Mountain Weather Research and Forecasting: Recent Progress and Current Challenges [1 ed.] 9400740972, 9789400740976

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Mountain Weather Research and Forecasting

Springer Atmospheric Sciences

For further volumes: http://www.springer.com/series/10176

Fotini Katopodes Chow • Stephan F.J. De Wekker Bradley J. Snyder Editors

Mountain Weather Research and Forecasting Recent Progress and Current Challenges

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Editors Fotini Katopodes Chow Department of Civil and Environmental Engineering, MC 1710 University of California, Berkeley Berkeley, CA 94720-1710 USA

Stephan F.J. De Wekker Department of Environmental Sciences University of Virginia McCormick Rd. 291 Charlottesville, Virginia USA

Bradley J. Snyder Meteorological Service of Canada #201 401 Burrard Street Vancouver, BC, Canada

ISBN 978-94-007-4097-6 ISBN 978-94-007-4098-3 (eBook) DOI 10.1007/978-94-007-4098-3 Springer Dordrecht Heidelberg New York London Library of Congress Control Number: 2012940730 © Springer Science+Business Media B.V. 2013 This work is subject to copyright. All rights are reserved 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

This book is the result of a multiyear effort that began with the organization of a workshop designed to bring researchers and forecasters together to discuss current progress and challenges in mountain weather. The chapters herein represent the topics from this Mountain Weather Workshop, which took place in Whistler, British Columbia, Canada, 5–8 August 2008. The inspiration for the workshop and book arose under the guidance of the American Meteorological Society (AMS) Mountain Meteorology Committee. One of the main goals of the workshop was to bridge the gap between the research and forecasting communities by providing a forum for extended discussion and joint education. The workshop consisted of lectures given by 13 distinguished speakers, several discussion opportunities in small groups, and a day of laboratory exercises designed for forecaster training for the 2010 Winter Olympics in Vancouver. The lectures provided a detailed overview of important and emerging topics in mountain meteorology. About 100 participants attended, roughly evenly split among forecasters, researchers, and graduate students (see Fig. 12.2 for a picture of participants). One of the highlights of the week was a group activity to design the best observation and modeling system to nowcast for the Olympic ski jump event; this was an excellent opportunity for researchers and operational forecasters to work together and “bridge the gap.” The lectures from the workshop can be accessed online in the COMET MetEd tutorial collection (http://www.meted.ucar. edu/training module.php?id=878). The chapters in this book have been written with the intent to provide a thorough overview of each topic with an emphasis on recent research and progress in the field, especially since the last collection of topics in mountain meteorology was published more than two decades ago (Blumen 1990). It is our hope that this new offering will be used extensively in mountain weather courses at universities and forecast offices and also used as a general reference book for researchers, forecasters, and students. Readers will be provided with a broad understanding of the fundamental principles driving flow over complex terrain, including historical context for recent developments and future directions for researchers and forecasters. For academic

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Fig. P1.1 View of the PEAK 2 PEAK gondola connecting Whistler and Blackcomb mountains, looking across toward Blackcomb. Whistler village is on the far left (© James Dunning. Reprinted with permission)

researchers, the book will provide some insight into issues important to the forecasting community. For the forecasting community, we hope the book will provide training on fundamentals of flows specific to mountainous regions which are notoriously difficult to predict, understanding of current research challenges, and an opportunity to learn about the latest contributions and advancements to the field. Our goal of bridging the gap between research and forecasting with this book is aptly captured in the image below showing Whistler and Blackcomb mountains, connected by the new PEAK 2 PEAK gondola, built for the 2010 Winter Olympics, bridging the gap between the two mountains (Fig. P1.1). The first chapter provides an overview of mountain weather and forecasting challenges specific to complex terrain. This is followed by chapters that focus on diurnal mountain/valley flows that develop under calm conditions (Chap. 2) and dynamically driven winds under strong forcing (Chap. 3). The focus then shifts to other specific phenomena that are difficult to understand and predict in mountain regions: Alpine foehn (Chap. 4) and boundary layer phenomena and air quality (Chap. 5). The following two chapters address processes that bring wet mountain weather, in the form of rain, snow, or other hydrometeors, with a discussion of specific orographic precipitation processes (Chap. 6) and the details of microphysics parameterizations (Chap. 7). Having covered the major physical processes, the book shifts to observation and modeling techniques used in mountain regions. First, a detailed discussion of field measurements in complex terrain is given (Chap. 8).

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Then, the following three chapters describe the basics of mesoscale numerical modeling (Chap. 9), model configuration and physical parameterizations such as turbulence (Chap. 10), and model applications in operational forecasting (Chap. 11). The book concludes with a chapter that discusses the current state of research and forecasting in complex terrain, including a vision of how to bridge the gap in the future (Chap. 12). We are quite fortunate to have a set of conscientious and thorough authors who have contributed their knowledge and expertise to create this book, largely in their spare time. We are also extremely grateful to the many reviewers who were involved in ensuring the quality of this book. Given the length of some of the chapters, we were particularly impressed by the care they took to thoroughly review the chapter content, from comments on overall structure to details on style and formatting. Funding to support the publication of this book and for student travel to the workshop was provided by the National Science Foundation (NSF) (award ATM0810090). Funding for the workshop was provided by the American Meteorological Society (AMS), the University Corporation for Atmospheric Research (UCAR) acting on behalf of the Cooperative Program for Operational Meteorology, Education and Training (COMET), and the Meteorological Service of Canada (MSC). The workshop was mainly organized by us (editors of this book) with the help of many others on the AMS Mountain Meteorology Committee, in addition to Cara Campbell at AMS. We thank our colleagues who were AMS Mountain Meteorology Committee members with us over the years (Brian Colle, Lisa Darby, Mike Meyers, Stephen Mobbs, Greg Poulos, Heather Reeves, Alex Reinecke, Simon Vosper, Doug Wesley, and David Whiteman) and members of the AMS publications department (Peter Lamb, Sarah Jane Shangraw, and Ken Heideman) for their support of this effort.

Contents

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Mountain Weather Prediction: Phenomenological Challenges and Forecast Methodology .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Michael P. Meyers and W. James Steenburgh

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Diurnal Mountain Wind Systems . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Dino Zardi and C. David Whiteman

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Dynamically-Driven Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 121 Peter L. Jackson, Georg Mayr, and Simon Vosper

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Understanding and Forecasting Alpine Foehn . . . . . .. . . . . . . . . . . . . . . . . . . . 219 Hans Richner and Patrick H¨achler

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Boundary Layers and Air Quality in Mountainous Terrain . . . . . . . . . . . 261 Douw G. Steyn, Stephan F.J. De Wekker, Meinolf Kossmann, and Alberto Martilli

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Theory, Observations, and Predictions of Orographic Precipitation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 291 Brian A. Colle, Ronald B. Smith, and Douglas A. Wesley

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Microphysical Processes Within Winter Orographic Cloud and Precipitation Systems . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 345 Mark T. Stoelinga, Ronald E. Stewart, Gregory Thompson, and Julie M. Th´eriault

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Observational Techniques: Sampling the Mountain Atmosphere.. . . . 409 Robert M. Banta, C.M. Shun, Daniel C. Law, William Brown, Roger F. Reinking, R. Michael Hardesty, Christoph J. Senff, W. Alan Brewer, M.J. Post, and Lisa S. Darby

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Mesoscale Modeling over Complex Terrain: Numerical and Predictability Perspectives. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 531 James D. Doyle, Craig C. Epifanio, Anders Persson, Patrick A. Reinecke, and G¨unther Z¨angl

10 Meso- and Fine-Scale Modeling over Complex Terrain: Parameterizations and Applications.. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 591 Shiyuan Zhong and Fotini Katopodes Chow 11 Numerical Weather Prediction and Weather Forecasting in Complex Terrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 655 Brad Colman, Kirby Cook, and Bradley J. Snyder 12 Bridging the Gap Between Operations and Research to Improve Weather Prediction in Mountainous Regions .. . . . . . . . . . . . . . . . 693 W. James Steenburgh, David M. Schultz, Bradley J. Snyder, and Michael P. Meyers Author Index.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 717 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 725

Contributors

Robert M. Banta NOAA Earth System Research Laboratory, Boulder, CO, USA W. Alan Brewer NOAA Earth System Research Laboratory, Boulder, CO, USA William Brown National Center for Atmospheric Research, Boulder, CO, USA Fotini Katopodes Chow Department of Civil and Environmental Engineering, University of California, Berkeley, CA, USA Brian A. Colle School of Marine and Atmospheric Sciences, Stony Brook University/SUNY, Stony Brook, NY, USA Brad Colman NOAA/National Weather Service, Seattle-Tacoma, WA, USA Kirby Cook NOAA/National Weather Service, Seattle-Tacoma, WA, USA Lisa S. Darby NOAA Earth System Research Laboratory, Boulder, CO, USA Stephan F.J. De Wekker Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA James D. Doyle Naval Research Laboratory, Marine Meteorology Division, Monterey, CA, USA Craig C. Epifanio Texas A&M University, Texas, USA Patrick H¨achler Federal Office of Meteorology and Climatology MeteoSwiss, Zurich, Switzerland R. Michael Hardesty NOAA Earth System Research Laboratory, Boulder, CO, USA Peter L. Jackson University of Northern British Columbia, Prince George, BC, Canada Meinolf Kossmann Climate and Environment Consultancy, Deutscher Wetterdienst, Offenbach am Main, Germany

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Daniel C. Law NOAA Earth System Research Laboratory, Boulder, CO, USA Alberto Martilli CIEMAT Unidad de Contaminacion Atmosferice, Madrid, Spain Georg Mayr University of Innsbruck, Innsbruck, Austria Michael P. Meyers NOAA/National Weather Service, Grand Junction, CO, USA Anders Persson UK MetOffice, SMHI, Norrk¨oping, Sweden M.J. Post NOAA Earth System Research Laboratory, Boulder, CO, USA Patrick A. Reinecke Naval Research Laboratory, Marine Meteorology Division, Monterey, CA, USA Roger F. Reinking NOAA Earth System Research Laboratory, Boulder, CO, USA Hans Richner Institute for Atmospheric and Climate Science (IACETH), ETH, Zurich, Switzerland David M. Schultz Division of Atmospheric Sciences, Department of Physics, University of Helsinki, Finland Finnish Meteorological Institute, Helsinki, Finland Centre for Atmospheric Science, School of Earth, Atmospheric and Environmental Sciences, University of Manchester, Manchester, United Kingdom Christoph J. Senff NOAA Earth System Research Laboratory, Boulder, CO, USA Cooperative Institute for Research in the Environmental Sciences, Boulder, CO, USA C.M. Shun Hong Kong Observatory, Kowloon, Hong Kong Ronald B. Smith Geology and Geophysics Department, Yale University, New Haven, CT, USA Bradley J. Snyder Meteorological Services of Canada, Vancouver, BC, Canada W. James Steenburgh Department of Atmospheric Sciences, University of Utah, Salt Lake City, UT, USA Ronald E. Stewart Department of Environment and Geography, University of Manitoba, Winnipeg, MB, Canada Douw G. Steyn Department of Earth and Ocean Sciences, The University of British Columbia, Vancouver, BC, Canada Mark T. Stoelinga 3TIER, Inc, Seattle, WA, USA Julie M. Th´eriault National Center for Atmospheric Research, Boulder, CO, USA Gregory Thompson National Center for Atmospheric Research, Boulder, CO, USA

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Simon Vosper Met Office, Exeter, UK Douglas A. Wesley Compass Wind, Denver, CO, USA C. David Whiteman Atmospheric Sciences Department, University of Utah, Salt Lake City, UT, USA Dino Zardi Atmospheric Physics Group, Department of Civil and Environmental Engineering, University of Trento, Italy Gunther ¨ Z¨angl Deutscher Wetterdienst, Offenbach, Germany Shiyuan Zhong Department of Geography, Michigan State University, East Lansing, MI, USA

Chapter 1

Mountain Weather Prediction: Phenomenological Challenges and Forecast Methodology Michael P. Meyers and W. James Steenburgh

Abstract This chapter summarizes the modern practice of weather analysis and forecasting in complex terrain with special emphasis placed on the role of humans. Weather in areas of complex terrain affects roughly half of the world’s land surface, population, and surface runoff, and frequently poses a threat to lives and property. Mountain weather phenomena also impact a diverse group of users, which may have both beneficial and detrimental implications on societal and economic levels. Advances in forecast skill derive not only from advances in numerical weather prediction, geophysical observations, and cyber infrastructure, but also improvements in the utilization of these advances by operational weather forecasters. Precipitation skill scores during the past two decades, for example, show that operational weather forecasters have maintained a consistent threat score advantage over numerical precipitation forecasts. Although the role of human forecasters is evolving, for many applications, the so-called “human-machine mix” continues to provide an improved product over what can be produced by automated systems alone. To produce the best forecasts possible for the benefit of society, it is crucial for the mountain meteorologist to possess an in-depth knowledge of mountain weather phenomena and the tools and techniques used for atmospheric observations and prediction in complex terrain.

M.P. Meyers () National Weather Service, 2844 Aviators Way, Grand Junction, CO 81506, USA e-mail: [email protected] W.J. Steenburgh Department of Atmospheric Sciences, University of Utah, Salt Lake City, UT, USA F. Chow et al. (eds.), Mountain Weather Research and Forecasting, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-4098-3 1, © Springer ScienceCBusiness Media B.V. 2013

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1.1 Introduction Contemporary mountain weather forecasting involves the integration of geophysical observations, numerical and statistical analysis and modeling, and human cognition to meet the challenges posed by a diverse range of terrain-induced phenomena. This integration, known as the “human-machine mix” (Snellman 1977), produces significantly better forecasts than can be produced by automated systems alone, with the value added by human cognition representing a 5–10 year advance in numerical weather prediction skill (Bosart 2003; Steenburgh et al. 2012, Chap. 12). The human-machine mix is only effective, however, when operational meteorologists possess in-depth knowledge of mountain weather phenomena and the tools and techniques used for atmospheric observation and prediction in complex terrain. In this chapter we provide a review of the major phenomenological challenges confronting mountain meteorologists and qualitatively describe the contemporary forecast process, with emphasis on the human element over complex terrain. Our goal is to provide a foundation for subsequent chapters that focus on specific mountain weather phenomena or forecast tools and techniques, including numerical weather prediction, which ultimately must be integrated to produce societally relevant forecasts. We conclude with a discussion of ongoing forecast applications in areas of complex terrain.

1.2 Phenomenological Challenges in Complex Terrain Mountains cover 25% of the Earth’s land surface, contain 26% of the global population, and produce 32% of the surface runoff (Meybeck et al. 2001). Hills and plateaus account for another 21% of the land surface, 20% of the population, and 19% of the runoff. Thus, the weather in areas of complex terrain affects roughly half of the world’s land surface, population, and surface runoff. The numbers are greater if one considers the remote effects of mountains on the general circulation, storm tracks, moisture transport, and river runoff. The protection of lives and property from high impact events is a forecast priority; in addition, accurate forecasts of day-to-day mountain weather variability benefit commerce and the general public. For instance, many mountain recreationalists are impacted by mountain weather. In the United States, the total number of people who participated in outdoor activities in 2007 is estimated at 217 million (Cordell 2008). Outdoor recreation (camping, snow sports, rafting, hiking, hunting and fishing, etc.) contributes $730 billion to the economy annually and supports 6.5 million jobs (1 in 20 U.S. jobs) according to the Outdoor Industry Association (http://www.outdoorindustry.org). In addition to the general population, numerous other industries are dependent on weather that occurs over complex terrain. The primary phenomenological challenges confronting mountain meteorologists include: (a) snow and (b) ice storms produced by orographic precipitation and/or

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terrain-induced cold advection and cold-air damming; (c) floods, landslides, and debris flows generated by orographic rainfall and/or terrain-induced deep convection; (d) droughts; (e) extreme wildfire spread and behavior driven by fuels, topography, and weather; (f) severe local windstorms created by high-amplitude mountain waves and gap flows; (g) severe convective storms; and (h) cold-air pools and associated air quality hazards. In addition to loss of life, high-impact weather events generated by these phenomena can produce staggering economic losses, often requiring participation from government entities to address them. To adequately meet these phenomenological challenges, forecasters need not only a strong foundation in mountain meteorology (also see: Whiteman 2000), but also knowledge in areas such as climatology, hydrology, ecology, land-surface processes, and societal vulnerability.

1.2.1 Snowstorms Snowstorms (also see Chaps. 6 and 7) exert a heavy toll on public safety and transportation. The average annual cost of snow removal for public roadways in the United States exceeds US $2 billion (Doesken and Judson 1997; National Research Council (NRC) 2004). Thornes (2000) estimated that the United Kingdom spends over US $2 billion annually on direct and indirect costs related to winter maintenance of roadways and road traffic delays. Airport delays and closures cost US $3 billion annually for US carriers and produce adverse sociological impacts for the travelers. The potential benefits from improved forecasting of snow and icing diagnostics at U.S. airports exceed US $600 million annually (Adams et al. 2004). In mountainous regions, the economic losses due to snow-related highway closures are considerable (Fig. 1.1). For example, in Europe, during a prolonged snowy period in February 1999, more than 40 tourist resorts in the Swiss Alps were cut off from the outside world due to road closures for up to 14 consecutive days, resulting in indirect costs of US $200 million (N¨othiger and Elsasser 2004). In the United States, losses produced by the snow-related closure of Interstate 90, the major highway bisecting the Cascade Mountains of Washington State, are estimated at US $700,000 per hour, and similar shut downs of Interstates 70 and 80 through Colorado and Wyoming, respectively, approach US $1 million per hour. Poor driving conditions due to weather cause over 1.5 million vehicular accidents in the United States annually with total economic costs of US $42 billion dollars. These vehicular accidents result in 800,000 injuries with 7,400 fatalities indirectly related to poor weather conditions (National Research Council 2004). A conservative estimate of the annual costs of weather-related vehicular accidents in Canada is US $1.1 billion dollars (Andrey et al. 2001). Snowstorms seriously impact urban corridors adjacent to mountain locations. Personal claims from the March 2003 Colorado Front Range Blizzard exceeded US $93 million. However, with the bad comes the good: during the blizzard the

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Fig. 1.1 Snow removal in the southwestern Colorado Mountains (Courtesy of the Colorado Avalanche Information Center [CAIC] and the Colorado Department of Transportation [CDOT])

snowpack in the Colorado Rockies went from inadequate to above 100% of average. A senior agriculturist for the Western Sugar Cooperative in eastern Colorado called it a billion-dollar storm due to its positive impact on the snowpack (Kohler 2003). Avalanches are another potential impact of winter storms in complex terrain (Fig. 1.2). Recent major weather related avalanche disasters have killed 14 in S´uðav´ık, Iceland in January 1995; 20 in Flateyri, Iceland in October 1995 (J´ohannesson and Arnalds 2001); and 55 in Swiss and Austrian villages in February 1999 (Keiler et al. 2005). Avalanche disasters are not restricted to mountainous regions. On New Year’s Day 1999, nine were killed in Kangiqsualujjuaq, Quebec when an avalanche ran down a steep hill and hit the local school (Branswell 1999). Conversely, mountain snowstorms can be a winter recreationalist’s dream (Fig. 1.3) and provide benefits for the winter recreational economy. There are approximately 6,000 ski resorts with nearly 400 million skier days per year (i.e., 1 day of downhill skiing or snowboarding with a pass/ticket) globally (Hudson 2002; Skistar 2009). Europe is the largest market with 200 million skier days per year, followed by North America with 80 million skier days per year (http:// www.nsaa.org/nsaa/press). The ski industry in the United States has annual revenue of approximately US $12 billion (Scott 2006). Additionally, in North America, snowmobilers spend more than US $28 billion annually on equipment, clothing,

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Fig. 1.2 Avalanche over the southwestern Colorado Mountains (Courtesy of CAIC and CDOT)

accessories and vacations (US $6 billion in Canada) (International Snowmobile Manufacturers Association http://www.snowmobile.org). Avalanches can, however, pose a hazard for these recreationists. From 1991 to 2001, the International Commission of Avalanche Rescue (http://www.ikar-cisa.org) reports nearly 1,500 fatalities due to avalanches with France and the United States having the two highest percentages of deaths.

1.2.2 Ice-Storms The advection and/or entrenchment of cold air by cold-air damming (Forbes et al. 1987; Bell and Bosart 1988) and orographic channeling affect the locations of rainsnow transition zones in winter storms (also see: Chaps. 6 and 7). The January 1998 ice storm that devastated the northeastern United States and southeastern Canada

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Fig. 1.3 Recreational skiing in Colorado (Courtesy of Meyers)

produced 80–100 mm of freezing rain over a 5 day period, causing more than US $4 billion in economic damage, including US $3 billion in Canada (Reagan 1998; Roebber and Gyakum 2003). Cold-air channeling within the St. Lawrence, Ottawa River, and Lake Champlain valleys enabled the persistence of low-level cold air within the precipitating region, controlled the position of the surfacebased freezing line, and enhanced precipitation rates through frontogenesis. Such orographic channeling can also lower freezing levels and snow levels in interior basins and mountain passes, such as the Columbia River Basin, Snake River Plain, Columbia River Gorge, Snoqualmie Pass, and the Frazier River Valley in the Cascade Mountains and Coast Range of western North America (e.g., Decker 1979; Ferber et al. 1993; Steenburgh et al. 1997).

1.2.3 Floods, Flash Floods and Debris Flows Floods are among the most common of geologic hazards worldwide. Typically, most river systems flood (i.e., leave their confining channels and flow outward onto the

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adjacent floodplain) every year or two. There are two types of floods: regional floods that can last for several weeks or months, and flash floods that last for minutes to hours. Both are dangerous and capable of adversely impacting lives and property (National Research Council 2005; http://www.azgs.state.az.us/). Flooding produced by orographic precipitation is responsible for many of the weather-related natural disasters in mountainous regions. Of the 13 weather-related disasters observed in the western United States since 1980 with damages and costs exceeding US $1 billion, four were produced by heavy and/or persistent orographic precipitation and associated surface snowmelt (Lott and Ross 2006). In the United States, floods cost upwards of US $6 billion and about 140 people are killed by floods each year (Knutson 2001). In Europe, losses from the Italian Piedmont floods of 1994 included 64 casualties and US $9 billion in property damage (LinneroothBayer and Amendola 2003; Barredo 2007). The damage and fatalities produced by these events frequently extend over the flood plains well removed from the orography responsible for the precipitation enhancement. Orography also contributes to localized but extremely hazardous flash floods by influencing the formation and movement of deep convection and mesoscale convective systems. Well documented examples include the Rapid City Flash Flood of June 1972, which killed 238 and produced US $100 million in property damage in South Dakota; the Big Thompson Canyon Flood of July 1976, which killed 145 and produced US $25.5 million in property damage in Colorado; the Vaison-LaRomaine Flash Flood of September 1992, which killed 46 and produced US $460 million in property damage in southeastern France (Maddox et al. 1978; S´en´esi et al. 1996; Barredo 2007); and the September 2002 severe flood event in the western Mediterranean mountainous region of southern France (Nuissier et al. 2008; Ducrocq et al. 2008) which killed 24 people and produced an economic damage estimated at nearly US $2 billion (Huet et al. 2003). Debris flows can occur on steep slopes where loose, unconsolidated earthen materials, such as soils and rocks, experience gravitational acceleration during heavy rains, glacial melt or snowmelt (Iverson 1997). Debris flows can move downslope rapidly, at speeds of greater than 10 m s1 ; their less viscous, finegrained relative, mudflows, have been clocked traveling at 40 m s1 in steep mountain canyons. Wildfires may potentially increase the risks for debris flow development by destroying vegetation and making soils more hydrophobic (Cannon et al. 1998, 2001, 2003; Cannon and Reneau 2000). The major hazards of debris flows are from the impact of earthen materials, such as boulders and rocks, and being buried or carried away by the flow. Debris flows can be devastating to life and property. In the United States, damage estimates due to debris flows are close to US $3 billion annually (Restrepo et al. 2008). During December of 1999 exceptionally heavy rain triggered catastrophic floods and landslides along portions of the mountainous coastal region of northern Venezuela (Lyon 2003). Over 10,000 fatalities were reported and the cost of reconstruction was estimated at nearly US $2 billion.

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1.2.4 Droughts One long duration weather phenomenon which may impact short term decision making for a mountain meteorologist, including hydrologists and fire weather meteorologists, is drought. Droughts come in various forms, which may impact society with varying intensities and durations. By definition, a drought is “a period of abnormally dry weather sufficiently prolonged for the lack of water to cause serious hydrologic imbalance (i.e. crop damage, water-supply shortage, etc.) in the affected area” (American Meteorological Society 1986). On an annual basis, average losses and costs in the United States due to drought are estimated to exceed US $8 billion (Knutson 2001). The main water source for over 30 million people in the mainly arid climate of the southwestern United States is the Colorado River. Snowmelt from mountain snowpack provides over 70% of the water supply for this region (Chang et al. 1987; Christensen et al. 2004), and the estimated benefit of water storage exceeds US $350 billion dollars annually (Adams et al. 2004). Water is also the driving force behind the agricultural industry of the southwestern United States. In California, the agriculture industry accounts for nearly US $150 billion annually according to the California Department of Food and Agriculture (http://www.cdfa.ca.gov/). The economic impacts on the agricultural community due to droughts can be tremendous. The University of California, Davis, estimated that US $2.8 billion in agriculture-related wages, and as many as 95,000 jobs across the valley were potentially lost due to the 2008 drought (Howitt et al. 2009). Droughts can adversely impact the winter recreational industry, such as skiing and snowmobiling, which depends on mountain snowpack. For example, many skiers and snowboarders tend to favor lower-density, abundant snow (Steenburgh and Alcott 2008), and low quality or meager snow can affect the demand for ski days (Englin and Moeltner 2004). Summertime recreational use is not immune from low snowpack. Low runoff during drought years can significantly reduce white-water rafting revenue, which in Colorado alone, attracts 540,000 visitors and generates US $150 million annually. Recreational fishing and hunting may also be affected by drought. The impact on fish and other aquatic life due to drought may be significant (Matthews and Marsh-Matthews 2003). Drought-depleted ecosystems and wetlands would have a drastic effect on other wildlife. Drought is not as visually obvious as other weather phenomena in the mountains, but it is perhaps the most devastating to the ecological state because it can significantly weaken a forest’s defenses against insect infestation and wildfires (Morris and Walls 2009). Recently, various populations of bark beetles are impacting the western United States and western Canada with unprecedented levels of tree mortality (Fettig et al. 2007). For instance, beetles have devastated several million acres of trees in Colorado and Wyoming by the end of 2008 (Robbins 2008). Extreme drought conditions in mountainous regions may also lead to increased wildfire activity, as was the case in 1988 (Yellowstone National Park Fire) and in 2002 (Hayman, Missionary Ridge and Coal Seam fires in Colorado).

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Fig. 1.4 2002 Big Fish Wildfire in Colorado (Photo by Mike Chamberlain; courtesy of the NOAA/NWS/GJT)

1.2.5 Wildfire Behavior Prescribed and unplanned wildfires (Fig. 1.4) impact tens of millions of acres annually around the world (also see Chap. 2). In the western United States, where the wealth and development of communities has migrated to the wildlands or the wildland-urban interface over the past few decades, there have been eight wildfires since 1980 that have produced more than US $1 billion in damage (Lott and Ross 2006). Of particular safety concern for firefighters are the conditions that lead to fire “blowups”, which cause rapid fire spread. Wildfires over complex terrain are especially susceptible to these blowups, due the diurnal changes of surface wind direction and speed, as well as the surface mixing of synoptic and convectivelydriven winds. One of the most devastating wildfires, the Big Burn of 1910, killed at least 78 firefighters and burned millions of acres in northern Idaho and western Montana (National Wildfire Coordination Group 1997). This wildfire raised political awareness of the economic and human impacts produced by wildfires. More recently, from 1990 to 2006, there were 310 fatalities during western US wildland fire operations, including the 1994 Storm King wildfire (14 fatalities) (National Wildfire Coordination Group 2007). The number one cause of death during this time period

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was burnovers (40%), “a situation where personnel or equipment is caught in an advancing flamefront” (National Wildfire Coordination Group 2007), and secondly due to aircraft and vehicular accidents (30%). Wildfires often have an adverse impact on recreation and tourism. After the devastating wildfires in Yellowstone National Park in 1988, visits to the park dropped 15% the following year (National Park Service 2009). High wildfire danger may result in the closure of wildland areas, which negatively impact recreation and logging.

1.2.6 Severe Windstorms Created by High-Amplitude Mountain Waves and Gap Flows Terrain-forced flows such as downslope windstorms and gap winds can produce severe winds, many of which have exotic names like the Chinook along the eastern slopes of the Rocky Mountains, the Mistral of southeast France, the Bora of Slovenia, Croatia, and Bosnia, the Zonda along the east slopes of the Andes in South America, the Taku in Alaska and the F¨oehn of central Europe (also see: Chaps. 3 and 4). Surface winds during extreme downslope windstorms can exceed hurricane force (>33 m s1 ) and associated turbulence, rotors, and aircraft icing present a threat to aviation safety (Nance and Colman 2000). Downslope windstorms are also associated with the rapid spread of wildfires (e.g. Santa Ana [southwest United States], F¨oehn, Chinook), making some regions which experience these winds particularly prone to extreme fire weather behavior. Terrain-forced flows are also a concern for maritime travel and commerce in and near mountainous coastal zones around the world. It even has been suggested that these downslope windstorms are often associated with illnesses ranging from migraines to psychosis (Soyka 1983). Less frequent downslope windstorms sometimes occur in a synoptically uncommon flow pattern and represent a difficult forecast problem given their low frequency. In October 1997, while a blizzard was occurring over the Front Range of Colorado (Poulos et al. 2002), an easterly downslope windstorm was occurring over the Mt. Zirkel Wilderness in the north central Colorado Rockies (Meyers et al. 2003). This easterly downslope wind event had devastating ecological consequences, resulting in 13,000 acres of forest blowdown in the Routt National Forest. Although orography also produces thermally driven winds, they are not typically severe. Exceptions include large-scale katabatic flows such as those that occur along the coast of Antarctica, which can become violent, particularly if they are accelerated through interactions with local topography or enhanced by the largescale pressure gradient (e.g., Parish and Bromwich 1998).

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1.2.7 Severe Convective Storms Mountainous terrain can have an indirect impact on tornado development by modifying airmasses downstream over the plains. One scenario occurs when the mountains modify the plains environment by providing an elevated mixed layer which results in a higher severe weather potential for tornado development (Lanicci and Warner 1991). Over the mountains, tornadoes are more infrequent than their plains counterparts, but can be significant when they do form. Tornadoes and funnel clouds occur occasionally over the Rocky Mountains during the late spring and summer (Bluestein and Golden 1993). These tornadoes usually develop in non-supercell storms because the vertical shear is usually too weak for supercell formation. Similar type storms have been observed in Switzerland (Linder and Schmid 1996). However, mountain tornadoes can potentially be devastating. Fujita (1989) documented an F4 tornado that crossed the Continental Divide within Yellowstone National Park in Wyoming in 1987. This tornado traveled 24 miles and leveled 15,000 acres of mature pine forest. On 11 August 1999 an F2 tornado developed southwest of downtown Salt Lake City, Utah, and moved directly through the city. This tornado resulted in one fatality, more than 100 injuries and US $170 million in damages (Dunn and Vasiloff 2001). Bosart et al. (2006) analyzed a longlived supercell that became tornadic over complex terrain in Massachusetts, on 29 May 1995. The F3 tornado left a 50–1,000-m-wide damage path that stretched for 50 km. Other documented supercell tornadoes over complex terrain include those over the hilly terrain of the upper Rhine Valley of Germany (Hannesen et al. 2000) and over the Colorado Mountains (Bluestein 2000). Another potentially devastating severe wind that occurs in proximity to mountain locations is the downburst wind or the smaller scale microburst ( N 2 then m is imaginary and the physically realistic solution is for the disturbances to decay exponentially with height away from their source, in this case the orography. For mountain waves, the source is of course stationary, implying that the frequency of the waves (in a fixed frame of reference), ¨, is zero. Equation 3.15 then reduces to a relationship between the vertical and horizontal wavenumbers and the background flow properties, namely m2 D

N2  k2: UN 2

(3.16)

According to (3.16) we should therefore expect mountain waves with long horizontal wavelengths to have vertical wavelengths which are relatively short. The vertical wavelength will increase with decreasing horizontal wavelength until, for disturbances which are sufficiently short, m becomes imaginary and the wave motion decays in the vertical. If we consider the case of monochromatic waves generated by a simple sinusoidal mountain range with wavelength, , the significance of the non-dimensional parameter FL becomes clear. Mountain waves will only exist when N=UN > k, or alternatively when FL D UN =.NL/ < 1, where the scale L is related to the wavelength by L D /(2 ). For values of FL > 1 the waves generated have a frequency greater than N, so that the flow cannot support mountain waves and disturbances will decay exponentially with height. Such flows are illustrated schematically by Fig. 3.1. It is now useful to define the group velocity, cg D .@!=@k; @!=@m/. This describes the direction and rate of propagation of information or energy by the waves. The group velocity is the velocity with which a “packet” of waves travels through the atmosphere. From (3.14) we can show that Nm2 @! D UN ˙ 3 @k 

(3.17)

Nmk @! D 3 ; @m 

(3.18)

and

where  D jj. If the background wind was to vary sufficiently slowly with height that the dispersion relations still hold locally, then from (3.17) we can see that as UN ! 0, m ! 1 and from (3.18), @!=@m ! 0. This implies that as a wave

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b 5000

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3000

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z (m)

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2000

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1000

1000

0

0

-10000 -5000

0 5000 10000 x (m)

-10000 -5000

0 5000 10000 x (m)

Fig. 3.1 Streamlines over sinusoidal mountains with wavelength 10 km. The wind speed and Brunt V¨ais¨al¨a frequency are independent of height with N D 0.01 s1 and (a) UN D 10 ms1 and (b) UN D 20 ms1 . In (a) the value of FL is approximately 0.628 and therefore propagating mountain waves occur. In (b) FL  1.26 and the wave motion decays exponentially with height

approaches a level where the wind (resolved in the direction of the horizontal wavevector) falls to zero, the vertical wavelength tends to zero and the rate at which wave energy propagates in the vertical also tends to zero. Therefore wave energy does not pass through such a level. The wave energy is dissipated at such “critical levels” and reflection may occur as a result of nonlinearity. The latter is thought to be an important mechanism in the dynamics of downslope windstorms, where the breaking of waves in the troposphere may result in a mountain wave induced critical level above the mountain. The angle at which a packet of waves will propagate away from the mountain is determined by the ratio of expressions (3.17) and (3.18). Choosing the sign of vertical propagation to be positive (so that wave energy radiates vertically away from the mountain) it can be shown that the angle of wave energy propagation, ˛, away from the mountain is given by   @! @! 1 tan ˛ D D m=k: @m @k

(3.19)

Equations 3.16 and 3.19 tell us that when the horizontal wavelength of mountain waves is sufficiently long that k  N=UN , the vertical wavenumber m  N=UN and the wave motion is non-dispersive; the angle of propagation is near vertical. The motion associated with these long wavelengths is, to a good approximation, in hydrostatic balance. For flows across broad smooth mountains (with FL  1) for which the majority of the mountain spectrum consists of long wavelengths, the wave motion is therefore contained in a narrow beam above the mountain. Wave energy radiates vertically and little wave motion is encountered downwind. For shorter horizontal wavelengths whose k is less than, but not significantly less than N=UN , the waves are dispersive. In this case the angle ˛is reduced (and depends on the wavenumber, k) and the wave motion is non-hydrostatic. Therefore for narrow

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Fig. 3.2 The mountain waves generated by flow over (a) broad and (b) narrow ridges when the upwind profile consists of constant stability and wind speed (N D 0.02 s1 and U D 20 m s1 ). Color shading denotes vertical velocity (m s1 ) and isentropes are denoted by line contours (interval 5 K). In (a) the width-scale L is 10 km and FL D 0.1, resulting in a hydrostatic mountain wave response in which the waves propagate vertically and the wave motion is restricted to a vertical beam above the mountain. In (b) L is 1 km and FL D 1. In this case the wave motion is non-hydrostatic. The waves propagate horizontally as well as vertically and wave motion is present in a dispersive tail to the lee of the ridge

mountains, where FL < 1 and a significant portion of the mountain spectrum is made up of short wavelengths, wave energy radiates in the downstream direction as well as in the vertical, resulting in the appearance of “lee wave” motion downwind. Examples of the hydrostatic and non-hydrostatic wave fields associated with broad and narrow mountain ridges, respectively, are illustrated in Fig. 3.2. The wave fields shown are those which occur in flow over two-dimensional ridges of the  1 commonly used bell shaped form h.x/ D H 1 C x 2 =L2 . The upwind profiles have constant stability and wind speed (N D 0.02 s1 and UN D 20 ms1 ) and the wave fields shown are linear solutions, computed using (3.21) (see below). For the broad mountain, where L D 10 km and FL D 0.1, wave motion is only observed immediately above the mountain. These hydrostatic mountain waves propagate vertically into the upper atmosphere. In contrast, for the narrower mountain, when L D 1 km and FL D 1, the dispersive nature of the energy propagation (implied by the k dependence in (3.19)) means that short wavelength waves have a horizontal component to their propagation and hence wave motion appears downwind of the ridge as well as above it. In practice, the complexity of real mountain ranges means that they are made up of a wide spectrum of horizontal scales and thus we should expect a range of responses from the mountain wave field. The very shortest scales, perhaps associated with individual peaks or narrow valleys, may in general be too short to force wave motion and their associated disturbances may decay with height. For longer scales, we can expect both a vertically propagating hydrostatic wave response as well as non-hydrostatic waves which trail downwind of the mountain range. It is

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worth bearing in mind that the increase of wind strength with height through the troposphere, typical of mid-latitudes, implies that wave motion which is hydrostatic (and hence vertically propagating) at low levels, may in fact respond in a more dispersive non-hydrostatic manner aloft. The shorter, non-hydrostatic, wavelengths may themselves be greatly affected by changes in wind and stability with height. As we shall see in Sect. 3.3, this will often result in a trapped lee-wave response, where the wave energy is contained within the troposphere. In order to understand how mountain waves are affected by height variations in wind and stability we shall return to (3.9–3.11) but this time drop the assumptions of zero shear and constant stability. Note that we have dropped the Boussinesq approximation for the time being, since density is a function of height in (3.10). We seek solutions to the steady versions of the equations with the form i.kxCly/ O  0 D .z/e :

(3.20)

Substituting such expressions into (3.9–3.11) results, after some algebra, in the vertical structure, or Taylor-Goldstein equation for mountain waves in a sheared flow with non-uniform stability, namely d dz



 _  1 d  _ Nw C 2  h 2 w D 0; N dz

(3.21)

where h D .k; l/ is the horizontal wavevector, h D jh j, wO (h , z) is a complex vertical velocity amplitude and the function 2 , often called the Scorer parameter, is given by 2 .z/ D

1 d2 N N 2 h 2  .U:h /: 2 N h dz2 N h/ U: .U:

(3.22a)

For flow over a two-dimensional ridge, the wave field is made up of horizontal wavevectors with a single direction, perpendicular to the ridge. In this case the expression for 2 simplifies further to 2 .z/ D

1 d 2 Ur N2 ;  Ur 2 Ur d z2

(3.22b)

where Ur is the wind speed resolved in the direction perpendicular to the ridge. The presence of density in the first term of (3.21) results in the general growth of mountain wave amplitude with height which can lead to wave breaking in the upper atmosphere. This breakdown of wave motion can lead to the generation of turbulence and a net drag force on the mean flow. The latter is commonly parameterized in global weather prediction and climate models. Note that this wave growth effect would not have been accounted for if we had retained the Boussinesq approximation in the derivation of (3.21); the first term on the left-hand side would then have been simply d 2 w=d O z2 .

