parcels are not easily lifted above LCL and LFC. In this situation, strong forcing from synoptic-scale disturbances and fronts will be more important than the topographic forcing. In contrast, humid conditions will provide a favorable condition for boundary-layer air parcels to be lifted above LCL and LFC with only a weak forcing from the complex and complicated topography even under synoptically undisturbed conditions.

14.5 Concluding Remarks Moist conditions such as those seen in the summer monsoon season in East Asia provide a unique feature for the development of mesoscale precipitating systems. Moisture fluctuations in the free troposphere affect the structure, intensity, and evolution of mesoscale precipitating systems. Very humid situations provide a favorable condition for the formation of MAUL, which will contribute to enhancing the development of mesoscale precipitating systems. Moisture variation is an important process whether MAUL will appear. Through the examination of predictability of deep convection over an mountain topography, the fluctuation and variability of moisture also play a key role in characterizing the generation of deep moist convection over topography and hence in determining the predictability of moist convection

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affected by topography. In order to deepen our understanding on the predictability of mesoscale precipitation, intrinsic predictability of thunderstorm development under diverse environmental conditions should be investigated in further studies. The environmental impacts on mesoscale precipitating systems, as revealed in this chapter, can be applied to investigate the effects of climate change impacts on precipitation. Under a projected future climate with global warming, the temperature lapse rate will be smaller (which means that the atmosphere is stabilized), whereas the moisture content will increase. These environmental changes will definitely affect the structure and intensity of mesoscale precipitating systems and the resultant rainfall hazards. A more in-depth analysis and predictability study of mesoscale precipitating systems in very humid environments should be further explored. Acknowledgements The comments from a reviewer are greatly appreciated in improving the original manuscript. I would like to thank Prof. Seon Ki Park who is the editor of this book for encouraging me to contribute a chapter. I would like to acknowledge the funding support from JSPS Kakenhi 20H00289 and 21H01591 and also by the MEXT-Program for the advanced studies of climate change projection (SENTAN) Grant Number JPMXD0722678534.

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Chapter 15

Quantitative Precipitation Forecasts Using Numerical Models: The Example of Taiwan Chung-Chieh Wang, Shin-Hau Chen, Pi-Yu Chuang, and Chih-Sheng Chang

Abstract The quantitative precipitation forecast (QPF) is a challenging area in modern numerical weather prediction but is crucially important and demanded by the society, especially those of heavy-rainfall events due to their high potential to cause hazards like flooding, landslide, and debris flow. During the past decade, heavyrainfall QPFs have been shown to improve considerably by using a cloud-resolving model at a grid size of 2.5 km in Taiwan, where its steep topography enhances the rainfall from two major sources: typhoons (July–October) and Mei-yu (May–June). Within the short range of day 1 (0–24 h) to day 3 (48–72 h), the threat score (TS) of 24-h QPFs for all typhoon events is about 0.7 at the lowest threshold of 0.05 mm (per 24 h), but stays ≥ 0.2 (indicating certain skill) up to almost 500, about 450, and over 250 mm on days 1–3, respectively. Moreover, for the top 7% rainiest events, the short-range QPFs have TSs close to 1.0 at 0.05 mm on days 1–3 and about 0.3 higher than those for all events up to 50 mm, changing to 0.2 higher at 100 mm, and 0.1 higher at 350 mm. Thus, as previously found, the skill level is higher for larger rainfall events, in contrast to the common beliefs of many. Although not as high as for typhoons, the skill of Mei-yu QPFs is also improved, and the TSs for the largest 4% of events with high potential for impacts on days 1–3 are around 0.95 at 0.05 mm and stay ≥ 0.2 up to 200 mm on days 1–2 and 150 mm on day 3, respectively. At lead times beyond the short range, the time-lagged approach using the cloud-resolving model has been demonstrated to be a feasible and effective method for ensemble with high-quality QPFs for typhoons. At the longer range with high forecast uncertainty, it produces various realistic scenarios associated with different storm tracks, among which the worst-case scenario is very useful for early preparation. This scenario tends to be produced earlier than five days before landfall. As the typhoon approaches and the uncertainty decreases, the predicted tracks converge toward the best track, and the most-likely scenario emerges for the authorities to make proper adjustment. The

C.-C. Wang (B) · S.-H. Chen · P.-Y. Chuang · C.-S. Chang Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan e-mail: [email protected] S.-H. Chen e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_15

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above results are likely applicable to many regions in East Asia due to similar characteristics in rainfall and topography to Taiwan. In the future, continuous improvement will take place toward more members with a cloud-resolving capability, and new methods from artificial intelligence and machine learning can also contribute and help make better QPFs and model forecasts in general. Keywords Quantitative precipitation forecast (QPF) · Heavy rainfall · Cloud-resolving model · Typhoon · Taiwan

15.1 Introduction Precipitation is among the most important parameters in meteorology. As all freshwater on Earth comes from precipitation, the survival of humans and essentially all other living things on the surface of the Earth depends on it. In ancient times, access to freshwater allowed civilizations to establish and thrive. Today in the modern society, precipitation still deeply affects people’s daily lives and well-being. Therefore, quantitative precipitation forecast (QPF) is under constant and heavy demand and has many applications (Olson et al. 1995; Golding 2000; Mullen and Buizza 2001), and nowadays it relies mainly on numerical weather prediction (NWP) models through a scientific approach. However, QPF remains a highly challenging area (e.g., Fritsch and Carbone 2004; Cuo et al. 2011) because precipitation is the end product of a series of complicated and nonlinear dynamical and physical processes, some of which occur at the molecular level. This is especially true for heavy and extreme rainfall events, which occurs mostly at meso- and microscales and can evolve rapidly with time (e.g., Walser and Schär 2004; Clark et al. 2007, 2009), and cause weather hazards such as flash floods, landslides, and inundation of urban areas and agriculture lands. Located at the periphery of the Western North Pacific (WNP), the East Asian countries (Fig. 15.1a) share many common features in their rainfall climatology. In the summer, tropical cyclones (TCs), or typhoons, bring concentrated rainfall in periods of typically 1–2 days. The monsoon system is also active in this region between the Eurasian Continent and the Pacific (e.g., Tao and Chen 1987; Chen 1994; Ding and Chan 2005). Associated with the seasonal onset of the southwesterly summer monsoon and its northward migration, repeated occurrences of slow-moving fronts also bring an annual rainy period called the Mei-yu (meaning “plum rain”) season in South China and Taiwan (Kuo and Chen 1990; Ding 1992; Chen 2004), Baiu in Japan (e.g., Akiyama 1973; Ninomiya and Akiyama 1992), and Changma in Korea (e.g., Kang et al. 1999; Lau and Ploshay 2009; Chang et al. 2018). This pre-summer rainy season is another period prone to heavy rainfall from organized mesoscale convective systems (MCSs) associated with the front and embedded in the summer monsoon flow (e.g., Jou et al. 2011). In the cold season, extratropical

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Fig. 15.1 a Geography and topography (m, color) of the East Asia and Western North Pacific, and the 2.5-km CReSS domains used for three-day (black solid) and eight-day forecasts (scarlet solid) for Taiwan, and for Typhoon Haiyan (2013) for the Philippines (blue dotted), b the detailed terrain of Taiwan (m, color) with the two major mountain ranges in Taiwan: the Central Mountain Range (CMR) and Snow Mountain Range (SMR), marked, and the locations of rain gauges (blue dots) in 2015

cyclones and winter storms can also produce blizzards and heavy precipitation in mid-latitude regions such as Central and North China, Korea, and Japan (e.g., Chen et al. 1991), but in this chapter we focus mainly on heavy rainfalls in the warm season. Along the collision zones among the Eurasia, Philippines, and Pacific Plates, the geology in many East Asian regions is also young and similar with steep and complex topography, such as the Philippines, Taiwan, Korea, and Japan (Fig. 15.1a). Such steep topography, when impinged by warm, moist, and unstable flow in the lower troposphere, acts to uplift the oncoming flow to reach saturation and trigger deep convection and, therefore, increases the rainfall amount at its windward slopes and reduces it at the leeside (Smolarkiewicz et al. 1988; Rotunno and Ferretti 2003; Lin 1993; Lin et al. 2001). This enhancement effect, as occurred during the extreme rainfall event of Typhoon (TY) Morakot (2009) in Taiwan for instance (Ge et al. 2010; Fang et al. 2011; Yu and Cheng 2013; Wang et al. 2013, 2022d), is the main reason why the highest rainfalls in the world are all recorded at locations with steep terrain (Table 15.1). Besides mechanical uplift, the topography also exhibits dynamical blocking effects on the prevailing flow when the flow is weaker or more stable (e.g., Pierrehumbert 1984; Manins and Sawford 1982; Smolarkiewicz et al. 1988; Banta 1990; Sever and Lin 2017) and dictates the low-level convergence and thus the occurrence and configuration of convection (e.g., Overland and Bond 1995; Yeh and Chen 2002; Wang et al. 2005). The topography also has diurnal thermal effects

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Table 15.1 World records of greatest rainfall amounts (mm) over different accumulation lengths from 12 to 96 h from the World Meteorological Organization World Archive of Weather and Climate Extremes (http://wmo.asu.edu/#global, accessed on 20 October 2022). The location, elevation, and date are also given Duration (h)

Amount

Location

Elevation (m)

Date

12

1144

Foc-Foc, La Réunion

2290

7–8 January 1966

24

1825

Foc-Foc, La Réunion

2290

7–8 January 1966

48

2493

Cherrapunji, India

1313

15–16 June 1995

72

3930

Cratère Commerson, La Réunion

2310

24–26 February 2007

96

4936

Cratère Commerson, La Réunion

2310

24–27 February 2007

that induce regional circulation (such as mountain-valley and land-sea breezes) and impact the development of local convection, especially in the summer with stronger solar radiation (Chen et al. 1999; Kerns et al. 2010; Ruppert et al. 2013; Wang et al. 2022c). Given the above background of rainfall climatology in East Asia with a certain degree of similarity, the subtropical island of Taiwan (Fig. 15.1b) is selected as an example to review and report the experiences and efforts to advance the QPFs there in recent years in this chapter. Due to their hazardous and high-impact nature, the QPFs for heavy-rainfall events in the two major rainfall seasons: typhoon (July to October) and Mei-yu (May and June), are emphasized, as opposed to ordinary rainfall events that usually only cause some inconvenience in people’s daily lives. Also, for cold-season QPFs in the mid-latitude regions of East Asia are not included in this chapter, as mentioned. The remaining part of this chapter is arranged as the following. In Sect. 15.2, the commonly used verification methods for QPFs by numerical models are introduced and reviewed. The QPFs by deterministic models at the short range (within 72 h) for both typhoons and Mei-yu are discussed in Sect. 15.3, including an update for Mei-yu results herein. Then, efforts to produce ensemble QPFs with probability information at longer lead times beyond the short range (up to eight days) are reviewed and discussed using TY Matmo (2014) as an example in Sect. 15.4. In Sect. 15.5, the directions for further improvements in the near future are discussed with some examples. Finally, the conclusion and summary are given in Sect. 15.6.

15.2 Verification of Model QPFs There are many different objective and quantitative methods to verify model QPFs, each suitable for certain situations to reveal model’s performance in some specific aspects. To choose the appropriate method to verify model QPFs effectively is a topic worthy of an entire chapter of its own (e.g., Jolliffe and Stephenson 2003;

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Wilks 2011). Nevertheless, it is always recommended that the subjective “eyeball” verification is used which was needed to ensure that the objective methods give results consistent with human judgment; i.e., they are being used properly. Here, some of the most commonly used methods, particularly those that will be shown later in this chapter, are reviewed and discussed to provide a sufficient background context on the verification of model QPFs. These methods include categorical statistics based on contingency tables (Sect. 15.2.1) and some other widely used measures (Sect. 15.2.2) such as the mean squared error (MSE). A recently introduced measure called the Similarity Skill Score (SSS), which uses the MSE to measure the overall similarity between the observed and predicted rainfall patterns against the worst possible MSE, also provides a good indication on the overall quality of model QPFs.

15.2.1 Categorical Statistics Traditionally, the categorical skill measures, or categorical statistics, are perhaps the most widely used matrix to verify model QPFs. This method is suitable for dichotomous (yes/no) events, where an “event” is defined as reaching a specified rainfall threshold at a verification point in QPFs and “no event” if that threshold is not met (e.g., Schaefer 1990; Mason 2003; Wilks 2011). In the 2 × 2 contingency table, the outcome of a model forecast at a set of N total verification points can therefore be classified into four mutually exclusive categories, as illustrated schematically in Fig. 15.2a: hits (H, event in both observation and prediction), misses (M, event in observation but no event in prediction), false alarms (FA, event in prediction but no event in observation), and correct negatives (CA, no event in both observation and prediction), where N = H + M + FA + CN. Subsequently, several scores such as the probability of detection (POD) of observed events, success ratio (SR) of model predictions of events, threat score (TS), and bias score (BS) can be computed as the following (Schaefer 1990; Mason 2003; Wilks 2011): H , H+M

(15.1)

H , H + FA

(15.2)

H , and H + M + FA

(15.3)

H + FA . H+M

(15.4)

POD = SR = TS =

BS =

From the equations, it is apparent that the values of POD, SR, and TS are all bounded by 0 and 1, and the higher the better. Also, with the same numerator but a smaller denominator, both POD and SR must be no lower than the TS, which is also

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Fig. 15.2 a Schematic of observed and forecast rainfall areas reaching a specified threshold over a given accumulation period and the four areas of hits (H, green), misses (M, blue), false alarms (FA, yellow), and correct negatives (CN, light gray). The total verification points N = H + M + FA + CN. b Schematic of rainfall intensity distribution with time from an event at a location in the observation (blue) and two model predictions (scarlet and green), and the selection of two different accumulation period lengths A and B

known as the critical success index (Schaefer 1990). The false alarm ratio (FAR, = 1 − SR), i.e., the incorrect fraction of all events predicted by the model (the lower the better), is another parameter often used (e.g., Barnes et al. 2009). The BS is the ratio of predicted events to observed ones and therefore reflects under-(BS < 1) or overprediction (BS > 1) by the model. Obviously, the most ideal value of the BS is unity, but it can vary from 0 to N − 1 in theory. For visualization, all four measures can be shown at the same time using the performance diagram (Roebber 2009), where the abscissa is the SR and ordinate is the POD. Typically, the categorical statistics is computed at a series of fixed rainfall thresholds from low to high for the target period of verification, either for individual forecasts or for multiple forecasts over a longer period, such as a season or several seasons. Toward higher thresholds, the rainfall areas inevitably become smaller (see Fig. 15.2a), so fewer and fewer points get involved in the calculation. Once the threshold exceeds the peak amount in either the observation or forecast (i.e., its area shrinks to zero in Fig. 15.2a), there can be no hits and TS = POD or SR = 0. Thus, these three scores tend to decrease toward higher thresholds, where they can also become unstable due to fewer points involved. This is especially true for the BS, which has a much larger range than the other scores. Therefore, for multiple forecasts over longer periods, the statistics of all forecasts need to be combined into one contingency table before the scores are computed, so as to increase the sample size, and thus the stability and representativeness of the results. For high-resolution QPFs, one known issue of the categorical measures is “double penalty,” which refers to a disadvantage for models that are capable of predicting certain rainfall events but not at the correct location and/or time, when compared to those that cannot predict the events at all (e.g., Ebert and McBride 2000; Clark et al. 2007). For example, for migratory rainfall systems such as the MCSs, squall

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lines, and TCs, model simulations and predictions often exhibit location and timing errors, usually more serious at longer ranges. While location errors are used more often to illustrate the problem of double penalty (e.g., Davis et al. 2006), Fig. 15.2b gives a schematic example of timing errors. Suppose the histogram of a rainfall event in observation is the blue curve, and two model predictions for that event (scarlet and green) occur too early with a somewhat shorter duration. Because the event magnitude (or amplitude) is correct in Model 1 (scarlet), subjective verification by humans would always judge it to be the better prediction. However, if length B is chosen as the accumulation period, then both models missed the actual event in the second period, while Model 1 has a higher FAR (lower SR) than Model 2 in the first period, it is penalized twice (both miss and false alarm) for predicting a stronger event (although accurate in magnitude) in the wrong accumulation period. So, the matrix would tell us that Model 2 performed better, which is an incorrect assessment. In Fig. 15.2b, we can also see that by choosing a longer accumulation period (length A), this timing error can be largely tolerated and the issue is partially remedied. In space, a longer accumulation period would also allow us to verify whether the rainfall system in the model “sweeps across” areas similar to the observation during a given time frame, instead of whether it appears at the precise location at the right time (which is of low likelihood). So, besides what length of accumulation we are interested in verifying in the QPFs, usually dictated by the impact duration of the rainfall systems involved, the question also comes down to what kind of timing error is typical and reasonable at different ranges and thus should be tolerated in the verification. At the present time, it is recommended that accumulation periods of at least 1 h are used within the range of 6 h, at least 3 h are used within 12 h, at least 6 h within 1 day, ≥ 12 h within 2–3 days, and ≥ 24 h beyond the short range (≥ 72 h). As shown above and in Fig. 15.2a, hits are required for categorical scores (e.g., POD, SR, and TS) to rise above zero, but they can be difficult to come by at high resolution due to the nonlinearity of the dynamic atmosphere, leading to the issue of double penalty. Under such circumstances, some fuzzy or neighborhood methods that do not require direct hits or exact matches can be used (e.g., Ebert 2008), such as the fractional skill score (FSS, Roberts and Lean 2008) or those reviewed below in Sect. 15.2.2. Object-oriented or entity-based verification is another class of methods suitable for evaluating model’s performance in predicting migratory mesoscale rainfall systems (e.g., Ebert and McBride 2000; Brown et al. 2004; Davis et al. 2006; Marzban and Sandgathe 2008; Wernli et al. 2008; Wang et al. 2020a, b). Because these methods were developed more recently, there tends to be fewer studies available for comparison, and variations in the definition of “rainfall objects” and the characteristics of model outputs may introduce some difficulty in judging for improvements. Also, they typically need gridded rainfall dataset at high enough quality, which may not be available for some regions, perhaps more so for those surrounded by oceans (e.g., Wang et al. 2022g). On the other hand, hits represent the ability to predict enough amounts of rainfall at the correct location during a given time span, so they are desired if attainable at all. This is especially true in regions where the major hazards from heavy rainfall are flash floods, inundation, landslides, and debris flows, etc., and thus correct prediction

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in rainfall location plays a vital role in hazard warning, preparation, and mitigation. The East Asia including Taiwan fits this description in general, and the complex topography also acts to enhance rainfall mainly through mechanical uplifting as mentioned. Therefore, categorical statistics are still often used in Taiwan to verify model QPFs. This choice is also tied to the high predictability of heavy rainfall (from typhoons and MCSs during the Mei-yu season) in Taiwan, very much linked to its topographic effects, and this linkage will be demonstrated in later sections, mainly through examples.

15.2.2 Other Measures Many statistical parameters have also been used to gauge the overall degree of agreement (or disagreement) between the observed and forecast rainfall amounts, which vary continuously both in time and space. These parameters are well known and widely used in the scientific community (e.g., Barber 1988; Stanski et al. 1989; Wilks 2011), and they include the mean error (or mean bias), mean absolute error, mean squared error (MSE), root mean squared error, standard deviation, and correlation coefficient, to name a few. Because each of these parameters focuses on a certain aspect of errors, they have limitations and bad forecasts can, at times, show good values. For heavy rainfall that can be highly concentrated with large variations in space, good forecasts in subjective verification may have large statistical errors, especially at high resolution (similar to the double penalty issue in space). Also, compared to categorical measures, these parameters are often not as revealing regarding the nature of the errors and how to improve the models. Thus, they are used more extensively for field variables (such as geopotential height, temperature, and moisture amount), whose mean values at fixed levels are within a certain range, than for model QPFs. Nevertheless, when used in combination, these parameters can still be very useful to provide certain types of information on rainfall errors. Since the categorical measures (Sect. 15.2.1) are the main method for QPF verification, here we only describe those other parameters that will appear later in this chapter. Among the measures mentioned above, the MSE (of rainfall) is defined as: MSE =

N 1 ∑ (Fi − Oi )2 , N i=1

(15.5)

where F i and Oi are the rainfall amounts in the forecast and observation at the ith point, respectively, among a total of N points. By squaring the values, larger errors carry greater weights and are emphasized in MSE, which is often a desirable feature for users aiming for improvement. Using the MSE, a new skill score named the Similarity Skill Score (SSS) has been developed to measure the overall similarity between two patterns (Chen and Wang 2022; Wang et al. 2022g), and it is defined as:

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SSS = 1 −

1 N

∑N

− O i )2 ), ∑N 2 2 i=1 Fi + i=1 Oi

( 1 ∑N N

373

i=1 (Fi

(15.6)

where the variables have the same meaning as in Eq. (15.5), and thus the numerator in the second term on the right-hand side (RHS) is the MSE. The SSS is essentially the skill measured against the worst possible MSE, where the forecast rainfall never overlaps with the observed pattern (and therefore the MSE is the denominator in the second RHS term). In this worst case, SSS = 0, and SSS = 1 if the two rainfall patterns have a perfect match, i.e., F i = Oi at each among all of the points. In fact, the SSS is formulated the same way as the FSS (Roberts and Lean 2008), but the latter employs the fractions of grid points reaching a given threshold in the model and observation in the second RHS term. For the evaluation of the rainfall probability derived from an ensemble of forecasts, the Brier score and Brier skill score (BSS) are used (e.g., Brier 1950; Murphy 1973; Bradley et al. 2008), where the latter is BSS = 1 −

∑N

(PFi − POi )2 (∑ i=1 ), ∑N N 1 2 2 PF + PO i i i=1 i=1 N 1 N

(15.7)

where PFi and POi are the probability in the forecast (0–1) and observation (either 0 or 1) at the ith point, respectively, among the N points. As one can see, Eq. (15.7) is formulated in the same way as Eq. (15.6) (and the FSS), and the numerator in the second RHS term is the Brier score (Brier 1950), i.e., the MSE of the forecast probability against the observation. Thus, BSS also ranges from 0 to 1, and the higher the better. For both the categorical scores and other measures (the SSS and BSS), raingauge data from both manned stations and automated sites (Hsu 1998) operated and maintained by the Central Weather Bureau (CWB) of Taiwan are used to verify model QPFs in this chapter. During our verification periods, there were around 500 sites over Taiwan (Fig. 15.1b), with higher density over the plain areas and lower density in the mountain interiors. In all instances, model QPFs are first interpolated (using bilinear method) onto the rain-gauge locations, where the various scores are computed.

15.3 Deterministic QPFs at the Short Range 15.3.1 Numerical Model and Experiments Most of the results shown and discussed in this chapter were obtained using the Cloud-Resolving Storm Simulator (CReSS, Tsuboki, and Sakakibara 2002, 2007). Details of this model can be found in another chapter of this book and some earlier

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studies (Wang 2015; Wang et al. 2016a, 2021a, 2022a, b, f), so it is only briefly described here. The CReSS model is a cloud-resolving model (CRM) using a terrainfollowing vertical coordinate with a single domain without nesting. All clouds are simulated explicitly using a bulk cold-rain scheme with a total of six water species (see Table 15.2): vapor, cloud water, cloud ice, rain, snow, and graupel (Lin et al. 1983; Cotton et al. 1986; Murakami 1990; Ikawa and Saito 1991; Murakami et al. 1994). Parameterizations for subgrid scale processes include turbulent mixing in the planetary boundary layer (Deardorff 1980; Tsuboki and Sakakibara 2007) and radiation and momentum and energy fluxes at the surface (Kondo 1976; Louis et al. 1982; Segami et al. 1989), with the use of a substrate model (Table 15.2). The CReSS model has been used by the lead author’s group to perform real-time forecasts for Taiwan since 2006, initially for the Mei-yu season using a relatively small domain. Since 2010, routine experiments four times a day out to at least 72h year-round, at a horizontal grid size (Δx) of 2.5 km (432 × 360 points) with 40 vertical levels have been achieved (Table 15.2). The domain was enlarged to 600 × 480 in 2012 (also Fig. 15.1a) and further to 800 × 600 in 2018, when the range was also extended to 120 h. For all these runs, real-time analyses and forecasts by the National Centers for Environmental Prediction (NCEP) Global Forecasting System (GFS, Kanamitsu 1989, Kalnay et al. 1990, Moorthi et al. 2001, Kleist et al. 2009), first at a resolution of 1.0° and later at 0.5° (also every 6 h) and freely available, have been used as the initial and boundary conditions (IC/BCs, Table 15.2). Table 15.2 Basic configuration of the 2.5-km CReSS used in the three-day (deterministic, since 2010) and eight-day forecasts (time-lagged ensemble, since May 2012), including initial and boundary conditions (IC/BCs) and major physical options Forecast type

Three-day forecasts

Eight-day forecasts

Projection

Lambert Conformal (center at 120°E, secant at 10°N and 40°N)

Grid spacing (Δx)

2.5 km

Domain size (x × y) August 2010–April 2012

1080 km × 900 km

–

May 2012–June 2018

1500 km × 1200 km

1860 km × 1360 km

Since July 2018

2000 km × 1500 km

Vertical levels and Δz

40 levels, 0.2–0.663 m (0.5 m)a

Frequency

Every 6 h

IC/BCs

NCEP GFS analyses/forecasts (1° × 1° or 0.5° × 0.5°, 26 levels)

Cloud microphysics

Bulk cold-rain scheme (six species)

PBL parameterization

1.5-order closure with turbulent kinetic energy prediction

Surface processes

Energy/momentum fluxes and shortwave/longwave radiation

Soil model

41 levels, every 5 cm to 2 m deep

a

Every 1 day or 6 h (for cases)

The vertical grid spacing (Δz) of CReSS is stretched (smallest at the bottom), and the averaged spacing is given in the parentheses

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At the lower boundary of CReSS, terrain elevation data and the NCEP-analyzed sea surface temperature (SST) are also provided. For further details regarding the model configuration and experiments, the readers are referred to the original studies referenced in later sections.

15.3.2 QPFs for Typhoons Located along the major path of TCs in the Western North Pacific, Taiwan is hit by 3–4 typhoons on average each year (Wang 1989; Wu and Kuo 1999). Due to the topographic enhancement of TC rainfall on the windward slope (cf. Fig. 15.1b), it has long been recognized that the rainfall pattern on the island at any instant is largely controlled by the relative location of the storm, when the TC is close enough (e.g., Chang et al. 1993; Cheung et al. 2008; Su et al. 2012). For example, Fig. 15.3 shows the rainfall climatology in Taiwan taken from Cheung et al. (2008, their Fig. 4), obtained from 62 typhoons during 1989–2002, when the TC center is inside each of the 2° × 2° box among a total of 4 × 4 such boxes [as shown from (a) to (p)] covering the region of 19°–27°N, 118°–126°E surrounding Taiwan (blue box). One can see that, when the TC center is south of 23°N (near southern Taiwan or over the Bashi Channel, Fig. 15.3i–k and m–o), the rainfall is mostly along the eastern slope of the Central Mountain Range (CMR, see Fig. 15.1b), as the cyclonic TC circulation would produce mainly an easterly flow to impinge on the island. If the TC center is off the coast of eastern Taiwan, northern Taiwan would receive much rainfall (Fig. 15.3c, g, k). Similarly, when the typhoon center is around northern Taiwan, rainfall would be produced over the western slopes of the mountains (Fig. 15.3a, b, e). Thus, a large component of TC rainfall is phase-locked to the topography of Taiwan and fixed in location, and the total rainfall brought to the island by a typhoon is often dictated by its track near Taiwan, including the moving speed. This phenomenon of significant orographic rainfall also allows for a potential to produce more accurate QPFs in Taiwan if a realistic TC track can be predicted beforehand. Based on the above concept, Lee et al. (2006) developed a climatological model to predict TC rainfall in Taiwan, by assembling the composite rainfall of short segments (every hour) from past events with similar center locations along the projected track of the TC being predicted. Lee et al. (2013) further augmented the database of historical typhoons to 1989–2011 and separated the model into those for TCs with two different basic track directions near Taiwan: westward and northward. Hong et al. (2015) applied the same idea and developed the Ensemble Typhoon QPF (ETQPF) system at the CWB, by using the lagged predictions every 6 h from two 5-km ensemble systems, such that specific characteristics of individual storms and the stochastic nature of the NWP (e.g., Lorenz 1963; Epstein 1969) can both be taken into account. The ETQPF system included a 20-member ensemble using the Weather Research and Forecasting (WRF) model (Skamarock et al. 2008) at the CWB and another 18 members using the WRF and the Fifth-generation Pennsylvania State University−National Center for Atmospheric Research Mesoscale Model (MM5; e.g., Dudhia et al. 2005) provided

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Fig. 15.3 TC rainfall climatology in Taiwan. Each small panel from a–p depicts the distribution of averaged rain rate (mm h−1 , contoured every 2 mm h−1 ) when TC centers are located in that 2° × 2° latitude–longitude box relative to Taiwan (dotted blue) inside the larger rectangular area of 19°– 27°N, 118°–126°E (blue). The climatology is derived from 62 TCs during 1989–2002. Reproduced from Cheung et al. (2008). © Authors 2008. Distributed under the CC BY 3.0 License

by the Taiwan Typhoon and Flood Research Institute (TTFRI) at the time (Hsiao et al. 2013). In Fig. 15.4, an example of the ETQPF system from Hong et al. (2015) as applied to TY Fanapi (2010) is shown. For this event, all TC center locations in outputs at 3-h intervals from the 38 members initialized every 6 h from 1200 UTC 15 to 0000 UTC 20 September 2010 (excluding the first 9 h in each 72-h run during

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spin-up) are plotted in Fig. 15.4a as small dots, each associated with a 3-h rainfall pattern in Taiwan. Then, a track is entered with the projected TC center locations every 3 h (thick red curve), and the system screens out the qualified patterns (those with a center within 30 km from the projected locations) to construct the average rainfall patterns at 3-h intervals and eventually obtain the total rainfall in Taiwan over a given period of interest. For the 24-h period from 1800 UTC 18 to 1800 UTC 19 September during TY Fanapi (2010), the observed rainfall is shown in Fig. 15.4b, and the ETQPF is seen to be capable of producing a pattern of 24-h QPF (Fig. 15.4a) quite similar to the observation (Hong et al. 2015). However, one should be aware that two factors would limit the performance of this system in real time. First, as reviewed above and also noted by the authors themselves, one major uncertainty in TC QPFs in Taiwan lies in the track errors in forecasts, yet the CWB best track (no track errors) was used in Fig. 15.4 instead of a predicted track at some earlier time. This is not possible in real time, as the best track is not known. Second and similarly, for an operational system, any model results after the fact cannot be used, for example those generated after 1800 UTC 18 September if the 24-h QPF starting from 1800 UTC 18 September (as in Fig. 15.4c) is to be produced and used as a forecast soon thereafter.

Fig. 15.4 Example of the ETQPF of Hong et al. (2015) as applied to TY Fanapi (2010). The lagged ensemble has 38 5-km members executed every 6 h, with a range of 3 days. a TC centers every 3 h from all the runs (dots), each associated with a 3-h rainfall prediction as exemplified by the small panel, the track (CWB best track) used for prediction (thick red line), and the runs included for the QPF using a radius of 30 km (black circle) at each location along that track. b The observed and c constructed 24-h rainfall from the ETQPF in Taiwan (mm, scale to the right) from 1800 UTC 18 to 1800 UTC 19 September during Fanapi. All panels from Hong et al. (2015). © American Meteorological Society. Used with permission

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The 2.5-km CReSS model has also been used to perform real-time forecasts four times a day and out to three days at the National Taiwan Normal University (NTNU) since 2010 (cf. Fig. 15.1a) as mentioned, and the idea was to use cloudresolving resolution and configuration typical for research (e.g., Wang et al. 2005, 2011, 2012, 2013) in forecasts to better simulate the convection and topographic effects of Taiwan. This Δx of 2.5 km is close to the recommendation by Gentry and Lackmann (2010) for operational use and would remain to be the finest model grid in routine operation in Taiwan for about a decade. The performance of this 2.5-km CRM in 24-h typhoon QPFs within three days in Taiwan was thoroughly evaluated using categorical measures by Wang (2015) and Wang et al. (2016a, b) for 15 TCs during 2010–2012 that the CWB had issued warnings. The results have been recently updated to include three more seasons of 2013–2015 in Wang et al. (2021a) and thus for a total of 29 typhoons and 193 24-h target periods (including both 0000–0000 and 1200–1200 UTC). The results of Wang et al. (2021a) are replotted in performance diagrams and shown in Fig. 15.5a–c, for day 1 (0–24 h), day 2 (24–48 h), and day 3 (48–72 h) QPFs, respectively. In Fig. 15.5, the overall scores for all the target segments during the 29 TCs are plotted in gray, at nine different thresholds from 0.05 to 1000 mm (per 24 h). Compared to Wang et al. (2021a), results at several thresholds are omitted here for better clarity. For the subsets of increasing larger events in terms of peak rainfall in the observation, i.e., those exceeding 200, 350, 500, and 750 mm, the scores are plotted in blue, red, black, and orange, respectively. While each higher class contains roughly half the number of segments (given in parentheses) from the class below, the scores are each computed from a single contingency table with entries from all of its segments. In Fig. 15.5d, the total number of points involved in the calculation in each group across the original thresholds is shown. As one can see in Fig. 15.5a–c, while the TS values in each group decrease with increasing thresholds (from upper right to lower left), all the points are close to the diagonal line (BS values close to 1), indicating little overall bias, except for the more extreme groups of ≥ 500 mm on day 3. At such a longer range, the model QPFs tend to under-predict rainfall in TCs that turn out to be very rainy (i.e., mostly those with a direct hit). For 0–24-h QPFs on day 1 (Fig. 15.5a), the TSs for all segments are 0.73 at 0.05 mm, 0.36 at 200 mm, and 0.18 at 500 mm, respectively. For the same target periods, the day 2 (24–48 h) QPFs exhibit TSs that are only slightly lower (0.72, 0.33, and 0.16 at 0.05, 200, and 500 mm, Fig. 15.5b), despite the forecasts were initialized one day earlier (compared to day 1 QPFs). At the even longer range on day 3 (48–72 h), the corresponding TSs are 0.71, 0.22, and 0.08 and are not as skillful toward high thresholds (Fig. 15.5c). As the larger and rainier events are more hazardous and impactful, the QPFs for them are of key interests. In Fig. 15.5a–c, one can also see that the TS values for the larger-event groups at a given threshold are all exclusively higher without exception. For example, compared to the values for all events, the TSs of day 1 QPFs for the largest group with peak amounts ≥ 750 mm (orange), which represents roughly the top 7% of events, rise from 0.73 to 1.0 at 0.05 mm, from 0.51 to 0.78 at 50 mm, from 0.36 to 0.50 at 200 mm, and from 0.18 to 0.22 at 500 mm, respectively (Fig. 15.5a). Similarly, the TS of day 2 QPFs at 200 mm rises from 0.33 (for all events) to 0.49 (for

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Fig. 15.5 Performance diagrams of 24-h QPFs by the 2.5-km CReSS at nine rainfall thresholds (0.05 to 1000 mm, per 24 h, see legend) at the range of a day 1 (0–24 h), b day 2 (24–48 h), c day 3 (48–72 h) for all segments (gray) from 29 typhoons during 2010–2015 in Taiwan, as well as for subsets with an observed peak rainfall amount exceeding 200 (blue), 350 (red), 500 (black), and 750 mm (orange), respectively (see insert, number of 24-h segments given in parentheses). TS values at 50, 200, and 500 mm are labeled (rounded to two decimal places), and results of deterministic forecasts for 8 August (0000–2400 UTC) during TY Morakot (2009) are also plotted (purple). d Total numbers of verification points involved to compute the TS (i.e., H + M + FA) in day 1 QPFs for the various groups and Morakot across the thresholds (in logarithmic scale)

the group ≥ 750 mm, Fig. 15.5b), and the corresponding score on day 3 rises from 0.22 to 0.31 (Fig. 15.5c), respectively. Taken from Wang et al. (2013), the scores of two deterministic 4-km CReSS runs (out to 48 h) for TY Morakot (2009), the largest event in Taiwan since 1959, are also plotted in Fig. 15.5a, b for comparison. Targeted at the 24-h period on 8 August (in UTC, the daily peak rainfall was 1663 mm, Wang et al. 2022d; cf. Table 15.1), the TSs for Morakot were even higher than those for the group of ≥ 750 mm and reached 0.28 at 500 mm on day 1 with some underforecasting (Fig. 15.5a) and 0.5 at 500 mm and 0.4 at 1000 mm on day 2 (Fig. 15.5b). As found by Wang (2015), this dependency of categorical scores on rainfall event size

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in Taiwan, where TSs for larger events clearly rise higher (at the same thresholds), indicates an improved skill of QPFs for larger and more hazardous events. This finding defies the common belief that the QPF skill for extreme events is poor and limited. In contrast, it is a fundamental property of categorical measures that should exist more or less throughout the East Asia, in regions with similar characteristics to Taiwan with apparent topographic control in rainfall. The examples of seven typhoons in Taiwan are shown in Fig. 15.6, including TYs Fanapi (2010), Megi (2010), Saola (2012), Soulik (2013), Matmo (2014), FungWong (2014), and Soudelor (2015). These TCs were the rainiest case in their season (the second rainiest for Megi and Matmo) and also shown in Wang (2015), Wang et al. (2021a), or Wang et al. (2022f) but replotted. Using subjective verification, one can see that the 2.5-km CReSS was capable of predicting the track and rainfall in Taiwan in close agreement with the observation for most of them, not only on days 1 and 2 (within 48 h) but also on day 3. Only for Matmo, the track was too east and far from Taiwan (just outside the plotting domain) and thus the predicted rainfall was not enough on both days 2 and 3 (Fig. 15.6e), and the track for Megi on day 2 was also too close (Fig. 15.6b). For TY Saola (2012), the track prediction on day 3 was also too far away, and thus the rainfall was under-predicted (Fig. 15.6c). On the other hand, for Megi (2010), the predicted track on day 2 was too close and even made landfall (Fig. 15.6b), but the rainfall pattern still resembled the observation and that on day 3, which had a better track. This is because the rainfall in northeastern Taiwan and along the eastern slopes associated with Megi was long distance and far from the TC, so the accuracy of the track prediction was not as critical. Later, Matmo will be used as our example in Sect. 15.4 to demonstrate the time-lagged strategy for ensemble, so its results in deterministic forecasts are also shown here. The TS and BS values of CReSS QPFs for the seven typhoons at the three different ranges from day 1 to day 3 (all targeted for the same 24-h period shown in the first column of Fig. 15.6) are presented in Fig. 15.7. Except for Matmo (556 mm), the observed peak rainfall amounts of all the target periods exceeded 750 mm and thus belong to the rainiest class (i.e., orange curves) in Fig. 15.5. For these rainy TC periods, the TSs tend to be quite high (linked to the dependency property) and can often reach ≥ 0.5 at 200 mm and around 0.2 at 500 and even 750 mm (Fig. 15.7, left column), in agreement with Fig. 15.5 (orange curves). The TSs decreased at longer range in some cases, most evidently on day 3 for Saola and days 2–3 for Matmo (Fig. 15.7c, e) associated with the under-prediction mentioned earlier. In some other cases, the TSs at the three ranges can be very similar, such as those for Soulik and Soudelor (Fig. 15.7d, f), and the skill at a longer lead time is not necessarily lower than that at a shorter one if the track can be well predicted (e.g., day 3 versus day 2 QPF for Fanapi and day 2 versus day 1 QPF for Saola). Typically, the BSs of the QPFs for these periods were quite close to unity as long as the threshold is not too high, and the observed rain areas were not too small in size, say, less than 10% in the observed-based rate, i.e., the fraction of points reaching a given threshold in N), also in agreement with Fig. 15.5.

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Fig. 15.6 a1 Observed and predicted 24-h rainfall distributions (mm) over Taiwan by the 2.5-km CReSS at the ranges of a2 day 1 (0–24 h), a3 day 2 (24–48 h), and a4 day 3 (48–72 h), respectively, for the period of 19 September (in UTC, same below) during TY Fanapi (2010). b–g As in a except for the target period of b1–b4 21 October during TY Megi (2010), c1–c4 1200 UTC 1–1200 UTC 2 August during TY Saola (2012), d1–d4 1200 UTC 12–1200 UTC 13 July during TY Soulik (2013), e1–e4 22 July during TY Matmo (2014), f1–f4 1200 UTC 20–1200 UTC 21 September during TY Fung-Wong (2014), and g1–g4 1200 UTC 7–1200 UTC 8 August during TY Soudelor (2015), respectively. The tracks are plotted with TC center locations every 3 h (dots, open circles at 0000 and 1200 UTC), and peak rainfall amounts (mm) are also marked (triangles). Panels in a and b are reproduced from Wang (2015). © American Meteorological Society. Used with permission; Panels in d are adapted from Wang et al. (2021a) and those in c and e–g are replotted from Wang et al. (2022f). Both © Authors 2022. Distributed under the CC BY 4.0 License

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Fig. 15.6 (continued)

Overall, the long-term verification and examples reviewed and presented in this section show that the CRMs, when configured using high enough resolution (Δx ≈ 2.5 km), are capable of predicting TC rainfall in Taiwan with certain skill, even at very high thresholds of 500–750 mm (per 24 h). This is especially true for rainy typhoons, where higher TS values are found at the same thresholds compared to those for smaller, less rainy, and ordinary TC events.

15.3.3 QPFs for Mei-yu Events The QPFs during the Mei-yu season (May–June) by the 2.5-km CReSS within the short range have also been evaluated by Wang et al. (2022b), initially for the three seasons during 2012–2014. Similar to the typhoon QPFs shown above, 24-h QPFs from only the runs initialized at 0000 and 1200 UTC are verified, although the

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Fig. 15.7 a1 TS and a2 BS of 24-h QPFs by the 2.5-km CReSS at the ranges of day 1 (0–24 h, black), day 2 (24–48 h, red), and day 3 (blue), all targeted for the period of 19 September (in UTC, same below) during TY Fanapi (2010). b–g As in a except for the target period of b1, b2 21 October during TY Megi (2010), c1, c2 1200 UTC 1–1200 UTC 2 August during TY Saola (2012), d1, d2 1200 UTC 12–1200 UTC 13 July during TY Soulik (2013), e1, e2 22 July during Matmo (2014), f1, f2 1200 UTC 20–1200 UTC 21 September during TY Fung-Wong (2014), and g1, g2 1200 UTC 7–1200 UTC 8 August during Soudelor (2015), respectively. For each target period, the observed maximum rainfall (mm, rounded to integer) and base rate at 10% (vertical dashed line in right panel; see text for definition) are marked. Panels in a, b are replotted from Wang (2015). © American Meteorological Society. Used with permission; Panels in d are replotted from Wang et al. (2021a) and those in c and e–g are adapted from Wang et al. (2022f). Both © Authors 2022. Distributed under the CC BY 4.0 License

forecasts were made four times a day. This choice is to fit the target periods of 0000– 0000 or 1200–1200 UTC to allow for evaluation at fixed ranges of days 1–3. In Wang et al. (2022b), the day 1 (0–24 h) QPFs for all segments (without classification) have TSs of 0.60, 0.18, and 0.15 at 0.05, 100, and 250 mm (per 24 h), respectively, and thus show considerable improvements over 5-km models (TS ≤ 0.1 at 100 mm and

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TS ≤ 0.02 at 250 mm). At longer ranges, the TSs at the same thresholds are 0.63, 0.13, and 0.10 on day 2 (24–48 h) and 0.60, 0.10, and 0.03 on day 3 (48–72 h), respectively. As expected, the skill scores for Mei-yu rainfall are lower than those for typhoons in Taiwan, since typhoon rainfall is often of stronger forcing (from stronger flow). Nonetheless, in Wang et al. (2022b), the strength of the CRM was found to lie mainly in the topographic rainfall in Taiwan rather than migratory events that are more difficult to predict with precision. In addition, as in the typhoon QPFs, the results in the Mei-yu regime also show higher TS values in larger rainfall events when the 24-h segments are stratified by observed rainfall amounts. Below, the categorical skill scores of Mei-yu QPFs at the short range by the 2.5km CReSS as in Wang et al. (2022b) are presented, but extended through 2017 to include a total of six Mei-yu seasons. As shown in Fig. 15.8, the averaged Mei-yu rainfall in the six seasons of 2012–2017 exhibited two maxima over the mountain regions: one along the windward side of southern CMR (~1300 mm) and the other near the intersection of CMR and SMR (> 1000 mm), consistent with earlier studies (e.g., Yeh and Chen 1998; Chien and Jou 2004; Chi 2006; Wang et al. 2017). Again, the rainfall pattern shows a strong tie to the topography. During May–June of 2012– 2017, there were a total of 698 24-h segments (0000–0000 and 1200–1200 UTC) after those influenced by TCs were screened out. These 698 segments are classified into five groups from large to small, if at least 10% of rain gauges reached 50 mm (group A), 25–50 (group B), 10–25 (group C), 1–10 mm (group D), or less (group X). Note that these five groups are exclusive to each other; i.e., any one segment could only be classified into one group (the highest one to meet). These five groups, following their order, have 108, 113, 134, 210, and 133 segments and thus account for 15.5, 16.2, 19.2, 30.1, and 19.1% of the total sample. From group A, a subset that has ≥ 10% of rain gauges reaching 130 mm is also identified and named the A+ group, which contains 27 segments and represents the rainiest 3.9% in our sample during the six Mei-yu seasons. Here, a total of 13 rainfall thresholds are used, from 0.05 to 500 mm (per 24 h), computed in the same way as for typhoon QPFs (one 2 × 2 table for each score data point). The performance diagrams in Fig. 15.9a–c show the overall scores of the 24-h QPFs for all segments and groups A and A+ by the 2.5-km CReSS, at the three ranges of day 1 to day 3, respectively. Here, the relationships between these three groups are similar to those in Fig. 15.6a, as group A represents the rainier 16% in all the samples, whereas group A+ is roughly the rainiest top 1/4 in group A. For all the samples without classification (black), the overall TSs at 50 and 200 mm (per 24 h) are 0.29 and 0.13 on day 1 (0–24 h, Fig. 15.9a), 0.23 and 0.12 on day 2 (24–48 h, Fig. 15.9 b), and 0.21 and 0.08 on day 3 (48–72 h, Fig. 15.9c), all slightly lower at low thresholds but slightly higher at higher thresholds compared to those in Wang et al. (2022c, d). For increasingly larger events, again the QPFs perform better in TSs, and for instance, their values at 200 mm rise to 0.15 and further to 0.20 for groups A (amber) and A+ (scarlet) on day 1, to 0.16 and 0.20 on day 2, and to 0.10 and 0.13 on day 3, respectively (Fig. 15.9a–c). At low thresholds, the TSs for the larger events (groups A and A+ ) are also significantly higher at all three ranges and reach 0.88–0.95 at 0.05 mm, compared to 0.55–0.6 for all events. For

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Fig. 15.8 Spatial distribution of averaged total rainfall (mm) per Mei-yu season (May–June) during 2012–2017. Elevation height contours at 250 m (light gray) and 1 km are also plotted

group A, the curves are generally the closest to the diagonal line with 0.7 ≤ BS ≤ 1.5, especially on days 2 and 3. For all segments, however, some over-prediction exists between 25 and 200 mm (per 24 h), as BSs rise to about 1.25–1.6. For the largest 4% of events in group A+ , on the other hand, some under-prediction appears toward the higher thresholds, especially ≥ 200 mm on day 1 (Fig. 15.9a) and over 50 mm on day 3 (Fig. 15.9c). This phenomenon on day 1 is likely linked to model spin-up and is similar to the under-prediction of rainy TC events on day 3 at a longer range (cf. Fig. 15.5c). For the smaller event of groups B, C, and D, their results of day 1 QPFs are plotted in Fig. 15.9d for comparison. As seen, their TSs at the lowest threshold of 0.05 mm (per 24 h) decrease from 0.9 for group A (Fig. 15.9a), to 0.68, 0.50, and 0.28 for groups B, C, and D (Fig. 15.9d), respectively. So, the TSs at fixed thresholds drop lower in smaller events, mainly because of a reduction in rain-area sizes reaching those thresholds (Wang 2015). However, since these are small events and non-hazardous, the lowered TSs do not matter much. On days 2 and 3, the differences between larger and smaller event groups are similar, so the results of groups B-D are not shown here. Overall, although the skill of Mei-yu QPFs is not as high as that for typhoon rainfall, considerable improvements are made using the CRM at Δx = 2.5 km. If we select TS ≥ 0.2 to indicate a certain level of skill, then this is achieved up to 100 mm for all events and up to 200 mm for the largest events in group A+ on day 1 (Fig. 15.9a), up to 75 and 200 mm on day 2 (Fig. 15.9b), and up to 50 and around 150 mm on day 3 (Fig. 15.9c), respectively. The verification results are especially good on day 2, where the overall skill is only slightly lower than that on day 1. Thus, certain skill exists even at heavy-rainfall thresholds in the Mei-yu season.

