ADVANCED - University at Buffaloxintao/publications/Fan_12_FAPAR.pdfADVANCED REMOTE SENSING...

ADVANCEDREMOTESENSING

Terrestrial Information Extraction and Applications

Edited by

SHUNLIN LIANG

XIAOWEN LI

JINDI WANG

AMSTERDAM • BOSTON • HEIDELBERG • LONDONNEW YORK • OXFORD • PARIS • SAN DIEGO

SAN FRANCISCO • SYDNEY • TOKYO

Academic Press is an imprint of Elsevier

Preface

Chapters Titles Authors

1 A Systematic View ofRemote Sensing

S. Liang, J. Wang,B. Jiang

PART 1 Data Processing Methods and Techniques

2 Geometric Processingand PositioningTechniques

X. Yuan, S. Ji, J. Cao,X. Yu

3 Compositing,Smoothing, and Gap-Filling Techniques

Z. Xiao

4 Data Fusion J. Zhang, J. Yang

5 Atmospheric Correctionof Optical Imagery

X. Zhao, X. Zhang,S. Liang

PART 2 Estimation of Surface Radiation Budget Components

6 Incident Solar Radiation X. Zhang, S. Liang

7 Broadband Albedo Q. Liu, J. Wen, Y. Qu,T. He, X. Zhang

(Continued)

As the technology of remote sensing hasadvanced over the last two decades, the scientificpotential of the data that it produces has greatlyimproved. To better serve society’s needs, theimmense amounts of aggregated satellite dataneed to be transferred into high-level productsin order to improve the predictive capabilitiesof global and regional models at different scalesand to aid in decision making through variousdecision support systems. A general trend isthat the data centers are distributing morehigh-level products rather than simply the rawsatellite imagery.

An increasing number of researchers froma diverse set of academic and scientific disci-plines are now routinely using remotely senseddata products, and the mathematical and phys-ical sophistication of the techniques used toprocess and analyze these data have increasedconsiderably. As a result, there is an urgentneed for a reference book on the advancedmethods and algorithms that are now availablefor extracting information from the hugevolume of remotely sensed data, which areoften buried in various journals and other sour-ces. Such a book should be highly quantitativeand rigorously technical; at the same time, itshould be accessible to students at the upperundergraduate and first-year graduate studentlevel.

To meet this critical demand, we have identi-fied and organized a group of active researchscientists to contribute chapters and sectionsdrawn from their research expertise. Althoughthis is an edited volume with multiple authors,

xi

it is well designed and integrated. The editorsand authors have made great efforts to ensurethe consistency and integrity of the text.

In addition to the introductory chapter, thisbook consists of five parts: (1) data processingmethods and techniques; (2) estimation of land-surface radiation budget components; (3) estima-tion of biophysical and biochemical variables;(4) estimation of water cycle components; and(5) high-level product generation and applica-tion demonstrations. The titles and authors ofthe individual chapters are as follows:


8 Land-SurfaceTemperature andThermal InfraredEmissivity

J. Cheng, H. Ren

9 Surface LongwaveRadiation Budget

W. Wang

PART 3 Estimation of Biophysical and BiochemicalVariables

10 Canopy BiochemicalCharacteristics

Z. Niu, C. Yan

11 Leaf Area Index H. Fang, Z. Xiao,Y. Qu, J. Song

12 Fraction of AbsorbedPhotosyntheticallyActive Radiation byGreen Vegetation

W. Fan, X. Tao

13 Fractional VegetationCover

G. Yan, X. Mu,Y. Liu

14 Vegetation Height andVertical Structure

G. Sun, Y. Pang,W. Ni, W. Huang,Z. Li

15 Above-GroundBiomass

G. Sun, W. Sun,S. Liang, Z. Zhang,E. Chen

16 Vegetation Productionin TerrestrialEcosystems

W. Yuan, Z. Chen

PART 4 Estimation of Water Balance Components

17 Precipitation Y. Liu, Q. Fu,X. Zhao, C. Dou

18 TerrestrialEvapotranspiration

K. Wang. R.Dickinson, Q. Ma

19 Soil Moisture Contents S. Liang, B. Jiang,T. He, X. Zhu

20 Snow WaterEquivalence

L. Jiang, J. Du,L. Zhang, J. Shi,J. Pan, C. Xiong

21 Water Storage Y. Liu, P. Song


PART 5 Production Generation and ApplicationDemonstrations

22 High-Level LandProduct Integration

D. Wang

23 Production and DataManagement Systems

S. Liu, X. Zhao

24 Land-Cover and Land-Use Changes

X. Zhu, S. Liang,B. Jiang

PREFACExii

Chapter 1 presents introductory material andprovides an overview of the book. From thesystem perspective, it briefly describes the essen-tial components of the remote-sensing system,ranging from platforms and sensors, modelingapproaches, and information extraction methodsto applications.

Part 1 includes four chapters on data process-ing. Chapter 2 is the only chapter that presentsthe methods and techniques for handlinggeometric properties of remotely sensed data.These include the calibration of systematicerrors, geometric correction, geometric registra-tion, digital terrain model generation, and digitalortho-image generation.

Chapter 3 seeks to reconstruct spatial andtemporal continuous high-quality imagery. Asthe temporal resolution of satellite observationsgreatly increases, images are more often contam-inated by clouds and aerosols that partially orcompletely block the surface information. Twogroups of techniques are presented. The firstgroup deals with composite methods for aggre-gating the fine temporal resolution (say, daily)to the coarse resolution (say, weekly or monthly),and the second discusses smoothing and gap-filling methods to eliminate the impacts of cloudsand aerosols at the same temporal resolution.

Chapter 4 introduces the basic principles andmethods of data fusion for integrating multipledata sources on the pixel basis, which have

PREFACE xiii

different spatial resolutions, and are acquiredfrom different spectra (optical, thermal,microwave). This chapter focuses mainly onlow-level data products. (The methods for inte-grating high-level products are introduced inChapter 22.)

Chapter 5 introduces methods for correctingthe atmospheric effects of aerosols and watervapor on the optical imagery. Other atmosphericcorrection methods are discussed in Chapter 8for thermal-IR data and in Part 4 for microwavedata.