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The propagation of mountain waves is affected by the variations in 2 .z/ which arise from changes in the background wind profile or static stability. As a rule, the increase of wind speed with height through the troposphere means that 2 will decrease with altitude, implying that short wavelength wave motion (for which 2  h 2 > 0 at low levels) may decay with height at higher altitudes. In general the first term on the right-hand sides of (3.22a and 3.22b) tend to dominate over the second, although the latter term can be important across jets where there may be rapid changes in vertical wind shear. The importance of variations in 2 will become more apparent in Sect. 3.3 when we consider the phenomenon of wave reflection, which can result in the channeling of wave energy downwind and the long trains of waves, commonly known as trapped lee waves. Traditionally most studies of mountain waves have assumed that the atmospheric boundary layer is sufficiently shallow that it will have only a small impact on their generation. Its role has been largely ignored and frictionless, free-slip lower boundary conditions have been assumed. Recently, however, the importance of boundary-layer processes has come to light in a number of studies. From the point of view of wave generation, modeling studies have demonstrated how the boundary layer will generally have a damping effect, reducing the amplitude of the waves, the strength of downslope winds and the tendency for wave breaking (e.g. Richard et al. 1989; Peng and Thompson 2003; Vosper and Brown 2007). Notably Smith et al. (2002) concluded that the presence of a stagnant boundary layer beneath the Alpine mountain peaks had a significant attenuating effect on mountain waves observed during MAP. Recently the influence of the boundary layer on wave generation has been illuminated using linear theory by Smith et al. (2006), Smith (2007) and Jiang et al. (2006) who showed that absorption of wave energy in the boundary layer can result in a decay of trapped lee-wave motion downstream. We shall return to this point in Sect. 3.3. For situations where the combination of mountain height, upstream wind and stability are such that the non-dimensional mountain height, HO , is of order unity or greater, the linear equations of motion no longer provide an accurate description of the flow. In such situations the flows are nonlinear and the deceleration of the wind on the upwind side of the mountain can be sufficient to cause stagnation and the appearance of a region of blocked flow upstream (e.g. Smith 1980). The flow below mountain crest may then be diverted around the flanks rather than over the summit, sometimes separating from sides and forming a wake region downwind. In general the mountain waves will steepen as HO increases above unity, eventually leading to wave breaking immediately above and downwind of the mountain (e.g. Smith 1980; Miranda and James 1992). This low-level wave breaking enhances the lee-slope acceleration and is thought to be an important process in the development of downslope wind storms. The turbulent dissipation in the wave breaking region also contributes to the development of the downstream wake (e.g. Sch¨ar and Durran 1997). The wake may take the form of a long uniform region of decelerated flow extending from the mountain (e.g. Smith et al. 1997) or consist of an attached vortex pair (Smolarkiewicz and Rotunno 1989) which under some circumstances

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b(x)

(x)

F=1

F>1

h(x)

hydraulic jump

F 1) everywhere, terrain and the height of the interface move in tandem but the excursion of the interface height is less than the excursion of the terrain (Fig. 3.3, bottom, right). The most common situation for downslope windstorms, however, is an asymmetric descent of the interface from upstream across the crest to some distance downstream (Fig. 3.3, bottom, left). For that to happen, the influence coefficient (i.e. the term in square parentheses) has to change sign as the flow crosses from the upstream to the downstream side. A location has to exist where F2 D 1. For a solution to exist, this location has to be at the crest where @h/@x D 0. Conditions of asymmetry and regularity render the crest a so-called “control”. We are no longer free to set an arbitrary combination of layer depth and volume flux rate q. If one is set, e.g. the layer depth, the flow rate follows. And, since the interface has to descend on both sides in the asymmetric case, the flow has to be subcritical (slow and thick) upstream and supercritical (fast and shallow) downstream. The height descends with subcritical flow upstream and supercritical flow downstream. At the control, i.e. the crest, the Bernoulli equation (conservation of energy) is ½ u2 C g c D gH0 , where H0 is the far-upstream depth of the fluid. Combining the Bernoulli equation with (3.27) for F2 D 1, results in c D 2/3 H0 . At the control, the fluid depth has already decreased by one third of its value far upstream. Note that for the more general case when @b/@x ¤ 0 at @h/@x D 0, the control need not be at the crest but where 

1 @h 1 @ C D0 b @x  @x

(3.30)

This regularity condition includes one of the dependent variables, the height of the interface . Further downstream the flow will eventually return from a supercritical to a subcritical state, slow down and thicken again. The turbulent transition zone is a hydraulic jump, in which momentum is conserved but kinetic energy is dissipated. For the asymmetric case of interest for gap flow and downslope windstorms, the depth of the reservoirs on either side of the topographical constriction/crest will differ with the larger depth on the upstream side.

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Using a single layer of constant density is the most frequent application of hydraulic theory to the atmosphere. However, hydraulic theory can be formulated for two layers (Armi 1986; Armi and Riemenschneider 2008) or more including continuous stratification. For continuous stratification, an analytical solution exists, which is described in Sect. 3.5 on gap flow.

3.3 Lee Waves and Rotors A special kind of non-hydrostatic wave motion occurs when the variation of the Scorer parameter, 2 , with height is such that vertically propagating wave motion is partially reflected back down towards the ground. In the typical case where 2 > h 2 in the lower and mid-troposphere (due to relatively low wind speeds or high stability, for example) and 2 < h 2 in the upper troposphere, the wave energy will become trapped within the lower layer and ducted horizontally downstream. Such trapping is generally only partial, due to the fact that 2  h 2 will often be positive in the lower stratosphere and wave motion is able to “tunnel” through layers of 2 < h 2 . In cases where the trapping is strong the waves may be ducted horizontally for hundreds of kilometers downstream. Such waves are commonly referred to as trapped lee waves and they are responsible for the long regular trains of clouds which form in the wave crests downwind of mountain ranges and which are readily seen in satellite imagery. A schematic diagram, illustrating the structure of the trapped lee wave is provided in Fig. 3.4. Examples of satellite images of lee-wave cloud formations are shown later in Figs. 3.6 and 3.9. Typical horizontal wavelengths of trapped lee waves observed in the troposphere lie in the range 5–30 km. Increased stability at low levels (for example due to an inversion layer at the boundary layer top) or reduced low-level wind speeds will favor the existence of shorter horizontal wavelengths, while reduced stability and increased winds will increase the wavelength. As we shall see in Sect. 3.3.2, according to linear theory at least, the horizontal wavelength of trapped lee waves is a function of the upwind profile of wind and stability rather than the mountain shape. Mountain waves are often associated with turbulence, and one particularly severe phenomenon which causes turbulence at low-levels is the mountain-wave rotor. This term is used to refer to a region of recirculating airflow with horizontal vorticity, orientated parallel to the ridge crest. Rotors are typically accompanied by strong near-surface downslope winds which decelerate rapidly at the rotor’s leading upwind edge, where boundary-layer flow separation takes place and air parcels are lifted away from the surface. Downwind of the separation point, the mean near-surface winds are generally slack or weakly reversed below the rotor, but are usually highly turbulent, exhibiting a high degree of temporal and spatial variability. Rotors are recognized as posing a significant hazard to aviation and have been cited as contributing to numerous accidents and damage to aircraft. Additionally

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Height

2 kH

rgy

ene ve

ene

Wa

ve

Wa

rgy

Trapping layer

l2 Separation point

Lee−wave (Type I) rotor

Fig. 3.4 Schematic diagram illustrating the structure of the trapped lee wave (flow is from left to right). The Scorer parameter, 2 , profile is such that a trapping layer exists in which 2  h 2 > 0. Upward propagating wave energy is reflected back down towards the ground at the top of this layer, resulting in net downwind horizontal propagation of wave energy. In the situation shown here the waves are of sufficient amplitude that flow separation occurs beneath the wave crests and a turbulent (type I) rotor forms

rotor circulations may also have an important impact on the transport of pollutants and aerosols in mountainous terrain, serving as a mechanism for transport from the boundary layer into the free troposphere. Based on observations and recent modeling (Hertenstein and Kuettner 2005), rotors have been classified into two types: the rotors which form under the crests of trapped lee waves (type I) and the jump-like rotor (type II), in which the wave motion is replaced by a deep turbulent layer downwind of the mountain. The latter is thought to contain the more severe turbulence, but is probably relatively rare. The distinction between the type I and II rotor is clear, although as discussed later the definition of the type II rotor itself is rather loose, and covers a variety of different flow types including low-level wave breaking and hydraulic jumps. Remarkable examples of rotor clouds and dust transport are provided by Fig. 3.5 which shows instances of rotor formation in the Owens Valley, to the east of the Sierra Nevada mountain range in California, USA. The deep turbulent region and lack of smooth wave clouds seen in Fig. 3.5a and b seems to fit the description of the type II rotor. Figure 3.5c provides a clear example of rotor clouds associated with a type I rotor beneath a train of lee waves which formed downwind of the Rocky Mountains near Boulder, Colorado.

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Fig. 3.5 Rotor clouds and blowing dust over the Owens Valley during mountain wave events in the lee of the Sierra Nevada on (a) 5 March 1950 during the Sierra Wave Program (SWP), (photographed by Robert Symons) and (b) 25 March 2006 during IOP-6 of the Terrain induced Rotor Experiment (T-REX) (photographed by Barbara Brooks from the FAAM BAe-146 aircraft). In both cases the flow is westerly (from right to left) and the Sierra Nevada Mountains are on the right-hand side of the photographs. (c) Rotor clouds on 2 December 2003 in a train of trapped lee waves in the lee of the Rocky Mountains, near Boulder, Colorado (photographed by Rolf Hertenstein) (From Hertenstein and Kuettner 2005, reproduced by permission of Tellus)

While mountain waves and trapped lee waves have been the subject of much attention from the atmospheric science community over the last few decades, rotors have received relatively little attention. However, improvements in observational techniques and increases in computing power have prompted a surge in interest in the rotor problem and there have been several recent field campaigns and numerical modeling studies aimed at understanding the formation and characterizing the properties of rotors.

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a

b 8 7 6

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5 4 3 2 1 0 −4

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Fig. 3.6 Measurements of lee-wave activity over Scotland on 11 March 2000 made by (a) radiosonde measurements at 1012 UTC and (b) high-resolution visible satellite imagery at 1507 UTC. Plot (a) shows fluctuations in the ascent rate of a radiosonde launched from the Isle of Arran after the mean ascent rate has been removed. Image (b) shows lee-wave cloud over much of Scotland. The coastline and Isle of Arran are also shown (Figures are adapted from Vosper 2003. Reproduced by permission of the Royal Meteorological Society)

3.3.1 Observations 3.3.1.1 Lee Waves As discussed previously, lee-wave cloud patterns are frequently observed in highresolution satellite imagery. Their vertical motion is also often readily seen in fluctuations in the ascent rates of radiosondes. Figure 3.6a shows an example of a moderate amplitude lee wave as observed by a radiosonde launched on the Isle of Arran, in south-west Scotland, UK. Fluctuations of amplitude around 2 m s1 are evident in the ascent rate of the balloon between the ground and 6 km. As shown by visible satellite imagery in Fig. 3.6b, the waves observed by the radiosonde form part of an extensive train of lee waves in a north-westerly airstream. The origin of the waves is clearly not the mountains and hills of Arran itself (though they undoubtedly contribute towards the wave activity) since the wave motion extends over much of Scotland and far upwind. Research aircraft are commonly used to make measurements of lee waves during field observation programs. Over the past few decades there have been numerous observational research campaigns in which lee waves have been measured by research aircraft above and downwind of mountain ranges. Recent examples include the measurements made during PYREX, MAP and, most recently, T-REX. Aircraft observations are particularly powerful when conducted with multiple

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Fig. 3.7 Vertical velocity (m s1 ) measured by three research aircraft over the Sierra Nevada Mountains during a coordinated T-REX mission on 25 March 2006 (IOP-6). Measurements made by the NCAR HIAPER are shown in blue, UK FAAM BAe146 measurements are shown in red and University of Wyoming King Air (UWKA) measurements are shown in black. The UWKA data above 7 km and just below 6 km share vertical velocity scales with the neighboring BAe146 legs. Data from the three aircraft were obtained over a period of just under 5 h. The HIAPER and BAe146 tracks, which were almost perfectly aligned, were offset 3–4 km to the north from the shown UWKA tracks (From Grubiˇsi´c et al. 2008. © American Meteorological Society. Reprinted with permission)

aircraft, coordinated in such a way to provide a comprehensive picture of the wave field. Figure 3.7 provides such an example, with lee-wave measurements made during T-REX over the Sierra Nevada Mountains. The measurements were made using three research aircraft flying simultaneously at different altitudes. The utility of aircraft measurements is enhanced further through the use of remote sensing instruments, such as backscatter lidar, which can detect the presence of clouds. This technique was used to good effect during MAP to obtain a detailed picture of the wave and cloud field over the Alps (see Fig. 3.8).

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Fig. 3.8 Vertical displacements (solid curves) inferred from aircraft vertical velocity measurements and airborne lidar backscatter (colour, dBZ) on a north–south cross section over the Alps on 20 September 1999 during MAP. The airflow is from the south (left-hand side) (From Smith et al. 2007 reproduced from Doyle and Smith (2003). Reproduced by permission of the Royal Meteorological Society)

3.3.1.2 Rotors Compared with the waves themselves, observations of rotors are relatively scarce. One of the earliest observations of rotors was that by Mohoroviˇci´c (1889), who observed rotor clouds during bora events along the northern Adriatic coast in Croatia. Grubiˇsi´c and Orli´c (2007) provide an interesting account of Mohoroviˇci´c’s (largely forgotten) work, along with observations of rotor clouds elsewhere which were published around the same time. Some of the best observations have come from the pioneering work of the Sierra Wave Project (SWP) and the Jet Stream Project (JSP) in the 1950s (Holmboe and Klieforth 1957; Grubiˇsi´c and Lewis 2004) of mountain waves and rotors over the Sierra Nevada. Rotors were also observed

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during the Colorado Lee Wave Program in the late 1960s and early 1970s (Lester and Fingerhut 1974). Following this, there have been few organized campaigns targeted at observing rotors. Recently, however, rotors have again become the focus of observational programs. Mobbs et al. (2005) have obtained measurements of the near-surface flow downwind of the Wickham range on the Falkland Islands during episodes of rotor activity. Similar ground based measurements of lee-wave induced flow separation were made by Sheridan et al. (2007) downwind of the Pennines in the UK and Darby and Poulos (2006) observed rotor evolution in the Rocky Mountains using several measurement techniques, including research aircraft, Doppler lidar and wind profiler systems. Very recently, attention has returned to the Sierra Nevada Mountains with a two-part observational campaign focused on the rotor formation in the Owens Valley. The first, pilot-phase of the campaign, the Sierra Rotors Project (SRP), took place during the spring of 2004 and consisted primarily of ground based measurements in the Owens Valley (Grubiˇsi´c and Billings 2007). The second phase, the Terrain induced Rotor Experiment (T-REX) took place during spring 2006 and involved a comprehensive set of observing systems, including research aircraft and a wide range of ground based and remote sensing instrumentation. T-REX has provided detailed systematic measurements of mountain-wave rotors and the datasets will shed new light on the dynamics of rotors. For obvious safety and logistical reasons, in-situ aircraft measurements of rotors are relatively rare, the exceptions being those made during the early SRP and JSP and very recent T-REX campaigns. Most observations, by necessity, have been made by ground-based instrumentation or use remote sensing instruments on airborne platforms. One technique deployed in recent field campaigns (e.g. Mobbs et al. 2005; Sheridan et al. 2007; Grubiˇsi´c and Billings 2007) has involved the deployment of large numbers of automatic weather stations (AWSs) over a small area to provide a well resolved picture of the surface “footprint” of rotor motion aloft. Figure 3.9 shows an example of such measurements obtained in the lee of the Pennine hills in northern England, UK. The measurements show a region of relatively low surface pressure, within which the near-surface winds undergo considerable acceleration. Downwind of this region the flow is decelerated by an adverse (positive) pressure gradient. A region of high surface pressure sits downwind of the low pressure and the flow within this region is very slack, and at times is reversed. As we shall see in Sect. 3.2, this type of pattern is consistent with the theoretical ideas of how lee waves influence the near-surface flow. Clearly AWS measurements offer some interesting insights into the impacts of lee waves and rotors on the surface flow, but remote sensing techniques provide the best chance of observing the vertical and three-dimensional flow structure. Figure 3.10 shows Doppler lidar observations of the velocity field made during the T-REX campaign. The lidar was situated in the Owens Valley and the measurements shown are for IOP-6 which included periods of large amplitude mountain wave

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Fig. 3.9 Lee-wave cloud over the UK and near-surface flow observations beneath the lee waves in the Vale of York, northern England. Frame (a) shows high resolution visible satellite imagery on 17 March 2005 at 1000 UTC. Frame (b) shows a snapshot of the 10 min average 2 m wind vectors measured by AWSs in the Vale of York (in the lee of the Pennines hills) on the same day at 2010 UTC. Colour contours indicate the surface pressure perturbations (units hPa) at each site in the AWS array. Terrain contours are depicted by solid lines with an interval of 50 m. The inset in (b) shows the flow measurements upwind of the Pennines. The boxed area in (a) indicates the location of the northern Pennines and the Vale of York (Figures are adapted from Sheridan et al. 2007. Reproduced by permission of the Royal Meteorological Society)

and rotor activity. For the times shown in Fig. 3.10 strong westerly and southwesterly winds were present on the west side of the valley (west of the lidar site) with relatively weak northerly along-valley winds to the east. The scans show clear evidence for a rapid reversal of the westerly flow approximately 1–2 km to the west of the lidar, indicating the existence of a recirculating rotor within the valley. The lidar scans showed a high degree of temporal variability at this time, indicating that the flow within the rotor was highly turbulent and that the structure of the rotor was very transient. The few existing in-situ measurements made by aircraft in rotors suggest that the presence of extreme turbulence is most likely connected with vortices whose scale is perhaps only a few hundred meters, and therefore much smaller than that of the main rotor. For example, several vertical gusts exceeding 10 m s1 (and as large as 20 m s1 ) were experienced in a 50 s period during a JSP research flight when an aircraft penetrated a rotor (Holmboe and Klieforth 1957; Doyle and Durran 2007). Lidar measurements obtained near Boulder, Colorado (Banta et al. 1990) also suggest the presence of small scale vortices within the main rotor recirculation. Similarly, the recent T-REX lidar observations support the existence of these small-scale intense subrotors.

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Fig. 3.10 Lidar scans of the low-level flow in the Owens Valley, east of the Sierra Nevada mountains, during an episode of large amplitude mountain wave and rotor activity. The data shown are from IOP-6 of the T-REX campaign. Frame (a) shows a PPI scan of Doppler lidar radial velocity measurements obtained in the late afternoon on 25 March 2006. Green and blue colors indicate flow toward the lidar while yellow and red indicate flow away from the lidar. The dashed line indicates the orientation of the RHI scan shown in (b). Gray lines in (a) indicate terrain contours, which are plotted every 200 m. The RHI scan was obtained about 4 min after the PPI scan (From Grubiˇsi´c et al. 2008. © American Meteorological Society. Reprinted with permission)

3.3.2 Theory 3.3.2.1 Lee Waves As discussed earlier, we can expect trapped lee waves to form when the Scorer parameter decreases with height in a suitable manner. The form of 2 .z/ determines both the wavelength and the wave amplitude variation with height. At this stage it is helpful to consider a very simple problem in order to illustrate the theory for lee waves in more complex and realistic situations. Consider the case of a two-layer stratified flow in which the stability takes constant (but different) values, Nl and Nu

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in lower and upper layers, respectively. We shall assume that the wind speed, UN , is constant across both layers and for convenience define the height of the interface between the two layers to be at z D 0, with the ground located at z D d. We shall also make the Boussinesq approximation, thus eliminating the density terms in (3.21). We seek wave-like solutions to (3.21) of the form w O l D Al e iml z C Bl e iml z

(3.31)

wO u D Au e imu z ;

(3.32)

and

where wO l and wO u are the complex vertical velocity amplitudes in the lower and upper layers, respectively, ml 2 D Nl 2 =UN 2  k 2 and mu 2 D Nu 2 =UN 2  k 2 are the corresponding vertical wavenumbers (squared) and Al , Bl and Au are complex constants. Note that (3.31) expresses the fact that we expect both upward and downward propagation of wave energy in the lower layer, the latter being caused by partial reflection at the layer interface, whereas (3.32) assumes that wave energy in the upper layer will radiate freely in the vertical. We now impose matching conditions at the interface. Firstly we require that an air parcel on the interface must move with the vertical velocity of the interface. If the interface has shape z D &.x/ then this is described by D& D w on z D &: Dt

(3.33)

Letting & D &e O ikx and linearizing (3.33) then gives the matching condition _ _ ikUN  D w on z D 0 and this must be satisfied by air parcels both immediately above and below the interface. Since the mean wind, UN , is the same in both layers this becomes wO l D wO u at z D 0. The second matching condition applied at the interface states simply that the pressure on both sides is the same, namely, POl D POu on z D 0. This implies that d wO l d wO u D on z D 0: dz dz

(3.34)

Substituting these conditions into (3.31) and (3.32) and manipulating the resulting expressions for Al , Bl and Au then gives wO l D

2Al Œml cos.ml z/ C i mu sin.ml z/ ml C mu

(3.35)

2Al ml imu z e : ml C mu

(3.36)

and wO u D

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10

Wavelength (km)

Fig. 3.11 The theoretical resonant lee-wave horizontal wavelength plotted as a function of wind speed U for the two-layer stability case with Nu D 0.01 and Nl D 0.02 s1 . Data are plotted for lower layer depths, d, of 3, 4 and 5 km

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d=3 km d=4 km d=5 km

8

6

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The constant Al is obtained from a free-slip lower boundary condition which simply states that air parcels at ground level follow the mountain profile, z D h(x). Thus, on the mountain surface we have w D Dh/ Dt. Linearizing and writing h.x/ D _ _ O ikx then gives w N he l D i U kh on z D d. Substituting this into (3.35) then gives _ m cos.m z/ C im sin.m z/ l l u l : w O l D UN ikh ml cos.ml d /  imu sin.ml d /

(3.37)

as the solution in the lower layer. Equation 3.37 contains singularities whenever ml and mu are such as that the denominator is zero. This occurs when tan.ml d / D i ml =mu

(3.38)

and corresponds to the existence of resonant wavemodes. These resonant waves are the naturally occurring trapped lee waves and as such require only an infinitesimal amount of forcing by the orography. Their horizontal wavelength is determined by the implicit relationship described by (3.38). Note that the occurrence of the imaginary number, i, on the right-hand side of (3.38) means that solutions are only possible when mu itself is imaginary, and hence the wave amplitude will decay with height in the upper layer, consistent with the fact that the wave response is trapped in the lower layer. Examples of solutions to (3.38) are presented in Fig. 3.11 which shows how the resonant horizontal wavelength varies with wind speed for a case where the lower and upper-layer stabilities are Nl D 0.02 and Nu D 0.01 s1 , respectively.

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According to (3.38) the theoretical horizontal wavelength of the resonant trapped waves is purely a function of the background profile rather than the shape of the orography. This is also true more generally, for any profile of wind and stability. In general theoretical predictions for the resonant wavelength are only available for a small class of idealized profiles such as the two-layer case considered above. Vosper (2004) performed a similar analysis to that presented here and showed how linear theory can be used to describe the behaviour of trapped lee waves which form in a temperature inversion layer. More generally, however, for real profiles of wind and stability, such resonant solutions cannot be determined analytically and numerical approaches must be used. By discretizing (3.21) the resonant wavemodes can be sought and the linear trapped lee wave solutions can then be computed (e.g. Sawyer 1960; Vergeiner 1971). For three-dimensional flows the resonant wavemodes will in general lie along lines in (k,l) space (Sawyer 1962) and the wave field will be made up of contributions from wavemodes along such lines. Note that although it is generally accepted that linear theory can provide a reliable prediction of the horizontal wavelength of trapped lee waves (at least in cases where the nondimensional mountain height, HO  1) the same is not always true of the wave amplitude. Although linear theory has been used widely for lee-wave prediction (and as discussed in Sect. 3.3 certainly can prove useful from a forecasting perspective) several studies (e.g. Smith 1976; Durran and Klemp 1982; Durran 1992; Vosper 2004) have shown how broad mountains, whose horizontal scale exceeds the leewave wavelength, will provide little forcing at the resonant wavenumbers. The amplitude of the waves will then be determined by nonlinear processes. For HO > 1 nonlinearity can also have an important influence on the horizontal wavelength, when for instance, the mountain range consists of two (or more) ridges, separated by a valley. Grubiˇsi´c and Stiperski (2009) have shown how, in this case, when the two ridges are of similar height, the ridge separation has a strong controlling influence on the horizontal wavelength. In common with most previous studies, the above discussion of trapped lee wave behaviour makes no attempt to account for the influence of the atmospheric boundary layer. As well as exhibiting a rich variety of phenomena itself in complex terrain (see Chaps. 2 and 5), recent work has shown that the boundary layer can have a significant impact on both the generation and then the attenuation of lee waves. Notably Smith et al. (2002), motivated by observations of lee waves during MAP, developed a simple theory for the absorption of wave energy by a stagnant layer which filled the valleys between individual mountain peaks. Whereas a solid lower boundary reflects downward propagating rays back upwards, the theory allows for partial absorption of wave energy by the stagnant layer, which results in the downwind decay of the lee wave motion. The process is illustrated by the schematic diagram in Fig. 3.12. More recently, studies (Smith et al. 2006; Jiang et al. 2006) have examined how the boundary layer acts to attenuate the trapped lee wave motion and suggest a faster downwind decay in shallow nocturnal boundary layer conditions, with slower decay when the boundary layer is deep and convective. The boundary layer also plays an important role in mountain wave induced flow separation, and thus has a crucial part to play in the dynamics of rotors.

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Fig. 3.12 A schematic of the propagation of wave energy for trapped lee waves when a stagnant layer of air fills the valleys between mountain peaks. The triangles represent the lower mountains, with the lee waves generated by the higher peak which penetrates into the ambient flow. The dashed line labelled zref marks the top of the stagnant layer. The upper dashed line represents the level of wave reflection due to a decreasing Scorer parameter. The slanting wave rays are parallel to the local group velocity and indicate the direction of energy propagation. The downgoing wave amplitude, B, is reduced by partial absorption at zref (Figure taken from Smith et al. 2007. Reproduced by permission of the Royal Meteorological Society)

3.3.2.2 Rotors The theoretical and numerical challenges posed by mountain wave rotors have meant that, until recently, relatively little progress has been made toward understanding their dynamics or the conditions in which they form. Nevertheless, the recent surge in interest in this area has resulted in some significant progress. By necessity, most of the recent advances in understanding the dynamics of rotors have come from numerical simulation rather than analytical theory, although some limited progress towards understanding the process of flow separation, with which rotors are intimately linked, has emerged from analytical treatments. The focus, to date, has tended to be on the type I, lee-wave rotor. The formation of rotors is clearly connected to the occurrence of boundary-layer separation and the relationship between separation and the mountain-wave motion aloft. Although theories have existed for several decades as to how the pressure gradient due to lee waves might induce flow separation (e.g. Lyra 1943) these ideas have only recently been tested using numerical simulations. Doyle and Durran (2002) have shown, through numerical simulations of two-dimensional trapped lee waves, how the adverse (positive) pressure gradient which occurs beneath the leading upwind edge of a wave crest will act to decelerate the flow. Once this gradient is sufficiently large the flow will separate away from the surface and a (type I) rotor will form. Doyle and Durran (2002) and later Vosper (2004) have shown how surface friction is vitally important to obtaining realistic simulations of rotors. Its effect is to both reduce the wind speed towards zero at the surface, thereby enhancing the influence of the pressure gradient, thus promoting separation, and to generate a sheet of high horizontal vorticity along the lee slope of the mountain,

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Fig. 3.13 Streamlines and horizontal vorticity (units s1 ) for a simulation of lee-wave (type 1) rotors in flow over a two-dimensional ridge. Horizontal vorticities greater than 0.03 s1 are shaded in color. Horizontal wind speeds less than or equal to zero are shown using blue isotachs (every 2 m s1 ) (From Doyle and Durran 2002. © American Meteorological Society. Reprinted with permission)

which is lifted aloft by the waves when the flow separates. This is illustrated by Fig. 3.13 which shows a two-dimensional simulation of a type I rotor (Doyle and Durran 2002). The occurrence of flow separation and its relationship with the trapped lee-wave amplitude has been studied in further detail by Vosper et al. (2006) and Jiang et al. (2007). In the former study a theory was developed which suggests that, for twodimensional waves, a critical lee-wave pressure amplitude exists, beyond which flow separation will occur under the wave crests. This critical amplitude can be expressed non-dimensionally as p=.u2 /, where p is the amplitude of the pressure fluctuations exerted by the waves on the ground (assumed constant through the boundary layer) and u is the surface friction velocity of the background flow. Vosper et al. have shown how this critical non-dimensional amplitude increases as a function of surface roughness and this can be explained by the fact that, for a smoother surface, the surface stress will be reduced and the near-surface winds will be stronger. A larger pressure gradient is therefore required to reverse the flow. Note that this result is contrary to what occurs for a laminar flow where separation occurs more readily for a smooth surface. Jiang et al. (2007) have also demonstrated the link between boundary-layer separation and trapped lee wave amplitude and found that separation depended largely on the ratio of the vertical velocity maximum to the surface wind speed. Separation was far less sensitive to other factors such as the

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Fig. 3.14 The along ridge component of horizontal vorticity (colour shading, interval 0.02 s1 ) and flow vectors in a cross section through a type I rotor. The results shown are for a threedimensional simulation of flow over an infinitely long two-dimensional ridge. The vortex sheet is lifted away from the surface and then broken up by shear instability, resulting in intense subrotors which move along the interface between the main rotor and the wave field (From Fig. 7(c) of Doyle and Durran 2007. © American Meteorological Society. Reprinted with permission)

mountain height and slope. Jiang et al. also found that the onset of separation was sensitive to the surface sensible heat flux. A positive heat flux tends to inhibit the occurrence of separation by increasing vertical turbulent mixing and thus enhancing the surface wind speed. A negative (downward) heat flux appears to have the opposite effect. By performing very fine-resolution numerical simulations, Doyle and Durran (2007) have begun to illuminate the internal dynamics of trapped lee-wave (type I) rotors. Their simulations have shown how, once lifted away from the surface by flow separation, shear instability along the upstream leading edge of the rotor can break up the sheet of high horizontal vorticity into small intense vortices, or subrotors. Doyle and Durran’s simulations illustrate the importance of three-dimensional effects in the dynamics of these subrotors. Even for waves generated by a strictly two-dimensional ridge, the tilting and in particular the stretching of vorticity which is present in a three-dimensional turbulent flow, contributes to the vorticity of the subrotors, meaning they can contain horizontal vorticity which far exceeds that of the main rotor. The subrotors are relatively long lived, being swept downstream along the interface between the main rotor and the lee wave and it seems possible that their existence is connected to pulsations in the wind that have been observed during downslope wind events (see Sect. 3.4.1). An example of this behaviour is shown in Fig. 3.14 (Doyle and Durran 2007). In the less realistic situation where the turbulence is restricted to be purely two-dimensional the subrotors are much less intense and are short-lived, being eventually entrained into the main rotor recirculation. Recently, new studies using eddy-resolving simulations have been used to explore the role of turbulence in mountain-wave breaking (Epifanio and

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Qian 2008) and interactions between the turbulent boundary layer and lee-wave rotors (Smith and Skyllingstad 2009). This approach is clearly a powerful one and the ability to explicitly resolve turbulent eddy motion will perhaps allow a full understanding of the internal dynamics of rotors. Compared with the type I rotors, the more severe jump-like rotors have received much less attention. Vosper (2004), in a study of temperature inversion effects on lee waves, found that a hydraulic-jump-like response occurred in place of trapped lee waves if the potential temperature difference, , across the inversion was sufficiently large. The results from a set of two-dimensional simulations were used to construct a flow regime diagram which contained, in order of increasing , trapped lee waves on the inversion layer, lee waves which were sufficiently strong to induce flow separation and form (type I) rotors and, finally, regions of overturning and severe turbulence in the lee of the mountain. These latter conditions were somewhat loosely referred to as a “hydraulic jump” state. Hertenstein and Kuettner (2005) also performed two-dimensional simulations for flow with a strong temperature inversion and found that the solutions were sensitive to vertical wind shear across the inversion in the upstream flow. For sufficiently strong forward shear trapped lee waves formed with attendant type I rotors. Reduction in the shear, however, resulted in a downstream response more akin to a hydraulic jump (see Fig. 3.15). The relatively smooth lee-wave field is replaced by a deep turbulent layer which extends far downwind. Hertenstein and Kuettner explained the sensitivity to the wind shear in terms of the horizontal vorticity budget. The type of rotor that forms depends on the dominant sign of the horizontal vorticity as the flow separates from the surface. This balance is modified by the presence of vertical wind shear across the upstream inversion. Recently Jiang et al. (2007) have also examined the rotor types which can occur in the presence of an elevated temperature inversion. They found that a variety of different flow regimes could occur: (1) a steady undular jump regime, in which a hydraulic jump forms in the lee of the ridge; (2) a regime in which trapped lee-waves ride along the inversion layer behind the jump; (3) a propagating jump regime in which the jump propagates away downwind and (4) a mixing jump regime in which low-level wave breaking merges with a hydraulic jump below. These flow regimes all involve the generation of turbulence and are capable of causing boundary-layer separation, resulting in reversal in the lee of the mountain. In the sense that these flows are all clearly different to that of the type I, trapped lee-wave rotor, it is tempting to label the rotors associated with them all as type II, despite their differences.

3.3.3 Models and Forecasting The implications for aviation safety and risks to ground transport and property mean that there is a clear need to forecast lee-wave motion and rotor activity. Glider pilots can also benefit from wave forecasts since they can use the associated updrafts to stay aloft for long periods of time and to achieve high altitudes and great distances.

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Fig. 3.15 Potential temperature (contour interval 0.5 K) downwind of a two-dimensional ridge in a type II rotor simulation. The C signs mark the positions of three propagating eddies along the top of the rotor (From Fig. 7(b) of Hertenstein and Kuettner 2005. Reproduced by permission of Tellus)

The typical horizontal wavelengths of trapped lee waves mean that they are generally poorly resolved by numerical weather prediction (NWP) models. Global forecast models, whose horizontal resolutions are typically 25–50 km cannot hope to explicitly represent lee wave motion at all. The same is true for most current operational limited area models, whose resolutions are typically around 10 km. It is only with grid spacings of 1–2 km that we can really expect to properly resolve the waves. As for the prospects of explicitly resolving rotors, whose scales are considerably smaller than those of the lee waves themselves, this is likely to remain beyond the reach of operational models for some time. The above limitations of NWP models mean that other techniques must be used for forecasting lee-waves. Many of the methods used are based on obtaining approximate solutions to (3.21) with profiles of wind and stability taken from either NWP model or radiosonde data. Although it is possible to obtain numerical solutions to (3.21) which utilize the full available resolution of the forecast or radiosonde profiles, in the past the lack of computing resources available to bench forecasters has necessitated far simpler approaches. For example, the widely used Casswell (1966) calculation involves the assumption that 2 decays exponentially with height and an estimate for this vertical decay scale is obtained using profile data at only three heights. Because it utilizes such a small amount of information about the atmospheric state, and incorporates no detail of the actual orography, the Casswell method can at best provide only a very crude forecast of lee-wave activity.