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Fig. 15.9 Performance diagrams of 24-h QPFs by the 2.5-km CReSS at 13 rainfall thresholds from 0.05 to 500 mm (per 24 h, legend at bottom) at the range of a day 1 (0–24 h), b day 2 (24–48 h), and c day 3 (48–72 h) during six Mei-yu seasons (May-Jun) in 2012–2017 in Taiwan, for groups All (black), A (amber), and A+ (scarlet), respectively. TS values are labeled (rounded to two decimal places) at fixed thresholds of 0.05, 50, 160, and 500 mm (open symbols) or selected endpoints. d As in a but for groups All, B (blue), C (green), and D (purple, see text for details regarding the classification)

15.4 Ensemble QPFs at Both the Short Range and Beyond 15.4.1 Ensemble QPFs Using Time-Lagged Strategy Even though the skills for heavy-rainfall QPFs in Taiwan are much improved within the short range using CRMs at high resolution, as shown above in Sect. 15.3, these deterministic forecasts are in general regarded as having no probability information

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like an ensemble system and thus does not reflect the stochastic property of atmospheric motion and forecast uncertainty (e.g., Lorenz 1963; Epstein 1969). This is one major shortcoming that needs to be dealt with if possible. However, as high resolution is shown to be required for improved QPFs, the computational demand of an ensemble with a large number of members must be very high. In other words, under a fixed amount of computational resource, there exists a trade-off between model resolution and ensemble size (e.g., Zhang et al. 2019), and it is unlikely that both desired properties can be met, at least not at the present time in Taiwan. To explore feasible strategies, a time-lagged ensemble experiment using the 2.5km CReSS has been carried out once a day at 0000 UTC since 2012, using a larger domain (Fig. 15.1a, Table 15.2) and an extended forecast range out to eight days (Wang et al. 2016a, b). Given the QPF results within the short range, an additional reason for this new experiment is to find out whether decent QPFs can be produced at longer lead times beyond the short range, and how frequently such QPFs can be obtained. This time-lagged ensemble is mainly targeted at typhoons because their typical life span (at least about a week) is much longer than the MCSs in the Mei-yu season, and thus the TCs are more predictable at a longer lead time. Although the time-lagged approach is not new (e.g., Hoffman and Kalnay 1983; Toth and Kalnay 1993; Molteni et al. 1996), the experiment of Wang et al. (2016a) differed from earlier studies in that most earlier attempts were used within the short range (e.g., Mittermaier 2007; Lu et al. 2007; Yuan et al. 2008; Trilaksono et al. 2012), including the ETQPF of Hong et al. (2015). Thus far, the strategy proposed by Wang et al. (2016a) using an extended forecast range and an increased frequency (every 6 h) has been applied to more than a dozen of TCs hitting Taiwan (see Table 15.2), including TYs Kong-Rey (2013) in Wang et al. (2016a), Morakot (2009) in Wang et al. (2022a), Saola (2012), Soulik (2013), and Soudelor (2015) in Wang et al. (2022h) and several other cases in Chen and Wang (2022). Inside the short range, the system produces high-quality QPFs comparable to those shown in Sect. 15.3 (see Figs. 15.5, 15.6 and 15.7), as expected. Beyond the short range, moreover, the above studies collectively have also shown that the system takes the advantage of the high forecast uncertainty at longer lead times and thereby produces various rainfall scenarios in Taiwan associated with different tracks of the same storm. Among these tracks with a certain spread, there exists the worse-case (typically from a direct hit) and the actual scenario that turned out to occur. Also, the higher the uncertainty (which varies among the TCs), usually the larger the spread of the tracks and therefore a greater chance for the above two important scenarios (worse-case and actual one) to be covered. Thus, the value of the system at this stage (of longer lead times) is not in the accuracy of predictions, but rather, in its ability to provide various and yet realistic rainfall scenarios, in particular the worse-case one, for decision making and early preparation by the authorities (Wang et al. 2016a, b). As the TC approaches and the lead time shortens, the uncertainty reduces and the tracks in successive predictions converge toward the best track, the most-likely rainfall scenario emerges and the authorities can then make adjustments in their preparation. In Wang et al. (2016a, b), the longest range for a decent QPF made daily (at 0000 UTC) for six typhoons in 2012–2013, targeted at their most-rainy day, is on day 5.7

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Fig. 15.10 Threat score of 24-h QPFs by the best member among daily time-lagged 2.5-km CReSS runs (initialized at 0000 UTC) at the range of day 3 or longer, valid for the most-rainy day (in UTC) for the six typhoons in 2012–2013 (see legend), as a function of rainfall threshold (mm, per 24 h). The observed peak daily rainfall (mm, 884 mm for Saola) and lead time (D3 to D8 for day 3 to day 8, respectively) are given in the legend. Replotted from Wang et al. (2016b). © Authors 2016

on average, i.e., at 112–136 h into the integration and well beyond the short range, as shown in Fig. 15.10 (Wang et al. 2016b). Note that except for Tembin (2012), good QPFs were produced for all other five cases beyond the short range (from day 4 up to day 8), with TS > 0 often at thresholds not much lower than the observed peak amount (Fig. 15.10). For three other rainy TCs that the worse case turned out to occur in Wang et al. (2022h), the earliest successful QPFs were initialized 164 and 126 h before actual landfall in two cases, respectively, but only 55 h before landfall in the third event. Of course, such case-to-case variations must exist, as Morakot (2009) was also lower in predictability and decent QPFs only started to emerge at about 36 h before landfall (Wang et al. 2022a). Another important aspect is that this eight-day lagged forecasts executed every 6 h (Wang et al. 2016a, b) only utilize roughly the same computational resource as the 20-member three-day 5-km WRF ensemble, i.e., roughly half of the resource used in the ETQPF of Hong et al. (2015), which had 38 members. So, high-resolution lagged ensemble not only provides high-quality QPFs with very useful information at extended lead times for early preparation, but it is also affordable and feasible for operational use. Below, the event of Matmo (2014) is further used as an example to demonstrate the characteristics and usefulness of the eight-day 2.5-km CReSS time-lagged ensemble.

15.4.2 The Example of TY Matmo (2014) TY Matmo (2014) approached Taiwan from the southeast and made landfall through the middle section of the island in July 2014, with a landfall duration roughly from 1500 to 2100 UTC 22 July (Fig. 15.6e). Although it was not among the rainiest typhoons to strike Taiwan (Fig. 15.6), it serves as a good example to illustrate the usefulness of the 2.5-km time-lagged CReSS ensemble and therefore is selected here.

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As shown earlier, if the target period is chosen to be 22 July (in UTC), the day 1 QPF is quite accurate with TSs reaching 0.6 at 250 mm and 0.2 at 500 mm (Figs. 15.7e and 15.8e), but day 2 and day 3 QPFs (t 0 at 0000 UTC 21 and 20 July, respectively) are degraded due to under-prediction. When eight-day lagged ensemble forecasts at 6-h intervals are applied to Matmo (2014), the track forecasts by successive members are shown in Fig. 15.11. With t 0 between 0000 UTC 15 and 0600 UTC 16 July, several earliest runs produced very good tracks with landfall through Taiwan like the observation but with some reasonable timing errors, except the one initialized at 1800 UTC 22 July which tracked too far to the left with no landfall (Fig. 15.11a). On the other hand, the following several runs veered too far to the right and missed Taiwan, including those with t 0 from 1200 UTC 16 to 1200 UTC 17 July. Between 1800 UTC 17 and 1200 UTC 19 (Fig. 15.11a, b), most of the predicted tracks were better again and made landfall, with two exceptions at 0000 and 0600 UTC 18 that barely missed northern Taiwan (Fig. 15.11a). The three following runs (t 0 from 1800 UTC 19 to 0600 UTC 20 July) again produced tracks too far right to pass near Iriomote and Ishigaki Islands of Japan and without landfall in Taiwan. Finally, since 1200 UTC 20 July (Fig. 15.11b), good tracks were predicted again, with landfall in Taiwan and increasingly better agreement with the best track with time, until the last run initialized at 0000 UTC 22 July. The only exception was the one made at 0000 UTC 21 July, which was farther east without landfall in Taiwan (Fig. 15.11a). In Fig. 15.11, the predicted tracks by the lagged runs for Matmo swung back and forth several times, with good tracks (landfall through central Taiwan) made during 15–16, 18–19, and after 0600 UTC 21 July, respectively. A rather good attribute was that a direct hit (and the worse-case rainfall scenario) occurred in the earliest runs (with t 0 at 1200 UTC 15, and 0000 and 0600 16 July), a scenario that turned out to happen in Matmo, and giving the authorities the longest time possible to prepare

Fig. 15.11 JTWC best track (black) of TY Matmo (2014) and predicted tracks (colors, see insert at lower left) by the time-lagged ensemble every 6 h a from 0000 UTC 15 to 0600 UTC 18 July, and b from 1200 UTC 18 to 0000 UTC 22 July, respectively. Specific symbols denote the TC location at 0000 UTC of each day (see insert at upper right), and the thick lines depict the CReSS model domain. The Iriomote and Ishigaki Islands are marked in a. In b, tracks from those runs in a are plotted in light gray

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early. As illustrated in Fig. 15.11, the spread of the track was particularly large at the early stage due to the high uncertainty at longer lead times, and this property ensures a greater chance for the worse-case and actual scenarios to be covered by the ensemble. Indeed, the chance for Matmo to move outside the range shown in Fig. 15.11 would be very slim, and it would exert little impact on Taiwan if it did. While some might consider TC predictions at lead times beyond 4–5 days to be of little value because the uncertainty is too high and most runs are destined to be incorrect (both of which are true), we have shown and argued that the high uncertainty can be used to our advantage to make such an ensemble valuable at longer lead times, provided that the model resolution is high enough to provide realistic rainfall scenarios associated with different tracks. As the lead time decreases and uncertainty increases, the predicted tracks eventually converged toward the best track and became stable (Fig. 15.11b). Strictly speaking, this occurred after 0600 UTC 21 July for Matmo (about 33 h before landfall) and relatively late compared to some other cases in Wang et al. (2016a, 2022a, 2022h) and Chen and Wang (2022). This is an aspect of Matmo less than ideal. Different from that in Figs. 15.6e and 15.7e, the target period chosen here for 24-h QPF to examine for Matmo is over 0600 UTC 22–0600 UTC 23 July, with a slightly higher peak amount of 587 mm in observation, as depicted in Fig. 15.12 (enlarged panel). Also shown in Fig. 15.12 are the predicted rainfall distributions for this target period by the lagged ensemble every 6 h, with t 0 from 0600 UTC 15 to 0000 UTC 22 July (a total of 28 runs), together with the SSS value of each prediction. As one can see, when the track of Matmo was better predicted, the accompanied rainfall scenario in Taiwan was also in closer agreement with the observation with SSS ≥ 0.75, a criterion chosen somewhat arbitrarily. These decent rainfall predictions include those made at 0000 and 0600 UTC 16, 1200 UTC 18, 0600 UTC 19, 1800, UTC 20, and those since 1200 UTC 21 July (Fig. 15.12). On the other hand, when Matmo’s track was too far to the east, the QPF in Taiwan was much reduced with low SSS values as expected, including those made from 1200 UTC 16 to 1200 UTC 17 July (cf. Fig. 15.11). Thus, Fig. 15.12 confirms that the worst-case (and actual) rainfall scenario was made very early during 15–16 July. Also, within the short range since 0000 UTC 20 July, the QPFs made at 0000 UTC on 20 and 21 had the two worst tracks and among the lowest SSS (0.56–0.57), and thus the day 2 and day 3 results for Matmo in Figs. 15.6e and 15.7e were not so good. Overall, Figs. 15.11 and 15.12 again show that the rainfall pattern and amount brought by Matmo were highly dictated by its track, as in the majority of other TC cases reviewed in Sects. 15.1 and 15.3.2. Based on the results of lagged ensemble for Matmo, all the predicted tracks fairly close to Taiwan can be classified into two groups: those more accurate to make landfall in central Taiwan (and cross 122°E to the south of 24°N) and those less accurate to move farther to the east (and cross 122°E north of 24°N) but not beyond Ishigaki Island. Exclusive to each other, the two groups each consists of 11 runs, while other tracks outside this range are not classified. In Fig. 15.13, the probability distributions for the 24-h target period to reach the thresholds of 100, 200, 300, and 400 mm derived from these two groups are presented, with equal weights assigned to all members

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Fig. 15.12 Observed 24-h rainfall (mm, enlarged panel, peak value = 587 mm), from 0600 UTC 22 to 0600 UTC 23 July, during TY Matmo (2014) and the predicted rainfall (mm) for the same period by the time-lagged ensemble every 6 h, with initial times from 0600 UTC 15 to 0000 UTC 22 July as labeled. The same color scale (upper right) is used for all panels, and the SSS over Taiwan in each forecast is given inside the panel (lower right, bold if ≥ 0.75)

(arithmetic mean). The left group (better tracks) exhibits rainfall probabilities in much better agreement with the observed areas (thick black contours), with ≥ 70% chance in most of the actual regions at 100 and 200 mm (Fig. 15.13a,b), and ≥ 50– 60% at 300 and 400 mm (Fig. 15.13c,d). The BSS values are also fairly good and decrease gradually from 0.68 at 100 mm to 0.30 at 400 mm. By comparison, the right group shows considerably lower probabilities and BSS values (by 0.2–0.27) across the heavy-rainfall range of 200–400 mm, due to their tracks being farther away from Taiwan (Fig. 15.13f–h). Only in the mountain regions in northern Taiwan at 100 mm (and 200 mm to some extent), the probabilities in the right group are not reduced (Fig. 15.13e). Overall, the quality of the probability information from the left group is considerably better than its counterpart. As the predicted tracks of Matmo swung back and forth (Fig. 15.11), these two scenarios of probabilities would appear in alteration among groups of successive runs, as given in Table 15.3. The runs with t 0 from 0600 UTC 15 to 0600 UTC 16 (5 runs), 1200 UTC 18 to 1200 UTC 19 (5 runs), and the last batch from 0600 UTC 21 to 0000 UTC 22 July (4 runs) produced more

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Fig. 15.13 Probabilities of 24-h QPFs (%, shaded, scale to the right) from the 11 time-lagged members with TC tracks more to the left (top row, see text for details) to reach the threshold of a 100, b 200, c 300, and d 400 mm, respectively, for the target period of 0600 UTC 22 to 0600 UTC 23 July during TY Matmo (2014). e–h As in a–d, but from other 11 members with TC tracks more to the right. In each panel, the BSS is given (lower right, bold if ≥ 0.5)

of the better tracks, and thus the derived probability distributions have BSS values (Table 15.3) similar to those from the left-track group in Fig. 15.13a–d. However, in general, the BSS values also gradually improve with decreasing lead time. On the other hand, those runs in between (from 1200 UTC 16 to 0600 UTC 18 and from 1800 UTC 19 to 0000 UTC 21 July) contained more members of worse tracks, and their BSS values (Table 15.3) resemble those from the right-track group. In an operational setting, a more straightforward method to derive the probabilities is to use a given number of most recent runs, perhaps with more weights placed on later runs as in Wang et al. (2022a). If five most recent runs are used for Matmo, the BSS values obtained at 0600 UTC 16, from 1200 UTC 17 to 0600 UTC 18, and at 1200 UTC 19, 0000 UTC 21, and 0000 UTC 22, respectively, would also be similar to those listed in Table 15.3 for the corresponding periods.

15.4.3 The Example of TY Haiyan (2013) for Landfall Intensity While high resolution can produce more realistic simulations of weather events and make improvements in nearly all aspects, it is more important in the successful predictions of some parameters than others. Besides the QPF, one other such process

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Table 15.3 BSS values of rainfall probabilities from time-lagged QPFs by the 2.5-km CReSS (every 6 h) initialized during different time periods, but all targeted for the 24-h period from 0600 UTC 22 to 0600 UTC 23 July during TY Matmo (2014), to reach six thresholds from 50 to 500 mm (per 24 h) Time period

Number of runs

Rainfall threshold (mm, per 24 h) 50

100

200

300

400

500

0600 UTC 15 5 to 0600 UTC 16 July

0.676

0.605

0.437

0.286

0.225

0.103

1200 UTC 16 8 to 0600 UTC 18 July

0.420

0.277

0.094

0.038

0.012

0.031

1200 UTC 18 5 to 1200 UTC 19 July

0.790

0.649

0.503

0.275

0.203

0.082

1800 UTC 19 6 to 0000 UTC 21 July

0.795

0.574

0.286

0.097

0.013

0.037

0600 UTC 21 4 to 0000 UTC 22 July

0.869

0.741

0.631

0.464

0.317

0.255

is the rapid intensification of TCs (e.g., Braun 2002; Gentry and Lackmann 2010; Kanada and Wada 2015) and their subsequent landfall intensity. Recently, the case of Super Typhoon (STY) Haiyan (2013) that struck the central Philippines was studied by Wang et al. (2022e), similarly using the 2.5-km CReSS and time-lagged approach every 6 h but with a much larger model domain to accommodate the long track of the case (Fig. 15.1a), and the results are briefly reviewed here. STY Haiyan (2013) is known for its record-breaking intensity at landfall at around 0000 UTC 8 November (e.g., Soria et al. 2016), with sustained surface wind speed estimated to be as high as 85 m s−1 by the JTWC (e.g., Shimada et al. 2018), and the induced storm surges of up to 6–7 m killed more than 6000 people (e.g., Mori et al. 2014; Mas et al. 2015). However, such extreme intensity is almost always poorly captured by the global models due to their coarse resolution. In Wang et al. (2022e), not only the 2.5-km CRM was used, but its earlier forecast that best matched the intensity estimate in real time was also recycled as the initial field, similar to Liu et al. (2020). This combination is proven to be an effective method (Fig. 15.14), as all the 6-hourly lagged runs since 1800 UTC 3 November predicted a storm intensity at least category 3 (50 m s−1 ), all those (except for one) since 1800 UTC 4 November reached category 4 (58 m s−1 ), and all those since 0000 UTC 6 November reached category 5 (69 m s−1 ) at or near landfall for Haiyan (Fig. 15.14a). If the minimum central mean sea-level pressure (MSLP) is used for intensity (Fig. 15.14b), the results are nearly the same. Therefore, not only the QPFs but also other TC attributes like the landfall intensity can benefit from this feasible strategy using high-resolution models.

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Fig. 15.14 JTWC estimated (brown) and predicted a maximum sustained surface wind speed (m s−1 , at 10-m height) and b minimum central MSLP (hPa) by the 2.5-km lagged CReSS runs (color) for the period of 4–8 November, using the NCEP GFS as IC/BCs (up to 0000 UTC 6 November) but CReSS’ own prediction from the run at 0000 UTC 6 November as IC since t 0 at 0600 UTC 6 November. The criteria of category 3–5 are marked. The initial time of each run (color, see legend) is depicted by a square, and the peak intensity category attained between 0000 UTC 7 November and landfall is also given to the right of the panel. Adapted from Wang et al. (2022e). © Elsevier. Used with permission

15.5 Future Direction In previous sections, cloud-resolving models using time-lagged strategy with an extended range have been shown to be effective in producing high-quality QPFs at heavy-rainfall thresholds for Taiwan, where the topography exerts a strong control in rainfall production, even under the constraint of limited computational resources. However, it can still be improved, especially in a couple of its weaker points in a relative sense. Below, the future directions of heavy-rainfall QPFs in Taiwan are

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discussed using some examples, aimed to strengthen the information on QPFs as provided by such an ensemble system. One obvious direction is to increase the number of high-resolution members, so that the probability information can be more complete and evolve faster to provide the users with the most updated information as possible. Another direction is to make use of artificial intelligence and machine learning to enhance the usefulness of the QPFs, in the example here, to assess the likelihood of occurrence of each model prediction to assist on decision making and hazard preparation.

15.5.1 Toward More Members and Higher Resolution Due to its highly efficient usage of computational resource, the time-lagged strategy using CRMs discussed in Sect. 15.4 (and e.g., Wang et al. 2016a, b, 2022a, 2022h) represents the best feasible solution at the present time when high resolution is needed under a limited resource. With one run every 6 h, there are only four members per day, and this is obviously less than ideal for a more responsive and rapid evolution of striking probability of the storms. With the continuous development of computer technology, one direction for future improvement is of course to increase the number of high-resolution members, so that the ensemble information from the latest trend can be quickly updated. However, for many operational centers that are not as resourceful, this requires time and may not be achieved as rapidly as desired. Before 2018, two three-day 5-km ensemble QPF systems had been established in Taiwan, the first at the CWB (20 members) and the second at the TTFRI (18 members), as used in the ETQPF system of Hong et al. (2015) and reviewed in Sect. 15.3.2. To support the field campaign of the Taiwan Area Heavy-rainfall Observation and Prediction Experiment (TAHOPE)/Precipitation of Rainfall Extremes Campaign in the Pacific (PRECIP) held from 23 May to 10 August 2022 and further advance the QPFs in Taiwan, the Taiwan Area Heavy-rainfall Prediction Experiment (TAHPEX) was established since 2019 as the modeling and prediction component of TAHOPE in Taiwan. As given in Table 15.4, the TAHPEX project consists of 13 models, contributed from the CWB and several research groups, and also one member of the Model for Prediction Across Scales (MPAS) from the National Center for Atmospheric Research (NCAR) of the USA. Among them, ten are regional CRMs, with Δx = 1 km in three and 2.5–3 km in the other seven models. The other members are global models, but the Δx is also around 3 km near Taiwan in MPAS and around 4.8 km in the CWB Finite Volume ver. 3 (FV3) GFS (Table 15.4). Most of them have a forecast range of 120 h. During the dry run periods (1–15 June 2019 and 1–15 June 2020), pre-TAHOPE/PRECIP trail run (21 May–15 June 2021), and the entire field phase of TAHOPE/PRECIP campaign in 2022 (23 May–10 August), real-time forecasts were carried out with up to 32 runs per day, and approaching the ensemble size used on TY Morakot (2009) by Zhang et al. (2010), Fang et al. (2011), and Fang and Kuo (2013). Thus, through team work and the contribution from research groups and the operational sector, the large computational demand can be met to produce

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Table 15.4 13 TAHPEX models and their basic information No

Model

Δx (km)

No. IC/BCs of levels

Freq Range Institution PI (day−1 ) (h)

M01 CReSS

2.5 40

NCEP

4

120

NTNU

CC Wang

M02 WRF

3.0 45

NCEP

4

120

NTNU

FC Chien

M03 WRF

3.0 41

NCEP

4

120

NTU

MJ Yang

M04 WRF-D

3.0 52

NCEP

4

120

CWB

JS Hong

M05 TWRF

3.0 52

NCEP

4

120

CWB

JS Hong

M06 WRF

3.0 45

NCEP

3

120

NCU

PL Lin

M07 MPAS

3.0 55

NCEP

–

–

NCU

CY Huang

M08 CReSS-NHOES

2.5 40

NCEP, JCOPE2

2

120

NTNU

CC Wang

M09 MPAS

3.0 55

ECMWF 1 IFS

120

NCAR

R Rios-Berrios

~ 4.8 63

CWB

2

120

CWB

LF Hsiao

M11 CReSS

1.0 45

NCEP

1

108

NTNU

CC Wang

M12 WRF-D

1.0 52

NCEP

2

36

CWB

JS Hong

M13 SUM

1.0 42

NCEP

1

120

CWB

CH Chen

M10 FV3

The acronyms are: For model: WRF-D (deterministic WRF), TWRF (Typhoon WRF), NHOES (Non-Hydrostatic Ocean Model for Earth Simulator), SUM (Spectral Unified Model); for IC/BCs: JCOPE2 (Japan Coastal Ocean Prediction Experiment, ver. 2), ECMWF (European Centre for Medium-Range Weather Forecasts), IFS (Integrated Forecasting System); for institution: NTU (National Taiwan University), NCU (National Central University); PI (principle investigator)

four times as many runs as those used in the time-lagged ensemble of Wang et al. (2016a, b, 2022a, 2022h), although the forecast range is shorter. In real time, the ensemble information (such as ensemble mean, spread, and heavy-rainfall probabilities) is regularly updated, and the ensemble-based analysis results similar to those of Wang et al. (2021b) are also available. Thus, not only the high-resolution requirement can be met, the ensemble information can also be updated more timely and rapidly. Although the 1-km models are still few in number, they represent another step toward a higher model resolution, and their potential impacts on QPFs in Taiwan can also start to be assessed and understood in the near future.

15.5.2 Help from Artificial Intelligence and Machine Learning The artificial intelligence is another area of rapid development with potential applications in many fields, including in the NWP and QPFs. While many possibilities exist in the applications of artificial intelligence to assist human forecasters to make

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better forecasts, here we present an example from a recent study of Chen and Wang (2022) to provide some help in answering one of the most difficult questions in NWP prior to any event: How likely is a given forecast scenario to occur? In Sects. 15.3 and 15.4, we have shown that the QPFs made by CRMs are of high quality in Taiwan even at lead times up to about one week, if the storm track (which represents a reasonable overall evolution of the TC) can be well predicted. However, even with a multimodel ensemble and better probability estimates, “knowing in advance” remains to be highly challenging, and this is where the artificial intelligence can provide some help. In Chen and Wang (2022), machine learning was used to assess the quality of each QPF made by the eight-day lagged runs (every 6 h) for westward-moving typhoons. A total of ten such typhoons during 2012–2016 were chosen (Fig. 15.15) to form the dataset for training, through a neural network (five layers with 512 neurons in each layer) to minimize the MSE between the actual and projected SSS values of the rainfall accumulations in Taiwan over the impact period, defined to be when the TC center is within 300 km from the nearest coastline of Taiwan. The impact period was so defined in order for the method to be applicable in real time (such that a fixed duration cannot be pre-determined). However, the model TCs that do not cover the whole duration (i.e., all those with a TC center already inside 300 km from Taiwan at t 0 , or does not move to more than 300 km away before the end of integration at t = 192 h) were not qualified, and thus a total of 145 forecasts were used. From each one of them, a total of 105 parameters that reflect the impact period duration, rainfall magnitude, TC track through time, track errors in previous forecasts, and the spread of earlier track forecasts, etc., all available shortly after each forecast, were considered to be influencing factors of QPFs and used as inputs of training. While a detailed description is omitted here, the machine learning model performed training (using 3/4 of data) and adjustment (using the remaining 1/4 of data) repeatedly until the result converges and the best SSS estimates (to actual ones) are obtained. To meet the independent requirement, only data from the other nine cases were used for training and adjustment for each typhoon and then applied to the case in consideration to give estimates of SSS as indications on the overall quality of QPFs (Chen and Wang 2022). The results of Chen and Wang (2022) for three of the typhoons are shown in Fig. 15.16, including TYs Matmo (2014), Soudelor (2015), and Nepartak (2016). Because the training result also depends on the random ingestion of data, the outcome is not identical every time. Hence, the concept of ensemble was also applied and 100 sets of results were generated for each typhoon, and the projected (or estimated) SSS values at the tenth, fiftieth, and ninetieth percentiles are shown. For TY Matmo (2014), the observed impact duration was 36 h (from 0300 UTC 22 to 1500 UTC 23 July), and only the runs with t 0 between 1800 UTC 18 and 0000 UTC 21 July were available (Fig. 15.16a) due to the requirement to cover the whole impact period (within 300 km from Taiwan’s coastline). When compared to Fig. 15.12, one can see that, despite the difference in accumulation length, machine learning tends to indicate better QPF quality (i.e., higher SSS) when the actual SSS also rises higher (e.g., at 0600 UTC 19 and 1800 UTC 21 July, Fig. 15.16a) and vice versa when the

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Fig. 15.15 Observed tracks of the ten selected westward-moving typhoons (color) during 2012– 2016 and included in Chen and Wang (2022). Solid dots mark TC center locations at 0000 UTC during their life span. The thick black lines depict the CReSS model domain. Adopted from Chen and Wang (2022) and used with permission

actual SSS drops lower (e.g., at 0000 and 0600 UTC 20 July). Similar trends can also be seen for Soudelor (Fig. 15.16b, duration = 32 h) and Nepartak (Fig. 15.16c, duration = 56 h), especially the latter where a large range of SSS existed between good QPFs (SSS around 0.6–0.8) and bad ones (SSS ≤ 0.3). While Chen and Wang (2022) is a preliminary study, its results from machine learning already show a great potential in the future applications when the TC sample for training increases in number.

15.6 Conclusion and Summary In modern NWP, the QPF is one of the most important areas in constant and heavy demand by the society, especially the predictions of heavy rainfalls due to their hazardous nature. During the past decade or so, through the use of a CRM (the CReSS model) at a grid size (Δx) of 2.5 km, heavy-rainfall QPFs in Taiwan, where rainfall production is strongly influenced by its steep and complex topography, are shown to improve significantly. Therefore, the experience in this aspect in Taiwan is reviewed in this chapter, with some newly added and updated results. The main methods of QPF verifications adopted include categorical statistics (mostly of 24-h rainfall) at a series of rainfall thresholds and also the Similarity Skill Score (SSS)

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Fig. 15.16 Actual SSS of QPFs and the projected values at the tenth, fiftieth, and ninetieth percentile through machine learning (see insert) by lagged runs of 2.5-km CReSS at different initial times 6-h apart for three selected typhoons of a Matmo (2014), b Soudelor (2015), and c Nepartak (2016), respectively Adapted from Chen and Wang (2022) and used with permission

for rainfall patterns from deterministic forecasts and the Brier Skill Score (BSS) for rainfall probabilities in ensemble forecasts (see Sect. 15.2). With an increased model resolution, heavy-rainfall QPFs both from typhoons (July–October) and during the early summer Mei-yu season (May–June) within the short range (≤ 72 h) are improved in Taiwan (Sect. 15.3). For all 29 TCs during 2010–2015 (Fig. 15.6), the threat scores (TSs) on days 1–3 are all near 0.72 at the lowest threshold of 0.05 mm (per 24 h) and can reach 0.2 or higher up to almost 500 mm on day 1 (0–24 h), around 450 mm on day 2 (24–48 h), and over 250 mm on

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day 3 (48–72 h), respectively. As previously found, there exists a strong dependency of TSs on the magnitude of TC rainfall events, with higher TSs in larger events. For instance, for the largest 7% of events (those with a peak 24-h amount ≥ 750 mm in observation), the TSs are all close to 1.0 at 0.05 mm at all three ranges of days 1–3, and around 0.3 higher than those for all events up to about 50 mm (per 24 h), 0.2 higher at about 100 mm, and 0.1 higher at 350 mm at these three ranges (Fig. 15.6). Over higher thresholds, the differences tend to become smaller, as the statistics there are contributed from larger events more and more exclusively. For Mei-yu, verification of QPFs over six seasons (May-June of 2012–2017) shows that the TSs at 0.05 mm for all events are around 0.55–0.6 on days 1–3, but much higher near 0.95 for the largest 4% of events (Fig. 15.9). Similarly, for all events, they can reach ≥ 0.2 up to about 105, 75, and 55 mm on days 1–3, respectively, but up to 200, 200, and 150 mm for the top events (Fig. 15.9). Furthermore, for TCs that typically have a longer life span, it is shown that timelagged cloud-resolving ensemble (Wang et al. 2016a) is an effective and feasible strategy to provide high-quality QPFs not only inside the short range, but also beyond at lead times up to about one week under the constraint of a limited computational resource. At longer lead times, the method takes advantage of the higher uncertainty of the nonlinear atmosphere and generate different rainfall scenarios in Taiwan associated with different TC tracks. Among them, there exists the worst-case scenario (usually a direct hit) for the authorities to start early preparation. In past studies on several rainy typhoons (in which the worst case turned out to happen) and the new example of TY Matmo (2014) in Sect. 15.4, the averaged range for this scenario to occur (with SSS ≥ 0.75) is around day 5.5, but in some TCs (including Matmo) can be around one week before the actual landfall. As the storm approaches and the lead time shortens, the predicted tracks by successive runs converge toward the best track, and the most-likely scenario emerges with consistent high-quality QPFs (typically SSS > 0.8) similar to those inside the short range summarized above. At this point, the authorities can make adjustment in hazard preparation as needed. As computer technology continues to advance, the development of heavy-rainfall QPFs toward higher resolution and more members with cloud-resolving capabilities is expected in the foreseeable future. One such example is the TAHPEX project during 2019–2022 in Taiwan (Sect. 15.5.1). Such a development allows for more rapid and timely updates of ensemble (probability) information in real time. There will certainly also be more applications from artificial intelligence and machine learning, and an example from Chen and Wang (2022) is given here that can gauge the likelihood and confidence level of each QPF shortly after it is produced in real time (Sect. 15.5.2). In the future, this type of applications will certainly provide valuable information to the forecasters, other users of the QPFs, and decision makers alike and help further reduce the losses of heavy-rainfall events. The above series of studies using the CReSS model, in essence, demonstrate the importance of basic model resolution and configuration in order for the model to better resolve deep convection and topography and subsequently improve its capability to simulate heavy rainfall in a place like Taiwan. While such cloud-resolving capability might be difficult to achieve a couple of decades ago, now it has become

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feasible and practical. For heavy-rainfall QPFs (and some other parameters like the TC intensity), this capability should be ensured first, with higher priority over many other aspects, under the constraint of a limited computational resource. If model resolution is sacrificed for the need of multi-model ensemble to estimate forecast uncertainty, the QPFs are degraded and so are the derived probability information. This is not an ideal situation and should be avoided. As the rainfall climatology and topography in many Asian-Pacific regions are similar to those of Taiwan, the example and experience of heavy-rainfall QPFs on the island can be applied to improve the QPFs in these areas, especially those that are not as resourceful as the developed countries. However, we should note that there are also other avenues that can improve QPFs but not mentioned in this chapter. One such avenue is the improvement of initial fields through advanced data assimilation (DA) at various scales depending on the purpose, a topic covered and discussed in other chapters of this book. For the CReSS forecasts described above, the IC/BCs were provided in real time by the NCEP GFS, where the DA has already been performed. Finally, the development of global and regional models can also lead to improved quality in IC/BCs and in the QPFs, but this tends to be a gradual process through continuous efforts in the long term.

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Part V

High-Impact Weather Prediction

Chapter 16

Analysis and Forecasting of High-Impact Weather Systems in East Asia Using Numerical Models Dong-Hyun Cha and Donghyuck Yoon

Abstract We reviewed a range of studies to deepen our understanding and predict the occurrence of high-impact weather systems in East Asia using numerical models. First, we introduced a selection of numerical modeling methods to improve typhoon forecasts in East Asia, focusing on data assimilation, vortex initialization, physics schemes, boundary conditions, and model resolution. Numerical modeling studies on the analysis and forecasting of heatwaves (HWs) in East Asia are explored. Various modeling approaches to understand the local-to-large-scale mechanisms of HWs in East Asia are reviewed, and studies improving the predictability of HW events using advanced methods, such as soil moisture initialization and air–sea coupling, are also covered. Keywords High-impact weather systems · Typhoon · Heatwave · Forecasting · Analysis

16.1 Introduction East Asian countries are affected by a number of high-impact weather systems such as typhoons, heavy rainfall, severe snowfall, drought, heatwaves (HWs), and cold surges. One of the most high-impact weather systems in East Asia is typhoons, which are accompanied by strong wind gusts, torrential rainfall, and storm surges. Approximately 90 tropical cyclones (TCs) occur worldwide each year, of which approximately 25–30 typhoons occur in the western North Pacific (WNP). The formation of D.-H. Cha (B) · D. Yoon Department of Civil, Urban, Earth, and Environmental Engineering, Ulsan National Institute of Science and Technology, Ulsan, Korea e-mail: [email protected] D. Yoon e-mail: [email protected] D. Yoon Program in Atmospheric and Oceanic Sciences, Princeton University, New Jersey, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_16

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typhoons occurs more frequently with a higher level of intensity in the WNP than in other basins (Mendelsohn et al. 2012; Woodruff et al. 2013), with stronger typhoons impacting East Asian countries in recent decades (Park et al. 2014). Typhoons are severe weather systems that can cause human fatalities and property damage in the areas affected. Therefore, accurate prediction of the motion and intensity of typhoons using numerical models is critical to preparedness and evacuation in East Asia, where the potential for substantial damage from intense typhoons is high. In recent decades, frequent HWs have accounted for extensive socioeconomic problems in East Asia. In China, over 5500 patients were affected directly by an HW event in 2013 (Gu et al. 2016). In Korea, HWs during the summer of 1994 caused at least 3300 cases of HW-related illness (Kysely and Kim 2009) and record-breaking HWs occurred in 2013, 2016, and 2018, inducing many health and energy issues. In Japan, major HWs, which led to serious heat-related illnesses, were also reported in 2013, along with consecutive HWs in 2018–2020 (Hayashida et al. 2020). A deadly HW in 2018 was responsible for 42 deaths in Korea and 138 in Japan, with more than 3400 and 71,200 corresponding illnesses, respectively (Park and Chae 2020). HWs over Asia will become more frequent, intense, and prolonged in the future (IPCC 2013; Lau and Nath 2014; Lee and Lee 2016; Luo and Lau 2017). Therefore, in East Asia, precise forecasts of HWs using numerical models are necessary to reduce damage. In this section, we have explored the prediction and analysis of typhoons and HWs in East Asia using numerical models.

16.2 Numerical Modeling for Typhoon Forecasting Considerable progress has been made in typhoon forecasting using numerical models owing to the substantial increase in computing resources and advancements in observations. However, track and intensity errors in typhoon forecasts using numerical models are still considerable because of the uncertainties of the numerical model related to dynamics/physics and initial conditions. Numerous efforts have been made to improve typhoon modeling in terms of initial conditions, physical processes such as surface flux, convection, cloud microphysics, ocean feedback processes, and model resolution, which have been introduced in this section.

16.2.1 Impact of the Data Assimilation Method on Typhoon Forecasting Typhoon forecasts can be substantially improved by data assimilation (DA) methods, which use various observational data such as conventional data, remote sensing data, and dropsonde data. Typhoons generally form over the ocean where the number of sources of conventional data observations is relatively small. Therefore, in the WNP,

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the impacts of remote sensing data such as satellite radiance and coastal radar data and TC inner-core observations using reconnaissance aircraft including dropsonde and airborne Doppler radar have been commonly used in typhoon forecasting. Lin et al. (2022) improved the intensity prediction for Typhoon Hato by assimilating groundbased radar data using a multiscale correction framework and incorporating it into satellite ocean surface wind speed observations. Ito et al. (2018) used dropsonde data from the THORPEX Pacific Asian Regional Campaign (T-PARC) II to improve the forecasting of Typhoon Lan. Radiance data from satellite channels are also important in deepening our understanding of the environmental conditions affecting typhoon activities. The use of satellite data assimilation in typhoon forecasting using variational (Xu et al. 2013), ensemble-based (Schwartz et al. 2012), and hybrid (Xu et al. 2015) DA methods has been examined. Schwartz et al. (2012) conducted data assimilation experiments with a cyclic, limited-area ensemble adjustment Kalman filter (EAKF) to evaluate the effects of assimilating microwave radiances on the prediction of Typhoon Morakot. They have shown that assimilating microwave radiances with a limited-area EAKF improved typhoon forecasts. However, the degree of improvement differed among the intensity, track, and precipitation forecasts. Xu et al. (2013) investigated the impact of assimilating infrared radiances on the forecast of typhoon Megi using the threedimensional variational (3DVAR) method. They implemented a cloud-detection scheme in the Weather Research and Forecasting Data Assimilation (WRFDA) system to exclude cloud-contaminated infrared radiances and showed that the data assimilation of infrared radiances had a consistently positive impact on typhoon forecasting. Choi et al. (2017) investigated the impact of satellite radiance data assimilation based on the 3DVAR method on the simulation of binary typhoons. They have shown that radiance assimilation slightly improved the environmental fields and track forecasts of binary TC cases. However, the detailed effects varied depending on the specific case studies examined. When there was no direct interaction between binary TCs, radiance assimilation led to more accurate depictions of the environmental fields, resulting in improved track forecasts. They conducted two experiments, that is, the CONV experiment using only conventional data and the SAT_CONV experiment using satellite radiance data as well as conventional data and showed that track forecast errors for binary typhoons such as Chan-hom and Nangka were substantially reduced by satellite radiance data assimilation because it improved the steering wind forecast over the WNP (Fig. 16.1). The 500 hPa geopotential height error in the SAT_ CONV experiment was smaller than that of the CONV experiment. This indicated improved simulation of the western North Pacific subtropical high (WNPSH) by satellite radiance data assimilation (Fig. 16.2). However, satellite radian data assimilation did not decrease the track forecast errors in all binary typhoon cases. For the binary typhoons, which were affected by a direct interaction due to their proximity, the improvement from satellite radiance assimilation was considerably reduced. They explained that the errors in environmental parameters such as temperature and wind for the binary typhoons with a direct interaction could not be decreased by radiance data assimilation because they only assimilated clear-sky radiance data. Therefore,

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Fig. 16.1 Mean absolute track errors a, b and mean steering wind errors c, d of the CONV (blue line) and SAT_CONV (red line) experiments as a function of forecast lead time for typhoons Chanhom (left panels) and Nangka (right panels). From Choi et al. (2017). ©2017 American Geophysical Union. Used with permission

the number of available radiance data was relatively small owing to deep clouds around the two typhoons. Therefore, assimilating all-sky radiances can not only provide information on the environment of the typhoon but also on the typhoon itself. This means that it can further improve track and intensity forecasts. However, all-sky radiance data still have non-negligible uncertainties induced by clouds and it has been challenging to apply all-sky radiance data assimilation to typhoon forecasts. Recently, there have also been difficulties in the use of all-sky radiance data in typhoon modeling (Minamide and Zhang 2018; Xu et al. 2021). Minamide and Zhang (2018) examined the potential impact of assimilating all-sky infrared satellite radiances from Himawari-8 on typhoon forecasts by using an ensemble Kalman filter (EnKF). They found that hourly cycling assimilation of infrared radiance could not only improve the estimate of the incipient intensity but also the spatial distribution of the essential convective activity associated with the initial typhoon vortex.

16.2.2 Typhoon Vortex Initialization Mature typhoons always have a strong cyclonic vortex around the core region. Therefore, accurate determination of the initial conditions, and particularly the initial TC

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Fig. 16.2 Average analysis errors of 500-hPa geopotential height (shading, m) and wind (vector, m s−1 ) for the a SAT_CONV and b CONV experiments. Average analysis errors of 850-hPa temperature (shading, K) for the c SAT_CONV and d CONV experiments. An analysis error is defined as the difference between the analysis of the CONV or SAT_CONV experiment and the ERA-Interim reanalysis, and analysis errors over the cycling period were averaged. Sourced from Choi et al. (2017). ©2017 American Geophysical Union. Used with permission

vortex, is important for improving TC forecasts. Although remote sensing observations such as those from satellites and radar have been prominently advanced in recent years, there are still restrictions on fully resolving the three-dimensional typhoon structure. Thereby, vortex initialization methods are still used for typhoon forecasting. One vortex initialization method is the bogussing method, in which a bogus vortex generated by analytic empirical functions for surface pressure and wind is replayed with the vortex in the global analysis. Despite its simplicity, this method can improve track and intensity forecasts (Ueno 1989; Wang 1998; Kwon and Cheong 2010). However, it was difficult to generate an asymmetric TC vortex structure using this method. This method may result in physical and dynamical inconsistencies between the initial conditions and the forecasting model. Another method for vortex TC

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initialization is bogus data assimilation (BDA), which uses a data assimilation technique with an empirical bogus vortex that closely matches the observed TC intensity and structure (Zou and Xiao 2000; Xiao et al. 2006). The third vortex initialization method is dynamic initialization (DI) (Kurihara et al. 1993; Bender et al. 1993a, b; Nguyen and Chen 2011; Cha and Wang 2013; Liu and Tan 2016; Lee and Wu 2018). The DI method has the advantage that the dynamical and physical inconsistencies between the initial vortex and the forecast model are substantially reduced, while it requires extra integration of the forecast model to generate the initial vortex. Cha and Wang (2013) developed a DI-based vortex initialization scheme using cycle runs and applied it to a real-time forecasting system for typhoons over the WNP. In this scheme, cycle runs were conducted repetitively to spin up the axisymmetric component of the typhoon vortex. As the number of cycle runs increased, the horizontal distribution and three-dimensional structures around the typhoon core region were more accurately reproduced compared with the global analysis data (Fig. 16.3). Spectral nudging was applied during each cycle run to decrease the bias of the environmental fields, and the relocation method was used to reduce the initial position error. Cha and Wang (2013) also investigated the effect of the DI scheme by conducting numerical experiments with and without the scheme using the Weather Research and Forecasting (WRF) model. They showed that the DI scheme could overall reduce the position and intensity errors by 10% and 30%, respectively. The results have demonstrated that the DI scheme improved the initial TC vortex structure and intensity and provided warm physics spin-up, which reduced the initial shocks induced

Fig. 16.3 Surface wind speed (m s−1 ) (upper panels) and zonal–vertical cross sections of wind speed (m s−1 , shadings), and potential temperature (K, contours) across the typhoon center (bottom panels) at the initial forecast time at 00 UTC 31 August 2010 from the global forecast system (GFS) and cycle runs. From Cha and Wang (2013). ©2013 American Meteorological Society. Used with permission

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Fig. 16.4 Temporal evolution of the central sea level pressure (hPa) for Typhoon Megi from the best-track data (solid), the GFS, and the experiments with and without the DI scheme (DI and CTL runs, respectively). Different marks are used to distinguish forecasts with 10 different initial forecast times from 12 UTC 14 October 2010 to 00 UTC 19 October 2010. From Cha and Wang (2013). ©2013 American Meteorological Society. Used with permission

by the physical and dynamical imbalances between the high-resolution WRF model and global analysis data (Fig. 16.4).

16.2.3 Impacts of Boundary Conditions and Model Resolution on Typhoon Forecasting Generally, the limited-area model (LAM) or regional model has been applied to typhoon forecasting with high resolution because it requires fewer computing resources than the global model. However, a regional model requires lateral boundary

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conditions (LBCs) generated from the analysis of global models or forecast data. Therefore, typhoon forecasts using regional models are affected by LBCs. The predictability of regional models can be limited by error sources related to LBCs because regional models often face a systematic problem caused by inconsistencies between the simulated model fields and LBCs. A longer forecast lead time can cause lower predictability owing to inconsistencies and regional models require methods for reducing these inconsistencies. Spectral nudging (von Storch et al. 2000) has been widely used as an alternative technique to address this problem by providing large-scale forcing in the interior of the regional model. Moon et al. (2018) first applied spectral nudging to medium-range forecasts of typhoon track and intensity, and its effects were investigated using a high-resolution regional model. They found that spectral nudging could improve typhoon track forecasts when global model forecast data were nudged but tended to decrease typhoon intensity by suppressing the development of typhoons. Therefore, they optimized spectral nudging to improve the typhoon intensity forecast while maintaining the improvement of the track forecast. They conducted 51 experiments for 18 typhoons with optimized spectral nudging, which showed that the optimized spectral nudging could generally improve the track forecast, especially after 96 h (Fig. 16.5). Spectral nudging was particularly effective for typhoons that formed east of the WNP and then moved to Northeast Asia. Therefore, they selectively applied spectral nudging based on typhoon characteristics to increase the impact of spectral nudging. Typhoons are also substantially affected by oceanic conditions such as the sea surface temperature (SST) and ocean heat content because typhoons form and develop over the ocean. In most numerical weather predictions, the oceanic model was not used, so the prescribed SST was used as a low boundary condition over the ocean. The prescription of a fixed SST means that there is no coupled air– sea interaction, which may lead to substantial errors in the numerical modeling.

Fig. 16.5 Mean track error (left) and mean maximum surface wind error (right) averaged for the 51 typhoon forecasts. GFS refers to the global forecast system’s forecast data, and NOSN indicates experiments without spectral nudging. SN, OSN, and SOSN represent experiments using the original, optimized, and selective-optimized spectral nudging, respectively. From Moon et al. (2018). ©2018 American Geophysical Union. Used with permission

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Typhoon modeling studies (Mohanty et al. 2015; Srinivas et al. 2013) that used a fixed SST showed less effective forecast skill in the context of typhoon intensity because typhoon-induced SST changes were not accurately reflected during the simulations. SST is one of the most important factors for typhoon intensification processes because it provides energy in the form of latent and sensible heat fluxes. According to diverse typhoon properties such as size, intensity, and translation speed, typhoons can cool the SSTs around them by generally 5–6 °C, and up to 11 °C (Brand, 1971; Chiang et al. 2011; Wada et al. 2009). This occurs from vertical mixing and upwelling, and this cooler upper ocean environment suppresses typhoon intensification (Bender et al. 1993a, b; Chan et al. 2001). Therefore, the prescription of accurate SST variations may play an important role in typhoon forecasting. Park et al. (2022) examined the impacts of two SST datasets, that is, daily Optimum Interpolation Sea Surface Temperature (OISST) and hourly SST of HYbrid Coordinate Ocean Model (HYCOM) on the intensity and track forecast of two typhoons which successively hit South Korea in 2020. With relatively low temporal resolution, the OISST data did not effectively capture the SST changes during the landfall period compared to the HYCOM data (Fig. 16.6a). They also tested the sensitivity of typhoon forecasts to two SST datasets using the WRF model and showed that simulated typhoon intensities were significantly improved in the simulations with HYCOM data. Meanwhile, typhoon track forecast performances were similar in both runs. The experiment using the HYCOM SST data successfully reproduced the typhoon intensity and effective radius size during the landfall period, which was substantially overestimated in the experiments with the OISST data (Fig. 16.6b, c, d). This implies that the overall typhoon intensity and forecast performance during the landfall period can be improved when higher temporal-resolution SST data are used in the model boundary conditions. Their results have also highlighted the requirement of two-way air–sea interactions in typhoon forecasting by coupling the oceanic model with the atmospheric model. The impact of model resolution on typhoon forecasting is an important topic for improving typhoon forecasting using numerical models. Increasing the model resolution, particularly the horizontal resolution, may improve typhoon intensity forecasts because it affects the simulation of mesoscale features. As indicated by Chen et al. (2007), the horizontal resolution needs to be ~ 1 km to effectively resolve the core dynamics around the eye and eyewall of the TC. Davis et al. (2008) showed that the inner-core structure was sensitive to the model resolution, and the TC intensity forecast was further improved when the horizontal resolution increased to 1.33 km. However, a higher model resolution does not always increase the typhoon intensity because some features with higher resolution tend to weaken typhoons (Fierro et al. 2009). Increasing the horizontal resolution often enhances the simulated TC intensity, but there are relatively few impacts on the simulated TC tracks (Gentry and Lackmann 2010; Gopalakrishnan et al. 2011; Jin et al. 2014). Moon et al. (2021) also investigated the general impact of increasing the model resolution on typhoon forecasts using the WRF model. They showed that the WRF model with a coarser resolution of 12 km could not reproduce the intensification process, particularly for strong typhoons with a maximum intensity above 60 m s−1

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Fig. 16.6 a Time series of SST (°C) variations at the times when typhoon Haishen passed near the Tongyeong (34.4°N 128.2°E) stations. The OISST data are only provided at daily intervals. b Satellite infrared (IR) image and simulated outgoing longwave radiation (W m−2 , shading; OLR) in the c HY and d OI runs for typhoon Haishen at 00 UTC 6 September 2020. From Park et al. (2023). ©2023 Authors. Distributed under the CC BY 4.0 License

(Fig. 16.7). In contrast, the WRF model with a moving nesting domain of 4 km horizontal resolution more effectively predicted intensity forecasts for intense typhoons. They also showed that the sensitivity of the track forecast to the model resolution was relatively important for lower-latitude typhoons. Meanwhile, the track forecasts of typhoons moving to the mid-latitudes, which were primarily influenced by largescale features such as subtropical highs and mid-latitude troughs, were less sensitive to the model resolution.

