Advances in Land Remote Sensing: System, Modeling, Inversion and Application [1 ed.] 9781402064494, 1402064497

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Advances in Land Remote Sensing

Advances in Land Remote Sensing System, Modeling, Inversion and Application

Shunlin Liang Editor Department of Geography, University of Maryland, College Park, MD, USA

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Shunlin Liang University of Maryland College Park, MD USA

ISBN 978-1-4020-6449-4

e-ISBN 978-1-4020-6450-0

Library of Congress Control Number: 2007940919 c 2008 Springer Science+Business Media B.V. ° No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover illustration: From sensors and platforms, to information extraction and applications (compilation by S. Liang) Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com

Preface

This book is primarily based on presentations in the three reviewing panels of the 9th International Symposium on Physical Measurements and Signatures in Remote Sensing held at the Institute for Geographical Sciences and Natural Resource Research, Chinese Academy of Sciences, China, in October 2005. It presents a collection of review papers on remote sensing sensor systems, radiation modeling and inversion of land surface variables, and remote sensing applications. Each chapter summarizes the progress in the past few years and also identifies the research issues for the near future.

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Acknowledgements

This symposium series is affiliated with the International Society for Photogrammetry and Remote Sensing (ISPRS) Commission VII/I Working Group on Fundamental Physics and Modeling led by Professor Michael Schaepman (Chair, Wageningen University, the Netherlands), Professor Shunlin Liang (co-Chair, University of Maryland, USA), and Dr. Mathias Kneubuehler (Secretary, University of Zurich, CH, Switzerland) (2004–2012). It was sponsored and/or financially supported by the Institute of Geographical Sciences and Natural Resources Research (IGSNRR) of Chinese Academy of Sciences (CAS), Institute of Remote Sensing Applications (IRSA) of CAS, Chinese 973 Project “Quantitative Remote Sensing of Major Factors for Spatio-temporal Heterogeneity on the Land Surface” undertaken by Beijing Normal University, US National Aeronautics and Space Administration (NASA), International Society for Photogrammetry and Remote Sensing, IEEE Geoscience and Remote Sensing Society, and Scientific Data Center for Resources and Environment, CAS. This symposium would not be successful without scientific leadership by the International Scientific Committee and effective organization by the local Organizing Committee.

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International Scientific Committee

Professor Guanhua Xu, Minister of the Chinese Ministry of Science and Technology, China (honorary Chair) Professor Shunlin Liang, University of Maryland, USA (Chair) Dr. Fr´ed´eric Baret, INRA, Avignon, France Professor Mike Barnsley, University of Wales Swansea, UK Professor Marvin Bauer, University of Minnesota, USA Professor Jon Benediktsson, University of Iceland, Iceland Professor Jing Chen, University of Toronto, Canada Professor Peng Gong, University of California at Berkeley, USA Dr. David Goodenough, Pacific Forestry Centre, Natural Resources Canada Dr. Tom Jackson, USDA /ARS at Beltsville, Maryland, USA Dr. David Jupp, CSIRO Earth Observation Centre, Australia Dr. Yann Kerr, CNES/CESBIO, France Dr. Marc Leroy, MEDIAS, France Dr. Philip Lewis, University College London, UK Professor Deren Li, Wuhan University, China Professor Xiaowen Li, Beijing Normal University, China Professor Jiyuan Liu, IGSNRR, CAS, China Dr. John V. Martonchik, Jet Propulsion Laboratory, USA Professor Ranga Myneni, Boston University, USA Professor Ziyuan Ouyang, Institute of Geochemistry, CAS, China Dr. Jeff Privette, NASA /GSFC, USA Dr. Jon Ranson, NASA /GSFC, USA Professor Michael Schaepman, Wageningen University, The Netherlands Professor Jose Sobrino, University of Valencia, Spain Dr. Karl Staenz, Canadian Centre for Remote Sensing, Canada Professor Alan Strahler, Boston University, USA Professor Qingxi Tong, Institute of Remote Sensing Applications, CAS, China Dr. Michel Verstraete, JRC, Ispra, Italy Dr. Charlie Walthall, USDA /ARS at Beltsville, Maryland, USA Dr. Zhengming Wan, University of California at Santa Barbara, USA

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Organizing Committee Professor Jiyuan Liu, Director of IGSNRR, CAS (co-Chair) Professor Xiaowen Li, Director of Center for Remote Sensing and GIS, Beijing Normal University and Director of IRSA, CAS (co-Chair) Professor Dafang Zhuang, Execute Vice-director of Scientific Data Center for Resources and Environment, CAS (Vice Chair) Professor Mingkui Cao, IGSNRR, CAS Professor Changqing Song, Chinese National Foundation of Sciences Professor Renhua, Zhang, IGSNRR, CAS Professor Lixin Zhang, Beijing Normal University Dr. Keping Du, Beijing Normal University Professor Mengxue Li, National Remote Sensing Center of China Professor Boqin Zhu, Institute of Remote Sensing Applications, CAS Dr. Ronggao Liu, IGSNRR, CAS (General Secretary)

Shunlin Liang University of Maryland, College Park, MD, USA

Reviewers

Each chapter is anonymously reviewed by at least one reviewer. Their valuable comments and suggestions have greatly helped to improve the quality of the volume. Jing M. Chen University of Toronto, Canada Jan Clevers Wageningen University, The Netherlands Ruth DeFries University of Maryland, USA Alan R. Gillespie University of Washington, USA Hongliang Fang University of Maryland, USA Xiuping Jia The University of New South Wales, Australia David L.B. Jupp CSIRO Marine and Atmospheric Research, Australia Yann H. Kerr CNES/CESBIO, France Yuri Knyazikhin Boston University, USA Randy Koster NASA, USA Eric F. Lambin University of Louvain, Belgium Tiit Nilson Tartu Observatory, Estonia

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Paolo Pampaloni IFAC-CNR, Italy Bernard Pinty EC Joint Research Centre, Italy Jeff Privette NOAA, USA

Reviewers

Contents

1

Recent Advances in Land Remote Sensing: An Overview . . . . . . . . . . Shunlin Liang

1

Part I Remote Sensing Systems 2

Passive Microwave Remote Sensing for Land Applications . . . . . . . . . Thomas J. Jackson

3

Active Microwave Remote Sensing Systems and Applications to Snow Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Jiancheng Shi

4

Multi-angular Thermal Infrared Observations of Terrestrial Vegetation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Massimo Menenti, Li Jia, and Zhao-Liang Li

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Terrestrial Applications of Multiangle Remote Sensing . . . . . . . . . . . . 95 Mark J. Chopping

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Part II Physical Modeling and Inversion Algorithms 6

Modeling the Spectral Signature of Forests: Application of Remote Sensing Models to Coniferous Canopies . . . . . . . . . . . . . . . . . . . . . . . . . 147 Pauline Stenberg, Matti M˜ottus, and Miina Rautiainen

7

Estimating Canopy Characteristics from Remote Sensing Observations: Review of Methods and Associated Problems . . . . . . . . 173 Fr´ed´eric Baret and Samuel Buis

8

Knowledge Database and Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Jindi Wang and Xiaowen Li

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Contents

9

Retrieval of Surface Albedo from Satellite Sensors . . . . . . . . . . . . . . . . 219 Crystal Schaaf, John Martonchik, Bernard Pinty, Yves Govaerts, Feng Gao, Alessio Lattanzio, Jicheng Liu, Alan Strahler, and Malcolm Taberner

10

Modeling and Inversion in Thermal Infrared Remote Sensing over Vegetated Land Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Fr´ed´eric Jacob, Thomas Schmugge, Albert Olioso, Andrew French, Dominique Courault, Kenta Ogawa, Francois Petitcolin, Ghani Chehbouni, Ana Pinheiro, and Jeffrey Privette

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Spectrally Consistent Pansharpening . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 Ari Vesteinsson, Henrik Aanaes, Johannes R. Sveinsson, and Jon Atli Benediktsson

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Data Assimilation Methods for Land Surface Variable Estimation . . 313 Shunlin Liang and Jun Qin

13

Methodologies for Mapping Land Cover/Land Use and its Change . . 341 Nina Siu-Ngan Lam

14

Methodologies for Mapping Plant Functional Types . . . . . . . . . . . . . . 369 Wanxiao Sun and Shunlin Liang

Part III Remote Sensing Applications 15

Monitoring and Management of Agriculture with Remote Sensing . . 397 Zhongxin Chen, Sen Li, Jianqiang Ren, Pan Gong, Mingwei Zhang, Limin Wang, Shenliang Xiao, and Daohui Jiang

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Remote Sensing of Terrestrial Primary Production and Carbon Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Maosheng Zhao and Steven W. Running

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Applications of Terrestrial Remote Sensing to Climate Modeling . . . . 445 Robert E. Dickinson

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Improving the Utilization of Remotely Sensed Data . . . . . . . . . . . . . . . 465 John R. Townshend, Stephen Briggs, Roy Gibson, Michael Hales, Paul Menzel, Brent Smith, Yukio Haruyama, Chu Ishida, John Latham, Jeff Tschirley, Deren Li, Mengxue Li, Liangming Liu, and Gilles Sommeria

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Emerging Issues in Land Remote Sensing . . . . . . . . . . . . . . . . . . . . . . . 485 Shunlin Liang, Michael Schaepman, Thomas J. Jackson, David Jupp, Xiaowen Li, Jiyuan Liu, Ronggao Liu, Alan Strahler, John R. Townshend, and Diane Wickland

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 CD-ROM included

Contributors

Henrik Aanaes Informatics and Mathematical Modelling, Technical University of Denmark, Denmark [email protected] Frederic Baret UMR1114, INRA-CSE, 84914 Avignon, France [email protected] Jon Atli Benediktsson Department of Electrical and Computer Engineering, University of Iceland, Hjardarhaga 2-6, 107 Reykjavik, Iceland [email protected] Stephen Briggs European Space Agency, Via Galileo Galilei, 00644 Frascati, Rome, Italy [email protected] Sanuel Buis UMR1114, INRA-CSE, 84914 Avignon, France Ghani Chehbouni Institute of Research for the Development, Center for Spatial Studies of the Biosphere, UMR CESBio, Toulouse, France [email protected] Zhongxin Chen Key Laboratory of Resource Remote Sensing & Digital Agriculture, Ministry of Agriculture, Beijing 100081, China [email protected] Mark J. Chopping Department of Earth and Environmental Studies, Montclair State University, 1 Normal Ave, Montclair, NJ 07043, USA [email protected]

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Contributors

Dominique Courault National Institute for Agronomical Research, Climate – Soil – Environment Unit, UMR CSE INRA / UAPV, 84914 Avignon, France [email protected] Robert E. Dickinson School of Earth and Atmospheric Sciences, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332-0340, USA [email protected] Andrew French United States Department of Agriculture/Agricultural Research Service, US Arid Land Agricultural Research Center, 21881 North Cardon Lane, Maricopa, AZ 85238, USA [email protected] Feng Gao Earth Resources Technology, Inc., 8106 Stayton Dr., Jessup, MD 20794, USA Roy Gibson EUMETSAT [email protected] Pan Gong Institute of Agricultural Resources & Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China Yves Govaerts EUMETSAT, Am Kavalleriesand 31, D-64295 Darmstadt, Germany [email protected] Michael Hales NOAA, Silver Spring, MD 20910, USA [email protected] Yukio Haruyama JAXA, 1-8-10 Harumi, Chuo-ku, Tokyo 104-6023, Japan [email protected] Chu Ishida JAXA, 1-8-10 Harumi, Chuo-ku, Tokyo 104-6023, Japan [email protected] Thomas J. Jackson USDA ARS Hydrology and Remote Sensing Lab, 104 Bldg. 007 BARC-West, Beltsville, MD 20705, [email protected] Fr´ed´eric Jacob Institute of Research for the Development, Laboratory for studies on Interactions between Soils – Agrosystems – Hydrosystems, UMR LISAH SupAgro/INRA/IRD, Montpellier, France [email protected]

Contributors

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Li Jia Alterra Green World Research, Wageningen University and Research Centre, The Netherlands [email protected] Daohui Jiang Institute of Agricultural Resources & Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China David Jupp CSIRO Marine and Atmospheric Research, Canberra ACT 2601 Australia [email protected] Nina Siu-Ngan Lam Department of Environmental Studies, Louisiana State University, Baton Rouge, LA 70808, USA [email protected] John Latham Food and Agriculture Organization, Rome, Italy [email protected] Alessio Lattanzio Makalumedia gmbh, Robert-Bosch Strasse 7, 64296 Darmstadt, Germany Deren Li Wuhan University, 39 Loyu Road, Wuhan, 430070, China [email protected] Mengxue Li NRSCC, 15B, Fuxing Road, Beijing, 100862, China [email protected] Sen Li Institute of Agricultural Resources & Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China Xiaowen Li Research Center for Remote Sensing and GIS, Beijing Normal University, No.19 XieJieKouWaiDaJie Street, Beijing 100875, China [email protected] Zhao-Liang Li Institute of Geographic Sciences and Natural Resources Research, Beijing, China Shunlin Liang Department of Geography, University of Maryland, College Park, USA [email protected] Jicheng Liu Department of Geography and Environment, Boston University, 675 Commonwealth Ave., Boston, MA 02215, USA

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Contributors

Jiyuan Liu Institute for Geographical Sciences and Natural Resource Research, Chinese Academy of Sciences, Beijing, China [email protected] Liangming Liu National Remote Sensing Center of China Ronggao Liu Institute for Geographical Sciences and Natural Resource Research, Chinese Academy of Sciences, Beijing, China [email protected] John Martonchik Jet Propulsion Laboratory, Mail Stop 169-237, 4800 Oak Grove Dr., Pasadena, CA 91109, USA [email protected] Massimo Menenti TRIO/LSIIT, University Louis Pasteur (ULP), Strasbourg, France and Istituto per i Sistemi Agricoli e Forestali del Mediterraneo (ISAFOM), Naples, Italy [email protected] Paul Menzel University of Wisconsin, Space Science and Engineering Center, Madison, WI 53706, USA [email protected] Matti M˜ottus Department of Forest Ecology, FI-00014 University of Helsinki, Finland; Tartu Observatory, 61602 T˜oravere, Tartumaa, Estonia [email protected] Kenta Ogawa Department of Geo-system Engineering, University of Tokyo and Hitachi Ltd, Tokyo, Japan Albert Olioso National Institute for Agronomical Research, Climate – Soil – Environment Unit, UMR CSE INRA/UAPV, Avignon, France [email protected] Francois Petitcolin ACRI-ST, Sophia Antipolis, France [email protected] Ana Pinheiro Biospheric Sciences Branch, NASA’s GSFC, Greenbelt, MD 20771, USA [email protected]

Contributors

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Bernard Pinty Global Environment Monitoring Unit, IES, EC Joint Research Centre, TP 440, via E. Fermi, I-21020 Ispra (VA), Italy [email protected] Jeffrey Privette NOAA’s National Climatic Data Center, Asheville, NC 28801-5001, USA [email protected] Jun Qin Institute for Geographical Science and Natural Resource Research, Beijing, China [email protected] Miina Rautiainen Department of Forest Resource Management, FI-00014 University of Helsinki, Finland [email protected] Jianqiang Ren Key Laboratory of Resource Remote Sensing & Digital Agriculture, Ministry of Agriculture, Beijing 100081, China and Institute of Agricultural Resources & Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China Steven W. Running Numerical Terradynamic Simulation Group, Department of Ecosystem and Conservation Science, University of Montana, Missoula, MT 59812, USA [email protected] Crystal Schaaf Department of Geography and Environment, Boston University, 675 Commonwealth Ave., Boston, MA 02215, USA [email protected] Michael Schaepman Centre for Geo-Information, Wageningen University, Wageningen, The Netherlands [email protected] Thomas Schmugge Gerald Thomas Professor of Water Resources, College of Agriculture New Mexico State University, Las Cruces, NM, USA [email protected] Jiancheng Shi Institute for Computational Earth System Science, University of California, Santa Barbara, CA 93106-3060, USA [email protected] Brent Smith NOAA, Silver Spring, MD 20910, USA [email protected]

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Contributors

Gilles Sommeria World Climate Research Programme, WMO, CH-1211 Geneva, Switzerland [email protected] Pauline Stenberg Department of Forest Resource Management, FI-00014 University of Helsinki, Finland [email protected] Alan Strahler Department of Geography and Environment, Boston University, 675 Commonwealth Ave., Boston, MA 02215, USA [email protected] Wanxiao Sun Department of Geography and Planning, Grand Valley State University, USA [email protected] Johannes R. Sveinsson Department of Electrical and Computer Engineering, University of Iceland, Hjardarhaga 2-6, 107 Reykjavik, Iceland [email protected] Malcolm Taberner Global Environment Monitoring Unit, IES, EC Joint Research Centre, TP 440, via E. Fermi, I-21020 Ispra (VA), Italy [email protected] John R. Townshend Department of Geography, University of Maryland, College Park, MD 20742, USA [email protected] Jeff Tschirley Food and Agriculture Organization, 00153 Rome, Italy [email protected] Ari Vesteinsson Department of Electrical and Computer Engineering, University of Iceland, Hjardarhaga 2-6, 107 Reykjavik, Iceland Jindi Wang Research Center for Remote Sensing and GIS, Beijing Normal University, No.19 XieJieKouWaiDaJie Street, Beijing 100875, China [email protected] Limin Wang Key Laboratory of Resource Remote Sensing & Digital Agriculture, Ministry of Agriculture, Beijing 100081, China Diane Wickland NASA Headquarters, Washington, DC, USA [email protected]

Contributors

Shenliang Xiao Institute of Agricultural Resources & Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China Mingwei Zhang Institute of Agricultural Resources & Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 100081, China Maosheng Zhao Numerical Terradynamic Simulation Group, Department of Ecosystem and Conservation Science, University of Montana, Missoula, MT 59812, USA [email protected]

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Chapter 1

Recent Advances in Land Remote Sensing: An Overview Shunlin Liang

Earth’s surface is undergoing rapid changes due to urbanization, industrialization and globalization. Environmental problems such as water shortages, desertification, soil depletion, greenhouse gas emissions warming the atmosphere, deforestation, elevated coastal waterway sediment and nutrient fluxes, among other environmental problems, are increasingly common and troubling consequences of human activities. Policy decisions about the environment rely on accurate and reliable information, especially data and understanding leading to better predictions of natural hazards, epidemics, impacts of energy choices, and climate variations. Comprehensive, systematic Earth observations are key to forecasting Earth system dynamics. Predicting future scenarios of our planet’s habitability requires analysis of what has transpired in the past along with observations of present conditions and processes. Timely, quality long-term global data acquired through remote sensing is essential for the ongoing viability and enhancement of human society on Earth. The field of remote sensing (Earth observation) has developed rapidly. Many publications have documented its progress (e.g., the special issue of Remote Sensing Reviews with a set of papers reviewing the modeling and inversion of surface bidirectional reflectance distribution function (BRDF) (Liang and Strahler, 2000), and the edited or authored books on similar subjects (Liang, 2004; Myneni and Ross, 1991). To systematically summarize the achievements of terrestrial remote sensing in recent years and to set the research agenda for the near future, the 9th International Symposium on Physical Measurements and Signatures in Remote Sensing (ISPMSRS), held in October 2005 in Beijing, organized three review panels. The papers compiled in this book are largely from these panels and are organized into three parts, respectively. Part I of the book (corresponding to the first panel, chaired by Drs. David Jupp and Tom Jackson, with Drs. Ralph Dubayah, Michael Schaepman, Jianchen Shi, Stephen Ungar, and David Le Vine) focuses on remote sensing systems and sensors. As there are many different remote sensing systems (the result of various Shunlin Liang University of Maryland, USA S. Liang (ed.), Advances in Land Remote Sensing, 1–6. c Springer Science + Business Media B.V., 2008


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S. Liang

permutations of passive vs. active, specific domain of the electromagnetic spectrum sampled, and spectral channel bandwidth) currently in operation or planned to be operational in the future, this panel evaluated the capabilities of these systems for estimating key land surface variables and how they can best be improved and combined effectively. The panel presentations covered microwave, thermal-infrared (IR), hyperspectral optical, and Lidar remote sensing. Based on these discussions, four chapters are compiled on this subject, including passive microwave, active microwave, multiangle thermal IR, and multiangle optical remote sensing. In Chapter 2 on passive microwave remote sensing, Jackson identifies six factors in passive microwave sensor design that affect the retrieval of land surface properties: frequency, polarization, view geometry, spatial resolution, temporal coverage, and signal-to-noise ratio. While summarizing the features of three current relevant satellite instruments and two other satellite sensors, he points out that the low frequency observations (2.0 2.0-2.5 2.5.3.0 3.0-3.5 3.5-4.0 4.0-4.5 4.5-5.0 5.0-5.5 5.5-6.0

>35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 70-75

Angle LIDF a 56⬚ -0.30 52⬚ -0.20 49⬚ -0.10

Fig. 5.13 LAI, chlorophyll per leaf area (µg/cm2 ) and average leaf angle maps for a 3 × 4 km area of maize, retrieved by adjusting the SLC model against data from CHRIS for the Upper Rhine Valley test-site along the German/French border (July 2003)

and transmittance of green and brown leaves is calculated using the PROSPECT sub-model. The leaf angle distribution is approximated by parameters that describe the average leaf slope and the “bimodality” of the distribution. The spatial distributions of all three retrieved parameters delineated fields and the additional information obtained from the directional data showed that canopy structure was crop-specific but also changed with phenological development. The field pattern in the average leaf slope map (Fig. 5.13c) values was thought to result from different varieties of maize. When the average leaf angle was retrieved for the same site 2 weeks after the initial CHRIS acquisition, the overall average angle retrieved changed by about 10◦ to a more vertical distribution. This can be interpreted as maturation of maize where leaves become more vertical with development. The study showed that crop parameters retrieved from multiangle CHRIS data can provide input parameters essential for crop growth models. Garc´ıa-Haro et al. (2006) developed an approach called directional spectral mixture analysis (DISMA) for retrieving vegetation parameters with the focus on fractional cover and leaf area index. This seeks to combine a consideration of the spectral signatures of soil and vegetation components with an analytical approximation of the radiative transfer equation, resulting in a fast, invertible model suitable for use with discontinuous canopies. Data from the AirPOLDER and HyMap instruments were used to test the model and its inversion using a lookup table (LUT). Retrievals of LAI corresponded well to ground measurements of LAI, with an RMSE of 0.5–0.6 and an R2 of the fitting of around 0.92. The spatial distribution matched that obtained by inversion of the physically-based New Advanced Discrete Model (NADIM) radiative transfer code, also known as the Semi-discrete model (Gobron et al., 1997) (Fig. 5.14).

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 >3.5

Fig. 5.14 (a) Green LAI obtained via DISMA using AirPOLDER (b) the corresponding results from inversion of the physically-based NADIM radiative transfer code. The maps shows a 5 × 5 km area 28 km from Albacete, Spain; 1% and 7% of the pixels exceed the saturation value of 3.5 (From Garc´ıa-Haro et al., 2006. Copyright, IEEE. With permission.)

5.3.9 The Background in Canopy Reflectance Modeling Many researchers have recognized that for successful modeling of heterogeneous, clumped, or non-closed canopies it is important to account adequately for the contribution of the background of soil and understory (Gemmell, 2000; Ni and Li, 2000; Chen et al., 2005; Koetz et al., 2005b; Bach et al., 2005; Chopping et al., 2006a). In all canopies except closed – especially where the understory is heterogeneous – attempts to exploit canopy reflectance models can be confounded by spatial variation in background reflectance magnitude and anisotropy. In the last few years modelers have moved from the assumption of a Lambertian background, through imposing a single, static background BRDF, to attempts to estimate a spatially dynamic background BRDF. Recent work has shown that the soil/understory reflectance can be obtained for both coniferous and deciduous forests using MISR data, with the retrieved values following seasonal trajectories similar to those of adjacent grasslands, a partial validation of the approach (Canisius and Chen, 2007). Recent progress in dynamically estimating the anisotropic soil-understory contribution for discontinuous open shrub canopies in desert grasslands exhibiting a wide range of canopy-background configurations – including young, small honey mesquite shrubs over a dark grassland matrix and older, larger ones over bright, sandy soils – has been made using the simplified geometric-optical (SGM) model incorporating a kernel weighting approach with MISR data. Estimating the background contribution from MISR-derived LiSparse-RossThin model kernel weights while fixing number shrub density, shape and height at typical values and using numerical optimization to retrieve mean shrub radius has allowed the mapping of fractional shrub cover at landscape scales in the United States Department of

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Agriculture (USDA), Agricultural Research Service (ARS) Jornada Experimental Range in southern New Mexico. A root mean square error of 0.03 in fractional cover with respect to values estimated from high resolution IKONOS panchromatic imagery was obtained (measured fractional cover range: 0.03–0.19); however only a moderate proportion of the variation in the measured data was explained by the estimated data set, with an overall R2 of 0.19 (Chopping et al., 2006b). When the same algorithm was used to predict fractional shrub cover for pastures a few kilometers from the study area for which independent estimates were available (from image segmentation on a 0.6 m QuickBird panchromatic image), the distributions exhibited an improved spatial correlation (Fig. 5.15) and an R2 of 0.47 was obtained with two model variants (Fig. 5.16). When the algorithm was applied with MISR data over much larger areas – for the Jornada Experimental Range (∼783 km2 ) and the Sevilleta National Wildlife Refuge (∼1, 000 km2 ) and their environs – the maps include trees on the San Andres mountains, in other elevated areas (e.g., Summerford Mountain in the Jornada), and in the riparian environments of the Rio Grande (southwest quadrant of the Jornada map and center of the Sevilleta map), in addition to shrubs. The resulting distributions compare well with those of trees in the MODIS Vegetation

Fig. 5.15 (a) QuickBird shrub map for pasture 12 in the Jornada, red = shrub, white = background (b) shrub cover aggregated to 250 m cells; brighter = greater shrub cover (c) retrieved using MISR red band data to invert the SGM GO model (d) MISR/SGM shrub cover map for pastures 8/9 in the Jornada (e) the corresponding QuickBird map (From Chopping et al., 2006c. Copyright, American Geophysical Union.)

0.30

y = 0.4358x + 0.0208 R2 = 0.4676

0.20

0.10

0.00 0.00

++ + + + ++ + + + ++ + + + + + + + + ++ + + +++ + +++ + + ++ ++ + ++ +++ ++++ + ++ ++ + + + + + ++ ++ +

0.10

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Fractional Shrub Cover (QB-NIH)

Fractional Shrub Cover (MISR/SGM)

Fractional Shrub Cover (MISR/SGM)

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0.30

y = 0.5427x + 0.0777 R2 = 0.4824

0.20

+

0.10 + + ++ +

0.00 0.00

++ + + + + + + + ++ ++ + ++ + + + +++ ++ + + + + + + + ++ + + + +++ + ++ + ++++ +++ + + + + +++ ++ + + + ++ ++ ++ + ++ +

0.10

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Fractional Shrub Cover (QB-NIH)

Fig. 5.16 Retrieved vs. measured shrub cover (a) SGM (b) SGM with sunlit crown unweighted by the fraction viewed (i.e., kC = 1.00) (Reproduced from Chopping et al., 2006c. Copyright, American Geophysical Union.)

Continuous Fields (VCF) percent tree cover maps (Fig. 5.17). Note that the MISRderived map includes all large woody plants: it is based on exploiting the canopy structure information encapsulated in the multiangle reflectance data (Chopping, 2006). Subsequent inversions of the SGM that allowed the crown shape parameter to vary indicated that it is possible to obtain regional maps of canopy height as well as crown cover, allowing estimates of aboveground woody biomass. Retrievals of cover, canopy height, and biomass showed good matches with US Forest Service maps, with coefficients of determination of 0.78, 0.69, and 0.81, and absolute mean errors of 0.10, 2.2 m, and 10.1 Mg/ha, respectively, after filtering for high model fitting error, the effects of topographic shading, and a small number of outliers (Chopping et al., 2007; http://csam.montclair.edu/∼chopping/wood/).

5.3.10 Land Cover and Community Type Mapping Many studies have shown that there is much potential for improving the accuracy of land cover classification if patterns in the angular domain as well as the spectral domain can be exploited (Abuelgasim et al., 1996; Hyman and Barnsley, 1997; Bicheron et al., 1997; Sandmeier and Deering, 1999). Chopping et al. (2002) showed that the kernel weights of Li-Ross LiSK models obtained by adjusting a LiSparse-RossThin variant against accumulated multiangle data from the NOAA AVHRR provide contingency tests for community types in semi-arid environments in Inner Mongolia Autonomous Region (IMAR; 10 types) and New Mexico (NM; 19 types) that are superior to those obtained using maximum-value compositing using the Normalized Difference Vegetation Index (NDVI) as the criterion (denominated MVC), and in particular perform better in the worst case: the kernel weights

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Fig. 5.17 Woody plant fractional crown cover map obtained by adjusting the SGM geometricoptical model against MISR red band data (a) in the Sevilleta National Wildlife Refuge in central New Mexico (b) % tree cover from the corresponding MODIS VCF product (c) in the Jornada Experimental Range in southern New Mexico, dotted line is the tree-shrub boundary from the VCF map (d) % tree cover from the corresponding VCF map product. Solid lines indicate the boundaries of the Sevilleta and fencelines in the Jornada. (Reproduced from Chopping et al., 2006c. Copyright 2006 American Geophysical Union.)

provided minimum reliabilities of 83% and 69% for IMAR and NM experiments, respectively, compared to only 11% and 26%, respectively, with the MVC data set. These performances were reflected in Kappa Index values of 0.93 and 0.91 for the IMAR and NM spectro-directional data sets against 0.74 and 0.46 for the MVC data sets, respectively (the Kappa Index is a means to test two data sets to determine the extent to which their similarities or differences are due to chance). When directional

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information was incorporated into the signatures, errors of omission or commission fell from ∼24% and ∼51% obtained with MVC to only ∼6% and ∼8% for the IMAR and NM experiments, respectively. More robust cross-validated tests of classifications of multiangle remote sensing metrics from MISR and nadir-spectral data from the An (nadir) camera have demonstrated that using multi-angular data and anisotropy patterns raises the overall classification accuracy importantly. Su et al. (2007) studied maximum likelihood and support vector machine (SVM) algorithms for mapping community types in the Jornada Experimental Range and the Sevilleta National Wildlife Refuge, New Mexico (19 classes). Half of the samples were randomly selected as the training set and the other half retained as the testing set. A total of 66 classifications were performed with various combinations of data sets: the ρ0 , k, and b parameters of the MRPV model (see Canopy Openness, above); the isotropic, geometric and volume scattering kernel weights of a Li-Ross BRDF model; the structural scattering index; and MISR surface reflectance estimates. Using multiangle data raised the overall classification accuracy from 45.4% obtained with nadir observations only to 60.9%, and with surface anisotropy patterns derived from MRPV and LiSparseRossThin BRDF models (separately) an overall accuracy of 67.5% can be obtained with a maximum likelihood classifier. Using a non-parametric SVM algorithm the classification accuracy was increased to 76.7%. Note that the classes in these experiments are community types that often differ very subtly in terms of their spectral signatures, rather than broad land cover types (Fig. 5.18).

Fig. 5.18 Community type maps for the Sevilleta National Wildlife Refuge. (a) LTER vegetation map (b) MISR maximum-likelihood classification (c) MISR support vector machine classification (Reproduced from Su et al., 2007. Copyright, Elsevier. With permission.)

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5.4 Other Applications Most applications – or prototype applications – of multiangle remote sensing of land have been concerned with vegetation canopies. However, there are other important Earth Science applications that are often tangentially related to vegetation, including estimating land albedo and the Earth’s radiant energy budget (see Chapter 9); snow and ice; and mapping dust emission sources to simulate the likelihood of large emissions.

5.4.1 Snow and Ice Multiangle remote sensing data are able to provide important additional information on Earth surfaces covered with snow and ice. For example, differentiating between clouds and snow or ice surfaces using spaceborne detectors is difficult because the surface may often be as bright and as cold as the overlying clouds, and because polar atmospheric temperature inversions sometimes mean that clouds can be warmer than the underlying surface. Mega-sastrugi ice fields in East Antarctica, with dunelike features as high as 4 m and separated by 2–5 km – a result of unusual snow accumulation and redistribution processes influenced by the prevailing winds and climate conditions – appear more like cloud formations: they exhibit a rippled appearance. However, the Angular Signature Cloud Mask (ASCM), a MISR product (Di Girolamo and Wilson, 2003) is able to detect clouds over snow and ice as well as over ocean and land (Fig. 5.19). MISR imagery indicated that these mega-sastrugi were stationary surface features between 2002 and 2004. (a)

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Fig. 5.19 (a) December 16, 2004 MISR image over Antarctica, showing sastrugi (b) colorcoded image showing the Angular Signature Cloud Mask results (Courtesy of the MISR Team, NASA/JPL/Caltech, and L. Di Girolamo and M.J. Wilson, University of Illinois.)

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Hendriks and Pellikka (2004) presented a study of the multiangular reflectance of a glacier surface. They used multiple ALTM (Optech, Ontario, Canada) digital metric camera frames acquired from the air on August 12, 2003, to examine the angular spectral reflectance response of snow, firn, and ice surfaces on the Hintereisferner glacier in Austria. The camera was operated in color infrared (CIR) mode, resulting in images in three spectral bands: green (510–600 nm), red (600–720 nm) and near-infrared (720–800 nm); the pixel size varied between 0.25–0.30 m as a result of topography. They found important differences in the angular signatures of the three surface types and compared their results to MISR imagery (local mode: nominal 275 m footprints at all angles and in all four bands). Their results showed that MISR data reveal the backscattering of dirty ice, firn and old snow; BRF increases going from the nadir image in the backward direction and at the viewing camera Ca (60◦ ) backwards, BRF is 30% higher relative to the value in the nadir viewing camera (An) (Fig. 5.20). Multiangle views provide unique sub-pixel resolution information about the ice sheet surface that can be used to improve the characterization of climate and ice dynamics processes. Nolin et al. (2002) had previously shown that MISR data can be used as a proxy for surface roughness. They developed a normalized difference angular index (NDAI) using a combination of forward and backward scattered radiation in the MISR red band at the 60◦ fore and aft viewing angles of the MISR instrument. A positive (negative) NDAI value indicates that backward (forward) scattering exceeds forward (backward) scattering and that the surface is rough

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Fig. 5.21 Ice sheet surface classes for 2000–2005 derived from ISODATA classification of summer NIR albedo and NDAI from MISR images acquired in the vicinity of the Jakobshavn glacier and its upland drainage basin. Contour lines of elevation are at 250 m intervals (Reprinted from Nolin and Payne, 2006. Copyright, Elsevier. With permission.)

(smooth). The NDAI was shown to be highly correlated with surface roughness derived from an airborne laser altimeter. Nolin and Payne (2006) used the ISODATA clustering technique with NIR albedo and NDAI values from surface hemisphericaldirectional reflectance for consecutive MISR summer images from 2000–2006 over an area in the vicinity of the Jakobshaven glacier in Greenland. The classified maps (Fig. 5.21) demonstrated good spatial and temporal consistency for seven ice sheet classes for all 6 years; moreover, the classes roughly correspond with glacier facies mapped previously by other researchers. The classes differ in albedo, roughness (including the presence of crevasses), wetness, and the age of the snow at the surface. Nolin (2004) performed a study using data from MISR to demonstrate how the angular pattern of reflectance from vegetation over snow can provide information on forest cover density. This is important in snow studies as vegetation structure and density affect the dynamics of snow accumulation and ablation and affects the ability to estimate snow-covered area accurately from satellite-based sensors. The study area was located in north-central Colorado. MISR red band level 1B2 (top-of-atmosphere radiometrically and geometrically calibrated spectral radiances) data from 15 February 2002 were converted to top-of-atmosphere bidirectional reflectance factors – no atmospheric correction was applied. The Rahman– Pinty–Verstraete (RPV) semi-empirical parametric model was successfully used to simulate the angular patterns of reflectance. The model’s k parameter was used to characterize the angular signatures of selected pixels. In the RPV model this parameter is used to quantify the degree by which the observed bi-directional reflectance

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factor data resemble a bowl- or bell-shaped pattern. The results showed distinct patterns in the retrieved k parameter values, with a marked dependence on density and cover type. Non-forested areas exhibited a bowl-shaped pattern (k < 1.0) of reflectance versus viewing angle. Low-density deciduous forests also exhibited this bowl-shaped reflectance pattern, changing as density increases. Other forest cover types show transitional patterns between bowl and bell shapes and distinct bellshaped patterns (k > 1.0) for higher densities (Fig. 5.22). The relationship between k and density does not hold for forest cover densities that approach 100%. For a density of 99%, the fir – spruce forest cover type has a distinct bowl shape and a k value of only 0.69. This is in agreement with previous work indicating that sub-pixel homogeneity (whether because of sparse vegetation cover or extremely dense vegetation cover) will result in k < 1.0. This study indicated from a qualitative standpoint that multiangle reflectance data captures information on forest cover density at the sub-pixel scale.