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Nowadays numerical solutions to (3.21) can be obtained (e.g. Lane et al. 2000; Vosper and Mobbs 1996) with, by modern standards, only very modest computing resources. Predictions can be made of the wavelength and vertical structure of the resonant lee waves with very fine vertical resolution (e.g. tens of metres). An example of such an approach, adopted for use in opertational forecasting is given by Shutts (1997). A set of solutions to (3.21) is obtained over a range of horizontal wavevector directions (centered on the low-level wind direction) and then one particular solution is chosen. The actual vertical velocity associated with the chosen wavemode can only be calculated if the spectral composition of the underlying orography is known. Since the Fourier spectrum of real orography is generally very irregular and for practical purposes can only be computed for a discrete set of wavelengths, Shutts instead suggests assuming a power-law dependence (on the horizontal wavenumber) for the vertical velocity at some height near the ground (the wave “launching height”). A vertical profile of horizontally averaged vertical velocity can then be estimated by applying suitable scaling to the solutions to (3.21). Shutts (1997) has demonstrated the success of the technique by comparing forecasts with observations. Although the Shutts method can provide the forecaster with a prediction of wave amplitude and horizontal wavelength, it does not provide a detailed picture of the lee-wave motion. In terms of assessing the likelihood of rotors, since (3.21) is based on inviscid theory which takes no account of boundary-layer processes, it cannot be used to predict how the lee waves will affect the near-surface winds. Detailed predictions such as these can only be made using a more complex threedimensional numerical model. While the computational requirements of using a complex NWP model are, in practice, too restrictive, it is possible to obtain detailed three-dimensional solutions using simplified models. One such example is provided by Vosper (2003) who constructed a numerical finite-difference model to solve the linearized equations of motion, the Boussinesq version of (3.9)–(3.11). The model provides detailed predictions of the wave field over the real complex orography during steady upwind conditions and the simplifications to the equations of motion permit these solutions to be obtained with only a relatively modest computer, such as a desktop PC. The neglect of nonlinear terms and moist and turbulent physical processes undoubtedly compromises the accuracy of the predictions, however Vosper (2003) demonstrated that for the Isle of Arran, which contains mountain peaks as high as almost 900 m, the model provides accurate predictions of lee waves. Comparisons with radiosonde observations show that, with sufficiently accurate upwind profile data, both the amplitude and phase of the waves can be accurately predicted. Recent developments to the above linearized numerical model include the incorporation of a linear turbulent boundary layer scheme (King et al. 2004) which allows the representation of the influence of waves on the near-surface flow. The model, 3DVOM (3-D Velocities Over Mountains), is currently used operationally at the UK Met Office to produce 1 km-horizontal resolution predictions of the lee-wave field every 6-h for separate hilly regions of the UK and Ireland, as well

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as the Falkland Islands. An example of such a forecast for the Pennines in northern England, validated against observations made by a research aircraft, is shown in Fig. 3.16. The model provides a good quantitative description of the wave field, both in terms of wave amplitude and phase. Also shown are the predictions made by a full NWP model (the Met Office Unified Model) run in a nested configuration at 1 km resolution. The results are similar to those of the far simpler and cheaper 3DVOM calculation. For larger mountains, where the linearized equations are no longer valid, we would not expect a linear model to provide a quantitatively accurate forecast, and a fully nonlinear model is required. Such an approach has been adopted as a research activity in support of various recent field campaigns. For instance, the NRL COAMPS model was used routinely to provide guidance for mission planning during T-REX. Wave forecasts for the Sierra Nevada and Owens Valley area were provided throughout the campaign on a series of nested grids, the finest of which had a 2 km resolution (Grubiˇsi´c et al. 2008). These forecasts proved to be a highly useful and valuable part of the experiment planning process. An example of such a forecast is shown in Fig. 3.17. The requirements of such models are discussed in detail in Chap. 9, along with the issue of predictability of nonlinear mountain waves. Compared with the techniques available for forecasting lee waves, the knowledge available for forecasting rotors amounts to very little. Field campaigns have provided some insight into the conditions under which rotors occur, but this tends to be location-specific and the scientific knowledge is not sufficiently well developed to be applied more generally. For example, the occurrence of a strong upwind temperature inversion at, or around, the mountain height, along with unidirectional flow across the mountain ridge, is known to be conducive to lee-wave motion and it is generally thought that backward wind shear above the mountain top will promote rotor formation. While these ideas are not inconsistent with current scientific understanding, the theoretical and numerical studies which have addressed the problem are so far too limited to provide any firm guidance as to the kind of rotor motion which might occur, let alone the severity of the turbulence which might be encountered. The ability of the very high-resolution numerical models to simulate the dynamics of rotors (e.g. Doyle and Durran 2007) provides some hope that in the future operational NWP models will have the ability to explicitly represent rotor effects. Note, however, that much further research in this area is required, both in terms of increasing our understanding, and also of the techniques needed to make the best use of the high-resolution models.

3.4 Downslope Windstorms Downslope windstorms have a long and rich history of scientific investigation and have formed an important part of the meteorological literature for over 70 years. They are a type of large-amplitude mountain wave that can occur downwind of mountain barriers resulting in strong, often gusty low-level flow that accelerates

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Fig. 3.16 3DVOM forecasts of lee-wave vertical velocity (blue line) over the Pennines, northern England, UK, valid at 12 UTC on 17 November 2004. The forecasts are compared with observations made by the UK FAAM research aircraft along east–west flight legs at 1,350 and 1,080 m above sea level (black line). Also shown are the predictions made by the Met Office Unified Model run at 1 km resolution (red line) and the underlying terrain (shaded)

Fig. 3.17 Vertical velocity (colour, interval 0.5 m s1 ) and potential temperature (contour interval 6 K) from a real-time 30-h COAMPS forecast for the innermost 2 km resolution grid valid at 2100 UTC 25 March 2006 during T-REX IOP 6. The cross section illustrates the type of product that was available for mission planning purposes (From Grubiˇsi´c et al. 2008, Fig. 5. © American Meteorological Society. Reprinted with permission)

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down the lee slopes of the mountain. Under the right conditions, wind speeds in downslope windstorms can be two to three times the wind speed at the mountain top level. Necessary ingredients for downslope windstorms include a sufficiently large mountain barrier, as well as strong across-barrier winds and a stable atmosphere, both near the mountaintop level. They are observed in many places downwind of mountains and are often given local names. Several mechanisms have been proposed to explain the strong winds associated with these events. These include an analog to hydraulic flow (Long 1954; Smith 1985; Durran 1986; Klemp and Durran 1987), the amplification of vertically propagating gravity waves by constructive interference as they reflect off a preexisting critical layer, usually near the tropopause (Klemp and Lilly 1975), and a similar reflection of upwardly propagating waves off a self-induced critical layer created by wave breaking (Peltier and Clark 1979). The theoretical and practical understanding of downslope windstorms has also been informed by rich datasets from several critically important field programs, most notably the Pyrenees Experiment (PYREX Bougeault et al. 1993), the Alpine Experiment (ALPEX Smith 1987), the Mesoscale Alpine Programme (MAP Bougeault et al. 2001; Smith et al. 2007) and the Terrain induced Rotor Experiment (T-REX Grubiˇsi´c et al. 2008).

3.4.1 Observations Downslope windstorms are observed in many places downwind of mountains and are often given names. Locally named downslope windstorms in specific areas include: Rocky Mountains (Boulder windstorm, chinook), Western Washington (East winds), Alps (deep foehn winds – refer to Chap. 4 in this volume), Eastern Adriatic (bora winds), Southern California (Santa Ana winds), Argentina (Zonda), Utah (Wasatch winds), southeast Alaska (Taku wind) etc. These winds are sometimes categorized depending upon whether they are a warm wind or a cold wind. Warm downslope windstorms are often referred to as foehn or chinook-type winds, while cold downslope windstorms are often called bora-type winds. Chinook or foehn events normally occur when an existing cold pool is displaced by an air mass descending a lee slope that is warmed adiabatically as it descends (see Chap. 4 for a detailed discussion). It is thought that latent heat release on the windward side of the mountain barrier may contribute to the relative warmth of foehn winds. Bora-type downslope windstorms typically occur (in Western Washington State, and on the Adriatic coast) when cold continental air displaces a warmer maritime air mass, so is manifested as a relatively cold wind. The circumstances forming a bora may instead form a gap wind if there is a channel that cuts through the mountain barrier. The classification of downslope windstorms as bora- (cold) type or as foehn(warm) type is not always helpful, as it is sometimes difficult to make a definitive categorization and some phenomena like the Boulder downslope windstorm can occur as both warm and cold events. Also, a foehn is a general warm downslope wind that may or may not be classified as a windstorm.

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One of the best known downslope windstorms is the storm that occurs periodically, usually during winter, in Boulder Colorado, that is characterized by very strong winds with peak gusts as high as 60 m s1 . This downslope windstorm has been studied extensively due to its intensity, but also due to the high concentration of meteorologists who live nearby and directly experience it. Brinkmann (1974) analysed 20 Boulder windstorms finding that they are characterized by strong gusts, are non-stationary, are associated with a surface pressure minima under the disturbance, followed by a pressure jump downstream, that results from a hydraulic jump. Brinkmann found that common upstream conditions include an inversion or stable layer just above the mountain top, in combination with strong winds at that level. The most studied Boulder downslope windstorm event is that of 11 January 1972 (e.g. Klemp and Lilly 1975, 1978; Clark and Peltier 1977; Peltier and Clark 1979, 1983; Clark and Farley 1984; Durran 1986; Doyle et al. 2000), since it was the subject of special aircraft observations that provided rare in-situ observations of the mountain wave structure (Lilly and Zipser 1972; Lilly 1978) (Figs. 3.18 and 3.19). This event was characterized by a very large amplitude mountain wave extending through the troposphere into the lower stratosphere. A stable layer below the mountain wave is behaving like a hydraulic supercritical flow layer as the isentropes lower in the lee of the mountain (Fig. 3.18) with associated strong winds in excess of 60 m s1 (Fig. 3.19) and terminating in a hydraulic jump that is indicated by sharply rising isentropes and decelerating wind speeds. The surface winds during this event were very strong and gusty (Fig. 3.20). Observations of severe gustiness are quite common in downslope windstorms and may be caused by subrotors embedded in the flow. For the 11 January 1972 Boulder windstorm, gusts appear to have a period of slightly more than a minute, however longer period wind pulsations have also been observed for less severe events (Durran 1990). The gust structure of a moderate Boulder windstorm was documented by Neiman et al. (1988) using Doppler lidar. They found the gusts had a period of approximately 4 min, extended several hundred meters above the surface and appeared as a coherent structure that propagates downwind at approximately the mean wind speed. The foehn-type wind (see Chap. 4) can take the form of a downslope windstorm. An important similarity between the 11 January 1972 Boulder windstorm in Figs. 3.18–3.20 and the deep Alpine foehn (look ahead at Fig. 3.30 (bottom)) is the presence of a weakly stable, nearly mixed region above the descending flow. The Alpine deep foehn case additionally had a nearly mixed region below the flowing layer on the upstream side. An example of an Alpine foehn downslope windstorm event from MAP is shown in Fig. 3.21 (Jiang and Doyle 2004). It has many similarities with the 11 January 1972 Boulder downslope windstorm shown in Figs. 3.18–3.20: specifically the lower stable layer that descends and accelerates that is surmounted by a turbulent unstable region with sharply rising isentropes and across-barrier flow decreasing or reversing. The bora is a downslope windstorm that occurs along the northeastern Adriatic coast from Trieste, Italy to southern Croatia (Dalmatia) and has been frequently documented in the European literature since the mid-nineteenth century (Yoshino 1976; Jurˇcec 1981; Grisogono and Beluˇsi´c 2009). Other bora-like winds that have

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Fig. 3.18 Cross section of potential temperature field observed in the 11 January 1972 downslope wind storm illustrating the strong mountain wave extending through the troposphere and the lowerlevel zone of supercritical flow and hydraulic jump between Boulder and Denver (From Lilly 1978. © American Meteorological Society. Reprinted with permission)

Fig. 3.19 Cross section of u-component of the wind (m s1 ) from aircraft flight data and sondes observed in the 11 January 1972 downslope wind storm (From Klemp and Lilly 1975. © American Meteorological Society. Reprinted with permission)

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Fig. 3.20 Anemometer trace from Southern Hills Junior High School in Boulder Colorado, on 11 January 1972 from 2,000 to 2,330 MST. Speed is in miles per hour (1 mph D 0.45 m s1 ) (From Klemp and Lilly 1975. © American Meteorological Society. Reprinted with permission)

been studied occur near Novorossiysk on the Black Sea’s northeastern coast, at Novaya Zemlya in the Russian arctic, and near Lake Baykal (Yoshino 1976). The bora occurs under similar synoptic conditions as the gap flow through the fjords and windstorms along the western coast of North America, described in Sect. 3.5. A strong anticyclone over eastern or/and central Europe often in conjunction with cyclonic conditions in the Mediterranean results in a strong pressure gradient directed across the Dinaric Alps that separate the interior of the continent from the Adriatic coast (Tutiˇs and Ivanˇcan-Picek 1991; Ivanˇcan-Picek and Tutiˇs 1995, 1996). Arctic air associated with the anticyclone deepens and eventually spills through passes onto the coast (Jurˇcec 1981; Yoshino 1976; Smith 1987), usually resulting in a decrease in air temperature. The strongest bora winds occur during winter and at night, with generally ten “bora days” per month each winter season (Yoshino 1972; Baji´c 1989). A stable layer usually exists at mountain crest level (Yoshino 1976) indicating the importance of hydraulic dynamics in describing the flow. Before ALPEX it was thought that the bora was a type of katabatic flow – accelerating downslope due to its density. It is now understood that the bora is a type of downslope windstorm, with hydraulic/mountain wave characteristics (Smith 1987). Klemp and Durran (1987) conducted two dimensional numerical simulations of the bora and found that the flow resembled hydraulic flow over an obstacle, and that the pressure gradients created by thermal differences on either side of the Dinaric Alps were sufficient to generate the bora. The bora winds are strongest downwind of gaps in the Dinaric Alps and can maintain their speed as localized jets across the Adriatic sea for some distance (Zecchetto and Cappa 2001), presumably decreasing speed when a transition from supercritical shooting flow to subcritical flow occurs in a hydraulic jump. Gohm and Mayr (2005) simulated an Adriatic deep bora case with a high resolution mesoscale model and found the strongest bora

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Fig. 3.21 Cross section through the central Alps on 21 October 1999 showing (a) isentropes (every K), backscatter from SABL lidar (in grayscale) depicting clouds and regions of strong turbulence (indicated by symbol ƒ), (b) has the along-flight wind component (every 2 m s1 ) added in black contours with the region of reversed flow hatched. The flow pattern resembles classical downslope wind event with plunging isentropes indicating the shallow hydraulic flow separated from the air aloft by a turbulent region with overturning isentropes and a wind reversal (From Jiang and Doyle 2004. © American Meteorological Society. Reprinted with permission)

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flow downwind of gaps. They found the simulated bora was diurnally modulated: during the night the stable surface layer upstream increased the bora strength, while the developing convective boundary layer during the day reduced the gravity wave amplitude and strength of the downslope bora flow. Gohm et al. (2008) simulated a bora downwind of a gap that formed a jet with hydraulic jump features in the middle of the gap and lee wave/rotor features on the edges of the jet. In western Washington, downslope windstorms have been documented to occur when cold arctic air and associated high surface pressure moves southward over the interior of the continent. The coast-parallel Cascade mountain chain separates the interior arctic air from the maritime air on the coast resulting in a large pressure gradient across the mountain barrier as the continental high moves south. In this situation, strong downslope winds can form, especially downwind of passes or gaps in the mountain barrier such as the Stampede gap (Mass and Albright 1985; Reed 1981) where winds during these events typically reach 15–25 m s1 (Mass and Albright 1985). The air flows down the slope and over the inland waters of Puget Sound where a readjustment in boundary layer depth takes place and wind speeds diminish with the flow splitting around the Olympic Mountains resulting in strong easterly flow through Juan de Fuca Strait. A very similar downslope windstorm has been documented near Juneau in Alaska, the so-called Taku windstorm. This windstorm also involves downslope acceleration in the lee of a gap (Colman and Dierking 1992; Dierking 1998; Bond et al. 2006) under very similar synoptic conditions as the Cascade windstorms. In the case of the Taku wind, there is an interplay between downslope windstorm dynamics as discussed below, and gap wind dynamics discussed in Sect. 3.5, since this area is also comprised of many gaps dissecting the coastal mountain barrier, and both gap winds through channels and the stronger downslope winds tend to occur at the same time with the lee trough induced by the downslope windstorm enhancing gap flows through local channels. The Santa Ana is a type of downslope windstorm occurring along the coast of southern California when a large area of high pressure forms over the Great Basin between the Rocky Mountains and Sierra Nevada Mountains. When a thermal low pressure area over coastal California is advected offshore, the pressure gradient and wind speeds can be enhanced. Santa Anas tend to occur most frequently between October and February with December being the month of peak occurrence (Raphael 2003). About 20 events occur per year with the average duration being 1.5 days (Raphael 2003). Santa Anas are often enhanced during the night by a land breeze with typical observed wind speeds of 15–20 m s1 , gusting to over 25 m s1 . The air flowing out of the high turns anticyclonically, is channelled through the canyons and warms adiabatically due to compression as it flows downslope towards the coast. The hot, dry, strong wind is associated with increased wildfire risk in California and can modify temperature and currents in the nearby coastal upper ocean. The winds can persist offshore for a hundred or so kilometers and are associated with high wave conditions on the northeast side of the Southern California Bight Channel Islands.

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3.4.2 Theory Downslope windstorms are large-amplitude mountain waves that undergo a hydraulic transition giving strong, supercritical flow on the lee slope. There is a rich history of theoretical work on this phenomenon that has suggested several mechanisms to account for downslope windstorms. These theories have been well described and developed in a number of excellent reviews of this subject (e.g. Smith 1979, 1989; Durran 1990; Baines 1995), and so will not be repeated in detail here. The primary theories include an analog to hydraulic flow (e.g. Long 1954; Smith 1985; Durran 1986; Klemp and Durran 1987), the amplification of vertically propagating gravity waves by constructive interference as they reflect off a pre-existing critical layer, usually the tropopause (Klemp and Lilly 1975), and a similar reflection and amplification of upwardly propagating waves off a selfinduced critical layer created by wave breaking (Peltier and Clark 1979). While there has been debate over the relative importance and frequency of downslope windstorms caused by these different mechanisms, it seems that the fundamental dynamics are qualitatively explained as an analog to the hydraulic flow of water over an obstacle resulting in rapid, supercritical flow along the obstacle’s lee slope, which terminates in a turbulent hydraulic jump (see subsection 3.2.3). In the lower left panel of Fig. 3.3, the supercritical flow of hydraulic theory over the lee slope, corresponds to the zone of strong downslope winds near the surface. The first mechanism, based on two-layer hydraulic theory with a deep upper layer, was originally proposed by Long (1954), and used by Houghton and Kasahara (1968), Houghton and Isaacson (1968) and Arakawa (1968, 1969). In the classical hydraulic approach the flow of air over a mountain is modeled by fluid flowing over a barrier using the shallow water equations (Eqs. 3.6–3.8, development described in Sect. 3.2.3). Strong winds occur on the lee slope when the fluid (air) goes from subcritical flow upstream, to supercritical flow over the mountain, becoming subcritical again downstream as kinetic energy dissipates in a turbulent hydraulic jump. In a classical hydraulic model, if the incoming subcritical flow is too rapid to become critical at the mountain crest which acts as a control point, then a wave can propagate upstream to “correct” the incoming flow. When applied to the atmosphere, the main weaknesses of this theory are that it does not allow continuous stratification, or vertical propagation of energy above either the free surface or rigid lid upper boundary condition. However this theory is attractive because of its simplicity and its apparent inclusion of important features observed in downslope windstorms. Also, it is not uncommon for the atmosphere to have a sharp change in stability, via elevated inversions and stable layers, which encourages the atmosphere to behave as a simple hydraulic system. When a stable layer is present near mountaintop level, hydraulic effects can occur. A mechanism for downslope windstorms which would allow for the possibility of vertical energy transport (Klemp and Lilly 1975) is the amplification of linear vertically propagating gravity waves, by waves reflected off the tropopause (or some other layer where the Scorer parameter, (3.22a), changes rapidly). The presence of

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Fig. 3.22 Isentropes from a two-dimensional numerical simulation of a two-layer atmosphere over a 600 m high mountain. Flow is from left to right. (a) Top of the lower stable layer is at 1,571 m (one quarter of a vertical wavelength). (b) Top of the lower stable layer is at 3,142 m (one half of a vertical wavelength) which corresponds to nonlinear resonance resulting in shooting supercritical flow on the lee slope terminating in a hydraulic jump (Figure from Durran 1986. © American Meteorological Society. Reprinted with permission)

vertically propagating mountain waves can be diagnosed from the isentropes. If there is an upstream tilt of the isentrope phase, this indicates vertically propagating wave energy that can be reflected downward by a critical layer (see Fig. 3.2 for examples of this). The wave amplitude is determined by the superposition of these upward and downward propagating modes and will depend upon whether or not the atmosphere is “tuned” to constructive interference. Klemp and Lilly found that the strongest downslope wind response occurred when the tropopause was located half a vertical wavelength above the ground. With this linearized model of the flow equations the vertically propagating and amplifying gravity waves cause lower pressure and accelerated winds on the lee slopes with the wind strength proportional to the mountain height. As the theory is linear, its general applicability to large amplitude waves has not been determined (Durran 1986). It seems that while the mechanism involving linear theory proposed by Klemp and Lilly in which the predicted downslope wind response scales with H2 can account for the strongest Boulder downslope windstorms in the case where the profiles of U and N are constant (i.e. a single layer structure), it is unsuccessful with nonlinear effects becoming important when there are vertical variations in these profiles and the flow more closely resembles classical hydraulic flow (Durran 1986, 1990) as shown in Fig. 3.22. Durran (1986) examined the importance of nonlinear amplification for an atmosphere with a twolayer stability structure, finding that in this case, nonlinear effects become important, even with non-dimensional mountain heights as low as 0.3 – values which would have insignificant nonlinear effects in an atmosphere with a single layer stability structure.

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The third mechanism proposed (Clark and Peltier 1977, 1984; Peltier and Clark 1979, 1983; Clark and Farley 1984), suggests large amplitude waves and downslope winds occur after a developing vertically propagating mountain wave breaks. Wave breaking occurs when the isentropes become vertical and the air becomes unstable and overturns. The area of wave breaking creates a self-induced critical layer with strong mixing and wind reversal. In this layer, where the wind component in the direction of the horizontal wavevector goes to zero, the vertical wavelength and the rate of vertical energy propagation also tends to zero as discussed in Sect. 3.2.2. In this situation, if the distance between the self-induced critical layer and the mountain is suitably tuned, it may trap and reflect upward propagating waves resulting in resonance and strong surface winds. Peltier and Clark’s (1983) theory of wave amplification for the numerically simulated downslope windstorm uses linear theory and the assumption that the wave breaking region acts like a critical layer where the Richardson number, Ri D N2 /(dU/dz), is less than ¼. According to Peltier and Clark’s results, the critical layer will produce amplification only when it is located about ¼ C n/2 (n D 0,1,2 : : : ) vertical wavelengths over the terrain. The selfinduced critical layer produced by wave breaking is similar to a turbulent mean-state critical layer that would be produced when the stability becomes too low to provide a sufficient restoring force for gravity waves, which occurs when the Richardson number is less than ¼. It is believed that nonlinear waves that encounter such a critical layer are reflected by it without losing much amplitude (Durran 1990). The importance of wave breaking for the 11 January 1972 downslope windstorm as well as for other cases with constant upstream wind and stability (constant U and N) has been verified by many numerical simulations (e.g. Doyle et al. 2000). Whether or not wave breaking occurs will depend on the non-dimensional mountain height exceeding a critical value. For flow across a two dimensional ridge, Huppert and Miles (1969) found the critical non-dimensional mountain height for gravity wave breaking was 0.85. Smith and Grøn˚as (1993) found a critical non-dimensional mountain height of 1.1 ˙ 0.1 for an isolated Gaussian hill in three dimensional flow. In each simulation when the critical non-dimensional mountain height was exceeded, the wind stagnated aloft over the lee slope, isentropes overturned in wave breaking and there was a strong downslope wind response. A critical level will explicitly exist when there is a reverse shear in the approaching wind – U decreases with height and perhaps even reverses. If this occurs at the correct altitude for a resonant response, then strong downslope winds can result. The theory proposed by Smith (1985) and Smith and Sun (1987) extends classical hydraulic theory, by using a concept of local hydraulics in which the atmosphere can have constant stratification rather than layers separated by a density interface, and the hydraulic nature of the flow only manifests itself when a transition to supercritical flow occurs on the lee slope below a layer of stagnant fluid. In local hydraulics, the flow approaching the mountain may “select” a critical streamline which splits becoming the upper boundary of the accelerated flow (Fig. 3.23), decoupling it from a turbulent layer of well-mixed air aloft. It is the presence of this stagnant region that provides the decoupling allowing the flow to produce a shallow layer-like flow that can spill over terrain and resemble classical hydraulic

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Fig. 3.23 (a) Schematic diagram of a downslope windstorm based on aircraft observations and numerical simulations. In this case a certain critical dividing streamline encompasses a turbulent region of uniform density ¡c indicated by the inverted “v” shapes. In this local hydraulic approach, continuously stratified air approaches the mountain barrier and acquires hydraulic characteristics of supercritical flow after the critical streamline divides. (b) Flow over a mountain from the Smith (1985) local hydraulics model. U0 D 20 m s1 , N0 D 0.01 s1 (From Smith 1985. © American Meteorological Society. Reprinted with permission)

supercritical flow and even produce a hydraulic jump. In this theory, when the nondimensional mountain height, Hˆ D NH/U is small, or if a wind reversal exists at the wrong altitude the fluid may not form a neutral decoupled region with hydraulic flow, but instead form continuous vertically propagating gravity waves (Smith and Sun 1987). According to this theory, amplification of a mountain wave is possible across a range of critical layer heights from 1/4 C n to 3/4 C n, where (n D 0,1,2 : : : ) vertical wavelengths above the terrain, in contrast to the predictions of Peltier and Clark. Durran and Klemp (1987) and Bacmeister and Pierrehumbert (1988) used numerical experiments to compare the theories of Smith (1985) and Peltier and Clark (1979, 1983) and found that when there is a mean state critical layer, the mountain waves interact with this layer to form a local region of turbulent flow, and that the essential elements of hydraulic theory explain the acceleration on the lee slopes of mountains. This occurred in Durran and Klemp’s experiments whenever Hˆ exceeded 0.2 and there was a mean state critical layer between ¼ and ½ vertical wavelengths above the terrain (Durran 1990). In their experiments a deep layer with Ri < ¼ developed above the topography and a strong downslope wind response was found with this configuration when Hˆ exceeded 0.4. Reed (1981) and Mass and Albright (1985) were able to use a simple Bernoulli equation and gap wind dynamics based on a balance between the pressure gradient force and inertia to account for the observed wind speeds in the cases they studied in US Pacific Northwest. Colle and Mass (1998) set out to examine the relative importance of mountain wave/hydraulic dynamics versus simple gap flow dynamics by analysing a number of past events in western Washington State, as well as using idealized mesoscale model simulations. They found that a combination of the

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across-barrier pressure gradient and across-barrier flow at crest level explained 82% of the variance in windstorm severity there. The presence of a critical layer (region of flow reversal needed for reflection of vertically propagating waves) appeared to be of less importance in storm evolution. However in cases with strong cross-barrier flow at mountain crest level, the lack of a critical layer below 400 hPa resulted in weaker surface winds unless a region of strong stability existed near crest level, in which case the flow behaved hydraulically. For cases with weak cross barrier flow at crest level, the presence of a critical layer was less important, as they postulated a self-induced critical layer could be created and strong surface winds could ensue. One remarkable feature of many severe downslope windstorm events is the severe gustiness of the wind. The observed gustiness of the 11 January 1972 Boulder downslope windstorm (Fig. 3.20) was investigated by Clark and Farley (1984) using two and three-dimensional numerical models. They found gust structures were only apparent in the three-dimensional simulations and hypothesized that the gustiness was produced by an intrinsically three-dimensional competition between wave enhancement by gravity wave dynamics and wave destruction by convective instability. The apparent requirement of three-dimensions for gustiness was contradicted by Scinocca and Peltier (1989) however who were able to produce realistic gusts (which they call pulsations) in their two-dimensional simulations. Peltier and Scinocca (1990) demonstrate that the simulated pulsations are due to KelvinHelmholtz instability at the wind shear interface between the low level shooting flow and the wave-induced stagnant layer. The Kelvin-Helmholtz instability is a secondary instability that occurs after the downslope windstorm has formed when Ri < ¼ in the flow and appears to initiate just upstream of the mountain crest. Afanasyev and Peltier (1998) demonstrate the importance of the Kelvin-Helmholtz mechanism and further demonstrate how in a fully three-dimensional simulation, the Kelvin-Helmholtz billows are eroded by a convective instability and dissolve into a turbulent background flow as they move downstream. The Kelvin-Helmholtz instability as a mechanism to explain the pulsations has been suggested and modeled for the bora as well (Beluˇsi´c et al. 2007). Most of the earlier theoretical work using linear theory, as well as numerical modeling studies in the past has assumed that boundary-layer effects are not important for downslope windstorms. However numerical simulations of the 1972 Boulder windstorm by Richard et al. (1989) as well as work by Georgelin et al. (1994), ´ Olafsson and Bougeault (1997), Peng and Thompson (2003), Smith et al. (2002, 2007) and Smith et al. (2006) has illustrated the importance of the boundary layer on absorbing mountain wave energy and both attenuating downslope windstorm strength and limiting its extent downwind. Georgelin et al. (1994) studied the effect of subgrid scale orographic roughness on orographic flows from PYREX. They found that correctly accounting for subgrid scale orography improved model predictions. It reduced mountain wave amplitude, but increased blocking as well as ´ leeside low-level turbulence. Olafsson and Bougeault (1997) conducted idealized simulations to investigate the effects of rotation (f ) and surface friction on mountain wave drag. They found that the effect of friction was to suppress wave breaking,

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especially for NH/U less than 3, and that the combined effects of rotation and drag were to constrain the drag and flow patterns to resemble those predicted by linear theory. Smith et al. (2002) discussed the effects of a low-level stagnant layer on the mountain wave, finding that it reduced the wave amplitude and was able to absorb downward reflected gravity waves, preventing lee wave generation. Jiang and Doyle (2008) modeled a downslope wind event in Owen’s Valley during the TerrainInduced Rotor Experiment, and found in this narrow valley that the downslope winds varied diurnally through an interaction with the thermal structure in the valley. Overnight, when the valley filled with cool air, strong downslope winds were restricted to the upper lee slope. After sunrise, surface heating in the valley weakened the downslope winds, eventually decoupling the valley air from the strong westerlies above the mountain top. As the valley air continued to warm during the afternoon, the mixed layer extended beyond the top of the valley which caused a transition as a shallow layer of cooler air from the westerlies above the mountain top descended and flowed across the whole valley. These simulations serve to illustrate the important connections with diurnal mountain circulations (Chap. 2). Until recently, “dry” dynamics were used to understand downslope windstorm formation. Doyle and Smith (2003) used a numerical model to isolate the influence of latent heat in mountain wave generation by running the COAMPS model with and without latent heating and examining the differences (Fig. 3.24). They found that if the latent heating in a shallow layer upstream was strong, the lee downslope wind response increased significantly. This occurred because the latent heating resulted in a decrease in stability aloft creating a critical layer there that decoupled the low level flow allowing it to behave as a hydraulic layer. Such a mechanism – the interaction between low level latent heating and the establishment of critical layer aloft resulting in a downslope windstorm – suggests a mechanism explaining how warm foehn winds are able to descend on the lee side of the Alps.

3.4.3 Models and Forecasting The previous section has outlined the theoretical basis for understanding downslope windstorm formation. This understanding has developed over time through a fusion of analytical approaches involving careful analysis and judicious simplifications to the governing equations, as well as through idealized and realistic experiments with numerical models of increasing complexity and accuracy. This section will discuss how this theoretical understanding can be applied to model and forecast downslope windstorms using synoptic interpretation and NWP as well as statistical methods. More information on the application of mesoscale models and NWP models is provided in Chaps. 9, 10, and 11. While NWP models are essential to understand and forecast most meteorological phenomena, there are limitations in the application of NWP to downslope windstorms. These limitations, such as model resolution and the vertical coordinate system, as well as predictability will be discussed later in this section as well as

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Fig. 3.24 Cross section of potential temperature (contours every 3 K) and vertical velocity (contours every 2 m s1 with upward velocities greater than 2 m s1 shaded) for a COAMPS simulation of flow from south (left) to north (right) of a mountain wave event across the central Alps on 20 September 1999, (a) includes latent heating and (b) has latent heating turned off. Note the more strongly plunging flow and downslope wind response in (a). The shallow upslope latent heating has tuned the atmosphere for nonlinear resonance (From Doyle and Smith 2003. Reproduced by permission of the Royal Meteorological Society)

in Chaps. 9 and 10. However, even if NWP models do not accurately represent mountain waves directly, they can still provide important information on upstream vertical profiles of wind and stability. This information may be interpreted using knowledge of downslope windstorm mechanisms, to infer whether or not a strong downslope wind response is likely. Let us summarize some of the key findings from observations and theoretical work that relate conditions in the upstream environment to downslope windstorm occurrence. The type of mountain wave, and whether or not any waves will occur depends on topography, wind and stability profiles. The following conditions are necessary, although not necessarily sufficient for a strong downslope wind response: • A significant mountain barrier. Long mountain barriers that are asymmetrical with a shallow windward slope and a steep lee slope are particularly conducive to downslope windstorm development (Smith 1977; Lilly and Klemp 1979; Hoinka 1985). This limits the occurrence of downslope windstorms to specific geographic regions. • The presence of a moderate to strong wind component in the across-barrier direction (7–15 m s1 or more, depending on the mountain) at an elevation near the mountaintop level. • Stable stratification. This is necessary to provide a restoring force for a gravity wave response. • A non-dimensional mountain height, Hˆ D NH/U, somewhat close to 1 (i.e. Hˆ not 1 or 1). If Hˆ is too small, the flow will easily go over the mountain without a mountain wave response. If Hˆ is too large, the flow will be completely blocked by the mountain barrier and not able to flow over the mountain.

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A strong downslope wind response closely resembles supercritical hydraulic flow. The circumstances that encourage this type of flow can arise in several ways. One way is if the background atmospheric state has a layered stratification. The presence of an inversion or isothermal layer at or just above the mountain top level enhances hydraulic effects and the possibility of a strong supercritical flow response on the lee slope. The importance of such a stable layer is verified in the Boulder downslope windstorm climatologies of Brinkmann (1974) and Colson (1954). Reduced stability or cross barrier winds further aloft can also decouple the low-level flow and allow it to behave like a shallow hydraulic layer (Smith 1985; Baines 1995). If the cross-barrier winds increase aloft in the presence of an inversion near mountain top level (i.e. there is forward shear), there is a possibility of either lee waves or enhanced downslope winds. A rule of thumb that can be used to differentiate the two mountain wave forms, is to compare the cross-barrier wind component at mountain top level with the winds 2,000 m above the mountain top. If the winds aloft increase to over 1.6 times the winds at mountain top level, then lee waves rather than a downslope windstorm are more likely (COMET 2008). Since gravity waves require a restoring force (buoyancy) and therefore a stable atmosphere – they will not propagate through a neutral or near neutral turbulent layer, which can therefore act as a mean-state critical layer (Ri < ¼) resulting in the reflection of vertically propagating mountain waves. Therefore the presence of such a mean-state critical layer above a stable layer can be diagnostic of a downslope windstorm event. Vertically propagating mountain waves can also be reflected by a self-induced critical layer (a layer where the cross-barrier wind component goes to zero) that can form when vertically propagating mountain waves break, forming a turbulent “dead” zone of air that effectively decouples the lower level flow, allowing it to behave hydraulically. Such a wave breaking situation can occur in an atmosphere with constant U and N where the mountain is large enough (Clark and Peltier 1977). In addition to wave breaking resulting in a self-induced critical layer and the existence of a mean-state critical layer, a critical layer can also be formed by wind shear, when the wind component in the cross-barrier direction goes to zero, either by the wind speed decreasing or by the direction shifting to a barrier-parallel direction. It is thought that jet streak dynamics could also play a role in downslope windstorm development. Specifically the right-exit region of a jet streak is a zone of upper level convergence and downward vertical velocity. If this zone occurs near a ridgeline of sufficient height in a jet that is oriented perpendicular to the ridge, then it can contribute to a subsidence inversion or stable layer near the mountain top, which can lead to a downslope windstorm. Many of these factors for practical forecasting of downslope windstorms are well illustrated in a COMET MetEd interactive module on forecasting downslope windstorms (register for MetEd and then go to http://www.meted.ucar.edu/mesoprim/mtnwave/) (COMET 2008). The previous section has discussed numerical modeling of downslope windstorms from a research and process perspective – high resolution models have been used extensively in idealized and realistic simulations to shed light on the

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mechanisms responsible for downslope windstorm events. There are also numerous examples where numerical models have successfully simulated many aspects of downslope windstorms, in hindcast mode (e.g. Doyle and Shapiro 2000; Colle and Mass 1998). NWP models are of course a key tool for operational forecasting. Are operational NWP models of use in downslope windstorm predictions? One major issue is whether the models have sufficient vertical and horizontal resolution and accuracy to capture mountain wave activity. It is generally accepted that to properly resolve a wave-like feature in a numerical model, there must be six to eight grid points per wave, so that the model resolution must be finer than 1/6 of a wavelength. To properly resolve mountain waves, model horizontal resolution should be on the order of 1 km, and certainly less than 10 km. Current operational NWP models (as of 2011) are close to achieving 10 km or finer horizontal resolution, so in the future will be able to provide realistic simulations of mountain wave activity and downslope windstorms, although there are still questions concerning the predictability of these phenomena which will be discussed below. Other issues related to downslope wind forecasting by numerical models that are summarized by Smith et al. (2007) include inaccuracies associated with the vertical coordinate system over mountains. The commonly used terrain following coordinate system has difficulty in accurately representing the horizontal pressure gradient force. This led Sch¨ar et al. (2002) to propose a new coordinate system that has smoother and more horizontal levels at mid and upper levels and thereby reduce the truncation errors and high frequency noise in the model (see Chap. 9). Klemp et al. 2003 found that errors and spurious gravity waves could be generated in numerical models in the conversion between terrain-following and Cartesian coordinates if the transformation of the advection terms and pressure gradient terms was not done consistently. Another issue related to the sigma coordinate system concerns the application of horizontal diffusion on sloping sigma surfaces. Horizontal diffusion is commonly applied to control model errors. If it is applied along the terrain following coordinates which slope with the terrain, this can conflate vertical gradients with horizontal gradients leading to errors especially when there are strong vertical gradients such as inversions (Smith et al. 2007). Z¨angl (2002b) developed a true horizontal diffusion scheme for the MM5 model that was shown to improve its ability to simulate topographic flows (see further discussion in Chap. 9). Although increasing computer power and improving NWP models with everincreasing resolution holds promise for the prediction of downslope windstorms, the predictability of these phenomena remains a major unresolved issue. Lorenz (1969) hypothesized that the growth rate of perturbations increases as the scale of a phenomenon decreases, implying that the predictability of mesoscale phenomena whose scales are on the order of 10 km, may only be a few hours in advance. However, the fact that downslope windstorms are forced by topography implies that they ought to be inherently more predictable than mesoscale phenomena that do not have such a strong organizing influence (Anthes et al. 1985). The enhanced predictability of downslope windstorms was first demonstrated by Klemp and Lilly (1975), who used a linear two-dimensional model to predict the occurrence of downslope windstorms

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in Boulder, Colorado. They initialized their model using soundings from NWP model forecasts, and made predictions valid approximately 5 h in advance of the windstorm, successfully predicting events where observed gusts were in excess of 25 m s1 . More recent studies have not been as encouraging. Nance and Colman (2000) used a high-resolution two-dimensional nonlinear mesoscale model that was initialized with upstream soundings from 12 to 18 h NWP model forecasts in order to support operational forecasting of downslope wind events in seven regions in the United States between 1993 and 1997. They found that the model improved upon existing forecasting methods which were based on a decision tree (Brown 1986), but also had a high “false alarm” rate, implying difficulty in distinguishing windstorm events from null events. During MAP, many studies were able to successfully simulate mountain waves of various types (e.g. Smith et al. 2002; Smith and Broad 2003; Doyle and Smith 2003; Volkert et al. 2003). As pointed out by Smith et al. (2007) these successful cases were characterized by stationary non-breaking waves, and results from other cases that were characterized by non-stationary waves were not as successful (e.g. Jiang and Doyle 2004; Smith 2004; Jiang et al. 2005; Doyle and Jiang 2006). Doyle et al. (2000) compared two-dimensional simulations by 11 different numerical models initialized with an identical sounding representing the 11 January 1972 Boulder downslope windstorm event. While all models predicted downslope winds and wave breaking in the lower stratosphere, the models had different temporal evolutions of the wave breaking. Doyle and Reynolds (2008) tested the sensitivity of the same downslope windstorm event to small variations in initial conditions by performing ensemble simulations in a high-resolution two-dimensional numerical model. Each ensemble member was constructed by perturbing the upstream sounding by small amounts corresponding to typical radiosonde measurement errors. They found that for this case there was a large spread in the ensembles with a 25 m s1 range in the modeled downslope wind speed. Half the ensemble members simulated a trapped lee wave response and the other half simulated large-amplitude wave breaking in the lower stratosphere with a hydraulic jump and a strong downslope wind response. The bimodal distribution of the ensemble members led them to conclude that when there is such a transition across a regime boundary (between non-breaking and wave breaking responses), the use of ensemble statistics such as the ensemble mean may not be appropriate. Reinecke and Durran (2009a) used a three-dimensional NWP model to conduct ensemble simulations of two downslope windstorms observed during T-REX. One case was a wave breaking downslope windstorm, while the second case was a layered case characterized by strong low-level stability in which wave breaking was not important. For each case they conducted 70 ensembles by perturbing the initial conditions across a range representing uncertainty in the initial conditions. They found that the forecasts were very sensitive to the initial conditions, especially for the wave breaking case where the difference in the downslope wind speeds predicted by the strong ensemble members minus the weak ensemble members grew to 28 m s1 after only 6 h of forecast. The layered case was found to be somewhat more predictable with the difference in downslope wind speeds growing to 22 m s1 after 12 forecast hours. The results of these recent

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downslope wind predictability studies indicating sensitivity to initial conditions, do not suggest much confidence should be placed in the accurate and precise strength, timing, or location of downslope winds predicted beyond 12 h in advance. Despite this, operational NWP models are capable of predicting the overall synoptic setting for these storms up to several days in advance. This currently allows a forecast of downslope windstorm occurrence without necessarily being able to precisely predict the location, timing or strength. As computer power continues to increase, high resolution NWP models could be implemented in operational forecast settings as a nowcasting tool to make short-range precise and accurate forecasts. Further discussion on predictability issues can be found in Chap. 9 (Sect. 9.9). ˇ Zagar and Rakovec (1999) discuss a dynamic downscaling approach to obtain a high resolution wind field that they call “dynamic adaptation”. The approach interpolates a coarse resolution NWP forecast onto a fine-resolution mesoscale model grid, and then runs a simplified version of the mesoscale model for between 30 and 45 min to obtain a high-resolution wind field. The approach was successfully applied to a strong wind event: a foehn in the Ljubljana basin in Slovenia, in which diurnal boundary layer variations which cannot be properly represented by the approach, were not important. The advantage of the approach is its low computational cost, and it seems to hold promise as a forecast tool in an operational setting for strong dynamically forced flows. As a less computationally and technically intensive forecast tool, it is possible to develop statistical models to predict downslope windstorms at specific locations. Mercer et al. (2008) used a 10 year Boulder windstorm dataset together with a set of 18 predictors to train and test statistical models to predict the downslope wind speed. They tested linear regression and neural network models but found that a support vector regression model performed best and was able to predict downslope wind speed with an RMSE of 4–6 m s1 . Given the likelihood of limited predictability (i.e. short prediction lead times), at least for strong, highly nonlinear downslope windstorms, the ability to observe their occurrence is very important. Mountain waves, including downslope windstorms can be observed in a variety of ways. Of course, direct observation of the downslope wind response at surface observing stations is the best indication of occurrence; however stations do not exist in every location. Satellite imagery can also be useful. If there is sufficient moisture for clouds to be present, a zone of descending air is often indicated in satellite imagery by a gap in the cloudiness that may indicate mountain wave formation.