16.2.4 Sensitivity of Typhoon Forecasting to Physics Parameterizations TC forecast performance is highly sensitive to the applied physics parameterization schemes. The choice of physical schemes, such as the planetary boundary layer (PBL), cumulus parameterization, and cloud microphysics schemes, is especially important in highly accurate TC forecasting. The PBL scheme can play an important role in the development and maintenance of a typhoon because it controls air–sea interactions with moist conditionally symmetrical neutral upward flow in the eyewall through the secondary circulation of a typhoon (Emanuel 1986). The effect of the PBL scheme on typhoon forecasts in East Asia has also been examined. Loh et al. (2011) investigated the sensitivity

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Fig. 16.7 Time series of mean maximum wind speed forecast (top) and mean cross-track biases (bottom) for TCs with three intensity categories (lifetime maximum intensity (LMI) < 60 m s−1 , 60 m s−1 < LMI < 75 m s−1 , and 75 m s−1 < LMI). From Moon et al. (2021). ©2021 Authors. Distributed under the CC BY 4.0 License

of Typhoon Vamei’s (2001) simulation to four different PBL schemes using the Pennsylvania State University (PSU)/National Center for Atmospheric Research (NCAR) mesoscale model version 5 (MM5). They found that the simulated TC intensity performance differed according to the choice of PBL schemes because the simulation of heat exchanges over the ocean and moisture in the PBL around the TC core depended on the PBL scheme. Kanada et al. (2012) demonstrated that the subgrid-scale vertical mixing length and vertical eddy diffusivity in PBL schemes substantially enhanced the TC intensity and development of the inner-core structure. Ming and Zhang (2016) showed that the surface exchange coefficients for enthalpy (Ck ) and momentum (Cd ) affected the intensity and structure of Typhoon Morakot (2009). Larger values of the Ck /Cd ratio tended to increase the intensity of typhoons. Coronel et al. (2016) also examined the impacts of surface drag and vertical mixing on the intensity and structure of Typhoon Megi and found that frictional perturbations affected low-level wind structures by inducing a gradient wind imbalance. Ruan et al. (2022) compared the performances of typhoon forecasts from local and nonlocal closure PBL schemes and showed that the intensity and structure of Typhoon Mangkhut (2018) during rapid intensification were more effectively reproduced by the local closure PBL scheme. This simulated a larger friction velocity and stronger surface latent and sensible heat fluxes related to a higher PBL height and enhanced vertical mixing.

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The convective parameterization scheme (CPS), which is directly related to convective processes and precipitation formation, can substantially affect typhoon forecasts. Research on the sensitivity of typhoon forecasting to CPS has predominantly been conducted using regional climate modeling with relatively low resolution. This is because deep convection around the typhoon core and the associated diabatic heating are mainly determined by the CPS owing to the coarse resolution. Sun et al. (2014a, b) simulated Typhoon Megi (2010) using two different cumulus parameterization schemes (CPS) in a regional climate model with a 20 km horizontal resolution. They showed that the TC track and intensity forecast performances were simulated differently in sensitivity simulations using two different CPS. Owing to the stratiform precipitation of the storm and strong anvil showers from the CPS, the WNPSH weakened, and large-scale steering flow became anomalously northward, leading to an unrealistic early recurvature of Typhoon Megi. This mechanism has resulted in different typhoon tracks by changing the simulated typhoon structure and its surrounding environment. Villafuerte et al. (2021) also emphasized that the choice of CPS resulted in a different strength of WNPSH and a different track forecast performance. In high-resolution numerical modeling, the cloud microphysics parameterization scheme (MPS), which describes the formation and growth of various water substance variables in clouds, can play an important role in typhoon forecasting by controlling the phase changes of hydrometeors within clouds. The latent heat released in the convective clouds within typhoons depends on microphysical processes, and it can facilitate a warm-core structure in the eye. This is essential for the development and maintenance of circulation within typhoons. The sensitivity of typhoon forecasts in East Asia to MPS has been extensively examined. Sun et al. (2015) simulated Typhoon Megi using four different MPS in the WRF model. They showed that the simulated track and intensity were sensitive to the choice of MPS because the intensity simulation could substantially affect the simulation of the WNPSH intensity, resulting in different track forecasts among the sensitivity experiments. Chan and Chan (2016) simulated six typhoons over the WNP with three different MPS in the WRF model and showed that the simulated TC intensity and size were sensitive to the choice of MPS because of the different amounts of diabatic heating released in the simulated typhoons. Park et al. (2020) investigated the impacts of two MPS, that is, simple and sophisticated schemes, on rapidly intensified typhoons over the WNP with westerly movement at low latitudes and poleward movement in the subtropics, using a high-resolution (2 km for the core region) WRF model. They found that the simulated typhoon intensity and inner-core structure were sensitive to MPS owing to the distinct hydrometeor species and their distributions with the schemes. The sensitivity of the simulated tracks to MPSs was greater for poleward-moving typhoons than for westward-moving typhoons. They examined the effect of the difference in typhoon intensity on simulated typhoon size and motion by comparing f- and β-plane experiments. For mid-latitude TCs, the sophisticated MPS improved the track and intensity prediction compared to the simple MPS. The sophisticated MPS effectively captured westward-shifted tracks during the rapid intensification process (Fig. 16.8). This can

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Fig. 16.8 Streamlines averaged at 300–850 hPa, TC motion vector (black vector), and steering flow vector (blue vector) in the experiments with a simple MPS (WSM3) and b sophisticated MPS (WSM6) for the northwestward moving TC CHABA at 0000 UTC 03 Oct 2016 (24-h forecast hour). Red and black lines indicate typhoon tracks of the best track and simulations, respectively, and the typhoon mark represents the TC location of the best track at the forecast hour. From Park et al. (2020). ©2020 American Geophysical Union. Used with permission

be attributed to the improved simulations of TC intensity, size, and the associated β-effect by sophisticated MPS. In contrast, the simple MPS underestimated these characteristics owing to low latent heat release. Therefore, the TC track moving northwestward was then shifted eastward. Consequently, their results imply that a sophisticated MPS is required to improve mid-latitude typhoon forecasts. In high-resolution typhoon modeling using nesting methods, convection related to spiral rainbands in the outer domains with coarser resolution is usually simulated by CPS. Meanwhile, deep convection around the eyewall within the innermost domain with higher resolution is explicitly resolved by MPS. Therefore, the impact of CPS and MPS can concurrently be significant in typhoon forecasts. Park et al. (2023) investigated the impacts of CPS and MPS on real-time forecasts of typhoons recently affecting South Korea using the WRF model, which had two domains with 12–4 km resolutions. They showed that there was a significant difference in the simulated typhoon track and intensity performances depending on the physics schemes. Overall, the track forecast and intensity prediction tended to be more sensitive to CPSs and MPSs, respectively (Fig. 16.9). This was because CPS affected the simulation of environmental conditions related to typhoon motion such as the subtropical high, whereas MPS determined the core dynamics associated with typhoon intensity including diabatic heating. Optimization of physical schemes for typhoon forecasting in East Asia is needed according to the model configuration, such as the model resolution and domain setting, because of the high sensitivity to physical schemes of typhoon activities.

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Fig. 16.9 Comparison of a track and b intensity spreads between the convective parameterization schemes (CPSs) and cloud microphysics parameterization schemes (MPSs) used in this study at each forecast hour for all simulated typhoon cases (blue: MPS, red: CPS). From Park et al. (2020). ©2023 American Geophysical Union. Used with permission

16.2.5 Future Directions for Typhoon Forecasting Although typhoon forecasts with numerical models have been improved owing to increasing computing resources and observation data, continuous efforts are still required. State-of-the-art observation data from GPS occultation, sail drones, dropsondes, and Doppler radars should be assimilated to improve typhoon forecasting. Typhoon forecasts can be substantially improved by the assimilation of all-sky radiance data, which reduces the uncertainties related to clouds by applying statistical methods or machine learning techniques. As computing resources advance, there is the potential to employ numerical models with a relatively high resolution that can explicitly resolve convection for typhoon forecasts. The moving nesting technique is widely used to increase the model resolution for simulating typhoon core regions. However, this method has a systematic problem related to lateral and lower boundary conditions. Therefore, it is necessary to use a convection-permitting model with a single domain rather than moving nested domains in typhoon forecasts. The optimization of physics schemes and the application of scale-aware physics schemes are needed as the model resolution for typhoon forecasts increases. Ensemble prediction using high-resolution regional models should be considered for advanced stochastic typhoon forecasts. Also, stochastic perturbation methods have been introduced in recent studies. Li et al. (2020) compared the forecast performances of the multi-physics approach together with the stochastic methods and showed that the probabilistic skills for typhoon forecasts could be somewhat improved by adding stochastic perturbations. Stanford et al. (2019) increased the sensitivity of simulated deep convection by adding a stochastic perturbation method to ice microphysics parameterizations. However, so far, few studies have found

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the impact of stochastic parameterization schemes on deep convection and TCs in detail. Therefore, it is needed to investigate the impact of stochastic parameterization schemes, particularly on typhoon forecasts in East Asia. Moreover, studies on future changes in typhoon activities over the WNP should be more actively conducted using regional climate models, which can explicitly resolve typhoons due to the finer model resolution.

16.3 Numerical Modeling for Heatwave Analysis and Forecasting 16.3.1 Investigation of Local-to-Large-Scale Factors for East Asia HWs Using Numerical Models East Asian HWs are predominantly driven by an anticyclonic anomaly from the western North Pacific to East Asia (Park and Schubert 1997; Xue-Zhao and Dao-yi 2002; Ding et al. 2009; Lee and Lee 2016; Yoon et al. 2018; Yoon et al. 2020). Other local-to-large-scale meteorological factors such as the Foehn effect from high mountain ranges (Takane and Kusaka 2011; Yoon et al. 2018) and teleconnection as a zonal/meridional planetary wave pattern (Choi et al. 2020; Hong et al. 2020; Kim et al. 2021) are being highlighted as other significant contributors to East Asian HWs. In these cases, numerical models can be used as useful tools to investigate the physical and dynamic mechanisms behind HW-related atmospheric conditions.

Local-Scale Factors The Foehn effect is the warming of the surface temperature on the lee side of a mountain due to descending air, and it can contribute to the intensification of HWs in these regions. It is traditionally believed to cause precipitation upwind of mountains. However, other mechanisms have been proposed that are not associated with rainfall on the windward side of the mountain using a numerical model and it has been suggested that major local-scale factors amplify HW events in East Asia (Lee 2003; Byun et al. 2006; Takane and Kusaka 2011; Yoon et al. 2018). Takane and Kusaka (2011) have determined the physical process based on the “Foehnlike” effect for an extremely high-temperature event in the Tokyo metropolitan area. Their investigation using a high-resolution WRF model found that Foehnlike wind, that is, diabatic heating with turbulent diffusion and sensible heat flux over the wind side had a more substantial impact on enhancing the HW event in the Tokyo metropolitan area than the traditional Foehn mechanism. Yoon et al. (2018) also conducted a numerical experiment to examine the impact of topography over the southeastern region of Korea during the 2015 HW event. They concluded that the experiment with a high mountain range simulated higher surface air temperatures

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over the analysis region than the experiment with decreased topography (Fig. 16.10). In line with the findings of Takane and Kusaka (2011), they also discovered a Foehnlike mechanism with flow blocking due to the stratified layer over the windward region during the southeastern Korean HW event.

Large-Scale Factors At a larger (planetary) scale, several climatic patterns such as Scandinavia (SCAND) and circumglobal teleconnection (CGT) patterns related to arctic-related climate indices such as the Atlantic Multi-decadal Oscillation, AMO; Arctic Oscillation, AO; North Atlantic Oscillation, and NAO have recently received attention (Lee and Lee 2016; Yeo et al. 2019; Choi et al. 2020; Yoon et al. 2020). These patterns play an important role in the development of HWs over East Asia and are characterized by a high-pressure system in the downstream region of the wave train. This anticyclonic anomaly leads to extremely warm conditions, producing clear skies, low cloudiness, diabatic heating with descending motion, and warm advection. Numerical models have been used to determine the origin of the teleconnection pattern associated with the East Asian HW. Choi et al. (2020) identified the drivers of SCAND teleconnection patterns. By reproducing the SCAND pattern by forcing upper-level transient vorticity and lowlevel diabatic heating over the North Atlantic and western Russia in the stationary wave model (Fig. 16.11), they found that the recent enhancement in the HW-related teleconnection pattern was driven by an increase in land–atmosphere interaction over Eurasia. Hong et al. (2020) represented the association between planetary waves originating from the North Atlantic and HWs over East Asia using the Geophysical Fluid Dynamics Laboratory (GFDL) atmospheric model (AM). By comparing the modeling results prescribing AMO-like SST anomalies to monthly climatological SST, they identified the development of a planetary wave with a downstream anticyclone anomaly over Northeast China. Kim et al. (2021) examined the thermal source of the meridional wave pattern, including the Pacific–Japan pattern, resulting in HW-related circulation over East Asia by using a linear baroclinic model.

16.3.2 Improvement of East Asia HW Forecasting Skills in Numerical Modeling In addition to exploring the physical or dynamic mechanisms of HWs, numerous challenges are being addressed to improve the HW forecasting skills of the numerical model. In this section, two major methods, that is, soil moisture initialization and air– sea coupling, used to improve East Asia HW modeling performance are introduced.

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Fig. 16.10 Surface air temperature difference (°C) between CTL and TOPO (shading) and 10-m horizontal wind vector (m s−1 ) in CTL (arrow) over domain 2 at a–c 02 LST and d–f 14 LST and the cross section of potential temperature (K; contour) and specific humidity (g kg−1 ; shading) with zonal and 100-fold vertical wind vector (m s−1 ; arrow) at g–i 02 LST and j–l 14 LST. The dates are 07/24, 08/04, and 08/10 in order from the left column of the figure. The black solid line in a–f indicates the city boundaries. CTL experiment indicates no change in topography, TOPO experiment indicates decreased topographic height over the southeastern region of Korea. From Yoon et al. (2018). ©2018 American Geophysical Union. Used with permission

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Fig. 16.11 a SCAND-like teleconnection pattern in the 200-hPa streamfunction anomalies (106 m2 s−1 ) simulated by the stationary wave model (SWM) forced by the idealized transient vorticity forcing over the Atlantic Ocean (green contours). b The stationary wave response in the 200-hPa streamfunction anomalies by SWM forced by the idealized diabatic heating (green contours) over western Russia. c The sum of a and b represents the amplification of the SCANDlike teleconnection pattern by diabatic heating in western Russia. From Choi et al. (2020). ©2020 Authors. Distributed under the CC BY 4.0 License

Impact of Soil Moisture Initialization on East Asia HW Simulation Extremely high-temperature events can be amplified by dry soil-induced land–atmosphere interactions because the surface energy is predominantly transferred to the atmosphere as a sensible heat flux rather than the latent heat flux from the lack of soil moisture (Seneviratne et al. 2010). An association has been observed between soil moisture deficit and high-temperature anomalies among various HWs (Fischer et al. 2007; Hirschi et al. 2011; Miralles et al. 2014, 2019; Saini et al. 2016; Seo et al. 2019, 2020; Zhang et al. 2020). The frequency of compound dry–hot extremes over Northeast Asia increases with drying surface conditions and is expected to maintain this trend in the future (Erdenebat and Sato 2016; Sato and Nakamura 2019; Kong et al. 2020; Zhang et al. 2020; Ha et al. 2022). The role of land–atmosphere interaction in East Asian HW simulation has also received attention as a part of improving

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the simulation performance of numerical models (Zeng et al. 2014; Erdenebat and Sato 2018; Wang et al. 2019a, b; Seo et al. 2020; Yoon et al. 2023). The impact of the initial soil moisture conditions on the East Asian HW was explored by adjusting the soil moisture. Zeng et al. (2014) examined the response of high-temperature weather in 2003 to initial soil moisture conditions using the WRF model. They controlled the initial soil moisture conditions for four groups of simulations from – 50% to + 50% and compared the 24 h integration results to the control run, which used the original soil moisture value. The results showed that dry–hot HWs over the analysis region could be intensified as the initial soil moisture conditions became drier (i.e., – 50%) by affecting the decrease in latent heat flux from the surface to the atmosphere. Wang et al. (2019b) also conducted a sensitivity test to examine the impact of the initial soil moisture conditions on three severe HW cases over Eastern China using the WRF model. Consistent with the results of Zeng et al. (2014), the decline in initial soil moisture led to favorable conditions for severe HWs, including anticyclonic anomalies (Fig. 16.12). Beyond impact assessment, the importance of accurate representation of land– atmosphere interaction in East Asia HW simulation has been emphasized in several studies for improving the forecasting (hindcast) skills of the numerical model (Erdenebat and Sato 2018; Seo et al. 2020; Yoon et al. 2023). Erdenebat and Sato (2018) showed that the WRF model includes soil moisture–atmosphere interaction to simulate a more realistic heat event in 2002 over Northeast Eurasia than the experiment without the interaction, that is, using prescribed satellite-based soil moisture. The simulation performance of the heat-wave-favorable circulation patterns and surface air temperature also improved.

Fig. 16.12 Average daily maximum surface air temperature (unit: °C) during the (A), (G), (M) three HWs in the observation, and (B)–(F), (H)–(L), (N)–(R) in five sensitivity simulations initialized with different initial soil moisture. The green box indicates the region (18°–38°N, 105°–123°E). Results show the response of extreme heat events according to the initial soil moisture conditions. From Wang et al. (2019b). ©2019 Authors. Distributed under the CC BY 4.0 License

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Given that most of the recent numerical models can integrate the land–atmosphere feedback process by coupling the land surface model to the atmospheric model, recent studies have aimed to improve HW simulation performance by initializing representative soil moisture conditions. In this context, soil moisture fields have been produced from a stand-alone land surface model by forcing meteorological reanalysis and observation data (Rodell et al. 2004; Koster et al. 2004; Kumar et al. 2008; Santanello Jr et al. 2019; Seo et al. 2019) and prescribed into the numerical model. Regarding the East Asian HW, Seo et al. (2020) produced spin-upped soil moisture conditions using the offline Joint UK Land Environment Simulator (JULES) land surface model forced by the Japanese 55-year Reanalysis (JRA-55) and prescribed the soil moisture data into the Global Seasonal Forecast System version 5 (GloSea5) model initial field. They developed improved ensemble seasonal forecasting skills for large-scale atmospheric conditions including wave-like tri-pole structure over the Eurasian continent, which is strongly related to the 2016 Eurasian HW, by comparing experimental results from employing initialized and climatological soil moisture fields (Fig. 16.13). In addition to the seasonal time scale, Yoon et al. (2023) also examined the impact of soil moisture initialization on the simulated regional climate during the three weeks (i.e., medium-range time scale) of the 2016 Northeast Asia HW by using the WRF model. They obtained advanced soil moisture estimates by assimilating Soil Moisture Active Passive (SMAP) satellite retrievals in the Noah land surface model. The WRF experiment initialized by the assimilated soil moisture product exhibited the observed surface air temperature and 500 hPa geopotential height over Northeast Asia compared to the results from the experiment initialized by the NCEP Final Analysis (FNL) data. In Week 1, the soil moisture initialization experiment simulated warmer surface air than that of the non-initialized experiment, which was induced by the negative anomaly of the latent heat flux over Mongolia. The mid-level geopotential height became stronger and spatially expanded in response to the thermal low induced by the warmer surface air temperature, and further increased during Weeks 2 and 3.

Impact of Air–Sea Coupling on East Asia HW Simulation Given that most areas of East Asia are located in the monsoonal region, East Asia HW-related atmospheric patterns such as the western North Pacific subtropical high, can be affected by the condition of the ocean surface (Kim and Hong 2010; Cha et al. 2016). Recent regional modeling studies have suggested that air–sea coupling has an advantage over a corresponding atmosphere-only model in simulating HWrelated circulation patterns by including physical and dynamic interactions between the atmosphere and ocean (Li et al. 2018; Kim et al. 2020; Yoon 2022). Li et al. (2018) compared the simulation results from the uncoupled and coupled regional models and showed improved HW simulation performance in the air–sea coupled case. They categorized the HW days into two types, that is, Foehn favorable and no-Foehn HWs, and presented a reducing bias of lower-to-upper-level circulation patterns in the air–sea coupled model. In the uncoupled simulation, barotropic

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Fig. 16.13 Spatial patterns of surface air temperature and upper troposphere height from the observation and model simulations during the HW period. Observed anomaly map of a surface air temperature (unit is °C) and b 300 hPa eddy height (unit is m) during the 2016 Eurasia HW active period (25 July–25 August). The anomaly map of Exp4 c surface air temperature and d 300 hPa eddy height compared to 20 years (1991–2010) GloSea5 hindcast. Difference maps of these variables for e, f Exp1, g, h Exp2, and i, j Exp3 compared to Exp4. The dotted area in e–j represents statistical significance at the 95% level from the student’s t-test. From Exp1 to Exp3, one of the sets of initial conditions was replaced by the model climatology, such as for soil moisture (Exp1), ocean (Exp2), and sea ice (Exp3), respectively. Exp4 was initialized with all anomalous observed states in July 2016. The impact of soil moisture initialization is shown in a–f. From Seo et al. (2020). ©2020 Authors. Distributed under the CC BY 4.0 License

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anticyclonic bias prevailed over Northern China on Foehn favorable and no-Foehn heat-wave days, and the northwesterly in the lower troposphere, which was a major dynamic driver of Foehn favorable HWs, was not strong. However, the biases in uncoupled experiments were substantially reduced as the spatial patterns of the western North Pacific subtropical high and low-level monsoon flow over East Asia improved in the coupled simulation (Fig. 16.14). Kim et al. (2020) conducted an air–sea coupled modeling experiment adapting the Unified Model (UM) system to improve the simulation performance of Kamchatka blocking, which has been highlighted as one of the main synoptic factors for the 2016 East Asia HW (Yeh et al. 2018; Yoon et al. 2021). They confirmed that the air–sea coupled experiment produced an improved representation of the blocking high over the Kamchatka Peninsula within a 10-day forecast period. Yoon (2022) also reported an improvement in simulation performance for Kamchatka blocking in the 2016 East Asia HW event when an atmosphere–ocean coupled modeling system was used compared to the atmosphere-only model. The analysis showed an improved air–sea mechanism in the coupled experiment by suppressing unrealistic positive feedback

Fig. 16.14 Observed composite horizontal wind anomalies for Foehn favorable HW days in Northern China: a 250 hPa, b 500 hPa, and c 850 hPa (units: m s−1 ). The yellow shaded areas are statistically significant at the 95% confidence level according to the student’s t-test. For the horizontal winds, either the zonal or meridional wind anomaly is significant. d–f and g–i correspond to a–c but for the uncoupled simulation and the coupled simulation, respectively. The blue lines in figures c, f, and i denote the vertical section from the mountains to the plains. Results show a representative northwesterly in the coupled experiment. From Li et al. (2018). ©2018 Springer Nature. Used with permission

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between the atmosphere and ocean, that is, development of an unrealistic trough over the western North Pacific induced by the imbalance between sea surface temperature and atmospheric variables related to evaporation.

16.3.3 Future Projection of East Asia HWs Using Numerical Models There has been a recent increase in the frequency and damage caused by HWs from global climate change (Meehl and Tebaldi 2004; IPCC 2013; Coumou et al. 2013; Perkins-Kirkpatrick and Gibson 2017). Given that East Asia has recently experienced a series of extreme HW events (Nakai et al. 1999; Kysely and Kim 2009; Sun et al. 2014a, b), attention has been paid to future projections of East Asian HWs. Therefore, numerical models have been extensively used to examine the changes in the properties of East Asian HWs under future climate scenarios (Sun et al. 2014a, b; Wang et al. 2018; Im et al. 2019; Wang et al. 2019a; Zhou et al. 2019; Min et al. 2020). According to Sun et al. (2014a, b), the mean surface air temperature over Eastern China has increased by 0.82 °C since the 1950s, with the five hottest summers, including 2013, all having occurred in the twenty-first century. They emphasized that the human contribution has caused a more than 60-fold increase in the likelihood of the 2013 case than the early 1950s and projected that more frequent HW cases will occur in the future, with 50% of summers being hotter than the 2013 summer in two decades, by using Coupled Model Intercomparison Project Phase 5 (CMIP5) model simulation under Representative Concentration Pathway (RCP) 4.5 emission scenario (Fig. 16.15). Wang et al. (2019a, b) also showed a future projection of HWs over China under global warming scenarios. In this study, future projections of quantitative indices for Chinese HW events based on HW frequency, duration, magnitude, intensity, accumulated occurrence days, and severity were examined by downscaling projection results from four CMIP5 models. According to their analysis, more areas will experience more frequent, stronger, and longer-lasting HWs in the future (Fig. 16.16). There were more significant increasing trends in the indices in the future than in the present, indicating that HWs will be stronger and more rapid in the future. They explained that the intensification of HWs could be largely related to changes in high-pressure systems, such as the western North Pacific tropical high. Im et al. (2019) integrated regional climate models under RCP scenarios and implied that HWs such as the summer of 2018 in South Korea can be statistically rare in the current climate but will become more normal if the global average temperature is allowed to increase by 3 °C. They emphasized that the heat stress index, that is, the wet bulb globe temperature, was projected to intensify the risks to a level that has never been observed before in the present climate (Fig. 16.17).

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Fig. 16.15 Time evolution of the frequency of summer temperature anomalies above 1.1 °C, relative to the 1955–1984 mean, in the reconstructed observations (1955–2013) and in the observationally constrained projections (2014–2072) under RCP4.5 (plus) and RCP8.5 (cross) emission scenarios (left-hand scale). The solid smooth curves are local regression fitting. The dashed curves represent projected ensemble mean temperature changes under the relevant emission scenarios (right-hand scale) and are shown here for reference. Results for RCP4.5 and RCP8.5 are represented by red and green, respectively. From Sun et al. (2014a, b). ©2014 Springer Nature. Used with permission

Fig. 16.16 Spatial distributions of future changes in a ratio for a HWN, b HWDU, c HWM, d HWI, e HWF, and f HWTI. Please refer to Wang et al. (2019a) for detailed definitions of each index. From Wang et al. (2019a). ©2019 Springer Nature. Used with permission

16.3.4 Future Directions for HW Forecasting As HW events are associated with various spatiotemporal factors, integrated approaches to understand the mechanism and development of HWs are required. The

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Fig. 16.17 Relationships among daily mean wet bulb globe temperature (WBGT, °C), daily mean temperature (°C), and daily mean relative humidity (%, gray dashed line) at 56 stations derived from climatological and 2018 observations and four projections under 0.48 °C (i.e., Reference), 2 °C and 3 °C global warming. Individual marks correspond to the “median” value at each station, which is obtained from the distribution for July and August. The colored horizontal lines indicate the risk level categorized by WBGT (Moderate: WBGT > 26, High: WBGT > 28, Extreme: WBGT > 32), which is sourced from Willett and Sherwood (2012). From Im et al. (2019). ©2019 Authors. Distributed under the CC BY 4.0 License

development of a global nested model with variable resolution and unified configuration is expected to help unveil the dynamic and physical properties of HWs across various spatiotemporal scales. The importance of soil moisture initialization in improving the simulation performance of land–atmosphere interactions in East Asia HW modeling has been highlighted. As various national meteorological institutes operate soil moisture initialization systems, further challenges are required to produce more accurate initial soil moisture fields with higher resolution, while the resolution of many numerical weather prediction models is becoming finer. Recent studies have focused on the correction or downscaling of soil moisture observations, including in-situ and satellite retrievals, using advanced machine learning techniques. Although various studies have implicated the necessity of air–sea coupling in East Asia HW simulation, there is still room for improving the forecast skill of extreme temperature events because of the insufficient representation of SST in the oceanic model (Kim et al. 2020). Given that it can be closely related to the prescription of the initial SST (Seo et al. 2020), more challenges are needed to produce an accurate and fine initial SST field. SST data assimilation and the effect of river discharge were also considered to improve the quality of SST initialization.

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Chapter 17

Conditional Nonlinear Optimal Perturbation: Applications to Ensemble Forecasting of High-Impact Weather Systems Wansuo Duan, Lichao Yang, Zhizhen Xu, and Jing Chen

Abstract The conditional nonlinear optimal perturbation (CNOP) method, which includes CNOP-I for identifying the optimally growing initial perturbation, CNOP-P for revealing the most sensitive parameters, CNOP-B for disclosing the boundary uncertainty that exerts the largest effect on forecasts, and CNOP-F for exploring the combined effect of kinds of model errors, is introduced. Their applications to the ensemble forecasting of tropical cyclone and convectional scale weather systems are reviewed to show the usefulness of CNOP-I, -P, and -F in estimating the initial error effect, model parametric error effect, and even the combined effect of kinds of model errors, respectively. The future outlook and prospects are also provided. Keywords Ensemble forecasting · Nonlinear optimal perturbation · Uncertainty · Tropical cyclone · Convectional scale weather systems

W. Duan LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China e-mail: [email protected] L. Yang (B) College of Resource Environment and Tourism, Capital Normal University, Beijing, China e-mail: [email protected] Z. Xu · J. Chen CMA Earth System Modeling and Prediction Centre, Beijing, China e-mail: [email protected] J. Chen e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_17

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17.1 Introduction Ensemble forecasting is performed to evaluate forecasting uncertainties. Ensemble forecasting is often implemented by superimposing a group of mutually independent initial perturbations on the initial analysis of the control forecast to estimate the initial uncertainties and then the associated forecasting uncertainties (Leith 1974). Ensemble forecasting provides the ensemble mean forecasting results of concerned weather and climate events, the ensemble mean forecast error quantified by the ensemble spread, and probabilistic information about the occurrence of concerned events (Buizza et al. 2005; Bowler 2006; Leutbecher and Palmer 2008; Buckingham et al. 2010). Due to the diversity and usefulness of ensemble forecast products, ensemble forecasting is an irreplaceable method in numerical predictions. The World Meteorological Organization (WMO) has treated ensemble forecasting as one of the main development strategies of numerical predictions. The traditional ensemble forecast, as introduced above, is applied to address the effect of initial uncertainties. Determining what kind of initial perturbations are more beneficial for estimating initial uncertainties and acquiring higher forecast skill is the essential issue of ensemble forecasting. Actually, the ensemble forecasting members are generated to neutralize the errors of the control forecasts and to make the members better characterize the true state. Since the errors of the control forecast often grow rapidly with time due to the instability of atmospheric and/ or oceanic motions, a group of rapidly growing initial perturbations are expected to superimpose on the initial analysis of the control run to neutralize the forecast error growth. Thus, only rapidly growing initial perturbations can help improve the ensemble forecasting skill (Mureau et al. 1993; Toth and Kalnay 1993, 1997). Various approaches have been introduced to generate the growing-type initial perturbations for ensemble forecasting, and some of them have gained great success in operational weather forecasting and climate predictions. Toth and Kalnay (1993) developed the breeding method to identify growing-type initial perturbations, i.e., the bred vectors (BVs), and applied it to the ensemble forecasting system at the National Centers for Environmental Prediction (NCEP) in 1992. The European Centre for MediumRange Weather Forecasts (ECMWF) introduced an alternative method of singular vectors (SVs; Mureau et al. 1993; Buizza and Palmer 1995; Molteni et al. 1996) and produced ensemble forecasts with great success. Ensemble forecasting, as mentioned above, requires growing-type initial perturbations superimposed on control forecasts to achieve higher forecasting skill; that is, it should be ensured that such initial perturbations grow rapidly during the forecast period. Notably, SVs possess clear dynamics to yield growing-type initial perturbations during the forecast period (Du et al. 2018). However, their fatal shortcoming is that they cannot cope with the impact of nonlinear physical processes on the amplification of the initial perturbations (Anderson 1997; Hamill et al. 2000; Mu 2000). To overcome this limitation, Mu et al. (2003) proposed the conditional nonlinear optimal perturbation (CNOP), which is an extension of the leading SV in the nonlinear regime. The CNOP fully considers the influence of

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nonlinear physical processes and represents the optimally growing initial perturbation in the nonlinear regime. Mu and Jiang (2008b) replaced the leading SV with the CNOP to produce ensemble initial perturbations and demonstrated higher forecast skills than SVs (also refer to Huo and Duan 2019; Zhou et al. 2021). To take into account fully nonlinear impacts in the development of the initial perturbations, Duan and Huo (2016) further formulated the orthogonal CNOPs (O-CNOPs) method to produce mutually independent nonlinear optimal initial perturbations for ensemble forecasting. The O-CNOPs have been shown to display a higher ensemble forecast skill than SVs and BVs and a more reasonable ensemble spread for estimating the uncertainty in a hierarchy of models (Duan and Huo 2016; Huo et al. 2019; Wang and Duan 2019; Wang 2021; Zhang et al. 2023a). The ensemble forecasting methods mentioned above focus on addressing the initial uncertainty effects and are only reasonable under a perfect model assumption. For the model error effect, it is much difficult to estimate its uncertainties. Despite this disadvantage, some methods have been designed to address the corresponding forecasting uncertainties. For example, the ECMWF proposed a stochastically perturbed parameterization tendency scheme (SPPT; Buizza et al. 1999) and stochastic kinetic energy backscatter scheme (SKEB; Shutts 2005), leading to important improvements in the ensemble forecast skill (Du et al. 2018; also refer to the special issue, Buizza 2019). Hou et al. (2006) also developed a stochastic total tendency perturbation scheme (STTP) to emulate model uncertainties in the NCEP global ensemble forecasting system in February 2010 (also refer to Hou et al. 2008, 2010). As argued above, the ensemble forecasting system also requires growing-type perturbations to account for the unstable growth of forecast errors. However, the randomness of these model perturbation methods limits their ability to fully capture the rapid growth behavior of forecast errors caused by model errors. To obtain the rapidly growing model perturbations, Barkmeijer et al. (2003) proposed using a forcing singular vector (FSV) closely related to the SVs, which represents a rapidly growing constant tendency perturbation in a linear framework. This constant tendency perturbation describes the combined effects of the model systematic errors and parts of state-dependent model errors that are not explicitly described in the model equations (Feng and Duan 2013). To obtain a higher forecasting level, Duan and Zhou (2013) proposed approaching this problem by using the nonlinear forcing singular vector (NFSV). The NFSV is the tendency perturbation that implants the full nonlinear effect and makes the forecast deviate from the reference state more significantly. Relative to the CNOP method mentioned above, Wang et al. (2020b) also referred to the NFSV as CNOP-F, a special case of the CNOP, particularly for addressing the model error effect. If the NFSV is employed in an ensemble forecasting framework, it could better encompass the truth and provide more reliable ensemble members. To achieve this purpose, Duan et al. (2022a) proposed a new approach based on a set of orthogonal NFSVs (O-NFSVs), following the idea of O-CNOPs developed in Duan and Huo (2016). The O-NFSVs provide mutually independent model tendency perturbations that enable the description of the forecast uncertainties caused by model errors. Furthermore, Zhang et al. (2023b) are trying to apply O-NFSVs to yield model perturbations to imitate the model uncertainties responsible for tropical cyclone (TC)

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forecasts by using the realistic Weather Research and Forecast (WRF) model. Preliminary results showed the usefulness of O-NFSVs in offsetting the model error effect on TC forecasts. To address the inevitable effects of both initial errors and model errors in numerical forecasts, Duan et al. (2022a) further developed C-NFSVs to combine all these uncertainty effects, which particularly consider the effect of initial and model error interactions and generalize the original NFSV only for measuring the model error effect, finally proposing a novel ensemble forecasting method. Although there have been ensemble forecasting systems that consider both initial error effects and model error effects (e.g., Buizza et al. 1999; Hou et al. 2010), they were built by superimposing the independent initial perturbations (such as SVs, BVs, or others) and the model tendency perturbations (e.g., SPPT or STTP). To date, no attention has been given to the dynamically coordinated growth of the initial and model perturbations, which may limit the skill of ensemble forecasts, and C-NFSVs may compensate for this gap. In this chapter, we would summarize the advances in ensemble forecasting with respect to the implementation of the newly developed CNOP method and its applications to high-impact weather system forecasting. The subsequent section will introduce the idea of the CNOP method, and then Sect. 17.3 presents the applications to ensemble forecasting studies, especially for tropical cyclone and convectional scale weather systems. In Sect. 17.4, a novel ensemble forecasting method, C-NFSVs, to estimate the forecast uncertainties caused by both initial errors and model errors is introduced, and its special case, the O-NFSVs is described, accompanied by its applications to TC forecasts. Finally, a summary and prospect are provided in Sect. 17.5.

17.2 Conditional Nonlinear Optimal Perturbation Since Mu et al. (2003) proposed the CNOP method (also refer to Mu and Duan 2003), it has been extended from the original CNOP representing the optimally growing initial errors (for convenience, hereafter CNOP-I; Mu et al. 2003; Mu et al. 2010) to additional CNOP-P for addressing the influences of optimally growing model parametric errors (Mu et al. 2010), CNOP-B for disclosing the boundary uncertainties that have the largest effect on forecasts (Wang and Mu 2015), and CNOP-F [i.e., the nonlinear forcing singular vector proposed in Duan and Zhou (2013)] for exploring the combined effect of various model errors. This section focuses on introducing the ideas of CNOP-I, -P, and -F, which have been applied in ensemble forecasting studies. The specifics are presented as follows. The dynamic equations responsible for atmospheric and oceanic motions are generally written as a nonlinear partial differential equation (Eq. (17.1)).

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⎧ ⎨ ∂U = F(U, P) ∂t ⎩ U |t=0 = U0

in Ω × [0, T ],

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(17.1)

where U (x, t) = [U1 (x, t), U2 (x, t), . . . , Un (x, t)] is the state vector, U0 is its initial value, F is the nonlinear differential operator, x = (x1 , x2 , . . . , xn ), t ≤ T (0 < T < +∞) is the time, P = (P1 , P2 , ..., Pm ) are model parameters, Pi represents one model parameter independent of time t, and Ω is a domain in the n-dimensional Euclidean space Rn . Since a forecast is often contaminated by initial and model errors, Eq. (17.1) is rewritten as Eq. (17.2) to represent forecast model equations consisting of both initial perturbation u 0 and parametric perturbation p. ⎧ ⎨ ∂(U + u) = F(U + u, P + p) ∂t ⎩ U + u|t=0 = U0 +u 0

in Ω × [0, T ],

(17.2)

where u represents the departure from the reference state U caused by the combined effects of initial and parametric perturbations. In this circumstance, when a nonlinear optimization problem is defined as in Eq. (17.3), its solution (u ∗0 , p ∗ ) represents the optimal combined mode of initial and parametric perturbations that satisfies a certain constraint and results in the largest departure from the reference state at time τ . Mu et al. (2010) referred to this combined mode as CNOP. J (u ∗0 , p ∗ ) =

max

(u 0 , p)∈Cu 0 , f

||u(τ )||,

(17.3)

where C confines the scope of the initial perturbation u 0 and parametric perturbation p. The CNOP has two special cases: the first case is CNOP-I, proposed by Mu et al. (2003), which is used to reveal the optimally growing initial perturbation when the parametric perturbation p = 0, while the second case is CNOP-P, which causes the largest departure from the reference state when the initial perturbation disappears (Mu et al. 2010). If one rewrites Eq. (17.2) as Eq. (17.4), its resultant forecast can be understood as being influenced by the combined effect of the initial error and the model errors contained in the total tendency. F˜ associated with the uncertainties in the sub-grid process parameterization, the external forcing and the stochastic noises, and other kinds of model uncertainties. ⎧ ⎨ ∂(U + u) = F(U ˜ + u) ∂t in Ω × [0, T ]. (17.4) ⎩ U + u|t=0 = U0 +u 0 If the total tendency F˜ is rewritten into two terms F 0 and f and F 0 represents the accurate tendency, then the term f represents the total tendency error. It is obvious that the tendency error f is composed of different kinds of model errors. In this sense,

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Eq. (17.4) can be expressed as Eq. (17.5). ⎧ ⎨ ∂(U + u) = F 0 (U + u) + f (x, t) ∂t ⎩ U + u|t=0 = U0 +u 0

in Ω × [0, T ].

(17.5)

Then, which tendency error will cause the largest forecast error at the forecast time when the initial errors are neglected? Eq. (17.6) would produce such optimal tendency error, or more generally, optimal tendency perturbation f ∗ . J ( f ∗ ) = max ||u(τ )||. f ∈C f

(17.6)

This optimal tendency perturbation is the nonlinear forcing singular vector (NFSV) proposed by Duan and Zhou (2013). Relative to the CNOP, Wang et al. (2020b) took the NFSV as a special case of the CNOP and denoted it as CNOP-F, particularly for exploring the combined effect of different kinds of model errors. Thus, a family of CNOPs has been achieved, including CNOP-I, -P, -F introduced above and CNOP-B formulated for exploring the boundary condition error that has the largest effect on the forecasting results by Wang et al. (2020b). All these perturbations fully considered the effects of nonlinear physical processes and have been shown to represent the optimally growing mode in their respective scenarios. One can search for the CNOPs by using existing optimization solvers such as Spectral Projected Gradient 2 (SPG2; Birgin et al. 2000) or Limited memory Broyden– Fletcher–Goldfarb–Shanno for bound-constrained optimization (LBFGS-B; Liu and Nocedal 1989) according to the descending direction provided by the gradients of relevant cost functions. Notably, some intelligent algorithms, such as particle swarm optimization (PSO) and genetic algorithms, have emerged to solve similar optimization problems. These algorithms do not calculate the gradient and may be applicable to models with different complexities. The CNOPs have been widely applied to reveal the sensitivity and uncertainties of atmospheric and oceanic motions and to address associated problems of target observations, data assimilation and ensemble forecasting of high-impact weather and climate events, such as TCs, atmospheric blocking, El Niño-Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), atmospheric environmental heavy air pollution and oceanic mesoscale eddies (Duan et al. 2022b). In this chapter, we would summarize the advances in ensemble forecasting studies for high-impact weather systems.

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17.3 Applications to Ensemble Forecasting for High-Impact Weather Systems In the applications of CNOPs, CNOP-I was applied to ensemble forecasting for addressing effect of initial uncertainties, and O-CNOPs were proposed to produce mutually independent ensemble initial perturbations as requested by ensemble forecasting (refer to the introduction; Duan and Huo 2016); subsequently, the O-CNOPs were applied to forecast TC tracks and achieved higher forecasting skills than the BVs and SVs methods (Huo and Duan 2019; Huo et al. 2019). For the model error effect, the CNOP-P, which, as introduced in Sect. 17.2, solves the optimal parametric perturbation, was employed in the ensemble forecasting of convective-scale weather systems based on its recognized sensitivity to parameter uncertainties (Wang et al. 2020a). Furthermore, considering that CNOP-P only accounts for the effect of model parameter errors and other kinds of model errors and that their interactions also substantially disturb weather and climate predictions, Xu et al. (2022a) adopted the NFSV [also referred to as CNOP-F in Wang et al. (2020b)] to measure the combined effect of various model errors to explore ensemble forecasting in convective-scale weather systems [also refer to Xu et al. 2022b]. Both CNOP-P and CNOP-F achieved much higher forecasting skills than the operational use of SPPT. In this section, we will provide a thorough overview of all CNOP applications to ensemble forecasts of high-impact weather systems.

17.3.1 Forecasts of Tropical Cyclone Events Associated with the Initial Error Effect For ensemble forecasting, to consider the effect of nonlinearity on ensemble initial perturbations, Mu and Jiang (2008a, b) introduced the CNOP method to SV ensemble forecasting by replacing the leading SV with the CNOP (also refer to Jiang and Mu 2009) and attempted to improve the related ensemble prediction skill. However, such an approach still involves linear approximation because nonleading SVs still have the role of ensemble initial perturbations. Inspired by this limitation, Duan and Huo (2016) developed O-CNOPs based on CNOP-I by applying Eq. (17.1). || || J (u ∗0 j ) = max ||u j,τ ||, u0 j ∈Cu 0 j

(17.7)

where Cu 0 j =

u0 j

|| || u||0 j ∈ Rn ||u 0 j || ≤ δ , j = 1 || , ∈ Rn ||u 0 j || ≤ δ, u 0 j ⊥Cu 0k , k = 1, . . . , j − 1 , j > 1

(17.8)

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Cu 0 j is one subspace of the whole phase space, Rn is the n-dimensional Euclidean space, “⊥”|| is the || orthogonality of vector spaces, u 0 j is the initial perturbation in Cu 0 j , and ||u 0 j || ≤ δ is the constraint condition (δ is a positive constant); then, u ∗0 j is the j-th CNOP-I. According to Eqs. (17.7) and (17.8), the first CNOP-I (i.e., u ∗01 ) possesses the largest nonlinear evolution in the first subspace, i.e., the whole space, and the j-th CNOP-I (i.e., u ∗0 j ) possesses the largest nonlinear evolution in the subspace orthogonal to the j − 1 CNOP-Is (i.e., u ∗01 , u ∗02 , . . . , u ∗0 j−1 ). These CNOP-Is constitute the O-CNOPs. The O-CNOPs are all derived from nonlinear model and fully consider the effect of nonlinearity (Duan and Huo 2016). Duan and Huo (2016) first used the famous Lorenz-96 model (Lorenz 1996) to test the dynamics of O-CNOPs. They found that when the initial analysis errors are fast-growing, the ensemble forecasts generated by O-CNOPs perform much more skillfully; however, for the slowly growing initial analysis errors, the ensemble forecasts generated by O-CNOPs achieve almost the same forecast skill as those generated by SVs when the ensemble initial perturbations are sufficiently small, whereas the ensemble forecasts generated by SVs possess higher skill when the ensemble initial perturbations are much larger. The authors also showed that the O-CNOPs are more applicable than the SVs for achieving much higher ensemble forecast skill of extreme events. In particular, the ensemble forecasts generated by the O-CNOPs require a very small number of ensemble members to achieve high forecast skills. Therefore, the O-CNOPs may provide another useful technique to generate initial perturbations for ensemble forecasting. Huo et al. (2019) further applied the O-CNOPs to the realistic Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) FifthGeneration Mesoscale Model (MM5; Dudhia 1993; Grell et al. 1994) for the ensemble forecasts of five TC tracks; furthermore, they made a thorough skill comparison with the SVs since they present different patterns from O-CNOPs [see Fig. 17.1, for the STY Matsa (2005)]. The results showed that the ensemble members generated by the O-CNOPs present large spreads but tend to be located on the two sides of real TC tracks and show agreement between ensemble spreads and ensemble mean forecast errors for TC tracks. This finding indicates that these members generated by the O-CNOPs are more feasible to reveal forecast uncertainties of TC tracks than SVs in terms of these TCs. The results also illustrated that the O-CNOPs of smaller amplitudes are more reasonable to construct the ensemble members for short lead–time forecasts but that those of larger amplitudes should be utilized for longer lead–time forecasts due to the stronger effects of nonlinearities. In particular, Huo and Duan (2019) compared O-CNOPs to the ensemble strategy of replacing the leading SV with the first CNOP-I (hereafter CNOP + SVs), as in Mu and Jiang (2008b), in an attempt to reveal the importance of the nonlinear effect in yielding ensemble initial perturbations. The authors showed that the CNOP + SV ensemble strategy is not necessary to produce greater ensemble forecast skill than that of the SVs, but it is certain that the O-CNOPs are more likely to cause much higher ensemble forecasting skill for TC tracks. These results indicate that the inclusion of fully nonlinear effects on ensemble initial perturbations enhances the ensemble forecasting skill for TC tracks.

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Fig. 17.1 Spatial structures of the temperature (shaded) and wind components (vectors) of the first five O-CNOPs and SVs for the STY Matsa (2005) at the level σ = 0.975, which were used to produce the ensemble perturbations. The columns list the structures in sequence, from the first to the fifth. From Huo and Duan (2019). ©2019 Springer Nature Publisher. Used with permission

With the more advanced WRF model, Zhang et al. (2023a) predicted another twelve strong TC cases by using the O-CNOPs ensemble forecasting method, and as expected, obtained much higher ensemble forecasting skill compared with the SVs, BVs, and random perturbations (RPs) methods (Fig. 17.2). In particular, the authors demonstrated that the ensemble members generated by the O-CNOPs are more likely than those made by BVs, SVs, and RPs to reproduce the tracks of unusual TCs, such as the sharp northward-turning track of Megi (1013) and the counterclockwise loop track of Tembin (1214). Zhang et al. (2023a) also showed that when the WRF was compared with MM5, its resultant ensemble forecasts made by the O-CNOPs still significantly increased the forecasting skill of the TC tracks in the control forecasts, although the control forecasts possessed a higher skill than MM5, while those generated by SVs and BVs only slightly improved it or became much worse. That is to say, the SVs and BVs are less functional in improving the track forecasting skill in the much more advanced WRF model for the twelve selected TCs. Based on the above findings, O-CNOPs are shown to be useful in estimating initial uncertainties and then yielding much higher ensemble forecasting skill from the realistic MM5 to the advanced WRF model for TC track forecasting. However, the results are still derived from a small number of TC cases and therefore are only indicative. Despite this finding, the results have made us confident in validating the usefulness by using more TC cases, even to apply O-CNOPs to the real-time forecasts of TCs. Other high-impact weather systems, even high-impact climate events, should also be used to investigate the effectiveness of O-CNOPs. Then, operational suggestions can be provided.