Part 2 focuses on estimation of surface radia-tion budget components. The surface radiationbudget is characterized by all-wave net radiation(Rn) that is the sum of shortwave (Sn) and long-wave (Ln) net radiation

Rn ¼ Sn þ Ln ¼ ðsY� s[Þ þ ðLY� L[Þ¼ ð1� aÞSYþ ðLY� L[Þ

where SY is the downward shortwave radiation(discussed in Chapter 6), S[ is the upward short-wave radiation, a is the surface shortwavealbedo (discussed in Chapter 7), LY is the down-ward longwave radiation, and L[ is the upwardlongwave radiation. Longwave net radiation (Ln)can be also calculated by

Ln ¼ εLY� εsT4s

where s is the Stefan-Boltzmann constant, ε issurface thermal broadband emissivity, and Ts issurface skin temperature. Estimation of ε andTs is discussed in Chapter 8, and LY and Ln arecovered in Chapter 9.

Part 3 focuses on the estimation of biochem-ical and biophysical variables of plant canopy.Chapter 10 introduces the various methods forestimating plant biochemical variables, such aschlorophyll, water, protein, lignin and cellulose.The biophysical variables discussed in this bookinclude leaf area index (LAI) in Chapter 11, thefraction of absorbed photosynthetically activeradiation by green vegetation (FPAR) in Chapter12, fractional vegetation cover in Chapter 13,

vegetation height and vertical structure inChapter 14, above-ground biomass in Chapter15, and vegetation production in terms of grossprimary production (GPP) and net primaryproduction (NPP) in Chapter 16. Various inver-sion methods are introduced in this part,including optimization methods (Section11.3.2), neural networks (Sections 11.3.3, 13.3.3and 15.3.4), genetic algorithms (Section 11.3.4),Bayesian networks (Section 11.3.5), regressiontree methods (Section 13.3.3), data assimilationmethods (Section 11.4) and look-up tablemethods (Section 11.3.6). Part 3 also discussesmultiple data sources besides optical imagery,such as Synthetic Aperture Radar (SAR) andLight Detection and Ranging (Lidar), and polar-imetric InSAR data.

Part 4 is on estimation of water balancecomponents. A general water balance equationis expressed by:

P ¼ Qþ Eþ DS

where P is precipitation (discussed in Chapter17), Q is runoff that is currently difficult to esti-mate from remote sensing, E is evapotranspira-tion (discussed in Chapter 18), and DS is thechange in storage to which three chapters arerelated: soil moisture in Chapter 19, snow waterequivalence in Chapter 20, and surface waterstorage in Chapter 21. In addition to opticaland thermal data, microwave data are dealtwith extensively in all chapters except in Chapter18. The gravity data with the GRACE data arealso briefly introduced in Chapter 21.

Part 5 deals with high-level product genera-tion, integration, and application. Chapter 22presents different methods for integrating high-level products of the same variable (e.g., LAI)that may be generated from different satellitedata or different inversion algorithms. The datafusion methods for integrating low-level prod-ucts are discussed in Chapter 4. Chapter 23describes the typical procedures for producinghigh-level products from low-level satellitedata and for developing a data management

PREFACExiv

system that is used for effectively handlinga large volume of satellite data. The last chapterdemonstrates how remote-sensing data productscan be used for land-cover and land-use changestudies, particularly on mapping the extent ofthree major land-use types (urban, forest, andagriculture), detecting changes in these land-use types, and evaluating the environmentalimpacts of these land-use changes.

One important feature of this book is its focuson extracting land-surface information fromsatellite observations. All relevant chaptersfollow the same template: introduction to basicconcepts and fundamental principles, review ofpractical algorithms with a comprehensive listof references, detailed descriptions of representa-tive algorithms and case studies, surveys ofcurrent products, spatiotemporal variations of

the variable, and identification of future researchdirections. The book includes almost 500 figuresand tables, as well as 1700 references.

This book can serve as a text for upper-levelundergraduate and graduate students in a varietyof disciplines related to Earth observation. Theentire bookmay be too lengthy for a one-semesteror one quarter class, but most chapters in Parts2e5 are relatively independent, and usinga subset of them will be useful in such classes.

The text can also serve as a valuable referencebook for anyone interested in the use and appli-cations of remote-sensing data. Ideally, thoseusing this book will have taken an introductoryremote-sensing course, but we have written it atsuch a level that even those who have had littleor no prior training in remote sensing can easilyunderstand the overall development of this field.

List of Contributors

Jinshan Cao School of Remote Sensing andInformation Engineering, Wuhan University, 129Luoyu Road, Wuhan 430079, China

Erxue Chen Institute of Forest ResourcesInformation Technology, Chinese Academy ofForestry, 1 Dongxiaofu, Beijing 100091, China

Zhuoqi Chen State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China and College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Jie Cheng State Key Laboratory of Remote SensingScience, Jointly Sponsored by Beijing NormalUniversity and the Institute of Remote SensingApplications of Chinese Academy of Sciences,19 Xinjiekouwai Street, Beijing 100875, China andCollege of Global Change and Earth SystemScience, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Cuicui Dou Nanjing Institute of Geography andLimnology, Chinese Academy of Sciences, 73East Beijing Road, Nanjing 210008, China andSchool of Earth Sciences and Engineering,Hohai University, 1 Xikang Road, Nanjing210098, China

Jinyang Du State Key Laboratory of RemoteSensing Science, Jointly Sponsored by theInstitute of Remote Sensing Applications ofChinese Academy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, China

Robert E. Dickinson Department of GeologicalSciences, University of Texas, Austin, TX 78712,USA

Wenjie Fan Institute of RS and GIS, PekingUniversity, 5 Yiheyuan Road, Beijing 100871, China

xvi

Hongliang Fang Institute of Geographic Sciencesand Natural Resources Research, ChineseAcademy of Sciences, 11A Datun Road, Beijing100101, China

Qiaoni Fu Nanjing Institute of Geography andLimnology, Chinese Academy of Sciences, 73 EastBeijing Road, Nanjing 210008, China andSchool of Earth Sciences and Engineering, HohaiUniversity, 1 Xikang Road, Nanjing 210098,China