3.5 Gap Winds Gaps criss-cross mountain ranges all over the world. Gaps also exist between islands, or islands and the mainland. They can be level or elevated with an elevation maximum in the gap whence they are commonly called passes or cols. Gaps provide a means for an air mass to advance to the other side of the barrier formed by

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Fig. 3.25 Cold continental air crossing the Coast Mountains through gaps and emanating as accelerating flows onto the Pacific Ocean. Flow is from right to left. Wind speed (see color bar) over water is derived from Synthetic Aperture Radar (SAR) data. Image date: 0224 UTC 29 January 2008 (Data courtesy of Alaska SAR Demonstration [AKDEMO] of NOAA’s STARCenter for Satellite Applications and Research)

mountain ranges. A distinctive feature of most gap flows is their asymmetry between the region upstream of the gap entrance and downstream of the gap. Upstream, the layer which flows through the gap is thick and relatively slow moving (subcritical in hydraulic terminology). As it approaches the gap, it thins and accelerates and becomes supercritical downstream of the gap.

3.5.1 Observations Regions in the world where gaps join two persistently different air masses see frequent gap flows. In this subsection, we will first look at observations from the earth’s atmosphere and the laboratory of flows through level gaps. Next we will look at elevated gaps, which have a vertical constriction added to the lateral one to form a pass or a sill. The northern part of the North American Pacific coast where long, coast-parallel mountain ranges separate cold wintertime continental air masses from warmer maritime ones is a preferred region for gap flows. Figure 3.25 shows a striking visualization of the surface wind field with jets emanating from various gaps in the Coast Mountains of British Columbia and Alaska. High wind speeds are only

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visible downstream of gaps, which provide a connection to the continental air mass east of the Coast Mountains. Highest wind speeds occur near the exit or even further downwind as seen in the southern part of the figure close to the coast. There, several gap jets merge to form one wide high wind speed streak. Even further away from the gap exits, the flow slows down but has to pass through another gap formed by the islands off the coast, where it reaches its overall maximum wind speeds near the exit of that last gap. Further visualizations of gap flow wind fields over water from synthetic aperture radar (SAR) measurements can be found in Pan and Smith (1999), Winstead et al. (2006), Liu et al. (2008), and Alpers et al. (2009), for example. Alpers et al. (2009) provide highly resolved wind fields over the Adriatic Sea and the Black Sea during six bora – gap flow events. Shelikof Strait, formed by Kodiak Island and the Alaska Peninsula (Fig. 3.26), is an example of a level gap. Colder air frequently lies northeastward on the other side of the mountain range barely visible at the horizon of the figure. Research aircraft flights (Lackmann and Overland 1989) provided the horizontal wind and temperature field at 80 m AGL shown in Fig. 3.26. Wind speeds between the entrance and exit regions nearly triple. Like in the previous example, the maximum is close to the exit of the gap and not at its narrowest part as simple continuity reasoning (“Venturi flow”) might suggest. Another important characteristic feature is that the upstream air is colder than the dowstream air, here by about 4 K. The Strait of Juan de Fuca (Fig. 3.27a) forms another level gap along the Pacific North American coast. In wintertime it is fed by cold continental air from east of the Cascade Range, which has passed through elevated gaps in the Cascade Range, i.e. the Strait of Juan de Fuca is the second gap through which the air streams. In the gap flow event shown in Fig. 3.27, the presence of hydrometeors provided backscatter for a Doppler radar on board of the NOAA-P3 aircraft, from which the three-dimensional wind field could be computed. The vertical structure of the flow along the strait is shown in Fig. 3.27. Wind speeds between entrance and exit of the gap double. It is remarkable that the abrupt thinning of the gap flow layer is coincident with a further speed-up. The gap flow layer is isolated from the flow aloft through a layer with southerly flow in almost perpendicular direction to the gap flow. Observations of gap flows in the laboratory (Armi and Williams 1993) reproduced in Fig. 3.28 show similar structures to the ones observed in the atmosphere. Similar to its cold and stably stratified counterpart in the atmosphere, the fluid in the laboratory experiment is continuously stratified, which is visualized by dyeing selected isopycnals to give an equivalent to isentropic cross sections in the atmosphere. An arrow indicates the narrowest part. When fluid is withdrawn at the bottom of the channel, the flow is similar to the one observed in the Strait of Juan de Fuca, shown in Fig. 3.27b. The flow accelerates through the channel as the depth of the gap flow decreases. Near the exit, the flow accelerates even more and its depth drops. A homogeneous stagnant layer forms as the streamlines split at the gap exit. This layer isolates the gap flow from the fluid aloft. A similar, nearly stagnant layer was observed in the Strait of Juan de Fuca example as well

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Fig. 3.26 Horizontal wind vectors (see reference vector for scale), isotachs (m s1 , dotted), and temperature (ı C, colored) of the gap flow through Shelikof Strait measured with the NOAA-P3 aircraft 80 m above the ocean on 28 March 1985. Inset shows a pseudo-3D view of Shelikof Strait between the Alaskan Peninsula and Kodiak Island viewed from SSE (Adapted from Figs. 6 and 8 of Lackmann and Overland 1989. © American Meteorological Society. Reprinted with permission. Inset figure © Google and NOAA)

as the location of the speed maximum closest to the ground (Fig. 3.27b). The equivalent to withdrawing fluid near the bottom of the laboratory channel is having the strongest pressure gradient in the flowing parts of the atmospheric gap flow close to the surface. Since the temperature differences of the air masses on either side of the gap are hydrostatically responsible for the bulk of the pressure difference, this translates into having the strongest temperature differences between the upstream and downstream side of the gap close to the surface.

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Fig. 3.27 (a) A pseudo-3D view from the W of the Strait of Juan de Fuca between Vancouver Island and the Olympic Mountains. (b) Wind vectors in the along-gap section and isotachs of along-section speed (contours in 3 m s1 steps and shading) computed from Doppler radar measurements onboard of the NOAA P3 aircraft. (c) Wind vectors and isotachs of the along-section speed (dashed contours in 3 m s1 steps andshading) and isentropes (solid, 3 K intervals) from numerical simulations. The gap flow in (b) and (c) is in the offshore direction from right to left, and is capped by southerly flow around 2 km MSL and onshore flow further aloft. (Part (a) © Google and NOAA. Parts (b) and (c) are from Colle and Mass 2000. © American Meteorological Society. Reprinted with permission)

When fluid is withdrawn from mid-levels of the channel (Fig. 3.28b), the flow response changes. The fluid accelerates through the gap and the flowing layer thins and accelerates with a parabolic wind profile and the jet maximum at the center of the gap flow layer at the exit of the gap. In addition to the isolating, stagnant and

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Fig. 3.28 Steady continuously stratified flow through a contraction. The linear continuous stratification is made visible by dyeing selected isopycnals in the upstream reservoir. The fluid accelerates through the narrowest section of the contraction (marked by the arrow) as the flow moves from left to right. (a) Level gap with fluid withdrawn through a slit at the bottom of the channel downstream of the gap. (b) Level gap with fluid withdrawn at the center height of the channel downstream of the gap. Vertical dye streaks are distorted by the flow and show the self-similar velocity profile of the Wood (1968) solution (cf. subsection 3.5.2). (c) Elevated gap, i.e. a sill was added at the narrowest section of the gap. Note the upstream flow in the contraction is the self-similar solution but that this solution changes in the neighborhood of the sill and accelerates down the lee slope (Adapted from Armi and Williams 1993. Reproduced by permission of Cambridge University Press)

homogeneous layer aloft, another such layer forms at the bottom. Just like for the case of bottom withdrawal, the flow is self-similar in the sense that at any position, the density and velocity profiles can be scaled with the height of the moving stratified layer. This self-similar structure upstream is a necessary component of any steady stratified flow from a reservoir and for it to exist, at least an isolating

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Fig. 3.29 A pseudo-3D from the N of the Wipp Valley in the central Alps at the border between Austria and Italy. The main gap with an altitude of about 2.1 km MSL with a small deep incision of the Brenner Pass at only 1.4 km MSL is embedded in the main Alpine crest (approximately 3 km MSL). The Wipp Valley merges with the Inn Valley via a nearly 200 m terrain drop at approximately right angles (© Google and NOAA)

stagnant intermediate layer needs to be formed above (cf. Armi and Williams 1993). The equivalent to a withdrawal at mid-levels of the gap flow is to have the strongest temperature differences between the upstream and downstream side and thus the largest hydrostatically produced pressure gradient at mid-levels. Elevated gaps, which are more commonly called “passes”, are constricted both laterally and vertically. One extensively studied one, Brenner Pass in the Alps, is shown in Fig. 3.29, a pseudo-3D view looking at the gap from the north. Topography is much more complicated than in the level gaps shown so far. The main gap, approximately 20 km wide, at 2–2.2 km MSL (“channel crest”) is cut into the main crest line of 3 km MSL. The channel formed by the valley north of the pass is no longer nearly straight as for the two previous strait examples but contains tributaries and a bend and its exit drops 200 m into another valley, which runs nearly perpendicular. Gap flows are possible in both directions, northwards and southwards, but only northward gap flows have been studied extensively. Three prototypical gap flows were found (Armi and Mayr 2007). The first one, shown in Fig. 3.30, has a (nearly) mixed flowing layer on the upstream side, which accelerates across the gap, before descending and thinning. Upstream, the flow is isolated by a blocked layer underneath and a cap with strong stability seen in the

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abrupt increase of potential temperature aloft. Downstream, the well-mixed gap flow layer has sped up. The speed maximum lies a few hundred meters above ground. The flow is no longer isolated underneath by a stagnant layer. Aloft, however, a wedge of (nearly) neutral and stagnant air has formed. Its lower boundary follows the descending gap flow whereas its upper boundary remains approximately horizontal. The flow above the gap flow is therefore unaffected by the underlying gap and channel topography. Since the gap flow layer is well mixed on both sides of the pass, this case is the “single-layer prototype”. The second prototype (second row in Fig. 3.30) differs from the first one by having a stably stratified gap flow layer upstream, typically with a linear increase of potential temperature with height. Upstream, the gap flow is isolated from the surface and from the flow aloft, respectively, by neutrally stratified, (nearly) stagnant layers.1 Downstream of the narrowest part, however, turbulent mixing takes place, both in an internal hydraulic jump and over the rough surface, quickly turning the stable stratification into a neutral one. The downstream part of the second prototype is thus similar to the first one. Also, a wedge of (nearly) stagnant and neutrally stratified air forms on top of the accelerating and descending gap flow layer downstream of the pass. Since a thin isolating layer is already present upstream of the pass, the thickness of the wedge is larger than for the single-layer prototype. Another common feature of both prototypes is that the flow aloft is unaffected by the underlying channel and pass topography and follows the horizontal isentropes. The upstream part of the second prototype corresponds to the analytical solution of Wood (1968), the downstream part is a single layer, making this case the “Wood – single-layer prototype”. Wood’s solution describes a self-similar flow that accelerates from an upstream reservoir to the control. It is the only known analytical solution in such a setting for a continuously stratified fluid and is described and derived in more detail in subsection 3.5.2. The second prototype is also observed in the laboratory (Fig. 3.28c) when a sill is added to the lateral constriction to form a pass or col. Upstream of the pass, the stably stratified gap flow is isolated from the channel bottom and the fluid aloft by neutrally stratified layers. The flow response downstream of the pass changes: the gap flow layer accelerates even more, thins and rebounds in an internal hydraulic jump at the downstream end of the sill. Further downstream, the gap flow layer is well mixed. The depth of the upstream isolating layer on top of the gap flow layer increases as the gap flow layer plunges downstream of the pass to form a thick (nearly) stagnant layer. This layer both isolates the gap flow from the fluid aloft and the fluid aloft from the underlying topography. The isopycnals remain horizontal, like the isentropes in the atmospheric case. The third, “hybrid” prototype (Fig. 3.30, bottom row) is so deep that the flow no longer only crosses through the gap but also over the crest. A downslope windstorm (or “deep foehn” as it is called in the Alps) is superimposed on the gap flow. The

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Fig. 3.30 Prototypes of gap flow across Brenner Pass in the central Alps. Single layer hydraulics: shallow gap flow (first row). Shallow, stably stratified gap flow with Wood’s (1968) self similar solution upstream turning into a single layer flow downstream (second row). Deep, stably stratified flow through the gap and across the crest (often called “deep foehn” or “downslope windstorm”) (third row). Soundings of potential temperature from upstream and downstream are shown to the left and right, respectively. Arrows in the vertical cross section show their respective locations. Topography in the sections is shown shaded, bounded by a dashed line at the valley floor. The solid bold line above the valley floor shows the average altitude across the gap “felt” by the flow. Isentropes are at 2 K intervals and arrows indicate along-valley speeds upstream and downstream of the gap (Adapted from Armi and Mayr 2007. Reproduced by permission of the Royal Meteorological Society)

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flowing layer on the upstream side is stably stratified as in the “Wood – single-layer prototype” and is isolated from the surface and from the flow aloft by a neutrally stratified (nearly) stagnant layer. The upper isolating layer is no longer at or below crest but clearly above it. The gap-crest flow layer plunges, accelerates and thins. However, the internal jump occurs only within the channel so that only the lowest portion of the deep flow can be mixed into a neutrally stratified part; the largest part of the flowing layer remains stably stratified downstream of the pass. Again, the upper isolating layer thickens into a deep wedge keeping the flow aloft from being affected by the underlying topography. Before the gap flow becomes established, all three prototypes have lower potential temperatures in the gap flow layer on the upstream side of the pass than in the air mass on the downstream side (Mayr and Armi 2008). Figure 3.31 shows stages in the evolution of a particular gap flow case using a sounding on the far upstream side of the pass and at the end of the channel. Prior to the onset of northward gap flow (i.e. towards the viewer in the accompanying topography Fig. 3.29), potential temperatures are higher on the southern side of the Alps than on the northern side to above the main Alpine crest as seen in the difference between the southern and northern radiosounding (center of Fig. 3.31). No northward gap flow occurred.2 Changes on the synoptic scale brought a warmer air mass to the north of the Alps and a colder one to the south so that potential temperature differences (center of Fig. 3.31) are colder south of the pass to an altitude just above the channel crest. Higher up in the channel to about 1 km above the main Alpine crest, however, potential temperatures are still higher on the southern side, Gap flow had commenced a few hours prior to the soundings. With the continuation of the synoptic development, the air mass to the south kept getting colder between 2 and 4 km MSL, i.e. channel to 1 km above the main Alpine crest, whereas the air mass to the north remained unchanged. Consequently, the gap flow layer deepened and extended even above the main crest, causing hybrid gap flow with superimposed cross-crest foehn flow. It must be emphasized that the driving mechanism behind this gap flow event was the air mass difference on both sides of the crest. During pure gap flow at times 3 and 4, the layer on top of the descending gap flow layer moved at speeds comparable to and even higher than the gap flow layer on the upstream side. Yet it did not descend but remained nearly horizontal since its potential temperatures were not low enough to descend.3 A colder air mass upstream of the gap was also noted in other observations of gap flow around the world. On the North American Pacific coast it is mostly cold wintertime continental air contrasting with warmer air over the Pacific Ocean (e.g. Cameron 1931; Overland 1984; Lackmann and Overland 1989; Colman and Dierking 1992; Bond and Macklin 1993; Finnigan et al. 1994; Jackson and Steyn 1994a; Pan and Smith 1999; Colle and Mass 2000; Collier 2002; Sharp and Mass

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Fig. 3.31 Changes in the air masses upstream and downstream of the Brenner Pass and their effects on the flow through the pass. At time 3 the potential temperature was for the first time lower to the south (center column) and very shallow gap flow occurred. The northward gap flow became deeper (time 4) and changed into a deep hybrid flow composed of deep foehn (“downslope windstorm”) and gap flow at time 5. At the end (curve 6), gap flow seized as the potential temperature difference vanished (From Mayr and Armi 2008. Reproduced by permission of the Royal Meteorological Society)

2004; Bond et al. 2006; Neiman et al.2006). Similarly, gap flows along the Adriatic and Black Sea coasts are driven by a colder continental air mass compared to the warmer air mass over the Mediterranean (e.g. Baji´c 1989; Grubiˇsi´c 1989; Glasnovic and Jurˇcec 1990; Gohm and Mayr 2005; Gohm et al. 2008; Grisogono and Beluˇsi´c 2009; Alpers et al. 2009). Sometimes cold air over the North American continent surges southwards from where it was formed and reaches as far south as the Central American Pacific Coast, causing gap flows in Mexico (e.g. Hurd 1929; Schultz et al. 1997; Steenburgh et al. 1998). Over Japan, where gap flows are called “dashikaze”, temperature differences might be caused by typhoons (e.g. Arakawa 1969; Ishii et al. 2007; Mashiko 2008). Colder air advected across the ocean can cause gap flows, e.g. on the Falkland Islands (Mobbs et al. 2005), through the Strait of Gibraltar (Scorer 1952; Dorman et al.1995), and through the Rhone Valley (e.g. Pettre 1982; Jiang et al. 2003).

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Different mechanisms lead to colder air upstream of gap flows in the interior of a continent (cf. Sect. 3.5.3). Examples of such observations are in Seibert (1990), Doran and Zhong (2000), and Mayr and Armi (2008). In many of the gap wind cases cited in the preceding paragraphs, cold continental air of the gap flow extends over the oceans. In this case, significant air-sea interactions can result as sensible and latent heat fluxes from the warm water surface alter the overlying air, and in turn the cold wind affects the oceans. Examples of the impact of strong, cold low level flow on the ocean, in this case of the bora, which often emerges as a gap-like flow onto the Adriatic, are discussed by Orli´c et al. (1994, 2006) who describe the complex response of the sea to strong bora winds. Enger and Grisogono (1998) use two-dimensional simulations to demonstrate that bora flow is extended over the warm sea due to the effect of the sea surface temperature on reducing N which allows the flow to remain supercritical for a greater distance by postponing the hydraulic jump. Gap flow over the Gulf of Tehuantepec has been found to induce coastal upwelling, as well as a lowering of sea surface temperature by as much as 8ı C (e.g. Schultz et al. 1997).

3.5.2 Theory Linearizing the governing equations about a basic state has been successfully used to (semi)analytically describe orographic flows. However, this approach fails to describe gap flows as shown by Pan and Smith (1999). In linear theory (e.g. Queney 1948; Klemp and Lilly 1975; Smith 1979, 1980), vertically propagating gravity waves cause lower pressure and accelerating winds on the lee slopes of a mountain ridge; their strength is proportional to the height of the mountain. Accordingly, the strongest pressure anomaly occurs along the lee slopes of the mountains on either side of the gap and not in the gap itself even when confluence at the gap entrance is included (Pan and Smith 1999; Z¨angl 2002c). Linearized gap flows are always weaker than the flow down the adjacent crests, contrary to what is often observed. Hydraulic theory, on the other hand, can describe gap flows. Its application to mountain flows was pioneered by Prandtl (1942) and Long (1953, 1954). It is fully nonlinear, which is an essential characteristic of asymmetric gap flows. Steady state is assumed in hydraulic theory. Further assumptions are made about the vertical structure of the air/fluid either by vertically averaging layers or by requiring self-similarity. Self-similarity means that, at any position, the density and velocity profiles can be scaled with the height of the moving stratified layer. Hydraulics in the atmospheric science community is often taken synonymously with its simplest, “single layer” case of one layer of constant vertical profile of potential temperature (or density in case of fluids). The theory of the single layer case is described in Sect. 3.2.3. Gap flows frequently have stably and continuously stratified rather than homogeneous, neutrally stratified air masses on the upstream side, as was shown in

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Fig. 3.32 Wood’s (1968) self-similar solution for stratified flow from a reservoir through a contraction, i.e. a level gap. Upper panel: vertical section with isopycnals and the vertical density profiles upstream and downstream of the contraction; lower panel: plan view. Flow from left to right

the previous section. The single layer theory must therefore be expanded. Wood (1968) could show that an analytical hydraulic solution exists for withdrawal from a reservoir of fluid with a known, arbitrary stratification through a level confluentdiffluent gap as shown in Fig. 3.32. Upon withdrawal, the uppermost and lowermost streamlines will respectively drop down and rise up as indicated in the figure. If the volume in these wedge-shaped regions is relatively small then the fluid filling them will originate from a relatively small range of depth in the reservoir and be thus of approximately constant density. This implies that the uppermost and lowermost streamlines are (approximately) also lines of constant pressure. The analytical solution is for the general case of arbitrary density distribution. Let 0 be the density at the uppermost streamline. The density increases by a total  to the lowermost streamline over the depth  of the flowing layer. At any height z, the density is thus 0 C ı. An analytical solution exists when the density and velocity distributions are self-similar, i.e. when they scale with the depth of the flowing layer  at each section. Then the density profile at all sections has the form ı z D F .ƒ/ where F() is determined by the far-upstream density   F 

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distribution. Exploiting the fact of constant pressure along the streamline and using Bernoulli’s equation for a streamline in the flow, yields the velocity, v, at an arbitrary height .0 C ı/ v2 D2 g Œzt .1/  zt 

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where zt is the height of the uppermost streamline. For example, with a linear stratification, F and G become F(ƒ) D 1  ƒ and 2G ./ D 3ƒ  4ƒ2 C ƒ3 , respectively, and the velocity distribution is parabolic-like. The analytical solution could be reproduced in the laboratory (Armi and Williams 1993, their Fig. 5) and is shown here in Fig. 3.28b. Note the continuous stratification far upstream in the reservoir. As it is withdrawn through the gap, well-mixed neutrally stratified and stagnant layers form above and below the flowing layer, which isolate it from the remaining fluid. Whether both isolating layers form depends on the height range over which fluid is withdrawn downstream of the gap. When it is withdrawn at the bottom, an isolating layer forms only at the top. The atmospheric equivalent is shown in observations and numerical simulations of a gap flow event through Juan de Fuca Strait in Figs. 3.27b and c. Similarly, when the fluid is withdrawn from the top of the channel, an isolating layer forms underneath only. And when the fluid is withdrawn from the center, both upper and lower isolating layers form as shown in Fig. 3.28b. For a particular flow rate, a range of densities 0 to 0 C  flows from the reservoir. As the flow rate changes, the range of densities drawn from the reservoir changes so that the flow at the narrowest section of the gap remains critical with respect to the longest wave mode. Note that a continuously varying density stratification results in an infinite number of wave modes. Thus there is an infinite number of sections which act as virtual controls in addition to the physical control of the narrowest cross section. Benjamin (1981), in a generalization of Wood (1968), showed that self-similar flows will tend to be realized whenever fluid is withdrawn from a continuously stratified reservoir. With a sufficiently high extraction rate downstream, the resulting flow is critical at the narrowest section and supercritical downstream of it. Even the longest (and fastest) wave mode is swept downstream in supercritical regions of the flow. The equivalent to a reservoir of continuously stratified fluid in the atmosphere is a different air mass on the upstream side of the mountain range. The withdrawal of that air through a gap is started when a relatively warmer air mass is on the downstream side. The pressure gradient force between the different air masses substitutes for the pump, which withdraws fluid in the laboratory experiments. At what vertical range that pressure gradient and air mass difference exist, determines where the isolating neutral layers will form. In the case of the Alps (Wipp Valley), it was mid-level since both upper and lower isolating layers were observed (Fig. 3.30 middle and bottom).

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b0 F 22 = 2

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Upstream bv Crest

b0 F12 = 2

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or Upper layer dominant downstream

Upstream bv

Crest

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Fig. 3.33 Two-layer hydraulic flow across a pass (lateral and vertical contraction). Upper panel: low to moderate flow rates with flow controlled at the narrowest part of the gap. Lower panel: high flow rates with supercritical flow at the narrowest section. When the lower layer dominates (left column) it remains supercritical downstream of the gap center and vice versa for an dominating upper layer (right column). In the figures Fi is the Froude number in layer i, b0 is the location of the primary control for the flow at the top of the hill, bv is the virtual control where the Froude number becomes unity (Adapted from Armi and Riemenschneider 2008. Reproduced by permission of Cambridge University Press)

Atmospheric gap flows can consist of more than one dynamically active layer. For two layers of comparable depths and flow rates, two unique controlled asymmetric flows are often possible (e.g. Armi and Riemenschneider 2008). They are determined by the difference in the fluid reservoirs (or air masses in case of the atmosphere) upstream and downstream of the gap. For relatively low flow rates, either the lower or upper layer can be active layers. As flow rates increase, there may no longer be the possibility of the two asymmetric solutions satisfying critical conditions at the topographic control, the narrowest section of the (level) gap. Instead, they merge upstream and the control moves upstream of the narrowest section as a “virtual” control. An additional possibility of two-layer flows are “exchange flows” with flow in opposite direction in each layer (cf. Baines 1995, Sect. 3.11). As was seen in Sect. 3.5.1 on observations of gap flows, the contraction in a gap can be only lateral (“level gap”), only vertical (constant width but bottom rises; “sill”), or a combination of lateral and vertical (“pass”). For two layer flow, a level gap directly contacts both layers. A sill, on the other hand, only directly contacts the bottom layer, and the response of the upper layer is indirect. Armi and Riemenschneider (2008) found analytical solutions for two-layer flows over a pass. Four different flow configurations are summarized in Fig. 3.33. When the lower layer dominates (upper left), it accelerates as the interface between the two

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layers first rises slightly but then descends even upstream of the crest. Compared to a single-layer flow, the presence of the upper layer keeps the interface higher at the center of the gap and also increases the flow rate, but both only by less than 5%. Such a small change is currently not detectable observationally in the atmosphere. The flow in the upper layer can even be in the opposite direction. When the upper layer dominates (upper right part of Fig. 3.33), the vertical contraction part of the pass is only communicated indirectly via the dynamics of the lower layer. The upper layer depth decreases as it accelerates towards the pass and becomes supercritical. As flow rates increase, only supercritical conditions can exist at the gap center and the transition from the subcritical conditions in the reservoir occurs further upstream at the virtual control (lower panel in Fig. 3.33). On its way towards the pass, the upper layer accelerates more than the lower layer (Armi and Riemenschneider 2008). Whether upper or lower layer dominate and remain supercritical downstream of the gap center, depends on the matching downstream conditions.

3.5.3 Models and Forecasting Modeling of gap flows has spanned the whole spectrum from idealized to realistic 4D-simulations. Shallow water models are used with surprising success along with non-hydrostatic numerical weather prediction models. Forecasting gap flows has not attracted much research interest yet but well-established practices exist in forecasting offices which have gap flows in their forecast region. An ingredientsbased method for forecasting gap flows is presented.

3.5.3.1 Models The most basic models to simulate gap flows are shallow water models, which numerically solve the single-layer hydraulic flow equations for one or two wellmixed layers. Pan and Smith (1999) used such a model developed by Sch¨ar and Smith (1993) to study gap flows at Unimak Island southwest of the Alaskan Peninsula but had limited data with which to initialize and compare their model. Jackson and Steyn (1994b) used a different hydraulic model, which also included friction. Flow through Howe Sound could be reproduced. Horizontal pressure gradients and turbulent friction were dominant in a force-balance analysis. The same model as in Pan and Smith (1999) was used for more intensively observed gap flows in the Wipp Valley with data from the Mesoscale Alpine Programme (Gohm and Mayr 2004) and for a case study of bora flow at the Adriatic coast (Gohm et al. 2008). Systematic parameter studies with the single-layer shallow water model for the Brenner Pass – Wipp Valley by Gohm and Mayr (2004) emphasized the dominant role of small-scale topographical features for details of the gap flow. Ridges protruding into the valley downstream of the pass, a widening or a turning of the valley can all be locations where supercritical flow returns

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to a subcritical state in a dissipative, turbulent hydraulic jump. For the Brenner Pass geometry, the vertical constriction rather than the lateral constriction was found to be largely controlling the flow. A comparison with detailed observations showed that the shallow water simulations included all basic features of the gap flows. A similarly successful replication was achieved for a bora flow at the Adriatic coast (Gohm et al. 2008), where the gap flow jets and hydraulic jumps were captured. At first, it is surprising that a single layer model can reproduce the essence of gap flows in realistic settings and continuous upstream stratification – a deviation from the neutral stratification in the numerical model. As Wood (1968) showed in his analytical solution discussed in Sect. 3.5.2 and as Armi and Williams (1993) showed in the laboratory, well-mixed nearly stagnant layers isolate the gap flow from the flow aloft so that disregarding the effects of the flow aloft as is done in the shallow water model has only small adverse affects on the simulations. Furthermore, Durran and Klemp (1987, cf. their Fig. 8) and Farmer and Armi (1999, their Fig. 3) showed that a continuously stratified flow over a ridge (vertical constriction), despite its continuous stratification is qualitatively similar to a single-layer hydraulic flow, especially when the depth of the continuously stratified system is less than one half of its vertical wavelength (Durran and Klemp 1987). The third reason for the success of the simple model is that turbulence near the surface, in hydraulic jump(s) and at the upper interface of the gap flow mixes shallower gap flows from a continuous to a neutral stratification. Numerical simulations solving the complete set of nonlinear governing equations have been used in varying degrees of idealization for the simulations of gap flows. Idealization of both topography and flow/air masses will be considered first, followed by idealization of only flow/air mass, and finally fully realistic flows. These fully non-linear simulations with mesocale numerical models confirmed turbulent friction identified in the hydraulic modeling of Jackson and Steyn (1994b) as an additional key parameter for gap flows, besides the shape of the underlying topography. Gap flow depths are of comparable magnitude to the depth of the planetary boundary layer. Highly idealized simulations with a geostrophically balanced frictionless background with uniform static stability leave the gap flow direction dependent on the shape of the topography, which is not supported by observations. For the balanced background flow parallel to an infinite ridge Sprenger and Sch¨ar (2001) and Z¨angl (2002a) found flow towards lower pressure. An isolated ridge, however, reverses the direction (Z¨angl 2002a). It splits the flow on its upwind edge, leading to anticyclonic flow on the left side (looking in flow direction) of the isolated ridge. This flow has an ageostrophic component directed towards the mountain, thus counteracting and slightly overpowering the larger-scale geostrophic pressure gradient. The addition of friction turns the low-level wind counterclockwise compared to the flow aloft, i.e. towards the region of lower largescale pressure (Z¨angl 2002a; Gaberˇsek and Durran 2006). Gaberˇsek and Durran (2006) quantified the importance of friction with volume-averaged momentum-flux budgets.

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Turbulent friction in the boundary layer produces filaments of anomalous potential vorticity, called potential vorticity banners, at the side walls of the gap (Ross and Vosper 2003), which are then advected further downstream. They can be found at large distances away from the gap and can also occur in radiatively driven downvalley flows with a lateral constriction at the terminus of the valley (Z¨angl 2004). Including the realistic topography of the Alps but keeping the geostrophically (except in the boundary layer) balanced initial flow fields with constant static stability throughout the troposphere, Z¨angl (2003) found 3D-propagation of gravity waves excited over adjacent ridges to be crucial for the acceleration of a gap flow in the Wipp Valley. The initial conditions, however, strongly deviate from the typical situation of two different air masses of limited vertical extent on either side of the gap. The limited depth leads to the self-isolation of the gap flow from the flow aloft (cf. Sect. 3.5.2). Including realistic initial conditions is one of the main difficulties for the numerical modeling of realistic gap flows. Detailed observations, especially vertical profiles in the proximity of gaps are typically sparse or none-existent. Even if they exist, making full use of them is difficult since more sophisticated methods than nudging for assimilating such data into mesoscale models (e.g. 4D-VAR, ensemble Kalman filters) are just emerging. As a result, the initial state of the mesoscale models is still dominated by the fields from global models, into which the mesoscale models are nested. The horizontal resolution of global forecasting models is currently (2010) at 16 km or coarser, so that model topography differs significantly from the real topography (e.g. the wider part of the valley south of Brenner Pass is about 0.7 km below the ECMWF T1279 topography). Initial conditions of the models therefore lack the sharp potential temperature steps on top of the gap flow layer, which occur often within only dozens or hundreds of meters. The smoothing introduced by the numerics during model integration aggravates the situation. In contrast, the sharp separation can easily be introduced to the much simpler hydraulic models. Gohm et al. (2004) compared model simulations of a gap flow and foehn event in the Wipp Valley with the rich data set of MAP. They attributed considerable discrepancies at the beginning of the event to deficiencies in the model profile upstream of the pass, where the flowing layer (and consequently the potential temperature step at its top) was too shallow. Given that the height of the gap flow layer on the upstream side, the mass flux through the gap, and the “withdrawal” on the downstream side are all related (cf. Sect. 3.5.2), a combination of deviations of the model from the real atmosphere both upstream and downstream might have been the cause. Later in the event, too much mass flowed across the pass and the gap flow layer did not descend as much as observed downstream of the pass. However, most of the prominent observable gap flow features like hydraulic jumps and cross-valley asymmetries of the flow are so much dominated by the underlying topography, that they were still found in the simulations. The simulation of a level gap flow event through the Strait of Juan de Fuca (cf. Fig. 3.27) also found cross-gap asymmetries

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caused by flow into the channel over one of its sides. One of the main advantages of the fully realistic simulations is the ability to obtain a complete (time-dependent) three-dimensional depiction of gap flows (Jackson and Steyn 1994a). Topography must be sufficiently resolved in the model for the correct amount of air to be withdrawn from the upstream side. Horizontal mesh widths for Wipp Valley simulations were as fine as 0.27 km in the innermost model domain and 0.8 km in the domain that spans both sides of the gap in Gohm et al. (2004) and Z¨angl et al. (2004). Reducing the 0.8 km grid spacing to 0.4 km further improved the results (Z¨angl 2006). A mesh of at least approximately 1 km was also needed for gap flow through the Columbia Gorge (Sharp and Mass 2002), with 0.44 km horizontal spacing also improving the results. When the flow (and the different air masses) are deep enough to “flood” the main crest into which a gap or pass is cut, downslope windstorms (or deep foehns as they are called in the Alps) are superimposed on the gap flows. Gap flows play then a relatively minor role in the total mass transport but otherwise their main characteristics remain similar (e.g. Colle and Mass 1998; Gohm et al. 2004; Z¨angl et al. 2004). Numerics and turbulence schemes are further challenges in correctly simulating gap flows with numerical models. Reinecke and Durran (2009b) in simulating mountain waves showed that second-order finite differencing schemes overamplified a standing mountain wave by about a third compared to fourth-order schemes within the nonhydrostatic regime with typically used horizontal resolutions of the mountain. Applied to the American Sierra Nevada, this translated to an overestimation of downslope speeds at the surface of 20 m s1 and of vertical velocity maxima by 10 m s1 (as seen in the study of Reinecke and Durran 2009b, see Fig. 9.18 in Chap. 9). Most numerical simulations of flows over mountains until recently were performed using second-order or third-order schemes. The large mountain waves and strong rebounds (often termed “wave breaking”) seen in Fig. 9.18 were common features of these simulations and also part of a scientific dispute over flow over an oceanic sill, where observations (Farmer and Armi 1999, 2001; Armi and Farmer 2002) could not be reconciled with numerical simulations (Afanasyev and Peltier 2001a, b). A large part of the discrepancy occurred at the top of the flowing layer, where small scale entrainment was observed but wave breaking on a much larger scale was modeled. Small scale entrainment was also found to be the important mechanism at the top of a stratified flow down a slope in the laboratory (Baines 2001, 2005). Gohm et al. (2008) found a strong sensitivity to the turbulence scheme of the top of the gap flow and the layer immediately above. An improvement of these schemes seems to be needed. At the ground, the height of the lowest model surface above the ground had a surprisingly large impact in sensitivity studies of gap flow reported in Z¨angl et al. (2008), even more so than the type of PBL scheme. Essential for the correct simulation of gap flows and the interactions between the different air masses involved is that horizontal diffusion of the mass field is truly computed horizontally, not along the terrain following coordinate surfaces (Z¨angl 2002b).