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Fig. 17.2 a1 Track errors (solid lines) at different forecast times for the control forecast and ensemble mean forecasts averaged for twelve selected TCs and the corresponding ensemble spreads (dotted lines) generated by the RPs (green), orthogonal BVs (yellow), SVs (purple) and O-CNOPs (blue); a2 the error reduction rate (i.e., skill improvement) due to the ensemble mean; and a3 the box-and-whisker plot for the skill improvement averaged for twelve TCs and all lead times, with a 95% confidence interval. The circles denote the maximum and minimum of the improvements for the twelve TCs; b1, b2, and b3 plot the Brier skill score, reliability diagram, and relative operating characteristic curve for the TC strike probability, respectively, generated by the four methods

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17.3.2 Forecasts of the Convectional Scale Weather System Associated with the Model Error Effect It is worth noting that convection-allowing ensemble prediction systems with high resolutions of 2–4 km have emerged as a major focus and become a hot topic of current research on numerical weather predictions. How to accurately address model uncertainties in a convective-scale system is a crucial issue in studies of convection-scale ensemble forecasts. Even if ensemble techniques have been applied, the ensemble members generated by the stochastically perturbed physics tendencies (SPPT; Buizza et al. 1999) utilized in operational centers still face new scientific challenges, especially the problem of under-dispersion. To address this under-dispersion issue, Wang et al. (2020a) applied the CNOP-P approach to the Global and Regional Assimilation and Prediction Enhanced System (GRAPES), which is a convection-scale ensemble prediction model, to detect the most sensitive parameters. Then, the authors formulated a kind of parameter perturbation by adding a group of stochastic perturbations to these sensitive parameters to depict the model uncertainty and conducted ensemble forecast experiments on relevant variables at convective scales. The authors showed that the relevant ensemble members, compared with those generated by the SPPT, enable a much larger spread for humidity and temperature over the troposphere and yield much more reliable forecasting skill on near-surface variables and precipitation. This study concludes that the application of the CNOP-P sensitivity to identifying parametric uncertainties greatly improves the ensemble forecasting skill of convectional scale weather systems, even to a higher skill than the SPPT employed in operational centers. It is easily recognized that the CNOP-P only accounts for the effect of model parameter errors, and other kinds of model errors also severely influence weather and climate predictions; in particular, these model errors are interactive. Considering this situation, Xu et al. (2022a) further adopted the CNOP-F [i.e., the NFSV in Duan and Zhou (2013)] to measure the combined effect of various model errors to explore the ensemble forecast of convective scales [also refer to Xu et al. 2022b]. The authors superimposed the structured NFSV on the SPPT perturbations and formulated new tendency perturbations (denoted by “SPPT_NFSV”) for ensemble forecasts. With these new perturbations, Xu et al. (2022b) conducted ensemble experiments by using the GRAPES convection-scale ensemble prediction model adopted in Wang et al. (2020a). The authors illustrated that the overall probabilistic skills are obviously improved by using the SPPT_NFSV and have an advantage over the SPPT (Fig. 17.3). Particularly, the authors demonstrated that the use of the NFSV enhances the forecasting skill of precipitation accuracy. It is inferred that additional structured nonlinear perturbations (e.g., the NFSV) superimposed on the SPPT can better represent model uncertainties in convection-scale ensemble forecasts and finally contribute to a more comprehensive characterization of model uncertainties for convective-scale forecasts. Either the CNOP-P or the NFSV provides more sensitivity information related to the model perturbations and thus leads to higher ensemble forecasting skill of

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Fig. 17.3 Probabilistic skill for 500 hPa zonal wind (left column) and temperature (right column). a and b show the domain-averaged RMSE of the control forecast (gray line), SPPT_NFSV experiment (red line), and SPPT experiment (blue line), with the ensemble spread for the SPPT_NFSV (red bar) and SPPT (blue bar). c and d represent the spread-error consistency, e and f depict the continuous ranked probability score, g and h illustrate the Talagrand rank histograms, and i and j indicate the outlier scores. From Xu et al. (2022b). @ John Wiley and Sons Publisher. Used with permission

the convectional scale system by reasonably enlarging the ensemble spread. This finding indicates that the errors of the control forecasts caused by model errors in the GRAPES often grow at a fast rate and that the model perturbations related to CNOP-P and NFSV provide growth behavior that is much closer to the dynamical growth of the model errors than the SPPT provides. Then, it is naturally questioned whether the model perturbation strategies implemented as above are most applicable for capturing the rapid growth behavior of the forecast errors induced by the model errors. In particular, for the NFSV, if the SPPTs are fully replaced by mutually

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Fig. 17.3 (continued)

independent NFSVs, similar to O-CNOPs, can they depict much better the model uncertainties that exhibit fast growth behaviors and obtain much higher forecast skill? All these questions deserve our in-depth investigations. It is expected that a more efficient and user-friendly ensemble forecasting method for addressing the model error effect, even the combined effect of model and initial errors, will be investigated.

17.4 A Novel Ensemble Forecasting Method for Addressing the Combined Effect of Initial and Model Errors and Its Special Case O-NFSVs Accompanied by Applications to TC Forecasts The ensemble forecasting mentioned in Sect. 17.3 focuses on considering either the initial uncertainties or model uncertainties. However, in realistic forecasting systems, the effects of both the initial errors and the model errors, especially the effects of their interaction, are inevitable (Nicolis et al. 2009). In this actual situation, the key question is how to correctly combine the initial errors and model errors to obtain reliable ensemble forecasting. As discussed in the introduction, although there exist ensemble forecasting systems that consider the combined effect of initial and model errors (e.g., Buizza et al. 1999; Hou et al. 2010), they yielded initial perturbations

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(such as SVs and BVs) only for measuring initial uncertainties and model perturbations (e.g., SPPT or STTP) merely for estimating model uncertainties and did not consider the dynamically coordinated growth of initial and model perturbations, which may limit the skill of ensemble forecasting. Duan et al. (2022a) generalized the original NFSV (also CNOP-F; refer to Sect. 17.2) for measuring model error effects and proposed C-NFSVs that combine the impacts of both model errors and initial errors, formulating a novel ensemble forecasting method that considers the dynamically coordinated growth of initial and model perturbations. The specific equations are Eqs. (17.9) and (17.10). || || J ( f ∗j ) = max ||u τ (r f j ; f j )||b , f j ∈C j

(17.9)

where Cj =

|| || f 1 ∈ Rn , || f 1 ||a ≤ σ f ,

|| || f j ∈ Rn || f j ||a ≤ σ f , f j ⊥Ck , k = 1, . . . , j − 1 , j > 1,

(17.10)

|| || and ||r f j ||a ≤ σ I ; r f j is the initial perturbation with r = σσ If and f j is the tendency perturbation used to offset the model errors in Eq. (17.4) [i.e., tendency errors f (x, t) in Eq. (17.5)], Rn is the n-dimensional Euclidean space, the symbol { · } refers to an ensemble of vectors, and the symbol ⊥ indicates the orthogonality; || · ||a and || · ||b are the norms that are applied to measure the amplitudes of the initial perturbations r f j and tendency perturbations f j and the departure from the reference state at time τ , respectively; σ f and σ I are positive constant numbers that constrain the amplitudes of the tendency perturbations and initial perturbations, respectively. The combined modes (r f ∗j , f ∗j ) are defined as the C-NFSVs. The C-NFSVs have two particular cases: O-CNOPs and O-NFSVs. The former has been proposed in Duan and Huo (2016) to address the initial error impact on the forecasts (refer to Sect. 3.1), while the latter estimates the model error impact, as proposed by Duan et al. (2022a). Duan et al. (2022a) adopted the famous Lorenz-96 model and demonstrated that ensemble forecasting based on O-CNOPs has a higher skill than that based on O-NFSVs in the early stage of the forecasts, while in the later stage of the forecast, the impact of the model errors becomes more prominent and ensemble forecasting based on O-NFSVs excels. The forecasts based on C-NFSVs, due to their optimization on both the initial errors and model errors, possess higher skill than those based on O-CNOPs and O-NFSVs during the whole forecast period. In Duan et al. (2022a), a simple combination of O-CNOPs and O-NFSVs was also compared with C-NFSVs; the results showed that the simple combination may cause inconsistent dynamical behaviors between the initial perturbations and the tendency perturbations and would degrade the ensemble forecasting skill, while the C-NFSVs possess additional dynamical features that lead to a higher forecast skill (Fig. 17.4). These results justify the advantage of using C-NFSVs in building ensemble forecasts.

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Fig. 17.4 Skill performance differences between the ensemble forecasts made by the combination of O-CNOPs and O-NFSVs when they obtain the highest skill scores and those made by C-NFSVs (red) and the skill performance differences between the combination of O-CNOPs and O-NFSVs with the same optimization period and perturbation amplitudes as in C-NFSVs and those made by C-NFSVs (blue). The horizontal axis denotes the lead time, and the vertical axis represents the differences in the RMSE, ACC, BS, and ROCA values. From Duan et al. (2022a). ©2022 American Meteorological Society. Used with permission

Considering that TC track forecasts have considerably improved during the past decades while the TC intensity forecasts remain challenging, Zhang et al. (2023b) adopted the special case of C-NFSVs, i.e., O-NFSVs for estimating the effect of model uncertainties to conduct TC ensemble forecasting experiments with the WRF model, with a focus on improving TC intensity forecasting skill (Fig. 17.5). The authors performed a comparison between the O-NFSVs and the traditional SKEB and SPPT schemes. The results demonstrated that the O-NFSV ensembles provide a better representation of the model uncertainties affecting TC intensification, with

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much better deterministic and probabilistic skills. Similar improvements were also extended to the forecasting skill for TC tracks, although the perturbations were not optimized for that specific purpose. Therefore, O-NFSVs could be a kind of perturbation structure that is able to describe the uncertainties in TC intensity and tracks. Furthermore, Zhang et al. (2023b) showed that such perturbations are also favorable for recognizing a TC’s rapid intensification process during forecast periods. Although the O-NFSV structures presented in Zhang et al. (2023b) are realized using mutually independent, growing-type tendency perturbations to represent model uncertainties for TC forecasts, ensemble forecasting to address the combined effect of initial and model errors has not yet been implemented. Therefore, a natural extension of this study will be conducted to explore the application of the C-NFSVs in TC forecasts. It is expected that when the O-NFSVs are properly combined with initial perturbations by the C-NFSVs, new highly reliable ensembles will be available

Fig. 17.5 Ensemble forecasts generated by O-NFSVs (a), SKEB (b) and SPPT (c) for track (1), Pmin (2), and Vmax (3) of TC Hato (201713). The black lines represent the control forecasts, the red lines denote the best tracks, the blue lines indicate the ensemble means, and the gray lines represent the ensemble members

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for further improving TC forecasting skill in terms of intensity and track, even the much more challenging TC precipitations. For the convectional scale weather prediction systems investigated above, it is also anticipated that the ensemble forecasting experiments using the C-NFSVs can be conducted to examine if they, compared with those using the NFSV_SPPT in Sect. 17.3, perform much well in depicting model uncertainties and achieving higher forecasting skill.

17.5 Summary and Prospect Studies on the CNOP method and their applications to ensemble forecasting for highimpact weather systems are summarized. The CNOP method which includes CNOPI for revealing the optimally growing initial perturbation, CNOP-P for extracting the most sensitive parameters, CNOP-B for determining the boundary condition uncertainty that exerts the largest effect on forecasts, and CNOP-F for exploring the combined effect of kinds of model errors, is introduced. These CNOPs fully consider the effect of nonlinearity and provide a way to obtain the optimally growing-type error mode for predictability studies, including ensemble forecasting in their respective scenarios. The CNOP-I, -P, and -F [i.e., NFSV] have been applied to the ensemble forecasting of high-impact weather systems. O-CNOPs were proposed to produce ensemble perturbations for estimating the initial uncertainties, and with the applications to the numerical models from the conceptual Lorenz-96 model to the realistic MM5 and further to the advanced WRF, they were demonstrated to have the ability to represent the initial error effect and to promote the ensemble forecasting skill. Especially for the TC track forecasts, O-CNOPs, compared with the operationally utilized SVs and BVs, provide the ensemble members that exhibit larger spreads but tend to be located on the two sides of real TC tracks and show much better agreement between ensemble spreads and ensemble mean forecast errors. Furthermore, O-CNOPs were illustrated to be favorable for reproducing the unusual TC tracks in forecasts. For the TC intensity forecasts, the O-NFSVs developed from the CNOP-F were used to depict the effect of model errors, and it was revealed that the ensemble members generated by the O-NFSVs have the ability to represent the model uncertainties affecting TC intensification and to provide much higher ensemble forecasting skills than the operationally employed SPPT and SKEB. This ability was also extended to the forecasting skill for TC tracks, although the O-NFSVs were not optimized for that specific purpose. For convectional scale weather systems, ensemble forecasting focuses on addressing the model uncertainty effect. An alternative perspective has been applied to provide the relevant sensitivities using both CNOP-P and CNOP-F, which have helped extract more sensitive ensembles or exert more unstable model perturbations on the SPPT ensembles, consequently promoting the ensemble forecasting skill of convectional scale weather systems to a higher level. To explore an ensemble forecast method to address the combined effect of initial and model errors,

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the C-NFSV perturbation scheme was proposed, and its particular feature of dynamically coordinated growth of initial and model perturbations was found to be responsible for the ensemble forecasting skill being higher than any simple combination between initial perturbations and model perturbations. It is hoped that the C-NFSVs can be continually applied in realistic forecasts for high-impact weather systems and further increase the forecast skill by reasonably estimating the combined effect of initial and model errors. In particular, comparisons between C-NFSVs and the combined modes of other types of initial perturbations (e.g., BVs or SVs) and other types of model perturbations (such as SPPT or SKEB) are worth performing in the future. Another interesting avenue in the development of C-NFSVs is to consider the effect of time-varying stochastic errors; a combined mode of C-NFSVs and random forcing tendency perturbations may cover a broader range of model errors and have potential for further improving the ensemble forecast skill. Either O-CNOPs for addressing initial uncertainties, O-NFSVs for interpreting the model uncertainties or C-NFSVs that combine initial and model error effects are worthy of further investigation, especially in applications to realistic models with different complexities for high-impact weather event and even high-impact climate event forecasting. Furthermore, it is noted that these perturbations are the optimally growing mode in nonlinear models in their respective scenarios; thus, it is naturally questionable whether associated ensemble forecasts prefer to achieve high skill in the forecasts of extreme events [also refer to Duan and Huo (2016)]. These will be the subjects of follow-up work. In addition, computational efficiency is a challenge of any ensemble forecast method; whether the presently popular machine learning algorithm can be combined with ensemble forecasting to save time and increase the efficiency of ensemble forecasting should also be explored. In any case, with the development of computing sciences and emerging disciplines and technologies, the above ensemble forecast methods would become much useful and applicable in realistic forecasts of high-impact weather and climate events. Acknowledgements WD was supported by the National Natural Science Foundation of China (Grant No. 41930971), and LY was granted by the National Natural Science Foundation of China (Grant No. 42105061).

References Anderson JL (1997) The impact of dynamical constraints on the selection of initial conditions for ensemble predictions: low-order perfect model results. Mon Weather Rev 125:2969–2983 Barkmeijer J, Iversen T, Palmer TN (2003) Forcing singular vectors and other sensitive model structures. Q J R Meteorol Soc 129:2401–2423 Birgin EG, Martinez MJ, Raydan M (2000) Nonmonotone spectral projected gradient methods for convex sets. SIAM J Optim 10(4):1196–1211 Bowler NE (2006) Comparison of error breeding, singular vectors, random perturbations and ensemble Kalman filter perturbation strategies on a simple model. Tellus A 58(5):538–548

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Chapter 18

Forecast and Numerical Simulation Studies on Meso/Micro-scale High-Impact Weathers Using High-Performance Computing in Japan Kazuo Saito, Takuya Kawabata, Hiromu Seko, Takemasa Miyoshi, Le Duc, Tsutao Oizumi, Masaru Kunii, Guixing Chen, Kosuke Ito, Junshi Ito, Sho Yokota, Wataru Mashiko, Kenichiro Kobayashi, Shin Fukui, Eigo Tochimoto, Arata Amemiya, Yasumitsu Maejima, Takumi Honda, Hiroshi Niino, and Masaki Satoh

Abstract Forecast and numerical simulation studies on meso/micro-scale highimpact weathers using high-performance computing infrastructures (HPCIs) in Japan are reviewed. First, we refer to the Japanese world top-ranking supercomputers (Earth Simulator, K computer, and supercomputer Fugaku). Next, we review symbolical scientific achievements on meso/micro-scale high-impact weathers (e.g., heavy K. Saito (B) · H. Niino · M. Satoh Atmosphere and Ocean Research Institute, University of Tokyo, Chiba, Japan e-mail: [email protected] H. Niino e-mail: [email protected] M. Satoh e-mail: [email protected] T. Kawabata · H. Seko · T. Oizumi · W. Mashiko · S. Fukui · E. Tochimoto Meteorological Research Institute, Tsukuba, Japan e-mail: [email protected] H. Seko e-mail: [email protected] T. Oizumi e-mail: [email protected] W. Mashiko e-mail: [email protected] S. Fukui e-mail: [email protected] E. Tochimoto e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_18

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rainfall and tornado) mainly obtained using the K computer and the supercomputer Fugaku. Keywords Numerical simulation · High-performance computing · K computer · Supercomputer Fugaku · High-impact weathers

18.1 Introduction Japan has a long history of numerical weather prediction. Around the end of 1953, a numerical prediction (NP) group was formed under the leadership of Prof. Shigekata Shono of the University of Tokyo. Detailed members and activities of the NP group T. Miyoshi · A. Amemiya · Y. Maejima Advanced Institute of Computer Science, RIKEN, Kobe, Japan e-mail: [email protected] A. Amemiya e-mail: [email protected] Y. Maejima e-mail: [email protected] L. Duc Institute of Engineering Innovation, University of Tokyo, Tokyo, Japan e-mail: [email protected] M. Kunii · S. Yokota Japan Meteorological Agency, Tokyo, Japan e-mail: [email protected] S. Yokota e-mail: [email protected] G. Chen Sun Yat-Sen University, Guangzhou, China e-mail: [email protected] K. Ito University of the Ryukyus, Okinawa, Japan e-mail: [email protected] J. Ito Tohoku University, Sendai, Japan e-mail: [email protected] K. Kobayashi Kobe University, Kobe, Japan e-mail: [email protected] T. Honda Hokkaido University, Sapporo, Japan e-mail: [email protected]

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have been described in Sect. 4 of Benjamin et al. (2019). Relay computers such as the Fujitsu Co. (FACOM 100), and the small electronic computer IBM 650 were used. In January 1959, the Japan Meteorological Agency (JMA) acquired a “super” computer, IBM 704 (with a core memory of 8 K words), and the operational numerical weather prediction (NWP) with a four-layer quasi-geostrophic model for the Far East area started in 1960, as the third full NWP operation in the world following the Sweden and USA (Nitta and Saito 2004). After the dawn of NWP, several studies on numerical modeling for operational NWP and research have been conducted in Japan and the world with the successive progress of high-performance computing infrastructures (HPCIs). So far, Japan has developed four world top-ranking HPCs since 1993; the Numerical Wind Tunnel, the Earth Simulator, the K computer, and the supercomputer Fugaku. In this paper, first, we refer to these HPCs in Sect. 18.2 and then introduce achievements by forecast and numerical simulation studies on meso/micro-scale high-impact weathers mainly using the K computer and the supercomputer Fugaku.

18.2 World Top-Ranking HPCs in Japan Figure 18.1a shows the world top-ranking supercomputers from June 1993 to November 2022. This figure was prepared for this article using data sources from the TOP500 list of the world supercomputer ranking (https://www.top500.org/). During these three decades, the top-ranking supercomputers were developed by three countries (USA, Japan, and China). The first No. 1 machine in the TOP 500 list was CM-5/ 1024 by the Los Alamos National Laboratory, which attained 59.7 Gflops by 1024 cores in the LINPACK benchmark (Rmax) in June 1993. The latest No. 1 machine in June 2022 is the Frontier at the Oak Ridge National Laboratory, which achieved 1102 Pflops using 8,730,112 cores. In these three decades, the computing performance of the top-runner machine was enhanced about 184,000,000 times. Japan developed six world top-ranking HPCs in this period.

18.2.1 HPCIs in Japan in the 1990s The National Aerospace Laboratory of Japan (which merged with the Japanese Aerospace Exploration Agency (JAXA) in October 2003) developed the Numerical Wind Tunnel (NWT) in partnership with Fujitsu in 1993. It was rated as the most powerful supercomputer by TOP500 from November 1993 to November 1995, except June 1994. NWT achieved 170.0 Gflops in Rmax and was used in a vast range of fields, from base research such as turbulence simulations to the development of aircraft and spacecraft. In 1996, two Japanese supercomputers replaced NWT the No. 1 positions in the TOP500 list. Hitachi SR2201/1024 at the University of Tokyo achieved 220.4 Gflops

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Fig. 18.1 Performance of TOP500 number-one computers from June 1993 to November 2022. a LIMPACK Rmax in Gflops. Colors of markers indicate countries (blue; United States, Red; Japan, yellow; China). b HPCG in Tflops. Originally depicted by the authors using data source from TOP500 (https://www.top500.org/)

in June, and its extended version, CP-PACS/2048 of Hitachi/Tsukuba Center for Computational Sciences, University of Tsukuba, achieved 368.2 Gflops in November.

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18.2.2 Earth Simulator The Earth Simulator was developed by the former National Space Development Agency of Japan (NASDA, current JAXA), the former Japan Atomic Energy Research Institute (JAERI, current Japan Atomic Energy Agency = JAEA) and the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), manufactured by the NEC Co. to simulate earth-scale phenomena for atmospheric research projects such as global warming. In June 2002, the Earth Simulator recorded 35.86 Tflops with the LINPACK benchmark, ranked at No. 1 for five consecutive terms in the TOP500 list. The Earth Simulator was a distributed memory parallel computer system which consists of 640 processor nodes (PNs) connected by a 640 × 640 single crossbar network. Each PN is a shared memory parallel computer with eight vector-type CPUs. The ratio of the effective performance to the peak performance was 87.2% with the LINPACK benchmark and 64.9% with the atmospheric general circulation code (AFES; AGCM for the Earth Simulator model). This high standard surprised/shocked researchers around the world. The Earth Simulator was used for a wide range of atmospheric research, including global warming and regional modeling. It also contributed to the development of the operational 20 km resolution global model (Nakagawa 2009) and the 5 km resolution non-hydrostatic mesoscale model (Saito et al. 2007) of JMA.

18.2.3 K Computer The K computer was jointly developed by the RIKEN Advanced Institute for Computational Science (AICS) and Fujitsu as the centerpiece of the Innovative HighPerformance Computing Infrastructure Project commissioned by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. In 2011 the K computer achieved 10.51 Pflops of performance, demonstrating Japan’s worldleading technology in parallel computing. The highly versatile K computer was used in a broad range of research areas, including medicine, space science, disaster prevention, manufacturing, and materials development. Although the TOP 500 No. 1 position of the K computer was replaced by successive supercomputers of USA and China after 2012 (Sequoia, Titan, Tianhe-2, and Sunway Taihu Light), the practical performance of the K computer was superior to these successors. Figure 18.1b indicates High-Performance Conjugate Gradients (HPCG) performance in Tflops in the TOP 500 list. The K computer kept the world No. 1 position until November 2017. As shown in Fig. 18.2, the practical high performance of the K computer was also proved by the GRAPH500 list of the world supercomputer ranking (https://graph500.org/). The K computer was at the position of No. 1 in the Breadth-First Search (BFS) benchmark in June 2014 and after 2015 until its retirement (June 2019).

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Fig. 18.2 Performance of GRAPH500 number-one computers from June 2012 to November 2022 for BFS benchmark in GTEPS. Colors of markers indicate countries (blue; United States, Red; Japan, yellow; China). Originally produced by the authors using data source from GRAPH500 (https://graph500.org/)

The HPCI Strategic Programs for Innovative Research (SPIRE), launched in Japan at October 2010, was an initiative aimed at leveraging the overwhelming power of the K computer to generate world-leading simulation research in five key strategic areas (Life science, New materials and energy creation, Disaster prevention, Manufacturing, Matter and the universe). SPIRE also aimed more generally to boost the creation of promotional frameworks for computer science and technology and to yield significant social breakthroughs. Field 3 of SPIRE, “Advanced prediction research for natural disaster prevention and reduction”, aimed at natural disaster prevention and mitigation, including weather and climate simulations and earthquake and tsunami simulations. More detailed examples of mesoscale meteorological applications using the K computer are described in Sects. 18.3.1 and 18.3.2.

18.2.4 Supercomputer Fugaku “Fugaku” is a supercomputer developed by Fujitsu and the RIKEN Center for Computational Science (R-CCS, the successor institute to AICS), as the successor to the K computer. It became the fastest supercomputer in the world in the June 2020 TOP500 list with Rmax of 416 Pfolps. After the November 2020 upgrade, Fugaku’s performance increased to Rmax of 442 Pflops (Fig. 18.1a). Fugaku also attained top spots in other rankings, including HPCG (Fig. 18.1b) and GRAPH500 BFS (Fig. 18.2). The “Program for Promoting Research on the Supercomputer Fugaku” was established for the early creation of results using Fugaku. The four focus areas on “Future development and challenges to general human issues”, “Strengthening the strategies to protect the lives and assets of citizens”, “Strengthening the competitiveness of industry”, and “Research foundation” with the 19 selected projects (https://www.rccs.riken.jp/fugaku/org-relations/promoting-research/) have been started since 2020. Early results on applications to mesoscale meteorology under the theme “Large

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Ensemble Atmospheric and Environmental Prediction for Disaster Prevention and Mitigation” is shown in Sect. 18.3.3.

18.3 Meso/Micro-scale Meteorological Applications Using K Computer and Fugaku 18.3.1 SPIRE Field 3 SPIRE was launched in October 2010 by MEXT, aiming to leverage the unprecedented power of the K computer to produce the world’s most cutting-edge simulation studies. JAMSTEC was designated as a strategic organization for Field 3, “Advanced Prediction Researches for Natural Disaster Prevention and Reduction” (https://www. jamstec.go.jp/hpci-sp/en/). A five-year research project of high-performance regional numerical weather prediction was conducted from FY2011 to FY2015 as one of the four research projects (Global climate and environmental changes, Mesoscale weather prediction, Earthquake, and Tsunami) of the SPIRE Field 3. The outcome of the global high-resolution atmospheric modeling studies has been reviewed by Satoh et al. (2017). As for mesoscale weather prediction, a subproject “Ultra-high Precision Mesoscale Weather Prediction” was conducted, aiming to forecast of mesoscale disasters such as torrential rains. A review of early outcomes in mesoscale meteorological applications has been published by Saito et al. (2013). On the project website (https://www.jamstec.go.jp/hpci-sp/en/strategy/mswp.html), the following seven results of the research are introduced. (1) Ensemble forecast experiments on tornadoes that occurred in Tsukuba on May 6, 2012 In this study, ensemble data assimilation experiments with a Local Ensemble Transform Kalman Filter (LETKF) were conducted using a cloud resolving numerical model (Japan Meteorological Agency Non-Hydrostatic Model (JMA-NHM); Saito et al. 2006, 2007; Saito 2012) to reproduce observed tornadoes. Figure 18.3 shows simulated rain water of an ensemble member at 20 m altitude (a) and its enlarged view around the simulated tornado with surface winds (b) with a horizontal resolution of 50 m using the K computer. A tornadic supercell on the Kanto Plain on May 6, 2012 was simulated. More detailed results including the relationship between the duration of intense vorticities and the vertical shear of the horizontal wind and the lower air humidity have been published by Seko et al. (2015). (2) Forecast experiments for the heavy rainfall event in northern Kyushu in July 2012 Data assimilation and ensemble forecast experiments for the heavy rainfall event that occurred in northern Kyushu in July 2012 were conducted, using LETKF with

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Fig. 18.3 a Simulated rain water (g kg−1 ) of ensemble member 4 at 20 m altitude with a horizontal resolution of 50 m using K computer for a tornadic supercell on the Kanto Plain on May 6, 2012. b Enlarged view around the simulated tornado with surface winds. After SPIRE website (https:// www.jamstec.go.jp/hpci-sp/en/research_results/tsukuba.html). Original figure on the website is animation

50 ensemble members, as the first full-scale experiment using the K computer. The results indicated that torrential rainfalls could potentially be captured 12–24 h before the occurrence with high probability. Figure 18.4b shows 3 h accumulated precipitation in a single forecast initiated on 1500 JST July 11, 2012, showing a good agreement with the corresponding observation (Fig. 18.4a). Probability of precipitation with a threshold of exceeding 50 mm per 3 h (Fig. 18.4c) was estimated from ensemble forecasts. Probabilistic information for strong rainfalls over specific areas with a lead time of 12–24 h was also discussed (Kunii 2014a). (3) Super high-resolution simulation of observed 3D structures of the sea-breeze front head by the Down-Scaling Simulation System (DS3) To realize the super high-resolution mesoscale forecast of sea breeze, a Down-Scaling Simulation System (DS3) was developed by combining the parallelized Computational fluid dynamics (CFD) model and the nested LETKF data assimilation system on JMA-NHM (Chen et al. 2015a, b). In this system, the short-range forecast from mesoscale analyzed data was used to drive the building-resolving CFD model. Using the K computer, a numerical experiment over a mesoscale domain of several ten kilometers was conducted with a super high resolution of several meters with individual buildings resolved.

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Fig. 18.4 a Observed 3-h accumulated precipitation from 0600 to 0900 JST, July 12, 2012. b Simulated 3-h accumulated precipitation in a single forecast initiated on 1500 JST, July 11, 2012. c Probability of precipitation with a threshold of exceeding 50 mm per 3 h estimated from the ensemble outputs. After SPIRE website (https://www.jamstec.go.jp/hpci-sp/en/research_results/ kyusyu.html) and Kunii (2014a, b)

Figure 18.5a shows the three-dimensional (3D) structures of a sea-breeze front observed by dual-Doppler lidar over Sendai Airport at 16 JST June 15, 2007. The aerosol is concentrated at the sea-breeze front and portrays the highly irregular features of the front head. Strong updrafts developed at the front head, while downdrafts are seen at the eastern rear of the front head. Figure 18.5b shows the DS3 forecast of the temperature and winds over Sendai Airport. Compared with the lidar observation, the numerical model is shown to reproduce well an inland intrusion of the sea-breeze front and its fine-scale structures. The forecast field presents the irregular features of the front head, with several lobes/clefts at a scale of several hundred meters. The formation dynamics of such 3D structures and the impacts of coastal buildings are also discussed by Chen et al. (2019). (4) Forecasting a large number of tropical cyclone intensities using a highresolution atmosphere-ocean coupled model Toward the aim of improving typhoon intensity prediction, a coupled mesoscale model (CMSM) was developed by JAMSTEC, the Meteorological Research Institute (MRI), and the University of the Ryukyus. CMSM consists of JMA-NHM that can represent the details of the inner core structure of a typhoon and an ocean model that accounts for changes in sea surface temperature associated with a typhoon passage. The K computer provided an opportunity of conducting 281 CMSM runs that include all the typhoons approaching the mainland Japan from April 2009 to September 2012 (Ito et al. 2015b). This was the first achievement in the world that quantifies the benefits of a high-resolution atmosphere–ocean coupled model in typhoon intensity forecasts based on a large number of simulations. The simulations exhibited that CMSM outperforms the existing forecast models in terms of typhoon intensity forecasts. As for the prediction of minimum sea level pressure, CMSM was better than the other models by about 20–30% at the forecast time of two days and by about 30–40% at the forecast time of three days. Regarding maximum wind speed, CMSM was better

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Fig. 18.5 a Aerosol concentration (indicated by the SN ratio of lidar scan) observed over Sendai Airport at 16 JST June 15, 2007. b Temperature and air flows over Sendai airport simulated by DS3 in 10-min forecast valid at 16:10 JST, June 16, 2007. The colorful background shows the ground temperature. The isothermal surface denotes the air temperature of 294 K. After SPIRE website (https://www.jamstec.go.jp/hpci-sp/en/research_results/ds3.html)

by about 10–20% at the forecast of two days and by about 20–30% at the forecast of three days. It is because CMSM successfully reproduces time-varying sea surface temperature and can resolve the inner core dynamics of typhoons (Fig. 18.6). (5) The 1000-member LETKF with the non-hydrostatic numerical weather prediction model on the K computer A 1000-member LETKF with JMA-NHM was implemented on the K computer by Kunii (2014b). This was the most extensive numerical experiment for the LETKF data assimilation with a high-resolution NWP model by using the K computer at that time. Figure 18.7 shows maps of the horizontal distribution of the error correlation of the horizontal wind at the 500-hPa level. When the error covariance is built up with 50 ensemble perturbations, it has noise patterns at distant locations (Fig. 18.7a). Horizontal localization suppresses the noise patterns, while the flow dependence around the center point is conserved (Fig. 18.7b). The error covariance with 1000 members shows a structure similar to that estimated by 50 ensemble members with localization (Fig. 18.7c). This indicates that the amount of 1000 ensemble members might be nearly sufficient to represent the error covariance for horizontal wind without covariance localization techniques. (6) Ensemble Kalman filter data assimilation and storm surge experiments of tropical cyclone Nargis Nargis was a severe tropical cyclone that formed in the Bay of Bengal and made landfall in the Irrawaddy delta of southern Myanmar in May 2008, resulting in massive damage and loss of life. The JMA-NHM-LETKF data assimilation system

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Fig. 18.6 Sea surface cooling beneath Typhoon Roki occurred in 2012. Initial time is 21 JST on August 25, 2012. After SPIRE website (https://www.jamstec.go.jp/hpci-sp/en/research_results/ cmsm.html) on visualization of Ito et al. (2015b). Original figure on the website is animation

Fig. 18.7 Maps of the horizontal distribution of the error correlation of the horizontal wind at the 500-hPa level from the center location (denoted by the cross marks) estimated from a 50 ensemble perturbations without localization, b 50 ensemble perturbations with localization, and c 1000 ensemble perturbations without localization. After SPIRE website (https://www.jamstec.go. jp/hpci-sp/en/research_results/enkf1000.html) and Kunii (2014a, b)

was adopted to show the predictability of Nargis and its storm surge (Duc et al. 2015). The use of assimilation of TC advisories was considered by choosing the observational error of central pressure as 8 hPa in the JMA-NHM-LETKF. The JMA-NHM forecast provided meteorological forcings for a subsequent storm surge

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Fig. 18.8 Simulated cloud images of Nargis and water levels by storm surge at 0500 UTC, 2008 May 2 based on the NHM-LETKF. After SPIRE website (https://www.jamstec.go.jp/hpci-sp/en/res earch_results/nargis.html) on visualization of Duc et al. (2015). Original figure on the website is animation

prediction using the Princeton Ocean Model (POM). The Nargis’ forecasted cloud image and its associated storm surge are depicted in Fig. 18.8. (7) Atmospheric Karman vortex shedding from Jeju Island, East China Sea Two cases of Karman vortex shedding in the lee of Jeju Island, South Korea, in the winter of 2013 were simulated using JMA-NHM and the K computer. Observed cloud patterns associated with the Karman vortex shedding were successfully reproduced (Fig. 18.9). A sensitivity experiment in which surface drag on the island is eliminated demonstrates that the formation mechanism of the atmospheric Karman vortex shedding is different from that behind a bluff body in classical fluid mechanics (Ito and Niino 2016). Several scientific achievements on mesoscale meteorology were also published in SPIRE Field 3, such as the assimilation of tropical cyclone track and wind radius data with LETKF (Kunii 2015), an extension of the Mellor-Yamada model to the Terra Incognita zone for dry convective mixed layers (Ito et al. 2015a), idealized numerical experiments on tropical cyclogenesis due to the Intertropical Convergence Zone (ITCZ) breakdown (Yokota et al. 2015).

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Fig. 18.9 Three-dimensional view of simulated cloud water mixing ratio overlaid on a Google Earth image at 0000 UTC on February 16, 2013. After SPIRE website (https://www.jamstec.go.jp/ hpci-sp/en/research_results/karman.html) on visualization of Ito and Niino (2016)

18.3.2 Post-K Priority Issue 4 Under FLAGSHIP 2020 After the SPIRE project, a Post-K project was conducted from FY2016 to FY2019 under the FLAGSHIP 2020 Project, initiated by MEXT and RIKEN AICS. The project has set the target of developing the next-generation flagship supercomputer of Japan as the successor of the K computer and a wide range of applications that would address top-priority social and scientific issues. Nine priority issues such as Health and longevity, Disaster prevention/Environment, Energy, Industrial competitiveness enhancement, and Basic Science (https://aics.riken.jp/fs2020p/en/index.html) were designated. Priority issue 4 was “Advancement of meteorological and global environmental predictions utilizing observational Big Data” by JAMSTEC, and its mesoscale application, sub A, was to improve the prediction accuracy of local high-impact weathers and to get a longer lead time with the aim of reducing weather disasters (https://www.jamstec.go.jp/pi4/en/sub_00.html). In most of the project period, the K computer was still used with a consortium of high-performance computing infrastructures in Japan. The concept of “big data assimilation” has been given by Miyoshi et al. (2016a). Several outstanding high-resolution simulations using the K computer were conducted within its four research targets (Target 1: Developments of data assimilation techniques for “Observation Big Data”, Target 2: Probability forecasts of floods and landslides by applying the outputs of ensemble forecasts, Target 3: Enhancing the precision of the numerical weather forecast models, and Target 4: Development of a local wind gust analysis system). Symbolical research achievements have been on

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Fig. 18.10 Large eddy simulation of entire tropical cyclone with a horizontal resolution of 50 m. After website (https://www.jamstec.go.jp/pi4/en/movie/03.mp4) on visualization of Ito et al. (2017). Original figure on the website is animation

the Post-K Priority Issue 4 sub A website (https://www.jamstec.go.jp/pi4/en/seika. html). Figure 18.10 shows a 3D visualization of a mass of water from a cross-sectional view of the center of the simulated typhoon. A large eddy simulation (LES) of the entire tropical cyclone with a horizontal resolution of 100 m was conducted by using JMA-NHM and the K computer (Ito et al. 2017). Three kinds of roll structures appeared in the boundary layer. The tornadic supercell event on the Kanto Plain on May 6, 2012 (Fig. 18.3) was further investigated by Yokota et al. (2016, 2018). Figure 18.11 indicates the 3D structure of the predicted tornadic vortex in one ensemble member of highresolution (50 m) ensemble prediction. Based on the ensemble forecasts, the sources of the rotation of simulated tornadoes and the relationship between tornadogenesis and mesoscale environmental processes near the tornado were analyzed. A more detailed structure of the tornado vortex on this event was simulated by Mashiko and Niino (2017) with a horizontal resolution of 10 m (Fig. 18.12). The simulated tornado repeatedly exhibits evolutions from one-cell to two-cell vortex, and subsequently to a multiple-vortex structure, where the vortex structure is sensitive to a swirl ratio. A numerical investigation of building damage during this tornado event was conducted by using hybrid JMA-NHM/engineering LES method (Kawaguchi et al. 2020). Other topics include “Ensemble data assimilation and forecast experiments for the September 2015 heavy rainfall event in Kanto and Tohoku regions with atmospheric motion vectors from Himawari-8” (Kunii et al. 2016), “Himawari-8 data assimilated simulation enables 10-min updates of rain and flood predictions” (Honda et al. 2018), “Mesoscale convective vortex that causes tornado-like vortices over the sea: A potential risk to maritime traffic” (Tochimoto et al. 2019).

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Fig. 18.11 Three-dimensional structure of the predicted tornadic vortex on the Kanto Plain on May 6, 2012 in one ensemble member of high-resolution (50 m) ensemble prediction. After PostK website (https://www.aori.u-tokyo.ac.jp/research/topics/2018/20180824.html) and Yokota et al. (2018)

Ultra-high-resolution NWP with a large domain was conducted using the K computer for a case study of the Izu Oshima heavy rainfall event on October 15– 16, 2013 (Oizumi et al. 2018). A downscale forecast experiment of a domain of 1600 km × 1100 km with a horizontal resolution of 250 m was performed. A lineshaped heavy rainfall event in August 2014 which caused debris flows in Hiroshima, western Japan was also simulated by Oizumi et al. (2020) with the same domain size. Detailed structures of the line-shaped precipitation system were reproduced (Fig. 18.13), and the dependency of simulated convective cells on model resolutions was investigated. Several scientific achievements on mesoscale meteorology were also published in Post-K Priority Issue 4, such as “New cost functions in the hybrid variationalensemble method” (Duc and Saito 2017), “Theoretical consideration on verification in the presence of observation errors” (Duc and Saito 2018), and “Feasibility study of the high-resolution regional reanalysis over Japan” (Fukui et al. 2018). Ensemble flood simulation for a small dam catchment using a distributed rainfall-runoff model and rainfall ensemble forecasts with 1600 member fourdimensional ensemble variational data assimilation (4D-EnVAR) by the K computer was conducted by Kobayashi et al. (2020). The ensemble flood forecasting using the 1600 rainfalls succeeded in indicating the necessity of emergency flood operation

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Fig. 18.12 Detailed structure of tornado vortex on the Kanto Plain on May 6, 2012 by numerical simulation with a horizontal resolution of 10 m. After website of AORI (https://www.aori.u-tokyo. ac.jp/research/topics/2018/20180824-1.html) on visualization of Mashiko and Niino (2017)

with the occurrence probability and a sufficient lead time regarding an extreme flood event.

18.3.3 Program for Promoting Research on the Supercomputer Fugaku As mentioned in Sect. 18.2, the supercomputer Fugaku started its operation in 2020. The “Program for Promoting Research on the Supercomputer Fugaku” is established by MEXT for the early creation of results using Fugaku. The four focus areas are “Future development and challenges to general human issues”, “Strengthening the strategies to protect the lives and assets of citizens”, “Strengthening the competitiveness of industry”, and “Research foundation” with the 19 selected projects. In Area 2, “Large Ensemble Atmospheric and Environmental Prediction for Disaster Prevention and Mitigation” was endorsed as the application issue to meteorology (https://cesd.aori.u-tokyo.ac.jp/fugaku/index.php). Three themes, 1. Short-

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Fig. 18.13 3-D representation of mixing ratios of cloud water with cloud ice (white) and rain water (blue) for the case of the Hiroshima heavy rainfall event on August 2014. After Fugaku website (https://cesd.aori.u-tokyo.ac.jp/fugaku/report_o.html) and Oizumi et al. (2020)

range regional prediction, 2. Global scale prediction, and 3. Advanced big data assimilation, and one theme-crossing technology for advanced large-scale data assimilation have been conducted. The main target of Theme 1 is the probabilistic forecast of severe weather such as torrential rain for a few days ahead, which includes “Mimic system for possible future operational NWP at JMA”, “Innovative application of probabilistic forecast”, and “Super high-resolution simulation of weather phenomena and application of AI” (https://cesd.aori.u-tokyo.ac.jp/fugaku/theme1_ en.html). Research results are on their website, https://cesd.aori.u-tokyo.ac.jp/fug aku/research.html, and https://cesd.aori.u-tokyo.ac.jp/fugaku/gallery.html. One of the early epoch-making achievements relating to Theme 1 using the supercomputer Fugaku was forecasts of the July 2020 Kyushu heavy rain using a 1000member LETKF (Duc et al. 2021). By running a 1000-member LETKF (Fig. 18.14), more information from observations was extracted and forecast uncertainties were better quantified. One of the main targets of Theme 1 research is “impact-based forecast”. Above mentioned 1000-member ensemble forecasts of precipitation have been used for input data in hydrological models, to extract warning information of hazard risks (Kobayashi et al. 2023; Oizumi et al 2023).

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Fig. 18.14 Surface precipitation forecasts by 1000-member LETKF. Reproduced form the Fugaku gallery website (https://cesd.aori.u-tokyo.ac.jp/fugaku/gallery.html) on achievement by Duc et al. (2021)

Another ambitious try to improve the very short-range forecast of precipitation is the 30-s-update data assimilation of phased array weather radar data using Scalable Computing for Advanced Library and Environment (SCALE)-LETKF (Lien et al. 2017). The trial was first made by using the K computer for a local rain case in Kyoto in 2013 (Miyoshi et al. 2016b) and succeeded by using the OakForest-PACS supercomputer of the Information Technology Center, University of Tokyo, for local rain cases in Kobe in 2013 and 2014 (Maejima et al. 2017; Amemiya et al. 2020). A 30-s-update 500 m mesh data assimilation system of phased array radar data in the Kanto plain was developed by Honda et al (2022), and the results using Fugaku were publicized on the RIKEN home page (https://weather.riken.jp/jp/kantomapscale/kantomap-scale.html) in near real-time during the period of Tokyo Olympic Games (Fig. 18.15). The more scientific discussion will be made by different papers in preparation. Call for papers in the special edition of the Journal of the Meteorological Society of Japan and SOLA on research on the frontier of atmospheric science with high-performance computing has been announced (https://www.metsoc.jp/jmsj/spe cial_issues_editions/JMSJ2022-23_HPC.html). The latest studies not reviewed in this article on meteorology, climate change, and environmental science with highperformance computing technology including Fugaku will be published in the special edition.

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Fig. 18.15 Example of near real-time very short-range forecast of precipitation by the 30-s-update 500 m mesh data assimilation of phased array radar data using Fugaku. After Fugaku gallery website (https://cesd.aori.u-tokyo.ac.jp/fugaku/gallery.html) and RIKEN website (https://weather.riken.jp/ jp/kantomap-scale/kantomap-scale.html). Original figure on the website is animation

Acknowledgements This paper reviewed studies supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) as “Field 3, the Strategic Programs for Innovative Research (SPIRE)”, the “FLAGSHIP 2020” project (Advancement of meteorological and global environmental predictions utilizing observational “Big Data”), and “Program for Promoting Researches on the Supercomputer Fugaku” (hp220167). The authors thank Tatsushi Tokioka, formerly of the Japan Agency for Marine-Earth Science and Technology, Keiko Takahashi of the Waseda University, Tetsuro Tamura and Masaharu Kawaguchi of the Tokyo Institute of Technology, Tadashi Tsuyuki and Pin-Ying Wu of the Meteorological Research institute, Guo-Yuan Lien of the National Taiwan University, and members of SPIRE, FLAGSHIP 2020, and the Fugaku projects. The K computer and the supercomputer Fugaku were developed by the RIKEN Advanced Institute of Computer Science and the RIKEN Center for Computational Science, respectively.