5.4.2 Dust Emissions Laurent et al. (2005) used POLDER multiangle data with a surface roughness parameter estimated from the Roujean kernel-driven model (Roujean et al., 1992). They used the geometric kernel weight normalized by the diffuse (isotropic) scattering kernel weight (i.e., geo/iso) to simulate dust emissions from deserts in East Asia

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(N. China and Mongolia). The approach was derived from work previously accomplished by Roujean et al. (1997) and employed an empirical relationship established by Marticorena et al. (2004). The composite surface roughness map they developed describes the spatial variability of the erosion threshold (10 m wind velocities) on dust emission frequency. The map was found to be consistent with geomorphologic interpretations from Landsat imagery and with soil properties described in the literature. The retrieved roughness lengths are in agreement with the roughness lengths experimentally determined over similar surface types in other deserts of the world. The authors computed dust emission frequencies for 3 years (1997–1998–1999) by combining the 10 m erosion threshold wind velocities, the European Centre for Medium-Range Weather Forecasts (ECMWF) surface wind fields, the snow depth and the soil moisture computed using the Food and Agriculture Organization of the United Nations (FAO) soil texture profiles, and ECMWF meteorological data. The simulated frequencies of significant dust emissions were compared to the frequencies of occurrence of Total Ozone Mapping Spectrometer (TOMS) Absorbing Aerosol Index (AAI) higher than 0.7. Both the location and the relative intensity of the highest dust emission frequencies identified from the simulations were in agreement with the observations (Fig. 5.23). 1

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Fig. 5.23 Monthly frequencies of significant simulated dust emissions (flux > 10−10 g cm−2 s−1 ) as a function of the monthly frequencies of TOMS AAI > 0.7 over the Taklimakan desert for the 3 years 1997, 1998, and 1999. Small dots represent individual data; circles represent the averaged frequency of simulated dust emissions for classes (5% width) of frequency of TOMS Absorbing Aerosol Index (AAI) > 0.7; the solid line represent the linear fit of the averaged data (without accounting for the last class which is not representative) (Reproduced from Laurent et al., 2005. Copyright, American Geophysical Union.)

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5.5 Some Considerations in Multiangle Acquisition 5.5.1 Near-simultaneous and Accumulated Sampling Near-simultaneous acquisition of multiple observations of the same area on the Earth’s surface is possible by viewing in the along-track direction. From low Earth orbit, multiple looks of the same area can be acquired over a time span of less than 10 minutes. This strategy may be contrasted with accumulated sampling, in which repeat multiangular coverage of a particular area is obtained with a wide cross-track swath and observations are accumulated during multiple orbits. Accumulation of multiangle data in this manner takes many days. This may degrade the angular data set to some degree, depending on how rapidly surface conditions change and – to some extent – on changes in the atmosphere, since it is more difficult to correct extreme conditions. For along-track systems, there will be delay of only a few minutes between the first and last acquisitions, whether the instrument employs multiple sensors (MISR), is tilted (CHRIS/Proba), has a conical scan (AATSR), or has a very wide field-of-view (POLDER). This lag is unavoidable unless a constellation of geostationary platforms is available – an unlikely scenario for the near future. Most Earth observing instruments for which the effects of the surface BRDF have been studied and – to a far lesser extent – exploited are across-track instruments on polar-orbiting instruments such as the AVHRR and MODIS. These systems are designed to view large swaths, covering the globe at least once per 24 h period. They are intrinsically off-nadir viewing devices but to be used as multiangle instruments, observations of the same land areas must be accumulated from multiple overpasses. In addition, sensors such as Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) on Meteosat Second Generation (MSG) geostationary satellites provide angular sampling through diurnal variation in illumination angles. The motivation for BRDF studies with accumulating instruments has been twofold: the need to adjust observations to a common Sun-target-sensor geometry for consistency (a much-touted but actually rather rare quality in Earth Observation in general); and to obtain more accurate estimates of terrestrial albedo than could possibly be obtained from a single view, since sunlight is never scattered in a perfectly diffuse manner at the surface. In the case of the MODIS BRDF/Albedo algorithm, an additional product is Nadir-equivalent BRDF Adjusted Reflectance (NBAR), defined as the best estimate of reflectance at nadir viewing at the mean solar zenith angle of the observations used to invert the Li-Ross BRDF model (in this case LiSparseMODIS-RossThick). NBAR was quickly found to provide superior performance in applications such as land cover mapping (Zhang et al., 2000). The possibility of obtaining additional surface information by exploiting the directional signal encapsulated in these data was something of an afterthought until the 2000s; however, in the last 5 years this has changed, with several studies addressing the retrieval of vegetation structural parameters such as LAI and fractional vegetation coverage (Camacho-de Coca et al., 2002; Chen et al., 2005).

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Accumulating instruments have one major advantage over those providing nearsimultaneous multiangular acquisitions: they provide greater spatial and temporal coverage. This is particularly important for global applications where cloud and cloud shadow contamination present a problem for instruments with revisit periods of less than a few days. However, near-simultaneous multiangle imaging provides some important advantages over accumulated sampling: • It greatly helps to solve the aerosol scattering problem over land and especially over bright surfaces – including deserts – where spectral information alone currently appears to be inappropriate. • Directional data sets acquired by accumulation may afford serious limitations for applications under those conditions where either the atmosphere or the surface – or both – change more rapidly than the accumulation period. This advantage is more applicable in some circumstances than in others and is probably more dependent on the development of the surface rather than that of the atmosphere. For example, changes owing to snowfall, snowmelt, flood, and fire may not be resolvable by accumulated sampling as they happen much more rapidly than the sampling rate. Near-instantaneous imaging is therefore the only way to assess surface directional properties under these circumstances. In other cases, for example, where changes in surface conditions are slow and/or sparse and intermittent, accumulated sampling is more acceptable. • There is the potential to assess information on canopy structure and retrieve LAI and fPAR with greater accuracy (Hu et al., 2003).

5.5.2 Angular Sampling The angular sampling of both multiangle imaging and accumulating instruments is determined by sensor design (field-of-view/swath), the platform on which the sensor is flown, and by the constraints imposed by the orbit into which the platform is injected. The first and last of these are straightforward. However, that the platform itself can impact the angular sampling regime of a sensor has a meaning restricted to satellites that are able to re-orient themselves in order to acquire multiple looks. Currently this definition applies to only one system: CHRIS on the Proba-1 satellite. In the future, increasing use of constellations of small, agile satellites such as Proba might be expected to provide greater flexibility in angular sampling. One such system concept developed at NASA/GSFC, dubbed Leonardo-BRDF has not yet been pursued (Wiscombe, 2000). The angular sampling provided depends on whether the instrument is an across-track scanner (using a revolving or oscillating mirror; e.g., AVHRR, MODIS, the forthcoming US National Polar-orbiting Operational Environmental Satellite System (NPOESS) Visible/Infrared Imager/Radiometer Suite, or VIIRS); an along-track scanner ((A)ATSR(−2)); multiple along-track moderate swath CCD arrays (MISR); or an along-track wide swath CCD array (POLDER/Parasol). Important issues with respect to angular sampling include:

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• The range of viewing and illumination zenith angles • The azimuthal coverage of the samples (how well the hemisphere is covered, particularly with respect to the principal and perpendicular planes) • The angular sampling density, particularly around the hot spot (rarely achieved) • The spatial resolution, determined by the size of the solid angle of the individual observing element, which is somewhat large for POLDER and much smaller for MISR and CHRIS • The interval over which the sampling is acquired (minutes for true multiangle imagers such as MISR, CHRIS, and POLDER; up to weeks for accumulators) • The frequency with which a given sampling may be repeated Since most instruments are flown on polar-orbiting platforms with sun-synchronous orbits having orbital inclinations only somewhat greater than 90◦ and acquisitions are made either side of local noon, across-track scanners tend to provide a sampling that is closer to the principal plane – where variation in radiance with viewing and illumination zenith is greatest – for mid-latitudes. Along-track imagers on platforms with sun-synchronous orbits such as MISR provide a sampling that is often far from the principal plane but approaches it with increasing latitude; and for any given latitude the sampling remains consistent. Owing to the Proba-1 orbit and the narrow field-of-view, CHRIS provides a less regular sampling from site to site and it is only occasionally able to image a target area from directly overhead view; Proba-1 has to be tilted at some – usually small – angle in the across-track direction so that the target area is viewed. The platform acquires images of the target when the zenith angle of the platform is one of the following: ±55◦ , ±36◦ and 0◦ . This means that the angles at which images are acquired vary from site-to-site, depending on their positions with respect to the orbital track. The pattern with which any site is accessible to the platform varies at roughly 8-day intervals, but with some change in sampling because the orbit does not repeat exactly (Barnsley et al., 2004). The POLDER design allows the most comprehensive sampling of the Earth’s radiation field from space to date. The very wide field-of-view (2, 400 × 1, 800 km2 ) allows observation of the same target under many different angular configurations (between 10 and 15 observations for each passage of the satellite), with view zenith angles up to ∼60◦ for the full azimuth range (Laurent et al., 2005).

5.5.3 Scale and Multiangle Observation The spatial scale at which multiangle observations over land are made has an important impact on the kinds of applications in which they might be used, as well as on data transmission rates and geographic coverage. Progress in remote sensing has often been measured in terms of increasing the sampling rate in the spatial domain, so that the smaller the ground sampling distance and the higher the spatial resolution, the better (NASA, 2000). Indeed, this is often postulated to be the major limitation of moderate resolution remote sensing devices: while wall-to-wall coverage is provided, heterogeneity in surface features cannot be resolved, limiting many applications,

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including cover type classification and the assessment of small-scale but widespread fragmentation in a variety of ecosystems (Phinn et al., 1996). However, this paradigm is flawed in certain respects: although high resolution imagers show the details of land features, this comes at the price of high data volumes monetary expense, and restricted coverage. Although multi-angle observation can only provide statistical metrics on sub-pixel structure, this is often sufficient to address the problem of interest. Moreover, data volumes are smaller and global coverage is achievable. For example, an hypothetical 10 m resolution single-angle imager generates ten times more data than a 100 m multiangle imager having ten angles, for the same swath; it can therefore cover a swath ten times wider for the same data volume. Note too that with multiangle remote sensing a small ground-projected instantaneous field-of-view (GIFOV) can be a disadvantage; specifically, for the radiometric, or 1-D, approach that seeks to derive “sub-pixel” information via variation in radiance with Sun and/or viewing angles and in which each “pixel” is treated independently. In this approach, if the GIFOV is small in relation to surface features such as trees or shrubs, there is a higher probability that an observation will include a sampling of elements that is unrepresentative of the surface as a whole; furthermore, it may also include important contributions from partial features at the extremities. These may result in noise-like fluctuations and adjacency effects in the angular signal that will impact on models that treat the surface as either a semi-infinite, homogenous, plane–parallel medium, or as a set of identical objects distributed spatially in a Poisson distribution (e.g., geometric-optical models). In both cases, an unrepresentative sampling of features and/or a large relative contribution from partial features at the edge of the GIFOV will obscure the angular signal. If the GIFOV is large in relation to surface features then the sampling of surface elements will be more representative and the periphery will make a relatively small contribution. Other considerations are that a large GIFOV may result in greater proportions of observations with unavoidable cloud and cloud shadow contamination and with mixtures of too many surface types. On the other hand, a very small GIFOV may also suffer from multiple scattering to/from adjacent footprints (“pixel cross talking”). Clearly, for any given landscape there is an optimum sampling resolution: if the GIFOV is much larger than the typical length scales then spatial trends in BRDF and parameters derived from model inversions will be less well-defined. There is also a sampling resolution that is the global optimum; i.e., over all surface types of interest. Following Pinty et al. (2002, 2004), Widlowski et al. (2005) addressed the question of the degree to which 1-D radiative transfer models can explain as well as describe the reflectance fields of 3-D forest targets of varying composition and complexity, over a range of spatial sampling scales (sensor ground sampling resolutions). Explaining these reflectance fields requires that the model’s internal parameters (state variables) match and are consistent with those of the 3-D target; it is not sufficient that the modeled anisotropy matches that of the target. Both conditions must hold if any model is to provide surface parameters on inversion which have meaning and utility in remote sensing applications; if they are not, there is considerable doubt on the reliability of surface parameters retrieved. The study tackled this problem through addressing two important questions:

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• Can 1-D models represent the anisotropy of a reflectance field generated by a more complex 3-D model at multiple spatial resolutions? and • Will the inversion of a 1-D model (at low spatial resolution where they are more appropriate) lead to systematic (and significant) biases in the retrieval of surface properties? These questions were pursued by using data sets for a level Scots pine landscape simulated by the Rayspread 3-D Monte Carlo raytracing model, using allometric relationships for a range of canopy parameter configurations in the red and near infra-red wavelengths. A 1-D model known as the Semi-discrete model (Gobron et al., 1997) was used to generate a large series of lookup tables for the comparisons. The study examined the impact of changing sensor GIFOV and foliage clumping on the match between the 3-D and 1-D models, as well as differences in interception, absorption and transmittance of solar radiation through and by the canopy arising from the 1-D and 3-D modeling. The conclusions were that 1-D models can provide good matches to reflectance fields generated by 3-D models in terms of both magnitude and directionality but that it does not follow that the 1-D model’s internal parameters and radiation budget match those of the 3-D target. It was shown that differences in the shape of the reflectance anisotropy between a 3-D target and its 1-D homologue – featuring identical spectral and structural properties with the exception of foliage clumping – lead to the retrieval of BRF-equivalent 1-D solutions with parameter values that diverge from those of the 3-D target. Part of this problem is understood as the problem of lack of uniqueness of solutions. A key finding is that for conifer forest canopies, an observation spatial scale of less than 100 m is more likely to introduce large discrepancies between the reflectance fields generated by 3-D and 1-D models for a wide range of conditions.

5.6 Conclusions This chapter has reviewed recent work towards exploiting solar wavelength remote sensing data acquired at multiple viewing angles from the air and space in applications in forestry, ecology, land cover mapping and land cover change, agriculture, hydrology, and glaciology, with important implications for enhancing ecological, crop growth, biogeochemical, hydrologic, and energy balance models. Even when excluding the numerous studies concerned with goniometric measurements, multiangle observations in the thermal wavelengths, and model development and simulation work, there has clearly been a great deal of activity over the last few years. Advances have been seen in a diversity of approaches, with notable gains for synergistic methods that seek to use multiangle data together with other kinds of remote sensing data and/or high resolution inventory data. The synergistic use of multiangle data with those from lidar instruments has provided an especially promising direction for the future, especially if the capability of models such as GORT to link multiangle and lidar data can be further developed. While canopy reflectance models have become more accurate, often incorporating a wider range of

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spectral measures, the hindrances to the use of geometric-optical models that have prevented widespread adoption in applications are being removed through methods for isolating the contribution of the soil/understory background from that of the upper canopy. Studies directed at assessing the gains from adopting the multiangle approach over nadir-spectral sensing, as well as obtaining meaningful and consistent metrics that characterize surface and canopy conditions, have universally found multiangle data to be valuable. Although efforts to exploit the additional, unique information available through multiangle remote sensing have been ongoing for many years, progress towards applications is accelerating, with high quality data sets available from MISR and MODIS on NASA’s EOS satellites, a third POLDER in orbit on Parasol, innovative new experimental systems such as CHRIS on Proba, greater demonstrated potential for satisfying multiple user groups in diverse disciplines (e.g., atmospheric science, ecology, glaciology, land management, and climate modeling), the realization of important synergies with active instruments, and a greater number of researchers engaged. This is borne out by the tenfold increase in the number of peer-reviewed publications using data from MISR, POLDER or CHRIS in the 10 years to 2005 (Fig. 5.24). Canopy reflectance modeling work with a variety of model types and improved reference data from high resolution imaging and lidar continues to shed new light on the constraints to robust retrievals of biophysical parameters and on important issues such as optimal scales of observation. Efforts continue to be made to engage remote sensing scientists with user groups (e.g., Chopping and Diner, 2005), although this is an ongoing task. Continued improvements in knowledge and understanding, together with greater experience with both near-simultaneous and

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accumulating multiangle instruments, will drive the design of future Earth observation systems. The examples presented in this chapter provide a good, albeit not exhaustive, indication of the range and depth of work that has been accomplished over recent years in just one area of multiangle remote sensing (terrestrial applications in the solar wavelengths). They reflect the progress achieved in the ten years since the NASA-sponsored Workshop on Multi-angular Remote Sensing for Environmental Applications (Privette et al., 1997) and point the way to further opportunities for making better use of the unique information provided by multiangle data over land. Acknowledgements Special thanks are owed to David J. Diner for his very valuable suggestions on the manuscript as well as the many others who helped me in compiling this review; and in particular Daniel Kimes, Alan Strahler, Bernard Pinty, Jean-Louis Roujean, Franc¸ois-Marie Br´eon, David Jupp, Jon Ranson, Jing Chen, John V. Martonchik, Anne Nolin, Rob Braswell, Julian Jenkins, Mike Barnsley, Wout Verhoef, Wenge Ni-Meister, Andres Kuusk, Soeren Hese, Hamlyn Jones, Raffaele Casa, F. Javier Garc´ıa Haro, Johan Hendriks, Petri Pellikka, Janne Heiskanen, Larry Di Girolamo, Mathias Disney, Wolfgang Lucht, Sampo Smolander, Gunar Fedosejevs, Mike Cutter, Gabriela Schaepman, and Michael Schaepman. I thank also the participants in the NASA/MISR Workshop on Multiangle Remote Sensing in Ecological Modeling not mentioned above. I must also acknowledge the many people not named here who sent me their recent and often unpublished work, and especially those whose work I could not incorporate here: I am deeply grateful. Any errors or omissions are uniquely mine.

Glossary 1-D 3-D AAI AATSR ADEOS ARS ASCM AVHRR BHR BOREAS BRDF BRF Cab CART CCD CHRIS CI CIR DISMA ECMWF EOS

One-dimensional Three-dimensional Absorbing Aerosol Index Advanced Along-Track Scanning Radiometer Advanced Earth Observation Satellite (Japan) Agricultural Research Service (USDA) Angular Signature Cloud Mask Advanced Very High Resolution Radiometer (NOAA) Bihemispherical Reflectance Boreal Ecosystem-Atmosphere Study (NASA) Bidirectional Reflectance Distribution Function Bidirectional Reflectance Factor Chlorophyll a + b content (leaves in a given canopy) Canopy Architecture Radiative Transfer (MISR LAI algorithm) Charge Coupled Device Compact High Resolution Imaging Spectrometer Clumping Index Color Infrared Directional Spectral Mixture Analysis European Center for Medium range Weather Forecasting Earth Observing System (NASA)

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FAO fAPAR GIFOV GLAS GO GORT HDRF ICESat IFOV ISRO LAD LAI Lidar LiSK LVIS MISR MODIS MRPV MSG MVC NADIM NBAR NDAI NDVI NIR NDHD NPOESS POLDER POVRAY PSLV RAMI RMSE RPV RT SAIL SAR SEVIRI SGM SSI TOMS UK USDA VCF VIIRS

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Food and Agriculture Organization of the United Nations fPAR Fraction of Absorbed Photosynthetically-Active Radiation Ground-projected (sensor) Instantaneous Field-Of-View Geoscience Laser Altimeter System Geometric-Optical (model) Geometic-Optical/Radiative Transfer (model) Hemispherical-Directional Reflectance Factor Ice, Cloud, and Land Elevation Satellite (NASA EOS) (sensor) Instantaneous Field-Of-View Indian Space Research Organization Leaf Angle Distribution Leaf Area Index (one-sided leaf area per unit ground area) Light Detection and Ranging (sensor) Linear, Semi-empirical, Kernel-driven Laser Vegetation Imaging Sensor Multiangle Imaging Spectro-Radiometer (NASA/JPL EOS) MODerate resolution Imaging Spectroradiometer (NASA EOS) Modified Rahman-Pinty-Verstraete (model) Meteosat Second Generation Maximum-Value Compositing (on NDVI) New Advanced Discrete Model (model) Nadir BRDF-Adjusted Reflectances (EOS MOD43B4 product) Normalized Difference Angular Index Normalized Difference Vegetation Index Near Infra-Red (sometimes written near-infrared) Normalized Difference between Hotspot and Darkspot National Polar-orbiting Operational Environmental Satellite System Polarization and Directionality of the Earth’s Reflectance Persistence of Vision Raytracer Polar Satellite Launch Vehicle (ISRO; India) Radiation Transfer Model Intercomparison (RAMI) Exercise Root Mean Square Error Rahman-Pinty-Verstraete (model) Radiative Transfer Scattering by Abitrarily Inclined Leaves (model) Synthetic Aperture Radar Spinning Enhanced Visible and Infra-Red Imager Simplified Geometric-optical Model Structural Scattering Index Total Ozone Mapping Spectrometer United Kingdom of Great Britain and Northern Ireland United States Department of Agriculture Vegetation Continuous Fields (MODIS product) Visible/Infrared Imager/Radiometer Suite (NPOESS)

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Chapter 6

Modeling the Spectral Signature of Forests: Application of Remote Sensing Models to Coniferous Canopies Pauline Stenberg, Matti M˜ottus, and Miina Rautiainen

Abstract The vertical and horizontal structure of forest canopies is one of the most important driving factors of various ecosystem processes and has received increasing attention during the past 20 years and served as an impetus for earth observation missions. In the remote sensing community, the variables which describe canopy structure are called biophysical variables, and are directly coupled with the fundamental physical problem behind remote sensing: radiative transfer in vegetation. There are basically three different approaches to interpreting biophysical variables from remotely sensed data: (1) empirical, (2) physically based, and (3) various combinations of them. The physical approach builds upon an understanding of the physical laws governing the transfer of solar radiation in vegetative canopies, and formulates it mathematically by canopy reflectance models which relate the spectral signal to biophysical properties of the vegetation. In this chapter, we will first outline the basic principles and existing physically based model types for simulating the spectral signature of forests. After this, the focus is on the specific issues related to applying these models to the complex 3D structure of coniferous canopies.

6.1 Introduction The assessment of many fundamental ecological questions at global scale is possible only through remote sensing, since integrated analyses of the biosphere, atmosphere and hydrosphere require simultaneous measurements over large areas. Pauline Stenberg Department of Forest Resource Management, University of Helsinki, Finland [email protected] Miina Rautiainen Department of Forest Resource Management, University of Helsinki, Finland Matti M˜ottus Tartu Observatory, T˜oravere, Tartumaa, Estonia S. Liang (ed.), Advances in Land Remote Sensing, 147–171. c Springer Science + Business Media B.V., 2008


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The three-dimensional (3D) structure of forest canopies is amongst the most important driving factors of various physiological and ecological processes. By analyzing the 3D structure of canopies, it is possible to detect growth patterns and phenological cycles of forests, as well as other changes such as insect or fire outbreaks and damages, illegal deforestation, and environmental stresses caused by drought or pollution. In the remote sensing community, the variables which describe canopy structure are called biophysical variables. Biophysical variables are coupled with the radiative transfer problem (Chandrasekhar, 1960) in vegetation (Ross, 1981) and can also be defined as state variables of the radiative transfer problem, in other words, the smallest set of variables which are needed to fully describe the physical state of the system at a given scale (Verstraete et al., 1996). However, mere description of the structure of the canopy through biophysical variables is not the only goal: the variables should be applicable for end-users in, for example, water and carbon cycle or climate modeling. It is obvious that measuring biophysical variables in situ is both laborious and time-consuming in forests – and impossible at global scale within a short time frame. Space-born monitoring is thus required, and algorithms for interpreting these variables from remotely sensed data need to be developed. Most common remotely sensed biophysical variables of forests include leaf area index (LAI), fraction of photosynthetically active radiation (400–700 nm) absorbed by vegetation (fPAR) and fraction of canopy cover (fCover). LAI and fCover are geometrical variables which are related to canopy gap fraction, i.e., the fraction of ground seen in a given direction (Nilson, 1977) – canopy gap fraction is in fact determined by LAI and its spatial distribution and leaf inclination distribution. fPAR, on the other hand, is an outcome of radiative transfer in vegetation, and the opposite of reflectance from vegetation. In addition, there are biophysical variables which are not geometric, but instead influence the spectral properties of scattering elements. An example of such variables is the chlorophyll content of green leaves (which also is closely connected to the nitrogen content of foliage). However, there is evidence that no clear distinction between foliar biochemistry and LAI can be made in practical remote sensing (Yoder and Pettigrew-Crosby, 1995). There are basically three different approaches: (1) statistical (empirical) and (2) physically based, and (3) various combinations of them (e.g., neural networks), to assess biophysical variables from spectral signals provided by optical satellite images. In the empirical approaches, commonly used in, for example, regional or national forest inventories, the vegetation characteristics of interest are estimated based on statistical relationships (regressions) obtained by collecting training data on the spectral signatures of a variety of objects. These methods are limited to a specified viewing and illumination configuration, and require large sets of reliable ground truth data. The physical approach, in contrast, builds upon an understanding of the physical laws governing the transfer of solar radiation in vegetative canopies and formulating it mathematically by reflectance models. Reflectance models, in turn, relate biophysical properties of the vegetation, or sets of canopy and stand parameters, to the spectral signal. Physically based methods are, at least in theory, more robust since they are not limited to a single configuration or vegetation biome type.

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Physically based methods have progressively become more and more attractive for the assessment or monitoring of biophysical characteristics of vegetation. They are the only methods which can fully take into use the versatile hyperspectral and multiangular information provided by the modern satellite sensors, and they are better suited for many current large scale applications than the empirical techniques. Several aspects must be considered when physically based models are developed for operational monitoring purposes. To begin with, the sensitivity of the model to the biophysical variable to be retrieved should be maximized. Simultaneously, undesired effects, for example from the atmosphere or terrain topography, should be eliminated as efficiently as possible using other available models and data. Finally, when considering the optimal model, the larger the area (e.g., the whole Earth), the more the model should rely on theory and the less on local data bases for input as the sets are usually not compatible from one region or country to another. In addition, we should take into account technical questions such as computation time required by the model. Canopy reflectance models were originally developed for agricultural crops, followed by broad-leaved forests, and even though presently there exist a number of reflectance models designed to be applicable also to conifers, some missing “difficult-to-model” properties and insufficient empirical data on some key parameters have still limited their optimal use. Several recent studies (Rautiainen and Stenberg, 2005a; Smolander and Stenberg, 2005) give quantitative support to the hypothesis put forward a long time ago (Norman and Jarvis, 1975; J. Ross, 1981– 2002, personal communication), that a major reason for the distinct spectral signature of coniferous forests lies in their hierarchical grouped structure, which governs the processes of multiple scattering within the canopy, as well as canopy absorption. Moreover, modeling tools are emerging by which grouping at different scales can be accounted for in canopy reflectance calculations. The effect of grouping on canopy PAR absorption and photosynthesis has been a well studied subject in forest production ecology (Oker-Blom, 1986; Leverenz and Hinckley, 1990; Wang and Jarvis, 1990; Oker-Blom et al., 1991; Nilson, 1992; Cescatti, 1997a) but only more recently, after becoming aware of the specific problems related to interpretation of satellite images over the boreal zone, has modeling the radiation regime of coniferous forests received increasing attention in the remote sensing community. The boreal zone spreads through Fennoscandia, Siberia, Alaska and Canada, and hosts a multitude of coniferous tree species adapted to the cold and drought climate conditions of the region. The forests are typically rather open with dense crowns (consisting of up to a few million needles per crown) and an abundant green understory and moss or lichen layer. The documented complex structure of the forests is further complicated by the fact that acquiring ground observations from many parts of the boreal zone is especially difficult due to the remoteness and climate of the region. For application of forest reflectance models in the boreal zone, remaining problems of high priority are thus how to model efficiently and sufficiently realistically (1) the hierarchic 3D canopy structure and (2) the contribution to the remotely sensed spectral signal from the background, typically composed of mixed green understory, and (3) how to separate the signals of the forest canopy layer and the understory from each other for correct interpretation of tree canopy biophysical variables from optical satellite images.

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In this chapter, we will first outline the basic principles and current status of existing models for simulating the spectral signature of forests. After this, we will focus on the specific issues related to applying these models in the boreal zone, including how to collect the required input data. Finally, more practical issues, such as application of ground truth data, model scaling and validation, will be addressed.

6.2 Modeling the Spectral Signature of Forests The basic premises for optical remote sensing of vegetation are that the solar radiation received by a remotely located sensor (e.g., on a satellite) upon interaction with the vegetation canopy carries in it the signature of the canopy, and that this spectral signature can be deciphered to obtain the information of interest (Goel, 1989). Satellite-borne sensors measure the mean intensities of radiation at different wavelengths emanating from a target on Earth. Correct interpretation of these measurements to yield the biophysical variables of interest requires an accurate specification of the relationships between these variables and the canopy leaving radiation field. This specification is quantified by canopy reflectance models. The models are parameterized using mathematical descriptions of canopy structure together with optical properties of the plant elements and the underlying surface to produce spectral signatures of canopy leaving radiation. In addition, the spectral and angular properties of the incoming radiation and the receiving sensor need to be specified (Table 6.1). Finally, the spectral signature depends on the resolution of the measurement (i.e., pixel size), which needs to be considered in defining the spatial scale of the model. Table 6.1 Variables affecting the spectral signature of a forest (excluding terrain topography and atmosphere) Sensor

Illumination

Forest tree layer canopy

Understory and soil

Zenith and azimuth viewing angles

Angles of incidence and azimuth

Wavelength band (i.e., spectral sensitivity)

Wavelength

Macroscale structure (distribution, size and shape of tree crowns) Microscale structure (distribution, size and shape of leaves, needles, shoots and branches) Other structural elements (e.g., distribution, size and shape of tree trunks and branches) Spectral properties of all the canopy elements

Geometrical structure (amount, distribution, size and shape of understory plants) Spectral properties of understory plants

Resolution

Soil optical properties (influenced by e.g., soil moisture and texture)

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The mathematical descriptions of the process of radiative transfer in vegetation canopies cover a range of different approaches, starting from the traditional turbid medium approach to geometric-optical and hybrid models, the main difference being the degree of detail at which canopy structure at different hierarchical levels is described (Table 6.1). The turbid medium approximation, introduced to modeling the radiation regime inside vegetation by Ross (1981), is based on the classical radiative transfer theory (Chandrasekhar, 1960). The radiative transfer theory has been successfully applied to predicting the distribution of shortwave (optical and infrared) photons in several media like atmospheres, stellar dust or water. Radiative transfer theory is, in principle, the law of conservation of energy written out for beams of radiation traveling in all possible directions in a volume filled with optically active, i.e., absorbing and scattering, material. It is thus a function of five coordinates: three spatial coordinates determining the elementary volume for which the energy conservation law is applied, and two variables defining the direction of the radiation beam. In the classical radiative transfer theory, the fate of a photon is determined by the probability of being absorbed or scattered while traveling a unit distance (these probabilities are called the absorption and scattering cross-sections, respectively). Additionally, interactions between different rays for each point are described by the probability distribution of directions the photon can be scattered in, measured relative to the photon’s traveling direction before scattering. This is called the photon scattering phase function. The equation of radiative transfer merely states that the number of photons exiting each elementary volume equals the number of photons entering the volume minus the number of absorbed photons, written out in a correct mathematical form. More generally, a source term has to be added for radiating media, e.g., inside stars or for the thermal infrared radiation in atmosphere. In the optical region under consideration in this chapter, no radiation is usually emitted by the medium. The difference between the classical radiative transfer theory and the turbid medium approach lies in the treatment of the directional properties of the medium: in the classical radiative transfer theory, the scattering phase function and the absorption and scattering cross-sections are assumed to be independent of the direction of photon travel. This assumption does not hold for the transfer of radiation inside a vegetation canopy. Thus, in the turbid medium approximation, plant cover is described as consisting of geometric elements which usually have a preferred orientation described, in turn, by a directional attribute. Now, the absorption and scattering cross-sections become functions of the direction of photon travel inside the canopy as well as of the actual shape of the elementary units (phytoelements) constituting the canopy. For example, in a canopy of preferably horizontal flat leaves, the probability of hitting a leaf while traveling a distance unit is much larger for a photon moving in the vertical direction than for one moving in the horizontal direction. Consequently, the interaction cross-section (sum of absorption and scattering crosssections) in such a canopy is larger in the vertical direction than in the horizontal. Orientation of plant elements is described by statistical distributions. For example, the orientation of leaves is described by the direction (inclination and azimuth) of their normal and that of stems, branches and needles by the direction of their axis.

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A number of different distributions suitable for describing the distribution of leaf normals of actual canopies are given in, e.g., Weiss et al. (2004). Cross-sections can be calculated from these distributions by integrating over all possible orientation angles. Other than implying that the scattering phase function and the cross-sections depend on direction within the canopy, the turbid media approach leaves the classical radiative transfer equations intact: canopy elements are still of infinitesimal size and do not cast shadows, i.e., the “far-field approximation” still holds. Although anisotropy (or dependence on photon travel direction) makes finding a solution to the radiative transfer equation more difficult and yields some traditional methods unpractical, a plethora of techniques is still available for finding an approximate solution. The basic equations for the radiation field can be found, for example, in the book by Ross (1981) or various other sources (e.g., Myneni et al., 1989). The crudest (and fastest) way of solving the radiative transfer problem for a plane-parallel turbid media (or in “slab geometry”) is by using the two-stream (Kubelka-Munk) equations. Only two directions, up and down, are used to describe the radiation field inside a horizontally homogeneous and infinite medium and the solutions can be found analytically. In its simplest form, the two stream model assumes isotropic distribution of both up- and downward traveling radiation, i.e., the intensity does not depend on view angle inside both hemispheres. This condition is clearly violated if direct solar radiation is present. To overcome the problem, the contribution of the direct beam is separated, thus creating an additional source for the remaining more isotropic diffuse radiation field. This technique is almost universally employed in all algorithms for solving the radiative transfer problem in plant canopies. This is because besides its extremely anisotropic character, direct illumination gives rise to the so-called hot-spot phenomenon (see discussion later in this chapter) that needs to be accounted for if measurements are taken near the backscattering direction. The solutions of the two-stream equation are analytical and thus extremely computer-efficient. It should also be noted that the two-stream equations cease to be approximations for a (theoretical) canopy of infinitesimally small horizontal ideally scattering leaves but, instead, give the exact analytical solution as the reflected and scattered radiation field inside such a canopy is isotropic. A classical example of an application of the two-stream approximation is the SAIL (Scattering and Arbitrarily Inclined Leaves) model (Verhoef, 1984, 1985). Besides the two fluxes, the model calculates intensities for two other directions: the solar direction (for reasons discussed above) and the view direction. This enables to take into account anisotropy in the distribution of reflected radiation. The absorption and scattering coefficients, and the scattering phase function are calculated from a distribution function of leaf inclination angles. Despite its age, the model is still used for remote sensing purposes, although sometimes modified to fit the particular needs or encapsulated in other models that include a higher level description of canopy structure (Kuusk, 1995; Kuusk, 2001; Andrieu et al., 1997). The SAIL model is reasonably accurate, and can take the competition from much more sophisticated 3D models, in the case of relatively homogeneous canopy types (crops, grasslands) that have a small number of structural parameters (Jacquemoud et al., 1995; Koetz et al., 2005; Meroni et al., 2004; Andrieu et al., 1997; Weiss and Baret, 1999; ZarcoTejada et al., 2003).