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3.5.4 Forecasting Forecasting methods for gap flows have been developed in local forecasting offices but have not yet progressed into easily accessible peer-reviewed literature. They are typically empirical and statistically based without establishing a direct physical connection between predictor and predictand. Some combine statistics and the fundamental characteristics of gap flows. An example is Drechsel and Mayr (2008), who use the frequency distribution of potential air mass difference on a model surface and reduced pressure difference across the barrier to probabilistically forecast the binary event of gap flow – yes or no. Following Doswell et al. (1996) an “ingredients-based” method is proposed here, which uses the physical understanding of gap flows. It is not regionally dependent (gap flows occur all over the globe) but flexible enough to be easily adaptable to local forecasting demands and to incorporate new observational or modeling advances as they become available. Gap flows occur due to different air masses on either side of a gap. The resulting pressure gradient is the main driving force. The altitude range of the air mass difference will determine the depth of the gap flow. Most forecasting applications will be interested in gap flows reaching the surface downstream of a gap. Unless the potential temperature of the air mass upstream of the gap is lower or at most the same as the potential temperature of the air mass downstream, an asymmetric gap flow with higher wind speeds downstream will not happen. The ingredients to create different air masses on either side of the gap will be examined progressing from large to small scales. On the large scale is the quasi-horizontal differential advection of air masses. Synoptic-scale systems may transport different air masses to opposite sides of the gap. Examples are cold fronts and subsequent mid-level troughs typically co-located with the coldest air passing over only one side of the obstacle (Fig. 3.34a). A complementary situation is that of warm fronts and mid-level ridges being confined to only one side. A combination of these two is also possible. Another mechanism on the large scale is air mass formation under anticyclones. Different surface characteristics on either side of the gap lead (diabatically) to different air masses (Fig. 3.34b). An example is the wintertime formation of cold air over the continent, which is separated by mountain ranges from relatively warm air over the ocean. Well-known regions are the Pacific Northwest and the Adriatic coast. Ocean-land contrasts also lead to large differences over the Falkland Islands and create a particularly large potential temperature step on top of the flowing layer (Mobbs et al. 2005). Advective and diabatic processes are also at work on the mesoscale to create sufficiently lower potential temperatures at one side of the gap to cause gap flows. Lower pressure further downstream of the gap can lead to ageostrophic flow of air towards the low pressure. Compensating subsidence with adiabatic temperature increase might be sufficient to raise potential temperatures higher than the ones

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a

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F 500

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c q

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Fig. 3.34 Forecasting gap flows: processes creating lower potential temperatures in the flowing layer upstream than near the surface downstream. (a) Large-scale differential advection from a cold front and upper level trough followed by a warm front. (b) Formation of air masses under a high pressure system (cold wintertime continent, warmer ocean). (c) Ageostrophic drainage of cold air towards low pressure caused by flow over the larger mountain range into which the gap is embedded. (d) Differential heating caused by upstream cloud-cover and (nearly) clear skies downstream

upstream of the gap. Causes for lower pressure further away from the gap can be an approaching cyclone or the topographic low pressure caused by flow over the whole mountain range, into which the gap is embedded (Fig. 3.34c). Low and/or mid-level cloud cover on one side of the gap with nearly clear skies on the other side will lead to much stronger diurnal warming near the surface on the clear side of the gap, raising potential temperatures above the ones on the cloudy side (Fig. 3.34d). Consequently, many gap flow regions have a climatological maximum in the afternoon. At nighttime, however, the radiative cooling can lower potential temperatures sufficiently to prevent the gap flow from reaching the ground. Differential heating between a valley atmosphere and the adjacent (flat) forelands will create valley wind systems (see Chap. 2). Given sufficient heating difference and a pronounced lateral constriction, e.g. at the exit of the valley, an asymmetric gap flow with strong acceleration downstream of the constriction can develop. It is most pronounced for nocturnal downvalley flow and has been observed and modeled for several Alpine valleys draining into the forelands (M¨uller et al.1984; Z¨angl 2004, and references therein, and Chap. 2 in this volume). Finally, at the meso-gamma scale, small-scale topographical features might exclude gap flow from small regions. A kink in the terrain will lead to flow separation when the potential temperature is similar to the one further underneath (i.e. nearly neutrally stratified). Lateral flow separation will keep some regions in the wake of the flow.

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Shear-induced turbulence from gap flow shooting over a cold pool downstream of the gap acts to increase the potential temperature step across the interface and the thickness of the interface by mixing in air of higher potential temperature from aloft and lower potential temperature from the cold pool, respectively. The thickness of the induced turbulent eddies depends on the thickness of the shear layer and the stratification of the flow, as expressed by a (gradient) Richardson number. These eddies pair with neighboring eddies to form larger vortices (Koop and Browand 1979), which increase the vertical extent of the mixing region at the interface several-fold (Koop and Browand 1979, Fig. 8). When the cold pool is shallow enough to be comparable to the size of the shear-induced eddies, these eddies and thus the gap flow can penetrate down to the surface and cause a sudden temperature increase there. The details are sensitive to the value of the Richardson number. Currently no routine observational methods exist to be able to exploit this “turbulence ingredient” for forecasting the break-in of gap flow through a cold pool. Observations and NWP forecasts still need to be improved to make the best use of such a conceptual, ingredients-based forecasting method. Vertical profiles of air masses on either side of the gap are observed in very few locations of the world only. The increase in the size of automatic weather station networks has put more stations into exposed locations like mountain tops, which provide coarse information about the vertical structure of the air mass. Vertical structures in NWP analysis and forecast products are strongly smoothed versions of the actual profile. However, sharp potential temperature steps over a few decameters only and wellmixed layers of a few hundred meters and their exact location are crucial for gap flow dynamics. An upper limit to the increase of speed from a station in the bottom part of the flowing layer upstream of the gap, vu , and a downstream station, vd can be computed from the potential temperature difference across the top of the flowing layer, ™, and how far the top of the layer has descended between upstream and downstream locations (e.g. Armi and Mayr 2007), h, which yields a pressure difference p: p D g

 h 0

(3.40)

Alternatively the pressure difference can be taken from weather stations (as long as they are in the flowing layers, see below) but have to be reduced to a common altitude (cf. Mayr et al. 2002, for a discussion of reduction methods). With the Bernoulli equation along a streamsurface: v2d D v2u  2

p 

(3.41)

This is an upper limit since it does not include the effects of surface friction, hydraulic jumps and the fact that the stations might not lie on the same streamsurface. In many locations, the only diagnostic tool available is pressure observations from valley/plain stations. Since pressure is an integral measure of the temperature

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profile aloft, the pressure difference across the gap can suffice for diagnosing (and forecasting) air mass differences and gap flows. Caution must be taken to account for blocked layers underneath gap flows. Especially upstream of passes they can be of substantial depth. As they do not flow across the pass, their contribution to the pressure difference needs to be discounted. A decrease of temperature by 3 K over a depth of 1 km increases pressure by 1 hPa.

3.6 Barrier Jets A barrier jet is an elevated wind maxima on the windward side of a mountain barrier, blowing parallel to the barrier. Barrier jets can occur when stably stratified flow approaches an extra-tropical mountain barrier and is blocked by the barrier for hours to days or longer. The blocked flow is forced to move up the barrier, and as the low level cool air is forced against buoyancy to rise, it cools adiabatically and creates higher pressure along the slope. The higher pressure against the barrier acts to decelerate and block the flow. With enough time, geostrophic adjustment can occur between the flow and the high pressure along the slope. This adjustment causes the flow to turn left (right) in the northern (southern) hemisphere, so that the high pressure is to the right (left) of the flow. Turbulent friction reduces the wind near the surface, and thermal wind considerations imply the strongest jet will lie above the largest horizontal temperature gradient. The general structure of a barrier jet is shown in Fig. 3.35.

Fig. 3.35 Schematic diagram showing a barrier jet as a low-level flow of strong winds (under the dashed line) parallel to the mountain barrier (flow is into the page). The flow is formed by the upslope movement of stratified air, increasing the pressure along the slope so that the pressure gradient force is balanced by the Coriolis force in the cross-barrier direction. The flow is ageostrophic in the along-barrier direction, where an antitriptic balance forms with the alongbarrier pressure gradient balanced by friction and inertia. H is the mountain height, L is the mountain half-width, and Lr is the internal Rossby radius of deformation (Lr D NH/f)

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3.6.1 Observations The across-barrier blocking, turning and acceleration of the wind has been documented in many coastal and inland mountain regions such as: north of the Brooks range in Alaska (Schwerdtfeger 1974) and southeast Alaska (Lackmann and Overland 1989; Overland and Bond 1993; Loescher et al. 2006; Olson et al. 2007), southwest British Columbia (Overland and Bond 1995; Doyle and Bond 2001), Washington State (Mass and Ferber 1990), Oregon (Braun et al. 1997), California (Doyle 1997; Yu and Smull 2000), east of the Appalachian and Rocky Mountains (Bell and Bosart 1988; Colle and Mass 1995), Taiwan (Li and Chen 1998; Yeh and Chen 2003), the Colorado Front Range (Marwitz and Toth 1993), windward of the Sierra Nevada (Parish 1982), southern Norway (Økland 1990), Antarctica (Schwerdtfeger 1975), and as a related phenomenon, the Southerly Buster in southern Australia (Baines 1980). A recent field experiment – the Southeast Alaska Regional Jets (SARJET) experiment (Winstead et al. 2006) – completed over the Gulf of Alaska in September and October of 2004 has provided new data (aircraft and Synthetic Aperture Radar) and modeling results that have contributed significantly to better understanding Barrier Jets. Barrier Jets can be categorized into a few broad groups: Classic barrier jets. In this case the onshore flow of stratified marine air onto a western coast is blocked by coastal mountains, resulting in wind turning into an along-barrier direction as a barrier jet near and upwind of the coastal mountains. These conditions: stratified air impinging on a flow-perpendicular mountain barrier, are common along mountainous coastlines on the western edges of continents – especially of North and South America. During winter, west coasts at mid-latitudes can be characterized by the regular passage of frontal systems across the coastal mountains often resulting in the onshore flow of stable air ahead of a surface warm front. The onshore (across-barrier) flow of cool marine air below the frontal inversion can be blocked by the coastal mountains, decelerate in the across-barrier direction and deepen, thereby creating a high pressure ridge along the mountain barrier. In the northern hemisphere, the onshore flow turns to the left along the barrier, both in geostrophic adjustment to this pressure ridge, and in response to decreased along-barrier Coriolis force as the onshore wind speed drops (Smith 1979). The enhanced across-barrier pressure gradient can result in a barrier jet in the coastal zone (e.g. Schwerdtfeger 1979; Parish 1982, 1983; Li and Chen 1998; Overland and Bond 1993, 1995). In a numerical simulation of a coastal jet that formed ahead of a land-falling cold front approaching the northern California coast, Colle et al. (2002) found the blocking of the onshore flow resulted in coastal pressure ridging and terrain-enhanced southerly winds that exceeded 25 m s1 (90 km h1 ). Considerable along-coast variability in the jet was noted, with reductions in speed downwind of Cape Blanco and Mendocino and accelerations adjacent to higher coastal topography. Numerical model diagnostics suggest that the low level blocking of flow impinging on coastal

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mountain ranges is often important for generating ageostrophic coastal jets in California and elsewhere (e.g., Doyle 1997). Essentially, this blocking contributes to pressure ridging upwind of the mountain barrier which then adjusts to form an along-barrier jet. The winds in the model jet were enhanced by 45% due to topographic blocking and peak winds of 22 m s1 were simulated (Doyle 1997). Olson et al. (2007) discuss the structure of various barrier jets observed in southeast Alaska during the SARJET experiment (Winstead et al. 2006), and found that classical jets had maximum winds over 30 m s1 at the coast between 600 and 800 m above sea level, extending approximately 60 km offshore. An illustration of a Classic Barrier Jet, over the waters of Southwest Alaska using Synthetic Aperture Radar (SAR) is shown in Fig. 3.36a (Loescher et al. 2006). Aircraft observations and MM5 simulations from SARJET of a classic barrier jet from Olson et al. (2007) are shown in Fig. 3.37a and b Hybrid barrier jets. In regions of complex terrain, such as the Pacific Northwest region of North America, interactions between different orographically forced mesoscale flows often occur. For example, the source of cold air along the windward slopes of North American west coast mountains can be gap flow exiting coastal valleys which is turned poleward by the Coriolis force as the flow undergoes geostrophic adjustment upon exiting the gap. This is the so-called “hybrid” barrier jet that is reported by Doyle and Bond (2001) and Loescher et al. (2006) who discuss the similar cases of high-latitude (strong f) gap flows in British Columbia and southeast Alaska where gap flows exiting onto a mountainous coastline develop characteristics of terrain-parallel barrier jets. This is illustrated over southeast Alaskan waters using SAR imagery in Fig. 3.36c (Loescher et al. 2006). The geostrophic adjustment of a low-latitude gap flow was modeled by Steenburgh et al. (1998). They found that the adjustment curvature was determined by an inertial circle – in their case due to weak Coriolis forcing, the gap flow never became a jet, however at higher latitudes since the inertial circle radius is inversely proportional to the Coriolis parameter, the gap flow can turn rapidly poleward, merging with the synoptic flow becoming a barrier jet. Overland and Bond (1995) suggest that cold air supplied by gap flow from the Strait of Juan de Fuca that separates Vancouver Island from the Olympic Peninsula on the west coast of North America, enhanced the barrier jet observed during the Coastal Observation and Simulation with Topography Experiment (COAST). Numerical modeling experiments by Doyle and Bond (2001) indicate that the cold air supplied by the gap flow was as important as the topography of Vancouver Island in enhancing the barrier wind. Olson et al. (2007) in an analysis of barrier jets over southeast Alaska found that hybrid jets with a maximum speed of approximately 30 m s1 at 500 m above sea level were displaced 30–40 km offshore (in contrast to classical jets which had maximum winds over the coastline). Aircraft observations and MM5 simulations from SARJET of a hybrid barrier jet from Olson et al. (2007) are shown in Fig. 3.37c and d. A conceptual model of the hybrid barrier jet over southeastern Alaskan waters is shown in Fig. 3.38d (Olson et al. 2007).

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Fig. 3.36 Synthetic Aperture Radar imagery of Barrier Jet surface winds over the coastal waters of southwest Alaska (Source: Loescher et al. 2006. © American Meteorological Society. Reprinted with permission)

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Fig. 3.37 Vertical cross sections across the width of barrier jets from IOP1 – classical barrier jet (panels a, b) and IOP7 – hybrid barrier jet (panels c, d) of the SARJET experiment in southeastern Alaska. Panels (a) and (c) are from aircraft observations and panels (b) and (d) are from MM5 simulations (Figures from Olson et al. 2007, Figs. 6c, d and 12c, d. © American Meteorological Society. Reprinted with permission)

Cold Air Damming. In situations where flow impinges on an eastward-facing mountain barrier, cold air damming can occur if cold air is present to the north (in the northern hemisphere). In this situation, the mountain may block the lowlevel flow, creating higher pressure along the mountain slope and northerly flow in which the across barrier pressure gradient is balanced by the Coriolis force and there is an antitriptic balance between friction, inertia and the pressure gradient in the along barrier direction so as cold air is advected to the south (northern hemisphere). The jet is effectively trapped against the topography by the Coriolis force and high static stability at the top of the cold air. These events have been documented east of the Appalachian Mountains (e.g. Bell and Bosart 1988), east of the Rocky Mountains (Colle and Mass 1995), among other locations. Marwitz and Toth (1993) in a Cold Air Damming event along the Colorado Front Range, found a northerly barrier jet formed by upslope flow with adiabatic cooling enhanced by cooling from evaporation and melting of falling precipitation. The jets formed by cold air damming on the eastern slopes of mountain barriers which advect cold air

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Fig. 3.38 Conceptual model of a hybrid barrier jet over the coast of southeastern Alaska. Thick arrows represent the gap flow, medium arrows the 1,000–1,500 m flow and thin arrows the low-level flow. T represents temperature anomalies (Source: Olson et al. 2007. © American Meteorological Society. Reprinted with permission)

southward, are somewhat analogous to the hybrid jets along the western slopes of mountains discussed above. In the case of hybrid jets, the cold air is supplied by gap flow of cold continental air through mainland inlets and the barrier jet advects the cold air poleward, while in cold air damming events the cold air originates on the barrier-jet side of the mountains and the cold air is advected equatorward. The “Southerly Buster” of southeastern Australia is an along-barrier jet resulting from the interaction of a midlatitude frontal system with the coastal orography. In this case, a relatively shallow cold front approaches southeastern Australia from the ocean and transitions into a barrier jet-type flow as the front is partially blocked on the inland side of the mountains but accelerates along the coast of New South Wales as the upper disturbance moves eastward across the region. A rapidly moving along-coastal barrier jet may form, whose leading edge (the front, which resembles a topographically trapped gravity current) is often marked by a roll cloud over the coastal Tasman Sea (Baines 1980). Since this leading edge separates the preceding warm offshore flow by the cool along-barrier jet, the local term “Southerly Buster” has arisen. The situation is in some ways analogous to the Cold Air Damming situation in North America discussed above. However there are also significant differences since the Australian landmass ends at mid-latitudes, the cold air source region is the cool ocean south of Australia rather than the continent, the westerly jet in the region contributes to the Southerly Buster, and the topography of the region is low compared to that of North America. Studies with mesoscale models

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(e.g., Howells and Kuo 1988; McInnes and McBride 1993; Reid and Leslie 1999) have attempted to isolate the various roles of season, time of day, topography, surface friction and heating in the evolution of the Buster. The Southerly Buster is similar to the orographic coastal jets observed and modeled over central California by Doyle (1997). Loescher et al. (2006) used Synthetic Aperture Radar (SAR) imagery from the Gulf of Alaska to document the spatial and temporal variability of barrier jets over the ocean in that region. SAR detects centimeter-scale capillary waves on the water surface that, with some knowledge of wind direction, can be related to wind speed. Therefore SAR imagery gives high resolution spatial images of wind speeds over water. Figure 3.36 documents the different categories of barrier jets that they found and suggested. Figure 3.36a shows a classic barrier jet – the flow has an onshore component with wind speeds higher than 20 m s1 near the coastline. Figure 3.36c depicts a hybrid barrier jet – the flow has an offshore component, and offshore gap flow can be observed exiting the mainland fjords, which undergoes rapid geostrophic adjustment into a coast-parallel direction upon exiting the gap. In Fig. 3.36d, a pure gap flow case, there is no turning of the wind upon exiting the gaps, therefore no barrier jet forms. They found that about 1/3 of all barrier jets were observed to have a sharp transition between the barrier jet flow and the weaker ambient flow, and called these “shock jets” – Fig. 3.36e. This form was associated with anomalously cold, dry air over the continent (Colle et al. 2006). Variable jets were observed 23% of the time (Fig. 3.36f) in which the along-barrier flow was found to vary considerably along the coast – this was associated with more convective conditions in which it was hypothesized that higher-momentum air from aloft was transferred locally to the surface via convection. Loescher et al. (2006) observed more barrier jets in the cool season than in the spring and summer. This was true of all barrier jets, but especially so for hybrid jets. This is expected since the gap flow component of hybrid barrier jets occurs mainly during the cold season when conditions exist for a large offshore-directed low-level pressure gradient: there is a strong contrast between the cold continental air favoring high surface pressure and the warmer coastal air favoring lower surface pressure. They also found a close association between percent occurrence of barrier jets and the coastal orography, with the most frequent occurrence of barrier jets associated with the highest topography within 100 km of the coast – this is illustrated in Fig. 3.39. The median speed was found to be 20 m s1 for both classic and hybrid jets. The median width, measured from the base of the terrain to the outer edge of the barrier jet was found to be 50 km for classic jets and 60 km for hybrid jets. They found that some hybrid jets detached from the coastline over part of their length, often by about 10 km. Olson et al. (2007) note that barrier jets over southeast Alaska reach a maximum strength when the onshore flow is oriented approximately 40ı from coast parallel suggesting the influence of ambient wind direction on barrier jet intensity and evolution. At this point, it is useful to point out that not all jets blowing parallel to mountain barriers are barrier jets. Coastally Trapped Wind Reversals (CTWRs) (also called Coastally Trapped Disturbances) are a type of coastal jet that has been extensively

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Fig. 3.39 Maximum terrain height found within 100 km of the Gulf of Alaska coastline compared with the frequency of barrier jets (From Loescher et al. 2006. © American Meteorological Society. Reprinted with permission)

studied along the West Coast of North America from California to British Columbia (e.g. Reason and Steyn 1992; Bond et al. 1996; Rogers et al. 1998; Jackson et al. 1999; Nuss et al. 2000; Reason et al. 2001; and others). While there are some apparent similarities – both phenomena result in southerly flow within a Rossby radius of the coastal mountains – the initiation mechanism is quite different. Rather than being forced by the onshore flow of stratified air, CTWRs are initiated by offshore (downslope) flow at mountain crest level to the north, and the creation of lower surface pressure offshore to the north of the disturbance, creating an along barrier pressure gradient (Mass and Bond 1996). CTWRs also propagate from south to north along the coast as surface ridges and are primarily a warm-season phenomenon.

3.6.2 Theory In its simplest form, at steady-state, a barrier jet is semi-geostrophic: it is in geostrophic balance with the across-barrier pressure gradient, while in the along-barrier direction, an antitriptic balance exists, in which the pressure gradient force is balanced by inertia and friction. However this simple force balance does not adequately address the normal situation when the atmosphere is not in steady state,

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nor does it tell us much about the mechanisms or conditions under which barrier jets form. Scale analysis of the governing equations (e.g. Smith 1979; Pierrehumbert and Wyman 1985; Overland and Bond 1993, 1995) has characterized the general dynamical nature of stratified flow impinging on a mountain barrier, and can help us understand the conditions under which barrier jets form even though these studies neglect complicating factors such as time variation, mesoscale topographic variation, friction, and diabatic effects. Important atmospheric properties that determine the amount of blocking and the distance away from the barrier that blocking will occur are determined by several dimensionless numbers: the non-dimensional mountain height (HO ), Rossby number (Ro), Burger number (B), and the Rossby radius of deformation (Lr). The non-dimensional mountain height, HO D NH=U , as discussed in Sect. 3.2.2, is a measure of the importance of vertical displacement by an obstacle and tells us whether or not the cross-barrier flow has sufficient kinetic energy to overcome the potential energy needed to cross a mountain barrier. If HO < 1 the flow has sufficient kinetic energy to go over the mountain, if HO > 1 the flow will tend to be blocked by the mountain leading to upstream deceleration (Pierrehumbert and Wyman 1985). The distance of upstream deceleration, and therefore the extent of the barrier jet, is approximately a Rossby radius of deformation from the mountain crest (Pierrehumbert and Wyman 1985). The across-barrier Rossby number, Ro D U/fL is the ratio of inertial to Coriolis forces and is a measure of the importance of the Earth’s rotation on the flow. It is 1 for geostrophic flow, and 1 when the effect of the Earth’s rotation is unimportant. The Burger number, B D NH/fL D RoHO , a dynamically scaled mountain slope, defines the general hydrodynamic regime for the influence of the mountain barrier on impinging flow. Finally, the Rossby radius of deformation, Lr D NH/f D BL is the length scale at which rotation effects are as important as stratification, and represents the maximum distance upstream of blocking by the mountains. In the expressions above, U is the across-barrier (onshore) velocity upstream, f is the Coriolis parameter, L is the mountain half-width, H is the mountain height, and N is the Brunt-V¨ais¨al¨a frequency. If the Burger number, B  1, the mountain is effectively gently sloped and the flow is over the mountain barrier and quasi-geostrophic. If B  1, the mountain is “hydrodynamically steep” and blocking is complete and does not depend on the mountain half width (Overland and Bond 1993, 1995). If 0.1 < B < 1, the flow is semigeostrophic and is modified by the slope of the mountain, primarily over the mountain (Pierrehumbert and Wyman 1985). For HO > 1 (i.e. when the flow is shallow compared to the mountain height), Overland and Bond (1995) suggest that the appropriate offshore distance scale for deceleration and the barrier jet should be Lr/Hˆ D U/f (instead of Lr), because the vertical scale in this case is not the mountain height, H, but an inertial or gravity height U/N found by setting HO D 1. In other words, the flow does not “feel” the full height of the mountain when HO > 1. Overland and Bond (1995) found that scaling arguments suggest the barrier jet strength enhancement is on the order of the incident across-barrier speed for HO > 1 and on the order of NH for HO < 1. The largest barrier jet response should occur when B > 1 and HO  1, since when HO > 1 that usually means U is small, and when HO < 1, N is likely to be small

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(Overland and Bond 1995). Smith (1979) discusses the importance of the width of an elevated plateau downwind of the mountain barrier, on upstream and downstream flow. He demonstrates that far upstream, the influence of a broad plateau is to induce cyclonic turning of the wind due to stretching of a column of air as isentropes aloft are displaced upwards. This causes the flow impinging on a mountain barrier to shift to more of a barrier-parallel orientation and enhances the formation of a barrier jet near the mountain. The scale analysis discussed above gives general guidance on barrier jet formation, but is probably not applicable to many aspects of jets created by landfalling storms. These storms are not uniform and in steady state, are subject to mesoscale topographic variability, diabatic and frictional effects, and hence the scaling assumptions are violated. However idealized 2D (Braun et al. 1999) and 3D numerical simulations (Olson and Colle 2009) can provide further insight. Idealized 2D numerical simulations conducted by Braun et al. (1999) explored the importance of mountain half width, height, as well as the width of an elevated plateau downstream of the mountain barrier, on barrier jet characteristics. They found that while the upstream deceleration is determined by the mountain half width and height, it is the downstream plateau size that determines the amount of upstream cyclonic turning and hence the strength of the barrier jet. The barrier jet strength also depends on the duration of onshore flow: reaching a steady value only after the time required for the flow to cross the mountain barrier. This finding is consistent with the theoretical work of Smith (1979) and was confirmed in the idealized 3D simulations with the realistic terrain of the Gulf of Alaska conducted by Olson and Colle (2009). Therefore it is expected that wide mountain barriers or mountains with wide plateaus would have the strongest barrier jet formation.

3.6.3 Models and Forecasting Mesoscale numerical models have shown good skill at capturing the essential features of barrier jets in a number of both idealized (e.g. Cui et al. 1998; Yeh and Chen 2003; Barstad and Grøn˚as 2005; Olson and Colle 2009) and realistic numerical studies (e.g. Olson et al. 2007; Doyle 1997; Colle and Mass 1995). This suggests that NWP models with sufficient spatial resolution should be able to adequately forecast these events. With a width in the across-barrier direction of approximately 50 km, it is likely that at least 10 km horizontal resolution would be required for accurate representation of classical barrier jets and cold air damming barrier jets. In cases of hybrid barrier jets, the model must have adequate resolution to simulate both the gap flow that delivers the cold air onto the coast, as well as the barrier jet itself. Since topographic gaps in mountain barriers are typically much narrower than the across-barrier jet scale, it seems likely that models with horizontal resolutions of 1–2 km would be required to adequately simulate hybrid barrier jets when gap widths are a few km. In southeast Alaska, Olson et al. (2007) successfully simulated hybrid jets with an inner grid of 4 km horizontal resolution which was sufficient

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to resolve the Cross Sound gap which is approximately 50 km wide. Routinely operated NWP models will achieve these resolutions as computing power continues to increase. While NWP models will continue to improve their ability to forecast barrier jets, much has been learned from studies that can aid in both the interpretation of NWP, as well as the creation of rules of thumb for diagnosis and forecasting of barrier jet events. The basic ingredients of course are that there must be a flow of stable air toward a mountain barrier for a sufficiently long period of time before a barrier jet can form. However this leaves several unanswered questions such as: How high must the barrier be? Are there critical values of Hˆ or B before barrier jets can form? What factors will determine the barrier jet width and wind speed enhancement? How long must the across-barrier flow exist before barrier jets can form? A climatology of barrier jets by Loescher et al. (2006) using SAR imagery over the Gulf of Alaska found that terrain height plays a key role in discriminating locations where barrier jets may form. They found that barrier jets occurred most frequently in locations where the maximum terrain heights within 100 km of the coast exceeded 2 km (Fig. 3.38), and that the maximum topography within 100 km of the coast was more important than the terrain height at the coast in determining barrier jet frequency. Hybrid barrier jets in this location were associated with major gaps in the mountain barrier as the gap flow turned to the right due to geostrophic adjustment upon exiting the gap. The synoptic conditions conducive to barrier jet formation in this region were investigated by Colle et al. (2006) who found that cool season jets (without shock or variable features) were associated with a deeper than normal upper-level trough approaching the Gulf of Alaska, and an anomalously high ridge over the northwestern North American continent, resulting in low-level southerlies and warm advection. They found that shock barrier jets had significant cold anomalies at low levels over the interior, and that variable barrier jets had weaker low-level stability that favored mixing of higher momentum air to the surface in localized areas. Idealized MM5 simulations using the realistic topography of southeast Alaska with an inner grid of 6 km resolution conducted by Olson and Colle (2009) provide insight into both the structure and synoptic characteristics useful for forecasting both classical and hybrid barrier jets in this location and possibly elsewhere too. They found that the broad inland plateau is essential to the strength of the barrier jet and results in an anticyclonic pressure perturbation along the windward slopes of mountains, especially for mountain perpendicular flow. This acts to turn the winds into a more barrier-parallel direction as much as 500–1,000 km upstream of the mountains. The timescale for this to develop was found to be the time required for the flow to cross the full mountain barrier. They found that barrier jet width tends to be narrower when the impinging flow is more perpendicular to the barrier. Gap flow from an inland cold pool could contribute to hybrid jets when the low level ambient flow was nearly barrier-parallel – this results in a hybrid barrier jet of greater width, with a jet maximum shifted further offshore. When the ambient flow was nearly barrier-perpendicular, the gap flows were reduced and only classical

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barrier jets formed. The greatest wind speed enhancements (nearly two times the component of ambient flow that is normal to the barrier) were for ´ • High Hˆ (2.5–3.3) consistent with other studies (Olafsson and Bougeault 1996; Braun et al. 1999; Petersen et al. 2003; and also with Colle and Mass 1995 for cold air damming east of the Rocky Mountains) • Lower wind speeds, and • Ambient wind directions that are 30–45ı from barrier-parallel. Olson and Colle (2009) also found that the barrier jet height was most dependent on wind speed with strongest winds (25 m s1 ) resulting in the deepest jets (900 m). Scaling arguments can provide guidance on the across-barrier scale, with the Rossby radius of deformation, Lr D NH/f defining the maximum barrier jet width, and this value being reduced by a factor of 1/HO to Lr=HO when the non-dimensional mountain height is greater than one.

3.7 Summary This chapter detailed flow phenomena that are dynamically forced when wind interacts with orography. Flow approaching a mountain barrier, will pass over it, flow through gaps or valleys that dissect it, or be blocked by the mountain and diverted horizontally around it. As we have seen, each of these scenarios results in different dynamically-driven wind phenomena. When air is able to pass over a mountain barrier under specific conditions, mountain waves are generated that can result in lee waves, rotors and downslope windstorms. Air flowing through channels that dissect a mountain barrier can result in gap flow arising from along-channel acceleration. If the air is blocked by a mountain barrier and diverted around it, then a barrier jet may form. This chapter described these various phenomena. Mountain waves are a common and important feature of atmospheric flow in mountainous regions. Long wavelength mountain waves have a tendency to propagate vertically into the middle and upper atmosphere where the waves eventually break, causing turbulence and a drag force on the flow. Shorter wavelength waves tend to propagate horizontally as well as vertically and wave motion appears downwind of mountain ranges. Wave reflection, caused by height variations in wind and stability, can enhance the downwind propagation through the formation of trapped lee waves in some circumstances and downslope windstorms in others. Mountain waves of sufficiently large amplitude can give rise to severe turbulence in the troposphere. The term mountain-wave rotor is used to describe horizontally oriented vortices which form under the wave crests. Rotors can be broadly classified into two types. The type I rotor is probably the most common and forms beneath the crests of trapped lee waves. Its formation is linked to boundary layer separation, which is itself caused by the strong pressure gradient exerted on the near-surface flow by the lee waves aloft. The rarer type II rotor resembles a hydraulic jump and is a deep layer of severe turbulence which forms downwind of the mountain,

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associated with low-level wave breaking and downslope windstorms. Its structure is not as well defined as the type I rotor and it is less well understood. Both types of rotor pose a significant risk to aviation safety and present a difficult challenge for forecasting. Downslope windstorms are a consequence of large-amplitude mountain waves that can form downwind of a mountain barrier in which the low level winds are accelerated on the lee slope, sometimes to two to three times the wind speed at mountain top level. They resemble the hydraulic flow of fluid over a rock with shallow supercritical flow corresponding to the strong downslope winds on the lee slope which terminate in a hydraulic jump. The circumstances resulting in this flow can arise in a few ways. If the atmosphere has an upstream layered structure that already resembles the structure of classical hydraulic flow, then the transition to a lower shooting flow is facilitated. If the atmosphere above the ridge has reverse shear (cross-barrier winds decreasing with height either through changing wind speed or direction) or decreasing stability above a lower stable layer then this may result in a mean-state critical layer which can act to reflect upward propagating mountain waves and decouple the lower layer, creating the conditions for shallow supercritical flow on the lee slope. If the atmosphere has constant stratification and the non-dimensional mountain height is sufficiently large, then vertically propagating mountain waves may break in the upper troposphere, creating a stagnant turbulent zone in which the cross barrier wind goes to zero resulting in a self-induced critical layer that acts like a mean-state critical layer. Gaps or valleys that dissect a mountain provide a means for an air mass to cross a barrier. Potential temperatures on the upstream side have to be lower than in the air mass downstream for asymmetric gap flows to develop where the layer, which flows through the gap, thins and accelerates with the highest speeds occurring downstream of the narrowest part of the gap. Gaps can be level or elevated and asymmetric gap flows are found all over the world. Hydraulic, non-linear theory best describes gap flows. An analytical solution exists even for continuously stratified flow, where nearly neutrally stratified and stagnant layers form above and/or below the gap flow layer to isolate it from the flow aloft and/or the underlying terrain (on the upstream side). Usually it is the narrowest section of the gap, which forms a “control” for the flow. Given a particular value of the upstream depth of the gap flow layer, only one value of the flow rate through the control is possible when flow transits from subcritical on the upstream side to supercritical on the downstream side, where it will eventually adjust to the downstream air mass in a hydraulic jump. Shallow water models are successful in numerically simulating gap flows. Full NWP models currently still face challenges to (1) properly resolve the underlying topography, to (2) handle turbulence near the ground and in the shear layer at the top of the gap flow and in the hydraulic jump, and to (3) contain the details of the air mass differences across the gap and the processes producing the hydraulic flow. An ingredients-based forecasting method identifies processes that lead to the formation of air masses with different characteristics on both sides of the gap. Barrier jets are elevated wind maxima that blow parallel to a mountain barrier on its windward side. When flow approaching a mountain barrier is blocked and

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diverted around the mountain then barrier jets may occur if the flow is blocked by the barrier for hours to days or longer. The blocked flow is forced to move up the barrier, and cools adiabatically creating higher pressure along the slope which acts to decelerate and block the flow. Geostrophic adjustment turns the flow left (right) in the northern (southern) hemisphere and a low-level barrier-parallel jet is formed between the surface and the mountain crest. Barrier jets have been observed in many places – and can occur in the extra-tropics (i.e. where rotational effects are important) wherever stratified flow approaches a significant mountain barrier. They have been described as classic barrier jets along the western slopes of mountains, as hybrids where gap flow of cold air from the east side of mountains contributes the low-level cold air needed for stratification, as cold-air damming events along the eastern slopes of mountains, and as resulting from the interaction of fronts as they approach mountains. Understanding of dynamically forced flows has progressed considerably thanks to observational, theoretical, numerical modeling (Chaps. 9 and 10), and computational advances over the past three decades. We have progressed from a quite limited linear, two-dimensional, “dry”, constant stability/constant wind understanding of these phenomena, to the consideration of more realistic conditions. Specifically, an understanding of the importance of effects such as non-linearity, three-dimensionality, moisture, varying wind and stability profiles, and boundary layer (Chaps. 2 and 5) effects, are now beginning to be more fully understood. As knowledge has developed, the consideration of these other factors has become increasingly important. Acknowledgements The authors thank the volume editors (Fotini Kapodes Chow, Stephen De Wekker and Bradley J. Snyder) for keeping us on track with their encouragement and organization, and for all of their efforts in bringing this book to completion. We also thank the three anonymous reviewers who provided many helpful comments that improved the chapter. We thank the authors and organizations who allowed us to use many of the figures in this chapter. The first author would like to acknowledge partial funding support of his research program from an NSERC Discovery Grant.

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Chapter 4

Understanding and Forecasting Alpine Foehn Hans Richner and Patrick H¨achler

Abstract This chapter focuses on the history, physics, climatology, forecasting and the broad effects of Alpine foehn on human populations. In the European Alps, foehn winds have been studied since the mid-1800s. The main focus of the investigations was the question of why foehn winds are so warm. While it soon became clear that adiabatic processes provide an explanation, the role of wet adiabatic rising on the upwind side of the Alps continued to be strongly debated. The so-called textbook theory for foehn – heat gain by wet adiabatic, forced lifting on the upwind side followed by dry adiabatic descent in the lee – represents only an extreme situation. Foehn occurs also with partial or complete blocking of the upwind air mass, i.e., with limited or no heat gain by wet adiabatic expansion. The second focus is on processes which lead to descending air masses after passing the mountain ridge. A discussion of the most important processes shows that there seems to be no theory which is applicable in all situations. Forecasting foehn is still a challenge to meteorologists. While the general foehn situation can be predicted reliably, today’s numerical models still often poorly simulate the sudden break in of potentially devastating foehn air in the lee. Efforts to improve this must continue because foehn storms have a significant societal impact (threat to transportation systems and massive increase of fire danger) as several recent incidents show.