Tao He Department of Geographical Sciences,University of Maryland, 2181 LeFrak Hall,College Park, MD 20742, USA

Wenli Huang Department of GeographicalSciences, University of Maryland, 2181 LeFrakHall, College Park, MD 20742, USA

Shunping Ji School of Remote Sensing andInformation Engineering, Wuhan University, 129Luoyu Road, Wuhan 430079, China

Bo Jiang State Key Laboratory of Remote SensingScience, Jointly Sponsored by Beijing NormalUniversity and the Institute of Remote SensingApplications of Chinese Academy of Sciences, 19Xinjiekouwai Street, Beijing 100875, China;School of Geography, Beijing NormalUniversity, 19 Xinjiekouwai Street, Beijing 100875,China and Department of GeographicalSciences, University of Maryland, 2181 LeFrakHall, College Park, MD 20742, USA

Lingmei Jiang State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; Beijing Key Laboratory for RemoteSensing of Environment and Digital Cities, BeijingNormal University, 19 Xinjiekouwai Street,Beijing 100875, China and School of Geography,

i

LIST OF CONTRIBUTORSxviii

Beijing Normal University, 19 Xinjiekouwai Street,Beijing 100875, China

Zengyuan Li Institute of Forest ResourcesInformation Technology, Chinese Academy ofForestry, 1 Dongxiaofu, Beijing 100091, China

Shunlin Liang State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China andDepartment of Geographical Sciences, Universityof Maryland, 2181 LeFrak Hall, College Park, MD20742, USA

Qiang Liu State Key Laboratory of Remote SensingScience, Jointly Sponsored by Beijing NormalUniversity and the Institute of Remote SensingApplications of Chinese Academy of Sciences,19 Xinjiekouwai Street, Beijing 100875, Chinaand College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Suhong Liu State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China and School of Geography, BeijingNormal University, 19 Xinjiekouwai Street,Beijing 100875, China

Yaokai Liu State Key Laboratory of Remote SensingScience, Jointly Sponsored by Beijing NormalUniversity and the Institute of Remote SensingApplications of Chinese Academy of Sciences, 19Xinjiekouwai Street, Beijing 100875, China

Yuanbo Liu Nanjing Institute of Geography andLimnology, Chinese Academy of Sciences, 73 EastBeijing Road, Nanjing 210008, China

Qian Ma College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Xihan Mu State Key Laboratory of Remote SensingScience, Jointly Sponsored by Beijing NormalUniversity and the Institute of Remote Sensing

Applications of Chinese Academy of Sciences, 19Xinjiekouwai Street, Beijing 100875, China;Beijing Key Laboratory for Remote Sensing ofEnvironment and Digital Cities, Beijing NormalUniversity, 19 Xinjiekouwai Street, Beijing 100875,China and School of Geography, Beijing NormalUniversity, 19 Xinjiekouwai Street, Beijing 100875,China

Wenjian Ni State Key Laboratory of RemoteSensing Science, Jointly Sponsored by theInstitute of Remote Sensing Applications ofChinese Academy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, China

Zheng Niu State Key Laboratory of Remote SensingScience, Jointly Sponsored by the Institute ofRemote Sensing Applications of ChineseAcademy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, China

Jinmei Pan State Key Laboratory of Remote SensingScience, Jointly Sponsored by Beijing NormalUniversity and the Institute of Remote SensingApplications of Chinese Academy of Sciences,19 Xinjiekouwai Street, Beijing 100875, China;Beijing Key Laboratory for Remote Sensing ofEnvironment and Digital Cities, Beijing NormalUniversity, 19 Xinjiekouwai Street, Beijing 100875,China and School of Geography, Beijing NormalUniversity, 19 Xinjiekouwai Street, Beijing 100875,China

Yong Pang Institute of Forest Resources InformationTechnology, Chinese Academy of Forestry, 1Dongxiaofu, Beijing 100091, China

Ying Qu State Key Laboratory of Remote SensingScience, Jointly Sponsored by Beijing NormalUniversity and the Institute of Remote SensingApplications of Chinese Academy of Sciences,19 Xinjiekouwai Street, Beijing 100875, Chinaand School of Geography, Beijing NormalUniversity, 19 Xinjiekouwai Street, Beijing 100875,China

Yonghua Qu State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofScience, 19 Xinjiekouwai Street, Beijing 100875,China, Beijing Key Laboratory for RemoteSensing of Environment and Digital Cities,

LIST OF CONTRIBUTORS xix

Beijing Normal University, 19 XinjiekouwaiStreet, Beijing 100875, China and School ofGeography, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Huazhong Ren State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; Beijing Key Laboratory for RemoteSensing of Environment and Digital Cities,Beijing Normal University, 19 XinjiekouwaiStreet, Beijing 100875, China and School ofGeography, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Jiancheng Shi State Key Laboratory of RemoteSensing Science, Jointly Sponsored by theInstitute of Remote Sensing Applications ofChinese Academy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, China

Jinling Song State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; Beijing Key Laboratory for RemoteSensing of Environment and Digital Cities, BeijingNormal University, 19 Xinjiekouwai Street,Beijing 100875, China and School of Geography,Beijing Normal University, 19 XinjiekouwaiStreet, Beijing 100875, China

Ping Song Nanjing Institute of Geography andLimnology, Chinese Academy of Sciences, 73 EastBeijing Road, Nanjing 210008, China andGraduate University of Chinese Academy ofSciences, 19A Yuquan Road, Beijing 100049, China

Guoqing Sun State Key Laboratory of RemoteSensing Science, Jointly Sponsored by theInstitute of Remote Sensing Applications ofChinese Academy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, Chinaand Department of Geographical Sciences,University of Maryland, 2181 LeFrak Hall,College Park, MD 20742, USA

Wanxiao Sun Department of Geography andPlanning, Grand Valley State University, 1Campus Drive, Allendale, MI 49401-9403, USA

Xin Tao Department of Geographical Sciences,University of Maryland, 2181 LeFrak Hall,College Park, MD 20742, USA

Dongdong Wang Department of GeographicalSciences, University of Maryland, 2181 LeFrakHall, College Park, MD 20742, USA