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If the media cannot be considered homogeneous in the horizontal directions, as is the case for many natural vegetation canopies, the radiative transfer equation can be solved in three dimensions (Myneni, 1990; Knyazikhin and Marshak, 1991). This approach is useful for highly structured scenes where the two-stream model cannot be adequately parameterized to include canopy heterogeneity. Once such a scene is generated based on measured data or a forest structure model, the canopy is divided into cells and the equation (or, after discretization, a set of coupled integrodifferential equations) is solved numerically using the discrete ordinates iterative approach on the grid (Myneni, 1990; Gastellu-Etchegorry et al., 1996; Knyazikhin et al., 1998a). This method is based on the calculation of radiation intensities in discretized directions. In each iteration, the contribution of radiation scattered to every discrete direction from all other directions is calculated for each canopy cell using a pre-calculated scattering matrix until the intensities converge to a solution. Naturally, this method, besides its mathematical complexity (which is further increased by using various convergence acceleration techniques), also requires a realistic description of the scene and reasonable cell-size to exclude shadowing effects. The method is computer-intensive but the results can be considered accurate as this method is based on the physical principles of radiative transfer. Another common method used for calculating radiation reflected by a canopy, for which a complete 3D description of the scene is given, is the Monte Carlo method. As the radiation field above plant canopy is composed of small contributions by individual photons, the angular and spatial variation in the intensity of reflected radiation can be viewed as a distribution function describing the possible exit directions and locations of light quanta. Monte Carlo methods (or ray tracing algorithms) are based on random sampling of this distribution. If a sufficient number of photons are traced, the counts of photons exiting in each direction are relatively close to the actual directional distribution of reflected radiation, although some numerical noise is inevitable. Although in studies of radiative transfer in canopies, the term “Monte Carlo” is commonly used to denote tracing the trajectories of photons in a realistic detailed 3D canopy scene (Gerstl et al., 1986; Ross and Marshak, 1988; North, 1996; Chelle and Andrieu, 1998; Govaerts and Verstraete, 1998; Thompson and Goel, 1998; Disney et al., 2006), Monte Carlo calculations can also be used to trace photons in a 3D turbid media with varying optical properties, like the geometricoptical approximation described below (Gerard and North, 1997; Garc´ıa-Haro and Sommer, 2002). An overview of the Monte Carlo modeling approach is given by Disney et al. (2000). If a 3D description of a scene is given, the reflected radiation field can also be calculated using the radiosity principle (Borel et al., 1991; Gerstl and Borel, 1992; Goel et al., 1991; Chelle and Andrieu, 1998; Garc´ıa-Haro et al., 1999; Qin et al., 2002; Soler et al., 2003). Radiation field inside the canopy is calculated using view factors for individual elements: if the illumination conditions of a particular canopy element are given, its brightness as viewed from the positions of all other elements can be calculated based on its geometry and scattering properties. The brightness of an object is a well-defined radiometric quantity that can be used to calculate the partial flux contributed by the object. Thus, if the magnitude and angular distribution

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of radiation field incident on a canopy element can be calculated from brightness of all other canopy elements and the intensity of the incident unscattered radiation, the brightness of the element as viewed from any point inside or above the canopy can be calculated. It is an iterative process complicated by the large number and mutual shading of elements present in a natural canopy. From the computing perspective, the most time-consuming task is calculating these view factors or solving the geometrical relations between each pair of foliage elements. Once these factors are known, calculations for different wavelengths for which only the scattering properties of elements are different, but not the geometry of the canopy as a whole are relatively fast. In the classical radiative transfer approach, the optical properties of the medium are assumed to change continuously (for the 3D case, this assumption is valid inside each cell). This is naturally not the case for actual vegetation canopies. The Monte Carlo and radiosity methods that describe the canopy as consisting of separate solid objects remove this restriction and take into account the mutual shading of elements (remove the far-field approximation). The assumption of discontinuities in canopy optical properties, or the existence of voids between scatterers, can also be inserted into the radiative transfer equation. The foliage are a density can be described using the statistical distribution of an indicator function, in other words, a function of the spatial coordinates that equals unity only if a scattering element is present at the point described by the coordinates. This leads to the stochastic radiative transfer equation in plant canopies (Menzhulin and Anisimov, 1991; Shabanov et al., 2000). Besides the mean reflecting properties of a canopy, this theory allows to calculate its statistical moments. Often the terms deterministic (“non-stochastic”) and stochastic are used as synonyms to 1D and 3D models, respectively. However, with the exception of Monte Carlo models, most of the existing canopy radiation/reflectance models, in fact use a non-stochastic approach in computing the spectral signatures. That is, even though the canopy structure may be described using statistical distributions, the canopy radiation field is solved for a mean realization (with average characteristics) of canopy structure. A truly stochastic approach, in contrast, would be to evaluate the 3D canopy radiation field for all possible statistical realizations of the canopy, and then average the corresponding radiation fields to obtain the ensemble average signature (Shabanov et al., 2000). The stochastic and non-stochastic approaches can result in different relationships between mean characteristics of canopy structure and canopy-leaving radiation. Sometimes, a more abstract description of the 3D structure of a natural forest canopy is required. The exact locations of all canopy elements are rarely known or reliably predicted for a forest canopy. Therefore, instead of describing the structure of a canopy by specifying the locations of the smallest canopy elements (e.g., leaves, needles or shoots), the canopy can be first divided into larger subunits. An obvious choice for the crudest first-level division would be the tree crown. The canopy can then be viewed as a congregation of geometrical tree crown envelopes with gaps between them. The locations of the tree crowns are described by a statistical distribution, thus accounting for mutual shadowing and the distribution of

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between-crown gaps. Depending on the accuracy by which the processes of radiative transfer are described in these models, the models are commonly categorized as geometric-optical or hybrid models, the term “hybrid” being a shortcut for “hybrid radiative transfer/geometric-optical model”. In the simplest form, a geometric-optical canopy reflectance model considers just the effect of the geometrical structure of a forest on the remotely sensed image (Li and Strahler, 1985, 1986, 1992; Welles and Norman, 1991; Chen and Leblanc, 1997). The image is supposed to consist of (sub-pixel-sized) regions of different brightness: directly illuminated tree crowns and ground, and shadowed tree crowns and ground. The fractions of these components are calculated using given illumination and view angles and mutual shadowing derived from geometrical considerations. These types of models can accurately account for only first-order scattered radiation, i.e., photons that reach the sensor having interacted only once with the geometric shapes comprising the canopy. Diffuse radiation is included using correction factors. This makes it difficult to use these models for different wavelengths where the optical properties of canopy elements are not similar. The share of first-order scattering can be calculated straightforwardly: this reflectance component, besides depending on canopy geometry, which is the same for all wavelengths, is a linear function of leaf single scattering albedo (leaf reflectance plus transmittance). Diffuse photons, on the other hand, interact with leaves (or other canopy elements) several times and the possible number of interaction is itself a function of leaf albedo at the specified wavelength. This makes canopy diffuse reflectance strongly nonlinear with leaf albedo, and results in highly wavelengthspecific diffuse radiation correction factors. Including the diffuse radiation field into the geometric-optical model leads to a hybrid radiative transfer/geometric-optical model (Nilson and Peterson, 1991; Li and Strahler, 1995; Ni et al., 1999; Atzberger, 2000; Chen and Leblanc, 2001; Huemmrich, 2001; Kuusk and Nilson, 2000; Peddle et al., 2004). The methods to include diffuse radiation can range from exact solutions (similar to those used in solving the 3D radiative transfer) to tracing the photons in the canopy comprised of crown envelopes seen as large chunks of turbid media (similar to the Monte Carlo approach). However, to maintain the high efficiency achieved by delineating the canopy into abstract crowns, a simple and fast approximation is often used. Now, the problem of finding reflected radiation intensity is divided into two sub-problems: (1) finding the first-order scattering component using a geometrical figure filled with absorbing and scattering foliage elements illuminated by a beam of direct radiation, taking into account mutual shadowing by other semi-transparent crowns, and (2) calculating the share of diffuse radiation using a simpler (e.g., twostream) solution of the radiative transfer equation. Naturally, in calculating both components one has to consider the effect of a partially reflecting ground surface or undergrowth. Joining the two sub-models is not an easy task: the multiple-scattering component has to be parameterized to include the effect of canopy structure so that conservation of energy and correct partitioning between first- and higher order scattering are maintained.

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Hybrid models are an efficient and flexible tool for describing the radiation regime of complex forests. The effect of different crown shapes can be included by using various geometrical shapes: ellipsoids and cones of different proportions are the most commonly used. Also, higher-order clumping can be introduced by further dividing the canopy into abstract objects and adding their contributions to total reflectance (e.g., Smolander and Stenberg, 2005). However, most models still assume that the crown envelopes are uniformly filled with scatterers, although from biological considerations and biometrical measurements it is known not to be true. Using more realistic foliage distributions would considerably affect the transparency of the crowns by introducing more clumping at both branch and whorl scale or by locating photosynthesizing material close to the crown edge. While accounting for higher-order structure usually leads to an increase in predicted transmittance if the higher-order objects are distributed randomly, a regular distribution of foliage clumps that has been suggested for natural canopies (Cescatti, 1997b) may diminish or even reverse the effect. The choice of the model to be used for solving a problem involving calculation of canopy reflectance or radiation balance clearly depends on many factors. The amount of required computer resources, manpower and time is clearly different for the different approaches. Also, the optimal choice depends on the object under investigation: for relatively homogeneous canopies (crops, grasslands), a two-stream model give very good results. Sometimes, if canopy reflectance calculations form only a small contribution to a larger problem under investigation that depends on many variables with possibly high uncertainties, the use of a simpler model is justified. This is clearly not the case for highly structured vegetation covers like shrublands or boreal coniferous forests where the canopy upper surface is not flat, and mutual shading and between-crown transmittance between tree crowns have to be taken into account. Also, the amount of a priori knowledge can be a limiting factor when constructing a detailed 3D description of a canopy. In this case, a less detailed approach with a smaller number of input parameters might be preferred, e.g., a hybrid geometric-optical/radiative transfer model. Another characteristic of the reflecting properties of a medium that contains finites objects filling a three-dimensional volume is the hot spot phenomenon. “Hotspot” is a bright area in a remotely sensed image opposite to the source of illumination caused by a lack of shadows in the exact backscattering direction. The width of this reflectance peak (or the size of the brighter area in an image) depends on the geometric properties of the reflecting medium. Based on their working principles, geometric-optical models take this phenomenon into account, but only partly. When looking from the direction of illumination, no shaded crowns can be seen. This results in an increase in the predicted reflectance. Yet, the hot-spot phenomenon is also produced at a finer level (e.g., leaves), which in turn leads to a distinct anisotropy of the brightness of tree crowns. In more sophisticated reflectance models, this leaflevel hot-spot is added to the wider hot spot created by crown structure. Also, a hot-spot correction can be added to models based on the radiative transfer equation (e.g., Gerstl et al., 1986; Marshak, 1989; Verstraete et al., 1990; Jupp and Strahler, 1991; Kuusk, 1991). The correction factor is semi-empirical due to the complex

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structure of vegetation canopies. The phenomenon itself is difficult to measure accurately since it tends to be in the shadow of the sensor. Due to common view angle configurations, it is also not registered by most remote sensing instruments. Apart from the choice of radiation transfer model and availability of adequate computing resources, quality of both structural and spectral input data has a large impact on model performance. Today, good-quality data of either sorts are scarce as they are difficult to measure and have a high natural variance. Moreover, as developing accurate radiative transfer models for vegetation canopies is a work in progress, a ready-made solution may very likely not yet exist. However, the models presented here (or, a quite up-to-date performance comparison can be found from RAMI website (http://rami-benchmark.jrc.it) (Pinty et al., 2004b)) cover a large number of approaches which, if adequate input is provided in terms of both measurement data and dedication, can be applied to a wide variety of problems. More information on the subject can be found, in addition to the works referred to in this section, from previously published reviews and textbooks (e.g., Myneni et al., 1991; Liang and Strahler, 2000). Canopy reflectance models can be constructed in many ways; some can be run in the forward mode, some both in the forward and inverse modes. In model inversion (discussed thoroughly in another chapter of this volume), radiation measurements are converted into variables of interest characterizing the target. In remote sensing of forests, invertible models can be used to infer biophysical variables from reflectances (or back-scattering) registered by the remote air-or satellite-borne sensors. Commonly used methods for the inverse estimation of vegetation characteristics from satellite images include (1) comparing the observed signal to a database of previously computed spectral signals for a wide selection of different canopies and choosing the closest matches (look-up tables, LUT) (Knyazikhin et al., 1998b), or (2) iteratively optimizing model input parameters to match the observed signal as closely as possible using different optimization routines (Kuusk and Nilson, 2000). Needless to say, the goodness of the estimates depends crucially on how realistic the model is. Another basic requirement for successful estimation is of course that the vegetation characteristic in question has a detectable influence on the spectral signal, and that measurement errors can be corrected for. Even so, a remaining limitation is the well known fact that the inversion problem is ill-posed: no unique solution exists but different combinations of input parameters produce the same spectral signal. To be able to solve the inverse problem, in other words, to reduce the array of possible solutions to one solution, we need to acquire information from outside the problem itself. Technical or mathematical advances do not remove the underlying ambiguity of the ill-posed nature of the inversion problem in remote sensing. Another central problem in inversion is scaling: the forest reflectance models assume that the given forest structure continues infinitely. However, often in the case coarse and medium resolution satellite images, the vegetation (forested area) may cover only part of the pixel. At best, thus, the “averaged solutions” to the inversion problem may be accurate at larger, often regional, scales but not at small scales.

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6.3 Structural and Spectral Characteristics of Coniferous Forests Northern hemisphere boreal forests, forming the largest unbroken, circumpolar forest zone in the world, are dominated by coniferous tree species. The radiation regime of coniferous forests is known to differ in many respects from that of other vegetation, e.g., broadleaved forests and agricultural crops (Norman and Jarvis 1975; Oker-Blom et al., 1991; Nilson, 1992). From the perspective of optical remote sensing, a specific problem encountered in the boreal forest zone is the poor performance of commonly used spectral vegetation indices (e.g., the NDVI) for the estimation of biophysical variables (such as LAI). One reason for the generally observed relative insensitivity of these indices to changes in LAI is apparently caused by an abundant presence of mixed green understory in boreal coniferous forests (Chen and Cihlar, 1996; Eklundh et al., 2001; Stenberg et al., 2004; Peltoniemi et al., 2005; Rautiainen et al., 2007). The influence of understory on the spectral signal naturally poses a problem also for the correct image interpretation using physically based models. In recent years, yet another phenomenon specific to coniferous forests has become a subject of increasing scientific interest by the optical remote sensing community. From empirical observations, it has long been known that coniferous forests have a lower reflectance, especially in the near-infrared (NIR), than broadleaved forests, but the physical background to this behavior is still partly unexplored. In the following, we will discuss how some conifer-specific characteristics affect the spectral signature of coniferous forests. There are several structural and spectral attributes which are specific to coniferous forests and require modifications to the radiative transfer models formulated for their broadleaved counterparts (Fig. 6.1). The non-flat, three-dimensional structure of conifer needles of varying, species specific shape, first of all, requires proper

Needles

Shoots Tree crowns, internal shoot distribution patttern

Fig. 6.1 Hierarchic structure of coniferous crowns: A three-layer scheme

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(re-)definition of some of the key variables and concepts of these models: e.g., the leaf orientation, the mean projection of unit foliage area (“G-function”), the leaf scattering phase function, and the leaf area index (Stenberg, 2006). These variables and distributions were all originally defined and derived under the assumption of flat leaves and, so, for example, equations given for the mean projection of planar leaf area (e.g., Warren Wilson 1967) are not directly applicable to needles but must be derived with consideration given to the needle shape (Oker-Blom and Kellom¨aki, 1982; Lang, 1991; Chen and Black, 1992). A more serious theoretical problem for modeling however arises from that in many coniferous species needles are closely grouped together as shoots. The resulting small-scale variation in needle area density cannot readily be represented in the formulation of the radiative transfer equation based on the concept of an “elementary volume”, which should be small enough that essentially no mutual shading between the elements exists but large enough for statistical laws to apply (Ross, 1981). It has been proposed, therefore, that the shoot should be treated as the basic structural element of coniferous canopies – an approach that has actually long been used in models of canopy light interception and photosynthesis (e.g., Oker-Blom and Kellom¨aki, 1983; Nilson and Ross, 1997; Cescatti, 1997a), but has not yet been fully implemented in forest reflectance models due to the lack of data and models describing the scattering properties of shoots (but see Smolander and Stenberg, 2003). More data are available on another key parameter entering the shoot based models, namely the shoot silhouette to total area ratio (STAR) (Oker-Blom and Smolander, 1988), which is conceptually analogous to the G-function defined for flat leaves (Nilson, 1971), but includes a clumping coefficient accounting for the mutual shading of needles in the shoot. The clumping or mutual shading of needles in shoots acts to decrease the interaction cross section area of a given amount of total needle area, i.e., the extinction coefficient, and this effect can in radiative transfer models be parameterized (quantified) using the STAR. The decrease in shoot single scattering albedo, as compared to that of a single needle, has also been shown to be closely related to STAR, which thus can be used to modify the scattering properties of an elementary volume containing shoots (Smolander and Stenberg, 2003). However, theoretical models and, above all, empirical data on the shoot scattering phase function for different species are still needed for correct parameterization of coniferous canopy reflectance models. In some current models (Knyazikhin et al., 1998b; Kuusk and Nilson, 2000), shoot level grouping is accounted for in quantifying (i.e., reducing) the extinction coefficient (interaction cross section area of the elementary foliated volume), but its effect on the volume scattering phase function has not yet been fully implemented. It should be noted that when shoots (instead of single needles, or needle surface area elements) are treated as the basic elements, the optical properties (transmittance and reflectance) of single needles no longer suffice to describe the scattering properties of the elementary volume in the radiative transfer equation. Also at higher levels of organization, coniferous forests display a distinct grouped pattern (Fig. 6.1). The canopies are typically formed of dense, narrow and deep tree crowns. Crown shape, volume, and density have a considerable effect on the total

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canopy reflectance, as well as on the bidirectional reflectance factor (BRF) of conifer stands (Rautiainen et al., 2004). The same properties, together with the stand density (number of trees per hectare), also determine how much of the background (forest floor) is visible to the satellite instruments. Because northern coniferous forests are often rather open, with an abundant green understory, the spectral signal is a complex mixture of (overstory) canopy and background reflectance.

6.4 Effect of Clumping on the Spectral Signal: p-Theory as an Example The high degree of grouping (or clumping) of foliage at different hierarchical scales in coniferous forest stands (Fig. 6.1) is considered to be the most important reason behind the different spectral signature of these forests, in particular the low reflectance in NIR, as compared to broadleaved forests (Nilson et al., 1999; Rautiainen and Stenberg, 2005a). Incorporating the effects of grouping in canopy reflectance models poses a true challenge as very detailed canopy descriptions cannot readily be integrated into models operating at large spatial scales – this is typically the case in remote sensing of vegetation. Thus, especially for large scale applications, it is important to search for some key parameters that could capture the most essential structural features of a forest stand. One such canopy structural parameter, proposed to govern canopy absorption and scattering, is the spectrally invariant (i.e., wavelength independent) “p-parameter” introduced by Knyazikhin et al. (1998b). The “p-theory”, in short, predicts that the amount of radiation scattered by a canopy (bounded underneath by a black surface) should depend only on the wavelength and the spectrally invariant parameter (p), which can be interpreted as the probability that a photon scattered from a leaf (or needle) in the canopy will interact within the canopy again – the “recollision probability” (Smolander and Stenberg, 2005; Rautiainen and Stenberg, 2005a). The usefulness of this parameter in practical applications depends on whether and how well p can be related to (or derived from) other commonly available forest stand data. Nonetheless, it is a powerful modeling tool because it links canopy absorption (α C ) and scattering (ωC ) at any wavelength (λ ) to the phytoelement (leaf or needle) scattering coefficient (ωL ) at the considered wavelength, while simultaneously preserving the law of energy conservation (Panferov et al., 2001; Wang et al., 2003). The relationship between canopy and leaf scattering coefficients is described by the simple equation:

ωC (λ ) =

ωL (λ ) − pωL (λ ) 1 − pωL (λ )

(6.1)

It follows from Eq. (6.1) that, at any given wavelength, the canopy spectral scattering coefficient (ωC ) decreases in a nonlinear fashion with increasing canopy aggregation or grouping (quantified by the p parameter). More importantly, in any given canopy (fixed p), the relationship between ωC and ωL is also nonlinear, implying that canopy

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structure (or grouping, specifically) does not only affect the magnitude of the canopy leaving radiation but also modifies its spectral distribution. Simulation studies and empirical measurements have provided support for the validity and usefulness of the p-theory. Equation (6.1) was shown to precisely predict the absorption and scattering in structurally homogeneous canopies simulated with a Monte Carlo model (Smolander and Stenberg, 2003; Smolander and Stenberg, 2005), and to hold true also in heterogeneous canopies (M˜ottus et al., 2007) simulated using the hybrid FRT model (Kuusk and Nilson, 2000). Another spectral invariant parameter (pt ) has been proposed to control canopy transmission, i.e., the part of the scattered radiation that exits the canopy downwards (Knyazikhin et al., 1998a, b; Panferov et al., 2001; Shabanov et al., 2003). This structural parameter so far lacks a clear physical interpretation, as has been given for the other spectral invariant – the recollision probability (p), but if it can be formulated and shown to be valid (both theoretically and empirically), the two parameters offer a simple and effective tool for parameterization of the canopy radiation budget. Namely, given the absorption (p value) and transmission (pt value), total reflectance (the upward scattered part of the incident radiation) is also known (because they all sum up to one). Thus, the spectral invariants p and pt would allow calculation of all components, i.e., spectral absorptance, transmittance and reflectance of the canopy shortwave radiation budget for any given wavelength knowing the leaf (or needle) scattering coefficient at the same wavelength. If the relationships between p and canopy structural parameters such as LAI are known, the spectral signature of the canopy can be predicted in terms of LAI or, conversely, inverse estimation LAI can be done based on measured canopy reflectance. The relationship described by Eq. (6.1), linking together canopy scattering coefficients at a specific wavelength to the leaf albedo at the same wavelength, can actually be applied at different hierarchical levels and provides a tool for scaling grouping effects. In the simulation studies by Smolander and Stenberg (2003, 2005), it was found that Eq. (6.1) could be used to scale from needle to shoot scattering by replacing p by the “recollision probability within a shoot” (psh ). Moreover, it was shown that the canopy level recollision probability (p) could be decomposed into (1) the probability (psh ) that the new interaction occurs within the same shoot where the first (former) interaction took place, and (2) the probability (pc ) that interaction occurs with another shoot in the canopy, according to the formula: p = psh + (1 − psh )pc

(6.2)

Equation (6.2), which in a similar manner could be further developed (decomposed) to account, e.g., for grouping at the crown level, shows how the whole canopy p value is affected by grouping at different spatial scales. For a given LAI, the p value increases with the degree of grouping present in the spatial dispersion of the leaf area. Thus, for example, considering a broadleaved and coniferous canopy with similar LAI and macro-scale structure (Table 6.1), the coniferous canopy would have higher p or, equivalently, a smaller escape probability for the radiation incident

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on the canopy. This explains, at least partly, the observed lower canopy reflectance (albedo) of coniferous forests as compared to broadleaved forests. Two shortcomings of the p-theory for practical applications should however be noted: (1) It describes only canopy scattering, i.e., the contribution from background reflectance must be modelled separately and (2) it is not able to describe the angular distribution of scattered radiation. To solve these problems, the p-theory should be combined with other physically-based reflectance modeling concepts. With increasing p, the scattered part of the radiation intercepted by the foliated canopy (the crowns), and thus also canopy reflectance, decreases. However, the effect of groping on whole stand reflectance is not as straightforward. To demonstrate the combined effect grouping has on canopy reflectance, on one hand, and on the contribution of understory reflectance, on the other hand, we use the simple parameterization model, PARAS (Rautiainen and Stenberg, 2005a). In this semi-physical model, forest BRF is calculated as a sum of the ground and canopy components: BRF = cg f (θ1 )cg f (θ2 )ρground + f (θ1 , θ2 )i0 (θ2 )

ωL − pωL 1 − pωL

(6.3)

The parameters of Eq. (6.3) are defined as follows: θ1 and θ2 are the viewing and illumination zenith angles, cgf denotes the canopy gap fraction in the directions of view and illumination (Sun), ρground is the BRF of the ground, f is the canopy scattering phase function, i0 (θ2 ) is canopy interceptance or the fraction of the incoming radiation interacting with the canopy, and ωL is needle (or leaf) scattering coefficient. With increasing degree of grouping (larger p), canopy interceptance (i0 ) simultaneously decreases while the canopy gap fractions (cgf) increase and, thus, the contribution from ground (understory) reflectance increases. Especially grouping at larger scale (between crowns) may more importantly influence the total stand reflectance through its effect on increasing the contribution from the background than through its effect on the canopy contribution. Incorporating the effect of shoot scale clumping in the PARAS canopy reflectance model was shown to produce realistic reflectance values in the nearinfrared (NIR) of coniferous forests. This can be seen as a major improvement since the low NIR reflectance observed in coniferous areas is one of the main anomalies that models have not been able to account for. The results give support to the hypothesis that in coniferous canopies large part of the clumping occurs at the shoot level and, thus, that the incorporation of shoot structural and spectral properties into current forest reflectance models will significantly improve their performance.

6.5 Scaling of Canopy Reflectance In the previous section, the term “scaling” was introduced to describe an application of recollision probability at different canopy grouping levels, i.e., the dimensionless scattering characteristics calculated at one level were applied at another, larger scale. This approach is similar to using downscaled models for predicting the behavior

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of the full-scale object. The procedure can be applied repeatedly as long as the character of the process (in our case, interaction of photons with canopy elements) remains unchanged. In optical remote sensing, the limit is determined by the ratio of photon wavelength to the size of the scatterers, i.e., radiative transfer is still determined by geometric optics, and refraction can be ignored. In the current section, “scaling” has a different meaning that is more familiar to the remote sensing community. Here, we use it to describe the spatial variation of canopies that has to be taken into account when comparing sensors with different view configurations (i.e., sensors that produce images with different pixel sizes). Generally, models can produce only point estimates of canopy reflectance, although most of them have a method to account for within-plot variability (statistical distribution of tree locations, etc.). This works well as long as the canopy is horizontally homogeneous (which is what these models actually presume) and its structure does not vary across a relatively large area, substantially exceeding the dimensions of a pixel in the image produced by the sensor. Natural forest canopies, however, almost never possess such a property: they include clusters of high tree concentrations and canopy openings, due to harvesting or windfall. As the reflectance process is strongly nonlinear, this heterogeneity is difficult to take into account in the spatially averaged pixels of remote sensing instruments. The scale at which model results can be related to the reflected signal in a straightforward way depends on the size of the structural units of the canopy. For example, models that utilize an assumption of a statistical distribution of tree locations predict an average signal produced by such a canopy and cannot be applied to model distinct patterns created by a particular configuration of individual trees or the variance of intensity in the image of a single crown. They were not designed for these purposes as overly detailed patterns are commonly not required for remote sensing of larger areas. Another reason is that biophysical variables (LAI, fCover) are defined for a larger canopy area and cannot be used to describe a single tree. When moving to larger resolutions, the models may also fail due to the nonlinearity of the radiative transfer problem and a highly varying or discontinuous distribution of tree locations. Canopy spectral properties are a function of spatial resolution (Tian et al., 2000; Pinty et al., 2004a), and especially in regions with a fragmented forest area, the signal will always be a mixture of reflectance from many different ground (soil/understory) and forest canopy compartments. This may lead to a situation where a model cannot be used as such (without alterations) to model signals by sensors with different spatial resolutions (Tian et al., 2002). The scaling problem affects the retrieval of different biophysical variables with varying severity. While some variables can be considered almost scale-independent (fCover, fPAR), predicting others (e.g., LAI) requires a careful consideration of spatial variation (Weiss et al., 2000). Algorithms for a correct treatment of the scaling problem of vegetation reflectance modeling are scarce although a physically-based theory for scaling was developed by Tian et al. (2002), for example. The incorporation of scaling algorithms directly in radiation transfer models is so far an almost unexploited subject (Widen, 2004).

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6.6 Use of Stand Inventory Data as Model Input Ground truth, or ground observations, is required for both developing and testing physically based forest reflectance models and their inversion. There are two general paths for acquiring this information: by conducting measurements or by using existing data bases (e.g., land cover maps, regional or national forest inventories, spectral data banks of common plant species). However, a general problem with all these data sources may be their age when compared to the more recently obtained remotely sensed image. Stand inventory data (which typically consists of information on tree species, tree height and diameter, and stand density or basal area) form a common input set required by most 3D forest reflectance models. However, stand inventories do not provide all the parameters typically included in physically based reflectance models, e.g., crown shape, leaf area density and orientation, nor do they include the biophysical variables of interest in this chapter (LAI, fPAR, fCover). Testing reflectance models should be done with a carefully measured, comprehensive input data set which includes all the input required by the model and which does not rely on other models (i.e., is not generated by other models). However, when operational inversion for obtaining biophysical variables (LAI, fPAR, or fCover in this case) is considered, such comprehensive data sets are not available, and other, let us say less appropriate, sets need to be utilized. A typical source would be regional or national forest inventory data bases which have recently become more suitable for the purpose in the boreal zone of North America and Europe. Traditionally forest mensuration science dealt with determining the volume of stands and logs and then studying stand growth and yield. Nowadays, however, the scope has widened and regional and national forest inventories have become more efficient environmental monitoring tools and are conducted to ensure the sustainable use of forests. Thus, they include more stand variables than tree height and diameter and form a better interface for forest reflectance models. Nevertheless, if forest reflectance models are run through a routine forest management data base (e.g., Rautiainen, 2005), there are several structural input parameters, such as crown shape, woody area index or shoot size, in the models which can hardly be obtained from these data bases. Thus, alternative solutions for obtaining the structural information need to be considered. A possibility worth exploring further would be to create realistic input data on these additional structural parameters from basic stand variables through regression models and allometric relationships. Such models exist for relating different biomass components of a tree or forest (e.g., Marklund, 1988) but parameters describing crown architecture have been of less interest in forest mensuration. In the context of radiative transfer modeling, one of the most central parameters not available from routine stand inventory data sets is crown shape which here serves as an example. Crown shape determines the limits of integration over the crown envelope and thus the scattering volume. Therefore, crown shape needs to be predicted from routine stand variables such as tree height and breast height diameter. This can be done by, for example, developing a crown shape model based on extensive measurements and then using the model to predict crown shape for a stand where it has not

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been measured (e.g., Baldwin and Peterson, 1997; Rautiainen and Stenberg, 2005b; M˜ottus et al., 2006). Alternatively, crown shape can be assumed to have a constant geometric shape (e.g., a cone or an ellipsoid) for a given tree species.

6.7 Concluding Remarks Remote sensing mapping techniques have traditionally been statistically oriented but physically based methods have progressively become more and more attractive because they are better suited for many current large scale applications related to global mapping of vegetation (e.g., Knyazikhin et al., 1998b). Implementation of physically based remote sensing methodology has become feasible thanks to the development of fast computer hardware and high resolution and multi-angular satellite instruments. The rapid technological and methodological development of satellite derived products offers a range of new possibilities for the mapping of terrestrial biophysical parameters such as vegetation type, forest cover (fCover) and leaf area index (LAI) from remotely sensed data (Myneni et al., 1997; Chen et al., 2002). Remote sensing based methodologies are especially important, and in fact the only feasible alternative, in regions where reliable field information is not available, is difficult to reach, or is too expensive. This, on the other hand, makes the importance of validation an even more crucial part of the development process aiming at producing trustworthy information righteously required by the end-users. Several research networks operate today on the refinement of remote sensing mapping methods and on validation of satellite derived biophysical products, such as LAI, fCover and fPAR, that are presently routinely generated by a range of sensors (Knyazikhin et al., 1998b; Morisette et al., 2006). For critical assessment of the accuracy of remotely sensed estimates of biophysical variables, there should be available a set of statistically representative (sufficient) and independent reference data with known accuracy. Also, special care should be taken that similar (standardized) measurement methodologies and designs are used to produce reference data of the variable of interest (Morisette et al., 2006). Global validation networks have a very important mission in providing these validation data needed for the further development of the remote sensing methodology. Physically based remote sensing methods still have room for improvement, and we have claimed in this chapter that there is especially a need to further develop reflectance models designed for coniferous forests, accounting for their complex 3D canopy structure and the small-scale variation in needle area density. The widely discussed global trends of greening and vegetation status require accurate algorithms for boreal forests. An efficient use of physically based forest reflectance models in the boreal coniferous forest zone would require that the model input data include variables such as crown shape and canopy cover, and spatial pattern of trees, to represent their clumped structure. In combination with standard forest inventory data, these key structural parameters would form a very valuable data base. It seems reasonable to believe that with better representation of the 3D canopy structure, the

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accuracy of remotely sensed estimates of canopy biophysical characteristics would improve considerably. Accordingly, future tasks of high priority include means to create realistic input data on crown shape, tree pattern and canopy cover from basic stand variables, for example through regression models and allometric relationships. In boreal forests, another limitation to successful application of canopy reflectance models is a typically large proportion of non-contrasting background reflectance in the visible and near-infrared (NIR) part of the spectra due to abundant mixed green understory. Stand inventory data do not include spectral properties of the forests, and there is a need for more data on the angular reflectance properties of common forest species, including not only understory vegetation but tree components, such as needles, shoots and bark. Use of the p-theory is for application in large scale remote sensing mapping methods is another question of large current interest. Can a simple parameterization model using the spectral invariants be built to mimic canopy reflectance with sufficient accuracy? It has already been shown, and put into practice in the MODIS LAI/FPAR algorithm, that the spectral invariants provide a powerful calculation tool in reflectance models and preserve the law of energy conservation. However, if one could derive specific relationships between the spectral invariants (p and pt ) and basic canopy structural parameters such as LAI and canopy cover, it would provide an effective tool by which the effect of the clumping of foliage at different hierarchical levels of the forest stand structure could be incorporated in forest reflectance models.

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Weiss M, Baret F (1999) Evaluation of canopy biophysical variable retrieval performances from the accumulation of large swath satellite data. Remote Sens. Environ. 70:293–306 Weiss M, Baret F, Myneni RB, Pragn`erea A, Knyazikhin Y (2000) Investigation of a model inversion technique to estimate canopy biophysical variables from spectral and directional reflectance data. Agronomie. 20:3–22 Weiss M, Baret F, Smith GJ, Jonckheere I, Coppin P (2004) Review of methods for in situ leaf area index (LAI) determination. Part II. Estimation of LAI, errors and sampling. Agric. For. Meteorol. 121:37–53 Welles JM, Norman JM (1991) Photon transport in discontinuous canopies: a weighted random approach. In: RB Myneni, J Ross (eds), Photon-Vegetation Interaction, Springer, BerlinHeidelberg, pp 389–414 Widen N (2004) Assessing the accuracy of land surface characteristics estimated from multiangular remotely sensed data. Int. J. Remote Sens. 25:1105–1117 Yoder B, Pettigrew-Crosby R (1995) Predicting nitrogen and chlorophyll content and concentrations from reflectance spectra (400–2500 nm) at leaf and canopy scales. Remote Sens. Environ. 53:199–211 Zarco-Tejada PJ, Rueda CA, Ustin SL (2003) Water content estimation in vegetation with MODIS reflectance data and model inversion methods. Remote Sens. Environ. 85:109–124

Chapter 7

Estimating Canopy Characteristics from Remote Sensing Observations: Review of Methods and Associated Problems Fr´ed´eric Baret and Samuel Buis

Abstract This article describes the methods and problems associated to the estimation of canopy characteristics from remote sensing observations. It is illustrated over the solar spectral domain, with emphasis on LAI estimation using currently available algorithms developed for moderate resolution sensors. The principles of algorithms are first presented, distinguishing between canopy biophysical and radiometric data driven approaches that may use either radiative transfer models or experimental observations. Advantages and drawback are discussed with due attention to the operational character of the algorithms. Then the under-determination and ill-posedness nature of the inverse problem is described and illustrated. Finally, ways to improve the retrieval performances are presented, including the use of prior information, the exploitation of spatial and temporal constraints, and the interest in using holistic approaches based on the coupling of radiative transfer processes at several scales or levels. A conclusion is eventually proposed, discussing the three main components of retrieval approaches: retrieval techniques, radiative transfer models, and the exploitation of observations and ancillary information.