H. Richner () Institute for Atmospheric and Climate Science (IACETH), ETH Zurich, Universit¨atsstrasse 16, Zurich CH-8092, Switzerland e-mail: [email protected] P. H¨achler Federal Office of Meteorology and Climatology MeteoSwiss, Kr¨ahb¨uhlstrasse 58, Zurich CH-8044, Switzerland e-mail: [email protected] F. Chow et al. (eds.), Mountain Weather Research and Forecasting, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-4098-3 4, © Springer ScienceCBusiness Media B.V. 2013

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4.1 Introduction Foehn is a prominent meteorological phenomenon occurring in practically all extended mountain ranges. “Foehn” is a generic term for a downslope wind that is strong, warm, and dry; WMO (1992) defines foehn wind as a “wind [which is] warmed and dried by descent, in general on the lee side of a mountain.” Its societal impact is considerable, be it in a favorable manner with regard to climatology (mild climate) or in a negative way (windstorms) with respect to aviation and traffic. Outside the Alps, foehn storms are often called downslope windstorms. While the term “foehn” originated in the European Alpine area, foehn winds occur all over the world where there are extended mountain ranges. Foehn winds are even observed in places where the mountain ridges are not that high such as in the United Kingdom. Depending on the place, foehn winds might have a different name such as, e.g., Chinook (North America) or Helm wind (UK). The rapid temperature rise and the dry air of foehn type winds have also led to numerous local, descriptive names such as “snow eater,” “grape cooker,” etc. Examples of some of these flows are given in Chap. 3, Sect. 3.4. This chapter continues the discussion of dynamically-driven winds from Chap. 3, but specifically focusing on the combined history, physics, climatology, forecasting and the broad effects of Alpine foehn on human populations. Alpine foehn presents a significant forecasting and modeling challenge, and has been the topic of study for close to two centuries. This chapter highlights this particular flow phenomenon because of the breadth of its impact and the peculiar challenges associated with forecasting. The chapter centers on recent results of the Mesoscale Alpine Program (MAP) and on ongoing research activities mainly in Switzerland, but touches also on activities in Austria and France. For research on foehn-type winds in other parts of the world, see e.g. Brinkmann (1974) (Rocky Mountains), Raphael (2003) (Santa Ana Winds), or McGowan et al. (2002) (New Zealand Alps). The overview encompasses statistical analyses of foehn occurrence in different Alpine regions, on the interaction of foehn flow and the cold pool, and on current techniques for forecasting foehn-related windstorms. Figure 4.1 shows a topographical map of the Alpine massif. A detailed list of terms and definitions is provided in the appendices to help clarify the varying terminology used to describe foehn events.

4.2 History of Foehn Research For many decades, foehn was the outstanding example to explain thermodynamic processes and the role of latent heat in the atmosphere. Hence, nearly every textbook contains a graph similar to Fig. 4.2. Driven by the synoptic scale pressure field, humid air is forced towards a mountain range. As it ascends by forced convection, it cools dry-adiabatically until reaching saturation. From then on, the rise is

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Fig. 4.1 Topographical map of the Alpine massif. The two dashed lines show the Gotthard cross section (western) and the Brenner cross section (eastern). Only those Alpine regions are labelled which are referred to in the text

Fig. 4.2 Schematic description of the “textbook theory” of foehn. Diagrams similar to this one are found in many textbooks on meteorology

wet-adiabatically until the air reaches the crest of the mountain range; as a consequence, clouds are formed and precipitation occurs. As the air descends in the lee of the mountain, it is heated dry-adiabatically; as consequence, the air becomes dry and reaches temperatures that – at equal elevation – are higher than the original

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Fig. 4.3 The “proof” that Hann was aware of the two types of foehn: Original illustration depicting Hann’s (1866) foehn theory in Ficker (1920). “Nordseite”: north side; “S¨udseite”: south side; “F¨ohn, Erw¨armung”: foehn, warming; “Luft in Ruhe”: air at rest. Note that north–south is reversed with respect to Fig. 4.2

temperature on the windward side. Because of the very clean and dry air on the lee side, visibility is outstanding (D>foehn window1 ), and over the crest, the piled-up clouds can be seen as the D> foehn wall (Fig. 4.2). As beautiful as this example is, in reality foehn winds often do not follow this classical textbook theory that is attributed to Hann (nineteenth century). In his “Lehrbuch der Meteorologie”, Hann (1901) describes both types of foehn (see Figs. 4.2 and 4.3) and mentions that many forms in between the two have been observed. Seibert (2005) concludes that Hann’s explanation was seriously distorted in the first half of the twentieth century. Particularly Austrian researchers repeatedly questioned the validity of the textbook approach. In his book “Environmental Aerodynamics”, Scorer (1978) wrote a chapter entitled “Foehn Fallacy” which gives at least two explanations for the warming of air masses which do not require the heat of condensation on the windward slope of the mountain ridge: mechanical stirring of a stably stratified air mass, and – more important – blocking. In the first case, the lower part becomes warmer and the upper part cools because the mixing produces a constant potential temperature, in the second case, potentially warmer air subsides in the lee. Analyses of data collected during and after the Alpine Experiment ALPEX in 1982 clearly confirmed that, at least in the Brenner cross-section, there was blocked air during most foehn cases. This is particularly true for the “century foehn” of November 8, 1982. In the Ticino region, i.e., south of the Gotthard, however, there was some light precipitation towards the end of this extreme foehn event (hourly mean winds up to 35 m s1 and gusts over 50 m s1 at the station G¨utsch, see Fig. 4.7). It is a little disturbing that not only popular publications but also modern textbooks often present only the theory depicted in Fig. 4.2 without discussing alternative foehn schemes. Austria and Switzerland were clearly the hotspots for foehn research. Innsbruck (Austria) is the place where scientists like Hann, Ficker, Hoinkes, Kuhn, Dreiseitl,

1

Terms preceded by “D>” are further explained in Appendix A.

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Steinacker, Seibert, Hoinka, Mayr, and Gohm have carried out their research; in the Swiss Alps it is mainly Billwiller, Wild, Streiff-Becker, Sch¨uepp, Frey, Gutermann and others who have made observations and developed their theories since the nineteenth century. In Switzerland, research was not quite as active as in Austria. However, in Switzerland, monks and pastors meticulously observed and recorded foehn events, this being particularly true for the Reuss Valley. Thanks to them, a quite homogenous time series for foehn events in Altdorf is available since 1864.

4.3 Characteristics of Foehn 4.3.1 Textbook Theory and Real Dynamics South foehn occurs in the Alpine region when a synoptic pressure field according to Fig. 4.4 exists. (For simplicity the following discussions is restricted to south foehn, however, some remarks related to north foehn and west foehn are given in Sect. 4.3.4.) Nowadays it is widely accepted that foehn winds can and do occur without precipitation. The lower the crest height, the more likely it is that advected air simply crosses the mountain ridge and, subsequently, descends, as already debated by Hann, Ficker and others and as depicted in Fig. 4.3. Trajectory analyses as well as tracer studies with ozone confirm this mechanism (Baumann et al. 2001).

Fig. 4.4 Synoptic pressure field producing foehn in the Alps

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Fig. 4.5 Suggested parameters for characterizing foehn types. A: depth of blocked air, C: crest height,  : difference in potential temperature

The fact that much foehn research was and still is being done along the rather flat Brenner cross-section, explains why in Austria the textbook theory was more fiercely queried than, e.g., in Switzerland. As a matter of fact, Hann (1866) already distinguished between foehn type I or “Swiss foehn type” (for what is here called the textbook theory) and foehn type II or “Austrian foehn type” (for the airflow without gain of latent heat and with reduced or no precipitation on the windward side). These two foehn types must be regarded as extremes, as anything in between can be observed. It must be stressed that even heavy precipitation on the upwind side is no proof for gain of latent heat; precipitation can stem from the lower air mass that is not part of the foehn flow. For describing a foehn case, it would be desirable to use as additional characterizing parameters (a) the height of the internal boundary between the lower, blocked air and the pressure driven foehn flow aloft, and (b) the difference ™ between the potential temperature of the two air masses (see Fig. 4.5). If sufficient information on the vertical structure is available, this parameter can be determined by trajectory calculations. In a textbook foehn case (i.e., type I), the value for A would be zero; in a foehn situation with total blocking on the upwind side (i.e., type II), the value for A would correspond to the ridge height C. The value for A could be expressed either in absolute units or in percent of the ridge height. There are at least two reported cases when foehn winds were observed simultaneously on both sides of the same mountain range (Frey 1986). This can only be explained by assuming subsidence of significant air masses over the ridge. In this 1986 event, south winds were in excess of 40 m s1 north of the Alps! On the other hand, it would be wrong to dismiss textbook theory completely. Observations clearly show that heavy precipitation can and does occur on the windward side of high mountain complexes during foehn. There are indications that this is more often the case south of the (higher) Gotthard than south of the (lower) Brenner massif. Although this suspicion has been brought up repeatedly after ALPEX, there are no statistical analyses that would prove this, and no firm statement can be made.

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4.3.2 The Effect of Topography Foehn areas are primarily defined by topography. Basically, airflow penetrates a given valley more easily the better the valley axis is aligned with the flow, and hence the fewer ridges further downwind hinder the flow. This situation can be described by saying that the flow is diffluent, the degree of the diffluence being controlled by topography. Based on these principles, the topography defines the foehn areas. In general, major valleys perpendicular to the ridge represent the areas with the highest foehn frequency (see Sect. 4.5). Valleys have a strong channeling effect on the flow. Because the cross section decreases as the flow further penetrates into the valley, the wind speeds can be higher near the ground than they are above. As observations show, the channeling effect (in the sense that the valley axis determines the direction of the flow) can reach up to heights well above the crest of the mountains bordering the valley in question. A forecaster’s rule says that foehn winds rarely descend more that 2,000 m behind the crest over which they streamed in. For this reason, foehn is seldom experienced in the region of Lake Thun, a tourist area just north of the Jungfrau region in Switzerland. A sound explanation in terms of dynamics for this rule is not available. When talking about foehn frequency at a given location, it is important to exactly define what is meant by saying, “There is foehn”. For some people it is sufficient to have a foehn airflow above the location which does not reach the ground, for others, the winds must actually touch down. During the winter period September to March, foehn reaches the downtown area of Zurich, Switzerland, on average only on 2–3 days, however, on 50–70 days, there is a foehn situation where the downtown remains in the calm cold pool while a possibly strong, certainly warmer foehn airflow exists a few hundred meters above. In some cases it is very clear whether foehn is present or not (see next section). However, for a foehn climatology, the definition of foehn can become crucial and problematic. Barry (2008, p. 173) discusses this issue and gives examples for definitions used in different foehn climatologies. The “Alpine Research Group Foehn Rhine Valley/Lake Constance” (AGF) has adopted objective definitions for both manual (AGF 2007) and automatic (see Sect. 4.6.1) foehn identification.

4.3.3 A Real Example of Foehn Characteristics Figure 4.6 shows how foehn manifests itself in one of Switzerland’s important foehn valleys, the Reuss Valley which is part of the so-called Gotthard crosssection (Fig. 4.7). The rise of temperature, the drop in relative humidity, the onset of high winds, and the constant wind direction occur simultaneously within minutes. Consequently, the onset and the breakdown of foehn can easily be determined. This is true for almost any foehn station that is located in the center of a not too broad foehn valley.

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Fig. 4.6 Example of foehn in Altdorf on January 2–7, 2008 as observed by the surface station. The horizontal axes are time axes, date and time is indicated below the first frame. TT temperature, UU humidity, ff wind speed, dd wind direction. The two red vertical lines mark the simultaneous abrupt changes in the variables at the onset of the main and of a secondary short foehn phase. Note how clearly foehn can be identified (Data kindly provided by MeteoSwiss)

Figure 4.6 also demonstrates that the breakdown of a foehn occurs usually in several phases. Or, as one of our colleagues once put it, foehn breakdown is a gigantic battle between two air masses, namely the foehn and the approaching cold front. As the foehn weakens, the cold air moves in, only to be pushed back for a limited period, a back-and-forth process which is repeated several times before the foehn flow breaks down for good.

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Fig. 4.7 The so-called Gotthard cross-section, the only south–north profile with only one ridge, and valleys practically perpendicular to it. In the south is the Leventina, in the north the Reuss Valley. The distance between Lugano and Altdorf is almost exactly 100 km

Table 4.1 Characteristic parameters for stations on the upstream side, the ridge, and the lee side for March 10, 2008, 1200 UTC (Meteorological data kindly provided by MeteoSwiss) Param z (m) p (hPa) T (ı C) ™ (ı C)

Lugano 273 970.0 6.5 8.9

Piotta 1,007 887.1 2.3 11.9

G¨utsch 2,287 752.8 4.5 18.1

Altdorf 449 943.1 13.1 17.9

Figure 4.8 shows a foehn occurrence, which proves that there are cases which indeed follow the textbook theory. There is significant precipitation and south wind on the upwind side. Table 4.1 shows that on the top of the ridge the potential temperature is markedly higher than on the upwind side (for the location of the stations see Fig. 4.7). Precipitation on the windward slope alone is not sufficient proof for the textbook theory, it merely indicates blocking. An increase of the potential temperature along the upwind slope, however, implies forced advection and, consequently, a type I foehn. For the Mesoscale Alpine Program, MAP, special efforts were made to densely instrument an area for foehn studies in the Rhine Valley (Richner et al. 2005). For some foehn cases, detailed investigations of the three-dimensional structure of foehn were made (Drobinski et al. 2003). A general summary of the main results related to airflow over and in mountains can be found in Drobinski et al. (2007). In these, the distinction between D> “shallow foehn” and D> “deep foehn” that had evolved during the last decades was clearly found in the life cycle of the foehn episode. As expected, compared to simple mountain cross-sections (like the aforementioned Gotthard cross-section), complex topographical features cause significantly higher complexity of foehn flow; a glance at the topography shown in Fig. 4.9 makes this statement understandable.

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Fig. 4.8 A foehn case on March 10/11, 2008 with precipitation on the upwind side. The horizontal axes are time axes, date and time is indicated below the first frame. Top frame: precipitation (RR) in Lugano (blue) and Magadino (red); next frames show temperature (TT), humidity (UU) and wind (ff ) for Altdorf (red), Lugano (blue), and G¨utsch (green); all data are surface data. The station Magadino lies 18 km north of Lugano, it is included to give a more representative measure of the precipitation intensity (Data kindly provided by MeteoSwiss)

Model runs for a MAP foehn case concluded that the simulation outputs essentially confirm the observed foehn dynamics (Jaubert and Stein 2003). However, it is also realized that the role of passes and valleys is not fully understood yet.

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Fig. 4.9 Topography around the Rhine Valley where foehn studies during MAP were conducted (Drobinski et al. 2003, reproduced by permission of Wiley and Sons)

Fig. 4.10 TKE values in the lee of the Alps during foehn. Yellow: values measured by aircraft, blue: values computed by the French “meso-NH” model (Lothon 2002, reproduced by permission of Marie Lothon)

At any rate, for a reliable foehn forecast, today’s mesoscale models are not yet sufficiently accurate, this despite the fact that they do produce realistic flow and temperature fields. Turbulence, on the other hand, is very poorly reproduced in model runs. Computed turbulent kinetic energy (TKE) values were orders of magnitudes lower than those observed by aircraft (Fig. 4.10). A detailed study of the observed turbulent properties of Alpine foehn events is found in Lothon et al. (2003).

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4.3.4 Foehn from Directions Other than South As mentioned, Alpine foehn also occurs in the reverse direction, i.e., with a northto-south airflow. This north foehn is almost always connected with precipitation in the north, i.e., north foehn does often follow the textbook theory. In addition to the difference of the dominating mechanisms, there are additional differences between south and north foehn. North foehn blows in the direction of the positive north–south (i.e., meridional) temperature gradient, hence, the warming effect of the foehn is less pronounced because the ambient temperature in the lee is also higher. Nevertheless, because of its low humidity, north foehn regularly dries the extended chestnut forests in southern Switzerland, and forest fires occur recurrently during north foehn season. Strong north foehn occurs also regularly in the Trentino, in South Tyrol, and in the Lombardy region of Italy; particularly strong events such as the one on January 27/28, 2008, are called “foehn bollente” (bollente [Italian] D hot, boiling). In the Piedmont region (Northern Italy, west of Milan), foehn occurs with westerly flow because the Alps bend here towards the south. West winds coming from France over the Ligurian Alps and the Maritime Alps (i.e., the part of the Alps between France and Italy, see Fig. 4.1) generate foehn with all its attributes in the region of Turin (Musso and Cassardo 2004; Di Napoli and Mercalli 2008). In France, very little research on foehn has been published. Buchot (1977) compared the foehn winds blowing from northeast to west in the Tarantaise (basically the region of the Is`ere Valley in Savoy) with the south foehn in Austria and Switzerland. From a statistical analysis covering 15 years, he concluded that there are no significant differences in the characteristics.

4.4 Foehn Dynamics 4.4.1 Leeside Motion Probably the least understood mechanism in the flow dynamics is the behavior of the air masses after passing the mountain ridge. Why does the air descend and not simply continue at the same height level? This question is even more justified by the fact that its potential temperature is in most cases higher, i.e., that a stable stratification is present! Steinacker (2006) has compiled the different theories that have emerged over the last century; the six theories summarized here follow largely his work; Figs. 4.11–4.16 are slight modifications of those found in Steinacker (2006). Probably the first person to write about the problem of the descending air was Wild (1901), a Swiss physicist who became interested in meteorological problems because he realized that weather influenced his astronomical observations. Quite some time later, Streiff-Becker (1933) came up with the so-called vertical aspiration

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Fig. 4.11 Schematic representation of the vertical aspiration theory after Streiff-Becker (1933)

Fig. 4.12 Schematic representation of horizontal aspiration theory after Ficker (1931). Solid lines represent isentropes before, dashed lines isentropes after the aspiration by the low

Fig. 4.13 Schematic representation of lee waves. Solid lines represent isentropes

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Fig. 4.14 Solenoid theory according to Frey (1944): effect of the rotational term due to the noncoincidence of temperature and pressure surfaces

Fig. 4.15 Schematic representation of the waterfall theory according to Rossmann (1950)

Fig. 4.16 Schematic depiction of the hydraulic jump theory according to Schweitzer (1953)

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theory (Fig. 4.11), an explanation which builds on the ideas of Wild, that potentially warmer air moves over colder air. After passing the ridge, it successively removes the stagnant, potentially colder air by turbulent erosion. By this process, the potentially warmer air from above sinks gradually into the valleys, replacing the colder air masses. In 1912, Ficker published the so-called horizontal aspiration theory or passive replacement flow theory (Fig. 4.12), a concept that he slightly modified again in 1931 and 1943. It was based on an earlier hypothesis by Billwiller (1899): An approaching low over the Atlantic sucks the near-ground air masses away, causing the potentially warmer air above to descend. The topography prevents the advection of air from the sides. Ficker assumed that air would flow out of the valleys just like water would flow out of a basin. A south–north oriented pressure gradient would cause an (ageostrophic!) near-surface flow. Hence, foehn is nothing but a replacement flow for the air lost in the valleys due to the depression. As a consequence, all places at a given elevation would simultaneously be subjected to the adiabatically warmed foehn air that represents this southerly replacement flow. Observations showed that flow over mountains caused the formation of waves that extend well beyond the obstacle (see Sect. 3.2.2 by Jackson et al.). Lyra (1940) and Queney (1948) were the first to present a theoretical analysis of waves in the lee of a mountain massif. Given the streamlines that emerged from their computations, the sinking of air masses in the lee could be regarded as a forced downslope motion (Fig. 4.13). In their often-referenced paper, Klemp and Lilly (1975) provide a detailed analysis of a strong downslope wind induced by lee waves such as can occur with foehn. They state that the observed amplification can occur only “if the upstream wind and stability profiles lie within sharply limited but plausible ranges.” Hence, depending on temperature, humidity, and wind profile, such a mechanism may be responsible for the downslope flow in certain cases, but will not in general. Based on observations, Frey (1944) developed the so-called solenoid theory (Fig. 4.14). Measurements showed that temperature in the lee of the Alps increases towards the north while, at the same time, the pressure falls. Hence, isothermal and isobaric surfaces are not at the same angle, resulting in a rotational acceleration (or solenoid). According to Frey’s theory, the kinetic energy of the moving foehn is not only determined by the pressure gradient, but also to a substantial degree to the strength of the rotational term; the kinetic energy is sufficient to remove the cold pool by a plain mechanically forced replacement. Rossmann (1950) and Sch¨uepp (1952) saw the cause for the descent of the flow in the D> foehn wall, i.e., in the clouds formed above the crest of the mountain ridge (Fig. 4.15). They assumed that the air in the cloud is colder and, therefore, denser than the air outside the cloud. This would result in a downward acceleration, the kinetic energy to be sufficient to penetrate the lee side valleys. This explanation became known under the descriptive name waterfall theory. Using fluid dynamics theory, Schweitzer (1953) proposed the phenomenon of the “stationary hydraulic jump” as an explanation for the descent of the foehn air after

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passing the ridge (Fig. 4.16; see also Sect. 3.2.3 by Jackson et al.). This phenomenon is observed (and theoretically well understood) on rivers and dams when the water is discharged at high speed into a region of significantly lower flow speed. The result of this transition is an abrupt rise of the slower moving fluid. Obviously, there is no generally applicable theory. Meteorologists have to live with the fact that various physical mechanisms are needed to explain the same phenomenon, but occurring under different conditions. It seems that the lee wave theory is rarely a reasonable explanation, while that hydraulic jump theory is often a quite plausible description of the observations. Brinkmann (1971) and Hoinka (1985a) discuss in detail how large amplitude lee waves and/or hydraulic jumps accelerate foehn flow in valleys perpendicular to the ridge. The solenoid theory explains quite well thermally driven wind fields such as mountain-valley wind systems. Whether it is an explanation in the dynamically driven foehn flow is not clear, here the rotational term could just as well be the result rather than the cause. The waterfall theory might be useful to explain local effects, however, it can hardly be regarded as general mesoscale phenomenon controlling the lee side flow. (For additional theoretical discussions related to these issues, see Chap. 3 Sect. 3.2 in this book.)

4.4.2 Dimmerfoehn Under certain conditions, precipitating clouds may be drawn over the ridge, far into the lee-side valleys. Nevertheless, foehn is present here. As a consequence of the significant cooling due to evaporation, the dewpoint depression is rather small, typically 1–7 K instead of the 10–20 K observed normally. An extreme case happened on November 16, 2002, when there was foehn in Altdorf with 95 mm of precipitation. This type of foehn is called D> dimmerfoehn (“dimmerig” or “dimmrig” [Swiss German] meaning dim, obscure). The airstream aloft shows typically cyclonic shear, which transports strong condensation from S to N. It was first described in the first half of last century by Swiss researchers and prompted a fierce and not always very scientific dispute between Austrian and Swiss meteorologists. The reservation Austrians had against this foehn type may be explained by the fact that dimmerfoehn is very rare; there are years without any such case, and it seems that this foehn type occurs even more rarely in Austria. Sometimes, the expression “dimmerfoehn” is also used for situations with southerly flow and strong haze, often caused by advected Saharan dust. Such a case occurred on April 27, 1993; it is well documented in Burri et al. (1999). (It must be noted that the definitions found for dimmerfoehn in different publications are not entirely consistent! The explanation given above is based on the original description by the Swiss meteorologist Streiff-Becker (1947), it was somewhat modified by subsequent, more accurate observations.)

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4.4.3 Interaction with Cold Pool When foehn winds descend in the lee of a mountain ridge, they clash with much cooler, stagnant air. If topography allows, this cold pool is usually flushed away, typically within hours. However, there are many cases where topography prevents the outflow of the cold pool; the Wipp and Inn Valley in Austria (with the Nordkette as downstream obstacle), and the lower Reuss Valley in Switzerland (with the Jura Mountains as obstacles) are prominent examples for this constellation. In addition, mere bends in the main valley axis can prevent the cold pool from being flushed out rapidly. On the Swiss Plateau, i.e., the area between the Alps in the south and the Jura Mountains in the north, often a cold pool of a few hundred meters depth remains while foehn flows over it. In winter, such a situation can persist for up to several days. The cold pool has a wedge-like form, the angle is typically 2ı . Of course, air in the cold pool remains calm, while the line where the foehn flow leaves the ground to flow over the cold air is very gusty. Over water, this border is easily seen by a spray line and by the haze usually present in the cold air. As the strength of foehn flow increases, it works its way downstream, gradually forcing the cold pool back. This can occur by three possible mechanisms or any combination thereof: (a) heating by convection, (b) erosion of the top by mixing and entrainment, and (c) static and dynamic displacement. During MAP, an attempt was made to directly measure the heat flux near the internal boundary between foehn and cold air by a small aircraft. The daily mean found was about 15 W m2 , almost exactly the same value that was measured at the ground. Hence, heating by convection and mixing at the top of the cold pool seem to be of similar importance for cold pool removal.

4.4.4 Waves Figure 4.17 depicts the two types of waves which commonly occur with foehn, namely lee waves at about crest height and above, and shear-induced gravity waves on top of the cold pool. Lee waves or simply mountain waves are stationary, hence they belong to the group of standing waves. Their wavelength is – depending on the width and shape of the mountain massif – anywhere between 5 and 10 km. Also the amplitudes depend on the geometry; they are typically of the order of 100–200 m. The amplitudes are largest at some intermediate level just above ridge height. (See also Chap. 3, Sect. 3.3.) In Alpine D> south foehn, the air has passed over the Mediterranean Sea and picked up substantial moisture. Consequently, when the air reaches saturation by adiabatic expansion at the wave crests, lens-shaped clouds (cumulus lenticularis or altocumulus lenticularis, see Fig. 4.18, D> foehn cloud) may be formed. Naturally,

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Fig. 4.17 The two wave types occurring with foehn: (a) above crest height the mountain lee waves (sometimes also called D> foehn waves) and (b) on top of the cold pool shear-induced gravity waves

Fig. 4.18 Lenticularis clouds over the Monte Rosa Massif near Zermatt in the Swiss Alps (Reproduced by permission of Andreas Fuchs)

these clouds are also quasi-stationary. Glider pilots were the first to describe lee waves; this phenomenon enables them to reach very high altitudes by cleverly utilizing the strong updrafts. However, lee waves can also cause severe turbulence, particularly when they break or when rotors are formed. Numerous accidents with small aircraft, commercial aircraft, balloons, paragliders, etc. were caused by lee waves or by turbulence associated with them. For a more thorough discussion of lee waves and rotors, see the reports of a recent study in the Sierra Nevada (Grubiˇsi´c et al. 2008; Grubiˇsi´c and Billings 2008), or the Pennines (Sheridan et al. 2007); the interaction between foehn-type wind and large amplitude lee waves is treated in detail by Beran (1967). Finally, a broad discussion is found in Chap. 3, Sects. 3.3 and 3.4.

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Fig. 4.19 Waves on cold pool in the Rhine Valley, looking SE. Foehn is from right to left, notice the weak counter flow in the cold air mass (Reproduced by permission of Andreas Walker)

Fig. 4.20 Waves on the cold pool seen by a sodar. In this time-height diagram, the height covered is 900 m, the total recording time about 2 h. Observations were made on October 1, 1976, about 45 km north of Altdorf in the Reuss Valley (at the north end of Fig. 4.7 in the cold pool) (Reproduced by permission of Werner Nater)

At the internal boundary between foehn flow and cold pool, there is a strong shear as well as a large temperature gradient. Wind speed in the foehn air might be typically 20 m s1 while it is virtually zero in the cold pool, the temperature differences between the two air masses is typically 5–15 K. Shear and different densities (due to temperature difference) cause gravity waves on top of the cold pool by the same mechanism by which waves appear on a lake’s surface when the wind blows over it. Waves on the cold pool can be seen when strong haze or fog is found in the cold air mass (Fig. 4.19), however, they can be made visible indirectly, e.g., with sodar, RASS or lidar (Fig. 4.20). These waves produce small fluctuations in surface pressure (0.1–1 hPa). Depending on the vertical profile of temperature and wind, their period is somewhat longer than the Brunt-Vaisala period (of the

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order of 10–20 min). Unlike lee waves, gravity waves propagate with a phase speed of roughly half the shear. Obviously, period (measured at a fixed location), phase velocity and wavelength are interdependent as described by the wave equation.

4.4.5 The Three-Dimensionality of Foehn While it is the aim of any science to find common mechanisms, to formulate general laws, describe systematic behavior etc., it must not be forgotten that in reality no two foehn cases are exactly alike. The case studies presented here were chosen more or less arbitrarily as “typical” and recent examples. Many disputes happened only because scientist X adjusted the theory to a specific foehn case while scientist Y did the same, but (a) in another topography und (b) for another foehn case. Hence, generalization must always be made with great caution. Insight into processes can be gained both by statistical analyses of many cases and by detailed case studies. While systematic statistical analyses of a sufficiently large number of foehn cases is lacking, there are numerous case studies, many of them very detailed. In the above discussions, foehn mechanisms are treated in two dimensions only. For a more precise analysis, the third dimension must, of course, be taken into consideration, too. However, if this is done, generally valid statements can only be made for the particular topography and the particular meteorological situation. It is obvious that tributary valleys do play an important role, and it is to be expected that a kink in the valley’s axis changes the flow pattern. But each synoptic weather pattern, and each vertical profile has its distinct effect on the dynamics and thermodynamics on the air masses involved. Because foehn represents an airflow more or less perpendicular to a mountain ridge, and because there are often gaps or passes in the ridges, there is a close connection between foehn and D> gap flow. The dynamics of foehn-related gap flow manifests itself in a particularly clear manner along the Brenner cross section, this because (a) the topography in the ridge area is well suited and (b) because foehn occurs here sometimes without clouds over the ridge and rarely with heavy upwind precipitation. Further details on D> gap flow and foehn can be found in Gohm and Mayr (2004), in Gohm et al. (2004), and in Chap. 3, Sect. 3.5 in this book. There are several detailed case studies on the three-dimensionality of foehn, each giving insight into characteristic properties of the case in question. Seibert (1990) collected south foehn studies that were made since the Alpine Experiment ALPEX in 1982 in the eastern part of the Alpine massif. Based on these studies she concluded that the textbook theory is not correct. As discussed above, such a statement goes too far. Sprenger and Sch¨ar (2001) show how – under D> shallow foehn conditions – the complex topography of the Alpine ridge can cause flow splitting. Similar studies were carried out by Z¨angl (2002). Using observations made during the Mesoscale Alpine Program MAP, Jaubert and Stein (2003) analyzed and modeled a foehn case that showed wave breaking and hydraulic jumps. Drobinski et al. (2003) looked at

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the scale interactions by which smaller scale topography influences the development and the characteristics of foehn. Across mountain passes, so-called gap winds occur in foehn situations. Examples of observations and a discussion of their theory are given in Chap. 3, Sect. 3.5.

4.5 Foehn Climatology In Austria, a map showing foehn regions was produced. The intention was to advise people suffering from discomfort supposedly caused by foehn (see Sect. 4.7.4). This map (Fig. 4.21) is primarily based on the experience of forecasters and only minimally on quantitative observations. As mentioned in Sect. 4.3.2, universal criteria for foehn in a given area are almost impossible to define. For a case with strong foehn, Gutermann (private communication) has produced a foehn map based on surface temperature (Fig. 4.22). While this map has the limitation of being a case study, it does show clearly where the foehn regions are. Statistical analyses of data from dedicated foehn stations show that foehn occurrence is highly variable, and that no trend is discernible in the last 140 years (Fig. 4.23; Richner and Gutermann 2007). In addition, the regional and seasonal variability is considerable. Figures 4.24 and 4.25 give some ideas about variability. Observations are made three times a day, morning, noon, and evening; the numbers refer to the number of such observations.

Fig. 4.21 Foehn regions in Austria and Bavaria. The different shadings represent the frequency of foehn (arbitrary scale) (Reproduced by permission of the Central Institute for Meteorology and Geodynamics [ZAMG], Vienna, Austria)

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Fig. 4.22 Case study showing the main areas in Switzerland where foehn reaches the surface (Reproduced by permission of Thomas Gutermann, data kindly provided by MeteoSwiss)

Fig. 4.23 Year-to-year variation of foehn occurrence at the station Altdorf. The vertical axis represents the sum of daily observations in the morning, at noon, and in the evening, the heavy line represents the 20-year running mean (Richner and Gutermann 2007, basic data kindly provided by MeteoSwiss)

Seasonal variations in foehn frequency (upper frame of Fig. 4.25) are caused by the changing general circulation pattern and, subsequently, by the resulting synoptic situations. The changes in the diurnal distribution of foehn activity (lower frame of Fig. 4.25) are the result of interactions of foehn flow with thermally driven local wind systems, i.e., mountain-valley winds. Note that the relative frequency of foehn at noon remains the same throughout the year.

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Fig. 4.24 Comparison of the yearly foehn occurrence at different Swiss stations. Values represent the mean yearly sum for the period 1973–1982. The value for Altdorf (ALT) for this period is 62.2 (Richner and Gutermann 2007, basic data kindly provided by MeteoSwiss)

4.6 Forecasting Problems Foehn forecasting rests on three pillars: (a) probabilistic methods based on a few observed or forecasted parameters, (b) on model output, and (c) (still very important!) on the skill of experienced forecasters.

4.6.1 Probabilistic Methods Forecasting foehn means predicting a mesoscale phenomenon based on a synoptic situation. Such forecasts are primarily based on the pressure field at different altitudes. Depending on the orientation of the isobars, foehn might develop in one valley and not in another, hence, different locations would require specific forecasting procedures. In the 1960s, Widmer developed for the foehn station Altdorf, Switzerland, a “foehn test” that was refined by Courvoisier and Gutermann (1971); it remains the operational tool until today. Two pressure gradients across the Alps plus the trend of one of these are used to compute an index. If the index is below a certain, season-dependent threshold value, the probability of foehn at

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Fig. 4.25 Seasonal variation of total foehn occurrences per month (upper frame) and relative frequencies of occurrence at the three observing times (lower frame) for the foehn station Altdorf. Yellow: morning, red: noon, blue: evening observations (Richner and Gutermann 2007, basic data kindly provided by MeteoSwiss)

Altdorf within the next 36 h is over 70%. The index allows also predicting the breakdown of foehn with even a slightly higher success rate. Figures 4.26 and 4.27 give an example of the Widmer Index and its potential for forecasting a foehn case in January 2008. Note that foehn breakdown is predicted when the Widmer index has passed though its maximum and starts to decrease again, hence, the prediction of the breakdown was not very good in this example. D¨urr (2008) developed an automated method for identifying, i.e., nowcasting foehn. His procedure is based on 10-min real-time data from the automated Swiss surface network. The most important predictors are the differences in potential temperature between the reference station G¨utsch (2,282 mASL, close to the Alpine ridge) and the locations for which foehn should be nowcasted. For the time being,

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Fig. 4.26 Example of Widmer Index for January 2008. The indices are computed from pressure differences across the Alps as forecasted for defined gridpoints. Different lines relate to different forecasts and pressure levels, or combinations thereof. The horizontal line represents the winter threshold; a value above this indicates foehn at Altdorf (note inverted vertical scale!). Data used here are the ECMWF and COSMO-7 forecasts of January 1 and 2; ECMWF forecasts for 10 days (dashed and dotted lines), COSMO-7 for 3 days (black and orange lines). COSMO-7 is the MeteoSwiss mesoscale forecasting model for the Alpine region with 6.6 km resolution (Data kindly provided by MeteoSwiss)

the application of this technique is restricted to locations on valley floors or near valley exits; since July 2008, the procedure is implemented as an automated routine diagnostic tool at MeteoSwiss. Quite recently, Drechsel and Mayr (2008) developed an objective, probabilistic forecasting method for foehn in the Wipp Valley (Innsbruck) based on ECMWF model output. As predictors, they use cross-barrier pressure differences and, additionally, the isentropic descent. A test over 3 years proved that – based on the two variables – reliable forecasts of up to 3 days for foehn and the associated gust winds can be made.

4.6.2 Model Forecasts As the resolution of models is improved, the topography of the complex Alpine terrain (and with this the foehn valleys) is more accurately represented. Consequently,

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Fig. 4.27 Comparison of observed (via humidity) and forecast (using the Widmer index) onset of foehn; zooming in on Fig. 4.26; January 2–5, 2008 (Data kindly provided by MeteoSwiss)

Fig. 4.28 Wind speed and temperature for the foehn stations Altenrhein (ARH, red) and Vaduz (VAD, blue). The time series with 10-min resolution are observations (fine lines), the series with 1-h resolution (heavier lines) are model data (H¨achler et al. 2011, reproduced by permission of Klaus Burri)

there are well-founded hopes that models will provide sufficiently accurate foehn predictions. At MeteoSwiss, COSMO-2, a 2.2 km grid size model, has been run operationally since February 2008. Figure 4.28 assesses its capability to analyze a foehn case

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(a test case from the pre-operational phase, Burri et al. 2007). For both stations, the analysis represents the onset of foehn too early. The increase in wind speed is significantly below the observations, the same is even more pronounced for temperature. In summary it can be said that COSMO-2 forecast fields and analysis fields overestimate the spatial foehn extension and mostly underestimate temperature and wind speed not only at the two stations investigated here, but at most locations. The modeled temperature gradient between valley stations and the Alpine ridge site G¨utsch (not shown here) never reached dry adiabatic conditions, this in contradiction to the observations. In an attempt to improve the situation, not only deterministic, but also statistical methods will be used the future. In particular, ongoing work shows that model output statistics (MOS) are a promising tool for improving foehn forecasting.

4.6.3 Open Problems In practice, the skills of experienced forecasters who are familiar with the local situations are still an indispensable prerequisite for a successful forecast. They know from experience how a somewhat different wind direction might influence the onset or breakdown of foehn in a given valley, how observed wind data must be interpreted to arrive at a correct prediction. On the other hand, any tool, be it based on probability or on model output, is a welcome and appreciated support giving a first approximation which is subsequently modulated with the forecaster’s experience and skill. The synoptic chart and particularly the surface pressure pattern is one of the most useful tools for predicting the onset of foehn. Here, the forecaster will focus primarily on the pressure pattern and the formation of the so-called foehn knee or foehn nose, the characteristic deformation of the isobars on the upwind side of the Alps (Fig. 4.4). It must be stressed, however, that the formation of the foehn knee alone is an insufficient indicator for foehn since this is purely a surface characteristic and does not say anything about the situation aloft. In this respect, the pressure gradient at ridge height (e.g. from 850 hPa maps) is a much more useful parameter. The breaking down of foehn is in most cases associated with an incoming coldfront from the west. In these cases, forecasting the breakdown can be achieved quite reliably by observing the progressive increase in surface pressure. If, however, a high moves in from the east, predicting the breakdown is rather difficult, there are no clear rules for this case. Nevertheless, it seems that further improvements in models – both in resolution and parameterization – will improve future forecasting of foehn. After the Mesoscale Alpine Program MAP, a few open problems became obvious. Among these is, as indicated, the role of the tributary valleys which is

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still not well understood. This is partly due to a lack of sufficient high-density observations, but also to a poor understanding of the interaction of air masses coming from different valleys. There are many locations where two or even more foehn valleys merge. Observations indicate that the flow does not necessarily merge, but that one foehn “stream” might cross over the other. Which flow will go over the other depends on the synoptic fields and the orography. The higher the elevation at which the winds cross the Alps, the higher are the resulting temperatures in the valleys due to dry stable structure of the atmosphere in the south. Thus, the warmer foehn streak (which crossed the ridge at greater height) flows over the colder one. This effect can be observed, e.g., in the area of the lake Walensee where airflow down the Rhine Valley (directly towards the lake of Zurich) interacts with airflow from the Linth Valley in the Glarus Alps. Also here, refined and higher resolving models might soon provide better solutions.