References Amemiya A, Honda T, Miyoshi T (2020) Improving the observation operator for the phased array weather radar in the SCALE-LETKF system. SOLA 16:6–11 Benjamin S, Brown J, Brunet G et al (2019) 100 Years of progress in forecasting and NWP applications. Meteor Monogr 59:13.1–13.67

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Chen G, Zhu X, Sha W et al (2015a) Toward improved forecasts of sea-breeze horizontal convective rolls at super high resolutions. Part I: configuration and verification of a down-scaling simulation system (DS3). Mon Wea Rev 143:1849–1872 Chen G, Zhu X, Sha W et al (2015b) Toward improved forecasts of sea-breeze horizontal convective rolls at super high resolutions. Part II: the impacts of land use and buildings. Mon Wea Rev 143:1873–1894 Chen G, Iwai H, Ishii S et al (2019) Structures of the sea-breeze front in dual-Doppler lidar observation and coupled mesoscale-to-LES modeling. J Geophys Res Atmos 124:2397–2413 Duc L, Kuroda T, Saito K et al (2015) Ensemble Kalman filter data assimilation and storm surge experiments of tropical cyclone Nargis Tellus A 67:25941. https://doi.org/10.3402/tellusa.v67. 25941 Duc L, Saito K (2017) On cost functions in the hybrid variational-ensemble method. Mon Wea Rev 145:2071–2082 Duc L, Saito K (2018) Verification in the presence of observation errors: Bayesian point of view. Quart J Roy Meteor Soc 144:1063–1090 Duc L, Kawabata T, Saito K et al (2021) Forecasts of the July 2020 Kyushu heavy rain using a 1000-member ensemble Kalman filter. SOLA 17:41–47 Fukui S, Iwasaki T, Saito K et al (2018) A feasibility study of the high-resolution regional reanalysis over Japan assimilating only conventional observations as an alternative to the dynamical downscaling. J Meteor so. Japan 96:565–585 Honda T, Kotsuki S, Lien GY et al (2018) Assimilation of Himawari-8 all-sky radiances every 10 minutes: impact on precipitation and flood risk prediction. J Geophys Res Atomos. 123:965–976 Honda T, Amemiya A, Otsuka S et al (2022) Development of the real-time 30-s-update Big Data assimilation system for convective rainfall prediction with a phased array weather radar: description and preliminary evaluation. J Adv Model Earth Sys. https://doi.org/10.1029/202 1MS002823 Ito J, Niino H (2016) Atmospheric Kármán Vortex shedding from Jeju Island, East China Sea: a numerical study. Mon Wea Rev 144:139–148 Ito J, Niino H, Nakanishi M et al (2015a) An extension of the Mellor-Yamada model to the Terra Incognita zone for dry convective mixed layers in the free convection regime. Bound Layer Meteorol 157:23–43 Ito J, Oizumi T, Niino H (2017) Near-surface coherent structures explored by large eddy simulation of entire tropical cyclones. Sci Rep 7:3798 Ito K, Kuroda T, Saito K et al (2015b) Forecasting a large number of tropical cyclone intensities around Japan using a high-resolution atmosphere-ocean coupled model. Weather Forecast 30:793–808 Kawaguchi M, Tamura T, Mashiko W (2020) A numerical investigation of building damage during the 6 May 2012 Tsukuba tornado using hybrid meteorological model/engineering LES method. J Wind Eng Indust Aerodyn 204:104254. https://doi.org/10.1016/j.jweia.2020.104254 Kobayashi K, Duc L, Oizumi T et al (2020) Ensemble flood simulation for a small dam catchment in Japan using nonhydrostatic model rainfalls. Part 2: flood forecasting using 1600 member 4D-EnVAR predicted rainfalls. Nat Haz Ear Sys Sci 20:755–770 Kobayashi K, Duc L, Kawabata T et al (2023) Ensemble rainfall-runoff and inundation simulations using 100 and 1000 member rainfalls by 4D LETKF on Kumagawa River flooding 2020. Prog Earth Plan Sci 10:1–22 Kunii M (2014a) Mesoscale data assimilation for a local severe rainfall event with the NHM–LETKF system. Weather Forecast 29:1093–1105 Kunii M (2014b) The 1000-member ensemble Kalman filtering with the JMA nonhydrostatic mesoscale model on the K computer. J Meteor Soc Japan 92:623–633 Kunii M (2015) Assimilation of tropical cyclone track and wind radius data with an ensemble Kalman filter. Weather Forecast 30:1050–1063

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Kunii M, Otsuka M, Shimoji K et al (2016) Ensemble data assimilation and forecast experiments for the September 2015 heavy rainfall event in Kanto and Tohoku regions with atmospheric motion vectors from Himawari-8. SOLA 12:209–214 Lien GY, Miyoshi T, Nishizawa S et al (2017) The near-real-time SCALE-LETKF system: a case of the September 2015 Kanto-Tohoku heavy rainfall. SOLA 13:1–6 Maejima Y, Kunii M, Miyoshi T (2017) 30-second-Update 100-m-mesh data assimilation experiments: a sudden local rain case in Kobe on 11 September 2014. SOLA 13:174–180 Mashiko W, Niino H (2017) Super high-resolution simulation of the 6 May 2012 Tsukuba supercell tornado: near-surface structure and its evolution. SOLA 13:135–139 Miyoshi T, Kunii M, Ruiz JJ et al (2016a) “Big Data Assimilation” revolutionizing severe weather prediction. Bull Amer Meteor Soc 97:1347–1354 Miyoshi T, Lien GY, Satoh S et al (2016b) “Big Data Assimilation” toward post-petascale severe weather prediction: an overview and progress. Proc IEEE 104:2155–2179 Nakagawa M (2009) Outline of the high resolution global model at the Japan meteorological agency. RSMC Tokyo-Typhoon Center Tech Rev 11:1–13 Nitta T, Saito K (2004) Early history of the operational numerical weather prediction in Japan. In: Paper presented at the symposium on the 50th anniversary of operational numerical weather prediction, University of Maryland, Maryland, 14–17 June 2004 Oizumi T, Saito K, Ito J et al (2018) Ultra-high-resolution numerical weather prediction with a large domain using the K Computer: a case study of the Izu Oshima heavy rainfall event on October 15–16, 2013. J Meteor Soc Japan 96:25–54 Oizumi T, Saito K, Duc L et al (2020) Ultra-high-resolution numerical weather prediction with a large domain using the K computer. Part 2: case of the Hiroshima heavy rainfall event on August 2014 and size dependency of simulated convection cores on model resolutions. J Meteor Soc Japan 98:1163–1182 Oizumi T, Kawabata T, Duc L et al (2023) An impact-based forecast for a severe flood event using a 1000-member ensemble prediction. Quart J Roy Meteor Soc (to be submitted) Saito K (2012) The Japan Meteorological Agency nonhydrostatic model and its applications to operation and research. Tech Atmos Model Appl 85–110. https://doi.org/10.5772/35368 Saito K, Fujita T, Yamada Y et al (2006) The operational JMA nonhydrostatic mesoscale model. Mon Wea Rev 134:1266–1298 Saito K, Ishida J, Aranami K et al (2007) Nonhydrostatic atmospheric models and operational development at JMA. J Meteor Soc Japan 85:271–304 Saito K, Tsuyuki T, Seko H et al (2013) Super high-resolution mesoscale weather prediction. J Phys Conf Ser 454:012073. https://doi.org/10.1088/1742-6596/454/1/012073 Satoh M, Tomita H, Yashiro H et al (2017) Outcomes and challenges of global high-resolution non-hydrostatic atmospheric simulations using the K computer. Prog Earth Plan Sci 4:1–24 Seko H, Kunii M, Yokota S et al (2015) Ensemble experiments using a nested LETKF system to reproduce intense vortices associated with tornadoes of 6 May 2012 in Japan. Prog Earth Planet Sci 2:1–12 Tochimoto E, Yokota S, Niino H et al (2019) Mesoscale convective vortex that causes tornado-like vortices over the sea: a potential risk to maritime traffic. Mon Wea Rev 147:1989–2007 Yokota S, Niino H, Yanase W (2015) Tropical cyclogenesis due to ITCZ breakdown: idealized numerical experiments and a case study of the event in July 1988. J Atmos Sci 72:3663–3684 Yokota S, Seko H, Kunii M et al (2016) The tornadic supercell on the Kanto Plain on 6 May 2012: polarimetric radar and surface data assimilation with EnKF and ensemble-based sensitivity analysis. Mon Wea Rev 144:3133–3157 Yokota S, Niino H, Seko H et al (2018) Important factors for tornadogenesis as revealed by highresolution ensemble forecasts of the Tsukuba supercell tornado of 6 May 2012 in Japan. Mon Wea Rev 146:1109–1132

Chapter 19

High-Resolution Simulations of Tropical Cyclones and Mesoscale Convective Systems Using the CReSS Model Kazuhisa Tsuboki

Abstract The Cloud Resolving Storm Simulator (CReSS) model is a nonhydrostatic and compressible equation model designed to simulate high-impact weather systems at high resolution to resolve individual convective clouds. CReSS began to develop from scratch in 1998 and has been optimized for massively parallel computers. The objectives of the CReSS are tropical cyclones, mesoscale convective systems, heavy rainfall, tornadoes, mid-latitude cyclones, and winter snowstorms. CReSS is used for numerical experiments and real weather forecasts. The source code of CReSS is available for scientific and commercial use, and CReSS has been used in many countries for many purposes. This chapter describes the fundamental formulations and technical characteristics of CReSS, as well as its scientific applications in many high-impact weather systems. Keywords CReSS · High-resolution simulation · Tropical cyclone · Mesoscale convective system · High-impact weather system

19.1 Introduction In the late 1990s, mainframe computers changed from single vector processors to massively parallel processors. Around that time, nonhydrostatic numerical models were developed in the world such as the nonhydrostatic model (NHM) of the Japan Meteorological Agency (JMA) (Ikawa 1988; Ikawa and Saito 1991), the Fifth-Generation Penn State/NCAR Mesoscale Model (MM5) (Grell et al. 1994), the Advanced Regional Prediction System (ARPS) (Xue et al. 1995), and the Regional

K. Tsuboki (B) Institute for Space-Earth Environmental Research (ISEE), Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan e-mail: [email protected] Typhoon Science and Technology Research Center (TRC), Yokohama National University, Yokohama, Japan © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_19

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Atmospheric Modeling System (RAMS) (Pielke et al. 1992). The numerical models were originally designed for single processor computers. There were no atmospheric numerical models for a parallel processor computer in the 1990s. At the end of the twentieth century, massively parallel computers became available in the atmospheric research field owing to the rapid development of computer technology, with the theoretical performance reaching tera-floating-point operations per second (Tera-FLOPS), the main memory of gigabytes, and the storage of terabytes. This rapid development of computer led us to posit high-resolution numerical simulations of mesoscale convective systems (MCSs) and tropical cyclones (TCs) could be performed using a cloud-resolving model (CRM). A possible definition of the CRM is given by the nonhydrostatic buoyancy term, composed of deviations in temperature and pressure, water vapor mixing ratio, and hydrometeor mixing ratios. CRMs are numerical models that explicitly calculate time-dependent prognostic equations for these terms. With the amazing development of parallel computers, we started developing a cloud-resolving regional numerical model in 1998 called the Cloud Resolving Storm Simulator (CReSS). Tsuboki and Sakakibara (2002) presented the first description of CReSS. Tsuboki (2008) presented high-resolution simulations of high-impact weather systems such as localized torrential rainfall, typhoons, and snowstorms. The CReSS model was used to study mesoscale weather systems and numerical weather predictions (NWPs). Because approximately 25 years have passed since the beginning of CReSS development, in this paper, we update the technical developments and applications of CReSS for TCs and MCSs. CReSS is a regional nonhydrostatic, compressible numerical model designed for a parallel computer to perform numerical simulations of clouds and storms. It was originally designed for high-end mainframe computers of the massively parallel type. In 2002, the first generation of Earth Simulator of the Japan Agency for MarineEarth Science and Technology (JAMSTEC) began operating. CReSS showed high performance on the Earth Simulator. By contrast, CReSS can be performed on several types of computers, including laptop computers. Accordingly, CReSS has been used in numerical studies and NWPs in several countries. The most important objectives of CReSS are high-impact weather systems, such as TCs and MCSs. Severe phenomena such as heavy rainfall, gusty winds, tornadoes, and lightning are also important objectives. They cause severe disasters and occasionally result in significant damage to society and the loss of life. Understanding their mechanisms and structures is important for predicting severe weather and mitigating disasters. Most high-impact weather systems consist of cumulonimbus clouds and organized systems often embedded in a large weather system. High-impact weather systems are multiscale systems ranging from cloud to synoptic scales. Characteristic weather systems in East Asia, for example, are monsoon systems (Baiu, Meiyu, and Changma), TCs (i.e., typhoons), cyclones and fronts, and snowstorms in a cold-air outbreak. In simulating these weather systems, a large computational domain and a high-resolution grid system are necessary to resolve individual classes of multiscale structures. Explicit calculations of convective clouds and detailed cloud microphysics are important for the quantitative simulation and accurate prediction of high-impact

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weather systems. For these types of computations, massive parallel computers with large amounts of memory are required. CReSS was developed to perform this type of parallel computation. In this paper, we summarized the basic characteristics of CReSS and the related computational processes. We developed CReSS as an application platform and coupled different processes with CReSS, for example, an ocean model, a lightning model, detailed cloud models, and data assimilation processes. These coupled processes were briefly summarized. Next, we introduced an example of a CReSS simulation. Our overall aim is to provide the details of CReSS and to descramble typical simulations using CReSS.

19.2 Basic Characteristics of CReSS 19.2.1 Brief Description The CReSS model is a three-dimensional, nonhydrostatic, and compressible equation model. Cumulus convections are calculated explicitly without parameterization. The horizontal coordinates are the orthogonal curvilinear type, including the orthogonal linear coordinates (Cartesian coordinates) as a special case. The vertical coordinate is a hybrid composed of a terrain-following coordinate and a height coordinate. By using a stretching technique for the vertical coordinates, the lower levels are calculated with fine grid spacing. Conformal map projections, such as the Lambert conformal projection, Mercator projection, and polar stereographic projection, and longitude-latitude coordinates are available for simulation. The prognostic variables are the three-dimensional velocity components, perturbations of pressure and potential temperature, water vapor mixing ratio, subgrid-scale turbulent kinetic energy (TKE), and mixing ratios and number concentrations of hydrometeors. A finite difference scheme is used for spatial discretization. The dependent variables are set on a staggered grid: the Arakawa C-grid horizontally and the Lorenz grid vertically. The mode-splitting technique is used for time integration (Klemp and Wilhelmson 1978). Terms related to sound waves in the basic equation are integrated with a small time step, and other terms are integrated with a large time step. Several types of initial and boundary conditions are available for the idealized and prediction experiments. In these numerical experiments, a wave radiating lateral boundary condition (e.g., Klemp and Wilhelmson 1978) is used if necessary. The computational domain of CReSS is nested in a coarse-grid model or grid point value data to perform a prediction experiment. Cloud microphysical processes are formulated using the bulk method of cold rain, based on Lin et al. (1983), Cotton et al. (1986), Murakami (1990), Ikawa and Saito (1991) and Murakami et al. (1994). The bulk parameterization of cold rain considers water vapor, rain, clouds, ice, aggregates, and graupel. The two moments of the liquid and ice phases are optionally available. The parameterizations of the subgrid-scale eddy motions in CReSS are the one-order closure of Smagorinsky (1963) or the 1.5order closure with TKE (Deardorff 1980). Heat, moisture, and momentum fluxes at

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the earth’s surface are calculated using the schemes of Louis et al. (1981) for land and Kondo (1975) for the ocean. A one-dimensional thermal conductivity model is used to calculate ground temperature (Segami et al. 1989). A one-dimensional diffusion model is used for the ocean mixing layer. For parallel processing in the calculation, the Message Passing Interface (MPI) and/or Open MP are used. CReSS adopts a two-dimensional domain decomposition horizontally. Communication between individual processing elements is achieved by the exchange of data in halo regions (the outermost regions) with neighboring subdomains (Tsuboki and Sakakibara 2002). A detailed description of CReSS is in Tsuboki and Sakakibara (2007).

19.2.2 Basic Equations Because the computation domain of most CRMs is a partial region of the earth, orthogonal curvilinear coordinates are typically used. Considering the two axes in the horizontal direction (.ξ ,.η) and one axis.z orthogonal to the two axes, the equations of motion can be expressed as follows: ( ) ∂u ∂u ∂u ∂u 1 ∂p m = − mu + nv +w − ∂t ∂ξ ∂η ∂z ρm ∂ξ [ ] ∂ 1 ∂ 1 uw −u − + (2Ωη w − 2Ωz v) + mnv v ∂ξ n ∂η m a ( ) ∂v ∂v ∂v ∂v 1 ∂p n = − mu + nv +w − ∂t ∂ξ ∂η ∂z ρm ∂η [ ] ∂ 1 ∂ 1 vw −u − + (2Ωz u − 2Ωξ w) − mnu v ∂ξ n ∂η m a ( ) ∂w ∂w ∂w ∂w 1 ∂p = − mu + nv +w − −g ∂t ∂ξ ∂η ∂z ρm ∂ z u 2 + v2 + (2Ωξ v − 2Ωη u) + a

.

(19.1)

(19.2)

(19.3)

where .u, v, w are the velocity components in the .ξ, η, and .z direction, which are defined as 1 dξ m dt 1 dη v= n dt dz w= dt u=

.

(19.4) (19.5) (19.6)

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a is the earth’s radius, and (.Ωξ , .Ωη , .Ωz ) are the components of the earth’s angular velocity vector. In considering the curvature of the earth, metric factors (stretching factors) .m, n are used in these equations. If the longitude-latitude coordinates are used, they are

.

1 a cos φ 1 n= a

m=

.

(19.7) (19.8)

The density of air .ρm includes water vapor and hydrometeors, and .g is the gravity acceleration. The symbols used in these equations are listed in Table 19.1. In generalized orthogonal curvilinear coordinates, the total derivative is expressed using metric factors as follows:

Table 19.1 Description of symbols used in the text Symbols Description .a .λ, φ .χ .ρa .ρm . x,

y, z, t

.ξ, η, ζ .u, v, w . p,

p0 , ∏

.Ω .cp , cv . Rd .L v .T .θ .ε .g .ψ .q x

Radius of the earth, constant Longitude, latitude π Colatitude, .χ = − φ 2 Density of dry air Density of air containing water substances Coordinates of three-dimensional space and time are the same as .xi (i = 1, 3) Curvilinear coordinates Three-dimensional velocity components ( ) Rd p cp Pressure, reference pressure, and Exner function .∏ = p0 Angular velocity of the earth Specific heats at constant pressure and at constant volume of dry air, respectively Gas constant for dry air Latent heat of vaporization Temperature Potential temperature Ratio of molecular weight of water vapor to average molecular weight of dry air, .ε = 0.622 Gravity acceleration of the earth Dependent variable Water substances other than water vapor (.qi , qc , qr , qs , qg )

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.

d ∂ ∂ ∂ ∂ = + mu + nv +w dt ∂t ∂ξ ∂η ∂z

(19.9)

A system of equations extended to a general orthogonal curvilinear coordinate system using metric factors can be used not only in a latitude-longitude coordinate system but also in various map projections. This allows the use of a common model equation system for each map projection without changing the equations; only the metric factors and Coriolis force terms are changed. Most map projections used in meteorology, such as the Lambert conformal projection, polar stereographic projection, and Mercator projection, are conformal, meaning that the angle between intersecting curves is preserved. In map projections, metric factors (.m, n) in the horizontal direction (.ξ , .η) are called “map factors” and are equal (.m = n) in these map projections. In the Lambert conformal projection, one or two reference latitudes .φ1 , φ2 , and one reference longitude .λ0 should be specified to determine the projection scheme. At the reference longitude, the azimuth is the same as that of the sphere. At the reference latitude, the distance is the same as that of the sphere. The map factor in this projection is ( ) ) ( cos φ μ−1 1 + sin φ1 μ .m = n = (19.10) cos φ1 1 + sin φ where .μ is the conic factor defined as ( μ = ln

.

cos φ1 cos φ2

)

(

) ⎤−1 π φ1 − ⎢ 4 2 ⎥ ⎢ln ( )⎥ ⎣ π φ2 ⎦ tan − 4 2 ⎡

tan

(19.11)

Polar stereographic projection is a conformal projection in which a sphere is projected from a viewpoint placed at the opposite pole on a plane tangent to the pole. In meteorology, a plane that cuts the earth along latitude .φ0 is often used. This latitude is called the reference latitude, and the length is accurate at this latitude. The map factor at latitude .φ in this projection is m=n=

.

1 + sin φ0 1 + sin φ

(19.12)

The Mercator projection is a cylindrical projection, and its coordinates are given by .

x = a cos φ0 Δλ y = a cos φ0 ln tan

(

π φ + 4 2

(

) = a cos φ0 ln

1 + sin φ cos φ

)

(19.13) (19.14)

19 High-Resolution Simulations of Tropical Cyclones …

489

where .φ0 is the reference latitude, and .Δλ is the longitude difference from the reference longitude. The map factor of the projection is m=n=

.

cos φ0 cos φ

(19.15)

According to Eq. (19.10), the polar stereographic and Mercator projections (19.12) and (19.15), formally correspond to conic factors .μ = 1 and .μ = 0, respectively. Topography, such as mountains and islands, is essential for atmospheric motion, cloud formation, and precipitation. It is intrinsically important to introduce terrain effects into CRMs; for this purpose, various vertical coordinates have been designed. CReSS uses a hybrid vertical coordinate system composed of terrain-following coordinates and a constant altitude coordinate system. The following part of this section describes the modifications of the basic equations in the terrain-following coordinates. Using the height of the ground surface .z sfc (ξ, η) and the height of the model domain .z top , the vertical coordinate .ζ is defined as ζ (ξ, η, z) =

.

z top [z − z sfc (ξ, η)] z top − z sfc (ξ, η)

(19.16)

and height .z (ξ, η, ζ ) is [

z sfc (ξ, η) . z (ξ, η, ζ ) = z sfc (ξ, η) + ζ 1 − z top

] (19.17)

Although the horizontal coordinates are orthogonal, the vertical coordinate is nonorthogonal curvilinear. Figure 19.1 shows a schematic representation of the vertical coordinate with velocity vectors. For the conversion between the .z and .ζ coordinates, the following non-zero Jacobian terms are used: J

. 31

J32 J11

) ( ∂z ∂ z sfc (ξ, η) ζ −1 = ∂ξ z top ∂ξ ) ( ∂z ∂z sfc (ξ, η) ζ =− −1 = ∂η z top ∂η ∂z z sfc (ξ, η) = J22 ≡ Jd = =1− z top ∂ζ =−

(19.18) (19.19) (19.20)

As .ζ is a monotonically increasing function with respect to .z, 1

.

G 2 = Jd

(19.21)

Then, the velocity components in the terrain-following coordinates considering the map factors are

490

K. Tsuboki

Fig. 19.1 Schematic of terrain-following coordinates and velocity vectors

U =u V =v dζ 1 W = = 1 (mu J31 + nv J32 + w) dt G2

.

(19.22) (19.23) (19.24)

The total derivative (19.9) in the coordinates becomes .

d ∂ dξ ∂ dη ∂ dζ ∂ = + + + dt ∂t dt ∂ξ dt ∂η dt ∂z ∂ ∂ ∂ ∂ + mu + nv +W = ∂t ∂ξ ∂η ∂ζ

(19.25)

The derivative of the scalar variable.φ with respect to.ξ, η, and.ζ may be changed to ] [ ∂ψ ∂ 1 ∂ .m →m 1 (Jd ψ) + (J31 ψ) ∂ξ ∂ζ G 2 ∂ξ ] [ ∂ψ ∂ 1 ∂ n →n 1 (Jd ψ) + (J32 ψ) ∂η ∂ζ G 2 ∂η ∂ψ 1 ∂ψ → 1 ∂z G 2 ∂ζ

(19.26) (19.27) (19.28)

Based on the aforementioned derivations, the basic equations for the nonhydrostatic regional model in the latitude-longitude coordinate system or other orthogonal map projection coordinate systems, considering topography, are expressed as follows:

19 High-Resolution Simulations of Tropical Cyclones …

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equations of motion are ] ( ) [ ∂u ∂ ∂u ∂u ∂u m 1 ∂ . = − mu + nv +W − (Jd p) + (J31 p) ∂t ∂ξ ∂η ∂ζ ρm G 21 ∂ξ ∂ζ [ ( ) ( )] ∂ 1 ∂ 1 uw + (2Ωη w − 2Ωz v) + mnv v (19.29) −u + ∂ξ n ∂η m a ] ( ) [ ∂v ∂ ∂v ∂v ∂v n 1 ∂ = − mu + nv +W − ( Jd p) + (J32 p) ∂t ∂ξ ∂η ∂ζ ρm G 21 ∂η ∂ζ [ ( ) ( )] ∂ 1 ∂ 1 vw + (2Ωz u − 2Ωξ w) − mnu v (19.30) −u + ∂ξ n ∂η m a ( ) ∂w ∂w ∂w ∂w 1 ∂p = − mu + nv +W − −g 1 ∂t ∂ξ ∂η ∂ζ ρm G 2 ∂ζ u 2 + v2 (19.31) + (2Ωξ v − 2Ωη u) + a equation of potential temperature is .

( ) ∂θ ∂θ ∂θ ∂θ 1 ∂ θ¯ = − mu + nv +W −w 1 + Src.θ ∂t ∂ξ ∂η ∂ζ G 2 ∂ζ

(19.32)

and pressure equation is ( ) ∂p ∂p ∂p ∂p (19.33) . = − mu + nv +W ∂t ∂ξ ∂η ∂ζ ) ] [ ( 1 1 1 1 dθm ∂ G2v ∂G 2 w ∂ G2u 2 1 − ρm cs 1 mn + + + ρm cs2 ∂ξ m ∂η n ∂ζ θ m dt G2 where .θm is a virtual temperature considering mixing ratios of water substances (“mass virtual temperature”). If .θ is the potential temperature of dry air, .qv is the water vapor mixing ratio; .qc , qr , qi , qs , qg are the mixing ratio of cloud water, rain, ice, aggregates, and graupel, respectively, .θm is defined as ] ) ) −1 ( qv 1 + qv + qc + qr + qi + qs + qg ε + qv ≈ θ (1 + 0.608qv )(1 − qc − qr − qi − qs − qg )

[( .θm = θ 1−

(19.34) (19.35)

The pressure equation (19.33) is derived from the equation of continuity and the equation of state, and .cs in (19.33) is the velocity of the sound wave. These equations have almost no approximation, except that the subgrid-scale turbulence terms are not included for simplicity. These are a system of equations that include the effects of topography and the earth’s curvature and consider the compressibility and nonhydrostatic terms of the atmosphere, as well as changes in atmospheric pressure (thermal

492

K. Tsuboki

expansion) due to nonadiabatic heating (.Src.θ) in the equation of potential temperature (19.32). The system can be used for various calculations in domains that include topography because the latitude-longitude coordinate system and various map projections are expressed in terms of map factors. Atmospheric waves are classified into sound waves, internal gravity waves, and Rossby waves, and the aforementioned equation system includes all these waves. We discuss this in detail in the text on time integration methods. In the aforementioned equation system, air density is determined from the equation of state, including the water content. However, the basic equation system can be rewritten while maintaining most of the basic characteristics of the atmosphere, such as compressibility, by replacing the air density with that of the basic field. This system is sometimes called a “quasi-compressible system” and is often used as the basic equation system for CRMs. Considering the deviations from the basic field for the density, pressure, and potential temperature, the simplicity of the system of equations increases. Because the deviations are sufficiently small compared to the basic field in the atmosphere, they have the advantage of preventing the degradation of calculation accuracy owing to numerical expressions, such as the cancelation of significant digits and round-off errors. In the basic equations of CReSS, the basic field is a function of only the vertical coordinate and is represented by a bar. The deviation field is a function of time and space and is represented by a prime. Density, temperature, and pressure are divided into the basic field and deviations as follows: ρ = ρ(ζ ¯ ) + ρ' θ = θ¯ (ζ ) + θ '

(19.36)

. m

p = p(ζ ¯ )+ p

(19.37) (19.38)

'

Hydrostatic balance is assumed in the basic field as .

∂ p¯ 1 ¯ = − G 2 ρg ∂ζ

(19.39)

Density deviation is considered only in the buoyancy term derived from the pressure gradient force and gravity terms in the vertical equation of motion. The buoyancy term is approximated as follows: .

−

∂p 1 ∂ p' ρ ' −g≈− − g 1 ρ¯ ρm G ∂ζ ρG ¯ 2 ∂ζ 1

1 2

buoyancy

Finally, we obtained the basic equations of CReSS as follows:

(19.40)

19 High-Resolution Simulations of Tropical Cyclones …

.

493

] ( ) [ ) ) ∂u ∂ ( ∂u ∂u ∂u m 1 ∂ ( ' ' p p + = − mu + nv +W − J J d 31 ∂t ∂ξ ∂η ∂ζ ρ¯ G 21 ∂ξ ∂ζ [am]

[

( ) ( )] ∂ 1 ∂ 1 uw + (2Ωη w − 2Ωz v) + mnv v (19.41) −u + ∂ξ n ∂η m a ] ( ) [ ) ) ∂v ∂ ( ∂v ∂v ∂v n 1 ∂ ( ' ' + p p = − mu + nv +W − J J d 32 ∂t ∂ξ ∂η ∂ζ ρ¯ G 21 ∂η ∂ζ [am]

[

( ) ( )] ∂ 1 ∂ 1 vw + ρ(2Ω ¯ −u + ρ¯ z u − 2Ωξ w) − mnu v ∂ξ n ∂η m a ( ) ∂w ρ' ∂w ∂w ∂w 1 ∂ p' − = − mu + nv +W − g 1 ∂t ∂ξ ∂η ∂ζ ρ¯ ρG ¯ 2 ∂ζ [am,gm]

[am]

+ ρ(2Ω ¯ ξ v − 2Ωη u) + ρ¯

.

u +v a 2

(19.42)

2

(19.43)

( ) ∂θ ' ∂θ ' ∂θ ' ∂θ ' 1 ∂ θ¯ + ρSrc.θ ¯ = − mu + nv +W −w 1 ∂t ∂ξ ∂η ∂ζ G 2 ∂ζ

(19.44)

[gm]

.

( ) ∂ p' ∂ p' ∂ p' ∂ p' = − mu + nv +W + ρgw ¯ ∂t ∂ξ ∂η ∂ζ ) ] [ ( 1 1 1 ∂ G2v ∂G 2 w ∂ G2u 2 1 + + − ρc ¯ s 1 mn ∂ξ m ∂η n ∂ζ G2 ( +

ρc ¯ s2

[am]

1 dQ 1 dθ − θ dt Q dt

)

(19.45)

where the buoyancy term in the vertical component of the equation of motion (19.43) is ⎤

⎡ .

−

⎢ θ' q ' + qc + qr + qi + qs + qg ⎥ ρ' p' qv' ⎥ ⎢ − 2 + − v g = g⎢ ⎥ ⎦ ⎣ θ¯ ρ¯ ρc ¯ s ε + q¯v 1 + q¯v [gm]

(19.46)

[am]

In these equations, the terms marked with [am] are related to sound waves, and the terms marked with [gm] are related to gravity waves. The first terms on the right

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K. Tsuboki

side in (19.41)–(19.45) and the Coriolis force term in (19.41)–(19.43) are related to Rossby waves. In addition to these equations, the conservation equations for the water vapor mixing ratio and the mixing ratio of hydrometeors are as follows: ( ) ∂qv ∂qv ∂qv ∂qv . = − mu + nv +W + Src.qv ∂t ∂ξ ∂η ∂ζ ( ) ∂qx ∂qx ∂qx ∂qx = − mu + nv +W + Fall.qx + Src.qx ∂t ∂ξ ∂η ∂ζ

(19.47) (19.48)

where .qx indicates the mixing ratio of each category of hydrometeors, such as cloud water (.x = c), cloud ice (.x = i), rain (.x = r), aggregates (.x = s), and graupel (.x = g). A detailed discussion is in Subsection “Cloud Microphysical Processes”.

19.2.3 Grid System and Time Integration Most atmospheric models use staggered grids in space, where the grid points are shifted for each physical variable rather than placed at the same point. Two vertical grid systems are often used in CRMs: the Lorenz grid system and Charney–Phillips grid system. For horizontal grid systems, Arakawa and Lamb (1977) presented five patterns for the arrangement of horizontal velocity components and scalar quantities. CReSS uses the Lorenz grid system in the vertical direction and the Arakawa C-grid system in the horizontal direction (Fig. 19.2). In this grid system, scalar quantities are placed at the center of the grid system, and the vertical and horizontal velocities are displaced by half the grid. The Jacobian position of the vertical coordinate transformation is shown in Fig. 19.2. Generally, internal gravity waves and Rossby waves are important for numerical weather predictions. However, owing to the presence of sound waves in compressible or quasi-compressible equation systems, special handling of sound waves is required for time integration. If the time integration of the compressible equation system is performed explicitly, the speed of the sound wave with the fastest phase speed restricts the time increments of the integration owing to the CFL (Courant–Friedrichs–Lewy) condition. However, important meteorological phenomena are related to internal gravity waves and Rossby waves, which propagate much more slowly. Therefore, the time increments must be large for efficient time integration. In avoiding the limitations of small time increments owing to sound waves, three types of time integration schemes have been used: semi-implicit scheme, modesplitting scheme, and mode-splitting with vertically implicit scheme. Figure 19.3 shows a schematic of the mode-splitting scheme. In this scheme, terms related to sound waves are integrated with a small time increment, and other terms are integrated with a large time increment. CReSS usually uses this scheme with the implicit integration of sound wave terms in the vertical direction.

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Fig. 19.2 Schematic of grid system used in CReSS. Vector-dependent variables (.u, v, w), scalar variables (.φ), and Jacobian terms are placed in the grid system

Fig. 19.3 Schematic of mode-splitting integration scheme

The mode-splitting scheme with implicit calculations in the vertical direction can be easily applied to large-scale parallelization because the physical space corresponds to the arrangement of the computational processing elements (PEs), and communication between PEs occurs only with adjacent PEs. In addition, only the terms related to sound waves are integrated in small time increments, whereas the other terms and physical processes are computed in large time increments. Consequently, computational efficiency does not deteriorate significantly. In the basic Eqs. (19.41)–(19.46), the sound wave terms indicated by [am] are integrated with a small time increment, and the other terms are integrated with a large

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K. Tsuboki

time increment. All terms in the equations of the perturbation potential temperature and mixing ratios are also integrated with a large time increment. CReSS uses the Crank–Nicolson scheme for implicit integration with a small time increment and the leapfrog scheme for a large time increment as follows: 1

ρG ¯ 2

.

ψ t+Δt − ψ t−Δt = Fψt 2Δt

(19.49)

where . Fψt for the dependent variable .ψ on the right side is all terms except the sound wave terms. When integrating non-sound wave terms with a large time increment using the mode-splitting time integration scheme with three-time levels, such as in the leapfrog scheme, there are not only physical modes but also noisy computation modes in the solution. This causes the separation of the solution between odd and even time steps. The time filter effectively suppresses the separation of the solution. CReSS uses Asselin’s time filter (Asselin 1972). This filter is time-weighted smoothing in the time direction that filters the values at time .t after those at time .t + Δt are obtained. If the dependent variables (.u, v, w, p ' , θ ' , qv , qx ) are expressed as .ψ, Asselin’s time filter is expressed as ) ( ψ t = ψ t + μa ψ t−Δt − 2ψ t + ψ t+Δt

.

(19.50)

where the values with bars represent filtered values. .μa is the filtering coefficient that should be approximately .μa = 0.1. A larger .μa results in a larger dissipation error. As is known from the example of the finite difference scheme for a onedimensional linear advection equation, the scheme is stabilized by adding an evenorder derivative term to the explicit scheme. The term added to stabilize the scheme is called the “numerical viscosity term”. In most CRMs, second- or fourth-order numerical viscosities are usually used. CReSS also uses these numerical viscosity terms. We let .ψ be an arbitrary dependent variable. The numerical viscosity term .Diff.ψ takes the following form: [ 1

.

G 2 Diff.ψ = νh

] ∂ n (ρψ) ∂ n (ρψ) ∂ n (ρψ) ¯ ¯ ¯ + + ν v n n ∂ξ ∂η ∂ζ n

(19.51)

where.n = 2 is the second-order and.n = 4 is the fourth-order numerical diffusion..νh and .νv are the horizontal and vertical viscosity coefficients, respectively, as functions of grid spacing and time increment size. It is better to use the fourth-order numerical viscosity because a higher-order derivative more effectively suppresses the high 1 wave-number component. In the actual calculations, .G 2 Diff.ψ is added to the time evolution equation for each dependent variable.

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19.2.4 Initial and Boundary Conditions Various initial conditions are possible in CReSS. The initial conditions for the idealized experiments are either a uniform field in the horizontal direction with a vertical sounding profile or characteristic equilibrium conditions such as hydrostatic equilibrium, geostrophic and thermal wind equilibrium, and gradient-wind equilibrium. Inhomogeneous ground conditions, such as topography, sea-land distribution, or sea surface temperature (SST) distribution, cause disturbances. However, in a uniform field, providing artificial triggers for disturbances is necessary. They are called the initial disturbance. Typical initial perturbations are thermal bubbles and random noises. In real weather simulations or weather forecasts, three-dimensional grid point values, including height, pressure, temperature, humidity, and horizontal velocity components, are necessary. These are provided by coarse-mesh models, objective analysis data, or coarse-mesh CReSS simulation results. If mixing ratios of hydrometeors and vertical velocity are available, they are used with the aforementioned grid point values in a warm start computation. Various types of boundary conditions are possible in CReSS. In an idealized experiment, periodic boundary, Neuman, Dirichlet, and radiation conditions are available. In real weather forecasting, the lateral boundary data should be provided as external forcing. They are usually functions of space and time, respectively. The data are coarse in space and time; therefore, they are spatially interpolated to the CReSS grid points and interpolated in time. Owing to the inconsistency between the external data and inner model calculation, unrealistic noise may occur along the lateral boundary. In suppressing this noise, a damping region is typically applied along the lateral boundary. Using these techniques, stimulating disturbances originally outside the model domain is possible. Figure 19.4 shows the simulation experiment of a typhoon entering the computational domain through the right lateral boundary. The typhoon was initially located outside the domain and was created in the domain by external boundary forcing as if it was entering from the outside through the boundary.

19.2.5 Upper Damping Layer Although the atmosphere extends to very high altitudes, the computational domain is typically limited to the lower atmospheres. The top of the model domain is usually lower than 25 .∼ 30 km high. Accordingly, a damping layer is necessary at the upper level of the model domain to suppress the unrealistic reflection of disturbances at the top of the model. The upper damping layer is incorporated into the calculation by adding the following terms to the right side of each equation for each dependent variable .ψ: ( ) ¯ . − γv ψ − ψ (19.52) where .ψ¯ is the external data or 0 in the case of a forecast experiment, and is the initial value or the value of the reference state in an idealized experiment. The parameter

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K. Tsuboki

Fig. 19.4 Simulation of a typhoon entering the computational domain through right lateral boundary. Color shading represents precipitation intensity; contours represent sea level pressure

γ is an attenuation coefficient that increases toward the top of the model. We let .z b be the altitude at the bottom of the damping layer and .γv be given as

. v

⎧ ⎨ 0, [ )] z < z b ( z − zb .γv = z ≥ zb ⎩ αv 1 − cos π z top − z b

(19.53)

where .z top is the top altitude in the model. Parameter .αv is a decay constant with the dimension of the inverse of time. This constant is approximately from 1/300 to 1/1800 s.−1 . The damping layer should be approximately 1/4 of the model top height of the model.

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19.2.6 Physical Processes Subgrid-Scale Turbulence Expressing the effects of subgrid-scale motion in terms of grid-scale quantities is called “turbulence parameterization” and is essential in numerical weather simulations. CReSS incorporates subgrid-scale turbulence in the computation using the one-order closure scheme of Smagorinsky (1963) or the 1.5-order closure with turbulence kinetic energy (TKE). For simplicity, we use the Cartesian coordinate system .xi = (x, y, z). Assuming .u i = (u, v, w) is the velocity component, the turbulence term .Turb.u i in the equation ¯ i' u 'j as of motion in .xi direction can be expressed using the stress tensor .τi j = − ρu follows: 1 ∂ τi j (19.54) .Turb.u i = ρ¯ ∂ x j Using the rate-of-strain tensor . Si j , the stress tensor is ( τ = ρν ¯ m

. ij

2 ∂u k Si j − δi j 3 ∂ xk

) .

(19.55)

where.δi j is Kronecker’s delta, and.νm is the eddy viscosity coefficient for momentum. This may differ in the vertical and horizontal directions. The molecular viscosity coefficient under shear stress is neglected because it is much smaller than the eddy viscosity coefficient. Similarly, for scalar quantities such as the potential temperature and water vapor .ψ, their turbulence terms are given by Turb.ψ =

.

∂ Hψi ∂ xi

(19.56)

where . Hψi denotes the turbulent flux of the scalar quantity .ψ in the .xi direction. According to Smagorinsky (1963) and Lilly (1962), the eddy viscosity coefficient in an isotropic atmosphere is given by ⎧ ⎨

) ( N2 2 , (CS Δ) Def − .νm = Pr ⎩ 0, 2

νm > 0

(19.57)

νm ≤ 0

where .CS is the Smagorinsky constant, .CS = 0.21, according to Deardorff (1972). Δ is the average grid spacing of the numerical model and .Def is the magnitude of deformation. . N is the Brunt–Vaisala frequency, and .Pr is the turbulent Prandtl number, which is usually a constant between 1/3 and 1, defined by

.

Pr =

.

νm . νh

(19.58)

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K. Tsuboki

In the case of an anisotropic atmosphere, the average grid spacing.Δ assumes different values in the vertical and horizontal directions. Another well-known turbulence parameterization is the 1.5-order closure with TKE. In this closure scheme, a time-dependent prognostic equation of turbulence kinetic energy . E is solved simultaneously with the other equations. As a function of TKE . E obtained from the calculation, the horizontal and vertical eddy viscosity coefficients .νmh , νmv are ν

. mh

1

= 0.1E 2 lh 1 2

νmv = 0.1E lv

(19.59) (19.60)

where .lh , lv represent the horizontal and vertical scales of the mixing length, respectively.

Surface Flux The bottom layer of the planetary boundary layer is called the “surface boundary layer”, which is strongly controlled by the earth’s surface and extends 20 .∼ 50 m from the surface. Within the surface boundary layer, the vertical fluxes of sensible heat, latent heat, and momentum are remarkably constant in the vertical direction and equal to the values at the ground surface. By using the magnitude of wind speed .|Va |, the surface stresses on the wind or momentum flux at the surface .τx , τ y [kg m s.−1 m.−2 s.−1 = N m.−2 ] are τ = ρa Cm |Va |u a τ y = ρa Cm |Va |va

. x

(19.61) (19.62)

where .Cm is a dimensionless quantity called the drag coefficient or bulk transfer coefficient with respect to momentum. The sensible and latent heat fluxes . HS , HL [J m.−2 s.−1 = W m.−2 ] are .

HS = − ρa cp Ch |Va |(Ta − Tg ) [ ] HL = − ρa L v Ch |Va |β qva − qvs (Tg )

(19.63) (19.64)

where .a and .g denote the first atmospheric layer and the ground surface, respectively. Ch is the bulk coefficient (dimensionless) for heat and water vapor,. L v is the latent heat of water evaporation, .qvs (Tg ) is the saturated mixing ratio for ground temperature .Tg , and .β is the evapotranspiration coefficient. The bulk coefficients .Cm , Ch are given by the scheme of Louis et al. (1981) that considers the roughness parameters of momentum, heat, and water vapor.

.

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501

Ground Temperature Because sensible and latent heat fluxes from the ground surface are functions of the ground temperature, calculating the time evolution of the ground temperature is essential for numerical weather prediction. The ground temperature is calculated by solving the heat conduction equation using a one-dimensional .m-layer model. Figure 19.5 shows the grid settings used to calculate the ground temperature. In this calculation, only vertical heat conduction is considered, and lateral heat diffusion is not considered. The system of equations for the time evolution of ground temperature for the .m-layer model is expressed as 2νg ∂ T1 G0 + = (T2 − T1 ) ∂t ρg Cg ΔZ 1 ΔZ 1 (ΔZ 2 + ΔZ 1 ) 2νg 2νg ∂ T2 =− (T2 − T1 ) + (T3 − T2 ) ∂t ΔZ 2 (ΔZ 2 + ΔZ 1 ) ΔZ 2 (ΔZ 3 + ΔZ 2 ) 2νg 2νg ∂ T3 =− (T3 − T2 ) + (T4 − T3 ) ∂t ΔZ 3 (ΔZ 3 + ΔZ 2 ) ΔZ 3 (ΔZ 4 + ΔZ 3 ) · · · · · ·· 2νg (Tk − Tk−1 ) 2νg (Tk+1 − Tk ) ∂ Tk =− + ∂t ΔZ k (ΔZ k + ΔZ k−1 ) ΔZ k (ΔZ k+1 + ΔZ k ) · · · · · ·· 2νg (Tm−1 − Tm−2 ) 2νg (Tm − Tm−1 ) ∂ Tm−1 (19.65) =− + ∂t ΔZ m−1 (ΔZ m−1 + ΔZ m−2 ) ΔZ m−1 (ΔZ m + ΔZ m−1 ) .

The temperature.Tm of the.mth layer is assumed to be constant during the computation period (Dirichlet condition). The heat capacity per unit volume of the ground .ρg Cg and thermal diffusion coefficient .νg are ρ Cg = 2.3 × 106

. g

νg = 7.0 × 10

−7

[J m−3 K−1 ], 2 −1

[m s ].

(19.66) (19.67)

In the time-dependent equations of ground temperature, .G 0 is the heat flux toward the ground, which is the sum of the net radiation . Rnet , sensible heat . HS , and latent heat . HL as follows: . G 0 = Rnet + HS + HL . (19.68) The net radiation is the sum of the solar radiation and the downward and upward longwave radiation. The time-dependent equations of ground temperature are discretized for numerical computation, and an implicit scheme is used for time integration. The intrinsic CReSS does not include the radiation processes of the atmosphere and clouds. The latest version of CReSS incorporates the Rapid Radiative Transfer Model (RRTM-G; 4.85), described by Mlawer et al. (1997) and Iacono et al. (2003) as the radiation process.

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K. Tsuboki

Fig. 19.5 Schematic of one-dimensional grid setting used in calculation of ground temperature

Cloud Microphysical Processes Cloud and precipitation physics are the most important processes in CRMs. CReSS incorporates bulk microphysical processes and has several options for microphysical processes: warm rain, cold rain, cold rain with two moments in the solid-hydrometeor process, and full two-moment cold rain. In the microphysical process of CReSS, liquid and solid hydrometeors are categorized as cloud ice (indicated by the suffix .i), cloud water (.c), rain (.r), aggregates (.s), and graupel (.g). Hail is another important category in the bulk scheme but is also included in the category of graupel. The prognostic variables are the mixing ratios of water vapor (.qv ) and each hydrometeor category (.qx , x = i, c, r, s, g). In the two-moment scheme, the number densities of each category of hydrometeors (. N x , x = i, c, r, s, g) are also dependent variables. The prognostic equations for potential temperature (.θ ), water vapor mixing ratio (.qv ), mixing ratios of hydrometeors (.qx ), and number density (. N x ) are ∂ ρθ ¯ ∂t ∂ ρq ¯ v ∂t ∂ ρq ¯ x ∂t ∂ Nx ∂t .

= Adv.θ − ρw ¯

∂ θ¯ + ρSrc.θ ¯ ∂z

(19.69)

¯ = Adv.qv + ρSrc.q v

(19.70)

¯ ¯ = Adv.qx + ρSrc.q x + ρFall.q x

(19.71)

= Adv.

Nx Nx Nx + ρSrc. ¯ + ρFall. ¯ . ρ¯ ρ¯ ρ¯

(19.72)

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503

Fig. 19.6 Schematic of cloud and precipitation quantities and processes in one-moment bulk cold rain process of CReSS

The terms “.Adv.” and “.Fall.” represent the time changes due to advection and fallout, respectively. In addition to these terms, turbulent processes term (.Turb.) and numerical viscosity term (.Diff.) are incorporated in the prognostic equations. All sources and sinks of variables are included in the “Src.” terms. These terms comprise many source and sink processes, and each process must be formulated theoretically or experimentally. The microphysical processes implemented in CReSS are shown in Fig. 19.6. The lines connecting the quantities of water substances in the figure represent conversion processes, and the symbols attached to the lines represent physical processes. Symbols with two or three uppercase letters represent physical processes, and their meanings are summarized in Table 19.2. The two additional subscripts represent the sources and sinks of hydrometeors. For example, .NUAvi represents the conversion of water vapor .v into ice .i through sublimation nucleation, and .CNcr represents the conversion of cloud water into rain through categorical conversion. These prognostic equations for microphysical processes are combined with timedependent equations of dynamics (19.41)–(19.45). Consequently, the equation system of the numerical model is closed and becomes solvable using numerical schemes.

19.2.7 Spectral Nudging Technique TC movement is primarily controlled by large-scale environmental flow. Because CReSS is a limited area model, the effect of large-scale flow on TCs is not always

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K. Tsuboki

Table 19.2 Physical processes in bulk cold rain scheme of CReSS Symbol Physical process .NUAvi .NUFci .NUCci .NUHci .SP .VD .CL .PG .AG .CN .ML .FR .SH

Deposition or sorption nucleation Condensation-freezing nucleation Contact nucleation Homogeneous nucleation Secondary nucleation of ice crystals Vapor deposition, evaporation, and sublimation Collection Graupel production Aggregation Conversion from one category to another Melting Freezing Shedding of liquid water

sufficient, and TC tracks are occasionally incorrectly simulated. To avoid this deficiency in a regional model, Tsujino and Tsuboki (2020) developed a spectral nudging technique for CReSS. In physical space, all dependent variables are expressed at grid points. They can be converted into a wave-number space by Fourier transformation. The small wavenumber parts correspond to the large-scale flow, which is mainly controlled by the environmental field. The middle and large wave-number parts are calculated by the inner nested model. The spectral nudging technique nudges only small wave-number parts for the given environmental conditions. A detailed description of the spectral nudging technique is given by Tsujino and Tsuboki (2020), who used this technique to successfully control the track of Typhoon Nancy (1961) without affecting storm intensity. The spectral nudging technique is significantly effective in the long-term simulation of TC. A simulation of Cyclone Winston (2016) is a typical case in which the spectral nudging technique was very effective in a long-term forecast experiment. Winston (2016) is one of the most intense TCs in the southwest Pacific Ocean, with a lifetime-minimum sea level pressure of 884 hPa on February 20, 2016. The lifetime of Winston was approximately 20 days and the cyclone showed an atypical track. A forecast experiment using CReSS at a horizontal resolution of approximately 2 km in a large domain (50.◦ longitude .× 29.◦ latitude) was performed from 1200 UTC on February 10 to 1200 UTC on February 26, 2016. The forecast experiment using the spectral nudging technique indicated that the simulated storm showed satisfactory agreement between the simulated storm track and the best track, although Winston showed an atypical track of very large looping (Fig. 19.7). Although the lifetime-minimum sea level pressure of the simulated Winston was 908 hPa, the rapid intensification to attain the maximum intensity on

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Fig. 19.7 Forecast experiment of Cyclone Winston (2016). The contours are sea level pressure, and the color levels are precipitation intensity (mm h.−1 ) at 0000 UTC on February 20, when the storm attained its maximum intensity. The black line is the track of the simulated storm, and the red line is the track of the observation. Closed circles indicate the center point of the storm at the initial time (1200 UTC on February 10, 2016), and open circles indicate the center point at the end of the simulation (1200 UTC on February 26)

February 19 and other intensity changes were roughly reproduced. This simulation example shows that the spectral nudging technique is very effective for controlling TC tracks in simulations.

19.2.8 Ocean Model Coupling Because the maximum intensity of TCs is strongly dependent on the ocean temperature, ocean temperature cooling due to the TC effect is crucial for accurately predicting TC intensity. CReSS incorporates a one-dimensional thermal diffusion model for the ocean area. This process considers the ocean mixing layer, and only the diffusion of heat is calculated. However, the decrease in ocean temperature is caused not only by diffusion, but also by upwelling (upward advection) due to Ekman pumping. Increasing the accuracy of forecast TC intensity requires that the ocean temperature be accurately calculated using a three-dimensional ocean model. Therefore, we coupled an ocean model with CReSS, the Nonhydrostatic Ocean model for the Earth Simulator (NHOES; Aiki et al. 2006, 2011). NHOES is a threedimensional, nonhydrostatic, Boussinesq approximation ocean model. It was coupled with CReSS to form a regional coupled atmosphere-wave-ocean nonhydrostatic model named CReSS-NHOSE (Aiki et al. 2015). NHOES uses a level-2.5 Mellor–

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Yamada–Nakanishi–Niino (MYNN) type turbulence closure model (Furuichi et al. 2012; Nakanishi and Niino 2009) for the ocean mixing layer. CReSS provides heat and water fluxes and wind stress to the NHOES, and the ocean model returns the SST to CReSS. Moreover, a wave model (Donelan et al. 2012) was incorporated into the coupled model to increase the accuracy of the air–sea interaction simulation. The exchange of momentum between the atmosphere and ocean is performed using the wave model. Consequently, the maximum surface wind region is not necessary to coincide with the region of the maximum wave height, and the wind direction is not always the same as the direction of wave propagation. Using CReSS-NHOES with a horizontal resolution of 2 km for both atmospheric and ocean parts, Kanada et al. (2017a) studied the rapid intensification process of Supertyphoon Megi (2010), which made landfall in the Philippines. The simulated Megi developed rapidly when the sea surface temperature was high inside the typhoon eye (inside the radius of maximum wind speed). However, when the sea surface temperature outside the radius of maximum wind speed was higher than that inside the radius, the development was slow. The results indicate that the local radial distribution of SST has a significant impact on the rapid intensification of Supertyphoon Megi. According to this research, a high-resolution coupled atmosphere-ocean model would facilitate the accurate prediction of typhoon intensity. CReSS-NHOES was also applied by Hirata et al. (2015) to study the explosive development of an extratropical cyclone owing to the moisture supply from the Kuroshio warm current and its extension. They simulated the cyclone and revealed that the cold conveyor belt (CCB) was dry, and a large amount of water vapor was supplied from the Kuroshio warm current to the CCB, which transported water vapor into the cyclone and played a crucial role in its explosive development.