Jindi Wang State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; Beijing Key Laboratory for RemoteSensing of Environment and Digital Cities, BeijingNormal University, 19 Xinjiekouwai Street,Beijing 100875, China and School of Geography,Beijing Normal University, 19 XinjiekouwaiStreet, Beijing 100875, China

Kaicun Wang College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China andState Key Laboratory of Earth Surface Processesand Resource Ecology, Beijing Normal University,19 Xinjiekouwai Street, Beijing 100875, China

Wenhui Wang I.M. Systems Group at NOAA/NESDIS/STAR, 5200 Auth Road, Camp Springs,MD 20746, USA

Jianguang Wen State Key Laboratory of RemoteSensing Science, Jointly Sponsored by theInstitute of Remote Sensing Applications ofChinese Academy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, China

Zhiqiang Xiao State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; Beijing Key Laboratory for RemoteSensing of Environment and Digital Cities, BeijingNormal University, 19 Xinjiekouwai Street,Beijing 100875, China and School of Geography,Beijing Normal University, 19 XinjiekouwaiStreet, Beijing 100875, China

Chuan Xiong State Key Laboratory of RemoteSensing Science, Jointly Sponsored by theInstitute of Remote Sensing Applications ofChinese Academy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, China

LIST OF CONTRIBUTORSxx

Chunyan Yan School of Earth Sciences andResources, China University of Geosciences,Beijing, 29 Xueyuan Road, Beijing 100083, China

Guangjian Yan State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; Beijing Key Laboratory for RemoteSensing of Environment and Digital Cities,Beijing Normal University, 19 XinjiekouwaiStreet, Beijing 100875, China and School ofGeography, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Jinghui Yang Chinese Academy of Surveying andMapping, 28 Lianhuachi West Road, Beijing100830, China

Xiang Yu School of Remote Sensing andInformation Engineering, Wuhan University, 129Luoyu Road, Wuhan 430079, China

Wenping Yuan State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China and College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Xiuxiao Yuan School of Remote Sensing andInformation Engineering, Wuhan University, 129Luoyu Road, Wuhan 430079, China

Jixian Zhang Chinese Academy of Surveying andMapping, 28 Lianhuachi West Road, Beijing100830, China

Lixin Zhang State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China; Beijing Key Laboratory for Remote

Sensing of Environment and Digital Cities, BeijingNormal University, 19 Xinjiekouwai Street,Beijing 100875, China and School of Geography,Beijing Normal University, 19 XinjiekouwaiStreet, Beijing 100875, China

Xiaotong Zhang State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China and College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Xin Zhang State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China and School of Geography, Beijing NormalUniversity, 19 Xinjiekouwai Street, Beijing100875, China

Zhiyu Zhang State Key Laboratory of RemoteSensing Science, Jointly Sponsored by theInstitute of Remote Sensing Applications ofChinese Academy of Sciences and Beijing NormalUniversity, 20 Datun Road, Beijing 100101, China

Xiang Zhao State Key Laboratory of RemoteSensing Science, Jointly Sponsored by BeijingNormal University and the Institute of RemoteSensing Applications of Chinese Academy ofSciences, 19 Xinjiekouwai Street, Beijing 100875,China and College of Global Change and EarthSystem Science, Beijing Normal University, 19Xinjiekouwai Street, Beijing 100875, China

Xiaosong Zhao Nanjing Institute of Geography andLimnology, Chinese Academy of Sciences, 73 EastBeijing Road, Nanjing 210008, China

Xiufang Zhu Department of Geographical Sciences,University of Maryland, 2181 LeFrak Hall, CollegePark, MD 20742, USA

C H A
P T E R
12

Fraction of Absorbed PhotosyntheticallyActive Radiation by Green Vegetation

A

O U T L I N E

12.1. Definitions 38
4
12.2. FAPAR Field Measurements 385

12.3. Monte Carlo (MC) simulation 386
12.3.1. Monte Carlo Simulation Theory 386 12.3.2. A Simulation Experiment 387
12.4. Empirical Retrieval Methods 393
12.4.1. Empirical Methods Based
on the LAI
393 12.4.2. Vegetation Index-based Methods 393
12.5. Popular Remote-Sensing FAPARProducts 395
12.5.1. MODIS Retrieval Algorithm 395 12.5.2. JRC_FPAR Retrieval Algorithm 398
12.6. FAPAR Retrieval Method Based onthe Hybrid Vegetation Spectral Model 400
12.6.1. The Starting Equation
of the FAPAR Model
400
dvanced Remote Sensing DOI: 10.1016/B978-0-12-385954-9.00012-5 383

12.6.2. Validation of the Model withMonte Carlo Simulations
401
12.6.3. The Field Validation
403 12.6.4. The Retrieval Algorithm
of FAPAR
404
12.7. Case Study 406
12.7.1. Study Region and Dataset 406 12.7.2. FAPAR Retrieval Using
a Hyperspectral MultiangleImage
406 12.7.2.1. Preprocessing of
CHRIS Data
406 12.7.2.2. FAPAR Retrieval 408 12.7.2.3. Validation of
Retrieval Results
408 12.7.3. FAPAR Retrieval Using
the Multispectral Image
409 12.7.3.1. FAPAR Retrieval 411
12.8. Summary 411

AbstractThe Fraction of Absorbed Photosynthetically ActiveRadiation by green vegetation (FAPAR) characterizesthe energy absorption ability of vegetation canopy. Itdescribes both the vegetation structure and the relatedmaterial and energy exchange processes, and it also

estimates the net primary productivity (NPP) usinga remote-sensing method. Some related concepts arediscussed in Section 1. Groundmethods for measuringFAPAR are briefly introduced in Section 2. In Section3, the factors affecting FAPAR will be analyzedby Monte Carlo simulation, which is the basis for

Copyright � 2012 Elsevier Inc. All rights reserved.

12. FRACTION OF ABSORBED PHOTOSYNTHETICALLY ACTIVE RADIATION BY GREEN VEGETATION384

remote-sensing retrieval. In Section 4, empiricalmethods of FAPAR retrieval will be discussed.FAPAR retrieval methods using radiative transfermodels or other physical models will be introduced inSections 5 and 6. Finally, a case study from the HeiheBasin, China, will be discussed in Section 7.