4.7 Societal Impact of Foehn 4.7.1 Climate Impact Foehn has serious impacts on the local climate that, in turn, influence agricultural possibilities in foehn valleys. Thanks to foehn winds, wine can be grown in areas where it otherwise would be impossible. Foehn storms (also called downslope windstorms) have also a major effect on the snowmelt, an effect, which is not particularly liked in skiing resorts.

4.7.2 Air Quality Foehn situations provide the most spectacular views of the mountains. As a consequence of the precipitation on the upwind side, the foehn air is usually very clean, there is no haze, and distant objects seem to be much closer (see Burri et al. 1999). Likewise, the air mass originating at high levels in foehn type II has much lower aerosol concentrations than the air it replaces in the valleys. The entire fantastic Alpine panorama can be seen from places where one normally does not see any mountains at all. On the negative side of these stunning postcard-views, however, are the increases in ozone concentration. Although the values seldom reach alarm levels, foehn air easily triples existing ozone concentrations (Baumann et al. 2001). Trajectory calculations and aircraft measurements prove that the higher concentrations are simply due to the descending of ozone-richer air from about 4,000 m over the Mediterranean region. Figure 4.29 depicts the situation for Altdorf for the foehn case discussed above.

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Fig. 4.29 Ozone during foehn at Altdorf in January 2008 (All data taken from an air quality station that is not collocated with the foehn station. Hence, temperature data is not exactly the same as in Fig. 4.5.) (Data kindly provided by “inLuft”, Central Switzerland [www.in-luft.ch])

4.7.3 Fires and Traffic Accidents The most striking danger from foehn events, however, was and still is the spreading of fires. The warm and very dry air combined with high wind speed supports and proliferates fires very efficiently. In the course of time, numerous towns have burned down completely. In 1861, 600 houses of the canton capital Glarus, Switzerland, were completely devastated during a foehn storm, and only recently, in 2001, a fire maintained by foehn winds in excess of 15 m s1 destroyed 15 houses in Balzers, Principality of Liechtenstein. During foehn situations, a few towns still activate a fire watch during nights, and smoking outside houses is strictly forbidden. In some mountain regions, it is – as a matter of principle – illegal to start fires outside specially designated fire areas. Foehn winds can be dangerous to flying. Professional pilots and local airports are well aware of the problems and issue the necessary warnings. At Innsbruck airport, e.g., special foehn procedures ensure that the most turbulence prone parts of the valley are avoided during climb out and approach in order to enhance safety and passenger comfort. However, when hot-air ballooning, paragliding, and similar sports became popular during the last third of last century, the number of severe accidents due to high winds and large shears increased significantly. Improved training, special safety courses, and specific information and forecasts have reduced, but not eliminated, this problem.

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Cable car accidents and even train accidents can be caused by strong and gusty foehn winds. Although all cable transportation systems are required to monitor wind speed and to have an alarm system, gusts and shears that slip between the different anemometers can surprise operators. Sadly, there was such an accident in January 2008 in the Jungfrau region. High winds during a foehn storm “derailed” the cable of a double chair cable lift. First, the lift stopped, and the cable was caught in the cable catcher, but a successive gust threw the cable out of the catcher, and the chairs dropped to the ground. One person died and several were severely injured; mean wind speed was about 25 m s1 which is below the alarm level of 28 m s1 . (An almost identical incident happened 2003 in Wangs-Pizol, Switzerland. That time the directly affected gondolas were empty and nobody was injured. The cause was again gust winds, this time associated with a thunderstorm front.) On February 15, 1925, a train was thrown from its track in a foehn storm in Strobl near Salzburg, Austria. Another spectacular accident happened during a severe foehn storm in the Jungfrau region on November 11, 1996: a double motor coach of a narrow gauge railway was blown from its track. Its mass of 43 t could not withstand a foehn gust of 52 m s1 ; four persons were injured, fortunately none seriously. On lakes, foehn storms hamper scheduled boat traffic; in extreme cases, operations have to be suspended. The Swiss town of Brunnen (which is directly in the main axis of the Reuss Valley) has built a special “foehn harbor.” It serves two purposes: (a) it is used by boats in storm situations as shelter, and (b) if wind and waves still allow the scheduled ships to navigate, they can dock in this harbor, which is better protected against the waves and gusts than the wharf in the center of the town. The most significant recurring damage caused by foehn winds is most probably that to boats, piers, and shores. After severe foehn storms, pictures of loose-torn boats lying on shores or damaged piers appear regularly in the news. The previously mentioned “century foehn” on November 8, 1982, destroyed not only numerous boats and yachts, but also the newly built pier of the town of Sisikon (Lake Uri).

4.7.4 Biometeorological Effects Still much debated are biometeorological effects of foehn winds. Interestingly, it is primarily in the Alpine area that people blame foehn winds for almost any ailment, accident, crime, and in particular for headaches. Sferics (electromagnetic radiation originating in the atmosphere), ion concentrations, and pressure fluctuations were considered as possible causes of foehn-related ailments. While recent measurements prove that neither sferics nor ion concentrations are correlated with foehn events, pressure fluctuations induced by gravity waves on the cold pool remain a possible link between foehn and man.

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Statistical analyses of pressure fluctuations and subjective well-being show that there is indeed a statistically significant correlation between the two. However, there is no proof of any cause-and-effect mechanism. The study of short-term pressure fluctuations did not take into account the actual weather situation. Since fronts also cause high amplitude pressure fluctuations, the positive correlation might simply reflect that people feel subjectively better when the weather is good. A direct analysis of the frequency of headaches and the occurrence of foehn (as defined in the Alpine weather statistics) did not produce any result. Interestingly, on the American continent the interest in biometeorological research seems to be picking up after a long phase of disinterest. There have been several research projects dealing with Chinook winds and headache, strokes, etc. However, so far no significant progress was made in relating ailments to foehn-type winds or weather in general (see, e.g., Cooke et al. 2000; Field and Hill 2002). Acknowldgments We thank our colleagues in the “Alpine Research Group Foehn Rhine Valley/Lake Constance” for their contributions and support. In addition, we acknowledge valuable suggestions from three anonymous reviewers for improvements of our text.

Appendix A: Explanation and Definition of Foehn-Related Terms Alpine Foothills Foehn A warm but humid wind on the Alpine foothills, in the lee the air is mostly calm. This is not a foehn in the meteorological sense. Anticyclonic Foehn Foehn in an anticyclonic situation with a high potential height of the 500 hPa level. Only partly cloudy in the south, and usually dry. Temperature gain in the foehn valleys due to adiabatic sinking, flow forced by southerly pressure gradient. Cyclonic Foehn Foehn in connection with a cyclonic regime, i.e. low potential height of the 500 hPa level. Causes cloudiness even in the classical foehn areas, but criteria for foehn are well pronounced. Develops in extreme cases to dimmerfoehn. Deep Foehn, High-reaching Foehn The classical foehn situation with a high-reaching SW flow driven by a high over northern Italy and a low over southern Germany; isobars show the typical foehn knee; lee waves, lenticularis clouds, foehn wall, often also lee side rotors are present; warm, dry winds with high speed reach the valley floors (Hoinka 1990). Dimmerfoehn A south foehn which does not immediately follow the topography in the lee, but touches the surface further downwind. The mountain ridge is in clouds that extend

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downwind. The comparatively calm area right downwind of the ridge is dark due to heavy clouds, hence the name (“dimmerig” or “dimmrig” [Swiss German] means dim, obscure). In rare cases, there is no precipitation but it is very hazy due to Saharan dust. Double Foehn The simultaneous existence of north and south foehn. Double foehn is a shortlived, very rare phenomenon which occurs when a cold high-pressure system in the lower troposphere moves quickly over the Alpine ridge while a stormy westerly flow is present a greater height (Frey 1986). Flat Foehn D> Shallow Foehn Foehn Air The warm and dry air produced by foehn. Foehn Bank D> Foehn Wall Foehn Break D> Foehn Window Foehn Clearance At distances larger than about 50 km downwind from the Alpine ridge, foehn winds become light, while they remain warm and dry. This leads to a significant reduction of cloudiness, i.e., to a clearing (Hoinka 1985b). Foehn Cloud Lenticularis clouds in the lee of the mountain barrier. They are caused by the lee waves associated with the foehn flow. Their orientation is parallel to the ridge, and because the lee waves are stationary, also the foehn clouds are quasi-stationary. Note: Lenticularis clouds are neither a prerequisite for, nor proof of foehn, they can occur with any airflow over a barrier. The term “foehn cloud” is not be confused with the D> foehn wall. Foehn Cyclone A cyclone in the lee of a mountain massif which is formed or enhanced by a foehn process. Foehn Gap D> Foehn Window Foehn Island The surface area where foehn touched down while the surrounding area is still covered with cold air. Foehn Knee, Foehn Nose, Foehn Wedge The typical deformation of the isobars (or isohypses) in a foehn situation. A highpressure wedge lies on the windward side of the mountain range, while in the lee a trough is formed. As a consequence, the isobars (or isohypses) bulge and take a nose-like or knee-like form. In the German literature, “foehn knee” (“F¨ohnknie”) is more commonly used, in the English literature the term “foehn nose” (F¨ohnnase) is normally found.

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Foehn Nose D> Foehn Knee Foehn Pause Foehn winds do not blow constantly, but there is varying intensity and sometimes cessations. Such an interruption is called foehn pause (the German “Pause” means break, pause, intermission). Foehn pauses occur predominantly during the early morning hours before sunrise when cold air masses intrude. Rarely, the term foehn pause is used for the region delimiting the foehn air from the ambient air, this analogous to “tropopause”, “stratopause”, etc. Foehn Period This term deals with the duration or simply with the occurrence of foehn at one or several stations. The use of the term by different research groups is very diverse, hence, there is no generally accepted definition. Foehn Phase A rather general term used by Alpine foehn researchers for classifying the different development stages of a foehn situation; the definition of the phases might differ among different authors. The systems used by Ficker and by Streiff-Becker (1933) differentiated three phase, the recent system introduced by Seibert (1990) has four: Phase I: cold air masses on both sides of the Alps Phase II: warm advection from W or SW, development of temperature gradient and, as consequence, pressure gradient across Alpine ridge, D> shallow foehn develops Phase III: approaching trough changes flow to SW or S, speed and humidity increase, pressure gradient reaches maximum, D> deep foehn develops, precipitation in the upwind region Phase IV: passing of cold front, breakdown of foehn, often formation of a cyclone in the N. Foehn Storm A potentially destructive storm as result of a foehn situation. A foehn storm is characterized by its sudden occurrence in a practically calm situation and its intermittent nature during its onset. After the initial phase, wind speed remains high but steady. Additionally, the fast moving air is, as a result of the foehn mechanism, significantly warmer than the displaced air. Foehn storms belong into the category of downslope windstorms where they are often referred to as warm downslope windstorms. Foehn Tongue The area covered by foehn air flowing out of foehn valleys. Foehn Trough The trough in the lee of the mountain range formed dynamically by the flow across the barrier. Foehn Wall, foehn bank In those situations where foehn occurs with precipitation on the windward side of the mountain range, the clouds can be seen from the lee side as a “wall” topping

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the mountain ridge. Depending on the characteristics of the foehn flow, the clouds can be dragged over the ridge where they are dissolved while sinking. Under these conditions, the foehn wall has the appearance of a cap. Foehn Waves The lee waves or mountain waves associated with a foehn situation. Sometimes foehn waves become visible because they produce “foehn clouds”, i.e., cumulus lenticularis. Foehn waves must not be confused with the gravity waves occurring on the top of the cold pool. Foehn Wedge D> Foehn Knee Foehn Window, Foehn Gap, Foehn Break A cloud-free gap or clearance in the lee of the mountain range over which a foehn flow occurs. This gap is caused by the descending foehn air that is dry-adiabatically heated and, consequently, becomes dry. Foehnic Situation, Foehn-Like Situation Southerly flow which does not penetrate into the valleys. Foehn wall, foehn window, and lenticularis clouds may be present, visibility is very high. Free Foehn The sinking of air masses in the free atmosphere on a synoptic scale, particularly in high-pressure areas. The vertical motion is often brought to a standstill by an inversion that sometimes tops a fog layer. The increase in temperature and decrease in humidity caused by the dry-adiabatic sinking leads to dissipation of clouds. This process has nothing to do with mountain winds, and the use of the term “foehn” in this context is strongly discouraged. Gap Foehn (Gap Flow) D> Pass Foehn High-Reaching Foehn D> Deep Foehn Light Foehn Corresponds to phase II of the Innsbruck foehn strength scale (D> foehn phase). Pass Foehn, Gap Foehn A pass foehn exists when the foehn criteria are met at least at one mountain or pass station, but not at a valley station. The distinction between pass foehn and D> valley foehn was introduced to characterize also foehn situations in which the flow does not penetrate into the valleys. Another name for a D> foehnic situation. Sandwich Foehn A complex and short-lived three-layer flow situation along the Brenner cross section, first described during the Mesoscale Alpine Program MAP (Vergeiner and Mayr 2000): a shallow pressure-driven south foehn event below a decoupled flow from W or even NW, below the foehn flow a very stable cold pool which cannot be removed by the southerly flow. (In other areas, e.g., over the Swiss Plateau, such a situation can persist for up to several days; here the term is not used.)

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Shallow Foehn, Flat Foehn A foehn with all its characteristics in the downwind side valley but without the dominant southerly flow at high altitude, here flow can be from W or even NW. Shallow foehn can be regarded as compensation flow between different air masses on both sides of the mountain massif; it is often found in the lee of passes which form gaps in the mountain barrier (Seibert 1990). Strong Foehn Corresponds to phase III of the Innsbruck foehn strength scale (D> foehn phase). Talfoehn D> Valley Foehn Valley Foehn, Talfoehn A valley foehn is present when the criteria for foehn are fulfilled at least for one mountain station and at least for one valley station. Used in this sense, it is not a foehn type but a foehn phase. See also pass foehn. Also, the term “valley foehn” is a somewhat obsolete name for deep foehn used by Streiff-Becker. He used it to distinguish between deep foehn and Alpine foothills foehn (the latter not being a foehn in a meteorological sense).

Appendix B: Names of Foehn-Type Winds in Different Regions The German term F¨ohn originated most probably during Roman times. When the Romans conquered the territories north of the Alps in the first century BC, they found this stormy, warm, and dry mountain wind. From home, they knew a similar wind, the “favonius” (meaning “the favorable”), a warm and dry wind originating in northern Africa. Albeit the two winds are meteorologically very different, they do have similar characteristics; hence, it was logical that the Romans gave this name also to the warm wind they found north of the Alps. In the Raeto-Roman language (still spoken today as Rumansch by a minority in the Swiss Alps) “favonius” became “favuogn”, in its dialect “fuogn”. In the Old High German language “fuogn” became “ph¯onno” which over time gradually developed to the German name “F¨ohn” (the o¨ h spoken as in b-i-rd or l-ea-rn). As mentioned in Sect. 4.1, foehn winds in the meteorological sense occur wherever large mountain massifs exist. In meteorology, the general term “foehn” for the warm dry wind was chosen, because research started in the Alps, hence, the local name became also the scientific label. The following list is based on Schamp (1964), on information collected through personal contacts by Gubser (2006), and on internet searches. Aperwind (Alps) Foehn in Spring which melts the snow (apertus [lat.]: open; apern [ger.]: melting of snow).

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Aspre (Western Slope of Central Massif, France) Dry, warm easterly winds blowing from the Central Massif over the Garonne plain, also called “Lou Cantali´e”. Appenzeller F¨ohn (Eastern Switzerland) Regional foehn in the foothills of the Alps around Appenzell, St. Gallen, and Lake Constance. No southerly wind component at the Alpine ridge, but locally favorable foehn conditions. Occurs usually with westerly winds and falling pressure north of the Alps. Austru (Walachia, Romania) Foehn downwind of the Balkan Massif and the Transylvanian Alps from W to SW; occurs predominantly in winter, the associated clearing leading to severe radiation frost. Autan (Southern France) The Foehn in the lee of Cevenne Mountains and the Pyrenees from SE to E. Autan Blanc (Southern France) Particularly strong D> Autan with cloudless sky; can reach the Atlantic coast south of the Gironde. Autan Noir (Southern France) An D> Autan followed by rain steered by a low over the Bay of Biscay. Berg Wind (South Africa) Hot and dry foehn-like wind that blows from the highlands down to the coastal plateau; particularly Southwest Africa. Bohorok, Also Bokorot (Eastern Sumatra) Dry wind blowing from the Karo Plateau down to the plains of northeast Sumatra, a passat wind warmed by the foehn mechanism. Boulder Windstorm (Boulder, U.S.A.) A windstorm occurring basically with D> Chinook in Boulder, CO. Bregenzer Fallwind (Bay of Bregenz, Austria) An easterly to northeasterly foehn-type wind blowing form the Gebhardsberg and Pf¨ander, also called “Ostf¨ohn” (east foehn), “Falscher F¨ohn” (wrong foehn, because it comes from the unusual direction), or “Pf¨anderwind”. Broebroe, Brubru (Sulwesi, Indonesia) A gusty foehn-type easterly wind, part of the east monsoon near Makassar on the west coast of the island. Canterbury Northwester D> Northwester Cape Doctor (Capetown, South Africa) Maritime air masses, heated by a foehn-type process but still cold, flowing from False Bay over Capetown towards Table Bay.

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Chanduy (Mexico) Foehn-type wind in the area of Guayaquil, Mexico; occurs primarily during the dry season in the afternoon. Chinook (Rocky Mountains, U.S.A.) Warm and dry foehn-type west wind on the eastern slope of the Rocky Mountains. (In coastal regions of Oregon and Washington also a warm, humid sea breeze from SW passing over coastal areas, has nothing to do with foehn.) The American analogue to Alpine foehn, for details of the mechanism see Brinkmann (1973). Chinook Arch A striking feature of the D> Chinook, a band of stationary stratus clouds caused by air undulations over the mountains due to orographic lifting. Falscher F¨ohn D> Bregenzer Fallwind Favogn, Favuogn (Grisons, Switzerland) Romansh name for foehn. Gending (Java) Foehn winds over the northerly plains of Java during the SE monsoons. Ghilbi (Libya) Basically a hot desert wind often connected with sand storms. However, when passing over coastal mountain ranges, there is an additional foehn effect. Great Wind (Inner Asia) Foehn-type NE wind on the SW slopes of the Alatau. Guggifoehn (Bernese Oberland, Switzerland) The Alpine foehn in the region of the Lauberhorn mountain. Halny Wiatr (Poland) A south foehn in the High Tatra. Helm Wind (Northern England) A strong foehn-type wind from the Cross Fell, characterized by cloud caps on the mountain peaks, hence the name. Himmelsbesen D> Sky Sweeper Ibe (Western China) Strong wind through a gap, the Dzungarian Gate (separating the depressions of Lake Balkhash [Kazakhstan] and Lake Ala-Kul [Kyrgyzstan]). The wind is a gap wind similar to foehn. Jauk (Klagenfurt Basin, Austria) South foehn over the Karawanken mountains. Kˆachan (Sri Lanka) Foehn-type wind connected with the SW monsoon in the easterly parts of Sri Lanka. The Tamil speaking population calls it “solaha-kˆachan”, i.e., dry, burning monsoon.

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Kumbang, Koembang (Java) SE wind near Tijriban and Tegal on the north coast, the foehn effect is due to the Pembarisan mountains. Lenzbote (Alpine countries) Name of the spring foehn melting the snow (“Lenzbote” [ger.]: spring messenger). Levanto (Canary Islands) Foehn-type E wind particularly in the Orotava valley on Teneriffa. Livas (Greece) Any foehn-type wind. The name “Livas” (plural: “Lives”) is derived from “Lips”, a warm SW wind from the direction of Libya (which is a warm wind but not a foehntype wind). Ljuka (Carinthia, Austria) Local name of foehn, most likely derived from the Slovenian word “jug” meaning south wind. Llebetg, Llebejado (Roussillon and Eastern Pyrenees, France) Arabic or Catalan name of a foehn-type SW wind on the northern slopes of the eastern Pyrenees. Lou Cantali´e D> Aspre Megas (Greece) A foehn-type SW wind blowing from Parnassus towards Boeotia, particularly in the plain of the dried-up Kopais lake. Mikuni-Oroshi (Japan) The “downwind of Mikunitoge” is a foehn-type W to NW wind in the Tone valley near Maebashi (eastern coast). Moazagotl (Riesengebirge, Germany) The name of a peculiar cloud showing the lee waves. It is formed in the prefrontal stage of a foehn cyclone. Canterbury Northwester D> Northwester Montana Monsoon (Montana, U.S.A.) Popular name for the D> Chinook in the prairies of Montana. Northwester, Canterbury Northwester (New Zeeland) A warm and dry northwestly wind that reaches Canterbury Plain on South Island. Norder, Norther or Nortes (Gulf of Mexico, Central America) Actually a cold stormy wind, however, when blowing from the southeast it passes over the Isthmus of Tehuantepec, the blocking on the upwind side causes precipitation while in the lee, on the side of the Pacific foehnic clearing occurs.

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Ostf¨ohn D> Bregenzer Fallwind Pacific Wind (Colorado, U.S.A.) A name sometimes used for the Chinook. Pf¨anderwind D> Bregenzer Fallwind Puelche (Southern Chili) Foehn wind in the Andes, in Argentina the same wind is called Zonda. Rotenturm Wind, Talmac Wind (Transylvania, Romania) A foehn-type south wind near Sibiu (Hermanstadt) blowing from the southern Carpatians over the Rotenturm Pass into the Transylvanian Basin; sometimes also called Talmac Wind after the town Nagy-Talmacs near Sibiu. Santa Ana (California, U.S.A.) Northeastern foehn wind in the basin of Los Angeles, named after the river and the pass. Sky Sweeper (Majorca, Spain) Foehn-type NW wind over the coastal mountain ranges of Majorca, Spain. Note that among seamen the term “Sky Sweeper” (or its German translation “Himmelsbesen”) signifies any northeasterly wind in northerly latitudes. It causes a very clear view after “sweeping the clouds from the sky.” Solano (Spain) Foehn-type wind from south to southeast. (The name is also used for easterly winds from the Mediterranean Sea bringing monsoon-like precipitation.) Talmac, Talmesch Wind D> Rotenturm Wind Tenggara (Speimonde Archipel near Sulawesi, Celebes) F¨ohn-type winds during easterly monsoons in the wake of the southern peninsula of Sulawesi. Toureillo (Arri`ege, Southern France) South foehn from the Pyrenees in the Arri`ege Valley. Tsinias (Aegean Sea) Foehn wind from the southern cliffs of the islands in the Aegean Sea, name is mainly used on the island of Tinos. T¨urkenwind (Northern Tyrol, Austria; Rhine Valley, Switzerland) Foehn accelerates the ripening of corn (and other crop). In this region, corn is also called T¨urkenkorn (Turkish grain, instead of the German “Mais”, hence the name T¨urkenwind [Turkish wind]). Vent d’Espagne (Southern France) West to southwest foehn-type wind from the Pyrenees when a depression moves in north of them.

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Wambraw, Wambru (New Guinea) Southwesterly foehn-type wind over the Geelvink Bay in northwestern New Guinea during summer monsoon. Wasatch (Utah, U.S.A.) Easterly Chinook in the valleys of the Wasatch mountains. Zephyr (Colorado, U.S.A.) Another name for Chinook. Zonda (Argentina) Foehn wind in the Andes, in Chili the same wind is called Puelche.

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Richner, H. and Th. Gutermann, 2007: Statistical analysis of foehn in Altdorf, Switzerland. Extended Abstracts Volume 2, Int. Conf. Alpine Meteorol., June 4 to 8, 2007, Chamb´ery, France, 457–460. Richner, H., K. Baumann-Stanzer, B. Benech, H. Berger, B. Chimani, M. Dorninger, P. Drobinski, M. Furger, S. Gubser, Th. Gutermann, C. H¨aberli, E. H¨aller, M. Lothon, V. Mitev, D. Ruffieux, G. Seiz, R. Steinacker, S. Tschannett, S. Vogt, and R. Werner, 2005: Unstationary aspects of foehn in a large valley, part I: operational setup, scientific objectives and analysis of the cases during the special observing period of the MAP subprogramme FORM., Meteorol. Atmos. Phys., 92, 255–284. ¨ Rossmann, F., 1950: Uber das Absteigen des F¨ohns in die T¨aler. Ber. deutsch. Wetterd. US-Zone, 12, 94–98. Schamp, H., 1964: Die Winde der Erde und ihre Namen. Franz Steiner Verlag, Wiesbaden, 94 pp. Sch¨uepp, W., 1952: Die qualitative und quantitative Bedeutung der F¨ohnmauer. Meteorol. Rdsch., 5, 136–138. Schweitzer, H., 1953: Versuch einer Erkl¨arung des F¨ohns als Luftstr¨omung mit u¨ berkritischer Geschwindigkeit. Arch. Meteor. Geophys. Bioklimatol., A5, 350–371. Scorer, R.S., 1978: Environmental Aerodynamics. Wiley & Sons, 488 pp. Seibert, P., 1990: South foehn studies since the ALPEX experiment. Meteorol. Atmos. Phys., 43, 91–103. Seibert, P., 2005: Hann’s Thermodynamic Foehn Theory and its Presentation in Meteorological Textbooks in the Course of Time. From Beaufort to Bjerknes and Beyond, Algorismus, Issue 52, 169–180; ISBN 978-3936905-13-7. Sheridan, P.F., V. Horlacher, G.G. Rooney, P. Hignett, S.D. Mobbs, and S.B. Vosper, 2007: Influence of lee waves on the near-surface flow downwind of the Pennines. Q.J.R. Meteorol. Soc., 133, 1353–1369. Sprenger, M., and C. Sch¨ar, 2001: Rotational aspects of stratified gap flows and shallow foehn. Quart. J.R. Meteorol. Soc., 127, 161–187. Steinacker, R., 2006: Alpine foehn – a new verse to an old song. Promet, 32, 3–10 (in German). Streiff-Becker, R., 1933: Die F¨ohnwinde. Viertelj.schr. Naturforsch. Ges. Z¨urich, 78, 66. Streiff-Becker, R., 1947: Der Dimmerf¨ohn. Viertelj.schr. Naturforsch. Ges. Z¨urich, 92, 195–198. Vergeiner J. and G. Mayr, 2000: Case study of the MAP-IOP “Sandwich” foehn on 18th October 1999. MAP Newsletter, 13, 36–37. ¨ Wild, H., 1901: Uber den F¨ohn und Vorschlag zur Beschr¨ankung seines Begriffs. Denkschr. Schweiz. Naturf. Ges., 38, 99 p. plus appendix. WMO (ed.), 1992: International Meteorological Vocabulary. WMO No. 182, World Meteorological Organization, Geneva, Switzerland, 784 pp. Z¨angl, G., 2002: Idealized numerical simulations of shallow f¨ohn. Quart. J.R. Meteorol. Soc., 128, 431–450.

Chapter 5

Boundary Layers and Air Quality in Mountainous Terrain Douw G. Steyn, Stephan F.J. De Wekker, Meinolf Kossmann, and Alberto Martilli

Abstract In this chapter, the general problem of air pollution in mountainous terrain is discussed. Terrain effects on the spatial distribution and temporal variability of air pollutants are described including specific effects encountered in stable- and convective boundary layers and under dynamically driven conditions. The uses of numerical models, scale models, and observational studies are described as tools for understanding air pollution in mountainous terrain. Specific integrated regional studies of air pollution conducted in the Lower Fraser Valley, Canada and in the Upper Rhine Valley, Germany are used to illustrate the terrain effects. The chapter concludes with a discussion of approaches to forecasting air pollution in mountainous terrain.

5.1 Introduction In very simple terms, once emitted, the concentration of air pollutants in the atmospheric boundary layer is determined by a combination of chemical (production and destruction) and dispersion processes (the combined effects of dilution by mean D.G. Steyn () Department of Earth and Ocean Sciences, The University of British Columbia, Vancouver, BC, Canada e-mail: [email protected] S.F.J. De Wekker Department of Environmental Sciences, University of Virginia, Charlottesville, VA, USA e-mail: [email protected] M. Kossmann Climate and Environment Consultancy, Deutscher Wetterdienst, Offenbach am Main, Germany e-mail: [email protected] A. Martilli CIEMAT Unidad de Contaminacion Atmosferice, Madrid, Spain e-mail: [email protected] F. Chow et al. (eds.), Mountain Weather Research and Forecasting, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-4098-3 5, © Springer ScienceCBusiness Media B.V. 2013

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Fig. 5.1 Schematic of air pollution in a valley, illustrating elevated temperature inversion, multiple pollution sources, pollution plumes and cities with industrial, commercial and residential buildings. The country breeze is a thermally driven wind resulting from the horizontal temperature gradient between an urban area and the surrounding country (Modified from Elsom 1987)

wind advection and cross-wind diffusion). In flat terrain, or over the oceans or lakes, the dispersion processes are limited in the vertical by the depth of the atmospheric boundary layer, and in the horizontal only by wind speed, wind trajectory sinuosity, and the intensity of crosswind turbulence. In the near field (generally within 10 km from a pollution source), diffusion effects dominate while the pollution is still in a defined plume, while further downwind, boundary layer depth and mean wind speed become dominant. In mountainous terrain the matter becomes much more complicated. The atmospheric boundary layer responds to topographic forcing, and most of these meteorological variables are strongly altered, generally in ways which result in more severe pollution than would be expected from the same emissions in flat locations. These conditions are particularly severe in valley bottoms, along mountain slopes and in mountain basins, as indicated in Fig. 5.1. Many of the mechanisms which affect air quality in mountainous terrain have been described in detail in Chaps. 2 and 3, so references are provided here as appropriate. Humans settle in mountains for economic, strategic, historical or political reasons. In the year 2000, 720 million people (12% of world population) lived in mountainous areas, and 663 million of these people lived in developing or transition countries (Huddlestone et al. 2003), where restrictions on emissions of pollutants are generally less stringent than elsewhere. It is thus important to understand the fate and distribution of pollutants in mountainous environments. The history of pollution episodes shows that many notably polluted locations are in valleys or mountain basins, or topographically constrained coastal plains. These include examples like the Plateau of Switzerland, the Po Plain in Italy, The Los Angeles Basin in USA, Mexico City (also see Chap. 2), the Lower Fraser Valley in Canada (also see Chap. 8), and the Rhine Valley in Germany. The latter two examples will be examined as interesting case studies in this chapter, which will touch on particular atmospheric meteorological phenomena that are important in limiting atmospheric dispersion in mountainous regions.

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5.2 Boundary Layer Processes Relevant for Air Quality in Mountainous Terrain In locations of flat, homogeneous terrain, the boundary layer depth is constant in space, and varies temporally due to mechanically or thermally induced mixing or due to stabilization by radiative loss from the surface. In convective conditions, the boundary layer depth undergoes strong diurnal variation, as shown in Fig. 5.2. The overall result is that the boundary layer depth is identical to the mixed layer depth – the depth to which surface emitted substances (including air pollutants) will be mixed. In regions of complex, mountainous terrain, boundary layer depth varies strongly in both time and space. In general, boundary layer height will mirror terrain, but with suppressed amplitude. Local, topographic scale, up- and down-slope flows (as discussed in Chap. 2, Sect. 2.3) will enhance turbulent transport by adding smallscale advection to thermally driven convective motions. Most notably, thermally driven upslope flows will add substantially to the vertical transport of pollutants. In many cases the net effect will be a transport of pollutants well above the locallydetermined convective boundary layer (CBL) depth to form a regional pollution layer, often visible as a haze layer blanketing the mountains. This will contrast strongly with times under which strong surface cooling results in a surface based temperature inversion and very little turbulent mixing, and with katabatic winds carrying pollutants or clean air down into valleys and basins. Clearly, different largescale weather conditions produce strongly varying pollution potential everywhere, but particularly in the mountains. This section will elaborate on pollution in stable, convective and dynamically driven boundary layers in mountainous terrain.

Fig. 5.2 Conceptual model of the diurnal evolution of the convective boundary diurnal in flat terrain, showing various sub-layers. NBL is nocturnal boundary layer

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Fig. 5.3 Schematic representation of processes affecting the dispersion of air pollutants in a stably stratified boundary layer over complex terrain. (1) drainage flow, (2) slope flow detrainment, (3) urban heat island circulation, (4) terrain induced flow splitting and convergence, (5) mesoscale subsidence, (6) regional wind systems, (7) gravity waves, (8) intermittent turbulence (Jerome Fast, Pacific Northwest National Laboratory, operated by Battelle for the U.S. Department of Energy. Reprinted with permission)

5.2.1 Processes in Stable Boundary Layers Episodes of severe pollution are frequently associated with poor dispersion conditions occurring in stable boundary layers. While this association is found everywhere, mountain induced processes can lead to particularly poor air quality. A schematic illustration of nighttime air pollution dispersion processes over mountainous terrain is presented in Fig. 5.3. Most prominent is the negative effect of cold air pools forming in basin and many valleys during nighttime, as described in detail in Chap. 2, Sect. 2.4. Such cold air pools are characterized by very stable stratification, very low wind speeds, and weak or intermittent turbulent mixing. With human settlements and hence anthropogenic emission sources being mostly located at low terrain elevations, e.g. at the bottom of basins or along valley floors, pollutants emitted into cold air pools tend to accumulate to high concentrations. Particularly hazardous air quality conditions are likely to occur in persistent (multiday) cold air pools (Whiteman et al. 2001). Under synoptically quiescent conditions, thermally driven slope- and valley winds (Chap. 2) are very important as they maintain some degree of ventilation in valleys and basins. However, flow convergence associated with cold air draining from surrounding terrain elevations towards cold pools may favor the occurrence of stagnant conditions with weak winds (Kossmann and Sturman 2004; Corsmeier et al. 2006). Down-slope and down-valley wind systems typically advect relatively unpolluted air from rural surroundings at higher terrain elevations towards the densely settled and therefore more polluted valley and basin sites (Banta et al. 1997; Raga et al. 1999; Baumbach and Vogt 1999; Poulos and Zhong 2008). This phenomenon often results in the increase of concentrations of secondary pollutants such as ozone because of an influx of precursor substances stored in the residual layer

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(L¨offler-Mang et al. 1997; Raga et al. 1999; Salmond and McKendry 2002). Furthermore, down-slope or down-valley winds might re-circulate pollutants that have been carried away from the emission sources by daytime up-slope or up-valley winds. An example of mountain and coastal effects on pollutant re-circulation is described in Sect. 5.4.1 for the Lower Fraser Valley, BC (also see Chap. 8). In many cases the application of the topographical amplification factor concept (see Chap. 2, Sect. 2.4) is useful in distinguishing between pooling and draining valleys, and for a better understanding of the occurrence of valley/basin inversion break-up (McKee and O’Neal 1989; Sakiyama 1990; Whiteman et al. 1996). However, forecasting stable boundary-layer processes for air quality applications still represents a major challenge. Reasons for this include the high spatial model resolution required to resolve the most important processes and the difficulties with turbulence parameterization under very stable conditions. Stable boundary-layer processes in mountainous terrain have also been recognized as important in providing an understanding of carbon dioxide budgets, which are essential for climate change monitoring and projections (Sun et al. 1998; Eugster and Siegrist 2000).

5.2.2 Processes in Convective Boundary Layers Figure 5.4 presents a conceptual model of the diurnal development of the CBL over mountainous terrain (Fiedler et al. 1987; Whiteman et al. 2000). During the night and in the early morning hours, cold air accumulates in the valleys, resulting in greater atmospheric stability in valleys than over the mountain ridges (Fig. 5.4a). After sunrise, this leads to a slower development of the CBL in the valleys than over the mountain ridges (Fig. 5.4b). Development of the CBL in valleys is further suppressed by compensatory sinking motions as a result of mass removal by upslope flows (e.g. Whiteman 1982; De Wekker 2008; see also Chap. 2). After the inversion in the valleys has broken up the CBL approximately follows the terrain (Fig. 5.4c). Further development of the CBL depends on factors such as the total sensible heat input, the ambient stability and the strength of the synoptic scale sinking motions. This often leads to parallel CBL growth in the valley and surrounding mountain, and maintains the terrain-following CBL structure up to early afternoon. By late afternoon, due to faster CBL development over the valley, the CBL top may become a roughly horizontal surface (Fig. 5.4d). This general conceptual model has important implications for air pollution in mountain regions. Air pollutants that have accumulated in the valleys at night disperse upward during the morning hours. In deep valleys, breakup of the temperature inversion can take many hours and on some days does not occur, especially in the winter when incoming radiation is small. Once the surface-based temperature inversion breaks up, dispersion can occur in several ways, transport by upslope flows and convective mixing in the growing CBL being the most important of these. Due to these transport and mixing processes, mountain top locations often experience increased levels of air pollution after the break-up of surface based temperature inversions in adjacent valleys (e.g. Seibert et al. 1998).

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Fig. 5.4 Conceptual model of the daytime boundary layer development over mountainous terrain. (a) before sunrise, (b) early morning, (c) at noon, (d) late afternoon. Light grey shading represents topography. Dark grey shading illustrates strongly stable stratification in nocturnal cold air pools. Arrows denote horizontal and vertical flows. The wavy lines depict the upper limit of the surface generated convection. Vertical profiles of potential temperature are shown at several locations along the cross section (After Fiedler et al. 1987. Reprinted with permission)

The presence of mesoscale circulations and their interactions with the ambient flow and with boundary layer convection complicates boundary layer structure in mountainous terrain relative to that found over flat terrain. Very often, multiple elevated temperature inversions are found in the lower atmosphere over mountains leading to an ambiguous mixing height. In addition, aerosol layers are often found above these temperature inversions, making the common definition of mixing heights in flat terrain inoperable in complex terrain (De Wekker et al. 2004). Mechanisms that can explain the presence of aerosol (and other pollutants) above the CBL top are summarized in Fig. 5.5 (De Wekker et al. 2004). In this figure, aerosol layer (AL) heights are relatively uniform and reach a maximum altitude of about 4 km in the afternoon. The CBL heights are considerably lower than AL heights and show more spatial variability. CBL heights tend to follow the terrain more closely than AL heights, although the extent to which the CBL height follows

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5 ha

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Fig. 5.5 Conceptual diagram of mid-afternoon CBL in mountainous terrain (indicated by the shaded grey area). The curve labelled zi is the CBL height and the curve labelled ha is the AL height. The depicted mechanisms are (1) mountain venting, (2) cloud venting, (3) advective venting, (4) advection of aerosols from airmasses elsewhere and (5) plume convection that does not overshoot the CBL top (After De Wekker 2002. Reprinted with permission)

the terrain decreases during the day. The mechanisms contributing to deeper AL than CBL heights and indicated in Fig. 5.5 are the following: (1) mountain venting, (2) cloud venting, (3) advective venting, and (4) horizontal advection of aerosols from airmasses upwind of the area of interest. Mountain venting and cloud venting can occur simultaneously when an orographically induced thermal reaches lifting condensation level. All of these mechanisms have been observed to occur in a variety of field studies. For an overview, see Kossmann et al. (1999). As noted, observations and model results show that the extent to which the CBL height follows the terrain typically decreases during the day (Lenschow et al. 1979; Fiedler 1983; De Wekker et al. 2004). Stull (1998) derived an equation (applicable under free convection conditions) for the tendency of the CBL top to become more horizontal in the course of the day by applying the mass conservation equation for a CBL over hilly terrain. The results showed that advection, entrainment and friction contribute to making the CBL follow the terrain, while gravitational forces tend to level the top of the CBL. If there is more than just a light synoptic wind, the advection term was found to be dominant in making the top of the CBL follow the terrain. A major shortcoming of Stull’s theory is that it does not take into account the effect of thermally-driven flows.