7.1 Introduction Many applications require an exhaustive description of the spatial domain of interest that may cover a large range of scales: from the very local one corresponding to precision agriculture where cultural practices are adapted to the within field variability, through environmental management generally approached at the landscape scale, up to biogeochemical cycling and vegetation dynamics investigated at national, continental and global scales. Most of these applications are using our knowledge on the F. Baret and S. Buis UMR1114, INRA-CSE, 84 914 Avignon, France [email protected] S. Liang (ed.), Advances in Land Remote Sensing, 173–201. c Springer Science + Business Media B.V., 2008


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main physical, chemical and biological processes involved such as energy balance, evapotranspiration, photosynthesis and respiration. This knowledge is encapsulated into a variety of surface process models. However, to account for the spatial heterogeneity observed at all scales, dedicated imaging systems are required to get a distributed description of surface characteristics within the domain of interest. By its capacity to cover exhaustively large space areas, remote sensing provides a very pertinent answer to those requirements. However, remote sensing observations sample the radiation field reflected or emitted by the surface, and thus do not provide directly the biophysical characteristics required by the models for describing some state variables of the surface. An intermediate step is therefore necessary to transform the remote sensing measurements into estimates of the surface biophysical characteristics. Many methods have been proposed to retrieve surface characteristics from remote sensing observations. They span from simple empirical ones with calibration over experimental data sets, up to more complex ones based on the use of radiative transfer models. Radiative transfer models summarize our knowledge on the physical processes involved in the photon transport within vegetation canopies or atmosphere, and simulate the radiation field reflected or emitted by the surface for given observational configuration, once the vegetation and the background as well as possibly the atmosphere are specified. Retrieving canopy characteristics from the radiation field as sampled by the sensor aboard satellite needs to “invert” the radiative transfer model. This article aims at presenting the state of the art in the estimation of surface characteristics from remote sensing observations. Although this is a very general problem in remote sensing, it will be illustrated by examples taken in the solar domain (400–2,500nm), with emphasis put on the current operational algorithms that are mainly used for medium resolution sensors such as MODIS, MERIS, AVHRR, VEGETATION, POLDER and SEAWIFS. Among the possible canopy characteristics accessible from remote sensing in the reflective solar domain, we will focus on leaf area index (LAI), defined as half the developed area of green elements per unit horizontal soil (Stenberg, 2006). As a matter of fact, LAI is one of the key canopy state biophysical variables required by many process models to describe energy and mass exchanges in the soil/plant/atmosphere system.

7.2 Principles of Biophysical Variable Retrieval Algorithms Remote sensing data result from radiative transfer processes within canopies that depend on canopy variables, and observational configuration (wavelength, view and illumination directions). Canopy variables include the variables of interest for the applications such as LAI, and the other variables that are not of direct use for the applications but that influence the radiative transfer, such as soil background properties. The causal relationship between the variables of interest and remote sensing data corresponds to the forward (or direct) problem (Fig. 7.1). They could be

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Other variables Radiative transfer Variables of interest

Inverse problem

Observation configuration

Forward problem

Remote sensing data

Retrieval algorithm Prior information

Fig. 7.1 Forward (solid lines) and inverse (dashed lines) problems in remote sensing

either described through empirical relationships calibrated over experiments or using radiative transfer models based on a more or less close approximation of the actual physical processes. Conversely, retrieving the variables of interest from remote sensing measurements corresponds to the inverse problem, i.e., developing algorithms to estimate the variables of interest from remote sensing data as observed in a given configuration. Prior information on the type of surface and on the distribution of the variables of interest can also be included in the retrieval process to improve the performances as we will see later. A panoply of retrieval techniques currently used have been reviewed in the early 1990s by several authors (Asrar et al., 1989; Goel, 1989; Pinty and Verstraete, 1991) and more recently by Kimes et al. (2000) and Liang (2004). They can be split into two main approaches (Fig 7.2) depending if the emphasis is put on remote sensing data (radiometric data) or on the variables of interest to be estimated (canopy biophysical variables).

7.2.1 Canopy Biophysical Variables-driven Approach The approach requires first to calibrate the inverse model: a parametric model representing the inverse model is adjusted over a learning data set (Fig. 7.2, left). It mainly consists in adjusting the parameters to fit a response surface between reflectance values and the corresponding canopy variables of interest (LAI in this example). Once calibrated, the parametric model is run to compute the variables of interest from the observed reflectance values. The learning data set can be generated either using simulations of radiative transfer models, or based on concurrent experimental measurements of the variables of interest and reflectance data.

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Radiometric data driven approach

Biophysical variables driven approach Learning data set LAI

RT process

Reflectance

LAI

∆

LAI*

RT process

Reflectance

∆ Inverse Model

Reflectance Measurement

Parameters

Fig. 7.2 The two main approaches used to estimate canopy characteristics from remote sensing data for LAI estimation. On the left side the approach focusing on the biophysical variables showing the calibration of the inverse model. Once the inverse model is calibrated it can be applied using the measured reflectance as input. On the right side, the approach focusing on radiometric data showing the solution search process leading to the estimated LAI value, LAI ∗ . “∆” represents the cost function to be minimized over the biophysical variables (left) or over the radiometric data (right)

7.2.1.1 Calibration over Experimental Data Sets This was the first approach historically used, the reflectance in few bands being generally combined into vegetation indices (VI) designed to minimise the influence of confounding factors such as soil reflectance and atmospheric effects (Baret and Guyot, 1991). The relationships between VIs and canopy variables are calibrated over experimental observations (Asrar et al., 1984; Huete, 1988; Wiegand et al., 1990; Wiegand et al., 1992; Richardson et al., 1992). Recently Chen et al. (2002) used simple VIs to derive LAI estimates from AVHRR and VEGETATION across Canada. This was extended at the global scale by Deng et al. (2006). In agreement with several observations, these authors found that the relationships vary from one cover type to another as illustrated by Fig. 7.3. The development of such empirical transfer functions is limited by the difficulty to get a training data base that represents the whole range of possible conditions encountered over the targeted surfaces, i.e., combinations of geometrical configurations, type of vegetation and states including variability in development stage and stress level, and type of background and state (roughness, moisture). Measurement errors associated both to the variables of interest and to radiometric data may also propagate into uncertainties and biases in the algorithm and should be explicitly accounted for Fernandes and Leblanc (2005) and Huang et al. (2006). Further, since ground measurements having a footprint ranging from few meters to few decametres, specific sampling designs should be developed to represent the sensor pixel. This task is obviously more difficult for medium and coarse resolution sensors as outlined by Morisette et al. (2006). Higher spatial resolution observations could be used to extend the local ground measurements to the actual pixel size of medium or coarse resolution sensors.

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10 Coniferous Deciduous Mixed Others

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LAI

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0

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5 10 RSR VEGETATION

Fig. 7.3 Empirical relationships between LAI values as a function of the simple ratio vegetation index (RSR) computed for VEGETATION data for four types of canopies (After Chen et al., 2002)

7.2.1.2 Calibration over Radiative Transfer Model Simulations To avoid limitations associated to the empirical nature of the training data base, radiative transfer models could be used alternatively to generate a training data base. Radiative transfer models can be used to create a data base covering a wide range of situations and configurations. Several authors have therefore proposed replacing actual observations by numerical experiments based on radiative transfer model simulations to calibrate empirical relationships (Sellers, 1985; Baret and Guyot, 1991; Rondeaux et al., 1996; Leprieur et al., 1994; Banari et al., 1996; Huete et al., 1997; Verstraete and Pinty, 1996). Based on these principles, operational algorithms developed for medium resolution sensors are currently used: MGVI for MERIS (Gobron et al., 2000) further extended to other sensors, MODIS back-up algorithm based on NDVI (Knyazikhin, 1999), POLDER algorithm based on DVI computed from bidirectional reflectance factor (BRF) measurements normalized to a standard geometrical configuration (Roujean and Lacaze, 2002). Nevertheless, although quite often effective, VIs are intrinsically limited by the empiricism of their design and the small number of bands concurrently used (generally 2–3). This might not be a major problem for fAPAR and fCover variables that are relatively simple to estimate, but would be more difficult for variables such as LAI or chlorophyll content (Cab ) showing higher level of non linearity with reflectance measurements (Weiss et al., 2000). The efficient interpolation capacity of neural network (NNT) can be exploited to adjust surface responses (Leshno et al., 1993). Several authors have proposed such an approach since the beginning of the 1990s (Smith, 1992; Smith, 1993; Atkinson and Tatnall, 1997; Kimes et al., 1998; Abuelgasim et al., 1998; Gong et al., 1999;

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Danson et al., 2003). Neural networks were compared with a specific implementation of multiple regression, the projection pursuit regression, and were concluded to achieve very similar performances (Fang and Liang, 2005). Baret et al. (1995) demonstrated that NNT used with individual bands were performing better than classical approaches based on vegetation indices especially when calibrated with radiative transfer model simulations rather than with experimental observations. Weiss et al. (2002a) validated such techniques over a range of crops for estimating the main canopy biophysical parameters LAI and fCover from airborne POLDER instrument. Recently, several authors developed operational products for medium resolution sensors, starting from top of canopy level: Lacaze (2005) for POLDER, Bacour et al. (2006) for MERIS, and Baret et al. (2007) for VEGETATION instruments. Baret et al. (2006b) proposed an operational algorithm from the MERIS top of atmosphere data by coupling an atmospheric radiative transfer model to the surface one, exploiting explicitly 13 over the 15 bands of MERIS. Several ways may be used to build a data set for training empirical relationships depending on the performances targeted. Evaluation of the performances of an algorithm is generally achieved by computing the Root Mean Square Error (RMSE) value over a test data base made of representative cases. Best performances will therefore be obtained when the variables in the training data base are distributed similarly to those in the testing one, i.e., close to the actual distribution of the variables: the coefficients of the empirical transfer function will be optimized for these conditions, and uncertainties will be minimal for the most frequent cases. Although achieving poorer performances in term of RMSE, a more even distribution of the uncertainties may be alternatively obtained using uniform distributions of the variables. Note that, for a given number of cases simulated in the training data base, the density of cases that populate the space of canopy realization may rapidly decrease as a function of the number of required variables. Experimental plans may be used in this situation as proposed by Bacour et al. (2002b), in order to focus on the first order effects and interactions. Additionally, Baret et al. (2006b) proposed to steamline the data base in the reflectance space by retaining the cases that belong both to the simulated and actual remote sensing measurements spaces (Fig. 7.4). This allows discarding cases that were simulated but not actually observed. Conversely, it allows also identifying cases which are observed but not simulated. This is achieved by first compiling a large data base of reflectance measurements that should be representative of the possible situations available. Then the reflectance mismatch is

Simulations Cases not represented in the measured database

Actual measurements Cases not represented in the simulated database Training database: selection of cases in the intersection space

Fig. 7.4 Streamlining the simulated training data set by comparison to actual measurements. The intersection between the space of simulated radiometric data (in dark gray) with that of the actual measurements (in light gray) is used as the training data base

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computed for each case in the simulated data base: it is the minimum RMSE value computed between the reflectance in the simulated data base and the ensemble of actual measurements. A threshold corresponding to the uncertainties in the radiometric measurements is then used to decide whether a simulated case is rejected from the training data base. Additional criterions could be used to streamline the training data base, based on the expected consistency between several products such as LAI and fAPAR as proposed by Bacour et al. (2006). Although the use of radiative transfer models appears very appealing, this approach is however limited by several aspects. The first one is the capacity of the models to get a faithful description of the radiative transfer in canopies. Up to now, most radiative transfer models used are computer efficient ones allowing populating large training data base within few hours/days with a single regular computer. They generally correspond to simple description of canopy architecture which may not represent the actual one, particularly regarding the clumped nature of many vegetation types. This leads to model uncertainties that may dominate all other sources of uncertainties for some of the vegetation types. Recent advances in modeling more complex canopy architecture (e.g., Soler et al., 2001; Lewis et al., 2004) offer great potential for improvement. However, the second limitation will probably counterbalance these advancements: building a realistic training data set requires a fair description of the distribution and co-distribution of the corresponding architectural variables to define the actual space of canopy realization. For the simplest radiative transfer models (e.g., Verhoef, 1984; Kuusk, 1995; Gobron et al., 1997) at least three architectural variables are required (LAI, leaf angle distribution function and size of the leaves relative to canopy height), the distribution of which being very poorly known. This is even more difficult when using more complex and realistic architectural description that requires more variables. Note that in these approaches based on radiative transfer model simulations, radiometric measurements uncertainties have to be added to the simulations when building up the training data base. This allows more robustness within the training process and thus improved retrieval performances. Accounting for these uncertainties is also critical when large differences exist among bands used or when these uncertainties are strongly correlated. Canopy biophysical variables driven approaches present the advantage of being very flexible. For example, estimates of biophysical variables from one sensor could be used to constitute the training data base for another sensor. This could be applied over high spatial resolution products that are aggregated to coarser spatial resolution to generate an appropriate training data base. This could also apply to generate consistent products between sensors.

7.2.2 Radiometric Data-driven Approach While the previous approach was focusing on minimizing the distance between the variables retrieved from the inverse model and those from the training data set, the alternative approach is based on finding the best match between the measured

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reflectance values and those either simulated by a radiative transfer model or stored within a database made of experimental observations. No proper calibration step is required in this approach. However, several ingredients of these techniques are difficult to evaluate (uncertainties, parameters of the search algorithm) and need generally some tuning over a “prototyping” data set. The performances of the approach will both depend on the minimization algorithm itself and on the level of ill-posedness of the inverse problem as a function of measurement configuration and model and measurement uncertainties. Several minimization techniques have been used: classical iterative optimization, simulated annealing (Bacour, 2001), genetic algorithms (Fang et al., 2003; Renders and Flasse, 1996), look up tables and Monte Carlo Markov Chains (Zhang et al., 2005). However, classical iterative optimization techniques (OPT) and look up tables (LUT) have been the most widely used and will be described with more details below.

7.2.2.1 Iterative Optimisation (OPT) This classical technique consists in updating the values of the unknown input biophysical canopy radiative transfer model variables until the simulated reflectance closely fit the corresponding measurements (Goel and Deering, 1985; Kuusk, 1991a and 1991b; Goel, 1984a and b; Pinty et al., 1990; Jacquemoud et al., 1995; Privette et al., 1996; Bicheron and Leroy, 1999; Combal et al., 2000; Bacour et al., 2002a; Combal et al., 2002). A good review on optimization methods used in remote sensing for land applications can be found in Bacour (2001). The goodness of fit between measured and simulated reflectance spectra is quantified by a cost function (J) that may account explicitly for measurements and model uncertainties. The cost function may be theoretically derived from the maximum likelihood (Tarentola, 1987). When no prior information is available and when uncertainties associated to each configuration used are assumed independent and gaussian, J is assessed using norm L2, i.e., sum over the N observational configurations of the square of the difference beˆ weighed by the tween the measured reflectance values (R) and those simulated (R), variance (σ2 ) associated to both reflectance measurements and model uncertainties: (Rn − Rˆ n )2 σn2 n=1 N

J=

∑

(7.1)

However, because of the difficulty to provide an estimate of σ2 , several approximations have been used as shown in Bacour (2001). It spans from the simple ones such as norm L1 to norm L2 with no weighing of the configurations, up to more complex based on some modeling of the variance term (Table 7.1). The main limitation of OPT techniques is twofold. (1) Firstly, the algorithm might converge to a local minimum of the cost function that could be far away from the global one expected to correspond to the actual solution. This can be partly avoided by using a range of initial solutions, coupled with constraints on the range of variation of the variables to be estimated. The use of a priori information in the

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Table 7.1 The cost functions (J) used in several studies dealing with radiative transfer model inversion for canopy biophysical variables retrieval. N is the number of configurations (bands and directions); Rˆ n and Rn being respectively the simulated and measured reflectance values for configuration n. θν and φ are the zenith and relative azimuth view angles Cost function N

J= ∑

References

Rn −Rˆ n Rn

n=1 N 

Gao and Lesht, 1997)

 ˆ  J = ∑  RnR−nRn  n=1 N 

J= ∑

n=1 N

Rn −Rˆ n Rn +Rˆ n

(Qiu et al., 1998)

2

(Gobron et al., 1997)

J = ∑ (Rn − Rˆ n )2

(Goel and Thompson, 1984; Pinty et al., 1990; Privette et al., 1996; Braswell et al., 1996; Jacquemoud et al., 2000; Combal et al., 2002)

n=1 N

J= ∑ n=1 N



Rn −Rˆ n Rn

J = ∑ ωn n=1



2

Rn −Rˆ n Rn

(Nilson and Kuusk, 1989; Kuusk, 1991a and b; Bicheron and Leroy, 1999; Weiss et al., 2000) 2

; ωn =

cos(θν ·sin(φ ))+1 2

(Bacour et al., 2002a)

cost function generally improves the convexity of the error surface, which is critical as we will see later (Combal et al., 2002). The descent algorithm may also limit the trapping in a local minimum by reducing the rate of descent. However, a compromise has to be chosen between rapid convergence achieved with large descent rate, and limiting the probability of falling in a local minimum achieved with a slow descent rate. Further, the optimization algorithm may sometimes lack of robustness due to numerical problems occurring generally with very small values of J. The criterion used to stop the iterations is in addition not always easy to adjust, requiring some preliminary tests (Bonnans et al., 2006). (2) Secondly, the OPT algorithm requires large computer resources because of its iterative nature. However, there are ways to speed up the process by limiting the number of model runs for each iteration using the adjoint model that provides an analytical expression of the gradient of the cost function (Lauvernet et al., 2007). Nevertheless, OPT techniques are still difficult to use routinely and exhaustively over large images, although image segmentation may help reducing significantly the number of pixels to process, the optimization process being restricted to a limited set of representative pixels. Note that these techniques allow getting some estimates of the uncertainties associated to the solution under some assumptions. However, the distribution of the solution will be here always unimodal, conversely to what could be achieved with the other radiometric driven approaches. The main advantage of iterative optimization methods is their flexibility, allowing retrieving canopy characteristics from several observational configurations. It is even possible to invert radiative transfer models concurrently over several pixels. This opens great potentials for exploiting additional temporal or spatial constraints as we will see later.

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7.2.2.2 Look Up Tables This is conceptually the simplest technique, although its implementation is not trivial (Weiss et al., 2000). It is the basis of the MODIS and MISR LAI and fAPAR products (Knyazikhin et al., 1999). Firstly a large data base (the Look Up Table, LUT) is generated, consisting of sets of input variables of the canopy radiative transfer model used. Then, the corresponding reflectance values are simulated. The LUT can alternatively be based on experimental observations, although this requires a very good sampling of the space of canopy realization. Once the LUT has been generated, finding the solution for a given set of reflectance measurements consists in selecting the closest cases in the reflectance table according to a cost function, and then extracting the corresponding set of canopy biophysical variables. Note that the distribution of the solution could be obtained by accounting for the uncertainties associated to the reflectance values as discussed by Knyazikhin et al. (1998a and b). This technique overcomes some of the limitations of iterative optimization techniques. As a matter of fact, the search for the solution is global here, leading to the true minimum if the space of canopy realisation is sufficiently well sampled. Note that for generating the LUT, the space of canopy realization has to be sampled to represent the surface response, i.e., with better sampling where the sensitivity of reflectance to canopy characteristics is the higher (Weiss et al., 2000; Combal et al., 2002). This is different from the sampling of the training data base required in canopy biophysical variables driven approaches. The implementation of a LUT technique in algorithmic operational chains is very efficient because the radiative transfer model is run off-line. However, LUT techniques require a fixed number of inputs unless having very large tables that could be more difficult to manipulate. In addition, the way the solution is defined is not always based on solid theoretical background. The cases selected as possible solutions are either defined as a fraction of the initial population of cases (after tests and trials) such as in Weiss et al. (2000) or Combal et al. (2002). It can be also defined by a threshold corresponding to measurement and model uncertainties as in Knyazikhin et al. (1998a and b).

7.2.2.3 Bayesian Methods: Importance Sampling and MCMC Alternative methods are available which are based on statistical backgrounds: MonteCarlo Markov Chains (MCMC) and Importance Sampling (IS) (Makowski D., J. Hiller, et al., 2006). These two Bayesian methods approximate the posterior distribution, i.e., the distribution of the variables when the reflectance measurement is known. Although very little attention has been paid to these techniques at the exception of Zhang et al. (2005) who used with success the MCMC MetropolisHastings algorithm with MODIS data. However, Metropolis-Hastings algorithm is an iterative process that might not be well suited for operational applications at

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large scale, similarly to OPT methods. Conversely, IS methods that do not require multiple iterations might be efficient for this purpose and need to be properly evaluated for remote sensing applications.

7.3 The Under-determined and Ill-posed Nature of the Inverse Problem in Remote Sensing 7.3.1 Under-Determination of the Inverse Problem Estimating biophysical variables from remote sensing measurements is often an under-determined problem: the number of unknowns is generally larger than the number of independent radiometric information remotely sampled by sensors. In the case of a simple canopy radiative transfer model such as SAIL (Verhoef, 2002), canopy reflectance at the top of canopy (ρ toc ) for a given illumination and view geometry (θ s, θ v, ϕ ) is simulated (Eq. (7.2)) using three variables describing canopy structure that do not depend on wavelength (LAI, average leaf angle (ALA) and hot spot parameter (hot) as modelled by Kuusk (1995)), and leaf reflectance (refl) and transmittance (tran) as well as soil reflectance (Rs) that obviously depend on wavelength (λ ). ρtoc (λ, θs, θv, ϕ) = CAN(LAI, ALA, hot, re f l(λ ), tran(λ ), Rs(λ, θs, θv, ϕ), θs, θv, ϕ) (7.2) Several studies report that canopy (and soil) bidirectional reflectance distribution function (BRDF) could be decomposed using empirical or semi-empirical orthogonal functions with generally 2–4 kernels (Lucht, 1998; Br´eon et al., 2002; Weiss et al., 2002). Therefore, 7–9 characteristics (3 canopy structure, 2 leaf properties [refl, tran] input variables and the 2–4 terms describing soil BRDF, Rs(λ, θs, θv, ϕ) have to be estimated out of a maximum of 4 independent information derived from BRDF measurements in a single band. Retrieval of canopy characteristics from BRDF measurements in a single band is therefore not possible without introducing other information in the system, particularly when soil background plays a significant role, i.e., for low to medium LAI values. Similar observations are made when considering the reflectance spectral variation: leaf spectral properties may be described by a dedicated model such as PROSPECT (Jacquemoud and Baret, 1990) requiring at least 5 input variables: mesophyll structure parameter (N), chlorophyll (Cab ), dry matter (Cdm ), brown pigment (Cbp ) and water (Cw ) contents: [re f l(λ ), tran(λ )] = LEAF(N, Cab , Cdm , Cbp , Cw , λ )

(7.3)

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Soil reflectance Rs(λ , θ s, θ v, ϕ ) may be described by a model such as that proposed by Jacquemoud et al. (1992) and derived from that of Hapke (1981). It requires a single scattering albedo ω (λ ) that varies with wavelength and soil composition, between 1 to 4 phase function coefficients (αi ), and a roughness parameter (r). According to Price (1990), soil spectral variation, may be approximated as a linear combination of 2–10 end-members. This is assumed to apply similarly to the spectral variation of the single scattering albedo with weigh w j and end members ω j (λ ): ω (λ ) = ∑ w j · ω j (λ ) (7.4) j

The whole soil spectral and directional reflectance field could subsequently be simulated with at least five parameters: Rs(λ , θ s, θ v, ϕ ) = SOIL([w j ], [αi ], r, λ , θ s, θ v, ϕ )

(7.5)

Consequently, the whole spectral and directional top of canopy reflectance field could therefore be modelled by coupling together the soil, leaf and canopy reflectance models, which leads to at least 13 input variables. These 13 unknowns have to be estimated from the information content in remote sensing measurements. Most of currently available sensors for which operational biophysical products are available have a relatively small number of configurations: from two for AVHRR (red and near infrared bands), to 15 bands for MERIS (VIS and NIR) and MODIS (VIS, NIR, SWIR) with several bands dedicated to particular atmosphere, cloud, snow/ice, or ocean characteristics. In the case of multidirectional sensors, the number of configurations may be larger as in the case of MISR (36 configurations = 9 cameras ×4 bands), or POLDER (84 configurations = 14 directions ×6 bands). However, the actual dimensionality of remote sensing measurements is much smaller than the number of available configurations considering the relatively high level redundancy between bands (Price, 1994; Price, 1990; Liu et al., 2002; Green and Boardman, 2001) and directions (Zhang et al., 2002a and b; Weiss et al., 2002b). Although further investigation is required to better quantify the actual dimensionality of remote sensing observations, it is clear that retrieval of surface characteristics from reflectance measurements is an under-determined problem in many cases. Improving retrieval performances will require introducing ancillary information and constraints in the system.

7.3.2 Evidence of the Ill-posed Problem A problem is well posed if and only if its solution exists, is unique, and depends continuously on the data (Garabedian, 1964). Several authors have reported that the inverse problem in remote sensing is ill-posed (Knyazikhin et al., 1999; Combal et al., 2001; Baret et al., 2000) because of its under-determination and uncertainties attached to models and measurements. In addition, models may incorporate sets of

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Fig. 7.5 Actual reflectance measurements (left plot, solid lines representing the mean and standard deviations) and the corresponding closer simulations achieved with a simple turbid medium radiative transfer model (the series of dots). On the right, the input LAI and Cab (the “+” symbols) variables used to simulate the reflectance spectra shown on the left plot. The actual LAI and Cab measurements are displayed with their associated confidence interval (bold line corresponding to 1 standard deviation). Data acquired over a sugar beet experiment conducted in 1990

variables that appear always in combinations such as products between variables. In these conditions, very similar reflectance spectra simulated by a radiative transfer model (Fig. 7.5, left) may correspond to a wide range of solutions (Fig. 7.5, right). In the case illustrated by Fig. 7.5, high correlation is found between LAI and those leaf chlorophyll content estimated values. This compensation between variables was sometimes termed “ambiguity” (Baret et al., 1999) or “equi-finality” (Shoshany, 1991; Teillet et al., 1997). This may also indicate that the product LAI · Cab should be used in place of individual estimates of LAI and Cab . Although not appearing formally in the radiative transfer model, this product is physically meaningful from the radiative transfer processes perspective and corresponds to the actual optical thickness of the medium (Weiss et al., 2000). Measurement and model uncertainties may also induce instability in the solution of the inverse problem. This is particularly true for well developed canopies, where a small variation in the measured reflectance can translate into large variation of variables such as LAI, for which reflectance “saturates”, i.e., is very little sensitive to LAI variation. A proper sensitivity analysis should help quantifying interactions between input variables. A complementary sensitivity analysis conducted over the cost function could also help evaluating the identifiability of the solution, i.e., if output variables could be accurately retrieved from a given set of observations (Salteli, 2004). Regularization techniques are thus necessary to obtain a stable and reliable solution of the ill-posed inverse problem. This could be achieved both by using prior information on the distribution of the variables, and by exploiting some constraints on the variables. These two issues will be investigated separately in the following.

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7.4 Improving the Retrieval Performances 7.4.1 Using Prior Information If no remote sensing measurement is available, the best estimates of the variables would come from the prior information on their distribution (Fig. 7.6d), capitalizing, all the knowledge coming from bibliography, past experiments or experts. Conversely, when a radiative transfer model is available along with remote sensing measurements, the variables can be estimated by inverting the RT model without using any prior information. This will be illustrated using a simple example: estimating LAI from NDVI vegetation index. In this case the RT model consists in an analytical relationship as proposed by Baret and Guyot (1991): NDV I = NDV I∞ + (NDV Is -NDV I∞ ) · e−K·LAI 1

b

c

0.8

0.8

0.6

0.6

0.6

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(7.6)

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Fig. 7.6 Estimation of canopy variables by combining remote sensing measurements, radiative transfer model and prior information. All these pieces of information are represented by their probability distribution function (PDF): (a) PDF of remote sensing measurements in the simple case of NDVI; (b) PDF of RT model simulations (NDV I = f(LAI)) accounting for model uncertainties; (c) PDF of LAI as retrieved from RT model and NDVI measurement and their associated uncertainties, without using prior information; (d) PDF of LAI used as prior information; (e) Computation of LAI PDF as estimated from NDVI measurements and RT model, using prior information on LAI; (f) PDF of the solution (posterior distribution) when using only prior information (idem as plot d), using RT model and NDVI measurements and their associated uncertainties only, and using all the information available (RT model and NDVI measurements and their associated uncertainties and prior information). The three contour plots (b, c, e) are coded from white to black for zero to max PDF values with the same gray scale. Very simple assumptions on uncertainties models and values are used here just for illustration

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with NDV Is and NDV I∞ being respectively the bare soil and asymptotic values of NDVI, and K an extinction coefficient (K = 0.8). However, uncertainties are associated both with remote sensing measurements (Fig. 7.6a NDV Ir = ℵ(0.8, 0.1) where ℵ(x, σ2 ) means a Gaussian distribution with mean x and variance σ2 ) and the RT model (Fig. 7.6b RT model represented by Eq. (7.2) with a Gaussian noise ℵ(0, 0.1)). Accounting for these uncertainties in the form of the corresponding probability distribution function (PDF) allows deriving the PDF of the estimated variable (Fig. 7.6c). The small sensitivity of NDVI to LAI as compared to measurement and model uncertainties induce a relatively broad PDF for the larger LAI values (Figs. 7.6c, f). This corresponds to an ill-posed problem, where a wide range of possible solutions match very similar measurements. The combination of RT model, remote sensing measurements and prior information on the variables (here LAI = ℵ(2, 1.5) allows getting more reliable solutions accounting for all the sources of information available in an optimal way (Figs. 7.6e, f). The example provided above for a measurement value of NDV I = 0.8 could be extended to the whole range of NDVI values. It shows that the mode of the distribution of the solution corresponding to the maximum likelihood (maximum of the PDF) strongly depends on the type of input information used (Fig. 7.7, left). When only prior information is used, the mode stays constant and obviously independent from measurements. When RT model and measurements are used with their uncertainties, the LAI mode is generally close to the values obtained without considering uncertainties, assuming perfect model and measurements. However, over the saturation domain corresponding to NDVI values higher than 0.85, accounting for the uncertainties provides lower modal values because of the non linearity of the

5

LAI

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3

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1

Fig. 7.7 Mode (plot on the left) of the distribution of the solution (LAI) of the inverse problem as a function of the measured value (NDVI). The mode corresponds to the maximum PDF value, i.e., the maximum likelihood. Four estimates are displayed: using only prior information; using RT model (LAI = RT −1 (NDV I)) assumed to be perfect with perfect measurements (no uncertainities accounted for); using RT model and measurements with their associated uncertainities; using RT model and measurements with their associated uncertainities and prior information. On the right, the standard deviation of the distribution of the solution is also displayed for the several cases. The case with perfect RT model and measurements is not displayed here because its standard deviation is null by definition

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model. When prior information is used in addition to RT model and remote sensing measurements, differences of LAI mode are marginal over the domain where NDVI is sensitive enough to LAI. Conversely, over the saturation domain, LAI modal values are always lower (closer to prior information value) than those observed when not using prior information which would lead to a bias. However, the interest of using the prior information is clearly demonstrated when considering the standard deviation of the distribution of the solutions (Fig. 7.7, right). Introducing prior information in the inversion process provides a very significant reduction of the variability of the posterior distribution. This is obviously more important for the larger NDVI values corresponding to the saturation domain: in this case, very large scattering of the retrieved LAI values is expected when no prior information is used. Although the maximum likelihood is often used as “the solution”, the variability within the posterior distribution as represented by its standard deviation appears to be very informative and useful. The theory behind this Bayesian approach has been extensively described by Tarantola (2005). When restricting the solution as that maximizing the likelihood, i.e., corresponding to the maximum of the PDF, a general formulation of the cost function may be derived under Gaussian distribution assumption: ˆ + (Vˆ −Vp )t ·C−1 · (Vˆ −Vp ) ˆ t ·W −1 · (R − R) J = (R − R)       Radiometricinformation

(7.7)

Prior information

where Vˆ is the vector of the input biophysical variables estimates, R corresponds to the vector of remote sensing measurements of dimension N (the number of bands and directions used), Rˆ is the vector of the simulated reflectance corresponding to the solution Vˆ (the vector of canopy biophysical variables) and Vp the vector of prior values of biophysical variables. Matrices W and C are the covariance matrices characterizing respectively the radiometric and model uncertainties, and that of the prior information. Note that the first part of this equation corresponds to the distance between the measured and the simulated radiometric data. It simplifies into Eq. (7.1) if the covariance terms of matrix W are assumed to be zero, i.e., measurement and model uncertainties are independent between configurations. The second part of Eq. (7.7) corresponds to the distance between the values of the estimated variables and those of the prior information. Very few studies are currently based on this formulation of the cost function where prior information is explicitly used (Combal et al., 2002). Implementing the cost function as expressed by Eq. (7.7) requires some reasonable estimates of covariance matrices W and C as well as prior values Vp . The terms of W should reflect both measurement and model uncertainties. While some rough estimates of measurement uncertainties could be derived from the sensor specification, model uncertainties are far more difficult to estimate. Further, they may depend significantly on the type of situation considered, such as low or high vegetation amount. Even more difficult to estimate, are the covariance terms in W : measurement and model uncertainties may have important structure that translates into high covariance terms which are however very poorly known. When using simul-

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taneously a large number of configurations as in the case of hyperspectral observations, these covariance terms will be very important to account for: they will allow weighing properly the several configurations used. The difficulty to estimate the covariance terms explains why a small number of configurations is often selected when a larger number is available as in the case of hyperspectral and/or directional observations. Retrieval approaches should be used within well defined and if possible restricted domains. Larger domains will generally degrade retrieval performances since the prior information will be looser defined, similarly to the covariance matrices characterizing uncertainties. However, splitting the whole domain into a set of subdomains may introduce problems due to misclassification and attribution errors as observed by Lotsch et al. (2003), and artefacts at the limit between classes translating into more chaotic spatial or temporal variation of the solution. The way prior information is introduced in the inversion process depends on the inversion technique used. The cost function represented by Eq. (7.7) is used within iterative optimization and LUTs. Bayesian methods include the a priori distribution through the use of the Bayes theorem to estimate the a posteriori distribution. For biophysical variables driven approaches the training data base should reflect the actual knowledge on the distribution of the variables. Note that the difficulty in defining explicitly the covariance terms in the uncertainties on remote sensing inputs (RT model and measurements) for the radiometric data driven approaches remains in the biophysical variables driven approaches for the generation of the training data base. However, implicit introduction of these terms may be achieved when using a training data base made from actual satellite measurements as suggested by Bacour et al. (2006).

7.4.2 Using Additional Constraints 7.4.2.1 Coupling Models The radiative transfer in each element of the soil/leaf/canopy/atmosphere system is strongly coupled to the radiative transfer in the whole system. The simple example given previously to demonstrate the under-determined nature of the inverse problem in remote sensing shows that top of canopy reflectance could be written as:

ρ toc (λ , θ s, θ v, ϕ ) = CAN(LAI, ALA, hot, LEAF(N, Cab , Cdm , Cbp , Cw ), SOIL ([w j ], [αi ], r, λ , θ s, θ v, ϕ ) , θ s, θ v, ϕ ) (7.8) The same applies when retrieving some characteristics of the system from top of atmosphere reflectance (ρ toa ) measurements as usually achieved by sensors aboard satellite: ¨ Patm , Cwv , C03 , λ , θ s, θ v, ϕ ) ρ toa (λ , θ s, θ v, ϕ ) = ATM(ρ toc (λ , θ s, θ v, ϕ ), τ550 , A, (7.9)

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where ATM represents an atmospheric RT model such as 6S (Vermote et al., 1997) ¨ being respectively the aerosol optical or MODTRAN (Berk et al., 1998), τ550 , A, thickness at 550 nm and the Angstr¨om coefficient, Patm is the atmospheric pressure, Cwv is the water vapor content and C03 the ozone content. Retrieval of characteristics of some element of the system without solving (implicitly or explicitly) the whole system will therefore be sub-optimal as demonstrated below. Let consider retrieving leaf biophysical properties [N, Cab , Cdm , Cbp , Cw ] from top of canopy remote sensing observations in B wavebands using a decoupled system and an iterative optimization technique. For sake of simplicity, soil reflectance will be assumed to be known. Estimates of leaf properties could be achieved in two steps. First, estimate the variables [LAI, ALA, hot, re f l(λ ), tran(λ )] from the reflectance in each of the B bands. A cost function accounting for the reflectance in the B bands should be minimized with the constraint that [LAI, ALA, hot] does not vary with wavelength. The number of unknowns in the system will therefore be (3 + 2 · B) corresponding to the 3 canopy structure variables and the 2 (reflectance and transmittance) leaf optical properties time the B bands. The second step of the process consists in estimating leaf biophysical properties [N, Cab , Cdm , Cbp , Cw ] from the retrieved leaf reflectance and transmittance in the B bands. The variables [N, Cab , Cdm , Cbp , Cw ] are tuned by minimizing a cost function accounting for leaf reflectance and transmittance in the B bands. Obviously, increasing the number of bands will not improve the underdetermined nature of the problem because the number of unknowns in the first step of the process will grow twice faster. In addition, since no biophysical constraints are set on the spectral variation of leaf optical properties, canopy structure variables derived from the first step may express larger and unrealistic range of variation. The proper way to solve this type of problem is to minimize a cost function accounting for canopy reflectance over the B wavebands based on the coupled leaf and canopy models. In this case, the number of unknowns will be eight (the three canopy structure variables and the five leaf characteristics) which is independent from the number of wavebands used. This allows limiting the under-determined nature of the problem by increasing the spectral sampling. Most of the retrieval approaches from top of canopy radiometric observations are now using implicitly or explicitly coupled models as shown in Table 7.2. However, although offering great potentials as demonstrated recently (Baret, 2006b), the use of coupled atmosphere/surface models is still not very well developed because each sub-problem was handled by different communities.