19.2.9 Super-Droplet Method (SDM) The Super-droplet method (SDM), developed by Shima et al. (2009), was coupled with CReSS, and the aerosol impact on precipitation intensity was studied for a warm rain type precipitation. The SDM of warm rain calculates the time evolution of a set of particles (super-droplets). A super-droplet comprises aerosol or liquid-phase particles that have the same properties, namely radius, composition, and position in space. All super-droplets are transported by flow and sedimentation as a Lagrangian framework. The growth of particles in a super-droplet depends on the water vapor deposition process (condensation and evaporation) and collision and coalescence processes. The SDM can calculate the time evolution of the size distribution of particles with fewer computer resources than the bin method. Because the SDM is in the Lagrangian framework, computational diffusion is significantly reduced. An example of a CReSS-SDM experiment that examines the impact of aerosols on precipitation is a two-dimensional simulation of shallow warm rain. The grid spacing was 25 m horizontally and 10 m vertically. In each grid with a volume of 25 .× 25.×10 m.3 , 128 super-droplets were set at the initial time. The dimensions of

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Fig. 19.8 Two-dimensional experiments of shallow warm rain using CReSS-SDM with different initial aerosol concentrations. The left column shows the case of high aerosol concentration (ExpHI, 1050 cm.−3 ), and the right column shows the case of low concentration (ExpLW, 10.5 cm.−3 ). The upper panels are vertical cross-sections of the rain mixing ratio from the surface to a height of 3 km, and the lower panels are the cloud mixing ratios

the two-dimensional domain were 12,800 m horizontally and 5000 m vertically. We performed three sensitivity experiments with different initial aerosol concentrations: 1050 (ExpHI), 105 (ExpMD), and 10.5 cm.−3 (ExpLW). Figure 19.8 shows the mixing ratios of rain (upper panels) and clouds (lower panels) in ExpHI and ExpLW, respectively. The result of ExpMD is not shown because the result showed characteristics intermediate between ExpHI and ExpLW. A significant difference was observed in the cloud and precipitation amounts according to the initial aerosol concentration. When the initial aerosol number concentration was low (ExpLW), precipitation increased. The maximum rainfall intensity exceeded 80 mm h.−1 under such a low aerosol density. In this case, heavy rain formed through the collision-coalescence process of clouds and rain particles. No precipitation occurred when the aerosol concentration was 100 times as large as the low-concentration case. In this case, the evaporation of cloud droplets becomes dominant, and the lifetime of the cloud decreases. This study showed that SDM is highly useful in cloud and precipitation studies focusing on microphysical processes.

19.2.10 Radar Echo Nudging for Storm-Scale Prediction The nudging method is effective for real-time high-resolution forecasts using cloudresolving models owing to its low computational cost. CReSS is capable of nudging radar data. If .q is an arbitrary forecast variable, the nudging method is explained

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by a prognostic equation for .q with an additional external force term in the form of Newton’s damping. This term is referred to as the “nudging term”. The prognostic equation for variable .q is as follows: .

( ) ∂ ρq ¯ = F − αh ρ¯ q m − q obs ∂t

(19.73)

where quantities marked with .m are dependent variables of the model, and those marked with .obs are the observed quantities. The first term on right side . F denotes all other terms. In CReSS, the water vapor mixing ratio (.qv ) and mixing ratios of the precipitation category (rain, snow, and graupel) are the dependent variables (forecast variables). Nudging assimilation of the radar data is performed on these variables. If the radar is polarimetric, the hydrometeor categories are identified. If the radar is of the conventional type, the total mixing ratio of precipitation is separated into the mixing ratios of rain, snow, and graupel in proportion to the model-calculated ratios. The most important variable is the water vapor mixing ratio, which is not observable by radar. In the CReSS nudging method, the following assumptions were made. In the radar echo region of the precipitation, the relative humidity is 100% above the lifting condensation level. The relative humidity at the surface below the echo region is empirically assumed to be 95%, and it increases 100% linearly with height to the lifting condensation level. The assumed relative humidity is converted to the water vapor mixing ratio and used for nudging water vapor in the conservation equation of water vapor in the same manner as shown by Eq. (19.73).

19.2.11 Electrification and Lightning Processes Hydrometeor particles are usually charged in cumulonimbus clouds. If the intensity of the electric field in a cloud exceeds a threshold, lightning discharge occurs in clouds, between clouds, or between the ground and clouds. There are a positively charged region in the upper part of thunderclouds, negatively charged region in the middle layers, and positively charged region in localized areas in the lower layers. This positive–negative–positive structure is called the tripolar structure of charge distribution, and many thunderclouds usually form this tripolar structure of charge distribution. Takahashi (1978) found the riming electrification mechanism and explained the formation process of this tripolar structure. In this mechanism, when graupels and ice crystals collide, they are charged with opposite signs, depending on the temperature. CReSS incorporates riming electrification and lightning discharge processes. The time-dependent prognostic equation for the charge density . Q x of a particle category .x is as follows: .

∂ ρ¯ Q x ¯ ¯ ¯ = Adv.Q x + Turb.Q x + ρCP.Q x + ρFall.Q x + ρRE.Q x ∂t

(19.74)

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Fig. 19.9 Three-dimensional display of a quasi-stationary line-shaped MCS simulated by CReSS with a horizontal grid spacing of 500 m with electrification and lightning processes. Distributions of hydrometeors are indicated by different colors: green, cloud ice; pink, graupel; yellow, snow; white, cloud water; and blue, rain. Red and blue lines represent positive and negative lightning discharges to the ground, respectively. Yellow lines represent in-cloud and inter-cloud lightning

where terms on the right side represent advection, diffusion, cloud physics, and sedimentation. The last term, .RE.Q x , denotes riming electrification, which is added to the charge density equation. The lightning discharge processes are similar to those reported by MacGorman et al. (2001). Lightning discharge is initiated at a grid point when the intensity of the electric field exceeds a threshold (150 kV m.−1 ). The lightning pass propagates in positive and negative directions along the ambient electric field vector. The propagation stops at a point where the intensity of the ambient electric field becomes less than the threshold (15 kV m.−1 ). If the pass reaches a height of 500 m above ground level, it is considered as a cloud-to-ground discharge. The electric charge in the lightning pass is instantaneously neutralized. If the positive charge area is discharged to the earth, lightnings are called positive polarity strikes, and if the negative charge area is discharged to the earth, they are called negative polarity strikes. Figure 19.9 shows an example of the simulation of a quasi-stationary line-shaped MCS that develops north of Nagoya City. Each category of hydrometeors is indicated by different colors, and lightning passes are depicted by lines. The red and blue lines are positive and negative polarity lightning

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discharges, respectively, that occur in the convective regions of the MCS. In-cloud and inter-cloud lightnings were also simulated in convective regions and are depicted by yellow lines.

19.3 Impact of Increasing Resolution The simulation results obtained using CRMs strongly depend on the horizontal resolution of the model. Its increase is essential to resolve the detailed structure of the phenomena. To demonstrate the impact of high resolution, Fig. 19.10 shows simulation results of a supercell using CReSS with two different horizontal resolutions:

Fig. 19.10 Simulated supercell using CReSS with different horizontal resolutions of a 1 km and b 100 m. Color shadings are rain mixing ratio (g kg.−1 ), and arrows are horizontal velocity vectors at the height of 1 km

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1 km (Fig. 19.10a) and 100 m (Fig. 19.10b). In both experiments, the initial condition was a horizontally uniform field with a convectively unstable profile provided by the sounding observation. The simulated supercell with 1 km resolution shows a curved structure with moderate rainfall in the southern part of the cell, but the characteristic structure of the supercell is not clearly expressed. The 100 m resolution simulation showed a clear hook-shaped structure in the southernmost part of the cell, and a maximum rain mixing ratio of 5 g kg.−1 was more prominent. A tornado-like vortex was simulated in the hook-shaped region. This result clearly shows that an increased horizontal resolution can result in qualitative and quantitative improvements in supercell simulation. Although the horizontal scales of supercells and tornadoes differ by two orders of magnitude, recent developments in computer power have made it possible to simulate both on a common fine-grid system. Another example of a high-resolution experiment is the simulation of snow clouds developed in winter monsoon air streams over the sea. They are composed of convective clouds, but their horizontal scale is smaller than that of summer cumulonimbus clouds. When a cold air outbreak of the winter monsoon occurs over the sea surrounding Japan, many cloud streets form. Within convective cloud streets, a significantly developed cloud band occasionally extends from the continental coast to Japan, called the Japan Sea Polar Airmass Convergence Zone (JPCZ). Convective clouds composing the JPCZ are more developed and intense than the other snow cloud streets. They cause severe snowfall accompanying gusty winds and occasionally tornadoes along the coastal regions of Japan. Figure 19.11 compares the satellite observations of JPCZ with the simulation experiment using CReSS with 500 m resolution. The detailed structures of cloud streets over the sea and the JPCZ are clearly simulated. Some vortices are also simulated along the southwestern edge of JPCZ. The good agreement of the detailed

Fig. 19.11 Simulation of the Japan Sea Polar Airmass Convergence Zone (JPCZ) formed in the winter monsoon cold air stream using CReSS with 500 m resolution (right panel) and satellite observations (left panel)

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structure of snowstorm systems indicates the significant impact of increasing the horizontal resolution. If the resolution is as coarse as 1 km, detailed structures are not reproduced.

19.4 Cloud-Resolving Simulations of Tropical Cyclones TCs are the most important objective of CReSS. TCs have horizontal scales ranging from a few 100 km to more than 1000 km, and the computational domain should be several thousand kilometers, considering their movements. By contrast, TCs are composed of cumulonimbus clouds with horizontal scales of several to 10 km. In simulating an entire TC and its life cycle, a large computational domain is required while resolving clouds with high resolution, and the computation is extremely large-scale. Such simulations are now possible owing to the rapid development of computers, and CReSS has been applied to many TC simulations in different countries. In this section, studies on TCs using CReSS are reviewed. Because high-impact weather systems are the most important objectives of CReSS, TCs have mainly been studied by using simulations and numerical experiments. Typhoon Tokage (2004) is one such disaster-producing TC; it made landfall over western Japan on October 20, 2004, and the associated large amount of rainfall resulted in severe floods and landslides in many areas of western Japan. The maximum rainfall intensity was greater than 50 mm h.−1 , and the total rainfall amount was greater than 500 mm. There were 98 fatalities in Japan. Tsuboki and Sakakibara (2006) performed an experiment to predict heavy rainfall associated with Typhoon Tokage using CReSS with a horizontal resolution of 1 km in a large domain. A 36 h simulation was performed from 1200 UTC October 19, 2004. The simulation successfully reproduced the movement of the typhoon and its associated heavy rainfall. The rainfall intensity in western Japan sufficiently agreed with the JMA surface observations. The distribution of precipitation intensity at the surface showed heavy rainfall north of the typhoon center making landfall over Japan (Fig. 19.12). A detailed examination of the simulation indicated that abundant solid particles in the upper layer were produced by weak upward motions rather than intense convections. Snow and graupel were transported by the upper-level strong southerly to the Japan Seaside of central Japan, where they produced heavy rainfall. Because CReSS predicts the amount of each hydrometeor, a detailed process of the formation of heavy rainfall is clarified. The results suggest that the cloud-resolving model is suitable for studying the mechanism of heavy rainfall and for quantitative predictions of the rainfall amount and intensity in association with typhoons. When Typhoon Tokage (2004) approached western Japan, narrow, intense arcshaped rainbands were observed over the Pacific south of Japan by meteorological radars. The 1 km high-resolution CReSS successfully simulated arc-shaped rainbands and their transition behavior as the typhoon approached. Wang et al. (2021b) studied the formation mechanism of rainbands and found that they formed along a lowlevel frontal convergence zone between the southerly flow of the typhoon and the

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Fig. 19.12 Precipitation intensity (color levels; mm h.−1 ), sea level pressure (contours; hPa), and horizontal wind vectors (arrows; scale at the bottom m s.−1 ) at 0630 UTC on October 20, 2004, obtained from CReSS simulation of Typhoon Tokage (2004) at a horizontal resolution of 1 km. The black square indicates the heavy rainfall region that resulted in a severe flood

northerly flow from the Sea of Japan. High-resolution simulations are useful for studying small-scale precipitation systems. Typhoon Morakot (2009) caused devastating heavy rainfall events in Taiwan. A total rainfall amount of 3031.5 mm was observed with the landfall of Morakot, which resulted in the worst disaster in the past 50 years in Taiwan. Accordingly, Morakot has been studied (e.g., Liang et al. 2011; Wu et al. 2011). Wang et al. (2013a) successfully simulated the total amount, distribution, and timing of heavy rainfall caused by Morakot in Taiwan approximately two days prior to heavy rainfall using a 3 km resolution CReSS. In addition to the typhoon-monsoon flow interaction with mesoscale convective systems, the slow movement of storm increases the total amount of precipitation. Wang et al. (2012) found that the slowdown was related to the asymmetric latent heating structure of Morakot by using CReSS with a horizontal resolution of 3 km. Their sensitivity experiment with reduced moisture content showed an increase in typhoon transition speed and a decrease in rainfall amount. They emphasized the contribution of asymmetric heating to typhoon motion and the importance of cloud microphysics to improve the accuracy of the prediction of typhoon tracks. Similar types of typhoon slowdown of transition spend were found in Typhoon Fanapi (2010), studied by Wang et al. (2013b) using the 3 km resolution CReSS model. They successfully simulated the slowdown of the transition speed of Typhoon Fanapi with a change from a symmetric to an asymmetric structure, which caused heavy rainfall of more than 800 mm in Taiwan. According to the simulation and sensitivity experiments with reduced moisture content, they concluded that the sudden reduction in the transition speed of Fanapi was caused by asymmetric latent heating and not environmental flow.

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As shown by the observations, the heavy rainfall associated with Typhoon Morakot (2009) was prolonged by the west-east oriented intense rainbands on the west side of Taiwan. Wang et al. (2015) simulated convection in rainbands using CReSS with a 1 km horizontal resolution. They found an interaction between rainfall and the dynamic field and indicated that the pressure perturbation in the convective clouds enhanced the precipitation of rainbands. Chen et al. (2017) studied the rainbands on the west side of Taiwan in the Morakot case using a 3 km grid-spacing CReSS and found that the slowdown of the transition speed of Morakot is attributed to the asymmetric convection produced by the interaction between typhoon circulation and southwest monsoon flow. Wang et al. (2020) studied the impacts of the vortex structure of Morakot on extreme rainfall in Taiwan using CReSS with a 2.5 km horizontal resolution. They performed a control experiment and some sensitivity experiments in which the size and circulation strength of Morakot by the potential vorticity inversion technique. Their findings showed that a weaker storm does not necessarily decrease the total rainfall over Taiwan and that the strong southwesterly and its moisture supply were larger factors than the vortex structure. CReSS has been used to study TC dynamics, such as rapid intensification (RI), concentric eyewalls (CEs), and warm-core structures. The RI process is important for supertyphoon formation. Supertyphoon Haiyan (2013), which made landfall and caused a huge disaster in the Philippines, showed a significant RI. Kuo et al. (2019) performed a simulation of Haiyan, focusing on RI using CReSS with a horizontal resolution of 2 km. They used simulation results to diagnose dynamic efficacy and latent heating. They emphasize that model resolution is important for simulating the internal nonlinear processes of RI. The model results were also used by Tsujino and Kuo (2020) for potential vorticity mixing and the RI of Haiyan. Applying the piecewise potential vorticity inversion technique and an omega equation to the model results, they showed that potential vorticity mixing accounts for approximately 50% of the pressure fall during the RI onset. Using 2 km resolution CReSS, Hioki and Tsuboki (2021) studied the process of central pressure fall of Typhoon Wipha (2007) which showed an increase of maximum surface wind speed by 45 knots in 24 h and a central pressure fall by 40 hPa in 24 h. According to a backward trajectory analysis of air-parcels of the warm core during the simulated RI of Wipha, they found that the warm core comprises high equivalent potential temperature air originating from the lower troposphere and high potential temperature air from the lower stratosphere. They used forward trajectory analysis to show that air-parcels leave the eye through the eyewall throughout the troposphere, which eventually results in a central pressure fall during the RI period. CEs are also important objectives in TC research because they are characteristic of intense TC and occasionally cause errors in TC intensity estimates. Tsujino et al. (2017) performed a simulation of Typhoon Bolaven (2012), which showed long-lived CEs, to study the maintenance mechanism of CEs. Applying a budget analysis of equivalent potential temperature and trajectory analysis, they found that the entropy supply to the inner eyewall was sufficient after secondary eyewall formation and that moist air mass supplying entropy to the inner eyewall passed the outer eyewall region through the planetary boundary layer.

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Typhoon Lan (2017) was observed by dropsondes from 13.1 km in height in the T-PARCII (Tropical cyclones-Pacific Asian Research Campaign for Improvement of Intensity estimations/forecasts) project led by Tsuboki of Nagoya University. TPARCII conducted penetration observations in the eye of Lan and made dropsonde observations of the thermodynamic structure at the center of the eye. The observations showed that the warm core has two peaks of temperature deviation, called a double warm-core structure (Yamada et al. 2021). Using CReSS simulation, Tsujino et al. (2021b) studied the mechanism of a double warm-core structure observed in Typhoon Lan. In their simulation, horizontal grid spacing was approximately 2 km, and the lowest vertical resolution was 200 m, stretching with height. They successfully reproduced the double warm-core structure of Lan and used the model results to analyze the intensification and maintenance processes of the warm core. Utilizing a potential temperature budget and backward trajectory analysis, they found that the double warm-core structure is enhanced by axisymmetric subsidence warming in the eye, and the air mass of the subsidence is partly induced by inward acceleration in the subgradient regions of the eyewall. As shown in the case of Cyclone Winston (2016) simulation in Sect. 19.2.7, CReSS has been used for research on TCs in other ocean basins. Akter and Tsuboki (2012) studied Cyclone Sidr over the Bay of Bengal using CReSS. Sidr was the most devastating tropical cyclone; it made landfall over the Bangladesh coast on November 15, 2007. Sidr had an intense outer rainband to the east of its center and a significant frontal band to the northwest. The eastern rainband was long and intense, and prolonged heavy rainfall was maintained over the coastal region of Bangladesh. In the simulation of Sidr, a computational domain of 1500 km.× 1575 km horizontally was used with a horizontal resolution of 2.5 km. They showed that the eastern rainband was located between the synoptic-scale flows of a weakly sheared, gradient-balanced westerly and a strongly sheared, nongradient-balanced prevailing southerly. A simulation of the intense eastern rainband of Cyclone Sidr using a higher resolution than that in the aforementioned study was performed by Akter and Tsuboki (2010) using CReSS with a 1 km horizontal resolution. The high-resolution simulation showed that the rainband was composed of intense convective cells and that some cells had the characteristic structure of a supercell. They had a stronger updraft, more intense precipitation, and a longer cell lifetime.

19.5 Future Changes in TCs with Global Warming Although computer power has rapidly increased, it remains difficult for a global model to resolve the inner core structure of TCs in detail and to project the future intensity increase in TCs. A dynamic downscaling simulation (DDS) using a regional model nested in a global model is effective for studying future changes in TC activity with climate change. CReSS and CReSS-NHOES have been used for high-resolution DDS to study future intensity changes in TCs in the context of climate change. High-resolution cloud-resolving models are important for simulating the detailed

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Fig. 19.13 A three-dimensional display of a future supertyphoon developed in a warmed climate simulated by CReSS with a horizontal grid spacing of 2 km

structure and intensity of future TCs. They are particularly essential for quantitative simulations of very intense TCs. Figure 19.13 shows a simulated future supertyphoon using CReSS in the warming climate of the late twenty-first century. Because the horizontal resolution is 2 km, sufficiently high to resolve the inner core structure of a typhoon, a detailed and realistic structure of the TC inner core was obtained. The supertyphoon will make landfall over eastern Japan with a sea level central pressure of 880 hPa and a maximum surface wind speed of approximately 75 m s.−1 (Fig. 19.14). Such a detailed structure and quantitatively accurate intensity were obtained by high-resolution DDS using the CReSS. Tsuboki et al. (2015) performed this type of DDS for typhoons in the western North Pacific under the global warming climate of the late twenty-first century. To perform the DDS, CReSS was nested in the outputs of future projections provided by the global model experiment of the Meteorological Research Institute 20 km mesh AGCM, MRI-AGCM3.1 (Kitoh et al. 2009; Mizuta et al. 2006). The DDS results showed that the most intense future supertyphoon could attain wind speeds of 85 .∼ 90 m s.−1 and minimum central pressures of approximately 860 hPa, and the maximum latitude attained by future supertyphoons will become further north. This result suggests that risks associated with TCs will increase with climate change in the mid-latitude countries. Kanada et al. (2017b) studied the future enhancement of heavy rainfall associated with typhoons in mid-latitude regions. Using CReSS-NHOES, they conducted a

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Fig. 19.14 Horizontal display of a future supertyphoon shown in Fig. 19.13 when it makes landfall over eastern Japan. Color levels are precipitation intensity (mm h.−1 ), contours are sea-level pressure (hPa), and arrows are velocity vectors of the surface wind

pseudo-global warming (PGW) experiment on Typhoon Chanthu (2016), which made landfall over Hokkaido and caused severe floods. Typhoon Chanthu is characterized by predecessor rain (PRE; e.g., Cote 2007; Galarneau et al. 2010). They showed that rainfall in the PRE and typhoon circulation are more intense and more concentrated in the future warmer climate in the mid-latitudes. Kanada et al. (2019) extended this study to include more cases of typhoons that made landfall over Hokkaido by DDSs using CReSS-NHOES. They found an increase in the frequency of strong rainfall in eastern Hokkaido under a warming climate compared with the present climate in all typhoon experiments, while there was a decrease in the frequency of weak rainfall. These results indicate that intensity and frequency of heavy rainfall associated with typhoons could increase in future warming climates, even in high-latitude regions such as Hokkaido. Using CReSS with 4 km horizontal resolution, Kanada et al. (2020) performed many DDSs of typhoons that made landfall over Hokkaido in the present climate and the 4-K warmed climate experiments in the database for Policy Decision making for Future climate change (d4PDF) (Mizuta et al. 2017). Based on the 100 DDSs in each climate and comparing these two climate DDSs, they found that 12% of typhoons in the 4-K warmed climate experiment developed to an intensity not observed in the present climate, with a minimum central pressure of 925 hPa or less. Furthermore, they showed that such intense typhoons with axisymmetric structures could strike high-latitude regions, such as Hokkaido, when the baroclinicity of the environment is significantly reduced.

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To study the future change in a significant typhoon in mil-latitude with climate change, Kanada et al. (2021a) performed PGW climate experiments on the slowmoving intense Typhoon Trami (2018) using 1 km-mesh CReSS-NHOES. In the PGW experiment, differences in the typhoon environment were obtained from present and future climate projections using a global model and added to the environmental variables of Typhoon Trami. Because the resolution of the PGW experiment is sufficiently high, quantitative changes in the atmosphere and the ocean due to typhoons were obtained. Their results indicate that the SST decrease due to the typhoon is larger in the future climate than in the present climate, and the development of future typhoons is significantly suppressed, although the lifetime-maximum intensity of the storm is larger in the future climate. This study using the coupled model suggests that the air–sea interaction is a key factor in studying the future change in a mid-latitude intense typhoon. Kanada et al. (2021b) also used 1 km-mesh CReSS-NHOES to study the future change in rainfall amount associated with a very intense Typhoon Hagibis (2019). The typhoon brought a large amount of rainfall over eastern Japan and caused severe flooding. In the PGW climate experiment, they found that the outer rainband increased in intensity in the warmed climate and that the resulting rainfall amount increased; the increase in rainfall of the typhoon core region was suppressed owing to the SST decrease. The study showed that for more accurate prediction of future changes in typhoons and associated rainfall, it is important to use a high-resolution coupled atmosphere-ocean model, along with more accurate prediction of future changes in the oceans.

19.6 Heavy Rainfall Predictions In many regions worldwide, heavy rainfall is often caused by MCSs. In particular, heavy rain-producing MCSs often develop in monsoon systems and cause severe floods and landslides in East Asia. Monsoon systems in East Asia are characterized by quasi-persistent rain from late spring to early summer, referred to as Meiyu in Taiwan and China, Changma in Korea, and Baiu in Japan. Shurin (or Akisame) is a similar rainy season from late summer to autumn in Japan. Because these MCSs are composed of intense convective clouds, a cloud-resolving model is indispensable for their quantitative prediction, and the CReSS has been used for studies and forecasts of heavy rainfall. Heavy rainfall often occurs during the warm season in the western and central regions of Japan. Since this rainfall tends to be localized, they are typically called “localized torrential rain” in Japan. Other typical heavy rainfall events are caused by stationary line-shaped precipitation systems (SLPSs), also referred to as stationary line-shaped MCS, or simply as stationary rainbands. The significant characteristics of these heavy-rain-producing systems are their slow-moving speed and long-term maintenance. Consequently, the total amount of rainfall becomes extremely large, and disasters occur.

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SLPSs frequently occur in central Japan. Min et al. (2021) studied the formation mechanism of the SLPS on September 1, 2015, using CReSS with a horizontal resolution of 2 km. They performed a simulation experiment of the SLPS event and sensitivity experiments on the topography of the surrounding area. They found that the SLPS was formed by low-level convergence of the westerly with the warm and moist south-southwesterly from the channel to the south of the Kinki district. New cells in the SLPS successively formed at the southern end of the SLPS and were transported by the mid-level southwesterly; consequently, the SLPS formed in the Kinki district. The essential factor for SLPS formation was the abundant supply of water vapor transported by the south-southwesterly through the channel, but the topography was not essential for the formation of the SLPS. A heavy rainfall-producing convective line associated with the Meiyu front observed in Taiwan was studied by Wang et al. (2005) using CReSS. They performed a simulation of the convective line and sensitivity experiments of Taiwan topography with a 2 km grid size and found that the intensity and position of the convective line are highly sensitive to the terrain height. Wang et al. (2011) studied heavy rainfall over central Taiwan on June 8, 2007, using the 2 km grid CReSS model to clarify the triggering mechanism for deep convection. The simulation showed that preexisting storms produced pauses of cold outflow and gravity waves. Deep convection was triggered by the arrival of gravity waves ahead of the cold outflow, and this is referred to as the remote trigger of deep convection. Wang et al. (2014a, b) studied two propagating episodes of mesoscale convection that caused heavy rainfall in Taiwan. They performed a simulation experiment of the eastward and westward propagating characteristics of convective systems using CReSS with a 2.5 km resolution and showed that the simulation highly agreed with the observation. According to the simulation, the structure, environmental shear, and organization processes differ in the eastward and westward propagating systems. Wang and Huang (2009) performed a high-resolution simulation on a convective line formed off the southeastern coast of Taiwan in the Meiyu season using CReSS with grid sizes of 10, 2, and 0.5 km and showed the formation process of the convective line. Tsujino et al. (2021a) performed high-resolution experiments on afternoon thunderstorms in the Taipei metropolitan area, which often cause floods in the city area. They used the CReSS of the triple one-way nesting technique with an innermost domain of 300 m horizontal resolution to resolve individual cumulonimbus clouds. The comparison of the thunderstorm case and the no thunderstorm case demonstrated that environmental wind and moisture profiles are important for thunderstorm formation. Using a very high-resolution model, CReSS can simulate the detailed structure of cumulonimbus storms. Record-breaking heavy rainfall was caused by a back-building and quasi-stationary mesoscale convective system associated with the Changma front in southeastern South Korea on July 7, 2009. The maximum rainfall amount was 310 mm in less than 12 h in the Busan metropolitan area (Jeong et al. 2016a, b). Jeong et al. (2016a) simulated a heavy rainfall system using CReSS with a horizontal resolution of 2 km and showed that the quasi-stationary, back-building mesoscale convective system was successfully reproduced at approximately the correct location and time. They

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found that a cold pool produced by evaporative cooling was essential for the stationarity of the heavy rainfall system, according to a sensitivity experiment without evaporation. In Japan, extratropical cyclones occasionally cause heavy rainfall. Hirata et al. (2021) studied record-breaking heavy rainfall observed on Miyake Island, south of Tokyo, using CReSS with a horizontal resolution of approximately 2 km. They focused on the role of heat fluxes from the Kuroshio warm current in enhancing the frontal convective rainband formed in an extratropical cyclone. According to the control experiment and some sensitivity experiments on surface heat fluxes, they found that the latent heat flux from the Kuroshio Current significantly increased the near-surface moisture content and convective instability. The heat flux from the Kuroshio Current enhances the heavy rainfall-producing rainband of the extratropical cyclone.

19.7 Radar Data Assimilations Although the horizontal resolution of CReSS is sufficiently high to resolve individual cumulonimbus clouds, some MCSs fail to be simulated. In particular, (quasi-) stationary line-shaped MCSs are difficult to simulate, although they are the most dangerous precipitation systems among the various types of MCS. Occasionally, they develop in monsoon systems and cause severe floods and landslides in East Asia. Tsuboki and Luo (2020) successfully simulated a heavy-rain-producing MCS on July 5, 2017, in western Japan. Another stationary line-shaped MCS caused a severe disaster in northern Kyushu on the same day and near the western Japan MCS but was not successful in forecasting. A possible solution to this problem is the data assimilation (DA) of radar observations. There are different types of DA: a simple nudging method, the ensemble Kalman filter (EnKF), the three-dimensional variational method (3DVAR), and the fourdimensional variational method (4DVAR). For the application of real-time numerical weather prediction (NWP) at the storm-scale or convective-scale, simple nudging and 3DVAR are useful because of their lower computational cost than other methods. In improving short-range forecasting on a storm scale, blending radar data with NWP is expected to be a promising technique with a low computational cost. Using the nudging method explained in Sect. 19.2.10, we performed a prediction experiment of a line-shaped MCS that occurred north of Nagoya City on July 15, 2010. Heavy rainfall occurred locally in southern Gifu Prefecture from 1600 to 2300 JST (Japan Standard Time = UTC + 9 h) on July 15, with heavy rainfall of approximately 60 mm h.−1 (83.5 mm in 1 h 1912 JST). The rainband extends from southwest to northeast and is almost stationary. The control simulation without nudging radar data (Fig. 19.15a) shows a wide area of weak precipitation extending from the southwest to the northeast to the north of Nagoya City; however, no intense rainband was simulated. The experiment with radar data nudging (Fig. 19.15b) predicted a very intense rainband extending from the southwest to the northeast along

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Fig. 19.15 Simulation experiments of the quasi-stationary line-shaped MCS that occurred north of Nagoya on July 15, 2010, using CReSS: a control simulation and b simulation with radar data nudging. Gray arcs represent radar ranges used for nudging

the southeast edge of the wide-area precipitation. The maximum rainfall intensity of the rainband was approximately 100 mm h.−1 . This simulated rainband agreed with the observed line-shaped MCS in position and rainfall intensity. This result indicates that the nudging method is highly effective for the quantitative short-range forecasting of heavy-rain-producing MCSs with a low computational cost. Shimizu et al. (2019) demonstrated that thermodynamic variables derived from multiple radar observations are useful for convective-scale DA using a nudging technique. Thermodynamic variables, such as the potential temperature and water vapor, are important for dynamic balance at the convective-scale. They can be retrieved from multiple Doppler radars (Gal-Chen 1978; Hane et al. 1981). Shimizu et al. (2019) developed a thermodynamic retrieval method based on Liou et al. (2014) and derived the potential temperature from 1 min high-temporal Doppler observations of the MCSs. They also used a vapor adjustment scheme (Wang et al. 2013) and modified the water vapor mixing ratio in convective clouds above the lifting condensation level. The derived potential temperature was assimilated into the 1 km CReSS model with a 1 min update using the nudging technique (Stauffer and Seaman 1994). They applied this technique to a tornadic storm in Tokyo, Japan, and showed that the nudging technique provided a better storm forecast in the first 30 min. They also found that a finer temporal resolution of radar observations provided better forecast results, according to some sensitive experiments. Most convective-scale radar DAs employ precipitation radar (X-band or C-band radar). By contrast, Kato et al. (2022) used cloud radar (Ka-band) observations for DA using the nudging technique of a meso-gamma-scale MCS event. Similar to Shimizu et al. (2019), they assumed the saturation of water vapor in convective clouds and used the nudging technique to assimilate the water vapor mixing ratio in the 250 m

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NWP using CReSS. Because cloud radar detects convection before precipitation forms in clouds, earlier information on convection can be assimilated in the NWP. They showed that the heavy rainfall was predicted approximately 20 min after the end of the DA cycle. In the other experiment without radar data DA, precipitation was not predicted. These results indicate that the cloud radar DA with the nudging technique is highly promising for the NWP of localized heavy rainfall. Radar DA using 3DVAR is also effective for storm-scale NWP of heavy rainfall. Based on the 3DVAR of Barker et al. (2004) and Kato et al. (2017) developed a CReSS-3DVAR forecast system for an extremely heavy rainfall event that occurred in Tokyo, Japan, on July 24, 2015. They assimilated ground-based observations (radars, lidars, and microwave radiometers) with a 0.7 km horizontal gird size of the CReSS model. The results showed that the intense rainfall was successfully predicted. They also used a vapor adjustment scheme to adjust the relative humidity in the convective region observed by radar (Wang et al. 2013) and found that moisture adjustment is effective for convective-scale forecasts. The 3DVAR method effectively improves the convective-scale NWP, whereas an instantaneous 3DVAR causes discontinuity in the simulation because it usually disturbs the dynamic balance in the model. Shimose et al. (2017) found that spike noise appears in the surface wind speed. To suppress such artificial spike-like noise, they applied an incremental analysis update (IAU) with 3DVAR analysis. The IAU technique can relax the shock of instantaneous changes by using 3DVAR. In this technique, the difference between the first guess of model and the analysis, referred to as “increment”, is divided into small pieces, and they are added to the first guess during the IAU time window. The IAU with 3DVAR is very effective in convectivescale NWP, particularly for calculating high-frequency variables such as the velocity component. Shimose et al. (2017) applied CReSS-3DVAR with the IAU technique to tornadic storms in Tokyo on September 6, 2015. In this case, spike noise was significant in the 3DVAR simulation. Using the IAU technique, the spikes were successfully removed from the result of the 3DVAR, and the simulated wind speed agreed with the observations. This result indicates that the IAU technique is effective for the NWP in highly variable weather systems.

19.8 Tornado Simulations Cumulonimbus clouds, parent clouds of tornadoes, have horizontal scales of the order of 10 km, and tornadoes (tatsumaki in Japanese) that form within them have horizontal scales of several hundred meters. A horizontal resolution of several tens of meters is required to simulate tornadoes. Furthermore, strong cumulonimbus clouds that can produce tornadoes occur within larger-scale weather systems, such as TCs and fronts. Accordingly, each numerical simulation of tornadoes with their parent systems is a very large computation.

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Fig. 19.16 Three-dimensional display of a tornado in Japan on September 24, 1999, simulated using CReSS. The smoke-like white-gray levels represent the vertical vorticity that indicates a tornado. The color levels at the bottom indicate temperature anomalies at the surface

As an example of a tornado simulation, an idealized experiment of a supercell tornado that occurred in the outer rainband of Typhoon Bart (1999) on September 24 is presented. The environmental field was provided by the JMA sounding at 00 UTC September 24 at Shionomisaki, which showed a strong convectively unstable condition and relatively large vertical wind shear. The domain was a square of 48 km, and the horizontal resolution was 75 m. The lowest vertical grid spacing was 25 m, and the vertical grid spacing was stretched with height. Cloud microphysics was the bulk cold rain type. In the experiment, a convection cell began to develop immediately after the initiation of the calculation and split into left- and right-moving cells. The right-moving cell developed to form a supercell that was the parent cloud of the tornado and maintained its structure for a long period. In the southernmost part of the supercell, a very intense updraft was maintained along the gust front of the cold divergent wind. Tornadoes were generated and developed successively within the updraft. Figure 19.16 shows a three-dimensional representation of the vorticity in the southernmost part of the supercell, where the smoke-like structures correspond to the tornado. The color level at the bottom represents the temperature anomaly at the surface, and tornadoes develop near the gust front. The tornado vortex has a diameter from 300 to 400 m, which roughly corresponds to the observations. The tornadoes develop one after another in the updraft near the gust front and then weaken and dissipate as they move away from the gust front during the simulation period. Figure 19.17 clearly shows the successive development of tornadoes based on the maximum vertical vorticity and minimum negative pressure deviation in the

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Fig. 19.17 Time-height cross-section of the maximum vertical vorticity (upper panel) and minimum pressure deviation (lower panel) in the computation domain during the tornado simulation

computational domain. The time-height cross-sections of these variables indicate that tornadoes repeatedly occur with corresponding vorticity and pressure deviations. The time range of each vorticity indicates the longevity of each tornado, ranging from approximately 10 min to nearly 20 min for the longest tornado. Vorticity and pressure anomalies reach heights of 4000 .∼ 5000 m near the mid-levels of the supercell. Positive vorticity and negative pressure deviation maxima are present near the surface and weaken with increasing height. Vorticity and pressure deviation correspond to each other, indicating that they are in cyclostrophic balance, which is characteristic of tornadoes. Because the parent supercell and tornadoes are three-dimensional, a projection of the variables on a vertical plane shows their structures with more clarity. Figure 19.18 shows the projections of the maxima of vorticity, precipitation mixing ratio, and velocity in the tornado region on the x–z plane. The mixing ratio distribution shows a vault structure formed by a very intense updraft. The three series of vertical vorticity projections show that the vortex tube extends from the surface to the upper part of the supercell below the vault structure. The strong updraft below the vault stretches the vertical vorticity to form a tornado. Because the updraft is weak inside the tornado vortex, precipitation particles fall into the tornado when they reach a region with a large mixing ratio of precipitation particles.

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Fig. 19.18 Vertical extending development of the simulated tornado vortex on September 24, 1999, at a 0242, b 0244, and c 0247 UTC. The horizontal axis represents the distance in the x direction. Contours are vertical vorticity; color levels are the mixing ratio of total precipitation particles; and arrows are velocity vectors of x and vertical components, which are maximum values in the 5550 m width in the y-direction, including the tornado, and are projected on the x–z plane

In this experiment, supercell and tornado, which differ by two orders of magnitude on a horizontal scale, were simulated simultaneously on a common grid. This type of computation has no connection problem with the lateral boundary between the cloudscale and tornado-scale, which often occurs in nesting calculations. The experiment showed that tornadoes were spontaneously generated in the supercell based on the dynamics of the model. As another example of a tornado, we present the results of a simulation of a tornado that occurred in Kyushu, Japan, on September 17, 2006. Typhoon Shanshan (2006) moved northeastward to the west of Kyushu, and an outer rainband passed over the region where the tornado occurred. The tornado killed three people and caused a train accident in Kyushu, Japan. In this study, a forecast experiment with a horizontal resolution of 500 m was first conducted over a large area that contained the entire typhoon. Next, using this result as the initial and boundary values, a tornado forecast experiment with a horizontal resolution of 75 m was conducted. In the 500 m resolution experiment, intense outer spiral rainbands formed to the east of the center of the typhoon, and one of them passed over the region of tornado damage at 0500 UTC when a tornado occurred in Kyushu (Fig. 19.19). The cumulonimbus clouds comprising the rainband exhibited supercell characteristics. A high-resolution experiment was performed to study the relationship between the supercells and tornadoes, with a grid spacing of 75 m. The results show that a hook-shaped structure forms in the southernmost part of the supercell and that an intense tornado is simulated in the hook-shaped part of the supercell (Fig. 19.20). The horizontal diameter of the tornado was approximately 300 m, and its

526 Fig. 19.19 Horizontal distributions of the rain mixing ratio (color levels) and horizontal velocity (arrows) at the height of 1.9 km at 0505 UTC on September 17, 2006, obtained from the simulation experiment. The cross and rectangle indicate Nobeoka City and the region of the nested simulation, respectively

Fig. 19.20 Supercell simulated in the experiment with a horizontal grid spacing of 75 m at 0500 UTC on September 17, 2006. Color levels indicate the rain mixing ratio at the height of 200 m. Arrows indicate horizontal velocity. The circle indicates that the tornado occurred in the southernmost part of the supercell

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maximum vorticity was larger than 0.9 s.−1 . The pressure perturbation was approximately .− 24 hPa at the center of the tornado, and the maximum horizontal velocity reached 70 m s.−1 . The tornado extends up to a height of 2.5 km in strong upward motion. The simulation showed the detailed structures of the tornado and supercell formed in the typhoon spiral rainband.

19.9 Concluding Remarks A quarter of a century has passed since the development of CReSS started. During this period, computers have rapidly developed by replacing hardware with upgraded versions. However, the lifecycle of a numerical model is much longer than that of hardware, and the model has been improved. CReSS was originally written using FORTRAN 77 and re-coded using FORTRAN 90. It has been optimized for new mainframe computers. CReSS was originally developed for parallel processors and can now be used on computers with more than 10,000 processing elements. As the number of processing elements increases, computations with higher resolution and larger domains than those in previous studies will be possible, which will result in breakthroughs in simulations and predictions of weather systems, in particular, of MCSs and TCs. However, the knowledge of nature is insufficient, and the physics in the model must be improved further. There is much room for improvement in cloud microphysics, turbulence, planetary boundary layer, and surface layer. In particular, the exchange processes of heat, moisture, and momentum between the atmosphere and ocean below TC environments remain unclear. Sea spray is also one of the large unknown factors below the TC, although it may play an important role in intensity forecasting. Data for the improvement of the model and verification of the simulated results were insufficient. We need more observations of MCSs and TCs and collaboration between observations and numerical studies. In this chapter, the basics of CReSS and its applications are summarized. The author attempted to summarize studies using the CReSS as much as possible. However, some important research results could not be included in the text, for example, the cloud physics process in TC (Nomura and Tsuboki 2012; Nomura et al. 2012), winter supercells (Wang et al. 2009), quantitative precipitation forecasts (Wang et al. 2016, 2021a, 2022a, b, c), Superbomb (Hirata et al. 2019b), extratropical cyclones and the Kuroshio warm current (Hirata et al. 2018, 2019a), TCs and the Kuroshio warm current (Fujiwara et al. 2020a, b; Fujiwara and Kawamura 2021), CReSSLETKF (Yamaguchi and Nakakita 2008), and snow storms (Liu et al. 2004, 2006; Maesaka et al. 2006; Ohigashi and Tsuboki 2007). These studies will be referred to in other papers and manuscripts. The CReSS code is open for scientific and commercial applications. Fortunately, CReSS has been accepted by many users in many countries. It has been applied for many purposes including experimental and operational uses. The CReSS code is written simply and is flexible for incorporating different physical processes. It is

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relatively easy to modify and apply to many objectives. As aforementioned, CReSS has been used on massive parallel and laptop computers. However, improvements in physical processes and computation schemes will continue in collaboration. The author hopes this document facilitates the future use of CReSS and collaborations, and the author is very grateful to all users of CReSS and the readers. Acknowledgements All CReSS codes were written by Mr. A. Sakakibara of Chuden CTI Co., Ltd.; further improvements were made by Mr. K. Hasegawa of Chuden CTI Co., Ltd. They are indispensable in the development and improvement of the CReSS. The author would like to thank them for their cooperation and big efforts. The author also appreciates Professor Chung-Chieh Wang of the National Taiwan Normal University for his collaboration using CReSS. The spectral nudging technique was implemented by Dr. S. Tsujino at the Meteorological Research Institute of JMA. 3DVAR DA was developed by Dr. S. Shimizu of the National Research Institute for Earth Science and Disaster Resilience. The Super-droplet Method was developed by Professor S. Shima of the University of Hyogo, and the calculation of clouds was performed by Mr. K. Moriki. Electrification and lightning processes were developed by Mr. H. Kaneko. The author is grateful for their cooperation. He also thanks Mr. M. Kato of Nagoya University for his kind assistance. Simulations and calculations were performed using the Earth Simulator of JAMSTEC and the mainframe computers of the Information Technology Center, Nagoya University. A part of the research of this text is supported by JSPS KAKENHI (Grant Numbers JP16H06311 and JP21H04992).

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in a severe storm: evidence from nudging data assimilation experiments with a thermodynamic retrieval method. Q J R Meteorol Soc 145:2139–2160. https://doi.org/10.1002/qj.3548 Shimose K, Shimizu S, Kato R, Iwanami K (2017) Analysis of the 6 September 2015 tornadic storm around the Tokyo metropolitan area using coupled 3DVAR and incremental analysis updates. J Disaster Res 12:956–966 Smagorinsky J (1963) General circulation experiments with the primitive equations. I. The basic experiment. Mon Weather Rev 91:99–164 Stauffer DR, Seaman NL (1994) Multiscale four-dimensional data assimilation. J Appl Meteorol Climatol 33:416–434 Takahashi T (1978) Riming electrification as a charge generation mechanism in thunderstorms. J Atmos Sci 35(8):1536–1548 Tsuboki K, Sakakibara A (2002) Large-scale parallel computing of cloud resolving storm simulator. In: Hans PZ et al (eds) High performance computing. Springer, New York, pp 243–259 Tsuboki K, Sakakibara A (2006) The prediction experiment of a localized heavy rainfall associated with a typhoon using the cloud-resolving model: a case study of the heavy rainfall event in the northern Kinki District associated with the typhoon 0423 on 20 October 2004. J Jpn Soc Natl Disaster Sci 25(3):351–373 (in Japanese with English abstract) Tsuboki K, Sakakibara A (2007) Numerical prediction of high-impact weather systems. In: The textbook for seventeenth IHP training course in 2007. Hydrospheric Atmospheric Research Center, Nagoya University, UNESCO, 273 pp Tsuboki K (2008) High-resolution simulations of high-impact weather systems using the cloudresolving model on the earth simulator. In: Hamilton K, Ohfuchi W (eds) High resolution numerical modeling of the atmosphere and ocean. Springer, New York, pp 141–156 Tsuboki K, Yoshioka MK, Shinoda T, Kato M, Kanada S, Kitoh A (2015) Future increase of supertyphoon intensity associated with climate change. Geophys Res Lett 42:646–652. https:// doi.org/10.1002/2014GL061793 Tsuboki K, Luo Y (2020) High-resolution simulations of heavy rainfalls in association with monsoon systems and typhoons using cloud-resolving models. In: The multiscale global monsoon system. World scientific series on Asia-Pacific weather and climate, vol 11, pp 113–131 Tsujino S, Tsuboki K, Kuo HC (2017) Structure and maintenance mechanism of long-lived concentric eyewalls associated with simulated Typhoon Bolaven (2012). J Atmos Sci 74:3609–3634. https://doi.org/10.1175/JAS-D-16-0236.1 Tsujino S, Tsuboki K (2020) Intensity change of Typhoon Nancy (1961) during landfall in a moist environment over Japan: a numerical simulation with spectral nudging. J Atmos Sci 77:1429– 1454. https://doi.org/10.1175/JAS-D-19-0119.1 Tsujino S, Kuo HC (2020) Potential vorticity mixing and rapid intensification in the numerically simulated Supertyphoon Haiyan (2013). J Atmos Sci 77:2067–2090. https://doi.org/10.1175/ JAS-D-19-0219.1 Tsujino S, Tsuboki K, Yamada H, Ohigashi T, Ito K, Nagahama N (2021a) Intensification and maintenance of a double warm-core structure in Typhoon Lan (2017) simulated by a cloudresolving model. J Atmos Sci 78:595–617. https://doi.org/10.1175/JAS-D-20-0049.1 Tsujino S, Kuo HC, Yu H, Chen BF, Tsuboki K (2021b) Effects of mid-level moisture and environmental flow on the development of afternoon thunderstorms in Taipei. Terr Atmos Ocean Sci 32:497–518. https://doi.org/10.3319/TAO.2021.11.17.01 Wang CC, Chen GTJ, Chen TC, Tsuboki K (2005) A numerical study on the effects of Taiwan topography on a convective line during the Mei-yu season. Mon Weather Rev 133:3217–3242 Wang CC, Chen GTJ, Yang SC, Tsuboki K (2009) Wintertime supercell thunderstorms in a subtropical environment: numerical simulation. Mon Weather Rev 137:2175–2202 Wang CC, Huang WM (2009) High-resolution simulation of a nocturnal narrow convective line off the southeastern coast of Taiwan in the Mei-yu season. Geophys Res Lett 36(6):L06815. https:// doi.org/10.1029/2008GL037147

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Wang CC, Chen GTJ, Huang SY (2011) Remote trigger of deep convection by cold outflow over the Taiwan Strait in the Mei-yu season: a modeling study of the 8 June 2007 case. Mon Weather Rev 139:2854–2875 Wang CC, Kuo HC, Chen YH, Huang HL, Chung CH, Tsuboki K (2012) Effects of asymmetric latent heating on typhoon movement crossing Taiwan: the case of Morakot (2009) with extreme rainfall. J Atmos Sci 69:3172–3196 Wang CC, Kuo HC, Yeh TC, Chung CH, Chen YH, Huang SY, Wang YW, Liu CH (2013a) High-resolution quantitative precipitation forecasts and simulations by the cloud-resolving storm simulator (CReSS) for typhoon Morakot (2009). J Hydrol 506:26–41. https://doi.org/10.1016/j. jhydrol.2013.02.018 Wang CC, Chen YH, Kuo HC, Huang SY (2013b) Sensitivity of typhoon track to asymmetric latent heating/rainfall induced by Taiwan topography: a numerical study of Typhoon Fanapi (2010). J Geophys Res 118(D8):3292–3308. https://doi.org/10.1002/jgrd.50351 Wang CC, Hsu JCS, Chen GTJ, Lee DI (2014a) A study of two propagating heavy-rainfall episodes near Taiwan during SoWMEX/TiMREX IOP-8 in June 2008. Part I: synoptic evolution, episode propagation, and model control simulation. Mon Weather Rev 142:2619–2643 Wang CC, Hsu JCS, Chen GTJ, Lee DI (2014b) A study of two propagating heavy-rainfall episodes near Taiwan during SoWMEX/TiMREX IOP-8 in June 2008. Part II: sensitivity tests on the roles of synoptic conditions and topographic effects. Mon Weather Rev 142:2644–2664 Wang CC, Kuo HC, Johnson RH, Lee CY, Huang SY, Chen YH (2015) A numerical study of convection in rainbands of Typhoon Morakot (2009) with extreme rainfall: roles of pressure perturbations with low-level wind maxima. Atmos Chem Phys 15:11097–11115. https://doi.org/ 10.5194/acp-15-11097-2015 Wang CC, Huang SY, Chen SH, Chang CS, Tsuboki K (2016) Cloud-resolving typhoon rainfall ensemble forecasts for Taiwan with large domain and extended range through time-lagged approach. Weather Forecast 31:151–172 Wang CC, Lin KY, Davis CA, Huang SY, Liu SCS, Tsuboki K, Jou BJD (2020) A modeling study on the impacts of Typhoon Morakot’s (2009) vortex structure on rainfall in Taiwan using piecewise potential vorticity inversion. J Meteorol Soc Jpn 98:707–733. https://doi.org/10.2151/jmsj.2020036 Wang CC, Chang CS, Wang YW, Huang CC, Wang SC, Chen YS, Tsuboki K, Huang SY, Chen SH, Chuang PY, Chiu H (2021a) Evaluating quantitative precipitation forecasts using the 2.5 km CReSS model for typhoons in Taiwan: an update through the 2015 season. Atmosphere 12:1501. https://doi.org/10.3390/atmos12111501 Wang CC, Lin TC, Tsuboki K, Tsai YM, Lee DI (2021b) A modeling study of rainbands upstream from western Japan during the approach of Typhoon Tokage (2004). Atmosphere 12:1242 Wang CC, Paul S, Huang SY, Wang, YW Tsuboki K, Lee DI, and Lee JS (2022a) Typhoon quantitative precipitation forecasts by the 2.5 km CReSS model in Taiwan: examples and role of topography. Atmosphere 13:623. https://doi.org/10.3390/atmos13040623 Wang CC, Chen SH, Tsuboki K, Huang SY, Chang CS (2022b) Application of time-lagged ensemble quantitative precipitation forecasts for Typhoon Morakot (2009) in Taiwan by a cloud-resolving model. Atmosphere 13:585. https://doi.org/10.3390/atmos13040585 Wang CC, Chuang PY, Chang CS, Tsuboki K, Huang SY, Leu GC (2022c) Evaluation of Mei-yu heavy-rainfall quantitative precipitation forecasts in Taiwan by a cloud-resolving model for three seasons of 2012–2014. Nat Hazards Earth Syst Sci 22:23–40. https://doi.org/10.5194/nhess-2223-2022 Wang H, Sun J, Fan S, Huang X (2013) Indirect assimilation of radar reflectivity with WRF 3D-Var and its impact on prediction of four summertime convective events. J Appl Meteorol Climatol 52:889–902. https://doi.org/10.1175/JAMC-D-12-0120.1 Wu L, Liang J, Wu CC (2011) Monsoonal influence on Typhoon Morakot (2009). Part I: observational analysis. J Atmos Sci 68:2208–2221

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Xue M, Droegemeier KK, Wong V, Shapiro A, Brewster K (1995) Advanced regional prediction system, version 4.0. Center for Analysis and Prediction of Storms, University of Oklahoma, 380 pp Yamada H, Ito Tsuboki K, Shinoda T, Ohigashi T, Yamaguchi M, Nakazawa T, Nagahama N, Shimizu K (2021) The double warm-core structure of Typhoon Lan (2017) as observed through the first Japanese eyewall-penetrating aircraft reconnaissance. J Meteorol Soc Jpn 99:1297–1327. https://doi.org/10.2151/jmsj.2021-063 Yamaguchi K, Nakakita E (2008) Ensemble Kalman filter assimilation of Doppler radar data using the cloud resolving non-hydrostatic model with an aim to introduce polarimetric radar data assimilation. In: Proceedings of 7th international symposium on weather radar and hydrology, p 312

Chapter 20

Applications of Conditional Nonlinear Optimal Perturbations to Targeting Observation of Tropical Cyclones Xiaohao Qin, Mu Mu, Feifan Zhou, Boyu Chen, and Jie Feng

Abstract To augment the routine observational network for better forecasts of highimpact weather events, targeting observations (TOs) have developed rapidly during the past several decades over East Asia. In special, tropical cyclone (TC) forecasts have benefitted a lot from these field campaigns. In this chapter, research work and field campaigns of TOs are briefly overviewed. Then a method named the conditional nonlinear optimal perturbation (CNOP), which is utilized to identify the areas deserving additionally observed with priority in TOs, is introduced. Using some examples, we explain how to numerically use the CNOP method and demonstrate its impacts on TC forecasts and its latest application in real-time operational forecasts. We hope the information will be useful and inspiring for the readers of this book. Keywords Tropical Cyclones · Forecasts · Targeting Observation · Conditional Nonlinear Optimal Perturbations

X. Qin (B) State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China e-mail: [email protected] M. Mu · J. Feng Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China F. Zhou Key Laboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China B. Chen Weather Forecasting Office, National Meteorological Center, China Meteorological Administration, Beijing, China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_20

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20.1 Introduction to Targeting Observation 20.1.1 Definition Targeting observations (TOs) refer to the augmentation of additional observations in some specific but important areas. Here, the specific and important areas mean that the additional observations there are supposed to probably bring about much more benefits to the subsequent forecasts of high-impact weather events comparing with other areas (Snyder 1996; Majumdar et al. 2006), if the additional observations are assimilated into operational numerical weather models. Comparing with the conventional observations, TOs often utilize dropsondes launched from aircraft or balloons, additional rawinsonde ascents, and enhanced regular satellite observations.