FIGURE 12.1 The absorption rates for chlorophyll a andb and carotenoids and the total photosynthetic efficiency inthe PAR range.

12.1. DEFINITIONS

The Fraction of Absorbed PhotosyntheticallyActive Radiation (FAPAR) is the solar radiationabsorbed by green vegetation in the spectralrange from 400 nm to 700 nm. It is also denotedas FPAR in some publications. As the basicbiophysical parameter of vegetation, FAPARcan be used to estimate primary productivityand carbon dioxide absorption. It is an essentialinput in many land-surface models, includingcrop growth models, net primary productivitymodels, climate models, ecological models,water cycle models, and carbon cycle models(Liu et al., 1997; Reich et al., 1999; Cramer et al.,1999; Scurlock et al., 1999; Liang, 2004; Wuet al., 2004). FAPAR can also be used to describethe growth status and evolution of vegetation, forwhich it should theoretically be a better indicatorthan vegetation indices. FAPAR is currentlygaining more attention from the internationalcommunity, and it has been acknowledged asa climate parameter by the United NationsGlobal Climate Observing System (GCOS).Spatial distribution information about landsurfaces can be obtained instantaneously viaremote sensing. In particular, parameters withdifferent spatial and temporal characteristics,such as FAPAR, can be derived in this manner.Some sensors, including VEGETATION (VGT),Advanced Very High Resolution Radiometer(AVHRR), and Moderate Resolution ImagingSpectroradiometer (MODIS), have been able toprovide FAPAR information on a global andregional scale.

Photosynthetically active radiation (PAR) isthe incoming solar radiation in the spectral rangefrom 400 nm to 700 nm, which has been

discussed in Chapter 6. Green vegetation canabsorb PAR. The absorption rates for chloro-phyll a and b, carotenoids, and the total photo-synthetic efficiency in the PAR range areshown in Figure 12.1.

The total absorbed PAR by green vegetation(APAR) can be converted into biomass, whichis given by APAR¼ FAPAR� PAR.

The definition of FAPAR can apply to onlyvegetation. It does not include the vegetationreflectance or the solar radiation absorbed bythe background (e.g., the soil and lichens), exceptthe part that is reflected by the background andthen absorbed by the vegetation. Given theboundaries of the vegetation, atmosphere, andsoil, the solar radiation related to the canopy

FIGURE 12.2 Composition of the solar energy thataccesses the canopy.

12.2. FAPAR FIELD MEASUREMENTS 385

includes the following terms (Gobron et al.,2006): (incoming solar flux) IYTOC, (flux to theground) IYGround, (flux from the ground) I[Groundand (outgoing solar flux) I[TOC. These terms areshown in Figure 12.2. Note that irradiance andflux are not distinguished here for convenience.FAPAR can be calculated by

FAPAR ¼�IYTOC � IYGround þ I[Ground

� I[TOC

�.IYTOC (12.1)

When the proportion of vegetation in the areais close to 0 (pure soil), the incident solar radia-tion IYTOC is equal to the radiation that reachesthe ground IYGround, and the radiation reflectedfrom the ground I[Ground is equal to the outgoingsolar radiation I[TOC, then FAPAR¼ 0. The instan-taneous FAPAR is the FAPAR at a certainmoment, and the daily FAPAR is the integralof the instantaneous FAPAR over the cosine ofthe solar zenith angle.

12.2. FAPAR FIELDMEASUREMENTS

It is difficult to measure the APAR directlyand to estimate the FAPAR in the field.However, the APAR can be indirectly estimatedusing a continuous PAR measurement aboveand under the canopy. The FAPAR values can

be calculated indirectly by measuring the inci-dent radiation above the canopy, the canopyreflected, and the transmitted radiation.

The incident PAR was initially obtained bycalculations. In the 1970s and 1980s, somescholars began to measure PAR using instru-ments in observation points, such as sky radiom-eters and portable optical quantum instruments.However, as far as the observation of PARwithin the canopy is concerned, it is difficult tokeep the samples representative and maintainthe instruments at a horizontal level, which cancause large observation errors. At present,several long probe-shaped instruments arecommonly used, such as the ACCUPAR plantcommunity analyzer (Kiniry and Knievel, 1995)and the SUNSCAN canopy analysis system.The following instruments are more widelyused.

The PAR/Sunflerk photosynthetic activeradiation meter is produced by Decagon DevicesU.S. One hundred sensors are embedded in thesensitive region (12 mm � 0.8 m), and theyare sufficiently flexible to measure the instanta-neous PAR above and underneath the canopy.This instrument does not have the reflectionproblems of tubular radiation meters, and itcan easily be kept level, which improves theobservation accuracy and efficiency. However,PAR must be measured quickly to obtain accu-rate FAPAR observations; therefore, significantreplication is necessary. Under cloudy condi-tions, the changes in solar radiation can causelarge observation errors.

The SUNSCAN canopy analysis system isproduced by the Delta Company, U.K. The inci-dent PAR (including direct and diffuse PAR),transmittance of photosynthetically active radia-tion (TPAR), leaf area index (LAI), and manyother ecological indicators can be acquiredsimultaneously, which solves the issue ofsynchronization. Moreover, this system canalso record observations automatically. Thus, itis a highly useful agroecological observationalinstrument, and currently the most commonly

FIGURE 12.3 SUNSCAN field measurement.


used instrument for FAPAR measurement. Thissystem has been optimized for low regular cano-pies, including most agricultural crops. Accord-ing to Equation (12.1), we need to measureIYTOC, IYGround, I[TOC, and I[Ground when calculatingthe ground FAPAR (Figure 12.3).