7.4.2.2 Spatial Constraints Up to now, most retrieval algorithms are applied to independent pixels, neglecting the possible spatial structure as observed on most images. However, some authors attempted to exploit these very obvious patterns at high spatial resolution. The “object retrieval” approach proposed by Atzberger (2004) is based on the use of covariance between variables as observed over a limited cluster of pixels representing the same

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Table 7.2 Synthesis of the several algorithms currently used operationally to retrieve canopy biophysical variables. 1: (Lacaze, 2004); 2: (Knyazikhin et al., 1999); 3: (Gobron et al., 1999); 4: (Weiss et al., 2002; Baret et al., 2007); 5: (Chen et al., 2002; Deng et al., 2006); 6: (Bacour et al., 2006) #

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Atmosphere

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uncertainties

prior information

Kuusk LAI, ALA, hot

TOC

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measurements

Some variables fixed Range of variation

Hapke 3 typical + understorey

DISORD 6 biomes

TOC

LUT

measurements prescribed at 20%

specific values for 6 biomes

PROSPECT N, Cab, (Cw,Cdm, Cs)

5 typical soil unique BRDF

Gobron LAI, ALA, hot

TOA (MODTRAN)

Parametric

not specified

Range of variation (uniform distribution)

PROSPECT N, Cab, Cw,Cdm, Cbp

brightness parameter &reference spectra

SAIL LAI, ALA, hot, vCover

TOC

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TOC

Parametric

2 versions: - TOC version - TOA version (SMAC)

NNT

leaf

soil

POLDER LAI, fAPAR

PROSPECT N, Cab, (Cw,Cdm, Cs)

PRICE 2 abundances

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MODIS/MISR LAI, fAPAR

prescribed for each biome

3

MERIS MGVI fAPAR

4

VEGETATION CYCLOPES LAI, fAPAR, fCover

5

VEGETATIONCanada-Global LAI

Empirical relations for specific biomes using TM sensor and the corresponding ground measurements over some sites Prescribed BRDF model

6

MERIS LAI, fAPAR, fCover, LAIxCab

PROSPECT green/brown separated N, Cab, Cdm, Cw, Cbp

(1)

(2)

brightness parameter &reference spectra

SAIL, LAI, ALA, hot, vCover

model and measurements approximation of actual prescribed at 4% distribution (relative)

not specified

Specific relations for each biome

model and measurements approximation of actual prescribed at 4% distribution (relative)

class of object such as an agricultural field. Results show quite significant improvement of the retrieval performances for LAI, Cab and Cw , presumably because of a better handling of the possible compensation between LAI and ALA in the retrieval process as suggested by Atzberger (2004) and outlined by Jacquemoud (1993). Other approaches based on models with random effects (Faivre and Fischer, 1997) may be also very attractive, although rarely used within the land remote sensing community. They allow characterizing a population by their two first statistical moments (mean and variance). In the case of remote sensing applications, this could be applied over a cluster of P pixels belonging to the same class of surface as in the “object retrieval” approach of Atzberger (2004). The inversion process could be achieved by tuning both the mean and variance values of each input variable over the P pixels using iterative optimization techniques. The individual values of each pixel could be derived from the estimated mean and variance values of the variables and the departure between the actual radiometric measurements of the pixels and the mean values over the object. The under-determination of the problem could significantly decrease with this approach: the number of unknowns to estimate is independent on the number of pixels considered in the cluster and is just twice the number of variables to estimate (mean and variance). Although quite promising, these methods need further evaluation, and probably adaptation before being accepted and used by the remote sensing community. Note that only statistical distributions are used for both methods presented, although additional geo-statistical constraints could be exploited particularly for the higher spatial resolutions, based on variograms (Garrigues et al., 2006).

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7.4.2.3 Temporal Constraints The dynamics of canopies results from elementary processes under the control of climate, soil and the genetic characteristics of the plants that incrementally change canopy structure and optical properties of the elements. Very brutal and chaotic time course are therefore not expected, at the exception of accidents such as fire, flooding, harvesting, or lodging. The smooth character of the dynamics of canopy variables may be exploited as additional constraint in the retrieval process. K¨otz et al. (2005) proposed using a semi-empirical model of canopy structure dynamics to improve remote sensing estimates of LAI over maize crops. Results show a significant improvement of estimates, particularly for the larger LAI values where saturation of reflectance is known to be a problem. This approach requires a semi-empirical model of canopy structure dynamics (here LAI) describing the whole growth cycle with few parameters. In the case of the model used by K¨otz et al. (2005) five parameters are needed. In this case, the under-determined nature of the inverse problem will decrease only if more than five dates of remote sensing observations are available and well distributed over the growth cycle. However, because the parameters of the model of LAI dynamics have some biological meaning, prior information on them could be accumulated and efficiently exploited. More recently, Lauvernet et al. (2007) proposed a “multitemporal patch” inversion scheme to account for both spatial and temporal constraints. Reflectance data are here considered observed from top of atmosphere. Atmosphere/canopy/ leaf/soil RT models are thus coupled to simulate top of atmosphere reflectance from the set of input variables as stated by Eqs. (7.8) and (7.9). Spatial and temporal constraints are based on the assumption that the atmosphere is considered stable over a limited area (typically few kilometres) but varies from date to date, and that surface characteristics vary only marginally over a limited temporal window (typically ±7 days) but may strongly change from pixel to pixel. This has obviously important consequences on the under-determined nature of the inverse problem as demonstrated hereafter. The atmosphere characteristics [Patm , Cwv , C03 ], except the ¨ are assumed to be known from independent observations aerosol ones [τ550 , A], such as meteorological estimation or dedicated sensors or algorithms. The observational configuration [λ, θ s, θ v, ϕ ] is also known at the time of image acquisition. Soil reflectance was simply approximated as lambertian, with reflectance proportional to a reference soil spectra according to a brightness parameter Bs (Bacour et al., 2006). The brightness parameter is assumed to vary both from date to date and pixels to pixels, without any constraints. The forward model resulting from nesting the RT models presented previously could be written as a function of the ¨ with nA = 2 ten unknowns [N, Cab , Cdm , Cbp , Cw , LAI, ALA, hot, Bs, τ550 , A] atmosphere variables, nC = 8 canopy and leaf variables and ns = 1 soil variables. Let consider d dates of observation available over a limited temporal window during which the canopy variables are about constant, and a spatial window of p pixels for which the atmosphere is considered homogeneous. The number of unknowns, N(p, d) in the case of concurrent inversion of an ensemble of d dates and p pixels using the spatial and temporal constraints described above is therefore:

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N(p, d) = d · nA + p · nC + d · p · nS

(7.10)

Inverting the nested radiative transfer models concurrently over an ensemble of d dates and p pixels will significantly reduce the total number of unknowns. (N(p, d)) as compared to p times d independent instantaneous pixel inversions (p.d.N(1, 1)). Figure 7.8 shows that the number of unknowns to be estimated within the same inversion process for p pixels and d dates as compared to p.d single pixel and single date inversions (N(p, d)/(p.d.N(1, 1))) decreases significantly up to about 10 pixels. However, the main advantage over “ensemble” inversion is reached when applying concurrently the inversion process to several dates. Using two dates and more than 10 pixels allows dividing by almost 2 the number of unknowns. Note that these results concern only the number of unknowns, and is therefore applicable to any observational configuration characterized by a set of bands and directions. Results on the performances achieved demonstrate the interest of the approach for the estimation of most of the variables, particularly for the aerosol characteristics and for LAI, LAI × Cab and ALA canopy characteristics. However, again, this new approach was only demonstrated over RT simulations, and its interest should be verified over experiments with actual remote sensing data and the corresponding ground truth.

1 0.9

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7.5 Conclusion This overview of retrieval approaches is based on methods currently used, while alternative ways to solve the problem and hopefully improve the accuracy and robustness of estimates were briefly introduced. Several ingredients of the algorithms were identified apart from the retrieval techniques themselves: radiative transfer models, observations, additional information and constraints. We will briefly summarize the conclusions for each of these ingredients in the following.

7.5.1 Retrieval Techniques The several techniques investigated have been classified as radiometric variables or biophysical variables driven approaches. However, both types of methods could be either derived from actual measurements or based on radiative transfer model simulations. The best approaches are obviously the ones that will be trained over data sets that are as close as possible to the evaluation data set. For this very reason, canopy biophysical variables trained over empirical data sets would be ideal. In addition, canopy biophysical variables driven approaches present the advantage of being very computer efficient once trained, allowing easy implementation within operational processing chains. However, because of the difficulty of getting a large enough training data set representing the actual distribution of cases (observational configuration, type of canopies and state, background properties, eventually atmosphere characteristics), training data base made of radiative transfer model simulations is preferred. These hybrid techniques as termed by Liang (2004) require however the radiative transfer models to be well adapted to the type of canopy they target, and their adequacy to be quantified to properly input model uncertainties. In addition, the structure of uncertainties on the radiometric variables and distribution and codistribution of the input biophysical variables should be also known. An alternative approach currently not yet explored would consist in bridging the two retrieval approaches: actual sensor measurements are used to build the training data base allowing to keep all the structure of measurement uncertainties. This data base should be representative of the cases investigated, which might be possible by specific spatial and temporal sampling schemes as proposed by Baret et al. (2006a) in the case of global observations. The corresponding best estimates of canopy biophysical variables could be derived from inversion methods such as iterative optimization techniques for which all the information available should be exploited: fusion of all currently available sensors observations, prior information and spatial and temporal constraints. As a matter of fact, most radiometric variables driven approaches are very flexible and could easily ingest data from several sensors, bands and directions, at the expense of computer requirements which make these methods more difficult for an operational use. Conversely, canopy biophysical driven approaches are not as flexible as radiometric driven approaches: they are generally tuned for a limited set of

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observational conditions: using other configurations would require a specific training or a dramatic enlargement of the training data base. Retrieval methods will be more efficient when applied to a limited set of surface types as compared to a very generic (global) solution. Approaches based on a classification would thus allow closer adaptation to each class of both the radiative transfer model and prior information. However, attribution errors may significantly alter the performances. Using a continuous classification (Hansen et al., 2002; Hansen and DeFries, 2004; Schwartz and Zimmermann, 2005) will probably limit this source of uncertainties and avoid getting artefacts when two consecutive pixels will jump from one class to another. Biophysical variables estimates are generally integrated within other process models such as hydrology or biogeochemical cycling along with other ground observations. Quantification of the associated uncertainties is therefore required to properly merge these several sources of information. Current available products did not provide quantitative evaluation of the confidence interval around the solution, but are limited to qualitative indices. Bayesian approaches provide a direct access to the distribution of the solution of the inverse problem and may be very useful for estimating the uncertainties. Current operational algorithms need further developments to fully satisfy this important user requirement.

7.5.2 Radiative Transfer Models Performances of methods based on radiative transfer models are largely depending on the realism of the simulations. Radiative transfer models are based on a set of assumptions, particularly regarding the description of canopy architecture. A more realistic description of canopy architecture will require additional input variables and will be probably more demanding in computer resources. Knowledge of prior distribution and co-distribution of these additional canopy structure variables will constitute a limitation. Further, using such more realistic radiative transfer model requiring a larger number of unknowns will not necessarily improve the retrieval performances because the under-determination of the problem will be even more limiting. A compromise should therefore be found between the realism of the description of canopy structure, and its complexity. Particular attention should be paid on the definition of the variables used in the radiative transfer model that should match the one required for the application. For example, the original LAI definition (Stenberg, 2006) may be altered depending on the way and scale at which leaf clumping is accounted for (Chen and Leblanc, 1997). Great caution should be also paid when comparing retrievals with ground measurements or inter-comparing several products. As demonstrated here, holistic approaches based on the coupling of canopy, leaf and soil models are optimal for best performances. Eventually, coupled surface and atmosphere models would certainly help solving in an elegant way the retrieval of surface variables from top of the atmosphere observations.

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7.5.3 Observations and Ancillary Information The observational configuration is an important element that drives the accuracy of canopy biophysical variables estimation. It depends obviously on the variables targeted. For the time being, sufficient maturity is achieved for the estimation of LAI, fAPAR, the cover fraction, chlorophyll and water contents variables to implement operational algorithms for delivering the corresponding products to the user community. The interest of multidirectional and hyperspectral observations is still to be rigorously demonstrated for these variables by comparison over actual ground measurements. Frequent observations are required to monitor the dynamics of the vegetation that conveys a large amount of information on the functioning of the surface. With the hopefully venue of systems capable of high revisit frequency with high spatial resolution, new retrieval methods should be developed to exploit the temporal and spatial dimensions in addition to the more classical spectral and in a lesser way directional ones. This would allow benefiting from the spatial and temporal constraints and consequently reduce the number of unknowns to be retrieved. Ultimately, this approach will converge towards direct assimilation of top of atmosphere radiances into surface process models. However, the research community is not mature enough on the coupling between radiative transfer models and canopy process models. Radiative transfer model inversion had still to mature and improve the accuracy of surface variables estimation before jumping towards radiance data assimilation. Knowledge and management of uncertainties is one of the critical issues for the retrieval algorithms. If measurement uncertainties coming from the sensor are relatively well known, their structure (covariance between bands and directions for example) is poorly documented. This is even worse when considering model uncertainties that may change dramatically from place (and time) to place (and time) with presumably specific features (covariance between configurations). The other critical issue is the lack of prior information on the distribution of most land surface attributes. However, this could be accumulated from the numerous experiments organized in support of satellite images. A mechanism should thus be developed to capitalize on the information gathered within the remote sensing research community as well as other communities working with ecosystems. Note that getting high spatial resolution data will considerably ease the characterization of prior distribution of the variables, provided that each pixel could be properly classified. Any retrieval algorithm should be properly validated before delivering its products to the user community according to consensus protocols (Morisette et al., 2006). This process will not only provide a way to characterize the associated uncertainties, it will be also critical for improving the algorithms. A short feedback loop should therefore be set-up between algorithm prototyping and validation. When retrieval algorithms are based on radiative transfer modeling, this will implicitly merge observations and model to improve robustness and accuracy of the products at the expense of a decrease in the desired independency between the validation and calibration processes.

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Chapter 8

Knowledge Database and Inversion Jindi Wang and Xiaowen Li

Abstract Physical remote sensing models usually need dozens of parameters to have reasonable degree of precision. With limited information provided by remotely sensed observations, it is an ill-posed problem to estimate parameters through model inversion. Many researches have developed inversion models and algorithms. We developed a priori knowledge based inversion strategy and algorithm. The spectrum knowledge database of typical land surface objects has been established to provide the prior knowledge of model parameters. Some approaches are presented in this chapter, which include the uncertainty and sensitivity matrix for analysis of observation data and parameters, the model inversion method supported by the knowledge database, the scaling correction on estimated parameters. Some study directions in model inversion, such as how to accumulate and use spatial and temporal change knowledge, how to validate the parameter inversion results, are also discussed.

8.1 Questions on and Possible Answers to Physical Remote Sensing Model Inversion One of the primary problems of remote sensing science is the retrieval of information on land surface parameters from remotely sensed data. Since satellite remote sensing deals with a complex system coupling atmosphere and land surface, physical remote sensing models usually need several to tens parameters to describe the relation between land surface parameters and remote sensing signals for having reasonable degree of model precision. But, with limited information provided by remotely sensed observations, it remains a challenge to estimate parameters through remote sensing model inversion. In mathematics, it is an ill-posed problem Jindi Wang and Xiaowen Li Research Center for Remote Sensing & GIS Beijing Normal University, Beijing, China [email protected] S. Liang (ed.), Advances in Land Remote Sensing, 203–217. c Springer Science + Business Media B.V., 2008


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to estimate more model parameters from less observations. In past years, many researchers have developed new inversion models and algorithms (Verstraete et al., 1996; Myneni et al., 1995). Some inversion research has developed better cost function for physical model inversion. In addition, different kinds of mathematical optimization algorithms have been developed (Kimes et al., 2000; Kunsk, 1991). Verstraete et al. (1996) pointed out the main limitation and the necessary observations for obtaining successful model inversion. Kimes et al. (1991) presented the knowledge-based expert system for inferring vegetation characteristics. Fang et al. (2005) used a genetic algorithm to estimate leaf area index (LAI) of vegetation canopy with radiative transfer model inversion. Neural network methods were also used for model inversion (Smith, 1993). Liang (2004) summarized the main research achievements in estimating land surface biophysical variables and surface radiation budgets. As advances in the field of multi-angular remote sensing progress, bidirectional reflectance distribution function (BRDF) models can be inverted to estimate the structural parameters and spectral component signatures of land surface cover types, such as the MODIS albedo and LAI products. Some operational algorithms have been implemented to generate products of land surface parameters, such as albedo, LAI, fraction of photosynthetically active radiation (FPAR), net primary production (NPP) from MODIS and MISR observations at the spatial resolution of 250 m or 1 km. The surface BRDF and albedo product from POLDER has been developed at a pixel resolution of approximately 6 km. Some validation work on these data products has been carried out and it has been found that there are still some uncertainties on model, observation and reference data which influence the accuracy of these products (Morisette et al., 2006; Tan et al., 2005). However, when we want to improve the estimation accuracy of retrieved surface parameters to meet requirements of applications at different spatial scales, the inversion of physical remote sensing models is a very difficult problem that still requires further studies from the viewpoint of both information theory (Li et al., 1998) and the comprehensive practice of model inversion (Privette et al., 1997; Wanner et al., 1997; Li et al., 2000b; Liang, 2004). The real physical system that couples the atmosphere and land surface is extremely complex and it requires many parameters to describe it faithfully. Any physical model can only be an approximation of this real system, and a good model will have many important parameters to capture the major variations of the real system. However, remotely sensed observations are usually more or less correlated. The remotely sensed signal, no matter how fine its spectral and angular resolution, contains only limited information. Therefore, BRDF model inversion problems, such as those in geoscience generally, are usually underdetermined, making the use of a priori knowledge necessary. As the ancient philosopher Confucius pointed out, “Our knowledge consists of two parts – what we know, and what we know we don’t know”. In the case that remote sensing signals contain limited but valuable information, it is important to extract information about what we don’t know or what is uncertain, rather than to invert all model parameters at the same time, pretending that we know nothing. Using this principle in earlier work, we expressed a priori knowledge of model

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parameters as the best guesses for the associated uncertainties, and developed the a priori knowledge based inversion strategy and algorithm (Li et al., 1997). The results were encouraging, and thus we tried to formalize the approach, and to establish the a priori knowledge database of typical land surface parameters (Li et al., 2002).

8.1.1 A Priori Knowledge-based Inversion Strategy We developed a priori knowledge based inversion strategy and algorithm (Li et al., 1998, 2001) called, Multi-stage, Sample-direction dependent, Target-decision (MSDT) (Li et al., 1997). There are three questions should be answered in order to run the strategy. The first question is how to express the a priori knowledge and to make it available in model inversion algorithm. The second question is how to divide the model parameters set into subsets, in order to invert the parameters by using the most sensitive data. The third question is how to accumulate the knowledge during the inversion procedure, when we have one scene observing data or a data set containing more scenes of continuous observations. In our previous study (Li et al., 1998), the a priori knowledge of model parameters is expressed as a joint probability density, while a priori knowledge of the model accuracy and measurement noise is expressed as a conditional joint probability density. In inversion model, the a priori probability density function (PDF) of the observations can be defined, and can be used in the cost function based Bayesian inference theory. An important feature of Bayesian inversion is that there is no prerequisite number of independent observations for a successful inversion. So long as new observations are acquired, a priori probability density in parameter space can be modified to obtain posterior density, allowing knowledge to be accumulated. Taking the land surface spectral albedo inversion as an example, Li et al. (2001) showed how the a priori knowledge significantly improves the retrieval of surface bidirectional reflectance and spectral albedo from satellite observations. In the paper, the a priori knowledge are extracted from field measurements of bidirectional reflectance factors for various surface cover types in red and near-infrared bands. Bidirectional reflectance and albedo are retrieved by the kernel-driven BRDF model inversion that uses surface reflectance observations derived from orbiting satellites. A priori knowledge is applied when noise and poor angular sampling reduce the accuracy of model inversion. In such cases, a priori knowledge can indicate when retrieved kernel weights or albedos are outside expected bounds, leading to a closer examination of the data. If data are noisy, a priori knowledge can be used to smooth the data. If the data exhibit poor angular sampling, a priori knowledge can be used according to Bayesian inference theory to yield a posteriori estimates of the unknown kernel weights, where Bayesian theory is applied in the data space rather than in the parameter space. Extensive studies and simulations using 73 sets of field observations and 395 space-borne observation sets from the POLDER instrument demonstrates the importance of a priori information in improving inversions and BRDF retrievals.

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The further studies introduce Tarantola’s inversion cost function in to BRDF model inversion algorithm. Tarantola’s inversion theory has also been widely applied in geophysical inversion (Tarantola, 1987) and atmospheric remote sensing (Rodgers, 1976), because the inverse problems in those fields are even more illposed than in land surface remote sensing. Based on Tarantola’s theory, the cost function used in land surface parameters inversion is defined as the parameters’ posterior probability density, and can be expressed as

1 pM (X) = const · exp − ( f (X) −Yobs )T CD−1 ( f (X) −Yobs ) 2  −1 + (X − Xprior )T CM (X − Xprior ) (8.1) where Yobs is for observation data and Xprior is for a priori knowledge of parameters. The principle of the cost function is very similar to Bayesian inversion. One of its advantages is its ability to clearly express the errors of the model, the observed data, and the parameters’ initial value, with co-variances matrixes CD and CM respectively. This creates a new challenge on forming the error co-variances of model, data and parameters, this requires a great deal of a priori knowledge. Previous studies have demonstrated the effectiveness of the inversion model, using simulated data and field measurements (Yan et al., 2001; Wang et al., 2000). In these studies, the parameters’ initial values can be estimated by our field measurements, while the co-variance was set as the parameters’ standard deviation under the assumption that their estimated values have a normal distribution.

8.1.2 Uncertainty and Sensitivity Matrix of Parameters for Model Inversion It is important to examine the uncertainty and sensitivities of the parameters in model inversion, since we expect to estimate the values of parameters that are sensitive to observations and model, while giving certain values for other parameters that have relatively fewer uncertainties. To make the analysis of parameter uncertainty and sensitivity more effective, we defined the uncertainty and sensitivity matrix (USM), which is an objective expression of the prior knowledge. In order to construct the USM, we assume that a BRDF model has N spectral bands and K structural parameters and L spectral parameters of component materials, making K + N × L in total. Since the multiangular observations have M samples, the USM will have M × N rows and K + N × L columns. This matrix is too large to effectively use for calculations. Because the structural parameters are independent on the spectral band, we decomposed the matrix into a structural matrix that has M × N rows, K columns, where the N matrix of M × L spectral parameters corresponds to N bands, making a total N + 1 matrices. An element of the USM can be expressed as (Li et al., 1997),

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USM[i][ j] =

207


BRDF( j|i) BRDF(i)

(8.2)

where
BRDF( j|i) is the maximum difference of BRDF as a function of the jth parameter within its uncertainty, given the ith geometry of illumination and viewing; BRDF(i) is BRDF as predicted by the model at the ith geometry, when all parameters at their best guess values. These best guess values of parameters are also from the accumulation of prior knowledge, and they can be updated when further parameter estimates are obtained during the MSDT inversion procedure. This USM definition has three advantages: (1) the uncertainty of the initial guess for being inverted parameter is taken into account; (2) the USM is less dependent on the initial guess; (3) all elements of the USM have the same units, and are therefore quantitatively comparable. This USM has thus been used widely in our recent model inversion studies. It can also be applied for parameters sensitivity analysis for models and data in relative studies (Li et al., 1997; Gao and Zhu, 1997; Yan et al., 2001).

8.1.3 Getting the Prior Knowledge on Typical Land Surface Parameters As stated above, after developing the model inversion strategy, we recognized that the most important issue in remote sensing model inversion is accumulation of prior knowledge regarding the model parameters. Given that we are not only concerned with the validation of the model, but also with how to apply the inversion algorithm for land surface parameter estimation at the scale of remote sensing images, we have to consider establishing a very powerful prior knowledge database that assembles the initial estimates of the parameters and also their co-variance values during the inversion procedure. These initial parameter values and their co-variance matrix are also necessary for supporting data assimilation algorithms. In practice, we firstly classify the a priori knowledge into different levels: the general knowledge about the land surface, or “global knowledge”, knowledge related to land cover type, and target-specific knowledge. The means to accumulate knowledge at these levels may be different, but should include the following: 1. 2. 3. 4. 5.

Applicable forward model(s) Physical limits and probability density in model parameter space Statistics of model accuracy and noise in remote sensing signals Seasonal change associated with land cover types or targets Confidence of the above knowledge

Note that even a single observation can change the a priori PDF of more than one parameter significantly. Li et al. (1998) provided an example on how the accumulation of knowledge is achieved in parameter space. However, the required numerical integration in parameter space is time-consuming whenever parameters set is large, as is the case with the retrieval of surface BRDF and albedo from satellite data.

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Our recent approaches are to establish an a priori knowledge database of the parameters of typical land surface targets, including the spatial and temporal distribution knowledge of parameters. This knowledge database also includes the forward models, remote sensing data and a priori knowledge at both global and land cover type related levels. Based on the knowledge base, it is expected that the accuracy of land surface parameters estimation at the scale of remote sensing observations will improve (Wang et al., 2003).

8.2 The Spectrum Knowledge Database of Typical Land Surface Objects Establishing the spectrum knowledge database of typical land surface objects is significant for the development of quantitative remote sensing. The research on spectral features of objects is the foundation of remote sensing applications. Land cover and land use classification and image interpretation are usually based on the spectrum recognizing method. Many kinds of spectrum matching techniques have been developed. However, users cannot always obtain the desired accuracy for classification and identification. One of the problems is that the spectral data of objects measured at different scales are not comparable. It is rare to have the correct relation between the spectrum of objects measured indoors or in the field, and the spectral image data acquired through remote sensing observations. The available spectrum data measured indoors and in the field do not have enough corresponding descriptors to clearly determine the related spectral environmental variables. This can result in some confusion in spectrum applications using spectra matching and other image processing algorithms. The second problem is that we need to integrate the physical models and measurement data into a close linked system to allow models and data to be effectively applied for land surface parameters estimation. When the linked system is developed, the prior knowledge of the model parameters can be extracted from the database and the model prediction and parameters inversion algorithm can also be included in the system. That is our approach to convert the individual measurement data sets to be the knowledge database with the stated goal of having effective physical model explanations and predictions. The establishment of the spectrum knowledge database of typical land surface objects is supported by China’s National High Technology Research and Development Program. The spectrum knowledge database consists of the measuring spectral data set and related environmental variables of objects at different observing scales, the physical models set and a priori knowledge set which provide the main geographical background data for models.

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8.2.1 The Definition of Spectrum at Three Measured Scales To avoid confusion in spectral matching for land cover type recognition, we clearly defined and measured three kinds of spectrum for different observed objects, while considering the application requirements. The three spectrums are the spectrums of materials, endmembers and remote sensed pixels. The spectrum of materials is usually measured under well controlled measurement conditions in the laboratory. The measured objects can be crop leaves, mineral samples, and water samples. They are essential spectrum data of the spectrum database, and are usually taken as given variables in physical models. The so-called spectrum of endmembers is the spectrum of components of remotely sensed pixel, it is the basic parameter in general remote sensing models. The spectrum of endmembers is usually measured in the field, where the surface of the measured object is relatively uniform, and where the measuring FOV of sensor is less than pixel size. For example, in the scene integrated geometric optical BRDF model on canopy reflectance, the sunlit crown, sunlit background, shaded crown and shaded background are endmembers of the modeled forest pixel. Their spectrums are usually the main parameters of scene integrated models, which may differ from the spectrum of leaves and soils. The spectrum of remotely sensed pixels comes from remotely sensed observations, and is usually the main concern of users. Note that when we consider different modeling scales, the measured endmember spectrum and the spectrum of remotely sensed pixels should be used according to the scale of the application (Li et al., 2002; Wang et al., 2003).

8.2.2 Typical Land Surface Objects Spectrum Database In the spectral data set, for every typical object the measured data includes not only its surface spectra, but also the environmental variables of each observed object. The variables are all physical model parameters, which can be used to predict the spectra of a given surface object by a physical model. In the first step of the database establishment, the main typical land surface objects include three land cover types: the main crops growing in China, which are winter wheat, rice, maize, cotton and cole; rocks and minerals; and bodies of water. The collected data consist of two parts. One part is the individual spectrum data sets measured during the last 20 years. In order to keep this data available, we compiled the data following our own data collection standards. For instance, some of the data were measured in the laboratory and in standard well controlled measuring conditions, such as for minerals. The other part consists of new measurements. We first determined the environmental variables to be measured, which are dependent on the mature physical models, and widely required parameters for remote sensing applications. We established the technical criteria for remote sensing experiment instruments, laboratories and

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field sites, and also the technical criteria and requirements for the measurement of object’s spectrum and environmental variables. All new data measurements follow these criteria and regulations, ensuring that the measurements of surface spectra and environmental variables are made together. For those objects which surface features may change with time, such as crop vegetation canopy, we made measurements during each of their main growth stages across their entire growing season. These data sets with temporal changes can be used to extract the temporal change information of the canopy surface reflectance and canopy structural parameters, which is the most important prior knowledge for canopy reflectance model inversion and data assimilation.

8.2.3 From Spectrum Database to Knowledge Base To make the spectrum database applicable for quantitative remote sensing, we further describe how to develop the spectrum database to the spectrum knowledge base. We do this by integrating the spectrum database, the remote sensing image base, the remote sensing model base, and the geographic background database to create the spectrum knowledge database. The remote sensing model base is the key part of the knowledge base. The models describe the relationship between the spectrum reflectance measurements and related environmental variables. The spectra of materials, of endmembers, of remote sensing pixels and the measuring environment variables can be linked by models when the scale of observation is known. The geographic background knowledge data sets provide the prior knowledge of the model parameters for running the models. A significant function of the knowledge base is to make surface spectra simulation or prediction. Because there are too many types of land surface objects, the amount of objects we can measure is always limited. The potential change of the objects are infinite, we can not include all the cases for even one given object. For example, for winter wheat, we almost cannot obtain all the spectrum for its entire growing seasons from the different regions where it is planted. Considering the application of spectrum database, users may occasionally require the spectra of winter wheat for a given date from a specific place, which may not be stored in the database. The simulation or prediction of spectrum is achieved by using physical-based remote sensing models, and applicable empirical models on objects, such as crop simulation models, as well as the knowledge base. Therefore, our knowledge base developed the ability to simulate spectra. When the spectra of an object requested by the user is not in the database, the remote sensing models can be used to simulate the spectra, based on measured spectrum and environmental variables of similar land surface objects saved in the knowledge base. For example, our database stored some standard spectrum of winter wheat at its different growing stages, while the user requires the spectrum at a specific stage in order to predict its growing state from his remotely sensed image. The spectrum from existing spectrum and from related structural parameters of several growing seasons will be calculated with a

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spectral prediction modular. The crop simulation model will provide information about the growing tend, the geographic knowledge base will provide the information about phenological and regional characteristics. The spectral database will provide the spectrum of material and components, and also the structural parameters of a typical related winter wheat. In this way, the modular can interpolate and extend the spectrum in temporal and spatial scales, and also predict the spectrum at a given field of view of sensor, a given sunlight, and under the specific atmospheric conditions. The simulated spectra will provide the user with a reference. Spectra data extension is an important feature of our knowledge base. It can also be available as a research platform for studies on object surface spectra prediction and model validation. At present, in our knowledge base, the model base includes general models, physical models, and some special application models. The geographic background data includes the following: the DEM of 1:100,000–1:250,000 of the demonstration region, and land use map of the demonstration region, the base data of 1:4,000,000 covering the whole of China (DEM, physiognomy, vegetation, soil, geosciences, rivers and lakes), phenological phase of typical crops, Chinese geological map (1:5,000,000), such as Nonmetals Metals Mineral Resource Map, Mineral Resource Map and China water resource map (1:4,000,000). From the measured database, we can construct the prior knowledge of land surface parameters by the statistical data analysis. The a priori knowledge of parameters can be expressed as their mean and variance at spatial and temporal scales of the accumulated data. The establishment of the spectrum knowledge base allows knowledge based inversion strategy and algorithm to be used to process remotely sensed image (Wang and Li, 2004).

8.2.4 The Internet-based Spectrum Knowledge Database Service System The internet-based spectrum knowledge database service system includes the software system and its corresponding hardware environment. This system consists of several modules, such as spectrum querying, model calculation, knowledge querying, image management, application demonstrations, and system management. The spectrum and models in our knowledge database were all imported according to the data quality level regulations. The system also has several demonstrations of typical field remote sensing applications, which include the following: production estimation and growth monitoring of crops in North China; precise agriculture demonstration of winter wheat, demonstrations of cotton growth monitoring; rock and mineral mapping using airborne hyperspectral remotely sensed data; water quality evaluation of the Huangpu River in Shanghai with airborne hyperspectral remotely sensed data. By employing the explanations in the demonstration system, users can learn how to apply the spectrum and other data to extract required land surface parameters from remotely sensed images.

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8.3 Land Surface Parameters Inversion Supported by the Knowledge Database Based on the spectrum database, we propose our methods to estimate land surface parameters, which make effective use of the spectrum knowledge. There are two kinds of questions that need to be considered. One is how to abstract the spatial and temporal distribution of the prior knowledge of parameters from database. When we estimate vegetation parameters from remotely sensed data, the data we used can be from a scene covering large region, so we need to have the spatial distribution prior knowledge of parameters around the same region to support the prior knowledgebased inversion algorithm. When we want to understand the temporal changes of crop growth parameters during its growing seasons, we need to have the knowledge with temporal distribution of estimated parameters, such as when we perform data assimilation using a crop growth model. The second kind of questions we should consider is how to introduce the information on the spatial and temporal distribution of parameters into the inversion algorithm. The model we use for the inversion should be not only suitable for processing one special scene remotely sensed data, but also for the data that changes with time. A dynamic model should then be developed, and a data assimilation algorithm also should be developed. The new method should be able to perform time sequential matching for better estimation of parameters at given time and date.

8.3.1 Extract Spatial and Temporal Distribution of Land Surface Parameters From the spectrum database, we can extract the spatial and temporal distributed a priori knowledge of land surface parameters by means of statistical data analysis, as well as model predictions. To do this, we should first understand the kinds of spatial and temporal data that are available, and then how to make use of them. The prior knowledge data of parameters, which are applied in inversion and data assimilation algorithms, can be at several spatial and temporal scales. The prior knowledge data at different spatial scales can be categorized in two types. One type of data relate to the observed objects, but at different resolutions at which the data is acquired. The spatial resolution of acquired data could be at tens of centimeters, at tens of meters, or even at several kilometers. Another type of data relate to the spatial distribution variability from the same or different types of land surface objects. The spectrum database provides knowledge data by mainly focusing on the former kinds of data. For the latter, some geographic background data with several certain scales can be available. Looking at the example of inversion of vegetation canopy reflectance model, the function of prior knowledge provided by spectrum database can be the following: first, spectrum database can provide the spectrum of materials or endmembers, such as those of leaves and soil from the

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background of crop canopy, which can be used to fix some parameter values, if a model has too many parameters and there are only limited observations to be available for estimate the all model parameters. Secondly, the spectrum database can provide some statistical information of parameters, such as the parameters’ mean value and standard deviation, which can be used as initial guesses and the uncertainty index of parameters to be retrieved. For prior knowledge data at temporal scale, the spectrum database can provide some referencable parameters for dynamic models, while retrieving the variable information of land surface parameters. Looking again at the example of crop canopy reflectance model inversion, due to crop growth over time, the observed spectrum will change. The dynamic change spectral observations can provide an opportunity to retrieve biophysical and biochemical parameters of the crop surface. Thus, the dynamic spectral data of continuing growing vegetation can be used to extract some specific knowledge from the temporal sequence. This type of knowledge may be used to compensate for the limited information from remotely sensed data. In addition, the knowledge is useful for data assimilation. The continuous temporal knowledge of the parameters can be applied to compare with the dynamic model prediction, and then to provide reference feedback to adjust the model’s parameter estimation for the data assimilation procedure. This should result in a better estimation for parameters when their values change with time and with natural features, such as the leaf area index in the crop growth model.