20.1.2 Typical Cases An early test of TOs is the Hurricane Synoptic Flow experiments, which was conducted by the National Oceanic and Atmospheric Administration’s Hurricane Research Division in the north Atlantic basin from 1982 to 1996 (Burpee et al. 1996). As an important milestone, the Observing System Research and Predictability Experiment (THORPEX) program was established in 2003, which has greatly promoted the advancement of TOs. Since 2003, series of TOs have been conducted over the North Atlantic Ocean (Rabier et al. 2008), Western African (Agusti-Panareda et al. 2010), Europe (Wulfmeyer et al. 2008; Renfrew et al. 2008; Jansa et al. 2011), Western North Pacific (Elsberry and Harr 2008; Weissmann et al. 2011), and Scandinavia (Irvine et al. 2011). In these TOs, varies of weather events, such as tropical cyclogenesis, winter flow, heavy rainfall, and tropical cyclones, have drawn the attentions of both scientists and forecasters. Consequently, TOs have gradually stepped into a quasi-operational stage.

20.1.3 TOs on Tropical Cyclone Forecasts Tropical cyclones (TCs), as a typical type of high-impact weather event, have gained great concerns. Many field campaigns of TOs have been carried out and the results have demonstrated that all of the efforts are worthwhile. The operational Synoptic Surveillance program that followed from 1997 onwards has yielded positive results over the following decade. Assimilation of dropsonde data provided an average of 10–15% improvement in the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) track forecasts up to 60 h during the critical watch and warning period before the anticipated landfall (Aberson 2010). Results from the Dropsonde Observations for Typhoon Surveillance near the Taiwan Region

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(DOTSTAR) program (Wu et al. 2005) in the Western North Pacific (WNP) have been also encouraging. Assimilation of the targeting dropsonde data caused the average track errors for forecasts up to 3 days to be reduced by at least 14% (Wu et al. 2007b) for some numerical models. In particular, the DOTSTAR and the THORPEX Pacific Asian Regional Campaign (T-PARC) data were found to improve the track forecasts of two long-lived TCs by 20–40% in numerical models (Weissmann et al. 2011). Another evaluation by Chou et al. (2011) showed that the mean 1–5 day track forecast errors were reduced by 10–20% for DOTSTAR and T-PARC cases. In addition, Harnisch and Weissmann (2010) demonstrated that the assimilation of T-PARC observations in a circle of radius ~ 500 km from the storm improved the ECMWF track forecast more than the assimilation of observations exclusively in the TC inner-core or in areas remote from the TC. Aberson (2010) demonstrated that GFS forecasts of TC track were improved globally by the cumulative assimilation of Atlantic dropsondes, even in basins in which no aircraft missions took place (such as the Eastern North Pacific). More recently, the TOs on TCs have been concentrated on the TC intensity forecasts (Braun et al. 2016; Black et al. 2017). These experiments have provided data in both the inner-core and eye-wall of TCs, which has contributed to improved forecasts of rapid intensification (Feng and Wang 2019).

20.1.4 Techniques to Identify Observing Locations As we mentioned above, the identification of observation locations, where to conduct additional observations, has experienced a shift from a subjective way to an objective one. Nowadays, the popular objective techniques include the Singular Vectors (SVs; Palmer et al. 1998), Ensemble Transform Kalman Filters (ETKF; Bishop et al. 2001), and Adjoint-Derived Sensitivity Steering Vectors (ADSSV; Wu et al. 2007a). Regardless of the different theoretical foundations behind, all these techniques utilize linear approximations to varies degrees to identify the proper observing locations (referred to as “sensitive regions” below). Then Mu et al. (2003, 2009) proposed a fully nonlinear method named the conditional nonlinear optimal perturbation (CNOP) to identify the sensitive regions, which is a natural generalization of the leading SV in the nonlinear regime and fully considers the nonlinear evolution of the initial perturbations. Utilizing the CNOP method, the initial perturbation (referred to as “CNOP-type error” hereafter) that satisfies a certain physical constraint and nonlinearly evolves to the largest forecast error at a forecast time can be identified. Therefore, eliminating the CNOP-type errors in the initial conditions will probably reduce the forecast errors in the following days.

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20.2 Applications of CNOP to TOs for TC Forecasts 20.2.1 How to Identify CNOP Sensitive Region How to Resolve CNOP In mathematics, the CNOP-type initial error is obtained by solving an optimization equation with respect to the initial perturbations δx 0 , ( ) J δx ∗0 =

max

δx T0 C1 δx 0 ≤β

[M(X 0 + δx 0 ) − M(X 0 )]T C2 [M(X 0 + δx 0 ) − M(X 0 )], (20.1)

where M(. . .) denotes the forward integration (a forecast) of a numerical model with its initial condition. It is obvious that M(X 0 ) and M(X 0 + δx 0 ) represent two forecasts from the same numerical model but with different initial conditions X 0 and X 0 + δx 0 , respectively. And the difference is that an initial perturbation matrix δx 0 is superimposed on the original initial conditions X 0 . The superscript T is the transpose and [. . .]T [. . .] indicates an inner product, where the coefficient matrices, C1 and C2 , measures the form of the output. For example, C1 and C2 can be defined as the kinetic energy (Eq. 20.2), dry energy (Eq. 20.3), or total energy (Eq. 20.4) over a horizontal area D from the surface σ = 1 to a height of σ = 0 as 1 D

{ {1 [

{ {1 [ D

1 D

{

{1

[

'

'

] C p '2 u +v +w + θ dσ dD, Tr '

2

'

2

'

2

(20.3)

0

'

u2 +v2 +w2 + D

(20.2)

0

D

1 D

] ' ' ' u 2 + v 2 + w 2 dσ dD,

] C p '2 L 2 '2 g ' θ + q + p 2 dσ dD, Tr c p Tr Tr Ra

(20.4)

0

[ ] where u', v', w', θ ', q', p' respectively denotes the perturbations of the horizontal (u', v') and vertical (w') wind, potential temperature (θ '), mixing water ratio (q'), and pressure ( p'). The constants are given as L = 2.5104 × 106 J kg–1 , c p = 1005.7 J kg−1 , Tr = 270 K, and Ra = 287.04 J kg−1 K−1 . That is, the initial perturbations δx 0 and forecast errors [M(X 0 + δx 0 ) − M(X 0 )] can be transformed to the same or different perturbation energy as above. In specific, β limits the upper bound of the initial perturbations since the initial perturbations cannot be overlarge in operational forecasts. Usually it is pre-assigned according to the magnitude of the initial analysis error variance of each considered variable.

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First of all, a forecast M(X 0 ) with initial conditions of X 0 should be obtained as a reference state (unperturbed). In the subsequent calculation of CNOP, a first guess of the initial perturbation δx 0 is assigned, which usually includes some or all of the model variables as horizontal winds [u', v'], temperature or potential temperature [T ' or θ '], moisture [q'], pressure p', etc. Then the model M(. . .) is integrated forward with the initialization of X 0 + δx 0 to obtain the forecast M(X 0 + δx 0 ) (perturbed). The difference between M(X 0 ) and M(X 0 + δx 0 ) refers to the changes of forecasts due to initial perturbations δx 0 . Such changes are utilized to calculate the gradient of the cost function (∇ J ) with respect to the initial perturbations δx 0 using the adjoint model M. Here the gradient indicates the direction in which the cost function delete changes the fastest. Based on the automatic and iterative forward M(…) and backward integrations of its adjoint model M, which are governed by the spectral projected gradient 2 (SPG2) algorithm (Birgin et al. 2001), the initial perturbation δx 0 is optimized and updated until the convergence condition ∇ J ≤ ε is satisfied. Then the resultant initial perturbation δx ∗0 is just the CNOP-type initial error. After that, the CNOP-type initial error is transformed to the kinetic/dry/total perturbation energy according to C1 on each grid points and sorted in descending order. The grid points with large values comprise the CNOP sensitive region. The computational procedure for obtaining the CNOP-type initial error is shown in Algorithm 1. Algorithm 1 Computational procedure of CNOP-type initial error. /* k: iteration number; K: maximum iteration; ε: tolerance */ /* X 0 : initial conditions for numerical model (boundary conditions are also necessary for region model) */ /* M(X 0 ): forecasts initialized by X 0 , which is always fixed in the loop below */ /* δx 0 : first guess; β: upper bound of δx 0 in the form of C1 */ 1 Input: X 0 , M(X 0 ), δx 0 , k = 0,ε 2 while (k ≤ K ) do

! Start the loop

3 Integrating the numerical model to get ! Forecasts with initial perturbations ( ) k M X 0 + δx 0 δx k0 ) ( k 4 Calculating cost function J = M X 0 + δx k0 − M(X 0 ) in the form of C2 5 Calculating ∇ J k (i.e., the adjoint model or others)

! To determine the fastest descending direction of J k

6 Updating δx k0 (i.e., the SPG2 algorithm or others) 7 Determining if ∇ J k ≤ ε out of loop; else: k = k + 1

! Termination condition for the loop

8 endwhile 9 Output: δx ∗0 = δx k+1 0

! δx ∗0 is the CNOP

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Fig. 20.1 Identified CNOP sensitive regions at a single vertical level (σ = 0.7) based upon a kinetic, b dry, and c total perturbation energy for the TC case Meari (2004)

Examples Figure 20.1 shows the identified CNOP sensitive regions at a single vertical level of a numerical model1 based upon different C1 for the same TC case Meari (2004). It can be seen that the wind field presents similar pattern when dry energy and kinetic energy are utilized (Fig. 20.1a, b). However, they vary a lot if the moist energy is considered (Fig. 20.1c), which are more localized than the other two. The difference among the wind sensitive regions when using different constraints suggests a combined result of interactions between winds and other variables. Note that the temperature and moisture sensitive regions are consistently concentrated in the right two quadrants with respect to the TC center. For another TC case Matsa (2005), the identified CNOP sensitive regions based upon the total perturbation energy but with different β (upper bound of the initial perturbations) are shown in Fig. 20.2. It is clear that the general patterns of CNOPtype initial errors keep similar in these three plots when β varies a little (Zhou 2009).

1

The Mesoscale Model 5 (MM5; Dudhia 1993) has been utilized here.

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Fig. 20.2 Identified CNOP sensitive regions at a single vertical level (σ = 0.7) based upon the total perturbation energy [including horizontal wind (vector; unit: m s−1 ) and potential temperature (shaded, unit: K)] with different β for the TC case Matsa (2005)

20.2.2 Evaluations In the period of 2009–2019, series of research works have been done to quantify the influence of identified CNOP sensitive regions on TC track forecasts using hindcasts. Comparing with the real-time forecasts, hindcasts utilize historical TC cases to conduct the simulation. More differences between hindcasts and forecasts can be found in Table 20.1. Both the observing system simulation experiments (OSSEs) and the observing system experiments (OSEs) have been utilized to evaluate the effects of CNOP sensitive regions in these research works.

OSSEs Generally, OSSEs contain three basic components, first, a “truth” is generated by a nature run of a model, then simulated observations are produced by adding random errors to the truth, and finally the simulated observations are assimilated into the model to generate new initial conditions of a model (Hoffman et al. 1990). In Qin and Mu (2011), two hindcasts were obtained for seven TC cases over the WNP in 2009. One was generated by the ERA-Interim reanalysis from the ECMWF and the other was generated by the reanalysis from the NCEP, both forecasts were no longer than 72 h. The hindcast TC centers initialized of the ERA-Interim reanalysis during this period at 6 h intervals were deemed as the truth, and those initialized of the NCEP as the control. In consequence, the differences between these two hindcast tracks were defined as the track forecast errors without dropsonde data. Table 20.1 Major differences between hindcasts and forecasts Hindcasts

Forecasts

TC cases

Historical, happened already

To occur or is occurring

Initials for model

Reanalysis mostly

Real-time forecasts

Actual track and intensity

Known already

Unknown

Time limit for identifying sensitive regions

No

At least 24 h before the field campaign

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The sensitive regions were identified using the CNOP and SVs methods respectively for each TC case over a 24 h (i.e., from 0 to 24 h) optimization period, where the dry energy norm was utilized. With the TC case Mirinae (2009) for example, the shaded areas in Fig. 20.3 represent the identified CNOP/SVs (leading five) sensitive regions. Supposing that TOs were conducted at 24 h over the sensitive region, and twenty-three dropsondes (squares in Fig. 20.3) were sampled to collect the horizontal wind speed and direction, and temperature at three vertical levels, i.e., 850, 500, and 200 hPa. Note that no real observation data is needed in an OSSE, hence, the observations were simulated as the sum of the forecast in the truth at 24 h and random observational errors with the order of 10−1 of the analysis. These sampled data were assimilated into the MM5 by its three-dimensional variational data assimilation (3DVAR) system and to produce an undated ‘initial condition’ at 24 h, on which another TC hindcast track was predicted in the following 48 h (from 24 to 72 h). The differences between this track and that of the truth were defined as the track forecast errors with dropsondes. Comparisons between track forecast errors without and with dropsondes can indicate the influence of CNOP and SVs sensitive regions on TC track forecasts. The results for all seven investigated cases are shown in Fig. 20.4 including the absolute track forecast errors and relative differences from 24 to 72 h. A diamond above/beneath the diagonal indicates that the track forecast error with dropsondes is larger/less than those without dropsondes at corresponding times. The slopes of the dashed (dash-dotted) lines, which are the linear fits of the diamonds denote the magnitude of improvements due to the dropsondes: the shallower the slope, the greater the improvement. In occasions, the slope is larger than that of the diagonal, which means that dropsonde data has not contributed improvements averagely. On the other hand, the histograms show the corresponding relative differences in track forecast errors with and without dropsondes for CNOP and SVs. Negative (positive) values indicate a reduced (an increased) error by taking into account dropsonde data.

Fig. 20.3 Simulated dropping sites (squares) in sensitive regions (shaded) identified by a CNOP and b SVs for the TC case Mirinae (2009). From Qin and Mu (2011). ©2011 John Wiley and Sons. Used with permission

Fig. 20.4 Scatter diagrams of all track forecast errors for seven TC cases (left of each pair). The y-axis represents the track forecast errors with dropsondes, and the x-axis represents those without dropsondes. Filled and empty diamonds denote the results of CNOP and SVs, respectively. The color of each diamond indicates the forecast time. Histograms on the right of each pair are relative differences corresponding to each case. From Qin and Mu (2011). ©2011 John Wiley and Sons. Used with permission

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By taking the TC case Koppu (2009) for example, we notice that all of the data points except for three (forecasts from the SVs analysis at 30 and 54 h and from the CNOP at 24 h) were plotted in the lower right. At all forecast times, the track forecast errors from the SVs analysis were larger than those from the CNOP analysis except for 24 h. The dash-dotted line (SVs) had a steeper slope than the dashed line (CNOP). The largest error reduction was 158.6 (118.3) km for the CNOP (SVs) analysis at 36 h. Although the CNOPs and SVs sensitivities were identified over a 24 h (i.e., from 0 to 24 h) optimization period, the improvements were seen beyond this period. This result indicates that the improvement gained by deploying dropsondes in the identified sensitive regions extends beyond the optimization period (from 48 to 60 h in this case). The crossed bars show a strong reduction in TC position errors when considering dropsonde data from CNOP sensitive regions: the average relative difference during the period 24–60 h was − 45.7%. The error reduction obtained by dropsondes in SVs sensitive regions was − 21.7%. This finding indicates that the assimilation of additional dropsonde data from both sensitive regions can improve the track forecast of the TC case Koppu (2009). However, the degrees of improvement are different between the two methods: the improvement gained from CNOP sensitive regions was twice that from SVs. Six of the seven TC cases showed an improvement in typhoon track forecasts when dropsonde data were considered [the exception is the TC case Mujigae (2009)], but the degree of improvement varied from case to case. This improvement was not only seen for the optimization period when CNOPs and SVs were calculated, but for the next 24 h. In general, the dropsondes in identified CNOP sensitive regions can reduce track forecast errors by 13–46%, and by 14–25% in regions identified by SVs. In three of the improving cases, the improvement associated with CNOP sensitive regions was greater than that associated with SV sensitive regions, with the opposite outcome observed for the other three cases.

OSEs Compared with OSSEs, the observation data in OSEs are real data rather than simulated one. In Chen et al. (2013), they utilized the data of twenty TC cases from DOTSTAR to evaluate the effects of CNOP sensitive regions on TC track forecasts. In brief, they identified the sensitive regions for each TC case using the CNOP and leading SV (LSV) methods by the MM5, respectively, based on the total dry perturbation energy. Then they conducted five sets of hindcasts of 36 h for each TC case. In detail, no dropsonde data was assimilated in EXP 1, which denotes a reference TC track for the subsequent comparisons. While in EXP 2, all available dropsonde data in the actual field campaign were assimilated, hence, the hindcast TC tracks in this experiment indicate the influence of all dropsonde data (13–15), which is not related to any sensitive regions. In EXPs 3–5, the same amount of dropsonde data (3–5), but much less than that of all, were assimilated, which was according to the CNOP/LSV sensitive regions or at random. The detail differences among EXPs 1–5 can be seen in Table 20.2.

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Table 20.2 Major differences among EXPs 1–5 Number of assimilated dropsondes

Location of assimilated dropsondes

EXP 1

None

EXP 2

All available and case-dependent (13–15)

Actual dropping sites

EXP 3

3–5

In sensitive regions identified by CNOP

EXP 4

3–5 (Same as EXP 3)

In sensitive regions identified by LSV

EXP 5

3–5 (Same as EXP 3)

Selected at random

The actual dropping sites for the TC case Nida (2004) at 1200 UTC 17 May 2004 are shown in Fig. 20.5a, together with the track in the best track data. It can be seen that fifteen dropsondes were deployed at that time, and they were evenly distributed around the TC center. The sensitive regions identified by CNOP and LSV are shown in Fig. 20.5b, c (shaded), respectively. Obviously, CNOP and LSV indicated different sensitive regions: the CNOP sensitive regions were around the TC center, while the LSV displayed two separate sensitive regions, one was southwest with respect to the TC center, the other was to the east. In order to discriminate from all (EXP 2), four dropsondes to the north of the TC center (Nos. 7–10 in Fig. 20.5a) fell into the CNOP sensitive region were selected in EXP 3, and another four dropsondes to the southwest of the TC center (Nos. 11–14 in Fig. 20.5a) fell into the LSV sensitive region were selected in EXP 4 [denoted by the star (✩) in Fig. 20.5b, c]. Meanwhile, another four dropsonde (Nos. 7–10 in Fig. 20.5a) were selected in EXP 5. Then, all these data were assimilated and hindcast the TC tracks respectively. The impacts of different dropsonde data on the track forecast for the TC case Nida (2004) at 24 and 36 h are shown in Table 20.3. It is obvious that CNOP sensitive regions improved (positive values) the TC center forecasts at both 24 and 36 h in MM5, while LSV sensitive regions displayed an improvement and deterioration at 24 and 36 h forecasts, respectively. Moreover, the improvements obtained from the CNOP sensitive regions were greater than that from the LSV one. That is, CNOP was more effective than LSV for TOs and brought about more benefit for this case. Further experiments were conducted to evaluate the dependence of the identified sensitive regions on numerical models, which utilized the sensitive regions identified in MM5 to WRF model to hindcast the tracks again. The results showed that all available dropsonde data and CNOP/LSV sensitive regions helped improve the track forecast greatly (8.1–63.6% at 24 h and 7.5–35.0% at 36 h), despite the deteriorations (− 23.8% at 24 h and − 3.0% at 36 h) in EXP 5 without any consideration of sensitive regions. That is, observations deployed in CNOP sensitive region would result in greater improvements on TC track forecasts for this case. And the improvements from only four dropsonde in the CNOP sensitive regions were even greater than deploying fifteen dropsondes. Moreover, the sensitive regions identified in MM5 still made sense in another numerical model WRF for track forecasts. Figure 20.6 shows the relative track forecast errors from EXP 2–5 to those from EXP 1 at 24 and 36 h in MM5 for all twenty TC cases. Most of them were above zero, indicating that dropsondes can improve TC track forecasts. An average reduction of

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Fig. 20.5 a Actual dropping sites (1–15) of dropsondes for the TC case Nida (2004) and observed TC track, sensitive regions (shaded; dry perturbation energy, unit: J kg−1 ; vector; horizontal wind at σ = 0.7, unit: m s−1 ) identified by b CNOP and c LSV. From Chen et al. (2013). ©2013 American Meteorological Society. Used with permission

Table 20.3 Track forecast errors (unit: km) and corresponding relative ratios at 24 and 36 h of EXP 1–5 for the TC case Nida (2004) Error (24 h MM5)

EXP 1

EXP 2

EXP 3

EXP 4

202.23

202.23

161.36

170.20

Improvement Error (36 h MM5)

0 298.55

Improvement Error (24 h WRF)

79.83

Improvement Error (36 h WRF) Improvement

176.57

267.04

20.2% 260.30

15.8% 314.62

10.6%

12.8%

− 5.4%

48.34

29.02

73.36

39.4%

63.6%

126.33 28.5%

114.73 35.0%

8.1% 163.32 7.5%

EXP 5 202.23 0 279.59 7.0% 98.81 − 23.8% 181.85 − 3.0%

4.8% (4.3%) at 24 (36) h was obtained if all available dropsonde data were assimilated, which displayed the most significant improvement of all four experiments (EXP 2–5), except for CNOP at 36 h. Assimilating several dropsondes deployed in CNOP sensitive regions averagely reduced the TC track forecast errors by 4.3% (4.9%) at 24 h (36 h), which was 3.8% (1.7%) and 2.5% (1.2%) at 24 h (36 h) for LSV sensitive regions (EXP 4) and the random deployment of dropsondes (EXP 5). In general, the impact of dropsonde data on 36 h forecasts was less than that for 24 h

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Fig. 20.6 Ratios of track forecast errors of EXP 2–5 (All, CNOP, LSV, and random) to EXP 1 at a 24 h and b 36 h using MM5 for 20 cases. A positive number means improvement, and a negative number means deterioration. From Chen et al. (2013). ©2013 American Meteorological Society. Used with permission

forecasts. It is noted that using data from only three or four dropsondes deployed according to CNOP sensitive regions gave a comparable improvement to that of all in the accuracy of the forecasts, which could save considerable economic and human benefits. These findings also indicated that CNOP represent a useful method to determining sensitive regions for adaptive observations.

20.2.3 Applications in Real-Time Tropical Cyclone Forecasts Around 2020, we made a big progress that applying the CNOP technique into the real-time field campaign of TOs for TCs, which opened a new chapter of theoretical research and operational forecasts. Being different from the hindcasts aforementioned before, what we can know about a developing TC come from the forecasts, which contain much larger uncertainties than the reanalysis data (often used in the

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hindcasts). Hence, the effects of TOs on improving TC forecasts in this situation are in general relatively less obvious than that in the hindcasts.

Dropsondes In 2020, several operational centers and research department, i.e., the Hong Kong Observatory (HKO), the Taiwan Central Weather Bureau, the Shanghai Typhoon Institute of the China Meteorological Administration (CMA), have conducted series of field campaigns on four TC cases Higos (2020), Nangka (2020), Saudel (2020), and Atsani (2020) (Qin et al. 2023). In these field campaigns, the sensitive regions were identified by the Institute of Atmospheric Physics (IAP) of Chinese Academy of Sciences using the CNOP method and shared with the aforementioned organizations 24 h ahead of the observing time, which were allowed for the design of the aircrafts (dropsondes). The TC case Higos (2020) rapidly drew the attention of the forecasters when it intensified to a typhoon within a distance of < 200 km from the south coast of China at 1200 UTC on August 18, 2020. Initialed with the real-time forecasts issued by the ECMWF at 1200 UTC on August 16, 2020, the CNOP sensitive region focusing on the observing time at 0600 UTC on August 18, 2020 was identified by the WRF model. It is shown from Fig. 20.7a that the CNOP sensitive region covers the Bashi Channel, Taiwan Strait, and their adjacent lands, which corresponds to the border area between the subtropical high over the Korean Peninsula and Japan and the TC itself at that time. It indicated that uncertainties there likely induce shifts in the subsequent forecast track and intensity. Hence, it was inferred that reducing the uncertainties in the identified sensitive region would probably help reduce the subsequent forecast uncertainty in the area of concern (rectangle in Fig. 20.7a) greatly. From 0700 to 0900 UTC on August 18, 2020, the HKO released eight dropsondes (blue dots in Fig. 20.7a) from an aircraft. Only dropsonde No. 8 was inside and at the edge of the sensitive region due to an airspace issue. The forecast tracks of the TC case Higos (2020) as well as the forecast errors against the best track, including those without any assimilation and with all dropsonde data assimilated (referred to as CTRL and All, respectively), are shown in Fig. 20.7. In general, assimilating all dropsondes did not positively affect the track forecast for this TC, neither the moving direction nor the translation speed varied obviously between the forecasts in CTRL and All. With respect to the forecast intensity, the minimum sea level pressure (Pmin ) and near-surface maximum wind speed (V max ) maintained relatively steady around 1000 hPa and 14 m s−1 respectively in the CTRL in the forecast period (Fig. 20.7d), which failed to predict the actual intensification occurring in the former 6 h and displayed great intensity errors. This was partly attributed to the large track deviation from the actual one. After assimilating all dropsonde data, the forecast intensity showed modest (neutral) differences from that in the CTRL, which increased the average forecast errors by 8.3% (0.43%) for the Pmin (V max ) (Fig. 20.7e, f). That is, the dropsonde generally did not help improve the forecast skills in either track or intensity forecasts.

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Fig. 20.7 a Sensitive regions (shaded; the warmer, the more sensitive) identified by the CNOP method aiming at the forecasts in the verification area (small rectangle) and the geopotential (contour; 102 m2 s−2 ) at 500 hPa at 0600 UTC on August 18, 2020. The best tracks (BEST) and forecast tracks (30 h) without any assimilation of dropsonde data (CTRL) are respectively indicated by the red solid and black dotted lines. The released dropsondes (DROP) are dotted in blue. b shows the BEST (red), forecast tracks in the CTRL (black), after assimilating all dropsonde data (All; blue), and those inside the CNOP sensitive regions (Sen; magenta); c shows the track forecast errors (km) in the CTRL (black), All (blue), and Sen (magenta). The relative forecast errors with respect to the CTRL are denoted as the percentages. d–f are similar to the track but for the intensity

Since only dropsonde No. 8 was released into the sensitive region for this TC case, another forecast was carried out by assimilating only the dropsonde data to indicate the effect of CNOP sensitive region (referred to as “Sen” below for simplification). In general, the forecast moving direction in Sen was similar to that in both CTRL and All but with a faster translation speed, which leaded to a further westward landfall site (Fig. 20.7b). However, such relatively faster translation speed in Sen was close to the actual one and brought out an average forecast error reduction by 5.4%

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(Fig. 20.7c). Moreover, assimilating the single dropsonde data from No. 8 in the sensitive area reduced the average forecast error for the Pmin in the CTRL by 1.5% (Fig. 20.7e). Numerically, this is trivial; however, it transformed the general deterioration caused by all dropsondes to a slight improvement, indicating the advantage of CNOP sensitivity for this TC. Nevertheless, the average V max forecast error was slightly increased by 2.1% in this situation, which is also trivial but still represented a slight deterioration upon the neutral effect of assimilating all. The above results indicated TO with only one dropsonde according to CNOP sensitive regions exerted better effects than all eight dropsondes on track and intensity forecast, even though the absolute values were trivial for this TC case. For all four TC cases, both track and intensity forecasts were shown to be casedependent after the assimilation of all dropsondes (Fig. 20.8). However, the impact of CNOP sensitive regions on intensity forecasts was unanimously more positive than that of all. This unanimous positivity is manifested in the comparable or even larger benefits in both Pmin and V max forecasts for the TC case Atsani (2020); and a transformed effect from negative to positive when the single dropsonde inside the CNOP sensitive region for the TC case Higos (2020) was assimilated, despite a slightly increased forecast error on V max . However, more data are expected through field campaigns for TCs in the future, which will help us obtain statistical information about the effects of CNOP sensitive regions on TC forecast in real-time TOs.

Satellites In addition, Fengyun-4A Satellite has joined the team of TOs for TCs since 2020. Field campaigns were conducted for five TC cases, i.e., Chan-hom, Maysak, and Higos in 2020 and Chanthu and Conson in 2021 using the Geostationary Interferometric Infrared Sounder (GIIRS) onboard the geostationary Fengyun-4A satellite. Before each observing mission, the sensitive regions were identified using the CNOP method, and then the operational scanning path of the GIIRS was adjusted accordingly. Eight OSEs were carried out to verify the effects of the observations: two for the TC cases Chan-hom (2020), Maysak (2020), and Chanthu (2021) and one for the TC cases Higos (2020) and Conson (2021). Figure 20.9 shows the distribution of the assimilated temperature retrieval data within 400–700 hPa for two TC cases Chan-hom (2020) and Maysak (2020). Compared with the operational observations, the GIIRS data from the Fengyun-4A satellite provided a much denser observation network in clear sky situation, covering almost the environment of these two TC cases. Nevertheless, the areas near the vortex have fewer observations, probably as a result of the large uncertainties in the retrieval in this area caused by the concentration of clouds on the top of TCs (Li et al. 2021). This is a widely recognized challenge in the use of all-sky satellite data caused by the strong nonlinearity of cloud-affected radiance in dynamic and thermodynamic atmospheric profiles (e.g., Zou et al. 2015; Minamide and Zhang 2018; Zhang et al. 2018).

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Fig. 20.8 Averaged reductions of a track, b Pmin , and c V max forecast errors with respect to the CTRL after assimilating all (“All”) released dropsonde data and that in the CNOP sensitive regions (“Sen”) using a horizontal resolution of 30 km for four TCs

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K Fig. 20.9 Distribution of the temperature retrieval observations from GIIRS assimilated within 400–700 hPa in the model domain for the TC case Chan-hom at 0600 UTC on October 8 and the TC case Maysak at 0600 UTC on August 31 overlain by the 10-m surface wind field (vectors) of the first guess at the same valid time. Red stars represent the TC center. From Feng et al. (2022). ©2022 Elsevier. Used with permission

Two forecasts were carried out for each TC case, one assimilated conventional observations (referred to as “BASE” below for simplification)2 and the other additionally assimilated the GIIRS data (referred to as “BASE + GIIRS” below for simplification). And the results for all eight cases are shown in Fig. 20.10. It was shown that the track forecast errors in BASE + GIIRS with leading time longer than 2 d were obviously less than that in BASE for five TC cases including two for Chan-hom (2020), two for Chanthu (2021), and one for Conson (2021). In particular, the improvements reached up to 50% at day 3 for the TC case Chan-hom (2020) (Fig. 20.10a, b) and at day 3.5 for the TC case Conson (2021) (Fig. 20.10h). Moreover, GIIRS data helped correct the false forecast of landfall site in Taiwan in BASE for the TC case Chanthu (2021). By contrast, GIIRS data displayed trivial impacts on the track forecasts for the other TC cases Maysak (2020) and Higos (2020). Accurate initial conditions in BASE leaded to skillful track forecast for the TC case Maysak (2020), which left little space for further improvements by additional data. While for the TC case Higos (2020), it started to decay after making landfall on day 1. On average, BASE + GIIRS showed lower TC track forecast errors than BASE beyond 2.5 days (Fig. 20.10i). The reduction of the mean track errors reached nearly 100 km at 3 to 3.5 days which is statistically significant at the 0.05 level of the paired t-test.

2

The conventional observations were assimilated, including the AMSU-A and ATMS radiance observations, and GPS radio occultation and bending angle observations.

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Fig. 20.10 Tropical cyclone track forecast errors (units: km) for BASE (red) and BASE + GIIRS (green) verified against the best track forecast for the eight cases. Black stars in Fig. 20.3i indicate statistically significant differences between samples at a 0.05 level. From Feng et al. (2022). ©2022 Elsevier. Used with permission

Collaborating Platforms In a period from 8 to August 10, 2022, the CMA, IAP, HKO and Fudan University worked together and conducted real-time OSEs to capture the three-dimensional structure of TC Mulan (2022) over the northern part of the SCS, using dropsonde observations from a fixed-wing aircraft operated by the Government Flying Service of the Hong Kong Government, the GIIRS on board the Fengyun-4B satellite of the CMA, retractable meteorological balloons over South China (Fig. 20.11). This is the

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first collaborative effort from a ground–sky–space platform in China. In detail, three days ahead of the real-time conduction (i.e., approximately at 0600 UTC on August 5, 2022 for that planned on August 8, 2022, etc.), the SVs method was used to identify a primary area, and then the CNOP method was further applied to refine this area and finally provide the sensitive area to both CMA and HKO. Then the scanning area of the Fengyun-4B and flights of the dropsonde-equipped aircraft were accordingly determined for TOs. Moreover, the meteorological data were ingested in real time into the self-developed numerical weather prediction modeling system of the CMA. And the observational and forecast results were presented in the morning weather conferences of the CMA. The forecast tracks before and after the assimilation of the additional TO data are shown in Fig. 20.12a. Without these data, the TC was forecasted to move generally in a northwestward direction from 0600 UTC on August 8, 2022. However, the TC was forecasted to move westward first and then northward after assimilating the additional data, which is closer to the observation. With respect to the intensity (Fig. 20.12b), the forecast errors of the V max with TO data were generally less than that without in a forecast period of 36 h, with an average reduction of about 11%. The 24 h accumulated rainfall distribution forecasts and the Equitable Threat Score (ETS) for the model runs initiated at 0000 UTC 10 August 2022 were shown in Fig. 20.13. Compared with the forecast without additional TOs, the one with them was able to provide better results for higher rainfall categories despite similar ETSs for the

Fig. 20.11 Overview of the ground–space–sky observations on August 9, 2022: brightness temperature from GIIRS (K), wind vectors from dropsondes (blue wind barbs; knots), and round-trip drift radiosonde (colored lines). Colored dots denote the differences between observations and simulations after quality control of the longwave channel 32 (699.375 cm−1 ) at 0530 UTC August 9, 2022. From Chan et al. (2023). ©2023 Springer Nature. Used with permission

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Fig. 20.12 a Forecast tracks of TC Mulan (2022) before (red) and after (green) assimilating additional observations. The black line denotes the best track. b Forecast errors (m s−1 ) of the V max before (blue) and after (red) assimilating additional observations. From Chan et al. (2023). ©2023 Springer Nature. Used with permission

0.1 and 10 mm categories: for rainfall categories at or > 25 mm, there is a reduction of false alarms by three stations (eight stations to five stations); for rainfall category at or > 50 mm, two more stations are accurately forecast (five stations increasing to seven stations), and missed forecasts are reduced by two stations (twenty-seven stations reducing to twenty-five stations). As such, the ETSs for the 25 and 50 mm categories are higher. Fig. 20.13 The ETS before (blue) and after (red) assimilating additional TOs for different rainfall categories (mm). From Chan et al. (2023). ©2023 Springer Nature. Used with permission

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20.3 Summaries To augment the routine observational network, which cannot easily be varied at will, TOs have developed rapidly during the past several decades. Our East Asia has benefitted a lot from these field campaigns, especially on the TC forecasts. TOs can supply important data which efficiently reduce initial condition errors as well as their subsequent propagation and/or amplification of these errors in forecasts. Simultaneously, the CNOP method has also experienced a development from the proposition, and theoretical research, through to real-time application, which has been briefly introduced in this chapter. In addition, the CNOP method has also been used to identify the sensitive areas for TOs associated with the forecasting of other high-impact climate and weather events such as El Niño–Southern Oscillation, the Indian Ocean Dipole, heavy air pollution events, southwest vortices, oceanic mesoscale eddies, and the vertical thermal structure in the Yellow Sea (Mu et al. 2017; Duan et al. 2018; Chen et al. 2013; Hu et al. 2021; Jiang et al. 2022; Yang et al. 2022). These achievements are attributed to all the scientific researchers and engineers devoted to. Each tiny progress or mistake is worth remembering, and they have accumulated toward the valuable achievements and experience. However, there are lots of issues, open or unknown, to be fixed or revealed. We are always on the way.

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Chapter 21

Simulating Rapid Water Level Decrease of Lake Biwa Due to Typhoon Jebi (2018) Kohei Takatama, John C. Wells, Yusuke Uchiyama, and Takemasa Miyoshi

Abstract Typhoon Jebi hit the western part of Japan on September, 2018. As a result, the water level in the South Basin of Lake Biwa decreased by 1 m within a few hours after the typhoon passed. A numerical experiment using a high-resolution hydraulic model, forced by an atmospheric model, a river runoff model, and observed outflow well reproduced the water level drop. Water mass balance analysis and times series of wind speed over the lake indicate that this rapid drop in water level was caused by wind drag, in which southwesterly wind drove water from the South Basin to the North Basin. Keywords Typhoon Jebi · Hydraulic model · Wind drag

21.1 Introduction The powerful typhoon Jebi brought heavy rains and winds of up to 50 m per second to the western part of Japan on September 4, 2018. The strong winds caused serious damage in the region. Notably, the water level in the South Basin of Lake Biwa dropped more than 1 m within a few hours. This amplitude was more than an order of magnitude greater than the typical variations under normal conditions, and exposed a substantial area of the lakebed. It is also interesting that the minimum water level K. Takatama (B) · T. Miyoshi RIKEN Center for Computational Science, Kobe, Japan e-mail: [email protected] T. Miyoshi e-mail: [email protected] J. C. Wells Department of Civil and Environmental Engineering, Ritsumeikan University, Kusatsu, Japan e-mail: [email protected] Y. Uchiyama Department of Civil Engineering, Kobe University, Kobe, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9_21

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was observed 100 min after the typhoon passed. Such sudden water level changes bring a risk of flooding, although it did not happen in this event. Lake Biwa is the largest lake in Japan and consists of the North Basin with an area of 618 km2 and an average depth of 43 m and the South Basin with an area of 51 km2 and an average depth of 4 m. The dominant period of surface waves in Lake Biwa, known as Seiche (Kanari 1974), is about 4 h. The purpose of this study is to understand the mechanism of such a rapid water level change due to a strong typhoon. We investigated three effects: (1) direct water input/output effects, which is caused by river in-/out-flow and precipitation to the South Basin, (2) atmospheric pressure differences between the South Basin and the North Basin, and (3) wind drag, which induced a northward lake current. The second and the third effects changed the water level by pushing water through the strait between the South Basin and the North Basin. To quantify the contribution of each effect quantitatively, we performed a numerical experiment using a wellresolved hydrodynamic model, regional atmospheric model, river discharge model, and observed out-flow across a water gate.

21.2 Experimental Design We performed a high-resolution hydrodynamic simulation of Lake Biwa using the ROMS ocean model (Shchepetkin and McWilliams 2005). The horizontal resolution of the model was 50 m and there were 40 sigma vertical layers. The bulk parameterization of surface wind stress and surface net heat fluxes are based on Fairall et al. (2003). Integration proceeded in time from an initial state of rest, with a horizontally uniform temperature profile specified by interpolation of observed values at the Adogawaoki-chuo observatory1 in the center of the North Basin at Aug. 1, and the water level set to 0.0 cm. The regional atmospheric model Scalable Computing for Advanced Library and Environment (SCALE) (Nishizawa et al. 2015; Sato et al. 2015) was used to simulate the typhoon-induced atmospheric forcing for ROMS at hourly intervals and a spatial resolution of 1.0 km. Two nested domains were used for the simulation. The resolution of the outer domain over western Japan was 5 km, and that of the inner domain around Lake Biwa was 1 km with hourly output. The NCEP/GFS at 0.25° resolution was applied at the boundary of the outer domain at 5 km resolution, which then forced the boundaries of the 1 km nested inner domain. To compensate for the lack of reproducibility of the atmospheric model, the simulated wind speeds were multiplied by 1.3 to match the wind speed of the typhoon with ground observations surrounding Lake Biwa,2 when bulk surface momentum and heat fluxes were calculated in ROMS. 1

Water Information System, provided by Ministry of Land, Infrastructure, Transport and Tourism (MLIT), Japan. 2 Observation conducted by Japan Meteorological Agency (AMeDAS network).

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The river inflows to Lake Biwa were calculated using a runoff model (Kotsuki et al. 2011). The river channels in this model were defined by the Global Drainage Basin Database (Masutomi et al. 2009) upscaled to 1 km resolution. The land moisture condition was initialized at zero. After a 1-year spinup, the river model was driven by an atmospheric analysis data from the Japan Meteorological Agency Mesoscale Model (MSM, Saito et al 2007) from January 2015. Lake Biwa has one principal outlet, the Seta River at the southern end of the South Basin, whose discharge is controlled by the Seta Weir.3 The amount of outflow in ROMS was specified from the operational record at the water gate, limited however to 340 m3 s−1 to maintain numerical stability, which is slightly more than the maximum value of the gate specification under normal condition (300 m3 s−1 ). Although this value is smaller than the actual amount during the typhoon passage (estimated to be 900 m3 s−1 ), the impact on the temporal variation of the water level is considered to be small, as the gates were always fully open during this period.

21.3 Results Water level and surface current distributions at the time when the simulated water level in the South Basin was lowest (Sep. 4, 2018, 08:20 UTC) are shown in Fig. 21.1a. The base level was defined at each grid point as the average value before the typhoon came. At this time, the atmospheric simulation indicated that the typhoon had already passed the west side of Lake Biwa and had reached the Japan Sea, west of the Noto Peninsula (Fig. 21.1b). It caused southwesterly wind, thence a northeastward surface current over most of the lake. The water level decreased toward south, and it decreased more rapidly in the South Basin than in the North Basin. In the South Basin, the water level decreased toward the south, and very low values were found near the southwestern shore. In the North Basin, on the other hand, the water level increased northward, and the value was generally highest on the northeast shore. The maximum amplitude in the South Basin (− 80 cm) was much larger than that in the North Basin (+ 12 cm). In agreement with observations, water level also dropped rapidly in the model as shown in Fig. 21.2. At the location of the Mihogasakioki gauging station on the southwestern shore of the South Basin (135.866°E, 35.018°N), the simulated water level dropped from 00:00 UTC to 3:00 UTC by 10 cm, stagnated briefly, then dropped suddenly to − 78 cm from 05:00 UTC to 08:20 UTC. In the corresponding co-located observation, the water level increased slowly from 03:00 UTC to 4:50 UTC, then suddenly decreased to − 92 cm at 07:20 UTC. Most of the water level drop recovered rapidly in both the simulation and the observation. It recovered to − 17 cm within 2 h in the simulation and overshot to + 10 cm in the observation within 3 h. Then both returned to the normal level with some oscillation. Although there were differences 3

This hydraulic gate is operated by MLIT Kinki Regional Development Bureau Biwako Office https://www.kkr.mlit.go.jp/biwako/index.php.

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Fig. 21.1 a Simulated water level relative to the average level preceding the typhoon (color, cm) and surface current (vector, scale at lower right), and b simulated mean sea level pressure (color, hPa) and surface wind (vector) at the time when the water level in the South Basin was minimal (Sep. 4, 08:20 UTC). The circle in panel a indicates the gauging station. In the rectangular region of panel b, results obtained from the inner domain are superposed on those from the outer domain

between the simulation and the observation, such as the lack of increasing tendency before rapid decrease and relative delay of one hour in the simulated low water, our simulation reproduced the major features of this event. In both the simulation and the observation, the peak times came after the typhoon’s closest approach (6:00 UTC), and the respective time series of water level yielded a high correlation coefficient of 0.72. Fig. 21.2 Time series of the simulated (red line) and the observed (blue line) water level (cm) at the observatory point in the South Basin

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Figure 21.3 shows the distributions of water levels and depth-averaged current. Flow through the strait between the South and the North Basin can change the relative water levels by exchanging water. At the time when the simulated temporal water level change was fastest (07:20 UTC, Fig. 21.3a), the current in the strait was heading north, whence the water level decreased in the South Basin. In the North Basin, the current showed an anti-clockwise pattern, and its amplitude was large near the Ado River Delta (around 136.8°E, 35.32°N) on the western coast. Figure 21.3b shows that at the time of simulated low water, the vertically averaged current through the strait was nearly zero, in contrast to the surface current (Fig. 21.1a). In fact, there was no significant change in the meteorological field over Lake Biwa between 07:20 and 08:20 UTC (except that at 07:20 the typhoon was located slightly south of the position shown in Fig. 21.1b), which suggests that changes in currents during this one-hour interval were due to the increase in adverse gradient of hydraulic head from the South to the North Basin. At low water, the vertically averaged current across the strait was nearly zero (Fig. 21.3b), in contrast to the surface current (Fig. 21.1a). A water mass budget analysis of the simulation results helped us to evaluate the contribution of each effect. Figure 21.4a shows time series of net water mass input into the South Basin and its components: precipitation input, river inflow, river outflow, and discharge from the North Basin to the South Basin. The net mass input corresponds to the temporal change of the water level in the South Basin (Fig. 21.2). The mass balance was clearly dominated by the lake current component: the correlation/regression coefficients between them are 1.00 and 1.00. While the water level rapidly decreased, a large amount of water in the South Basin flowed into the North Basin, consistent with Fig. 21.3a. Such a shift can be caused by differences in atmospheric pressure or by wind drag, except for lake internal dynamics, but

Fig. 21.3 Same as Fig. 21.1a, but showing the depth-averaged current (vector) at the time when a the temporal water level change was maximal (07:20 UTC) and b the water level was lowest (08:20 UTC) in the South Basin

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it should be noted that ROMS did not account for the pressure effect. Before the typhoon came, the lake current component tended to be positive to compensate the river outflow. This southward current was consistent with typical observed major currents in Lake Biwa. Contributions of the precipitation and the river input, which increased the water level, were negligible. The river outflow cannot be ignored, but its magnitude is wholly inadequate to explain the drop in water level. From this process of elimination, one infers that lake currents into the North Basin caused the rapid water level change due to typhoon Jebi. To estimate the impact of atmospheric pressure differences on the observed water level, time series of sea level pressure averaged over Lake Biwa, and pressure over the South Basin minus pressure over the North Basin were calculated based on our atmospheric simulation (Fig. 21.4b). A positive pressure difference tends to lower the water level in the South Basin. A negative pressure difference slowly developed as the typhoon approached (before 04:00 UTC). Then, it rapidly increased (04:00– 08:00 UTC), and changed in sign at the time when the typhoon was the closest (06:00 UTC), to attain a maximum of 2.7 hPa. After that, the difference disappeared slowly. This rapid change of the pressure difference was generally in phase with the observed water level change. Therefore, if the pressure effect is represented in the model, the phase of the observed and simulated water levels could be close. However, since the spatial scale of the lake was much smaller than the typhoon, that amplitude was < 4 hPa, which under equilibrium would only induce a 4 cm water level difference. This might explain about half of the observed rise in water level as the typhoon approached. Also, the largest positive pressure difference explains only quarter of the difference in minimum water level between simulation and observation. Figure 21.4c shows the time series of the wind speed along the longest-axis of Lake Biwa, pointing north-northwest, as averaged over the whole lake, together with its sign-inverted hourly change, which causes mass transport by the wind drag. The along-axis wind speed was very small before the typhoon came (00:00 UTC). It rapidly accelerated from 05:00 UTC and attained its maximum value at 08:00 UTC, nearly an hour after the typhoon passed. It should be noted that the absolute wind speed was maximal at 06:00 UTC, when the typhoon was the closest to the lake, at which time the direction shifted suddenly from ESE to SSW. The change in along-axis wind speed was maximal around 07:00 UTC. Around 09:00 UTC, southwesterly wind was still strong, but diminishing. As seen from comparison of Figs. 21.1a and 21.3b, the vertically integrated current can flow in a different direction from the surface current or the wind. As the wind diminished, water returned from the north to the South Basin (Fig. 21.4a), consistent with the sign-inverted tendency, and restored the water level. Thus, the time series of the sign-inverted wind speed tendency were similar with that of the water input due to the lake current (Fig. 21.4a). Although the tendency led the mass input component, this can be explained by inertia of the lake. Therefore, the rapid water level decreasing can be explained by the wind drag effect.