12.3. MONTE CARLO (MC)SIMULATION

In order to establish the FAPAR retrievalmodel and determine FAPAR accurately, thefirst thing we should do is analyze the mecha-nisms which affect the radiation transfer ofphoton. According to Formula (12.1), FAPARcalculations rely on the incoming solar flux, theflux to the ground, the flux from the groundand the outgoing solar flux. The incoming solarflux is affected by the solar incident directionand atmospheric conditions. The flux to theground is determined by the canopy structure,including the LAI, leaf angle distribution(LAD), and the single scattering albedo of theleaf. The outgoing solar flux is also impactedby the soil reflectance. The factors influencing

these mechanisms are distinct and restrain eachother. So the various factors affecting FAPARmust be analyzed. Monte Carlo (MC) is a mathe-matical statistical method based on computersimulation, the radiative transfer process forphotons in the canopy can be simulated indifferent conditions. In this section, the MCFAPAR simulation is introduced for thispurpose. The results provide a theoretical basisfor FAPAR retrieval.

12.3.1. Monte Carlo Simulation Theory

Monte Carlo (MC) is a popular mathematicalstatistical method based on computer simula-tion. The results can be obtained throughrepeated random sampling, and the radiativetransfer process for photons in the canopy canbe simulated according to different canopystructure. Many studies of canopy reflectancehave been conducted using MC simulation.Govaerts et al. (1998) described four steps thatare used to calculate the radiative transferprocess within the canopy: generating the rays(photons) and determining the parameters ofthe photons that collide with objects (scenes),

12.3. MONTE CARLO (MC) SIMULATION 387

the type of collision and scattering direction, andthe information on the ray path (counting).

Specifically, these four steps include:

(1) Light Source: determining the incident zenithangle qs and azimuth angle 4s.

(2) Scene: determining the canopy leaf angledistribution type (G function), leaf areaindex, leaf reflectance, absorption,transmittance, and soil reflectance.

(3) The type of collision and scattering direction:determining if the photon is absorbed,reflected, or transmitted. If the photons arescattered, determine the direction of thescattering using the BRDF model.

(4) Counting: tracking the path of the photonsand calculating the resulting parameters,such as canopy absorption, reflectance,transmittance, and the BRDF and FAPAR.

Figure 12.4 shows a flowchart simulating theprocess through which photons transfer in thecanopy, where Lmax1, Lmax2, and Lmax3 are prede-fined threshold values.

12.3.2. A Simulation Experiment

In the following, we will introduce a simula-tion experiment we conducted. The parametersused include:

Photon incident zenith angle: 0e90 degrees.Photon incident azimuth: 0e180 degrees.Leaf angle distribution types: level, straight,tilt, extreme, uniform, spherical.Leaf area index of canopy: 0e10.Termination threshold of photon energy: 0.001.Photon number: if the value is more than 106,we use 10^6.

The reflectance, transmittance, and soil reflec-tance used in the simulation were obtained fromthe LOPEX93 (Leaf Optical Properties Experiment93) database. According to the spectral character-istics of the soil and vegetation, 18 points werenonuniformly sampled in the 0.4e0.7 mm region.The spectra are shown in Figure 12.5.

FAPAR from a single band was simulatedusing the MC method, with the canopyFAPAR having an average value of 18 points(Equation 12.2).

FAPAR ¼Xi

FAPARli=18 (12.2)

The input parameters, including the leaf areaindex, solar zenith angle, and leaf angle distribu-tion, were changed in the MC simulation toanalyze their impact on the FAPAR.

(1) Canopy reflectance, absorption in differentbands

Changes in the canopy reflectance andabsorption are the major factors that affectFAPAR; therefore, their variations (along withthe absorption bands) should be simulatedand analyzed first. When the incident directionof the sun is determined, the canopy reflec-tance spectra of the different leaf angle distri-butions in the 400e700 nm spectrum can beacquired via a MC simulation, as shown inFigure 12.6.

The main absorption bands of leaves are thered band (0.65 mm) and the blue (0.45 mm)band, whereas the main reflection band is thegreen (0.55 mm) band; therefore, the canopyabsorption increases with the changes in wave-length. The leaves exhibit high reflectance inthe near-infrared band, and the canopy absorp-tion begins to decline at approximately 0.7 mm.At 0.4e0.7 mm, the general trend in canopyabsorption moves from descending to ascendingand then to descending again.

If soil absorption is ignored, then the canopyreflectance will decline, and the soil absorptionwill increase; thus, the canopy absorption willalso decline (Figure 12.7). Because the soil isassumed to be a blackbody and the soil absorp-tion equals 1, multiple photon collisions betweenthe soil and the canopy are ignored.

When the vegetation type is planophile, theincident zenith angle is 30�, and LAI¼ 1, thesoil absorption, canopy reflectance, and canopy

N

Y

Y

Y

N

Y

N

Start

Generate random numbers and calculate the photon-free path (L1) according to

sθ , LAI and the G function

Calculate the possible largest distance Lmax1 photons cantravel within canopy and compare with L1

Photons hit the soil when passing throughthe canopy, reducing their energy

Obtain the outgoing direction, ifit meets the Lambetian

distribution

Calculate the free path (l3) in the outgoingdirection and the distance between the collisionpoint and the canopy edge (Lmax3)

Photons escape from the canopy

End

L1>Lmax1

Energy less than thethreshold

L3>Lmax3

Photons collide withleaves, reducing theirenergy

Energy less thanthe threshold

Generate random numbers anddetermine the path of the photons(reflection or transmission)

L2>Lmax2

Determine the leaf angle and generatea random azimuth from 0 to 2π,according to leaf angle distributionfunction and random number

Construct the local coordinatesystem of leaves according to theincident photon direction and thenormal leaf pattern

Convert to the canopy frame, if itmeets the lambertian distribution

Calculate the free path (l2) in the scatteringdirection and the distance between thecollision point and canopy edge (Lmax2)

Emitting zenith angle larger than π/2

LAI,sθ , canopy type

N

Y

N

N

FIGURE 12.4 The random flowchart of photon transfer processes in the canopy.


FIGURE 12.5 The soil reflectance, leaf reflectance, and transmittance spectra in the 0.4e0.7 mm region.

0.4 0.45 0.5 0.55 0.6 0.650

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

wavelength (micrometer)

Can

opy

refl

ecta

nce

LAI = 0.5LAI = 1LAI = 2LAI = 3LAI = 4LAI = 5

FIGURE 12.6 The canopy reflectance spectra for different LAIs (Considering the soil reflectance).