8.3.2 Inversion Model Based on Bayesian Network to Integrate Physical Model and Prior Knowledge Recent research has shown that combining the empirical formula method and the physical model inversion into a new hybrid inversion scheme for estimating surface parameters will be a promising trend (Fang and Liang, 2005; Liang, 2004). Following previous work on hybrid inversion, we build a new hybrid inversion scheme which uses a Bayesian Network (BN) to determine the mapping relationship between simulated reflectances and their corresponding biophysical parameters (Qu et al., 2005). As a hierarchical probability model, BN can not only be used as a non-parameters regression model, but can also be used to deduce information from multi-layered parameters (Marcot et al., 2001). This differs from other nonparameters regression methods, such as Neural Network. In our approach, we focus on the incorporation of prior knowledge derived from spectrum database and physical model into a unified framework. A simple Bayesian Network is illustrated as Fig. 8.1. Using the Bayesian Network to retrieve parameters, the posterior probability density distribution of A can be calculated using the observed data and their ancillary parameters, the following Eq. (8.3) can be derived using Bayesian theorems.

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Fig. 8.1 A simple Bayesian Network

C

A

Ancillary

Parameter space

B

p(A|B = bi ,C = ck ) ∝ p(C = ck )p(A|C = ck )p(B = bi |A)

Data

(8.3)

Where p(A|C = ck ) presents the prior knowledge of interested parameters, p(C = ck ) represent the probability distribution of other variables, such as time, location, elevation, land use, and other assistant information, which can affect the ancillary parameters, p(A|C = ck ) is the probability density distribution of the parameters to be derived after obtaining the above information. The two probability distributions can be obtained from the spectrum database, and the quantitative influence between them, i.e., p(A|C) can be obtained statistically by using data simulated by physical models. By extending the Bayesian theorem into the Bayesian Network, which uses a multifactor deducing method, the prior knowledge about the land surface parameters can be extracted from the spectrum database, and then can be combined with the physical model to retrieve the information on the desired parameters. By integrating the observed data and new information into a unified framework to infer knowledge, this new hybrid inversion scheme has shown that it can incorporate more information besides model parameters into the process of remote sensing model inversion to retrieve biophysical and biochemical parameters. The process of extracting knowledge from the historical database, and using it in the retrieving information from remote sensing models and remotely sensed data is the summingup of prior knowledge and new information. In this process, the information from newly obtained data can be updated and added to the existing knowledge on parameters. In our preliminary research, our proposed inversion approach was used and validated through retrieving the biophysical and biochemical parameters of winter wheat. We abstracted the prior knowledge of canopy reflectance model parameters from the spectrum database to obtain crop growth parameter distribution at different growth stages. We developed the inversion model based on the Bayesian Network to integrate the physical model and prior knowledge to estimated LAI and chlorophyll (a + b) with simulated BRDF spectral data, and to estimated LAI with ETM image (Qu et al., 2005).

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8.4 Parameters Scaling and Validation Scaling effects are the basic issues in remote sensing research. We studied the scaling effect in thermal infrared remote sensing models and the reciprocity principle when these basic physical principles are applied in processing special problems in remote sensing (Li et al., 2000a). When we estimate model parameters by remote sensing model inversion, one important question is whether the parameters require a uniform estimation value when observations are at different spatial scales. In our experiment of model inversion, one parameter may have different estimated values if the available remote sensing data are at different scales of observation. In such case, it is still a problem on how to improve the precision of model parameters estimation. Taking the estimation of crop planting area as example, we usually obtain different estimated area value from AVHRR data or from TM data. And the difference may not follow a certain formula when land cover types from the observed regions are different. This is mainly due to a greater amount of mixed pixels in AVHRR data, and the heterogeneity of land surface. It is very similar to the fractal problems, such as the coastline measurement using the data from different spatial resolution. In order to describe the difference resulting from different scales of observation, we proposed the concept of histo-variogram, defined as the “total fractal dimension”, and applied it to derive a formula for scaling correction on land surface parameter estimates (Zhang et al., 2003). We use LULC data as an example to study land use area estimation method using down-scaling. For the crop area estimates, we defined the initial area S0 which means the observed area at initial measured scale, stated its relation to the total fractal dimensions (d) and coefficients ( f (S0 )), and then applied it to up-scaling and down-scaling in crop area estimation. The estimated crop area of standard pixel (Sδ ) at different scale (δ) is expressed as Sδ = f (s0 )δ d−2

(8.4)

where ( f (S0 )) is the function of the initial area (S0 ) and with the same unit as S0 . δ is for measured scale, can be expressed with fractal of standard pixel. The relation between fractal (δ), coefficient (I) and standardized area (Sδ 0 ) is:     (Iδ i − Sδ 0 )/Iδ i = 1.62Dδ i + 0.03 δ0 (8.5) δi − δ0

where I is the f (S0 ) expressed in Eq. (8.4), can be calculated by Eq. (8.4) with the initial measured scale δi in the process of scaling-up, δ0 is for finer measured scale than δi , Sδ 0 is the crop area we want to estimate by down-scaling method at the measured scale δ0 . We can obtain the estimated area when the scale of the data is changing based on the down-scaling method. In this way, using LULC data, we obtain the result of crop plant area estimation result by the down-scaling method, where the relative error is less than 5% when the estimated pixel size is 16 times that of the original data.

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8.5 Summary and Discussion The previous research we described are our main ideas on remote sensing model inversion strategy and algorithm, base on the analysis of the special ill-posed inversion problem in land surface parameters inversion. The available land surface spectrum knowledge database provides useful models and a priori knowledge of model parameters. We are presently researching the following: 1. How to use spatial and temporal change knowledge in remote sensing model inversion? Based on our previous research, we introduce a dynamic model to obtain a time consequence of model parameters. The idea on data assimilation will then be applied to improve the precision and reliability of parameters estimation. 2. How to validate and evaluate the parameters’ inversion result when the raw data are at different scales? This is still a major problem filled with many uncertainties. The problem regards the scaling effect of models, parameters and observations. 3. How to meet users’ requirements for land surface parameters estimated by remote sensing data, so as to provide input for common land model (CLM)? In this case, the a priori knowledge of the parameters’ spatial distribution and temporal signature will be obtained from the knowledge base, and then used to invert these dynamic changing parameters by introducing the main idea of data assimilation.

References Fang H, Liang S (2005) A hybrid inversion method for mapping leaf area index from MODIS data: experiments and application to broadleaf and needleleaf canopies. Remote Sens. Environ. 94(3):405–424 Gao F, Zhu Q (1997) Process system of measured bidirectional reflectance in Changchun laboratory. J. Remote Sens. 1(Suppl):123–130 Kimes DS, Harrison PR, Ratcliffe PA (1991) A knowledge-based expert system for inferring vegetation characteristics. Int. J. Remote Sens. 12:1987–2020 Kimes DS, Knyazikhin Y, Privette J, Abuelgasim A, Gao F (2000) Inversion methods for physically-based models. Remote Sens. Rev. 18:381–439 Kuusk A (1991) Determination of vegetation canopy parameters from optical measurements. Remote Sens. Environ. 47:194–202 Li X, Yan G, Liu Y, Wang J, Zhu C (1997) Uncertainty and sensitivity matrix of parameters in inversion of physical BRDF model. J. Remote Sens. 1(Suppl):113–122 Li X, Wang J, Hu B, Strahler AH (1998) On utilization of prior knowledge in inversion of remote sensing models. Sci. China (Series D) 41(6):580–586 Li X, Wang J, Strahler AH (2000a) Scale effects and scaling-up by geometric-optical model. Sci. China (Series E) 43(Suppl):17–22 Li X, Gao F, Wang J, Strahler AH (2000b) Estimation of the parameter error propagation in inversion based BRDF observations at single sun position. Sci. China (Series E) 43(Suppl):9–16 Li X, Gao F, Wang J, Strahler AH (2001) A priori knowledge accumulation and its application to linear BRDF model inversion. J. Geophys. Res. 106(D11):11925–11935

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Li X, Wang J, Gao F, Strahler A, Su L (2002) Accumulation of spectral BRDF knowledge for quantitative remote sensing of land surfaces. Proc. The First Int. Symposium on Recent Advances in Quantitative Remote Sensing, Torrent, Valencia, Spain, 16 September 2002 Liang S (2004) Quantitative Remote Sensing of Land Surfaces. Wiley, New York Marcot BG, Holthausen RS, Raphael MG, Rowland M, Wisdom M (2001) Using Bayesian belief networks to evaluate fish and wildlife population viability under land management alternatives from an environmental impact statement. Forest Ecol. Manage. 153(1–3):29–42 Morisette JT, Baret F, Privette JL, Myneni RB, et al. (2006) Validation of global moderateresolution LAI products: a framework proposed within the CEOS land product validation subgroup. IEEE Trans. Geosci. Remote Sens. 44(2):1804–1817 Myneni RB, Maggion S, Iaquinta J, et al. (1995) Optical remote sensing of vegetation: modeling, caveats and algorithms. Remote Sens. Environ. 51:169–188 Privette JL, Eck TF, Deering DW (1997) Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS-like data. J. Geophys. Res. 102(D24):29529–29542 Qu Y, Wang J, Song J, Lin H (2005) A hybrid inversion scheme to estimate biophysical parameters of winter wheat: simulation and validation. Proc. ISPMSRS’05, Beijing,, 17–19 October 2005, pp 743–746 Rodgers CD (1976) Retrieval of atmospheric temperature and composition from remote measurement of thermal radiation. Rev. Geophys. Space Phys. 14(4):609–624 Smith JA (1993) LAI inversion using a back propagation neural network trained with a multiple scattering model. IEEE Trans. Geosci. Remote Sens. 31:1102–1106 Tan B, Hu J, Huang D, et al. (2005) Assessment of the broadleaf crop leaf area index product from the Terra MODIS instrument. Agric. Forest Meteorol. 135:124–134 Tarantola A (1987) Inverse Problem Theory – Methods for Data Fitting and Model Parameter Estimation. Elsevier, Amsterdam, The Netherlands, 613pp Verstraete MM, Pinty B, Myneni RB (1996) Potential and limitation of information extraction on the biosphere from satellite remote sensing. Remote Sens. Environ. 52:201–214 Wanner W, Strahler AH, Hu B, Lewis P, Muller J-P, Li X, Barker Schaaf CL, Barnsley MJ (1997) Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm. J. Geophys. Res. 102(D24):17143–17162 Wang J, Li X (2004) The spectrum knowledge base of typical objects and remote sensing inversion of land surface parameters. J. Remote Sens. 8(Suppl):4–7 (in Chinese) Wang J, Li X, Sun X, Liu Q (2000) Component temperatures inversion for remote sensing pixel based on directional thermal radiation model. Science in China (Series E) 43(Suppl):41–47 Wang J, Zhang L, Zhang H, Li X, Liu S (2003) Current progress of constructing the spectrum knowledge base of typical objects of land surfaces, ESA SPECTRA workshop in France (Italy), November 2003 Yan G, Wang J, Li X (2001) Making use of a priori knowledge of vegetation spectrum in inversion for canopy structure parameters. Proc. IGARSS’01, Sydney, Australia, 9–13 July 2001 Zhang H, Jiao Z, Yang H, Li X, et al. (2003) Research on scale effect of histogram. Sci. China (Series D) 45(10):1–12

Chapter 9

Retrieval of Surface Albedo from Satellite Sensors Crystal Schaaf, John Martonchik, Bernard Pinty, Yves Govaerts, Feng Gao, Alessio Lattanzio, Jicheng Liu, Alan Strahler, and Malcolm Taberner

Abstract Observations from a number of polar-orbiting and geostationary satellite sensors are now being used to produce operational land surface albedo products for range of modeling applications. The MODIS, MISR and Meteosat algorithms are presented as examples of the current strategies being employed to best exploit multi-day sequential, multi-angular instantaneous, and multi-temporal observations and accurately specify the reflective qualities of the underlying surface. While these retrievals represent a major advance in the remote sensing of the spatial and temporal heterogeneity of the surface, issues such as atmospheric correction, directional-tohemispherical conversion, and spectral interpolation remain to confound the satellite signal and introduce uncertainties and variability within and between products. Nevertheless, the potential of using multiple products and fusing recent observations with remotely sensed historical data must be explored as a realistic way to meet the needs of the modeling community. Keywords: MODIS · MISR · Meteosat · albedo · reflectance · anisotropy

Crystal Schaaf, Jicheng Liu and Alan Strahler Department of Geography and Environment, Boston University, Boston, USA [email protected] Feng Gao Earth Resources Technology, Jessup, USA John Martonchik Jet Propulsion Laboratory, Pasadena, USA Bernard Pinty and Malcolm Taberner Global Environment Monitoring Unit, IES, EC Joint Research Centre, Ispra (VA), Italy Yves Govaerts EUMETSAT, Darmstadt, Germany Alessio Lattanzio Makalumedia GMBH, Darmstadt, Germany S. Liang (ed.), Advances in Land Remote Sensing, 219–243. c Springer Science + Business Media B.V., 2008


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9.1 Introduction The availability of a large number of directional observations sampling the viewing hemisphere over a particular land surface can effectively capture its surface anisotropy and thus be used to accurately compute the surface albedo of that surface. While numerous samples may be possible in the field or laboratory, remotely sensed retrieval methods based on data from individual satellites usually must suffice with a limited number of directional reflectances of the surface, and the producers of such data sets must acknowledge that these observations may not necessarily represent a well-distributed sampling (Privette et al., 1997). Therefore a model is usually adopted to characterize the surface anisotropy – a model which can be inverted with a finite set of angular samples and then be used to predict surface reflectance in any sun-view geometry and derive surface albedo (Roujean et al., 1992; Walthall et al., 1985; Rahman et al., 1993; Engelsen et al., 1996; Wanner et al., 1997; Pinty et al., 2000a; Br´eon et al., 2002; Maignan et al., 2004). The acquisition of directional measurements from an individual sensor is determined by its scanning configuration and the platform’s orbital characteristics (Barnsley et al., 1994). However, cloud obscuration always reduces the number of clear-sky observations possible. Therefore, in the case of a single field of view sensor such as the MODerate Resolution Imaging Spectroradiaometer (MODIS), on board the polar orbiting Terra and Aqua platforms, an adequate directional sampling of surface reflectances can only be obtained by the accumulation of sequential observations over a specified time period. Multi-angular instruments such as the Multiangle Imaging SpectroRadiometer (MISR) instrument (also on board the Terra platform) obtain sufficient simultaneous directional observations to specify the surface anisotropy whenever a cloud-free acquisition is possible. Geostationary sensors (such as Meteosat) must trade numerous acquisitions under different illumination conditions during a day for directional observations to obtain the angular information necessary to sample the surface’s directional characteristics. Since 2000, all of these approaches have been implemented operationally to produce robust surface albedo fields for use in climate, hydrological, biogeochemical, and weather prediction models.

9.2 Background As a key land physical parameter controlling the surface radiation energy budget (Dickinson, 1983, 1995), global surface albedo with an absolute accuracy of 0.02–0.05 is required by climate models at a range of spatial and temporal scales (Henderson-Sellers and Wilson, 1983). Land cover-based schemes have historically been adopted in most of the land surface models and climate models for the parameterization and specification of surface albedo (Bonan et al., 2002; Sellers et al., 1996). Natural landscapes, however, are a collection of nested objects in a hierarchy and various processes control the biophysical characteristics at different spatial scales (Woodcock and Harward, 1992; Collins and Woodcock, 2000).

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Therefore, land surface models usually allow a sub-grid specification of land cover proportions to account for the heterogeneity of surface properties within a grid (Dickinson et al., 1995; Bonan et al., 2002), while the climate models are generally implemented at coarser spatial resolutions. However, the increasing spatial resolution of modern climate models makes it necessary to examine the spatial features of global surface albedo and the effect of spatial scales on the albedo specification. Therefore, a consistent and accurate global albedo data set is essential to the investigation of the sensitivity of climate to various types of forcing and to the identification of the effects of human activities. Satellite remote sensing represents the only efficient way to compile such consistent global albedo characterizations. Historically, global albedo data sets have been derived from the Advanced Very High Resolution Radiometer (AVHRR) (Csiszar and Gutman, 1999) and the Earth Radiation Budget Experiment (ERBE) radiometer (Li and Garand, 1994). With the advent of routine albedo products derived from MODIS (Gao et al., 2005; Schaaf et al., 2002; Lucht et al., 2000), MISR (Martonchik, 1997; Martonchik et al., 1998b), CERES (Clouds and the Earth’s Radiant Energy System), POLDER (Polarization and Directionality of the Earth’s Reflectances) which is currently on board PARASOL (Polarization & Anisotropy of Reflectances for Atmospheric Sciences) coupled with Observations from a Lidar (PARASOL) (Leroy et al., 1997; Hautecoeur and Leroy, 1998; Bicheron and Leroy, 2000; Maignan et al., 2004), and Meteosat (Pinty et al., 2000a,b), albedo data sets with spatial resolutions of 500 m to 20 km and temporal frequencies of daily to monthly are now available. Although the retrieval of albedo from these instruments represents a major advance in sensing the spatial and temporal surface heterogeneity, issues such as atmospheric correction, directional-to-hemispherical conversion, and spectral interpolation can still confound the satellite signal and introduce uncertainties. Most of these satellite products rely on sophisticated radiative transfer methods (Vermote et al., 1997; Berk et al., 1998; Liang et al., 1999; Liang, 2000) and bidirectional modeling (Roujean et al., 1992; Walthall et al., 1985; Rahman et al., 1993; Engelsen et al., 1996; Wanner et al., 1995; Wanner et al., 1997; Martonchik et al., 1998b; Pinty et al., 2000a, b) to obtain accurate surface quantities. The modeling community has enthusiastically begun to utilize these global and regional satellite albedo products as they have become available (Oleson et al., 2003; Zhou et al., 2003; Tian et al., 2004; Roesch et al., 2004; Knorr et al., 2001; Myhre et al., 2005a, b). With 5 or more years of data now available, interannual variations can be explored and short-term climatologies prepared which compensate for transient cloudiness or snowcover (Moody et al., 2005; Gao et al., 2005; Barlage et al., 2005). However, there remains the need to generate analogous surface albedo products prior to year 2000 and in particular over the last 25 years or so where Earth observing systems from space (e.g., the series of weather satellites) have been acquiring relevant data. Unfortunately, the design of the large majority of these global observation systems for environmental applications has been driven solely by demands in the domain of meteorology and weather forecasting and, as a consequence, these sensors do not fulfill some basic requirements for quantitative remote sensing applications over land, such as those related to the accurate sensor characterization, geolocation, and calibration.

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However, despite a number of technological limitations, these historical weather sensors constitute the only possible solution left to remote sensing scientists to assess such quantities as surface albedos at a global scale over the past decades. The required sequential accumulation of data over multiple days, i.e., for different view conditions, as adopted for MODIS sensors for inferring flux quantities from a number of instantaneous radiance measurements, can be extended to exploit the AVHRR series data archive (see for instance d’Entremont et al., 1999). An analogous strategy of sequential accumulation (but over every single day, i.e., for different solar illumination conditions), can be envisaged in the case of the archived measurements collected by sensors placed on a geostationary orbit. The exploitation of the reciprocity principle then allows the production for every sample area, of daily accumulated datasets of radiances measured at different viewing angles (see for instance, Lattanzio et al., 2006). Assuming thus that the geophysical system under investigation does not suffer from drastic changes during the period of data accumulation, e.g., multiple hours (days) for geostationary (polar) orbiting sensors, the temporal sampling of the radiance field for a given location can be interpreted as an angular sampling.

9.3 MODIS Albedo and Anisotropy Algorithm The operational MODIS albedo and anisotropy algorithm makes use of a kerneldriven, linear model of the Bidirectional Reflectance Factors (BRFs), which relies on the weighted sum of an isotropic parameter and two functions (or kernels) of viewing and illumination geometry (Roujean et al., 1992) to estimate the Bidirectional Reflectance Distribution Function (BRDF). One kernel is derived from radiative transfer models (Ross, 1981) and the other is based on surface scattering and geometric shadow casting theory (Li and Strahler, 1992). The kernel weights selected are those that best fit the cloud-cleared, atmospherically corrected surface reflectances available for each location over a 16-day period (Lucht et al., 2000; Schaaf et al., 2002). This model combination (Ross-Thick/Li-Sparse-Reciprocal or RTLSR) has been shown to be well suited to describing the surface anisotropy of the variety of land covers that are distributed world-wide (Privette et al., 1997; Lucht et al., 2000) and is similar to the kernel-driven schemes used to obtain anisotropy and albedo information by the POLDER (Leroy and Hautecoeur, 1998; Bicheron and Leroy, 2000; Maignan et al., 2004) satellite sensor. Once an appropriate anisotropy model has been retrieved, integration over all view angles results in a Directional Hemispherical Reflectance (DHR) or a black-sky albedo at any desired solar angle and a further integration over all illumination angles results in a BiMemispherical Reflectance (BHR) under isotropic illumination or a white-sky albedo. These albedo quantities are intrinsic to a specific location and are governed by the character and structure of its land cover. They can be combined with appropriate optical depth information to produce an actual (blue-sky) albedo for a specific time such as would be measured at the surface by field sensors under ambient

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illumination. The anisotropy models can also be used to compute surface reflectances at any other view or solar zenith angle desired. The spectral acquisitions can also be combined via narrow to broadband conversion coefficients (Liang et al., 1999; Liang, 2000) to provide broadband anisotropy information and thus broadband albedos similar to those routinely collected in the field with pyranometers and commonly used in large-scale models. The MODIS instruments on both Aqua and Terra have a 16-day repeat cycle and provide measurements on a global basis every 1–2 days. The 16-day period has also been chosen as an appropriate tradeoff between the availability of sufficient angular samples and the temporal stability of surface (Wanner et al., 1997; Gao et al., 2001). This assumption becomes tenuous during periods of strong phenological change such as vegetation greenup, senescence, or harvesting. By overlapping processing of the data such that retrievals are attempted every 8 days (based on all clear observations over the past 16 days), some of the phenological variability can be more accurately captured. Other periods of rapid change at the surface such as ephemeral snowfall also provide challenges in retrieving appropriate surface albedos. The MODIS algorithm addresses this by determining whether the majority of the clear observations available over a 16-day period represent snowcovered or snow-free situations and then retrieving the albedo of the majority condition accordingly. For those locations where the full anisotropic model described above can not be confidently retrieved due to poor or insufficient input observations, a backup algorithm is employed. This method (Strugnell and Lucht, 2001; Strugnell et al., 2001) relies on a global database of archetypal anisotropic model based on a land cover classification and historical high quality full model retrievals. This a priori data base is then used as a first guess of the underlying anisotropy and any available observations are used to constrain the model. While considered a lower quality result, Jin et al. (2003a, b) and Salomon et al. (2006) have found that this backup method often performs quite well under normal situations (e.g., Fig. 9.1). In view of the often insufficient angular sampling available, a synergistic use of multi-sensor observations has offered the best opportunity to improve both the coverage and the quality of global anisotropy and albedo retrievals. Terra has a descending equatorial crossing time of 10:30 a.m., while Aqua is flying in an ascending orbit with a 1:30 p.m. equatorial crossing time. By combining MODIS observations from both Terra and Aqua, more high-quality, cloud-free observations (under varying solar zenith angle) are available to generate better constrained model retrievals (see Fig. 9.1). Since the MODIS-Terra and MODIS-Aqua have similar instrument characterizations and utilize the same atmospheric correction algorithm, the combination of these data is fairly straightforward. However, the calibration and geolocation of both instruments must be continually monitored for compatibility and the quality of the aerosol retrieval from each sensor and its effect on the respective atmospherically-corrected surface reflectances must also be accounted for. In general, the combined Terra and Aqua MODIS product processing stream begins with a detailed quality check of each atmospherically corrected surface reflectance and then assigns various penalty weights to the individual observations according to

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the quality flag contained in each surface reflectance product (Schaaf et al., 2002). Thus, the quantified uncertainty of the sensor-specific surface reflectances is directly integrated into the retrieval. Results from the combined Terra-MODIS and Aqua-MODIS algorithm (Fig. 9.2) indicate that the increase in the number of observations does result in more higher quality retrievals and can decrease the use of backup retrievals by as much as 50% (Salomon et al., 2006). The MODIS BRDF/Albedo standard operational products (Lucht et al., 2000; Schaaf et al., 2002; Gao et al., 2005) provide the best fit RTLSR model parameters describing the surface anisotropy, black sky and white sky albedo quantities, the nadir (view-angle-corrected) surface reflectance of each location, and extensive quality information. The best fit RTLSR model parameters are retrieved for the first seven spectral bands of MODIS and three additional broadbands (0.3–0.7 µm, 0.7–5 µm, 0.3–5 µm). These anisotropy models are then used to compute white sky albedo and black sky albedo at local solar noon for the same seven spectral bands and three broadbands. The anisotropy models are also used to correct surface reflectances for view angle effects and provide BRFs at a common nadir view angle (Fig. 9.3). These Nadir BRDF-Adjusted Reflectances (NBAR) are computed for the seven spectral bands and are used as the primary input for the MODIS Land Cover and Land Cover Dynamics Products due to their stability and temporal consistency (Friedl et al., 2002; Zhang et al., 2003). In addition to the standard 500 m and 1 km tiled products in a sinusoidal projection, these same science data sets are

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Fig. 9.2 Quality improvement possible by combining MODIS observations from both the Terra and Aqua platforms. Top panel shows Terra alone (green high quality, red lower quality) while bottom panel shows Terra and Aqua (March 2006) MODIS Reflectance (MODO9GHK) 2004-126

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Fig. 9.4 MODIS global white sky albedo (from Terra and Aqua) March 2006

also routinely produced at a 0.05◦ spatial resolution in a global geographic (latitude/longitude) projection specifically for use by global modelers (Gao et al., 2005). In Fig. 9.4, the global false color field of spectral white sky albedo (March 2006) captures the seasonal variation due to vegetation phenology and snow cover extent.

9.4 MISR Albedo and Anisotropy Algorithm The Multi-angle Imaging SpectroRadiometer (MISR) on the EOS Terra platform consists of nine pushbroom cameras, viewing symmetrically about nadir in forward to aftward directions along the spacecraft track. Image data are acquired with nominal view zenith angles relative to the surface reference ellipsoid of 0.0◦ , 26.1◦ , 45.6◦ , 60.0◦ , and 70.5◦ in four spectral bands (446, 558, 672, and 866 nm) and with a crosstrack ground spatial resolution of 275 m to 1.1 km and a swath width of about 400 km (Diner et al., 1998). After these data are radiometrically calibrated, georectified, and averaged to a uniform resolution of 1.1 km, the land data undergo a series of processing steps, resulting in a myriad of surface parameters. The basic land surface products currently being generated include the spectral hemispherical-directional reflectance factor (HDRF) at the nine MISR view angles and the associated BHR. The HDRF is a measure of the directional reflectance of the surface under ambient atmospheric illumination (i.e., direct plus diffuse radiation). It is the ratio of the directionally reflected radiance from the surface to the reflected radiance from an ideal lambertian target under identical illumination conditions as the surface. The BHR is the HDRF integrated over all reflection angles in the upward hemisphere, i.e., it is the surface albedo under ambient atmospheric illumination. Related MISR surface parameters are the spectral BRFs at the nine MISR view

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angles and the DHR. The BRF and the DHR characterize the surface in the same way as the HDRF and BHR, respectively, but are defined for the condition of direct (i.e., collimated beam) illumination only. Thus, the top-of-atmosphere (TOA) MISR radiances are first atmospherically corrected to produce the HDRF and the BHR, surface reflectance properties as would be measured at ground level but at the MISR spatial resolution. The HDRF and BHR then are further atmospherically corrected to remove all diffuse illumination effects, resulting in the BRF and DHR. In addition to these spectral surface reflectance products, the BHR and DHR, integrated over the wavelength region of Photosynthetically Active Radiation (PAR) (400–700 nm), are also computed. The determination of these surface products requires that the atmosphere be sufficiently characterized in order for the correction process to occur. This characterization is accomplished by means of aerosol retrieval, a process performed on a region 17.6 × 17.6 km in size, containing the 1.1 × 1.1 km size subregions (Martonchik et al., 1998a, 2002a). After a surface BRF is determined at the subregion scale it is fitted to the three parameter modified Rahman–Pinty–Verstraete (MRPV) empirical model (Rahman et al., 1993; Engelsen et al., 1996), which provides a convenient representation of the surface scattering characteristics The details of the retrieval methodologies used to derive these various surface products have been described by Martonchik et al. (1998b). The unique capabilities of MISR’s multiple cameras allow for a simultaneous sampling of the surface anisotropy. By coupling the angular information with the spectral information, the MISR observations can be exploited to capture ephemeral effects such as springtime snow cover. On 17 April 2001 MISR observed a rural part of Manitoba and Saskatchewan about 110 km north of the US border (Path 34, Orbit 7083). Most of MISR’s imaging data have a resolution of 1.1 km, but all nine cameras in the red band (672 nm) and all four bands in the nadir camera take global data at the higher resolution of 275 m. Figure 9.5 shows two false color images of the Canadian scene at 275 m resolution, one emphasizing spectral information and the other, angular information. The image on the left is a multispectral color composite in which the MISR green band (558 nm), red band, and near IR band (866 nm) nadir view imagery are colored blue, green, and red. Here, vegetation appears red due to its high reflectivity in the near IR band and low reflectivity in the green and red bands. The image on the right is a multiangular color composite in which the 60◦ forward view, the nadir view, and 60◦ aftward view images are colored blue, green and red, respectively, essentially color coding the angular signature of the scene. Thus, for example, a region with a reflectance predominately in the nadir direction will appear green. Prominent features in both images are the Assiniboine and Qu’Appelle rivers, running southward and eastward, respectively. The bidirectional reflectance factors for three sites marked by yellow arrows in Fig. 9.5 are displayed in Fig. 9.6. The solar zenith angle is 42◦ and the azimuth angles of the BRFs are about 32◦ from the principal plane. The northern-most site is reddish in color in both composite images in Fig. 9.5, indicating vegetation with substantial backscatter. This backscatter signature is more clearly shown in the BRF plot in Fig. 9.6 The BHR (i.e., actual albedo), is 0.08 in the red band and the NDVI is 0.49, implying moderately dense vegetation. The eastern-most site also has a

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Fig. 9.5 Two false color images (275 m resolution) of an area (240 × 175 km) in central Canada on 17 April 2001 centered on the Saskatchewan–Manitoba border. The left image is a multispectral composite in which red (more like purple/blue in the pdf/doc versions of the images) indicates vegetation. The image on the right is a multiangular composite in which green indicates predominate scattering in the nadir direction Moderately dense vegetation (albedo = 0.08, NDVI = 0.49) Snowy forest (albedo = 0.18, NDVI = 0.24) Agricultural field with light snow (albedo = 0.18, NDVI = 0.13)

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vegetative character, colored purple and red in the multiangular and multispectral composites, respectively. However, the BRFs for this site are higher and with more forward scattering than for the previous site, and with an increased red band BHR of 0.18 and a lower NDVI of only 0.13. The brightening of the BRF, the increase

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in forward scattering, and the decrease in the NDVI is indicative of the presence of some snow in and among small scale vegetation, probably agricultural. The last site in Fig. 9.5 is located in Duck Mountain Provincial Park and is colored green in the multiangular composite and red in the multispectral composite. This color combination implies vegetation but with strong scattering in the nadir direction. The BRF plot in Fig. 9.6 shows this signature in more detail, and it is quite different than those from the other two sites. Here, the vegetation is a forest with snow on the ground between the trees. When viewing in or near the nadir direction, the snow is highly visible and the BRF is at its highest. As the view angle progressively increases, the ratio of snow cover to tree structure decreases, lowering the reflectance until, at the extreme off-nadir view angles, the BRF is virtually all canopy with its characteristic pronounced backscatter. During the 7 weeks from 14 August to 29 September 2000, numerous orbits of MISR data were analyzed and compiled for southern Africa, as part of the dry season campaign of the Southern Africa Regional Science Initiative (SAFARI-2000), an international effort to study linkages between land and atmospheric processes. During this period a number of AERONET sunphotometer sites (Holben et al., 1998) were operational over the region, providing independent determinations of aerosol optical depth which were compared to those retrieved using MISR data (Diner et al., 2001). This validation study produced very favorable results, allowing considerable confidence to be placed in the subsequent atmospheric correction procedures and in the quality of the retrieved surface products. Figure 9.7 is a true color, 1.1 km resolution mosaic of the surface DHR for southern Africa, derived from 27 orbital swaths accumulated during this time period. The bright feature in the center is the Makgadikgadi Pans, an extensive salt bed in Botswana. In the interior part of southern Africa, much of the land can be classified as savanna and grassland. Figure 9.8 shows the HDRFs in all four MISR bands for grassland not far from Johannesburg. The grass is dried out, as can be discerned from the monotonically increasing HDRF with wavelength. Using data from 15 August (Path 168, Orbit 3509), this particular site was positioned on the extreme western edge of MISR’s orbital swath, providing multispectral measurements within 1◦ of the retro-solar direction (direct backscatter). The resulting hotspot, due to an almost complete lack of shadowing within the structured surface, can be seen very clearly in Fig. 9.8 as an enhancement of the HDRF in all bands at 49◦ view zenith angle, which is also the solar zenith angle. The hotspot, while not common in MISR surface retrievals, does occur for a wide range of latitudes, appearing at different camera view angles, depending on the season. In addition to the standard MISR products available at 275 m or 1.1 km, many are also available in a format of monthly global maps at a spatial resolution of 0.5◦ in both latitude and longitude. An example of this type of map is displayed in Fig. 9.9, showing surface DHR in natural color for the month of September 2005. The individual 0.5◦ pixels are created by averaging all 1.1 km DHR values accumulated within that pixel for that month. The white specks evident in some areas are fill pixels where no 1.1 km DHR values were available for the entire month, due mainly to cloud activity.