21 Simulating Rapid Water Level Decrease of Lake Biwa Due to Typhoon … Fig. 21.4 a Simulated water mass input to the South Basin and its components (m3 s−1 ), b simulated sea level pressure averaged over Lake Biwa (red line, left axis, hPa) and pressure difference between the South Basin and the North Basin (blue line, right axis, hPa), and c wind speed along-long axis of Lake Biwa (red line, left axis, m s−1 ) and its sign-inverted tendency (right axis, m s−1 h−1 ). In panel a, purple line denotes the precipitation input, green line the river input, blue line the river output, and red line the lake current components

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21.4 Discussion and Conclusion Our numerical simulation system well reproduced the water level drop in the South Basin of Lake Biwa due to Typhoon Jebi (2018). The water level drop can be explained by the wind drag effect. The typhoon passed the west of Lake Biwa so that the strong northeastward wind along the long axis of the lake dragged the water from the South Basin to the North Basin. Because the area of the South Basin is much smaller than that of the North Basin, associated changes in water level tend to be about ten times stronger in the South Basin than the North Basin. However, we note that the wind drag effect is insufficient for explaining some minor variations in the simulated mass input (Fig. 21.4a). For example, accelerated along-axis wind from 05:20 UTC to 06:20 UTC was inconsistent with water input across the strait. This was possibly caused by lake internal dynamics. Small wind speed deceleration around 04:00 UTC caused small water input, and it might trigger a water mass transportation due to external gravity wave. This effect was passive for the response to the typhoon, but might play important role for determining the amplitude and phase. This was also consistent with the oscillation during the restoration phase of the water level after 07:20 UTC. Its period was nearly 4 h, which corresponds to the period of surface Seiche in the lake. Synchronization of the wind drag effect with the surface gravity wave might have magnified the water level change. The quite rapid water level restoration around 09:00 UTC under slightly decelerated wind (Fig. 21.4c) can be explained by such synchronization. The timescale of equilibration of water level, about 60 min in the South Basin, is rather close to the duration of the fastest decrease in atmospheric pressure, so water inertial effects probably pushed the drop in water level to exceed the equilibrium value of 4 cm. Taken together, these considerations suggest that atmospheric pressure contributed between 4 and 8 cm to the observed rise in water level in the observation, which is consistent with the early tendency. However, as concern as the subsequent drop in water level, it is of secondary importance overall as compared to the wind drag. There was a time lag between the typhoon’s approach and the water level change. Our experiment predicted low water level about one hour later than observation, and this was possibly caused by inaccuracy of the simulated atmospheric forcing. Notably, MSM atmospheric analysis data indicate that the along-axis wind speed attends its maximal value around 07:00 UTC (not shown), which is 1 h earlier than our experiment, and which corresponds closely to the time of low water in the South Basin. This one-hour difference was consistent with that separating the water level minima simulated by ROMS versus the observation. Though there was room for improving the accuracy of the atmospheric experiments (e.g., increasing the resolution to better resolve topographic effects on winds, and applying data-assimilation), the results clearly show that typhoon winds can dominate lake level fluctuations. The spatiotemporally smoothed wind direction relative to the lake was particularly important. If the typhoon had passed near the east of the lake and similarly strong winds had blown southward, a rise in water level of

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similar magnitude might have occurred, with a strong risk of flooding, especially if rainfall were intense. However, it is not obvious what temporal and spatial scales of wind influence lake levels, and there is also uncertainty at the interface in numerical models as to how the wind is transmitted to the lake. Therefore, the study suggests that caution should be exercised during the long period before and after the passage of a typhoon, while also taking into account the uncertainty of weather forecasts. Acknowledgements This work was supported by JST SICORP Grant Number JPMJSC1804. We are deeply grateful to Prof. Kumagai at Ritsumeikan University for providing us with topographic data of Lake Biwa. We also appreciate MLIT Kinki Regional Development Bureau Biwako Office for 10 min data on water levels.

References Fairall CW, Bradley EF, Hare JE et al (2003) Bulk parameterization of air-sea fluxes: updates and verification for the COARE algorithm. J Clim 16(4):571–591. https://doi.org/10.1175/1520-044 2(2003)016%3c0571:BPOASF%3e2.0.CO;2 Kanari S (1974) Some results of observation of the long-period internal Seiche in Lake Biwa. Jpn J Limnol 35(4):136–147. https://doi.org/10.3739/rikusui.35.136 Kotsuki S, Tanaka K, Kojiri T et al (2011) Development of water circulation model including irrigation. J Jpn Soc Civ Eng Ser B1 (hydraul Eng) 67(4):I_553-I_558 Masutomi Y, Inui Y, Takahashi K et al (2009) Development of highly accurate global polygonal drainage basin data. Hydrol Processes 23:572–584. https://doi.org/10.1002/hyp.7186 Nishizawa S, Yashiro H, Sato Y et al (2015) Influence of grid aspect ratio on planetary boundary layer turbulence in large-eddy simulations. Geosci Model Dev 8:3393–3419. https://doi.org/10. 5194/gmd-8-3393-2015 Saito K, Ishida J, Aranami S et al (2007) Nonhydrostatic atmospheric models and operational development at JMA. J Meteor Soc Jpn 85B:271–304. https://doi.org/10.2151/jmsj.85B.271 Sato Y, Nishizawa S, Yashiro H et al (2015) Impacts of cloud microphysics on trade wind cumulus: which cloud microphysics processes contribute to the diversity in a large eddy simulation? Prog Earth Planet Sci 2(23):167. https://doi.org/10.1186/s40645-015-0053-6 Shchepetkin AF, McWilliams JC (2005) The regional oceanic modeling system (ROMS): a splitexplicit, free-surface, topography-following-coordinate oceanic model. Ocean Modell 9(4):347– 404. https://doi.org/10.1016/j.ocemod.2004.08.002

Index

A Absolute mass, 159 Adaptive Mesh Refinement (AMR), 24 Adiabatic (adiabatically), 309, 311, 315, 316, 321, 326 Advanced Microwave Sounding Unit-A (AMSU-A), 298 Advanced Technology Microwave Sounder (ATMS), 298 Advanced Geostationary Radiation Imager (AGRI), 215 Advanced Regional Eta Model (AREM), 8 Aerosol, 507 Air–sea interaction, 418–420 Air temperature, 163 Akisame, 518 Albedo parameterization, 163 Allocation fraction, 161 Allocation of carbon, 158 Allocation ratio, 159 Allocation scheme, 158, 164, 169, 170, 173, 174 Allometric allocation scheme, 159 Allometric growth, 164 Allometric ratio, 159 Allometric scaling scheme, 173 All-sky radiance, 247, 249–252, 256, 257, 278, 279, 414, 424 All sky radiance assimilation, 118 Analysis increment, 112, 113 Arakawa C-grid, 494 Arc-shaped rainband, 512 Artificial intelligence, 366, 395–397, 400 AS scheme, see allometric allocation scheme Asselin’s time filter, 496

Assimilated carbon, 157–161, 165, 173 Assimilated carbon fraction, 161 Asymmetrical Convective Model version 2 (ACM2) scheme, 183 Atlantic Multi-decadal Oscillation (AMO), 426 Atmosphere-land surface boundary, 158 Atmosphere-land surface system, 158 Atmosphere-ocean coupled model, 469 Atmospheric forcing, 160, 163 Atmospheric General Circulation Model (AGCM), 283, 284, 286, 465 Atmospheric General Circulation Model for the Earth Simulator (AFES), 465 Atmospheric Model Intercomparison Project (AMIP), 18, 21 Atmospheric Motion Vector (AMV), 248, 250, 253, 256, 257, 272, 278, 298 Augmented Noah-MP, 157 Automated Synoptic Observing System (ASOS), 193 Automatic Weather Station (AWS), 182, 183

B Back-building, 519 Background Error (BE), 251, 279 Background Error Covariance (BEC), 295–297, 299, 301 Backward trajectory analysis, 514 Baiu, 484 Bare soil, 159 Baroclinic, 321, 324 Baroclinicity, 313, 318

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. K. Park (ed.), Numerical Weather Prediction: East Asian Perspectives, Springer Atmospheric Sciences, https://doi.org/10.1007/978-3-031-40567-9

569

570 BATS, see Biosphere-Atmosphere Transfer Scheme Beer’s law, 166 Beijing Climate Center–Atmospheric General Circulation Model (BCC-AGCM), 9–11, 13, 29 Benchmark, 463, 465 Between-crown gap, 166, 167 Between-crown gap probability, 166, 167 Bias error, 164, 167 Bias Score (BS), 369, 370, 378, 380, 383 Big data assimilation, 473, 477 Biosphere-Atmosphere Transfer Scheme, 162 Blocking, 426, 432 Bluff body, 472 Bogus Data Assimilation (BDA), 416 Bogussing, 415 Boreal, 159 Boreal ecosystem-atmosphere study, 159 BOREAS, see Boreal Ecosystem-Atmosphere Study Bougeault-Lacarrere (BouLac) scheme, 183 Boundary Condition (BC), 374, 394, 396, 401 Boundary layer, 474 Boussinesq approximation, 505 Breadth-First Search (BFS), 465, 466 Bred vector, 442 Brier Skill Score (BSS), 373, 391–393, 399 Brightness Temperature (BT), 249, 260 Brunt-Vaisala frequency, 499 Building-resolving model, 468 Bulk coefficient, 500 Bulk microphysical process, 502 Bulk transfer coefficient, 500 Bulk Richardson Number (BRN), 332, 344 Buoyancy term, 492 Butterfly effect, 115

C CAM-SE, 43, 44 Canadian land surface scheme, 162 Cancellation of significant digits, 492 Canopy albedo, 167 Canopy albedo parameterization, 167 Canopy density, 157 Canopy gap, 166, 167, 172, 173 Canopy gap probability, 166, 167 Canopy structure, 157 Canopy-soil process, 158 Carbon accumulation, 161

Index Carbon allocation, 158, 159, 161, 164, 165, 168, 173 Carbon allocation ratio, 158, 159 Carbon allocation scheme, 157, 160, 162 Carbon assimilation, 158 Carbon biomass, 161 Carbon exchange, 158 Carbon mass, 161, 165 Carbon storage, 164 Cartesian coordinates, 485 Categorical statistics, 369, 370, 372, 398 Central Mountain Range (CMR), 367, 375, 384 Central Weather Bureau (CWB), 373, 375, 377, 378, 395, 396 Changma, 484 Changma (Mei-Yu, Baiu), 308, 316 Charney-Phillips grid, 494 China Meteorological Administration (CMA), 9, 10, 13, 24, 26, 205, 207, 214 Chinese Academy of Meteorological Science Climate System Model (CAMS-CSM), 9–11 Chinese Academy of Meteorological Sciences (CAMS), 8, 10 Chinese Academy of Sciences (CAS), 21 CLASS, see Canadian Land Surface Scheme Clear-Sky Radiance (CSRs), 251, 413 Clefts, 469 Climate Prediction System (CPS), 9 Climate version of advanced Regional Eta Model (CREM), 8 Cloud-cleared radiances (CCRs), 215 Cloud fraction, 80 Cloud microphysics, 220–222, 237, 243, 374 Cloud Microphysics Parameterization Scheme (MPS), 422, 424 Cloud radar, 521 Cloud-radiation interaction, 118 Cloud-radiation scheme, 83, 102 Cloud-Resolving Model (CRM), 365, 374, 384, 394, 484 Cloud resolving numerical model, 467 Cloud-Resolving Storm Simulator (CReSS), 367, 373–375, 378–384, 386–389, 393, 394, 396, 398–401, 484 Cloud-to-ground discharge, 509 Coefficient of determination (R 2 ), 195 CO2 flux, 168

Index Cold conveyor belt, 506 Cold rain, 502 Cold stress, 170 Collision and coalescence processes, 506 Community Atmosphere Model (CAM), 10 Computational Fluid Dynamics (CFD), 468 Concentric eyewalls, 514 Conditional Nonlinear Optimal Perturbation (CNOP), 441, 442, 444, 535, 537–551, 554, 556 Conic factor, 488 Constant altitude coordinate system, 489 Contoured Frequency by Altitude Diagram (CFAD), 234–238 Convection-resolving simulation, 348, 353 Convective Available Potential Energy (CAPE), 332, 334–338, 340, 343, 344, 351 Convective cell, 475 Convective Parameterization Scheme (CPS), 422–424 Convective Rain Ratio (CRR), 321–325 Convective-scale weather system, 447 Convective system, 308, 309, 316, 319, 321, 326 Convective updraft, 332–335, 340 Correct negative, 369, 370 Coupled Mesoscale Model (CMSM), 469, 470 Coupled Model Intercomparison Project (CMIP), 12 Coupled Model Intercomparison Project Phase 5 (CMIP5), 433 Courant-Friedrichs-Lewy (CFL), 12, 23, 494 Covariance, 251, 279 Covariance Inflation (CI), 296, 297, 299–302 Crank-Nicolson scheme, 496 CReSS-3DVAR, 522 CReSS-LETKF, 527 CReSS-NHOSE, 505 CReSS-SDM, 506 Cropland (CL), 193–195 Crossbar network, 465 Cross-track Infrared Sounder (CrIS), 298 Crown density, 166 Crown depth, 167 Crown radius, 166 Cubed sphere, 43, 44, 56 Cumulus (CU), 180, 182

571 Cumulus Parameterization Scheme (CPS), 307, 309–311, 313, 316–318, 321, 322, 324–327 Cyclogenesis, 472 Cyclone Sidr, 515 Cyclone Winston, 504

D Data Assimilation (DA), 247, 249–251, 253, 260, 262, 264–267, 279, 283–286, 293, 401, 411–414, 435, 467, 468, 470, 473, 474, 477, 478, 520 Data assimilation of radar, 76 Data Assimilation of wind profiler, 77, 79, 253 Database for Policy Decision making for Future climate change (d4PDF), 517 Decaying season, 168 Deciduous Broadleaf Forest (DBF), 166, 174, 193–195, 197 Deciduous forest, 162, 165 Deciduous needleleaf forest, 166 Differential reflectivity (ZDR ), 218, 220, 222, 237 Diffuse albedo, 167 Diffuse insolation, 170 Diffuse radiation, 162, 167 4 Dimensional Ensemble Variational Hybrid (4DEnVAR), 118 Direct albedo, 167 Direct radiation, 162 Direct stiffness summation, 44 Dirichlet, 497 Disaster prevention, 465–467, 473, 476 Dissipation error, 496 Distributed memory parallel computer system, 465 Dolph-Chebyshev, 69 Dolph filter, 53 Domain, 468, 475 Doppler radar, 521 Doppler lidar, 469 Dormancy period, 168 Dormancy season, 171 Dormant season, 169, 174 Double warm-core structure, 515 Double penalty, 370–372 Downdraft, 469 Downscale forecast experiment, 475 Down-Scaling Simulation System (DS3), 468, 469

572

Index

Drag coefficient, 500 Dropsonde, 515 Dry convective mixed layer, 472 Dual-polarimetric parameters, 217, 240, 243 Dual-wavelength water vapor retrieval, 225 Dynamical Core Model Intercomparison Project (DCMIP), 6 Dynamic Downscaling Simulation (DDS), 515 Dynamic efficacy, 514 Dynamic blending, 66, 73–75, 101 Dynamic vegetation, 162 Dynamic Initialization (DI), 416, 417 DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND), 19, 28

Equations of motion, 491 ER, see Ecosystem respiration Error correlation, 470 Error covariance, 470 European Center for medium-range weather forecast HAMburg (ECHAM), 6, 11 European Centre for Medium-Range Weather Forecasts (ECMWF), 57, 299 European Organization for the Exploitation of Meteorological Satellites (EUMETSAT), 206 Evapotranspiration, 161 Evapotranspiration coefficient, 500 Evergreen broadleaf type, 161 Evergreen forest, 165 Evergreen needleleaf forest, 159, 166, 174 Extratropical cyclone, 520

E Earth’s angular velocity vector, 487 Earth’s radius, 487 Earth simulator, 461, 463, 465, 484 Earth System Model (ESM), 22 Ecosystem respiration, 157, 168 Eddy covariance flux, 168 Eddy viscosity coefficient, 499, 500 Effective leaf and stem area index, 167 Ekman pumping, 505 Energy budget, 158, 159 Energy flux, 173 Ensemble Adjustment Kalman Filter (EAKF), 413 Ensemble-based Forecast Sensitivity to Observations (EFSO), 58 Ensemble Data Assimilation (EDA), 295–297, 299, 300 Ensemble Kalman filter (EnKF), 284, 286, 291, 520 Ensemble forecast, 467, 468, 473–475, 477 Ensemble forecasting, 441–444, 446–449, 451, 453–458 Ensemble Kalman Filter (EnKF), 414, 470 Ensemble members, 467, 468, 470, 474 Ensemble Transform Kalman Filter (ETKF), 40, 537 Ensemble Typhoon Quantitative Precipitation Forecast (ETQPF), 375–377, 387, 388, 395 Equation of potential temperature, 491 Equation of state, 491 Equations of continuity, 491

F FA scheme, see fixed allocation scheme False Alarm, 369–371 False Alarm Ratio (FAR), 370, 371 Fast Fourier Transform (FFT), 12, 22, 23 Fields of View (FOVs), 208, 209, 215 Fifth-generation PSU/NCAR Mesoscale Model (MM5), 180 Fifth-generation Mesoscale Model (MM5), 375 Fine root mass, 165 Finite-volume Atmospheric Model of the Institute of atmospheric physics/ LASG (FAMIL), 9–11, 25, 29 Fixed allocation scheme, 158 FLAGSHIP 2020 Project, 473 Flood, 473–476 Foehn, 425, 430, 432 Foliage area volume density, 166 Forcing singular vector, 443 Forecasting uncertainty, 442, 443 Forest canopy, 160, 174 Forest cover, 174 Forest masking, 162 FORTRAN 77, 527 FORTRAN 90, 527 Forward trajectory analysis, 514 Four-dimensional (4D), 214, 215 Four-Dimensional Ensemble variational data Assimilation (4D-EnVAR), 475 Four-Dimensional Local Ensemble Transform Kalman Filter (4D-LETKF), 297

Index Four-Dimensional Variational Method (4DVAR), 520 Fractional Snow Cover (FSC), 191–193, 195–197 Fractional Skill Score (FSS), 283, 284, 288, 289, 292, 371, 373 Fresh snow albedo, 162, 174 Front, 468, 469 Fugaku, 461–463, 466, 467, 476–479 Fujitsu, 463, 465, 466 G Gaussian transformation, 284 Gaussianity, 284, 290, 291 Gauss-Lobatto-Legendre (GLL), 44 Generalized Conjugate Residual (GCR), 13, 14, 26, 27 Genetic Algorithm (GA), 179–181, 184, 196 GEOS-CHEM, 57 Geostationary (Geo), 205–207, 214 Geostationary Hyperspectral InfraRed Sounders (GeoHIS), 205–208, 212–215 Geostationary hyper-spectral IR Sounder (Geo-Sounder), 206 Geostationary Interferometric Infrared Sounder (GIIRS), 205–215, 550, 552–554 Geosynchronous and Extended Orbit (GEO-XO), 206, 207, 215 Gflops, 463, 464 Gibbs phenomena, 45 GLDAS, see Global Land Data Assimilation System Global, 163 Global final analysis (FNL) data, 185 Global Forecast System (GFS), 48, 185 Global land data assimilation system, 163 Global Positioning System-Radio Occultation (GPS-RO), 298 Global/Regional Assimilation PrEdiction System (GRAPES), 9–11, 13, 14, 26, 27 Global Forecast System (GFS), 13, 25, 374, 394, 395, 401 Global Positioning System (GPS), 247–249, 252, 257 Global Positioning System Radio Occultation (GPSRO), 247, 249, 250, 252, 256, 257, 278 Global-Regional Integrated forecast SysTem (GRIST), 10, 11, 14–19

573 Global Seasonal Forecast System version 5 (GloSea5), 430, 431 Global Spectral Model of the Japan Meteorological Agency (GSM JMA), 39 Global warming, 465 GPP, see gross primary production Graph 500, 465, 466 Gray zone, 146–152 Gray-zone physics, 56 Green vegetation fraction, 167 Grid-point Atmospheric Model of the Institute of atmospheric physics/ LASG (GAMIL), 9–13 Grid-scale, 316, 326 Grid spacing, 374 Gross primary production, 157, 168 Ground temperature, 501 Growing season, 157, 164, 165, 167–171, 174 Growth respiration, 161, 169 Gust front, 523 H Halo region, 486 Hazard risk, 477 Heat conduction equation, 501 Heat exchange coefficient, 85, 86 Heat flux, 159 Heavy rainfall, 332, 343, 346–352, 462, 467, 474, 475 Heavy rainfall (precipitation) mechanism, 307, 313, 316–318, 320, 321, 324, 326 Hierarchical System Development (HSD), 57 High-impact weather system, 484 High-Performance Computing Infrastructures (HPCIs), 461, 463, 465, 466, 473 High Performance Conjugate Gradients (HPCG), 465, 466 Himawari-8, 474 Hit, 369–371, 375, 378, 387, 389, 400 Hitachi SR2201/1024, 463 Hook-shaped structure, 511, 525 Horizontally Explicit Vertically Implicit (HEVI), 25 Humidity, 467 Hybrid vertical coordinate system, 489 Hybrid-4DEnVar, 41, 47, 49–53, 58 HYbrid Coordinate Ocean Model (HYCOM), 419

574 Hydraulic model, 559 Hydrological model, 477 Hydrometeor, 218, 219, 221–223, 227, 234, 236, 243, 247–249, 257 Hydrostatic balance, 492 Hyperspectral Infrared Sounder (HIS), 206, 207, 215 I Ice-microphysics, 316, 317, 321 ICLOUD, 82 Implicit scheme, 494 Incremental Analysis Updates (IAU), 53, 67–69, 522 Infrared (IR), 205, 206 Infrared Atmospheric Sounding Interferometer (IASI), 298 Initial Condition (IC), 295, 300, 374, 394, 396, 401 Initial data experiment, 107 Initial error, 441, 444–447, 453, 454, 457 Initial perturbation, 441–445, 447, 448, 453, 454, 456–458, 497 Initial time, 391, 394, 399 Initial uncertainty, 442, 443, 447, 449, 453, 454, 457, 458 Insolation, 161 Instability, 316, 322, 324, 326, 327 Institute of Atmospheric Physics (IAP), 6, 10, 12, 21, 23, 548, 553 Institute of Atmospheric Physics–Atmospheric General Circulation Model (IAP-AGCM), 8–11, 21–23 Instrumental error, 169 Integrated Forecast System (IFS), 299 Integrated Atmospheric Model Across Scales (iAMAS), 19, 20 Intercellular CO2 concentration, 161 Internal gravity wave, 492 International Geosphere-Biosphere Program (IGBP), 186 Intertropical Convergence Zone (ITCZ), 472 Intrinsic predictability, 333, 352–354, 357 Inverse density, 42 IR sounder (IRS), 206, 215 Iterated Reweighted Minimum Covariance Determinant (IRMCD), 79, 101 J Jacobian, 489

Index Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 465, 467, 469, 473, 479, 484 Japan Atomic Energy Agency (JAEA), 465 Japan Atomic Energy Research Institute (JAERI), 465 Japanese Aerospace Exploration Agency (JAXA), 463, 465 Japanese 55-year Reanalysis (JRA-55), 430 Japan Meteorological Agency (JMA), 206, 463, 465, 467–472, 474, 477, 483 Japan Sea Polar Airmass Convergence Zone (JPCZ), 511 Joint UK Land Environment Simulator (JULES), 430 K Kain-Fritsch (KF) scheme, 185 Kalman filter (EnKF), 46, 57 Kama-flood, 57 Karman vortex shedding, 472 K computer, 461–463, 465–470, 472–475, 478, 479 K index, 345 Korea Meteorological Administration (KMA), 183, 297 Korea Institute of Atmospheric Predictions (KIAPS), 40, 41, 47, 54, 56–58 Korea Integrated Model (KIM), 41, 44, 47–49, 51, 52, 54, 57 Korea Meteorological Administration (KMA), 38–40, 44, 47, 54, 58 Korean Integrated Model (KIM), 105–121, 295, 297, 298 Korean Institute of Atmospheric Prediction Systems (KIAPS), 105 Korean Meteorological Administration (KMA), 105–107, 116, 119, 121 Korean Meteorological Administration-Unified Model (KMA-UM), 105, 107, 109–113, 115, 119, 120 KPOP, 47, 54, 55 Kuroshio warm current, 506 L Laboratory of numerical modeling for Atmospheric Sciences and Geophysical fluid dynamics (LASG), 10 LAI, see leaf area index, 157, 162–174 Lake Biwa, 559–561, 563–566

Index Lambert conformal projection, 488 Land-atmosphere interactions, 158, 426, 428, 429, 435 Land cover, 157, 163 Land Cover Types (LCT), 159, 170, 190, 191, 193–195 Land surface, 158 Land Surface Model (LSM), 157, 158, 173, 174, 302 Land surface processes, 158, 160, 173, 174 Land use, 163 Landslide, 473 Land Surface Model (LSM), 46, 57 Large-eddy, 146, 147, 151 Large Eddy Simulation (LES), 46, 474 Latent heat flux, 157, 168, 428–430 Latent heating flux, 88, 91 Lateral Boundary Condition (LBC), 418 5-layer thermal diffusion (TD) scheme, 183 Lead time, 365, 368, 380, 387, 388, 390, 392, 397, 400 Leaf aging effect, 162, 165, 173 Leaf allocation, 164 Leaf area, 165 Leaf area index, 157, 173 Leaf area per unit mass, 162 Leaf Index (LI), 158, 167, 171–174 Leaf loss, 164, 173 Leaf loss process, 161 Leaf mass, 159, 171 Leaf stalk, 164 Leapfrog scheme, 496 Level-2.5 Mellor-Yamada-Nakanishi-Niino (MYNN), 506 Level of Free Convection (LFC), 334, 335, 346–348, 354–356 Level of Neutral Buoyancy (LNB), 334, 335, 346 LH, see latent heat flux Life science, 466 Lifting Condensation Level (LCL), 346, 354–356 Lightning discharge, 508 Limited Area Model (LAM), 417 Linear-shaped precipitation area, 346, 347 Litter, 171 Litter carbon pool, 171 Lobes, 469 Local Ensemble Transform Kalman Filter (LETKF), 41, 47, 51, 57, 58, 283, 286–288, 292, 293, 467, 468, 470–472, 477, 478 Localized torrential rain, 518

575 Local wind gust, 473 Longitude-latitude coordinates, 487 Longwave radiation, 159, 163, 174 Longwave infrared (LWIR), 207, 208, 214 Lorenz grid, 494 LSAI, see effective leaf and stem area index LSM, see land surface model

M Machine learning (ML), 213, 366, 395, 397–400 Maintenance respiration, 161, 164, 169, 173 Manufacturing, 465, 466 Map factor, 488 Map projection, 488 Maritime traffic, 474 Mass virtual temperature, 491 McICA, 45 Mean Bias (MB), 195, 196 Mean Squared Error (MSE), 369, 372, 373, 397 Measurement error, 168, 169 Medium-Range Forecasting (MRF), 128, 132, 137–143 Mei-yu, 365, 366, 368, 372, 374, 382, 384–387, 399, 400, 484 Mellor-Yamada-Janjic (MYJ) scheme, 183 Mellor-Yamada model, 472 Mellor-Yamada-Nakanishi-Niino level-2.5 (MYNN2) scheme, 183, 190 Mercator projection, 488 Meridional wind, 163 Mesoscale, 247, 248, 250, 253, 278, 466–468, 472, 473, 475 Mesoscale Convective System (MCS), 308–310, 312, 315, 326, 331–333, 335–338, 340, 341, 343, 344, 346, 348, 350, 351, 353, 354, 366, 370, 372, 387, 484 Mesoscale convective vortex, 474 Mesoscale environmental processes, 474 Mesoscale Model 5 (MM5), The, 421, 540, 542, 544–547 Mesoscale Model version 5 (MM5), 421 Mesoscale precipitating system, 331, 333, 335, 339–342, 344, 347–349, 351, 352, 354, 356, 357 Mesoscale Weather Numerical Forecast System of China Meteorological Administration (CMA-MESO), 210 Message Passing Interface (MPI), 12, 20, 486

576 Meteorological forcings, 471 Meteorological Research Institute (MRI), 469, 479 Meteosat Third Generation (MTG-3), 206 Metric factor, 487 Microphysics (MP), 180, 256 Microphysics Parameterization Scheme (MPS), 310, 316–318, 322, 326, 327 Microscale, 461, 463, 467 Microwave Humidity Sounder (MHS), 298 Microwave satellite data assimilation, 118 Ministry of Education, Culture, Sports, Science and Technology (MEXT), 465, 467, 473, 476, 479 Miss, 369–371 Mixed forest, 165, 166 Mixed Forest (MF), 193–195 Mixing length, 500 Mode-splitting scheme, 494 Model assessment, 162 Model Coupling Toolkit (MCT), 57 Model error, 441, 443–447, 451–454, 456–458 Model for Prediction Across Scales (MPAS), 395, 396 Model performance, 162, 171 Model uncertainty, 163 Model validation, 168 Model Output Statistics (MOS), 40 Model perturbation, 443, 444, 451, 452, 454, 457, 458 Model uncertainty, 443, 445, 451, 453–458 Model verification, 232 Moderate Resolution Imaging Spectroradiometer (MODIS), 160, 186, 193 Modified two-stream approximation, 166 Modified potential temperature, 43 MODIS, see Moderate Resolution Imaging Spectroradiometer Moist Absolutely Unstable Layer (MAUL), 350–352, 356 Moist Difference Total Energy (MDTE), 354–356 MRI-AGCM3.1, 516 MTS, see modified two-stream approximation Multi-moment Constrained finite Volume (MCV), 10, 11, 24, 25, 29 Multiple parameterization options, 157, 173

Index N National Center for Atmospheric Research (NCAR), 9, 12, 22, 180, 183, 395, 396 National Center for Environmental Prediction (NCEP), 25, 185, 374, 375, 396, 401 National Oceanic and Atmospheric Administration (NOAA), 206, 207 National Space Development Agency of Japan (NASDA), 465 Natural disaster mitigation, 466, 467 NCAR Community Atmospheric Model (CAM) scheme, 184 NCEP Final Analysis (FNL), 430 Near Real-Time (NRT), 478, 479 Negative polarity strike, 509 NEMO, 57 Nested, 468 Net primary production, 157, 164, 173 Neuman, 497 New materials and energy creation, 466 Noah land surface model with multiple parameterization options, 157 Noah land surface model with multiple parameterization options (Noah-MP) scheme, 183, 190 Noah land surface model with multiple physics options (Noah-MP), 180, 186, 187, 190, 197 Noah LSM, 160 Noah-MP, see Noah land surface model with Noah-MP, 57 Noah 3.0, 46, 48 Noise equivalent Delta Temperatures (NEΔT/NeDT), 209 Non-Gaussian, 283, 284, 291 Nonhydrostatic, 465, 470 Non-Hydrostatic Ocean model for the Earth Simulator (NHOES), 505 Non-Hydrostatic Model (NHM), 465, 467–472, 474 Nonlinear Forcing Singular Vector (NFSV), 443, 444, 446, 447, 451–454, 457 Nonlinearity, 284 Nonphotosynthetic leaves, 167 Nonphotosynthetic process, 167 Nonphotosynthetic stems, 167 Nonphotosynthetic vegetation, 160, 164 NPP, see net primary production Nudging method, 507 Nudging technique, 504

Index Nudging term, 508 Number density, 502 Numerical prediction (NP), 462 Numerical viscosity term, 496 Numerical Weather Prediction (NWP), 4, 7, 10, 13, 24, 26, 28, 179, 180, 196, 205, 207, 213–215, 248–250, 252, 253, 256, 295–297, 365, 366, 375, 397, 398, 462, 463, 467, 470, 475, 477, 484 Numerical Wind Tunnel (NWT), 463

O Observing System Simulation Experiment (OSSE), 218, 225, 227, 240, 541, 542 Omega equation, 514 One-dimensional diffusion model, 486 One-dimensional thermal conductivity model, 486 One-dimensional thermal diffusion model, 505 1.5-order closure, 499 One-order closure scheme, 499 Open MP, 486 Operational global model, 105 Optimum Interpolation Sea Surface Temperature (OISST), 419, 420 Orthogonal curvilinear coordinates, 486

P Pacific-Japan (PJ) pattern, 426 Parallel computing, 465 Parallel I/O (PIO), 20 Parameterization, 157 Parameterization scheme, 157, 160, 168, 173 PBL parameterization, 137, 146, 147, 180, 374 Pennsylvania State University (PSU), 180, 375 Performance diagram, 370, 378, 379, 384, 386 Phase shift, 157 Phenological carbon transport, 165 Phenology, 165, 173 Phenology scheme, 169 Photosynthesis, 157, 158, 161, 164–166 Photosynthetic ability, 158 Photosynthetic activity, 167, 168, 170 Photosynthetic assimilate, 158

577 Photosynthetic capacity, 162, 165, 167, 170, 173 Photosynthetic leaves, 167 Photosynthetic stems, 167 Physical parameterization, 160 Piecewise potential vorticity inversion technique, 514 Piecewise Rational Method (PRM), 14 Planetary Boundary Layer (PBL), 128, 132, 133, 137, 138, 145–148, 151, 179, 180, 182, 183, 186–190, 196, 197, 296, 302, 374, 420, 421 Plant respiration, 161 Polar stereographic projection, 488 Polar cold bias, 114, 118 Positive polarity strike, 509 Post-K Priority, 473–475 Potential temperature, 491 Potential vorticity inversion technique, 514 Practical predictability, 353, 354 Precipitation, 163, 168, 247–250, 253, 254, 257, 258, 261, 263, 265, 266, 268–272, 274, 277, 283–289, 291–293 Precipitation of Rainfall Extremes Campaign in the Pacific (PRECIP), 395 Predecessor Rain (PRE), 517 Predictability, 331, 333, 340, 352–357 Pressure equation, 491 Primary production, 157, 164, 168, 173, 174 Princeton Ocean Model (POM), 472 Probability Of Detection (POD), 369 Processor nodes (PNs), 465 Pseudo-Global Warming (PGW), 517

Q Q10 temperature coefficient, 161 Quality control, 76, 79, 101 Quantitative Precipitation Forecast (QPF), 180, 217–220, 227, 229, 230, 232, 238, 240, 243, 365, 366, 527 Quasi-compressible system, 492 Quasi-Normal Scale Elimination (QNSE) scheme, 183 Quasi-stationary line-shaped MCS, 509 Quasigeostrophic, 463 Quasi-Stationary Convective Cluster (QSCC), 342–345, 348

578 R Radar, 247–250, 252, 256, 257, 278, 279 Radar data assimilation, 218, 219, 227, 238–240, 243 Radial (Doppler) velocity, 217, 218, 221 Radial velocity, 248, 250, 252, 257 Radiance, 249, 251 Radiation condition, 497 Radiative Transfer Model (RTM), 249 Rain water, 467 Rapid intensification, 514 Rapid Radiative Transfer Model (RRTM), 501 Rapid Radiative Transfer Model (RRTM) scheme, 184, 190 Rapid Radiative Transfer Model for General circulation models (RRMTG) scheme, 184 Rapid Refresh Multiscale Analysis and Prediction System (RMAPS), 65, 93 Rapid Refresh Multiscale Analysis and Prediction System-ST (RMAPS-ST), 100–102 Rapid Update Cycle (RUC) scheme, 183 Rate-of-strain tensor, 499 Reflectivity, 217, 218, 221–223, 228, 234–238, 240, 243, 248, 252, 256, 257 Refractivity, 247, 249, 250, 252, 253, 256, 257, 278 Regional coupled atmosphere-wave-ocean non-hydrostatic model, 505 Regional modeling, 465 Regional Oceanic Modeling System (ROMS), 560, 561, 564, 566 Relative mass, 159 Relative humidity, 339, 341, 342, 345, 346, 348, 350–352 Relaxation-To-Prior Perturbation (RTPP), 296, 297 Relaxation to Prior Spread (RTPS), 286–288, 297, 299, 300 Representative Concentration Pathway (RCP), 433 RIKEN Advanced Institute for Computational Science (RIKEN AICS), 465, 473 RIKEN Center for Computational Science (R-CCS), 466, 479 Riming electrification mechanism, 508 RK3, 44 Rmax, 463, 466 RMSE, see root mean square error, 171

Index Root-Mean-Squared Error (RMSE), 185, 192, 193, 195–197, 299 Rossby wave, 492 Roughness parameter, 500 Round-off error, 492 RRTM-G, 45, 48, 501 RTTOV, 57 Runoff, 475

S SAI, see stem area index Satellite, 247–253, 256, 257, 259, 261, 263, 278, 279 Satellite observation, 159, 174 Satellite retrieval, 170 Scalable Computing for Advanced Library and Environment (SCALE), 478, 560 Scandinavia (SCAND) pattern, 426, 428 Schmidt transformation, 56 Sea breeze, 468, 469 Sea ice, 114, 115, 117, 118 Seasonal cycle, 157, 166, 167, 169, 174 Seasonality, 158, 168 Sea spray, 527 Sea Surface Temperature (SST), 375, 418–420, 426, 433, 435 Secondary eyewall formation, 514 Semi-implicit scheme, 494 Semi-Implicit Semi-Lagrangian (SISL), 13, 14, 26–28 Senescence, 165, 168 Sensible heat flux, 419, 421, 425, 428 Sensible heating flux, 88, 90 Sensitivity experiment, 472 Sequoia, 465 Shaded leaf fraction, 170 Shaded leaves, 161 Shading effect, 159 Shared memory parallel computer, 465 Short range, 365, 368, 371, 382, 384, 386–388, 390, 399, 400 Short-range forecast, 468, 478 Shortwave broadband, 163 Shortwave radiation, 163 Shurin, 518 SI, see stem index SI3, 57 Similarity Skill Score (SSS), 369, 372, 373, 390, 391, 397–399 Simple Arakawa-Schubert (SAS), 46

Index Simplified Parameterizations, primitivE-Equation Dynamics (SPEEDY), 286, 287, 292, 293 Single-scattering albedo, 163 Singular Vector (SV), 442, 537, 542–544, 554 Smagorinsky constant, 499 Snow age, 162 Snow albedo (SA), 159, 162, 167, 179, 190–193, 195–197 Snow albedo scheme, 158 Snow cover, 159, 163 Snow-covered albedo, 159, 162, 174 Snow-covered surface albedo, 157, 158, 160, 162, 164, 167, 171, 173, 174 Snow cover fraction, 159, 163, 173, 174 Snow depth (SD), 159, 179, 190–193, 195–197 Snow Mountain Range (SMR), 367, 384 Snow storm, 527 Snow surface albedo, 159, 162, 173, 174 Snow surface albedo scheme, 173, 174 Soil composition map, 89 Soil hydraulic parameters, 89, 90 Soil moisture, 161, 163 Soil Moisture Active Passive (SMAP), 430 Soil moisture initialization, 411, 426, 428, 430, 431, 435 Soil temperature, 161, 163 Soil texture data, 89 Solar zenith angle, 159 Sound wave, 492 South China Sea (SCS), The, 553 South Korea (SK), 179–182, 189–193, 195–197 Specific differential phase (KDP ), 220, 222, 237 Specific humidity, 163 Specific leaf area, 165 Spectral Element Method (SEM), 43–45 Spectral nudging, 416, 418 Spectral transform Atmospheric Model of the Institute of atmospheric physics/ LASG (SAMIL), 9–11, 25, 29 SPEEDY-LETKF, 286, 287, 292, 293 Spin-up, 68, 69 Squall line, 308, 309, 326, 332, 335–339, 341, 342, 344, 346, 347, 350, 353, 371 Stability condition, 332, 333, 335, 337, 339, 349 Staggered grid, 494 Stationary forest, 158

579 Stationary line-shaped MCS, 518 Stationary Line-shaped Precipitation System (SLPS), 518 Stem area index, 157, 162 Stem area per unit mass, 162 Stem index, 158, 174 Stochastically Perturbed Dynamical Tendency (SPDT) scheme, 296, 298, 299, 301 Stochastically Perturbed Parameterization Tendency (SPPT) scheme, 296, 298, 299, 301 Stochastically Perturbed Parameterizations (SPP), 51 Stochastically perturbed physics tendency scheme, 451 Stochastic Backscatter (SPBS) scheme, 296 Stochastic Kinetic Energy Backscatter (SKEB) scheme, 296, 443 Stochastic Perturbation Hybrid Tendencies (SPHT) scheme, 297–302 Stochastic perturbation method, 424 Stochastic Perturbations of Parameterization Tendencies (SPPT), 51 Stomata conductance, 161 Stomatal resistance scheme, 161 Storm surge, 470–472 Strategic Programs for Innovative Research (SPIRE), 466, 467, 472, 473, 479 Stress tensor, 499 Sub-grid scale, 307, 310, 318, 326 Subgrid-scale turbulence, 499 Success Ratio (SR), 369–371 Summer solstice, 164, 165 Sunlit leaf fraction, 170 Sunlit leaves, 161 Sunway Taihu Light, 465 Superbomb, 527 Supercell, 467, 474, 510, 525 Supercomputer, 461–463, 465, 466, 473, 476–479 Super-Droplet Method (SDM), 506 Supertyphoon Haiyan, 514 Supertyphoon Megi, 506 Surface air temperature, 168 Surface albedo, 157, 159, 164, 172, 174 Surface boundary layer, 500 Surface pressure, 163 Surface drag, 472 Surface-layer scheme, 85, 102 Swirl ratio, 474 SZ, see solar zenith angle

580 T T-PARCII, 515 Taiwan Area Heavy-rainfall Observation and Prediction Experiment (TAHOPE), 395 Taiwan Area Heavy-rainfall Prediction Experiment (TAHPEX), 395, 396, 400 Taiwan Typhoon Flood Research Institute (TTFRI), 376, 395 Targeting Observation (TO), 535–538, 542, 545, 547, 550, 554–556 Tatsumaki, 522 Teleconnection, 425, 426, 428 Temperate climate, 159 Temperate forest, 159, 160, 164 Temperature, 217–220, 223–228, 240, 243 Temperature lapse rate, 335–338, 340, 343, 345, 350, 357 Terrain-following coordinate, 489 Terra incognita, 472 Terrain-Permitting Thermodynamic Retrieval Scheme (TPTRS), 223, 225, 226 Tflops, 465 Thermal roughness, 85 Thermodynamic retrieval, 521 THORPEX Pacific Asian Regional Campaign (T-PARC), 413 Threat Score (TS), 365, 369, 388, 399 Three-dimensional variational method (3DVAR), 520 Three-dimensional variational (3DVAR) method, 413 Three-dimensional Variational DA (3DVAR), 67, 73 Thunderstorm, 331–334, 345, 353, 354, 357 Tianhe-2, 465 Time filter, 496 Time-lagged ensemble, 374, 387–389, 391, 396 Titan, 465 Tornadic vortex, 474 Tornado, 462, 467, 474, 522 Tornadogenesis, 474 Torrential rains, 467, 477 Total albedo, 159, 167 Total derivative, 487 Total Energy-Mass Flux (TEMF) scheme, 183 Tower measurement, 157, 162, 168 Tripolar structure of charge distribution, 508

Index Tropical Cyclone (TC), 366, 441, 443, 444, 447, 469, 470, 472, 474, 484, 535–538, 540–548, 550–556 Turbulence, 463 Turbulence Kinetic Energy (TKE), 128, 129, 136, 147, 148, 150, 151, 499 Turbulence parameterization, 499 Turbulent mixing, 127, 129, 137, 148–152 Turbulent Prandtl number, 499 Turnover rate, 161 Two-big-leaf model, 161 Two-dimensional domain decomposition, 486 Two moments, 502 Two-stream radiation transfer, 166, 173 Two-step Shape-Preserving Advection Scheme (TSPAS), 11 Typhoon, 365, 366, 368, 372, 375, 378–380, 382, 384, 385, 387, 388, 397–399, 469, 470, 474, 484 Typhoon Bart, 523 Typhoon Bolaven, 514 Typhoon Chanthu, 517 Typhoon Fanapi, 513 Typhoon Hagibis, 518 Typhoon Lan, 515 Typhoon Morakot, 513 Typhoon Nancy, 504 Typhoon Shanshan, 525 Typhoon Tokage, 512 Typhoon Trami, 518 Typhoon Wipha, 514 Typhoon Fanapi (2010), 376, 377, 380, 381, 383 Typhoon Haiyan (2013), 367, 393 Typhoon Jebi (2018), 559, 564, 566 Typhoon Matmo (2014), 368, 380, 381, 388, 389, 391–393, 397, 399, 400 Typhoon Morakot (2009), 367, 379, 387, 388, 395 U Unified Model (UM), 39, 40, 54, 432 University of Washington (UW) scheme, 183 Updraft, 469 Upper damping layer, 497 Upwelling, 505 Urban and built-up lands (UB), 193–195 V Vapor adjustment scheme, 521

Index Variational Bias correction (VarBC), 54 Vault structure, 524 Vegetation coverage, 88 Vegetation dynamics, 158, 161, 165 Vegetation effect, 157, 159, 160, 167, 174 Vegetation parameters, 159, 160, 162, 164, 172, 173 Vegetation phenology, 162 Vegetation seasonality, 162, 168 Vegetation structure, 158 Vegetation type, 163 Velocity of the sound wave, 491 Vertical shear, 467 Virtual temperature, 491 Visible (VIS), 162, 238, 314, 316, 318 Vortex initialization, 411, 414–416 Vorticity, 467

W Warm core, 514 Warm rain, 502 Warm start, 497 Water budget, 158 Water vapor deposition process, 506 Water vapor mixing ratio, 491 Water level, 559–564, 566, 567 Water Vapor (WV), 210–212, 219, 220, 224–226, 230, 243 Wave model, 506 Weather Research and Forecasting (WRF), 46, 48, 56, 170, 179–185, 189, 190, 196, 197 Weather radar, 478 Weather Research and Forecasting Data Assimilation (WRFDA), 413 Weather Research and Forcasting model (WRF model), The, 65, 68, 69, 82, 86, 89, 90, 100, 545, 546, 548 Weather Research and Forecasting Model-Advanced Research Model (WRF-ARW), 65 Weather Research and Forecasting (WRF) model, 317, 319, 375, 417, 419, 420, 422, 423, 425, 429, 430

581 Western North Pacific (WNP), 411, 536, 537, 541 Western North Pacific Subtropical High (WNPSH), 413, 422, 430, 432 Wet Bulb Globe Temperature (WBGT), 433, 435 White-sky albedo, 163 Wind drag, 559, 560, 563, 564, 566 Wind profiler, 67, 73, 78–80 Wind radius, 472 Winter albedo, 163 Winter surface albedo, 157, 158, 166, 167 Wintertime surface albedo, 164 Within-crown gap, 166 Within-crown gap probability, 166 Woody savanna (WS), 193–195 WRF, see Weather Research and Forecasting WRF Double Moment 5-class (WDM5) scheme, 185 WRF model coupled with the micro-GA (WRF-μGA, 184 WRF model coupled with the micro-GA (WRF-μGA system), 180, 184, 186, 189, 190, 197 WRF model’s Community Variational/ Ensemble Data Assimilation System (WRFDA), 65 WRF Single Moment Five-class microphysics scheme (WSM5), 46, 48

Y Yin-yang-grid global-regional UNified Model for the Atmosphere (YUNMA), 10, 11, 13, 26, 27 Yonsei university (YSU), 127, 129, 137, 139–143, 147, 148 YonSei University (YSU) scheme, 183 YSU PBL, 48, 84, 140–143, 145, 147, 148

Z Zonal wind, 163