0.4 0.45 0.5 0.55 0.6 0.650

0.1

0.2

0.3

0.4

0.5

0.6


va

lue

FAPAR

Soil Absorption

Canopy reflection

0.4 0.45 0.5 0.55 0.6 0.650

0.1

0.2

0.3

0.4

0.5

0.6

0.7


va

lue

FAPAR0

Soil Absorption0

Canopy reflection0

(a) (b)

FIGURE 12.7 The soil absorption, canopy reflectance and canopy absorption spectra. (a) considering soil reflectance and(b) assuming the soil is a blackbody (the LAD is planophile, LAI¼ 1).


absorption spectra, as simulated via the MCmethod, are as shown in Figure 12.7(a).

The canopy absorption spectra when the solarzenith angle is 30�, the LAD is planophile, andthe LAI equals 0.5 and 3.5 are shown in

0.4 0.45 0.5 0.55 0.6 0.650

0.2

0.4

0.6

0.8

1


FAPA

R

LAI=0.1

LAI=0.2

LAI=0.5

LAI=1

LAI=2

LAI=3

LAI=4

LAI=5

(a) (

FIGURE 12.8 The canopy absorption spectra under different(b) The incident zenith angle is 30 degrees, erectophile.

Figure 12.8(a). The canopy absorption graduallyincreases with increases in the LAI, but theincreasing trend becomes weaker. If the vegeta-tion type is erectophile, then the canopy absorp-tion spectra are as shown in Figure 12.8(b).

0.4 0.45 0.5 0.55 0.6 0.650

0.2

0.4

0.6

0.8

1


FAPA

R

LAI=0.1

LAI=0.2

LAI=0.5

LAI=1

LAI=2

LAI=3

LAI=4

LAI=5

b)

LADs. (a) The incident zenith angle is 30 degrees, planophile;


Absorption in an erectophile canopy is lowerthan that in a planophile canopy because thesolar zenith angle is small.

(2) The relationship between FAPAR, the LAI,and the leaf angle distribution function.

When the incident zenith angle is 30 degree,the LAD is planophile, and the LAI equals 0.2,0.5, or 1-9, the FAPAR values of the differentLAIs are shown in Figure 12.9(a). We find thatthe FAPAR increases when the LAI increases,but the trend becomes weaker. When the LAIis higher than 5, the FAPAR is saturated. Thecontrast between the actual soil and a blackbodysoil is shown in Figure 12.9(b). The soil reflec-tance leads to an increase in the FAPAR, butthe increase is not significant when the LAI isextremely small or large. The largest increaseoccurs when the LAI ranges from 1 to 5.

The relationship between FAPARs and LAIsunder different solar zenith angles is shown inFigure 12.10. The larger the solar zenith angleis, the greater the FAPAR (given the sameLAI). The physical reason is that when the solarzenith angle increases, the effective path length

(a)

FIGURE 12.9 The canopy FAPAR changes associated w(b) assuming that the soil is a blackbody.

of the photon in the canopy becomes longer,and the probability of an absorbed collision isgreater; therefore, the FAPAR increases. In addi-tion, the FAPAR is more easily saturated whenthe solar zenith angle is larger. When the sunzenith angle changes from 10�, 30�, or 50� to70�, the LAI values for which the FAPARbecomes saturated are 6, 5, 3, and 2, respectively.

The relationship between the FAPAR and thesolar zenith angles under different LAIs is shownin Figure 12.11. As shown in this figure, the ratethat the FAPAR increases in response to the solarzenith angle varies with the LAI. That is, thegreater the LAI is, the more easily the FAPAR issaturated as the solar zenith angle increases.When the LAI changes from 0.5 to 3, the FAPARincreases rapidly with the increase in the solarzenith angle. If LAI¼ 1, for example, the FAPARranges from 0.39 when the solar zenith angle is0 degree to 0.95 when the solar zenith angle is70 degree (an increase of 0.56), whereas theincrease is not significant when the LAI is toolow or too high. The reason is that when theLAI value is high, the FAPAR at the nadir direc-tion will be close to 0.9; therefore, the increase in

(b)

ith the LAI. (a) considering the true soil reflection, and

FIGURE 12.10 The relationship between the FAPAR and LAI under different solar zenith angles.

FIGURE 12.11 The FAPAR according to the solar zenith angle under different LAIs.


12.4. EMPIRICAL RETRIEVAL METHODS 393

the range will be small. When the LAI is low,there are very few leaves; and the FAPAR ofthe nadir direction will be small. Therefore, it isimpossible for the FAPAR to increase too much.

12.4. EMPIRICAL RETRIEVALMETHODS

The MC simulation results show that theFAPAR is not only closely related to the LAIand other parameters of the canopy structurebut also affected by the solar and the observationdirections. To date, a series of empirical andmodel algorithms have been proposed for esti-mating the parameters. Because of the correlativerelationship between the FAPAR and the LAI,the FAPAR is calculated as a function of theLAI and the extinction coefficient in some biogeo-chemical process models (Ruimy et al., 1999). Inremote-sensing research, the absorbed PAR ofthe canopy is often calculated using a linear ornonlinear relationship with NDVI (Prince andGoward, 1995; Tucker, 1979). The LAIeFAPARrelationship and the NDVIeFAPAR relationshipare widely used in the literature to estimate theGPP and Net Primary Productivity (NPP) atdifferent spatial scales (Field et al., 1995; Runninget al., 2004). This section mainly describes theempirical retrieval methods.

12.4.1. Empirical Methods Basedon the LAI

The FAPAR can be obtained using an empir-ical formula for the LAI. Wiegand et al. (1992)presented an expression for the FAPAR andLAI:

FAPAR ¼ 1� e�LAI; R2 ¼ 0:952;

RMSE ¼ 0:054(12.3)

Casanova (1998) also mentioned that due to theexponentially decreasing relationship betweenthe PAR penetrating through the canopy and

the incident PAR and LAI, the proportion ofintercepted PAR can be written as

FAPAR ¼ 1� e�K�LAI;

where K is the extinction coefficient (12.4)

However, the LAI and the canopy extinctioncoefficient must be determined first when usingthis method; therefore, it is not commonly usedin remote-sensing retrieval.