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Fig. 9.7 MISR true color, 1.1 km resolution mosaic of the surface directional-hemispherical reflectance (DHR) for southern Africa (14 August–29 September 2000) DRY GRASSLAND, SOUTH AFRICA Blue

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Fig. 9.9 Surface DHR in natural color for the month of September 2005

9.5 Meteosat Albedo and Anisotropy Algorithm The cornerstone of the retrieval algorithm for geostationary satellites developed by Pinty et al. (2000a) relies on the temporal sampling of geostationary satellites (data acquired every 15 or 30 min from sunrise to sunset) as if it were an instantaneous angular sampling of the radiance field emerging at the top of the atmosphere. The frequency of measurements of the same Earth location is indeed a unique capability offered by geostationary satellites that thus translates into an increasing number of conditions or positive constraints to be satisfied by the retrieval algorithm. The physics of the Meteosat retrieval aims at solving an inverse radiation transfer problem simultaneously with respect to the lower boundary condition, i.e., the surface bidirectional reflectance factor (BRF), and the aerosol optical thickness (Martonchik et al., 1998b, 2002b; Pinty et al., 2000a). All other effects due, for instance, to water vapour and ozone in the atmosphere are accounted for via a prescription of gas concentrations taken from either climatology and/or weather forecast models (re) analysis. In order to simplify the problem further, the gaseous absorption processes are treated separately from the aerosol-scattering-absorbing effects by the specification of two distinct atmospheric layers, one for the representation of the molecular absorption only and the other for the modeling of the coupled surfaceaerosol radiation transfer processes. The inverse algorithm is basically focusing on the estimates of key variables, namely the aerosol load and surface scattering properties, for which the a priori knowledge is quite limited or somewhat uncertain and the level of variability is quite high. The mathematics of the retrievals is established in such a way that the amplitude of the surface BRF is propagated to the top of the atmospheric scattering layer while its shape is modulated by the atmospheric scattering and absorbing properties

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(Pinty et al., 2000a). This is made possible thanks to (1) the mathematical formulation of the surface BRF model, namely the RPV model (Engelsen et al., 1996; Rahman et al., 1993) which separates the amplitude from the shape of the surface BRF and (2) the decomposition of some atmospheric functions like the upward and downward diffuse transmission with a Fourier expansion limited to the first two components. This approach proved to be computer efficient and accurate for modeling the radiance field at the top of a scattering-only atmosphere (Martonchik et al., 2002b). In this way, the angular field of the BRF at the top of the scattering atmosphere can be simply expressed as a sum of contributions invoking the coupling between the surface BRF shape and atmospheric scattering functions that can all be pre-computed and called during the retrieval procedure. For a given set of measured BRF values at the top of the atmosphere the latter procedure itself solves (1) a linear equation to calculate first the amplitude values of the surface BRF for the given pre-computed scattering functions and (2) a second order cost function estimating the closeness between the measured and the modeled BRF values at the top of the atmosphere. The retrieval procedure then ends up with an identification of probability distribution functions of the acceptable solutions, i.e., those satisfying one or multiple criteria depending on the number of degrees of freedom and the distributions of uncertainties in both the observations and in the forward model. The selection of the “most probable” solution for any given set of measured BRF amongst the set of acceptable solutions can be performed using various criteria including the identification of the solution corresponding to the arithmetic mean of the distribution of the amplitude of the surface BRF values. The solution retained is thus a set of model variables and parameters describing the surface scattering problem, such as the parameters characterizing the shape of the surface BRF and the effective aerosol loads, associated with the selected value for the amplitude of the surface BRF. The aerosol loads together with the surface scattering properties are given via effective optical thickness values for a prescribed aerosol type corresponding to average standard aerosol conditions regarding their detailed properties and vertical distribution as well. Since the retrieval strategy delivers the optimized set of the RPV model parameters characterizing the surface BRDF, one can generate DHR or black-sky albedo for any solar angle and/or BHR or white-sky albedo products (Pinty et al., 2000a). The abundance of cloudy conditions occurring during a day over the Earth disk sections sensed by geostationary satellites motivates the implementation of a procedure screening conditions that do not correspond to clear-sky cases. Pinty et al. (2000b) suggested adoption of an angular consistency check by which the daily top of the atmosphere radiance series for each individual pixel is used in an attempt to fit the MRPV model. This is based on a recursive filtering technique which identifies sequentially during the day, the outliers deviating significantly from the fitted MRPV model solutions. In the vast majority of the cases, larger (lower) radiance values than the MRPV fitted solutions are associated with cloudy (shadowed) conditions and the spatio-temporal fields of these outliers were shown to, indeed, display very consistent cloud fields and associated shadows along the course of the day

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(Pinty et al., 2000a). Measurements acquired at solar and view zenith angles larger than 70◦ or corresponding to cloud conditions are rejected. A minimum of six valid clear sky observations are necessary for the activation of the retrieval procedure. These cloudy as well as additional undesired conditions translate into incomplete geographic surface albedo map products. This caveat can be overcome by applying a time composite algorithm selecting, over a given composite time period, the particular day delivering the albedo value which is the closest to the average of the ensemble of values retrieved during that same time period. In this way, the geophysical values for each pixel can be delivered with all the relevant information used to generate them in the retrieval algorithm such as, for example, the number of observations used to perform the retrieval and estimation of the retrieval uncertainties among others. Sensors on board geostationary satellites sample the scattered solar radiance fields in a usually single, large (according to today’s standards) spectral band (see Fig. 9.10), e.g., ≈ 0.4–1.1 µm for Meteosat and GMS, 0.05–0.8 µm

Fig. 9.10 Examples of sensor spectral responses on board geostationary satellites in the solar domain (red line). The green solid line illustrates typical reflectance of green vegetation

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for GOES, which prevents us benefiting from advanced atmospheric correction algorithms based on multi-spectral information, as is possible for the MODIS and MISR sensors. Due to the fast spatio-temporal variability of the cloud, water vapor and aerosol fields, the crucial problem of accurately assessing/removing the undesired effects induced by these atmospheric components on the measured radiances remains to be solved on the sole basis of the available information gathered by the sensor or other sources of information. For those components, such as ozone, that have a non-negligible but still limited impact on the surface retrievals and whose variability remains somewhat small, the use of climatological values is generally acceptable. In most if not all cases to be addressed, the availability of a spectrally large single band only renders the partitioning between the surface and atmospheric contributions quite difficult since the scattering and absorption effects in the atmosphere are wavelength-dependent and coupled with spectrally variant surface properties. To date, the constraints imposed by operational exploitation infrastructures have not favored the processing of multi-sensor measurements assembled via data fusion procedures. This state of affairs encourages the development of albedo retrieval algorithms relying on the analysis of data (and data strings) collected by each geostationary sensor in stand alone mode. In turn, this places stringent requirements on the reliability and overall performance of the retrieval algorithm which thus, on the basis of a single spectrally large band, must be able to identify cloud occurrence and then solve, as well as possible, the coupled surface-atmosphere radiation transfer problem. In that context, multiple sensitivity test have to be conducted in order to optimize the crucial choices to be made such as, for instance, between the length of the period to perform sequential data accumulation, e.g., between a few hours and a few days, and the impacts of the assumption hindering this multi-angular data emulation procedure, e.g., no drastic changes in the geophysical system under investigation. Meteosat data processed with this algorithm have already been used in a variety of applications (see for instance, Pinty et al., 2000c; Knorr et al., 2001; Myhre et al., 2005b).

9.6 Fusion of Modern and Historical Surface Albedo Products Documenting the Earth climate and its variability requires access to reliable and accurate long time series of environmental products. Hence, archived meteorological satellite observations could contribute to the generation of climatic data records providing that (1) significant efforts are devoted to the improvement of the spectral characterization and calibration of these radiometers and (2) developing state of the art retrieval algorithms. The first point aims at reducing and controlling as much as possible the impact of measurements uncertainties on the accuracy of the retrievals while the second point similarly at model uncertainties. Previous studies have, indeed, already demonstrated the possibility to perform post-launch improvements of the radiometer characteristics (e.g., Govaerts, 1999). In the specific case of surface albedo retrieval, the science context set up by the requirements in the exploitation

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of data acquired by modern sensors such as those on board Terra and Meteosat Second Generation for instance has motivated a large number of studies addressing these points. The associated improved knowledge translates, in turn, into the development and use of better approaches for the optimal exploitation of measurements taken by “old generation” sensors. While active efforts are underway within the NASA community to couple MODIS observations to the historical AVHRR archives (Pedelty et al., 2007) considerable progress has already been made in exploiting historical geostationary satellite data to establish a historical data set of global surface albedo values. This requires the back processing and analysis of measurements assembled by the fleet of geostationary satellites over the past 25 years or so. The quality of these retrievals can be assessed by various means including first, the comparison of these retrieved albedo values against those operationally generated since year 2000 from modern and technologically advanced instruments such as MODIS and MISR (Pinty et al., 2004) and second, the intercomparison of surface albedo products generated over geographical regions of overlap that are, therefore, sampled simultaneously by two adjacent sensors together placed on geostationary orbit but located at different longitudes (Govaerts et al., 2004). In order to conduct comparison exercises of relevance for climate model applications, surface albedo products have to be made available over large spectral regions covering the energetically relevant solar domain [0.3–3.0 µm] split, whenever possible, into its broad visible [0.3–0.7 µm] and near-infrared [0.7–3.0 µm] parts. Achieving this step, usually called spectral conversion, requires developing appropriate tools to transform albedo product values, estimated over and weighted by the spectral response of the geostationary sensor, into values representative of the desired broad spectral range of interest (see for instance Liang (2000) and Govaerts et al. (2006)). One possible solution consists in approximating a parametric expression relating the measurements from the sensor to those that would be provided by an ideal rectangular shape sensor covering the solar domain of interest. Such an expression can be established on the basis of (1) a large number of simulations of top of atmosphere radiance fields of various geophysical situations that can be expected for the region of interest (e.g., vegetation with varying density, bare soils with different brightness, snow surfaces, coupled with a diversity of atmospheric conditions) and (2) a multi-regression analysis fitting at best the sensor-like values against those representative of the desired solar domain. This spectral conversion constitutes quite a delicate step and, as a matter of fact, its reliability relies strongly on the degree of coincidence between the distributions of the simulated and actual conditions. Its impact on the uncertainty of the final albedo products also depends crucially on the sensor spectral response function since the spectral conversion basically assumes that strong correlations exist between radiances taken across various wavelengths of the solar spectrum. Preliminary attempts to compare surface albedo products from modern sensors, such as MODIS and MISR, against those generated by the retrieval algorithm outlined here for geostationary satellites result into quite positive conclusions. Figure 9.11 illustrates an example of results to be expected when comparing

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Fig. 9.11 Scatterplot (density plot) between the MODIS white sky albedo and Meteosat BHR values retrieved between 20–65 ◦ W longitude and 40 ◦ S − 40 ◦ N latitude during the first 2 weeks of year 2001. This plot includes the high quality flag MODIS products only and the outliers from the two distributions have been removed (less than 5% of the total number of valid retrievals). The full, dashed, and dotted lines feature the fit obtained using the slope of the means, the linear regression, and the primary eigenvector, respectively

Meteosat and MODIS (considering high quality flags only) surface albedo products, in units of white sky albedo (BHR), over a large geographical region extending from Southern Europe and covering the entire African continent (between 20◦ W–65◦ N longitude and 40◦ S–40◦ N latitude. This figure is built from the analysis of products available during the first 2-week period of year 2001 after removal of outliers detected in large majority along the coastlines. The 10-day composite Meteosat products have been re-mapped into the MODIS Climate Modeling Grid at a spatial resolution of 0.05◦ . The MODIS and Meteosat spectral albedo products were both converted into an ideal rectangular shape (0.4–1.1 µm) in order to (1) make the best possible use of the available spectral information for both sensors, i.e., one large band in the Meteosat case and four narrow bands well distributed over this spectral interval in the MODIS case, and (2) minimize the uncertainties associated with the required spectral conversion. All three indicators used to characterize the statistical differences between the MODIS and Meteosat products, i.e., the slope of

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the means (full line), the regression line (dashed line) and the primary eigenvector (dotted line), show limited variability around the one-to-one line. The observed statistical differences are largely within the range of the systematic error/uncertainty due to the calibration knowledge (about 6% for Meteosat-7) (Govaerts et al., 2004) and/or model approximations (for instance, the decoupling of the gaseous absorption from the aerosol scattering effects). Figure 9.12 illustrates results from a comparison between the broadband black sky (DHR) albedo products generated, at 30◦ solar angle, by the analysis of the daily radiances collected during the first 10-day period of May 2001 by both GOES West (GOES-10) and GOES East (GOES-8) over the common land regions of the Earth disk that they jointly sample (see top panel in Fig. 9.12). These results illustrate the robustness of the albedo retrieval algorithm since its application yields differences between data sets from adjacent sensors that are well within the range of their estimated uncertainty level (about 10–15% for the GOES sensors) of their broadband albedo products. Figure 9.12 confirms earlier comparison results obtained by analyzing albedo products generated by two adjacent Meteosat sensors (Govaerts et al., 2004). The conclusions drawn from Figs. 9.11 and 9.12 suggest the generation of historical series of surface albedo products based on the exploitation of the fleet of geostationary satellites. Figure 9.13 is a demonstration example of an output from such an initiative which assembles broadband products (DHR at 30◦ Sun zenith angle) retrieved for the first 10-day period of May 2001 from five different satellites, namely GOES West and East, Meteosat-7 and Meteosat-5, and GMS-5. Table 9.1 provides statistics about these retrievals and the estimated uncertainties associated with each satellite retrievals. The measurement error includes both the radiometric uncertainties and approximations in the forward model. The estimated error on the DHR values is then derived from the uncertainty on the retrieved surface parameters. It thus looks feasible to build global albedo products for the last 25 years or so, for those places covered by archived data. These preliminary results open new avenues for the exploitation of geostationary archive data and prototype the fusion of such the generated products.

9.7 Summary The MODIS, MISR and Meteosat algorithms represent three complementary strategies for characterizing land surface reflectance anisotropy and obtaining measures of land surface albedo. Each algorithm makes use of the unique capabilities of its sensor to capture the spectral, spatial, temporal, and angular information necessary to accurately specify the reflective qualities of the underlying surface cover. With more than 6 years of MODIS and MISR observations now available, as well as the opportunity to utilize the historical geosynchronous satellite record, the modeling and data analysis communities enjoy unprecedented access to consistent, high-quality albedo and anisotropy data of the Earth’s land surface.

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Fig. 9.12 Comparison between broadband DHR (30◦ ) values retrieved over the common geographical region covered by both GOES West (GOES-10) and GOES East (GOES-8). The top panel corresponds to the density plot of the two DHR distributions for the period 1–10 May 2001. The bottom panel documents the histogram of the relative differences between the two distributions. The vertical lines colored in blue feature the mean value of these differences (dash-dotted) and one standard deviation from the mean (dashed)

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Fig. 9.13 Top panel: Location of operational geostationary satellites which archive data and are used to derived products shown in the bottom panel. The circles show the 60◦ viewing angle limit. Bottom panel: Illustration of the broadband surface albedo map derived from the application of the geostationary satellite retrieval algorithm on measurements taken simultaneously by GOES-8/10, Meteosat-5/-7 and GMS-5 over the period 1–10 May 2001 Table 9.1 Number of days processed during the 1–10 May 2001 period for each satellite. < Img/day > is the mean number of measurements available per day (note that some of the GOES images did not provide the nominal geographical coverage). is the average measurement relative error, i.e., including both the radiometric error and forward model uncertainty. is the mean estimated DHR relative error Satellite GOES-10 GOES-8 MET-7 MET-5 GMS-5

Nbr days





10 10 10 10 10

22.9 13.7 17.3 16.3 9.9

5.2% 6.8% 7.4% 10.0% 8.4%

12.5% 14.4% 8.7% 10.1% 10.5%

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Acknowledgements Authors Schaaf, Strahler, and Liu are supported by NASA (under grant NNG04HZ14) and by their colleagues on the MODIS Science Team while Martonchik is supported by the MISR Science Team. Authors Pinty, Govaerts, Lattanzio, and Taberner are grateful to the Japan Meteorological Agency (JMA) and the Satellite Services Group of the National Oceanic and Atmospheric Administration (NOAA) for providing the GMS-5 and GOES-8/-10 data, respectively. Their contributions would not have been possible without the support of the Global Environment Monitoring unit of the Institute for Environment and Sustainability at the Joint Research Centre, and EUMETSAT.

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Chapter 10

Modeling and Inversion in Thermal Infrared Remote Sensing over Vegetated Land Surfaces Fr´ed´eric Jacob, Thomas Schmugge, Albert Olioso, Andrew French, Dominique Courault, Kenta Ogawa, Francois Petitcolin, Ghani Chehbouni, Ana Pinheiro, and Jeffrey Privette

Fr´ed´eric Jacob Formerly at Remote Sensing and Land Management Laboratory Purpan Graduate School of Agriculture, Toulouse, France Now at Institute of Research for the Development Laboratory for studies on Interactions between Soils – Agrosystems – Hydrosystems UMR LISAH SupAgro/INRA/IRD, Montpellier, France [email protected] Thomas Schmugge Gerald Thomas Professor of Water Resources College of Agriculture New Mexico State University, Las Cruces, NM, USA Albert Olioso and Dominique Courault National Institute for Agronomical Research Climate – Soil – Environment Unit UMR CSE INRA/UAPV, Avignon, France Andrew French United States Department of Agriculture/Agricultural Research Service US Arid Land Agricultural Research Center, Maricopa, AZ, USA Kenta Ogawa Department of Geo-system Engineering, University of Tokyo Japan Francois Petitcolin ACRI-ST, Sophia Antipolis, France Ghani Chehbouni Institute of Research for the Development Center for Spatial Studies of the Biosphere UMR CESBio CNES/CNRS/UPS/IRD, Toulouse, France Ana Pinheiro Biospheric Sciences Branch, NASA’s GSFC, Greenbelt, MD, USA Jeffrey Privette NOAA’s National Climatic Data Center, Asheville, NC, USA S. Liang (ed.), Advances in Land Remote Sensing, 245–291. c Springer Science + Business Media B.V., 2008


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Abstract Thermal Infra Red (TIR) Remote sensing allows spatializing various land surface temperatures: ensemble brightness, radiometric and aerodynamic temperatures, soil and vegetation temperatures optionally sunlit and shaded, and canopy temperature profile. These are of interest for monitoring vegetated land surface processes: heat and mass exchanges, soil respiration and vegetation physiological activity. TIR remote sensors collect information according to spectral, directional, temporal and spatial dimensions. Inferring temperatures from measurements relies on developing and inverting modeling tools. Simple radiative transfer equations directly link measurements and variables of interest, and can be analytically inverted. Simulation models allow linking radiative regime to measurements. They require indirect inversions by minimizing differences between simulations and observations, or by calibrating simple equations and inductive learning methods. In both cases, inversion consists of solving an ill-posed problem, with several parameters to be constrained from few information. Brightness and radiometric temperatures have been inferred by inverting simulation models and simple radiative transfer equations, designed for atmosphere and land surfaces. Obtained accuracies suggest refining the use of spectral and temporal information, rather than innovative approaches. Forthcoming challenge is recovering more elaborated temperatures. Soil and vegetation components can replace aerodynamic temperature, which retrieval seems almost impossible. They can be inferred using multiangular measurements, via simple radiative transfer equations previously parameterized from simulation models. Retrieving sunlit and shaded components or canopy temperature profile requires inverting simulation models. Then, additional difficulties are the influence of thermal regime, and the limitations of spaceborne observations which have to be along track due to the temperature fluctuations. Finally, forefront investigations focus on adequately using TIR information with various spatial resolutions and temporal samplings, to monitor the considered processes with adequate spatial and temporal scales.

10.1 Introduction Using TIR remote sensing for environmental issues have been investigated the last three decades. This is motivated by the potential of the spatialized information for documenting the considered processes within and between the Earth system components: cryosphere [1–2], atmosphere [3–6], oceans [7–9], and land surfaces [10]. For the latter, TIR remote sensing is used to monitor forested areas [11–14], urban areas [15–17], and vegetated areas. We focus here on vegetated areas, natural and cultivated. The monitored processes are related to climatology, meteorology, hydrology and agronomy: (1) radiation, heat and water transfers at the soil–vegetation–atmosphere interface [18–24]; (2) interactions between land surface and atmospheric boundary layer [25]; (3) vegetation physiological processes such as transpiration and water consumption, photosynthetic activity and CO2 uptake, vegetation growth and biomass production [26–39]; (4) soil processes such as respiration

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and CO2 uptake, evapotranspiration and water depletion, spatio-temporal variability of soil moisture [39–43]; (5) long-term dynamics of land cover [44], land surface radiative budget [45–48], water shortage and drought [49]. TIR remote sensing allow retrieving emissivity and temperature, with various complexity degrees presented in Section 10.2. The remotely sensed information is collected from operational and prospective sensors, listed in Section 10.3. This information is characterized by temporal and spatial dimensions (Section 10.3.1), as well as by spectral and directional dimensions (Section 10.3.2). Then, inferring emissivity and temperature consists of developing and inverting modeling tools, by exploiting the dimensions of the collected information (Section 10.4). Based on TIR fundamentals (Section 10.4.1), simple radiative transfer equations directly link measurements to emissivities and temperatures of interest (Section 10.4.2), and simulation models describe the influence of radiative regime on measurements (Section 10.4.3). However, simple radiative transfer equations must be parameterized, and simulation models require significant information. Further, inversion is not trivial: most of simulation models are not directly invertible, and the numerous parameters to be constrained from remote sensing often make inversion an illposed problem (Section 10.4.4). The several solutions proposed to overcome these difficulties are assessed using validations, intercomparisons, and sensitivity studies (Section 10.5). Current limitations and proposed solutions are presented with an increasing complexity for the temperatures of interest (Section 10.6). Atmospheric perturbations are corrected by inverting modeling tools for atmosphere, and surface brightness temperature measurements are simulated using modeling tools for land surfaces (Section 10.6.1). Surface emissivity effects are removed using simple radiative transfer equations (Section 10.6.2). Reported performances suggest accuracies rather close to requirements, though refinements are necessary. Recovering temperature for the one source modeling of heat transfers is still not trivial, since the required parameterization significantly varies in time and space (Section 10.6.3). Recent studies suggested focusing on more elaborated temperatures: soil and vegetation components, optionally sunlit and shaded, and canopy temperature profile. Their retrieval is a forthcoming challenge, with efforts on measuring, modeling and inversion (Section 10.6.4). The paper ends with forefront investigations about space and time issues in TIR remote sensing: monitoring land processes with adequate spatial scales and temporal samplings, by using available remote sensing observations (Section 10.7).

10.2 Land Surface Emissivity/Temperature from TIR Remote Sensing This section defines the various terms considered in TIR remote sensing, which are related to land surface emissivity and temperature. We focus on their physical definitions and various interests. The corresponding equations are detailed in Section 10.4.

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– Surface brightness temperature is equivalent to the radiance outgoing from the target, by assuming a unity emissivity [50], and corresponds to the basic TIR remote sensing measurement. It is recovered from at sensor measurements performing atmospheric corrections. It can be assimilated, using modeling tools for land surface, into process models such as SVAT and crop models [18, 38, 39, 43]. – Ensemble waveband emissivity is needed to derive radiometric temperature from brightness temperature [50, 51]. It is also useful for retrieving ensemble broadband emissivity, a key parameter for land surface radiative budget [52–54]. – Ensemble radiometric temperature is emissivity normalized [50, 51]; and corresponds to kinetic temperature for an homogeneous and isothermal surface [55]. It is used to estimate surface energy fluxes and water status from spatial variability indicators: the vegetation index / temperature triangle [41, 56–58]; or the albedo / temperature diagram [23, 37, 59, 60]. It is also used for retrieving soil and vegetation temperatures from two source energy balance modeling [19, 24]. – Aerodynamic temperature is air temperature at the thermal roughness length [50]. It is the physical temperature to be used with one source models of surface energy fluxes based on excess resistance [61–63]. These can be SVAT models [39, 64]; or energy balance models [22, 23, 37, 59, 60, 65, 66]. – Soil and vegetation temperatures correspond to kinetic [67] or radiometric [68] temperatures. They are often used for two-source modeling. The latter can be SVAT models [43, 67, 69]; or energy balance models [20, 70, 71]. Retrieving these temperatures requires an adequate estimation of directional ensemble emissivity. – Sunlit and shaded components are refinements of soil and vegetation temperatures. They can significantly differ, according to various factors which drive the thermal regime: the water status, the solar exposure resulting from the canopy geometry and the illumination direction. These components are of interest for understanding canopy directional brightness and radiometric temperatures [58, 72–74]. – Canopy temperature profile, from the soil surface to the top of canopy, is the finest temperature one can consider. Similarly to sunlit and shaded components for soil and vegetation temperatures, this thermal regime is considered for understanding canopy directional brightness and radiometric temperatures, in relation with local energy balance within the canopy [75–78]. The seek accuracies vary from one application to another,according to the sensitivities of process models. For temperature, the goal is accuracy better than 1 K [79]. For emissivity, the goal is absolute accuracy better than 0.01 [80]. Recovering both relies on exploiting the dimensions of the TIR remotely sensed information.

10.3 Available Information from TIR Remote Sensing The four dimensions of the remotely sensed information are temporal and spatial (Section 10.3.1), and spectral and directional (Section 10.3.2). Due to orbital

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rules and technological limitations, current spaceborne sensors cannot provide full information over these dimensions. Further, the latter can be linked, according to the mission objectives: a daily monitoring with sun-synchronous sensor requires a kilometric resolution with an across track angular sampling. Exploratory missions with airborne and ground-based sensors are under progress, for assessing the potential of original remotely sensed information. Table 10.1 provides an overview of the main operational and prospective sensors. We deal here with recent, current and forthcoming US and EU missions.

10.3.1 Temporal and Spatial Capabilities The temporal dimension corresponds to the time interval between consecutive observations. It is of importance for monitoring land surface temperature and related processes: radiative and convective transfers, soil respiration and vegetation physiological activity. The spatial dimension corresponds to the ground resolution of the measurements. It is of importance for the meaning of surface temperature collected over kilometric size pixels which include different land units. Both dimensions are strongly correlated for current TIR spaceborne sensors: high temporal samplings for finer monitoring correspond to coarse spatial resolutions with larger heterogeneity effects, and reversely. The highest temporal samplings are provided by geostationary sensors: 15–30 min with GOES Imager [81] and MSG/SEVIRI [82], corresponding to ground resolutions between 2 and 4 km. Intermediate scales correspond to kilometric resolution sensors onboard sun-synchronous platforms, providing daily nighttime and daytime observations: NOAA/AVHRR [83], ADEOS/GLI [84], and Terra-Aqua/MODIS [85]. A 3 day temporal sampling with a 1 km resolution has been provided by ERS/ATSR-1 and -2, and ENVISAT/AATSR [86]. The highest spatial resolutions are 60 and 120 m from Landsat/TM & ETM [87], and 90 m from Terra/ASTER [88]; with 16-day temporal samplings. ASTER and Landsat/ETM missions have limited lifetimes, with currently no follow on TIR high spatial resolution missions from space. Regarding current possibilities, new spaceborne sensors are demanded, to monitor land processes with adequate temporal and spatial scales. Past missions IRSUTE and SEXTET proposed 40–60 m spatial resolutions with a 1-day revisit [89, 90] and SPECTRA proposed 50 m with 3 days [91]. MTI mission offers a 20 m resolution with a 7-day revisit [92], but the military context restricts the data access. Airborne prospective observations have allowed studying temporal and spatial issues, with metric resolutions and adjustable revisits. Let us cite the airborne missions TIMS [93], DAIS [94], MAS [95] and MASTER [96]; and the airborne-based ReSeDA program [97–99].

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Table 10.1 Nominal characteristics for operational and prospective sensors; in relation with recent, current and forthcoming US and EU missions. VZA means View Zenith Angle, VAA means View Azimuth Angle. Across (respectively along) track means viewing directions in a plan perpendicular (respectively parallel) to the satellite path. Sensor

Daytime Spatial Spectral sampling resolution features

Directional features

Spaceborne MSG SEVIRI

15 mn

3 km

GOES 10 and 12 Imager

30 mn

2–4 km

NOAA 15–17 AVHRR / 3

1 day

Terra-Aqua MODIS

1 MIR: 3.9 µm 1 latitude5 TIR: 8.7, 9.7, 10.8, 12, 13.4 µm dependent VZA 1 MIR: 3.7 µm 2 TIR: 10.8, 12 µm

1 latitudedependent VZA

1 km

1 MIR: 3.8 µm 2 TIR: 11, 12 µm

1 day

1 km

3 MIR: 3.8, 3.95, 4.1 µm 3 TIR: 8.6, 11, 12 µm

Across track VZA: ±55◦

ADEOS GLI

1 day

1 km

1 MIR: 3.7 µm 3 TIR: 8.6, 10.8, 12 µm

ERS-ATSR 1 and 2 ENVISAT-AATSR

3 days

1–2 km

1 MIR: 3.7 µm 2 TIR: 10.8, 12 µm

Along track VZA: 0, 55◦

Landsat 5–7 TM and ETM

16 days

120 m

1 TIR: 11.5 µm

Close nadir VZA

Terra ASTER

16 days

90 m

5 TIR: 8.3, 8.6, 9.1, 10.7, 11.3 µm

Close nadir VZA

TIMS (multispectral)

-

1–5 m

6 TIR: 8.4, 8.8, 9.2, . . . . . . 9.9, 10.7, 11.7 µm

DAIS (multispectral)

-

1–5 m

6 TIR: 8.7, 9.7, 10.5, . . . . . . 11.4, 12.0, 12.7 µm

Across track VZA: ±38◦

MAS / MASTER (multispectral)

-

1–5 m

10 TIR: 7.8, 8.2, 8.6, 9.1, 9.7, . . . Across track . . . 10.1, 10.6, 11.3, 12.1, 12.9 µm VZA: ±40◦

SEBASS (hyperspectral)

-

1–5 m

MIR: [2.5–5.3] µm TIR: [7.6–13.5] µm Spectral resolution > 0.1 µm

Close nadir VZA

Two temperature Box method

-

∼50 cm

1 broadband over [8–13] µm

Nadir VZA

Hyperspectral FTIR BOMEM suite

-

Few cm

Optical spectral range: [2–20] µm Nadir VZA Spectral resolution: 1 cm−1

Goniometric systems

-

Few cm

1 broadband over [8–13] µm

Across track VZA: ±55◦ Across track VZA: ±40◦

Airborne

Across track VZA: ±26◦

Ground-based

VZA ∈ [0–90◦ ] VAA ∈ [0–360◦ ]

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10.3.2 Spectral and Directional Capabilities The spectral dimension corresponds to the number and location of sensor wavebands within the TIR and optionally the MIR domains. The directional dimension corresponds to the number and angular distribution of viewing directions. Both dimensions are used for recovering emissivities and temperatures via modeling tools. The basic spectral configuration corresponds to TM and ETM, with 1 channel. Richer information is provided via two channels with GOES Imager, AVHRR and the ATSR suite; three channels with MODIS and GLI; and five channels with SEVIRI and ASTER. Additional MIR information can be combined with TIR information, to be used with continuous observations from geostationary sensors (SEVIRI, GOES Imager), or day night observations from sun-synchronous sensors (AVHRR, MODIS). The basic directional configuration corresponds to SEVIRI, GOES Imager, TM, ETM, and ASTER; with a single viewing direction. Richer information is collected from across track viewing with AVHRR, MODIS, GLI; and along track viewing with the ATSR suite. Across track viewing allows a daily monitoring, while sampling the angular dynamic within a given temporal window (16 days for MODIS). This is of interest for stable surface properties such as emissivity. For surface temperature which fluctuates, capturing the angular dynamic requires almost simultaneous observations. This is possible with ATSR along track bi-angular observations only, which is limited. Future spaceborne missions will pursue current ones for long-term records: the GOES suite [100], NPOESS/VIIRS following AVHRR and MODIS [101]. MTI provides original information: 2 MIR/3 TIR bands, 0◦ and 50◦ along track. At the airborne level, the spectral dimension has been investigated with multispectral (TIMS, DAIS, MAS & MASTER) and hyperspectral (SEBASS [102]) sensors, and the directional dimension has been assessed with video cameras (see [103] with the ReSeDA program). At the ground level, the spectral dimension has been explored with hyperspectral sensors (FTIR BOMEM [104]), or with broadband radiometers [105–107], and the directional dimension has been examined with goniometric systems [58, 108, 109]. In the context of monitoring land processes, the various types of information presented here are valuable for recovering land surface emissivity and temperature. Using this information requires designing modeling tools and inversion methods, either under development for prospective studies or with operational capabilities.

10.4 Developing Modeling Tools and Inversion Methods Modeling tools aim at forwardly simulating, with different complexities, measured brightness temperature from emissivities and temperatures of interest. Table 10.2 provides an overview of the modeling tools currently used. Based on TIR fundamentals (Section 10.4.1), simple radiative transfer equations directly link measurements

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Table 10.2 Listing of the modeling tools currently used, with an increasing complexity. The second rightmost column gives the related medium, and the rightmost column gives the types of land surface emissivity and temperature currently investigated with each tool. The modeling of atmospheric radiative transfer is considered here in the context of performing atmospheric corrections. Modeling tools

Literature examples

Related medium

Investigated land surface temperatures and emissivities

Simple radiative transfer equations Atmospheric radiative transfer

Eq. 10.6 [81, 178]

Atmosphere

• Brightness temperature (Atmospheric corrections)

Composite surface radiative transfer

Eq. 10.7 [12, 158]

Land surface

• Ensemble emissivity and radiometric temperature

Split Window and Dual Angle

Eq. 10.9 [125, 126]

Soil and vegetation radiative transfer

Eq. 10.10 [68, 127]

Land surface

• Soil and vegetation temperatures

Kernel-driven radiative transfer

Eq. 10.11 [128, 129]

Land surface

• Ensemble emissivity • Soil and vegetation temperatures

Radiative transfer

MODTRAN [134]

Atmosphere

• Brightness temperature (Atmospheric corrections)

Radiative transfer

Prevot’s [139] SAIL [74, 137]

Land surface

• Brightness temperature • Ensemble emissivity • Soil and vegetation temperatures with sunlit and shaded components

Geometric-optics

Kimes’s [141] Caselles’s [143] Yu’s [73]

Land surface

• Brightness temperature • Soil and vegetation temperatures with sunlit and shaded components

Geometric-optics radiative transfer

CUPID [147] Thermo [148] Jia’s [149] DART [76, 77]

Land surface

• Brightness temperature • Canopy temperature profile

Monte Carlo ray tracing

[127, 150, 151]

Land surface

• Brightness temperature • Ensemble emissivity • Soil and vegetation emissivities

Atmosphere and • Ensemble radiometric temperature land surface (atmospheric corrections)

Simulation models

to emissivities and temperatures of interest (Section 10.4.2), and simulation models describe the influence of radiative regime on measurements (Section 10.4.3). Next, inversion methods aim at backwardly retrieving emissivities and temperatures of interest from measurements (Section 10.4.4).

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10.4.1 Fundamentals in TIR Remote Sensing The use of TIR remote sensing to infer the temperatures of interest involves an aerodynamic issue for the related temperature, and a radiative issue for the other temperatures.

10.4.1.1 Aerodynamic Issue Aerodynamic temperature Taero is not radiative-based and cannot be remotely sensed. It is required for one source modeling of surface energy fluxes, since it corresponds to the value of the logarithmic-based air temperature profile Tair (z) at thermal roughness length zoh [110]. For a negligible displacement height, sensible heat flux H is expressed from the air temperature gradient between zoh and reference level zre f : H=

Tair (zoh ) − Tair (zre f ) rah (zoh , zre f )

with

Taero = Tair (zoh )

(10.1)

where rah (zoh , zre f ) is aerodynamic resistance for heat between zoh and zre f [111]. Due to larger resistance for heat transfers, zoh is lower than mechanical roughness length zom [112]. The link between both is the aerodynamic kB−1 parameter [113]:

zom kB−1 = ln (10.2) zoh The physical meanings of Taero and zoh are equivocal. Taero is an effective temperature for heat sources that are soil and vegetation [114]. zoh is an effective level for which Tair = Taero . Their retrieval from remote sensing is not trivial (Section 10.6.3). Nevertheless, Taero can be unequivocally derived from soil and vegetation temperatures Tsoil and Tveg , by merging one source and two source modeling [20, 115]: Taero =

Tsoil ra,soil

T

Tair (zre f ) rah 1 1 ra,veg + rah

veg + ra,veg +

1 ra,soil

+

(10.3)

where ra,soil (respectively ra,veg ) is aerodynamic resistance from the soil (respectively vegetation) to zom , and rah is aerodynamic resistance from zom to zre f [111].

10.4.1.2 Radiative Issue Apart from aerodynamic temperature, the land surface temperatures inferred from TIR remote sensing are radiative-based. Then, fundamentals deal with the TIR radiative regime within atmosphere and over land surfaces. This includes three mechanisms which drive the wave matter interactions: emission, absorption, and

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scattering. Emitted radiance L(λ , θ , T ) from a natural object at a kinetic temperature T is written: L(λ , θ , T ) = ε (λ , θ ) B(λ , T ) = ε (λ , θ )

π



C1 λ −5    exp TC2λ − 1

(10.4)

λ is the monochromatic wavelength. θ is the emission direction. B(λ , T ) is the blackbody emitted radiance, expressed from Planck’s Law. C1 and C2 are first and second radiative constants. Emissivity ε (λ , θ ) is the conversion factor from thermodynamic to radiative energy, lower than 1 for natural objects. This so-called e-emissivity definition is linked to emission mechanisms, since it is the ratio of the actual to the blackbody emitted radiances for the same kinetic temperature. Under local thermodynamic equilibrium, Kirchhoff’s Law assumes emissivity and absorptivity are equal. For opaque elements, emissivity is then linked to hemisphericaldirectional reflectance ρ (λ j , θ ): ε (λ j , θ ) = 1 − ρ (λ j , θ )

(10.5)

ρ (λ j , θ ) is the average of bidirectional reflectance over illumination angles [116]. This so-called r-emissivity definition is derived from Kirchhoff’s Law, and therefore linked to reflection mechanisms. Finally, emitted radiance from a given element can be reflected by other elements, inducing changes in radiation path, called scattering effects. Within the atmosphere, scattering is negligible: the radiative regime is driven by the temperature and density of absorbers and emitters (water vapor, CO2 , O3 , . . .). A clear atmosphere behaves as an horizontally homogeneous medium: the radiative regime primarily depends on vertical profiles for temperature and density of absorbers and emitters (Fig. 10.1). Over heterogeneous land surfaces with structured patterns, the radiative regime is more complex than within atmosphere: soil and vegetation act as emitters, absorbers and scatterers for canopy and atmospheric irradiances. Additional effects are surface and volume scatterings (Fig. 10.2). Surface scattering corresponds to shadowing effects for a geometric medium, with sunlit and shaded areas. Volume scattering corresponds to reflections between soil and vegetation: radiation is trapped within the canopy. TIR remotely sensed measurements result from the processes discussed above. Sensor brightness temperature is driven by vertical profiles for temperatures and densities of atmospheric constituents. Surface brightness temperature results from the radiative regime over a heterogeneous and non isothermal area. Then, emissivity and kinetic temperature are equivocal: the canopy acts as an effective medium with ensemble emissivity and radiometric temperature [50]. Besides, e- and r-emissivities differ according to vegetation amount, since spatial averaging for e-emissivity includes emitted radiance as an additional weighting factor [50, 117]. Due to its simpler formulation, r-emissivity is preferred [68, 71, 74, 118–120]. Further, the measured brightness temperature results from emission, but also from absorption and scattering of canopy and atmospheric irradiances. This induces spectral and directional variations, driven by (1) radiative properties of soil and vegetation

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Fig. 10.1 Atmospheric TIR radiative regime for an off nadir propagation. The key processes to be considered for atmospheric corrections are emission and absorption by atmospheric constituents. Within a horizontally homogeneous atmosphere, the radiative regime depends on the vertical fields of temperature and density for emitters and absorbers. Regardless of considered layer (zi or zk ), radiative regime is driven by atmospheric absorption (1), atmospheric emission (2), and surface emission through atmosphere transmission (3). (Adapted from [264].)