5.2.3 Dynamical Processes The dynamic modification of a larger scale airflow passing over mountainous terrain plays an important role in the transport, accumulation, and diffusion of air pollutants. In addition to mean wind speed and direction, turbulence intensities

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and structure are also subject to dynamical modification by the terrain. Dynamical dispersion processes in mountainous terrain include flow over and around hills and mountains, airflow channeling in valleys, barrier winds, gravity waves, flow separation, and the formation of traveling or standing eddies with horizontal or vertical axes (see Chap. 3). Turbulence intensities are often enhanced by flow separation because of mechanically generated turbulence in wind shear at separation zones, while highest wind speeds generally occur over exposed convex terrain formations such as mountain ridges or due to airflow funneling through terrain constrictions. Lowest mean wind speeds are usually observed at sheltered valley or leeside locations. Chapter 3 provides a detailed description of dynamical airflow processes over mountainous terrain. Furthermore, the current understanding of the well-known foehn winds (a strong downslope wind) is described in detail in Chap. 4. Foehn winds are important for the turbulent erosion of cold air pools in valleys and basins (Petkovsek 1992; Zhong et al. 2003). Hence, the onset of foehn winds often ends periods of poor air quality. A useful tool to determine whether air pollutants emitted at a certain height on the windward side of a mountain are likely to impinge on the mountain slope or pass over a mountain is the dividing streamline concept (see Chap. 3, Sect. 3.4.2). This concept is based on considerations of the kinetic and potential energy of the approaching flow via the Froude number (Chap. 3, Sect. 3.2.3). The Froude number can also be used to give a good indication of the characteristics of gravity waves possibly developing on the leeward side of a mountain. The wind climate in mountain valleys is often dominated by airflow channeling along the valley axis (Kalthoff and Vogel 1992; Smedman et al. 1996; Eckman 1998; Cogliati and Mazzeo 2006). A detailed discussion of mechanisms generating airflow channeling is given in Chaps. 2 and 3. The consequences of such channeling on plume dispersion are demonstrated in Fig. 5.6, which illustrates the dispersion of plumes in a valley and over the adjacent plain. Over the plain, plumes from neighboring sources only have intersecting centerlines if the regional wind blows parallel to the connecting line between the sources. Plumes from sources located along a valley, however, can be superimposed onto each other for almost all regional wind directions, because airflow channeling leads to a bimodal wind direction climatology in valleys. A consequence is that poor air quality situations resulting from plume interference are far more likely to occur in valleys than over a plain. Even more complex dispersion conditions occur in curved valleys, or at valley bifurcations, where airflow channeling is likely to generate zones of converging or diverging along-valley winds (Enger et al. 1993; Kossmann et al. 2002a; Kossmann and Sturman 2003; Dobrinski et al. 2006). Interaction of channeled along-valley winds and airflow across a mountain barrier potentially causes strong wind shear and often results in eddy formation. An example of such a dynamically-induced eddy with a horizontal axis is the rotor which is associated with the existence of lee waves. A favorable location for dynamical rotor formation, airflow channeling, and dust storm development is the Owens Valley in California (Grubiˇsi´c et al. 2008; Zhong et al. 2008). A lidar scan of

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Fig. 5.6 Idealised plumes from two sources within and two sources outside an north–south oriented valley. Circles in red show the location of sources. Dashed lines indicate the valley sidewalls. VG is the geostrophic wind vector and V0 is the channeled surface wind vector in the valley. The top panel shows terrain elevations along a vertical cross section, ‚(z) is the potential temperature profile

aerosol backscatter intensity across the Owens Valley during strong westerly flows across the Sierra Nevada Mountains is depicted in Fig. 5.7. The convergence of the aerosol-free westerly surface winds and of channeled aerosol-filled southerly winds along the Owens Valley leads to a lifting of aerosols up to 3 km above valley floor in this situation. The formation of eddies with a vertical axis and re-circulation of air pollutants within these eddies is quite common over mountainous terrain. For example, the Fresno Eddy shown schematically in Fig. 5.8 is generated by the interaction of local mountain winds in the San Joaquin Valley and a regional low-level jet, which is triggered by marine air intrusions in the San Francisco Bay area. Re-circulation over strong emission sources and hence accumulation of air pollutants within the Fresno Eddy is a very important mechanism for the build-up of high photochemical pollution levels in the area and in adjacent National Parks (Lin and Jao 1995; Bao et al. 2008). Such topographically induced eddies with vertical axes can occur under a wide range of atmospheric stratifications. Observations and modeling studies

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Fig. 5.7 Range Height Indicator (RHI) (vertical) lidar scan of aerosol backscatter intensity captured during the T-REX campaign in the Owens Valley around 0015 UTC 3 March 2006 (After De Wekker and Mayor 2009). The azimuth angle of the scan is 282ı . The white arrow directed toward the right indicates westerly flow down the east side of the Sierra Nevada slopes. This relatively clean air undercuts the aerosol-laden southerly flow in the Owens Valley, which has an easterly component, indicated by the white arrow directed toward the left. The lifting generated by the near surface flow convergence and the resulting recirculation is illustrated by the black arrows. The recirculation of the aerosol-laden air lasted for several minutes, as inferred from the animation of RHI scans. Range rings are drawn at every 2 km distance from the lidar (© American Meteorological Society. Reprinted with permission)

Fig. 5.8 Formation of eddies with vertical axes in the Central Valley of California (Bao et al. 2008). Recirculation and trapping of polluted air causes poor air quality in the area and often in surrounding National Parks (© American Meteorological Society. Reprinted with permission)

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indicate that conditions with a stably stratified atmosphere and moderate ambient winds are particularly favorable for the formation of these eddies, which have been discovered at many different locations around the world. Examples include the Melbourne Eddy or Spillane Eddy (Spillane 1978; McGregor and Kimura 1989), the Kanto Plain Eddy (Harada 1981; Kimura 1986), the Graz City Eddy (Oettl et al. 2001), the Schultz Eddy (Zaremba and Carroll 1999; Bao et al. 2008), and the Denver Cyclone (Wilczak and Christian 1990; Levinson and Banta 1995).

5.2.4 Interactions and Other Processes Under most synoptic conditions air pollution dispersion over mountainous terrain is complex because multiple thermally and dynamically generated processes occur simultaneously. For example, nighttime down-slope winds may interact with gravity waves on the lee side of mountains (Poulos et al. 2000), or airflow along valleys may be characterized by layers of opposing wind directions with either dynamically channeled winds or thermally driven mountain winds dominating in each layer (Schmidli et al. 2009). During daytime, atmospheric stability at valley and basin sites can be strongly modified by the advection of mixed layers formed over neighboring mountain ranges (Arritt et al. 1992; Stensrud 1993). The advection of elevated mixed layers and anabatic winds favor the formation of elevated pollution layers (Kossmann et al. 1999; Frioud et al. 2003; Henne et al. 2004) that may become subject to long-range transport. Down-mixing of these pollution layers due to growing CBLs can significantly enhance surface concentrations of air pollutants (Neu et al. 1994; McKendry et al. 1997). In most mountain areas surface cover is not uniform. Water surfaces and urban areas are often present in valley bottoms, for example. These surface heterogeneities generate thermally driven wind systems and roughness effects which are superimposed on mountain induced processes, often resulting in enhanced dispersion (Lu and Turco 1994; McGowan and Sturman 1996; Bischoff-Gauß et al. 1998; Millan et al. 1997; McKendry and Lundgren 2000; Ohashi and Kida 2002; Troude et al. 2002; Kalthoff et al. 2004; Bastin et al. 2004; de Foy et al. 2005). Figure 5.9 shows a situation from central Japan where sea/land breezes and multiscale orographically induced circulation systems cause a complex dispersion pattern of air pollutants emitted at the coast in Tokyo and in neighboring cities on the Kanto Plain (Kurita et al. 1990). The pollutants are carried inland during daytime by the sea breeze and anabatic valley and slope winds. Particularly strong heating in the central mountain basins causes the formation of a thermal low (Kuwagata and Sumioka 1991) and triggers the onset of plain-to-basin winds (Kimura and Kuwagata 1993). By the evening, the air pollutants emitted at the coast arrive in the central mountain basins of Japan where local emissions are low. Air quality in these remote regions therefore degrades significantly in the evening. During the night some of the polluted air is transported back towards the coast and possibly offshore by katabatic winds and land breezes.

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Fig. 5.9 Vertical cross section of pollutant transport processes across Central Japan, from the coastal regions to the mountainous inland region. Broken line denotes the average altitude of the mountainous central region. Vertical hatching a depression in sea level pressure, PA polluted air, TL thermal low, CL convergence line, UW upper level wind (only shown for 0600 Japan Standard Time (JST)), LB land breeze, MW mountain wind, VW valley wind, ESB extended sea breeze, LSW large scale wind toward the thermal low (Kurita et al. 1990) (© American Meteorological Society. Reprinted with permission)

In densely populated mountain basins with higher emissions than in the surrounding region, plain-to-basin winds are important because they advect relatively unpolluted air into the basin. However, the advection of cold air into the basin associated with the plain-to-basin wind might also cause strong reductions in mixing depth inside basins (Regmi et al. 2003). These effects of plain-to-basin winds on atmospheric stability and on the transport of clean or polluted air across mountain ranges or mountain passes have made these winds the subject of several investigations (De Wekker et al. 1998; Fast and Zhong 1998; Whiteman et al. 2000; Kossmann et al. 2002b; Zawar-Reza and Sturman 2006).

5.3 Research Tools Research tools typically employed in the study of air pollution in complex, mountainous terrain include observations, numerical models and physical (scale) models. While these tools are distinct, they are generally used in concert to provide maximum information from a combination of tools and approaches.

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5.3.1 Observations Many technical and logistical challenges exist when attempting to make meteorological measurements in mountainous terrain. Sites are often difficult to access and/or electrical power is not available. All those challenges recur when adding measurements of pollutants to meteorological measurements. In addition, the representativeness of single measurements in mountainous terrain is often for much smaller areas than corresponding flat terrain measurements because of the large spatial variability in pollution fields. Mountain top measurements are an exception, as under certain conditions they are representative of a regional or even larger scale. The solutions to the limited representativeness of air pollution measurements in mountainous terrain are exactly those for meteorological measurements – remote sensing, very dense networks and aircraft borne sensors. Aircraft measurements in mountainous terrain are made extraordinarily difficult by restricted and crowded airspace in mountains. Ultimately, the solutions to these difficulties involve a mix of fixed sensors monitoring the temporal changes (at many locations to also sample the spatial variability), with mobile platforms to fill in the spatial gaps, and remote sensing systems to provide broad coverage and data in inaccessible places. Chapter 8 provides a thorough discussion of these observational approaches. Examples of these solutions are provided throughout this chapter in descriptions of various field studies.

5.3.2 Numerical Modeling Difficulties involved in making atmospheric measurements in complex terrain would imply that much reliance would be placed on modeling as an adjunct to measurement. In many ways this has happened, but experience has shown that modeling in extremely steep, mountainous terrain has its own set of difficulties. Many of these difficulties are outlined in Chaps. 9, 10, and 11. Undoubtedly, the overriding advantage of numerical modeling of air pollution in complex terrain is that model output is available at locations where measurement would be impractical or even impossible. This allows investigation of the spatial structure of pollution fields, rather than the apparent structure, represented by the distribution of monitoring sites, which are only in locations that allow instrument operation. In many cases, this is driven by the availability of electrical power to drive the instruments. The major weaknesses of numerical models of air quality in complex terrain are similar to those of meteorological models in complex terrain that are used to drive them (see Chap. 10). Of paramount concern must be a consideration of mesoscale model grid resolution in relation to the scale of terrain-induced motions. In an ideal world, the model grid must be designed so that resolved scales of motion are smaller than dominant topographically induced scales of pollution advection and dispersion. In far too many cases, this ideal has to be compromised because of the computational

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cost of fine resolution grids, or because of the scales of motion being smaller than the finest resolvable scale of the mesoscale model being used. The technique of large-eddy simulation has been developed in recent years to allow application to real complex topography. However, successful application of this technique in weather and air quality forecasting is far from being realized. Furthermore, an improvement in spatial resolution in numerical models does not always imply improvements in simulations of atmospheric processes (see Chap. 10, Sect. 10.2.1). More research is certainly needed in this area.

5.3.3 Physical Modeling Physical scale models (either wind tunnels or water tanks) have been used to study a wide variety of atmospheric phenomena, including many in the field of air pollution meteorology. Most commonly, wind tunnel studies focus on plume dispersion, often in complex terrain, or around buildings (Plate 1982). Water tank studies are primarily used to study density driven phenomena (primarily anabatic or katabatic winds) in complex terrain (Chen et al. 1996). In many cases these studies are motivated by an interest in the topographic-scale (therefore smaller mesoscale) advection of pollutants in regions of complex terrain. Common target phenomena are the venting of pollutants out of valleys in anabatic flows, or conversely, the pooling of pollutants in low-lying areas because of katabatic flows. In common with all physical scale modeling of flow phenomena, the major challenge is ensuring that dimensionless governing parameters in the scale model match those in the full-scale world. This generally means that it is not possible to realistically model both turbulent diffusion and mesoscale advection simultaneously. These difficulties are compensated for by the fact that tank experiments are highly repeatable and permit measurements that are impossible in the field, and allow easy control and manipulation of external governing variables. An example of a tank study of an air pollution phenomenon in complex terrain is provided by Reuten et al. (2007) who examine pollutant trapping in a growing morning boundary layer along a steep sided valley wall. The technique has large untapped potential for studies that are locally specific, as well as generic. Some more examples of tank studies are provided in Chap. 2, Sect. 2.1.4.

5.4 Examples from Integrated Studies of Air Pollution in Complex Terrain The range and complexity of processes discussed so far indicate that local and regional air quality in mountainous areas could be severely compromised because of boundary layer meteorological processes found there. The need for scientifically

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supported air quality management strategies, and the development of air quality forecast tools has resulted in integrated, comprehensive air quality studies in many mountainous areas. These studies all capture, to varying degrees the processes discussed in isolation in this chapter. Understanding the effects of these processes on air quality is an important part of the air quality forecasts that have become increasingly popular and available in the last few years (Eder et al. 2010). Even though the level of sophistication of air quality models has increased, their performance in mountainous regions such as the Appalachian Mountains is poor (Eder et al. 2006). The incorporation of sophisticated air quality models in daily air quality forecasting follows the same process as the incorporation of numerical weather prediction models in daily weather forecasting. This process includes detailed evaluations of the performance of these forecast models. Model evaluations in mountainous terrain are particularly challenging for reasons mentioned earlier but they are extremely important to provide guidance to air quality forecasters. There are different ways in which such guidance for forecasters could be envisioned. One example would be to quantitatively assess the effects of terrain on atmospheric processes in case studies where these effects are shown to contribute to poor forecasts. These effects, such as modified boundary layer heights, wind channeling, thermally-driven flows, stagnation, etc., could then be incorporated into the daily forecasts. The detailed model evaluation that is at the core of improved forecast guidance requires: (1) significant interactions between operational forecasters and researchers, and (2) integrated, comprehensive air quality studies in mountainous areas. Such studies have been performed in the past, primarily driven by the need for scientifically supported air quality management strategies. In order to provide a glimpse into the fascinating complexity that is encountered when some of these processes occur simultaneously, or in sequence, we provide brief summaries of two examples of mountainous regions whose air quality has been studied in some detail. In undertaking this exercise, it must be recognized that human activities of notable size (and therefore resulting in substantial emissions), are seldom found on mountains, but rather in valleys, basins or plateaus surrounded by mountains. Our two examples will typify this.

5.4.1 Lower Fraser Valley, BC The Lower Fraser Valley (LFV) in British Columbia, Canada is home to the city of Vancouver and its surrounding municipalities, with a total population of roughly 2.2 million people. The valley is roughly triangular, with all three sides being approximately 100 km in length. The western margin of the valley is the inland waterway of the Strait of Georgia (Fig. 5.10). The LFV is flat bottomed, bordered to the north by the Coast Mountains, which rise steeply to an elevation of 2,200 m ASL, and to the south, by the slightly lower Cascade Mountains of Washington State, USA. The valley is subject to mild, wet winters with long periods under the influence

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Fig. 5.10 Map of the Lower Fraser Valley showing typical ozone plumes. (a) 1988 (pre controls), (b) 2003 (post controls)

of weak, occluded frontal systems, interspersed by often deep, cold, dry anticyclonic conditions (Oke and Hay 1994). In summertime, the LFV comes under the influence of an eastward extension of the Pacific High, resulting in warm, dry conditions, and very light synoptic winds. Emissions sources in the LFV are primarily due to the transportation sector, concentrated in the northwest portion of the valley, there being very little primary industry in the region. Wintertime air pollution is largely oxides of nitrogen (NOx) and particulate matter (PM), and is closely linked to transportation corridors. The most important summertime air pollution concern in the LFV is ozone and secondary PM (Steyn et al. 1997). The occurrence and spatiotemporal variability of summertime ozone and PM episodes is strongly influenced by the presence of interacting land/sea breeze circulations, and valley- and slopeflow systems. The strong recirculation of pollutants in these topographically driven flows and the presence of very shallow convective boundary layers (Steyn and Oke 1982; H¨ageli et al. 2000) lead to far more severe pollution episodes than might be expected, given the relatively small population and absence of heavy industry. Contributing to the severity of the episodes is vertical, horizontal and day-to-day

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Fig. 5.10 (continued)

recirculation of pollutants as indicated in Fig. 5.11. These three recirculation modes are driven by a complex interplay of slope flows, land/sea breezes and boundary layer mixing. These quasi-closed recirculation pathways are characteristic of the LFV summertime ozone episodes which occur under very weak synoptic forcing, and contribute to day-to-day buildup of pollutants within an episode. Evidence for the formation of the elevated polluted layer above the CBL by topographically induced advection of polluted air is given in Fig. 5.12. Chapter 8, Sect. 8.2 shows some of the meteorological, and therefore pollutant distribution complexities that arise from exchange of air between side valleys and the major LFV. Undoubtedly, pollutants stored in these side valleys by day are recirculated by down-valley flows at night. Figure 5.10 indicates typical ozone plumes before and after a program of NOx and VOC emission controls. The overall shape of both plumes is strongly affected by topographic barriers, and sea breeze channeling. The eastward (downwind) displacement of the more recent plume is hypothesized to be a result of changing NOx /VOC ratios resulting in a less reactive chemical mixture under essentially unchanged wind speeds (Ainslie and Steyn 2007).

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Fig. 5.11 Three modes of pollutant recirculation in the Lower Fraser Valley. (a) Pollutants emitted into the morning sea breeze are advected inland during the day and return by the landward arm of the land breeze at night. (b) Pollutants emitted into the evening land breeze area advected seaward during the night and return by the seaward arm of the sea breeze by day. (c) Pollutants emitted into the sea breeze by day are advected landward (solid heavy arrow) and carried aloft by upslope flows into the return flow, and are subsequently carried downward by subsidence (open arrow), entrained into the convective boundary layer and mixed downwards (small curved arrows)

5.4.2 Upper Rhine Valley The Upper Rhine Valley located in south western Germany, eastern France, and northern Switzerland is a densely populated and industrialised area where complex terrain meteorology and air quality issues have been of great interest for many years (e.g. Fiedler and Prenosil 1980; Fiedler et al. 1987; Fiedler 1992a, b; Fiedler and Zimmermann 1993; Fiedler and Borell 2000). In September 1992, the TRACT (Transport of Air Pollutants over Complex Terrain) field campaign was conducted in the Upper Rhine Valley providing a dataset with a high temporal and spatial resolution of the CBL over mountainous terrain (Fiedler 1992a; Fiedler and Borell 2000). Measurements from rawinsonde, tethersonde, research aircraft and sodar (see Fig. 5.13) on a cross section through the Black Forest Mountains were used to determine the spatial and temporal behavior of the CBL (De Wekker 1995; Kossmann et al. 1998; Kalthoff et al. 1998). The terrain is characterized by a sharp transition from the Rhine Valley to the Black Forest region, with a height difference of roughly 1,000 m over a horizontal distance of

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Fig. 5.12 Polluted boundary layer in LFV indicated by lidar backscatter superposed on profiles of potential temperature (white solid line) and specific humidity (white dashed line) and inferred AL height (dark line) measured on July 26, 2001 from 1314 to 1355 Pacific Standard Time. The mountain slope can just be seen rising to the right (north) of the figure. Sodar data indicate winds with a slight northerly component above the CBL top (Reuten et al. 2005) (© Springer. Reprinted with permission)

about 10 km. The analyses showed that during the morning hours, the mixed layer top followed the underlying terrain but generally tended to become more level, i.e., less terrain-following, over the course of the day. In summary, three types of afternoon CBL behavior were identified (Fig. 5.14). In the first type (typified by panel 1), the mixed layer over the Rhine Valley reached heights of about 2,000 m and the top of the mixed layer was relatively level over the investigation area. In the second type (typified by panel 3), boundary layer development in the Rhine Valley was delayed by the presence of fog, and the afternoon mixed layer stayed well below the mountain height. Consequently, the top of the mixed layer more or less followed the steep western slope of the Black Forest region in the afternoon. In the third type (typified by panel 2), the behavior was intermediate between the other types, with mixed layer heights over the Black Forest region a few hundred meters higher than over the Rhine Valley. A common feature of all three types of behavior is the presence of a relatively horizontal capping inversion over the Black Forest region. The mixed layer top obviously does not follow the individual small-scale ridges and valleys in the afternoon. Overall, smaller afternoon CBLs were observed over the mountain top site Hornisgrinde (the highest elevation in the investigation area) than in the Rhine Valley and the Black Forest region east of the Hornisgrinde. Applying one-dimensional mixed layer growth rate models for a valley and the mountain top site showed that for the valley site, relatively good correspondence was found with observations but that the mixed layer growth rates for

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Fig. 5.13 Vertical cross sections of potential temperature, specific humidity and horizontal wind vectors from the foothills of the Vosges Mountains (left) through the Upper Rhine Valley (center) to the Black Forest Mountains (right) at around 1300 Central European Summer Time (CEST) of 11 September 1992 (De Wekker 1995). White lines in the upper two panels represent balloon ascent paths or aircraft flight tracks

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Fig. 5.14 Schematic representation of three different types of afternoon mixed layer height (zi ) behaviour along a cross-section from the Upper Rhine Valley to the northern Black Forest derived from observations of the TRACT field campaign (De Wekker et al. 1997)

the mountain top site were clearly overestimated by these models (De Wekker 1995; Kossmann et al. 1998). De Wekker (1995) and Binder (1997) proposed the use of an effective sensible heat flux for use in growth rate models that implicitly takes into account the effects of advection, orography shape and other effects that influence CBL growth over mountain ridges. The large density of surface-based meteorological stations during TRACT allowed the identification of major wind systems in the Upper Rhine Valley and in some of the adjacent side-valleys (Fig. 5.15). The wind systems in the side valleys show a pronounced diurnal cycle with upvalley (downvalley) and upslope (downslope) winds during the day (night). The influence of these flows on the ozone concentrations during TRACT was studied by L¨offler-Mang et al. (1997). Stations in side-valleys of the upper Rhine Valley often showed less nocturnal ozone removal (compared to stations on flat terrain) or even a clear secondary ozone maximum in the night due to down-valley advection of ozone-rich and weakly polluted air from the mountains.

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The behavior of ozone and it precursors was also investigated in the Schauinsland Ozone Precursor Experiment (SLOPE) in 1996 in the southern part of the Upper Rhine Valley near Freiburg (Kalthoff et al. 2000; Fiedler et al. 2000). Meteorological and chemical measurements were carried out at several stations along the expected transport path between Freiburg in the Rhine Valley and Schauinsland, a mountain top location in the Black Forest. Results showed that not only mixing layer growth, but also flow splitting and mountain venting processes, induced on the slopes and in the side valleys play an important role in explaining the dispersion of pollutants up the Black Forest Mountains. Kossmann et al. (1999) showed similar results for

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the northern part of the upper Rhine Valley. Another important result from SLOPE is the strengthening and lowering of an elevated inversion caused by the advection associated with a thermally driven upvalley wind system. This process confined the air pollutants to a shallow layer near the surface and degraded the air quality. Similar interactions between thermally driven wind systems and CBL depth have been noted by Kossmann et al. (1998) and De Wekker (2008). The along-valley flow in the Upper Rhine Valley, which is evident in Fig. 5.15, is mainly due to pressure-driven channeling (Wippermann 1984; Gross and Wippermann 1987; Kalthoff and Vogel 1992). This type of channeling has been given much attention in the case of the upper Rhine Valley, and has important consequences for the dispersion of air pollutants (see Sect. 5.2.3).

5.5 Conclusion Throughout this chapter we have stressed that air quality in regions of complex, mountainous topography is frequently (and quite often severely) degraded because of meteorological processes and phenomena related to the topography. While we have chosen only two regions as examples to illustrate this, there exist many other locations that experience degraded air quality because of topographic effects. The difficulties of both atmospheric measurement and modeling in complex terrain mean that there will always be substantial uncertainty over air pollution problems in complex terrain. This uncertainty translates into difficulties in both forecasting pollution, and providing scientific guidance to policy makers. The current practice for routine air quality forecasts is to employ numerical models operating over regional and continental scales, as exemplified by Kang et al. (2009). The horizontal resolution of such forecasts is generally 10–20 km, a scale at which most of the phenomena discussed in this chapter are simply not resolved. This means that anyone wanting to forecast air quality in a mountainous region will have to take the forecast provided by model output, and interpret or modify it taking into account the phenomena and effects covered in this chapter. As these models develop and increase their resolution, and their ability to explicitly capture the phenomena discussed in this chapter, such forecaster intervention will become less important. It is unlikely however that it will ever become unnecessary. It must be emphasized that the quality of an air pollution forecast based on numerical model output will depend on a number of factors. The first among these will be the requirement of accurate model initialization and boundary conditions for both meteorology and atmospheric chemistry. These may be provided through data assimilation schemes, but chemical data assimilation requires measurements of many chemical species, which generally are not measured with sufficient detail. The second requirement is for accurate spatially, temporally and chemically resolved emissions data. Such data are generally not available in sufficient resolution. This difficulty is in most cases the major factor limiting the accuracy of air quality forecasts. The third requirement is for detailed and chemically realistic models of

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aerosol chemistry and physics. This matter is a topic for much current research, and therefore a source of much uncertainty in the context of operational air quality forecasts. These three requirements are seldom uniformly met, and so efforts to determine the source of deficiencies in air quality forecasts are made especially difficult because of interactions between multiple sources of model weaknesses. It is often unclear whether inadequacies in air quality models are due to meteorological, chemical or emissions (or all three) weaknesses. An additional difficulty arises because numerical models needed for air quality forecasts must perform both meteorological and chemical transformation calculations, resulting in a great increase in computational demand over pure meteorological modeling. The result often is that the spatial resolution is sacrificed in order to allocate computational resources to the chemical modeling. The resulting reduction in spatial resolution can result in mountain induced meteorological processes being inadequately resolved. Another consequence of the uncertainty surrounding air quality in mountainous terrain is that most studies of air pollution in such terrain combine both observations and modeling as approaches to building understanding. Both approaches will always be needed, with observations to tie model output to measured reality, and models to fill in the unmonitored spaces. Many phenomena become evident only through observation, and then subsequently, are better understood through the use of models, which then become the most important tools for making predictions, and exploring scenarios. Models and observations are tied in an upward spiraling process of development, and nowhere is this as evident as in studies of air pollution in complex terrain. In this way, the increasing demands of air quality forecasting will inspire further development of new parameterizations of meteorological processes, which will in turn make possible more accurate air quality forecasts in complex, mountainous terrain Acknowledgements The authors would like to thank the three anonymous reviewers and the book editors for their helpful comments that improved this chapter. We also would like to thank Prof. Franz Fiedler from the ‘Institute for Meteorology and Climate Research’ of the ‘Karlsruhe Institute of Technology’ (Germany) for his permission to use Fig. 5.4, Dr. Jerome Fast for his permission to use Fig. 5.3, and Eric Leinberger who drafted Figs. 5.1 and 5.11.

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Chapter 6

Theory, Observations, and Predictions of Orographic Precipitation Brian A. Colle, Ronald B. Smith, and Douglas A. Wesley

Abstract There have been rapid advances in the understanding of orographic precipitation during the past two decades given the advent of high resolution mesoscale modeling and numerous field studies around the world. This chapter begins with introducing the fundamental ingredients, processes, and scaling parameters for orographic precipitation. If the low level air is stable, terrain flow blocking can occur, which shifts the precipitation enhancement upwind of the barrier. Lowlevel diabatic cooling from evaporation and melting can enhance the near-surface stability and flow blocking. In contrast, latent heating within the cloud reduces the effective stability and the potential for flow blocking, which in turn results in stronger vertical motions over the ridges and increases the riming and precipitation fallout. For less stable flows, there are mountain gravity waves over the mountain that can change the depth and upstream extent of the orographic cloud, and lead to precipitation enhancements over individual windward ridges. Barrier dimension is also important, with wide barriers favoring precipitation enhancement upwind of the crest and more efficient water vapor removal from the ambient flow. If the ridges are very narrow, the mountain waves decay with height and have less impact on the precipitation. For unstable flow, the upslope flow can trigger convective systems or quasi-stationary banded precipitation. The various orographic processes are illustrated using several field study and modeling results. The prediction of orographic precipitation is discussed using a

B.A. Colle () School of Marine and Atmospheric Sciences, Stony Brook University/SUNY, Stony Brook, NY 11794-5000, USA e-mail: [email protected] R.B. Smith Geology and Geophysics Department, Yale University, New Haven, CT 06520-8109, USA D.A. Wesley Compass Wind, 1730 Blake St., Ste. 400, Denver, CO 80202, USA F. Chow et al. (eds.), Mountain Weather Research and Forecasting, Springer Atmospheric Sciences, DOI 10.1007/978-94-007-4098-3 6, © Springer ScienceCBusiness Media B.V. 2013

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1.33-km grid spacing simulation and sensitivity results from a linear orographic precipitation model for a flooding event over southwest Washington in early November 2006. The chapter concludes with a summary and areas for future work.

6.1 Introduction Orographic precipitation can be defined as the modification of rain, snow, and other hydrometeors resulting from the interaction of moist flow with topography. As noted by Sawyer (1956), the three important factors for orographic precipitation are: (1) the interaction of the ambient flow with terrain, (2) cloud microphysical processes, and (3) larger-scale atmospheric circulation. For enhanced precipitation growth to occur over the windward slope (Fig. 6.1), there is often a synergistic relationship between the large-scale ascent associated with an approaching baroclinic or tropical cyclone, and the moist dynamical flow (upslope) response, which is dependent on the magnitude of the upstream flow orientated perpendicular to the mountain, moisture, and stratification (Fig. 6.1). The microphysical processes and the time scale for available ice/water growth within the cloud can also modify the precipitation distribution. Atmospheric models and operational forecasters need to consider all of these factors in order to forecast precipitation accurately in areas of steep terrain. There has been a rapid advance in the understanding of orographic precipitation with the application of high-resolution models and new observational field datasets collected over various topographic barriers around the world (Fig. 6.2). During the last few decades these field studies have quantified various orographic precipitation processes for a broad spectrum of ambient environments and barrier dimensions (Table 6.1). For example, the Cascade Project in the early 1970s examined orographic airflow and microphysics over the Washington Cascades using aircraft (Hobbs et al. 1973; Hobbs 1975). During the 1980s, the Sierra Cooperative Pilot Project (SCPP) studied the airflow and precipitation processes over the Sierra Nevada Mountains of California using both ground-based radar and aircraft in situ sensors (Reynolds and Dennis 1986). The mesoscale flow and precipitation structures of storms approaching the U.S. West coast were also studied during the Coastal Observations and Simulation with Topography (COAST) experiments in December 1993 and 1995 (Bond et al. 1997) and in the California Land-Falling Jets (CALJET) and Pacific Land-Falling Jets (PACJET) experiments in 1998 and 2000–2002, respectively (Ralph et al. 1999; Neiman et al. 2002). Using airborne dual-Doppler radar data around the Olympic Mountains in COAST, Colle and Mass (1996) showed that three-dimensional winds can be synthesized from airborne Doppler radar over steep terrain. This helped put the precipitation in context with the three-dimensional flow, which motivated other subsequent orographic field experiments to use this airborne Doppler technology. For example, the IMPROVE II (Improvement of Microphysical PaRameterization through Observational Verification Experiment II) field program investigated the

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Fig. 6.1 Schematic diagram of the elements of orographic precipitation: upstream water vapor flux (Fw ), large-scale ascent, windward ascent, streamlines of theta-E, snow and graupel fallout, and windward precipitation within a distance P

Fig. 6.2 Location of orographic precipitation field projects around the world that involved radar, aircraft, and/or isotope measurements in areas of terrain (shaded). See Table 6.1 for a detailed list of the experiments and their focus

Table 6.1 Major orographic precipitation field studies around the world (shown on Fig. 6.2) that utilized radar, aircraft, and/or isotope measurements Number Project title Location Year Objective 1 N/A South Wales 1970s Precipitation enhancement over small hills 2 Sierra – Cooperative Project Sierra Mountains late 1970s–1980s Precipitation evolution, thermodynamics, and microphysics over a wide barrier with landfalling storms 3 Taiwan Area Mesoscale Experiment Taiwan 1987 The effects of orography on the Mei-Yu front and (TAMEX) on mesoscale convective systems 4 Hawaiian Rainband Experiment (HARP) Hawaii 1990 Diurnal variability of precipitation around isolated topography 5 Coastal Observation and Simulation with Olympic Mountains 1993 Precipitation and kinematic evolution over Topography (COAST) isolated barrier 6 Winter Icing Storms Project (WISP) Colorado Front 1994 Ice nucleation, super-cooled water, and Range precipitation evolution along the Front Range 7 Southern Alpine Precipitation Experiment New Zealand Alps 1996 Understanding the processes through which the (SALPEX) Southern Alps (narrow steep barrier) influence precipitation 8 Mesoscale Alpine Programme (MAP) Alps 1999 Linkage of moist dynamics (blocked and unblocked flow) with precipitation distribution and processes 9 California Landfalling Jets Experiment California coastal 1998, 2000–2001 Coastal precipitation enhancement, warm rain CALJET/Pacific Jets (PACJET) mountains processes, and atmospheric rivers 10 Improvement of Microphysical Central Oregon 2001 Precipitation processes and microphysics, and Parameterization through Cascades the role of gravity waves on precipitation Observational Verification Experiment (IMPROVE-2) 11 Intermountain Precipitation Experiment Wasatch Mountains 2001 Precipitation processes, diabatic impacts, and (IPEX) microphysics for narrow barrier 12 Southern Andes Project Southern Andes 2005 Air mass transformation and isotope analysis 13 Convective Orographic Precipitation Southwest Germany 2007 Study orographically-induced convective Experiment (COPS) precipitation

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microphysics and orographic cloud structures for frontal systems crossing the Oregon Cascades (Stoelinga et al. 2003). Baroclinic storm systems and moist southerly flow impinging on the Alps were documented in autumn 1999 during the Mesoscale Alpine Programme (MAP, Bougeault et al. 2001; Rotunno and Houze 2007). Meanwhile, the impact of more narrow and steep barriers on orographic precipitation, such as the Wasatch in Utah (IPEX, Schultz et al. 2002) and southern Andes (Smith and Evans 2007) have also been investigated. More tropical environments associated with three-dimensional island geometries were investigated in Taiwan during TAMEX (Kuo and Chen 1990) and Hawaiian Rainband Project (HARP) (Chen and Nash 1994). More recently, convective initiation over terrain was investigated over southwest Germany during the Convective and Orographicallyinduced Precipitation Study (COPS) experiment (Wulfmeyer et al. 2008). Significant loss of life and disruptions to the local economy can occur when flash flooding, avalanches, and transportation delays occur in association with heavy orographic precipitation as outlined in Chap. 1. There have been several flash convective flood events in areas of steep terrain, such as the southern slopes of the European Alps (Lin et al. 2001), southern Appalachians (Pontrelli et al. 1999), and the Colorado Front Range (Petersen et al. 1999). Along the mountainous U.S. West Coast, a plume of subtropical moisture associated with a landfalling baroclinic wave can interact with the steep coastal terrain to produce flooding over Pacific Northwest (Colle and Mass 2000; Lackmann and Gyakum 1999) and the California coast (Ralph et al. 2003). Meyers et al. (2003) and Poulos et al. (2002) investigated a heavy snow and blizzard event over the Front Range of the Rocky Mountains in 1997 that severely disrupted transportation during the 24-h snowfall event. Understanding the fine-scale precipitation structures over a topographic barrier is also important for hydrologic streamflow and river modeling. For example, Westrick et al. (2002) illustrated that the streamflow forecasts over the Washington Olympics and Cascades were sensitive to the observed and simulated precipitation distributions on the ridge and valley scale. Ralph et al. (2003) also showed that the peak river flows during CALJET were highly sensitive to the exact location of the windward enhancements and rain shadows. Landfalling hurricanes often create heavy rainfall and flooding in areas of terrain, such as hurricane Agnes along the Appalachians (Carr and Bosart 1978), and hurricane Dean over the mountainous island of Dominica (Smith et al. 2009b). Mesoscale atmospheric models, such as the Penn State – National Centers for Atmospheric Mesoscale Model (MM5; Grell et al. 1994) and Weather Research and Forecasting model (WRF; Skamarock et al. 2005), have been shown to realistically predict precipitation structures when run at