(reflectance and emissivity), (2) surface scattering with sunlit and shaded areas, and (3) volume scattering with the cavity effect. These three factors induce ensemble emissivity is anisotropic, with values greater than that of vegetation as the latter quantitatively increases [118, 121, 122]. Various modeling tools have been developed to simulate sensor and surface brightness temperature measurements. The first way is using simple radiative transfer equations for directly linking measurements to emissivities and temperatures of interest. The second way is using simulation models for understanding the influence of the TIR radiative regime on the measured brightness temperature.

10.4.2 Simple Radiative Transfer Equations Simple radiative transfer equations directly link TIR measurements to emissivities and temperatures of interest. Their advantages are linearity and simplicity, but most of them are limited to homogeneous media by assuming turbidity and azimuthal isotropy.

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Fig. 10.2 Surface (or geometric) and volume (or volumetric) scattering. Surface scattering induces shadowing effects with hotter and cooler elements. Volume scattering induces an increase of brightness temperature by adding a component to emission. (Adapted from [129].)

Measured brightness temperature at the sensor level Tbrs is linked to surface brightness temperature Tbs via the atmospheric radiative transfer equation:   B (λ j , Tbrs (θ , λ j )) = B (λ j , Tbs (θ , λ j )) τa (θ , λ j ) + B λ j , Tba↑ (θ , λ j ) (10.6)

θ is the view zenith angle. λ j is the equivalent waveband over the sensor channel j [123]. B(λ , T ) is the blackbody emitted radiance, expressed from Planck’s Law (Eq. 10.4). τa is the atmospheric transmittance, vertically integrated between the surface and the sensor. B(λ j , Tba↑ ) is the atmospheric upward radiance towards the sensor. Surface brightness temperature is expressed as the sum of canopy emission and scattering of atmospheric irradiance, via the composite surface radiative transfer equation:

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B(λ j , Tbs (θ , λ j )) = ε (λ j , θ ) B(λ j , Trad (θ )) + (1 − ε (λ j , θ )) B(λ j , Tba↓ (λ j )) (10.7) B(λ j , Tba↓ ) is the hemispherical average of atmospheric downward radiance. ε (λ j , θ ) and Trad (θ ) are ensemble emissivity and radiometric temperature. Ensemble emissivity can be expressed from emissivities of soil εsoil (λ j ) and vegetation εveg (λ j ), with the optional inclusion of a correction term d ε for the cavity effect [124]:

ε (λ j , θ ) = Fsoil (θ ) εsoil (λ j ) + Fveg (θ ) εveg (λ j ) + 4 d ε Fveg (θ ) Fsoil (θ ) (10.8) Fsoil (θ ), Fveg (θ ) are directional gap and cover fractions, with Fsoil (θ ) = 1 − Fveg (θ ). Brightness temperature measured from space can be linked to emissivity and radiometric temperature by merging Eqs. 10.6 and 10.7. Another possibility is simultaneously considering atmospheric and surface effects: Split Window (SW) and Dual Angle (DA) methods directly express radiometric temperature Trad as a spectral or angular difference between two brightness temperatures Tbrs at the sensor level [125, 126]: rs rs rs rs rs 2 Trad = Tb1 + A(Tb1 − Tb2 ) + B(Tb1 − Tb2 ) +C

ε1 + ε2 + D(ε1 − ε2 ) + E (10.9) 2

ε is surface emissivity. A, B, C, D, E are empirical coefficients. Indices 1 and 2 are two spectral channels for SW method, or two view zenith angles for DA method. The angular differencing uses variations in atmospheric transmittance between different paths for two view zenith angles. The spectral differencing uses variations in atmospheric transmittance due to different water vapor absorptions for two spectrally close channels. The emission term of Eq. 10.7 can be split into soil and vegetation components, which yields the soil and vegetation radiative transfer equation [68, 119, 127]: ε (λ j , θ ) B (λ j , Trad (θ )) = τ can (θ ) εsoil (λ j ) B(λ j , Tsoil ) + ω (θ , εveg (λ j )) B(λ j , Tveg )

(10.10)

Tsoil and Tveg are soil and vegetation radiometric temperatures [68]. τ can (θ ) and ω (θ , εveg (λ j )) are vegetation directional transmittance and fraction of emitted radiation. The angular effects can also be described with linear kernel driven approaches, by expressing the directional emission as a linear combination of generic shapes [128]:

ε (λ j , θ ) B (λ j , Trad (θ )) = N

∑ βi (λ j ) Ki (Tveg , Tsoil , εveg (λ j ), εsoil (λ j ), θ , θs , ϕ − ϕs )

(10.11)

i=1

θs is the solar zenith angle. ϕ − ϕs is the relative azimuth between illumination and viewing directions. βi,λ j are weighting coefficients. Kernels Ki describe gray body isotropy, volume scattering, and surface scattering. Various kernel formulations may be proposed, by linearizing different sets of complex equations. Kernel driven approaches are also used to derive ensemble r-emissivity from accurate

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hemispherical - directional reflectance (Eq. 10.5): [129] expressed TIR BRDF as a linear combination of generic shapes, following previous works over the solar domain [130–132].

10.4.3 Simulation Models Simulation models mimic the TIR radiative regime within atmosphere and canopies, to understand spatial, spectral and directional behaviors of brightness temperature measurements. These models are classified here via an increasing complexity: radiative transfer, geometric-optics, geometric-optics/radiative transfer, and ray tracing. Radiative transfer models are designed for turbid media (atmosphere, homogeneous canopies). Assuming turbidity and azimuthal isotropy, they split the medium into a finite layer number, and account for volume scattering between layers. For the atmosphere, volume scattering is negligible, and each layer is described with temperature and densities of absorbers and emitters. For canopies, soil and vegetation layers are described with temperature; and with densities of absorbers, emitters and scatterers, derived from LAI and LIDF. Brightness temperature is simulated using the stream concept: transmittance, upward and downward radiances are computed for each layer, and vertically integrated (see MODTRAN for atmosphere [133, 134] and SAIL for canopy [68, 74, 135–137]. Simulations can also be probabilistic calculations for photon interception, deduced from the directional gap fraction of each layer [118, 138, 139]. Geometric-optics models are designed for structured patterns over land surfaces, such as row crops of cotton or maize. Considering vegetation as an opaque medium, they account for surface scattering with shadowing effects. Sunlit and shaded areas are described via their cross sections, derived from canopy geometry (vegetation height, row size, etc.), illumination and viewing directions, and directional gap fraction within and between rows. Canopy brightness temperature is computed from the resulting spatial distribution of temperature [73, 121,140–143]. The finest radiosity models are geometric-optics/radiative transfer models, designed for complex land surfaces. By accounting for both volume and surface scattering, they are appropriate to vegetation patchworks. They can conjugate a radiative transfer and a geometric-optic module [144, 145]. They can be more complex, such as 3-Dimensional mock-ups based models. This allows a finer description of the radiative regime within canopies, but requires significant information about the micro-scale conditions. Examples are CUPID [146, 147]; Thermo [72, 148]; Jia’s model [149], and DART [76, 77]. Further, accounting for convective and energetic transfers allow understanding their influence on the radiative regime, such as with DART-EB [78]. The finest modeling degree is Monte Carlo ray tracing, which stochastically calculates photon trajectories within turbid or geometric atmosphere and canopies. A photon is tracked from birth (emission or penetration within medium) to death (absorption or escape from medium), with scattering based on probabilistic wave

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matter interactions. Millions of simulations describe spectral, directional and spatial behaviors. Ray tracing is used to assess the influence of multiple scattering on spatial aggregation and angular dynamics, over heterogeneous and non isothermal land surfaces [127, 150, 151].

10.4.4 Inversion Methods Retrieving variables from measurements is an inverse problem. Given a set of m measurements M for a physical system, with k known parameters K and p unknown parameters P to be retrieved, direct F and inverse F −1 problems are written [152]: ⎛⎡ ⎤ ⎤ ⎡ ⎞ ⎞ ⎛⎡ ⎤ ⎡ ⎤ M1 M1 P1 P1 ⎢ .. ⎥ ⎟ ⎟ ⎜⎢ . ⎥ ⎢ . ⎥ −1 ⎜⎢ . ⎥ ⎣ . ⎦ = F ⎝⎣ .. ⎦ , [K1 · · · Kk ]⎠ ⇐⇒ ⎣ .. ⎦ = F ⎝⎣ .. ⎦ , [K1 · · · Kk ]⎠(10.12) Mm

Pp

Pp

Mm

Inversion is possible if there are more independent equations than unknowns (m ≥ p). Direct inversion analytically writes the inverse problem. This is possible for simple radiative transfer equations (Section 10.4.2), but not for most simulation models (Section 10.4.3). For the latter, indirect inversion numerically sets parameters such as simulations agree with observations [153]. It has been improved for accuracy and rapidity, by calibrating neural networks, lookup tables, genetic algorithms or regression trees [152, 154]. Inversion can be a well-posed problem, when solving an overdetermined equation system using optimization techniques. However, it is usually an ill-posed problem, with several parameters to be constrained from few observations. Proposed solutions use a priori information about soil and vegetation properties, or parameter ranges [152, 155, 156]. Inversion over the TIR domain is not as developed as over the solar domain. This results from (1) additional micrometeorological complex influences, and (2) the lack of high resolution data. Atmospheric simulation models have been inverted calibrating neural networks [51], SW and DA methods (Eq. 10.9) [125, 126], or the atmospheric radiative transfer equation (Eq. 10.6) [157, 158]. Over land surfaces, simulation models have been assessed in the forward mode [72–74, 77, 144]. No investigation was found about their indirect inversion, but they can serve as references for parameterizing simple radiative transfer equations which are directly invertible. Thus, various formulations have been assessed for the soil and vegetation radiative transfer equation (Eq. 10.10), optionally accounting for multiple scattering and non linearities [68, 71, 118, 119, 127]. Further, inverting simple radiative transfer equations is often an ill-posed problem. For instance, inverting the composite surface radiative transfer equation (Eq. 10.7) from N multispectral observations includes N emissivities and radiometric temperature. Similarly, inverting the soil and vegetation radiative transfer equation (Eq. 10.10) or linear kernel driven approaches (Eq. 10.11) from multiangular observations requires angular parameters: ensemble, soil and vegetation emissivities; vegetation transmittance.

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10.5 Assessing Modeling Tools and Inversion Methods Modeling tools and inversion methods have been assessed experimentally through validation exercises, and theoretically via sensitivity studies. Validation exercises have been conducted over databases collected in the framework of various international programs such as FIFE [159], EFEDA [160], HAPEX [161], ReSeDA [97], JORNEX [162], FLUXNET [163], DAISEX [164], SALSA [165], SMACEX [166]. Assessments over these various datasets allow accounting for different biomes and climates. Some exercises were ground-based [73, 104, 145]. Most of them were airborne-based [94, 96, 103, 157, 167–169,170–174], for assessments in actual conditions by reducing spatial heterogeneity effects. Few validations were conducted using spaceborne observations with hectometric resolutions [175–179]; and with kilometric ones over areas almost homogeneous [180–182]. Original exercises based on classifications were designed for kilometric scale heterogeneities [126, 183], while new improvements for the solar domain should be implemented over the thermal one [184]. Complementary to validations, intercomparisons are now feasible thanks to multisensor missions such as Terra. This allows accounting for larger panels of environmental situations [158]. Validations and intercomparisons have also been performed using simulated datasets. This allow considering more conditions than measured datasets, and focusing on physics modeling without measurement intrinsic errors [81, 82, 126, 185]. Simulated datasets are necessary when dealing with elaborated temperatures: aerodynamic, soil and vegetation, sunlit and shaded components, and canopy temperature profile [68, 71, 73, 76, 118]. Indeed, validating the latter using measured datasets is not trivial, since the corresponding ground-based measurements are difficult to implement. Additionally to validations and intercomparisons, sensitivity studies allow assessing information requirements such as accuracies on remotely sensed information, medium structural and radiative properties. Examples are (1) accuracy on atmospheric status for retrieving brightness temperature [171, 178], (2) accuracy on observations, atmospheric status and land use for recovering ensemble emissivity and radiometric temperature [12, 157, 158, 169, 182, 186–188], (3) accuracy on canopy structural parameters and radiative properties for deriving soil and vegetation temperatures [68, 118, 189]. Finally, sensitivity studies of simulation models provide valuable information about the pertinent parameters for inversion [73, 76], with innovative approaches over the solar domain based on adjoint models (Baret et al., this issue).

10.6 Current Capabilities and Future Directions From the basic materials presented before, we focus now on current investigations, via an increasing temperature complexity. Success and failures suggest future directions.

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10.6.1 Surface Brightness Temperature Surface brightness temperature is derived from that at the sensor level by inverting modeling tools for atmosphere. It is simulated using modeling tools for land surfaces. In both cases, these tools are simple radiative transfer equations or simulation models.

10.6.1.1 Atmospheric Radiative Regime and Related Corrections Atmospheric corrections for the retrieval of surface brightness temperature can be performed inverting simulation models, via the calibration of the atmospheric radiative transfer equation (Eq. 10.6) for a given atmosphere [12, 81, 157, 158, 171, 172, 177, 178]. An operational context faces two challenges: reducing computation time to process millions observations, and accurately characterizing the atmospheric status. To reduce by a third-order computation time for simulation models without accuracy degradation, [190] implemented correlated-K methods, by quickly integrating waveband atmospheric absorption and emission. Predictor-based models accurately compute the latter for a range of reference profiles, to next differencing current ones and nearest predictors [191]. Multilayer computation based on water vapor continuum absorption can replace simulation models, with an accuracy degradation lower than 1 K [81]. Computation time can also be reduced via inversion by including a range of atmospheres into the simulation set. Expressing transmittance and upwelling radiance of Eq. 10.6 from atmosphere water vapor content and mean temperature yields an accuracy degradation lower than 2 K [180]. Neural networks can replace Eq. 10.6 considering atmospheric profiles and view zenith angle, with an accuracy degradation lower than 0.5 K [186, 192]. The atmospheric status can be well documented using ancillary information: measured profiles allow reaching a 1 K accuracy [171, 172, 177, 178], but meteorological networks are not dense enough for regional inversion. One alternative is profile simulation from meteorological models [193, 194]. Such information is soon available with a 3 h sampling, and a 0.25◦ latitude/longitude griding to be re-sampled to sensor resolutions via interpolation procedures [12, 195]. The relief influence is handled using digital elevation models, now available with decametric resolutions and metric accuracies [196]. Also, the TIR observations to be corrected can inform about the atmospheric status. Atmosphere absorption and emission can be retrieved from multispectral and hyperspectral observations, using variabilities of atmospheric properties [80, 197]. Thus, water vapor content was adjusted from ASTER multispectral observations, such as emissivity spectrum is flat over vegetation or water [185]. It was also inferred from the ATSR-2 SW channels with a 0.2 g. cm−2 accuracy, using the SWVCR which relies on the spatial variability of SW surface brightness temperatures [198]. Solar or TIR observations collected onboard the same platform also provide coincident information about the atmospheric status. [199] expressed water vapor

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content as a polynomial of MODIS near infrared radiance ratios, with a 0.4 g. cm−2 accuracy. Atmospheric sounders allow inferring profiles of temperature and water vapor density, using Eq. 10.6 or neural networks [3, 4]. Previous sounders such as TOVS permitted to reach a 0.4 g. cm−2 accuracy on water vapor content [200]. New sounders such as IASI [201], with finer spectral samplings and spatial resolutions, should provide accuracies better than 1 K and 10% for atmospheric profiles of temperature and humidity.

10.6.1.2 Land Surface Radiative Regime and Related Measurements Surface brightness temperature is simulated using simple radiative transfer equations or simulation models. The former provide easy and efficient solutions for assimilating TIR remote sensing data into land process models. The latter are fine and accurate solutions for understanding TIR remotely sensed measurements. To constrain land process model parameters, surface brightness temperature can be simulated using simple radiative transfer equations coupled with SVAT models. [39] coupled the composite surface radiative transfer equation (Eq. 10.7) with a crop and a one source SVAT model. The latter calculated ensemble radiometric temperature by closing the surface energy budget. R-emissivity was estimated using the SAIL TIR version of [136], documented by the crop model for vegetation structural parameters. Similarly, [67] coupled the soil and vegetation radiative transfer equation (Eq. 10.10) with a two source SVAT model. The latter calculated soil and vegetation temperatures by closing the energy budget for each, while setting soil and vegetation emissivities to nominal values. Calculating surface brightness temperature from simulation models requires information about vegetation structure (row crop, LAI, LIDF, cover fraction), soil and vegetation radiative properties (emissivity, reflectance), and thermal regime (canopy temperature distribution). The latter can be derived from a SVAT model, which solves local energy budget according to meteorological conditions (solar position, wind speed, air temperature), vegetation status (leaf stomatal resistance), and soil moisture. Then, simulation models mimic the radiative regime using more or less complex descriptions of the thermal regime: a unique vegetation temperature [73], soil and vegetation temperatures with optional sunlit and shaded components [74, 137], additional vegetation layer temperatures for specific crops [145], or canopy temperature profiles [78]. Simulation models are currently under development, verification and analysis [73, 74, 76, 78, 144, 145]. Current investigations focus on spectral behaviors [120], but especially on directional effects which allow normalizing multiangular observations (Fig. 10.3). For instance, [58, 72] angularly normalized water stress indices over row structured crops. Similarly, [202] normalized across track observations from sun-view geometry effects, for a daily monitoring at the continental scale.

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10.6.1.3 Partial Conclusions The various methods developed to perform atmospheric corrections are of interest, since they were designed for optimizing the collected information according to sensor configurations. Measured or simulated profiles are tributary to their representativeness, and coincident information relies on strong assumptions. Despite these limitations, significant progresses were made the last decades, with accuracies now close to 1 K. Current investigations focus on refinements rather than new developments. Simulating brightness temperature is ongoing for describing brightness temperature measurements, according to the various land surface behaviors: geometric like, radiative transfer like, or both. Validation results emphasized good performances with accuracies close to 1 K, though significant documentations are required about thermal regime, medium structure and radiative properties. Such simulation models will be of interest for future designs of inversion methods, conjointly to the solar domain (Section 10.4.4).

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10.6.2 Ensemble Emissivity and Radiometric Temperature Ensemble radiometric temperature is derived by directly inverting composite surface radiative transfer equation (Eq. 10.7), or indirectly inverting simulation models via differencing equations (Eq. 10.9). The first way is two-step based and requires previous atmospheric corrections. The second way is one-step based by simultaneously correcting atmosphere and surface effects. In both cases, performances depend on characterizing these effects. Inverting Eq. 10.7 is an ill-posed problem, with N equations from channel measurements and N + 1 unknowns being channel emissivities and radiometric temperature. Proposed solutions consist of adding an N + 1 equation. They are reported here via an increasing amount of information, according to the spectral, directional and temporal dimensions. 10.6.2.1 Single-Channel TIR Instantaneous Observations Radiometric temperature is derived from single channel observations using two step approaches. After atmospheric corrections, inverting the composite surface radiative transfer equation (Eq. 10.7) requires estimating waveband emissivity. The latter is inferred using in-situ observations, nominal values proposed by literature, or solar remotely sensed observations. This have been investigated for ground-based and airborne sensors during field experiments, and for spaceborne sensors such as the Landsat TM series. Considering ensemble emissivity increases with vegetation amount, it can be linked to NDVI [203], or to cover fraction (Eq. 10.8) neglecting spatial variabilities for soil and vegetation emissivities [177, 199]. However, low correlations were observed between AVHRR emissivities and cover fraction [188]; and between ASTER broadband emissivity and MODIS solar albedo [46]. Indeed, the link between emissivity and vegetation amount depends on canopy structure, cavity effect, and optical properties of soil and vegetation [136]. Besides, emissivity may decrease with the vegetation amount, according to the type of soil and the vegetation water status [120]. Good results were reported with TM and DAIS (1 K over semi-arid agricultural areas [174, 177]), but the use of in situ information at the local scale raises the question of method applicability. A promising way is using additional MIR data, which contain information on water content. For optimizing the temporal monitoring, another possibility is deriving single channel emissivity from multispectral ones, by conjointly using different sensors such as Landsat and ASTER. However, this is contingent upon the temporal stability of surface conditions between consecutive satellite overpasses. 10.6.2.2 Dual-Channel and Dual-Angle TIR Instantaneous Observations Radiometric temperature is recovered from dual channel and dual angle observations using SW and DA one step approaches, which require accounting well for

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atmospheric and surface effects [125, 126]. Most investigations deal with the SW method, since multispectral observations are more usual than multiangular ones. Various versions have been proposed for Eq. 10.9: linear or quadratic forms (B = 0 or B = 0), optional inclusion of emissivity (C = 0 or C = 0, D = 0 or D = 0), expressing coefficients from atmospheric water vapor content. Larger freedom degrees perform better [125, 126, 174, 183, 204]. Wavebands around 11 and 12 µm are the most appropriate for SW and DA assumptions, since they correspond to low variations of emissivity, spectrally and spatially [172, 174]. Calibration relies on simulations from emissivity spectral libraries and atmospheric radiative transfer [82, 125, 126, 204]. Operational use requires documentation. Atmospheric water vapor content is inferred from climatological database [183], the SWVCR [198] or near infrared radiance ratios [199]. Emissivities are derived from classifications [181, 182, 205], or from Eq. 10.8 with nominal values for soil and vegetation emissivities [172, 199]. Several validation exercises reported accuracies better than 1 K. Excellent results were obtained from TIMS without a priori information [172]. Using classificationbased knowledge of emissivity can perform well [181, 182], though significant subclass variabilities were observed [206, 207]. However, a 1 K accuracy usually requires local information on surface conditions for emissivity effects. Further, the lack of such information can induce errors up to 3 K [125, 126, 174, 183, 199].

10.6.2.3 Multispectral and Hyperspectral TIR Instantaneous Observations Radiometric temperature is derived from multispectral and hyperspectral observations using two step approaches. After atmospheric corrections, the ill-posed problem can be solved using either a priori information, or the spectral variability captured over the whole TIR range. This last possibility is very different from the two channel SW differencing which aims at avoiding emissivity variations. For multispectral observations, the NEM approach sets maximum emissivity to a nominal value [208], where the latter can be derived from Eq. 10.8 using a priori information about soil and vegetation emissivities [173]. The adjusted ANEM relies on land use [168, 170], and the MIR NEM is extended to MIR observations [209]. Rather than using a priori information, other approaches aim at benefiting the variability captured from multispectral and hyperspectral data, the latter providing finer spectral samplings. The TES algorithm derives minimum emissivity from the spectral variations, via an empirical relationship verified over most land surfaces for the TIR and the MIR domains [104, 157, 210–212]. Capturing larger variabilities with hyperspectral data increase TES accuracy up to 0.5 K [104]. To derive absolute emissivity from relative spectral variations, the alpha residuals logarithmically linearize Planck’s equation, with an optional improvement based on Taylor expansion for hyperspectral observations [213]. Taylor expansion also provides derivative approaches, such as the “Grey Body” method [123]. Finally, multispectral and hyperspectral observations are useful for deriving broadband emissivity via NTB conversions [52, 54, 207, 214].

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Fig. 10.4 Validation against sample-based laboratory measurements (squares), of ASTER/TES emissivity retrievals (circles), for eleven days over a gypsum site at the White Sands National Monument in New Mexico. TES derived emissivity spectra were averaged over the 11 acquisitions, where the corresponding standard deviation ranges from 10−3 to 10−2 . (From [265].)

Several validation exercises reported 1 K accuracies for NEM, with or without a priori information [168, 170, 173]. Good results were obtained for the TES algorithm (Fig. 10.4), with accuracies better than 0.01 on emissivity [176] and 1 K on temperature [173]. Similar performances were reported by [158] when intercomparing ASTER/TES and MODIS/TISIE retrievals (Fig. 10.5, the TISIE concept is presented below).

10.6.2.4 Multispectral MIR and TIR Consecutive Observations Solving the ill-posed problem to invert Eq. 10.7 is also possible using temporal series from geostationary or sun-synchronous daytime/nighttime observations. Assuming emissivity is stable between consecutive observations yields more equations than unknowns. Then, investigations rely on using TIR observations only [215], or MIR/TIR observations [12, 186, 188, 216]. TTM is a two step approach for inverting Eq. 10.7 over TIR consecutive observations [217]. Assuming surface emissivity is constant yields 2N equations for N + 2 unknowns: N channel emissivities and two radiometric temperatures. Then, two channels are enough for solving the ill-posed problem. TTM performs better

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Fig. 10.5 Intercomparison, over a Savannah landscape (Africa) and a semiarid rangeland (Jornada), of surface radiometric temperature retrievals from the MODIS/TISIE and ASTER/TES algorithms. Differences were lower than 0.9 K. (From [158].)

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with the SEVIRI finest temporal sampling, and with observations near daily temperature extrema [187, 215]. TISIE is a two step approach for inverting Eq. 10.7 over TIR and MIR daytime/nighttime observations. Raising emissivity ratios to specific powers yields relative variations independent of radiometric temperature. Assuming TISIE are stable between consecutive observations, MIR r-emissivities can be retrieved, and next TIR ones. Various TISIE versions were designed for AVHRR, MODIS, SEVIRI [12, 186, 188, 218]. Day Night Pair is a one step approach for inverting both Eqs. 10.6 and 10.7 over TIR and MIR daytime/nighttime observations. The system of 2N equations with N + 2 unknowns can be solved with k additional unknowns, as long as k ≤ N − 2. Thus, the 7 MODIS channels allow recovering five unknowns about atmospheric and surface effects [216]. The accuracies reported for these methods range from 0.5 to 2.5 K, and are slightly worse for TTM. They correspond to sensitivity studies for TTM and TISIE [186–188], to validation exercises over various study sites for Day Night Pair (Fig. 10.6) [181, 182], and to intercomparisons against ASTER/TES retrievals for TISIE [158].

10.6.2.5 Partial Conclusions Radiometric temperature is derived by indirectly inverting simulation models through differencing equations (Eq. 10.9), or directly inverting simple radiative transfer equations (Eqs. 10.6 and 10.7). Solving the ill-posed problem depends on

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the available remote sensing information. A priori information is needed to obtain good results with instantaneous single channel or dual channel / dual angle data. It can be avoided with more remote sensing information: instantaneous TIR and MIR data, instantaneous multispectral TIR data, or temporal series with dual channel data. Similarly, more surface and atmospheric parameters can be recovered with a larger amount of remotely sensed information. Reported accuracies have increased these last years, and are now closer to that required for further applications, i.e., 1 K. For instance, differences between retrievals from ASTER/TES and MODIS/TISIE were found lower than 0.9 K, though both methods differ in terms of using spectral, directional and temporal information [158]. However, ASTER/TES, MODIS/Split Window and MODIS/Day Night Pair were found very different over Northern America [206]. Current efforts are refinements rather than new concepts: disaggregation methods should allow benefiting the synergy between IASI hyperspectral and AVHRR kilometric sensors onboard METOP. Then, the next challenge is retrieving more elaborated temperatures, discussed below.

10.6.3 Aerodynamic Temperature Aerodynamic temperature Taero and thermal roughness length zoh are equivocal variables which cannot be directly recovered from remote sensing (Section 10.4.1). Therefore, investigations have aimed at substituting aerodynamic temperature by radiometric temperature Trad , by parameterizing a correcting factor in the sensible heat flux expression (Eq. 10.1). The physical meaning of sensible heat flux (Eq. 10.1) can be preserved using the Taero − Tair (zre f ) , empirically expressed from LAI [62]. Howmultiplicative factor Trad − Tair (zre f ) ever, studying this factor from simulations and measurements for growing sparse vegetation showed significant variations according to meteorological and surface conditions [63]. The correction factor can also be included in the kB−1 parameter (Eq. 10.2), which is then called thermal kB−1 [113]. It includes corrections for (1) the difference between thermal and mechanical roughness lengths, and (2) the difference between radiometric and aerodynamic temperatures. According to environmental conditions, thermal kB−1 varies from a vegetation type to another, and up to 100% in relative terms [113, 219]. Parameterizations based on near surface wind speed and temperature gradients depend on sensible heat flux [220]. Overall, formulating the thermal kB−1 seems almost impossible, since it is driven by several factors which vary in time and space: vegetation structure and water stress, meteorological conditions, canopy temperature profile and solar position [221–229]. A potential way for characterizing the kB−1 parameter would be multiangular TIR remote sensing [230]. However, using this information for deriving soil and vegetation temperatures seems more pertinent. First, these temperatures are

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functionally equivalent to aerodynamic temperature (Eq. 10.3). Second, they provide information for monitoring vegetation photosynthesis and soil respiration.

10.6.4 Directional Emissivity and Soil/Vegetation Temperatures Single directional radiometric temperature can be split into soil and vegetation components by closing energy balance for each. However, this relies on strong assumptions about vegetation water status [231–233]. The promising approach is then using multiangular TIR observations [20, 68, 71, 118, 119, 189]. No literature was found about retrieving soil and vegetation temperatures by inverting simulation models over multiangular data. Nevertheless, such models have been used for parameterizing the soil and vegetation radiative transfer equation which is directly invertible (Eq. 10.10). These parameterizations were designed considering the [8–14] µm spectral range. 10.6.4.1 Parameterizing the Soil/Vegetation Radiative Transfer Equation Inverting Eq. 10.10 requires estimating the involved parameters (ensemble emissivity ε (λ j , θ ), vegetation transmittance τ can (θ ), and vegetation fraction of emitted radiance ω (θ , εveg (λ j ))), with optional simplifications for easier use. Various complexity degrees have been proposed, listed in Table 10.3 (P1–P8). This introduces two new parameters. Hemispherical gap fraction σ f is directional gap fraction integrated over illumination angles, to account for atmospheric thermal irradiance down to the soil via the vegetation. The cavity effect coefficient α is the ratio of canopy to vegetation hemispherical-directional reflectance, to account for radiation trapping within the canopy. The finest parameterization (P1), proposed by [118], accounts for multiple scattering and cavity effect. The latter, which does not depend on LAI, was previously calculated as a function of LIDF and view zenith angle, by using the probabilistic simulation model from [139]. Similarly, [127] introduced effective directional gap ef f ef f ef f (θ ) fractions (P2). Fsoil (θ ) included single scattering of soil (θ ) and cover Fveg Fsoil ef f emission by vegetation. Fveg (θ ) included single scattering of vegetation emission by soil and vegetation. Half complex parameterizations (P3–P5) account for multiple scattering, with optional linearizations [68, 71]. The simplest parameterizations (P6–P8) do not account for cavity effect nor multiple scattering. They differ by their linearization degrees, and their assumptions about soil and vegetation emissivities [71, 119, 189]. Some of these parameterizations were assessed in direct mode for simulating directional ensemble emissivity and radiometric temperature [68]. Apart from simplest versions, most provided close results for directional canopy emissivity, with discrepancies lower than 0.01. For radiometric temperature, all provided similar results, with differences lower than 1 K. Next, differences decreased with atmospheric irradiance which compensates emission (Eq. 10.7). However, this is minor under

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Table 10.3 Listing of existing parameterizations (P1–P8) for the soil and vegetation radiative transfer equation (Eq. 10.10), with a decreasing complexity. The spectral dependence was removed since these parameterizations were designed considering the [8–14] µm spectral range. Labels fi refer to specific functions proposed by the corresponding references. The dependence on LAI and LIDF is implicitly included into directional gap and cover fractions Fsoil (θ ) and Fveg (θ ), the cavity effect coefficient α (θ ), and hemispherical gap fraction σ f [68]. Standard formulation

ε (θ ) B (Trad (θ )) = τ can (θ ) εsoil B(Tsoil ) + ω (θ , εveg ) B(Tveg ) Label

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Formulations   ε (θ ) = f3 Fsoil (θ ), εsoil , εveg , σ f , α (θ ) τ can (θ ) = Fsoil (θ )   ω (θ , εveg ) = f4 Fsoil (θ ), Fveg (θ ), εsoil , εveg , σ f , α (θ )

Remarks

ε (θ ) = f5 (Fsoil (θ ), Fveg (θ ), εsoil , εveg , σ f )   τ can (θ ) = f6 Fsoil (θ ), εsoil , εveg , σ f   ω (θ , εveg ) = f7 Fsoil (θ ), Fveg (θ ), εsoil , εveg , σ f

Accounts for multiple scattering

Accounts for multiple scattering and cavity effect

ef f ef f (θ ) εveg ε (θ ) = Fsoil (θ ) εsoil + Fveg e f f τ can (θ ) = Fsoil (θ ) ef f (θ ) εveg ω (θ , εveg ) = Fveg   ef f Fsoil (θ ) = f1 Fveg (θ ), σ f   ef f Fveg (θ ) = f2 Fsoil (θ ), σ f

Accounts for multiple scattering and cavity effect Effective parameterization

Linearizing P3 considering B(T ) ≈ σ T 4 Linearizing P3 considering B(T ) ≈ σ T

Accounts for multiple scattering

ε (θ ) = Fsoil (θ ) εsoil + Fveg (θ ) εveg τ can (θ ) = Fsoil (θ ) ω (θ , εveg ) = Fveg (θ ) εveg

Linearizing P6 considering B(T ) ≈ σ T Simplifying P7 considering εveg = εsoil = 1

clear sky conditions, with irradiance lower than 30 W. m−2 between 8 and 14 µm [234]. Finally, [127] observed analytical formulation P2 significantly diverged from a ray tracing reference when soil and vegetation emissivities were very different.

10.6.4.2 Inverting the Soil/Vegetation Radiative Transfer Equation The various parameterizations reported above have been assessed in inverse mode considering dual angle observations, nadir and 45◦ or 55◦ off nadir. Given soil and vegetation emissivities, dual angle measurements allow retrieving component temperatures. Off nadir angles above 45◦ are required to capture large angular dynamics and reduce observation errors [108, 109, 119, 144, 235–237]. Dual angle observations at 0 and 55◦ correspond to the ATSR suite viewing configuration.

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Error in leaves temperature retrieval (⬚C)

Error in soil temperature retrieval (⬚C)

Converging conclusions were reported about the documentation requirements for canopy structural parameters. Poorly estimating LIDF can result in errors on temperatures up to 1 K [118]. LAI must be known within 5% (respectively 10%) for a 0.5 K accuracy on vegetation (respectively soil) temperature [118, 119]. Similarly, a 7–8% relative error on directional cover fraction can induce errors on soil and vegetation temperatures from 1 to 3 K [189]. Such recommendations have to be compared with current accuracies on LAI retrievals from solar remote sensing, i.e., around 20% [238]. Diverging conclusions were reported about the documentation requirements for canopy radiative properties, the parameterization degree to be considered, and the performances. First, [118] concluded a 0.01 accuracy is necessary for soil and vegetation emissivities, whereas [71] claimed using unity values has no consequence. Second, [71, 119] concluded simple parameterizations similarly performed than complex ones, while multiple scattering and cavity effect can be neglected. Conversely, [68] reported it is necessary to account for multiple scattering (Fig. 10.7). Third, [68] concluded a 1 K accuracy can be reached on both temperatures, and better for vegetation than soil; whereas [71] reported lower errors for soil (