12.4.2. Vegetation Index-based Methods

The FAPAR can also be obtained by establish-ing its empirical relationship with the vegetationindex. It can be retrieved by establishing a regres-sion equation for the field-measured FAPAR andvegetation indices such as the NDVI, which canbe calculated from original images, reflectanceimages, and images after atmospheric correction.This method is convenient and flexible, but plantabsorption changes with seasonal changes and issensitive to vegetation type, growth stages, siteenvironment, and other factors. Thus, the appli-cations of this type of model are limited.

Studies have shown that the FAPAR andNDVI have a linear relationship under certainconditions (Hatfield Asar and Kanemasu, 1984,Sellers 1985, Goward and Huemmrich, 1992).Myneni et al. (1994) studied the relationshipbetween the NDVI and FAPAR under differentsoil and atmospheric parameters using the radi-ative transfer method. They discovered that therelationship is sensitive to the background, theatmospheric parameters, and the canopy bidirec-tional reflectance directional function. If thestudy is limited to the nearby subsatellite point,the effect of the atmospheric parameters andthat of bidirectional reflectance can be ignored,and the influence of background can also beignored if soil reflectance is medium. Therefore,Myneni et al. suggested that a linear relationshipbetween the NDVI and FAPAR is tenable whenthe solar zenith angle is less than 60 degree, theobservation angle of the nearby subsatellite


point is less than 30 degree, the soil backgroundreflectance is moderate (i.e., the approximateNDVI is 0.12), and the atmospheric optical thick-ness is less than 0.65 at 550 nm.

Roujean and Breon (1995) simulated the radia-tive transferprocesswithin the canopyandsurfacereflection using the SAIL model, focusing on therelationshipbetween theNDVIandFAPARunderdifferent solar zenith angles, observation zenithangles. and relative azimuth angles. They foundthat the relationship will improve when the solarzenith angle or view zenith angle increases. Theroute of the light lengthens when it enters fromthe side, and the impact of the backgroundreduces; however, itwill also induceNDVI satura-tion for large LAI values.

The alternative algorithm, which Myneniet al. (1999), used in MODIS FAPAR product,is also based on the empirical NDVI algorithm.In the Vegetation Photosynthesis Model (VPM),the FAPAR is a function of the MODIS-enhancedvegetation index (EVI) (Huete and Liu, 1996),and the difference between the EVI and NDVIis that the EVI adds blue reflectance based onthe NDVI.

In the Carnegie Ames-Stanford approach(CASA) model (Potter, 1993), the FAPAR algo-rithm also uses the linear stretch model for theNDVI (normalized difference vegetation index)and for the ratio vegetation index (1 þ NDVI)/ (1-NDVI) (Sellers, 1985, 1994). It followsthat FAPAR¼min ((SR e SRmin)/(SRmax eSRmin), 0.95) where SR is the ratio vegetationindex, SR¼ (1 þ NDVI)/(1eNDVI). Therefore,the FAPAR is a linear function of SR in the GLO-PEM model:

FAPAR ¼ ðSR� SRminÞðFPARmax

� FPARminÞ=ðSRmax� SRminÞ:

Compared with the NDVI and SR, the DVI(Equation 12.5) can eliminate the most impactof the soil background; the effect will beimproved significantly with sparse vegetation,but it is greatly influenced by the spectral and

directional character of the canopy. When thevisible reflectance and near-infrared reflectanceincrease at the same rate, the NDVI will remainunchanged, but the DVI will change. The DVIis suitable for use with sparse vegetation,whereas the NDVI is suitable for use with densevegetation. The renormalized difference vegeta-tion index (RDVI) (Equation 12.6) has a nearlylinear correlation with the FAPAR under anyvegetation coverage. However, having the sunor the sensor in a vertical position should beavoided because the soil background reflectancemakes the greatest contribution at that time.Many studies have also analyzed the relation-ship between the SAVI (soil-adjusted vegetationindex) (Huete, 1988) and the NDVI, DVI, andRDVI. When C is small (< 0.15), the SAVI issimilar to the NDVI. When C is large (> 0.85),the SAVI is similar to the DVI. WhenC¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

NIRþ VISp

, the SAVI is similar to theRDVI:

DVI ¼ NIR� VIS (12.5)

RDVI ¼ ðNDVI$DVIÞ1=2 ¼ NIR� VISffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNIRþ VIS

p

(12.6)

SAVI ¼ NIR� VISNIRþ VISþ C

ð1þ CÞ (12.7)

where C is a constant ranging from 0 to 1. WhenC tends toward 1, the impact of the soil lessens,but the bidirectional impact increases. NIR isthe reflectance of the near-infrared band andVIS is the reflectance of the visible band.

The FAPAR is partially determined by theNDVI and other vegetation indices and affectedby the internal components of the leaves. Daw-son (2003) showed that the chlorophyll contenthas a significant impact on FAPAR estimations,given a constant NDVI. When the NDVI valuesare identical, a higher chlorophyll content isassociated with a lower FAPAR value. Highchlorophyll content and an increase in under-story vegetation can lead to overestimation ofthe FAPAR. However, some field measurements

12.5. POPULAR REMOTE-SENSING FAPAR PRODUCTS 395

showed that the chlorophyll content and under-story vegetation have little impact on theFAPAR. The difference between the retrievalresults and the field measurements suggeststhat using the NDVI will result in significanterrors in the FAPAR estimations. Therefore,other factors should be considered when esti-mating the FAPAR, including the solar zenithangle, LAD, soil background, and FAPAR andFIPAR (the fractional PAR interception).

Yanhua Gao (2007, personal communication)summarized different FAPAR algorithms basedon the vegetation index or LAI (see Table 12.1).Some of them were based on one-dimensional(1D) or three-dimensional (3D) radiative transfer(RT) simulations.

12.5. POPULAR REMOTE-SENSINGFAPAR PRODUCTS

The most popular FAPAR products at presentare the AVHRR and MODIS global LAI/FAPARproducts. In addition, the Canadian remote-sensing center also established an FAPAR modelbased on the vegetation index, producinga national FAPARmap using AVHRR data every10 days with a spatial resolution of 1 km (Chen,1996). The European Commission Joint ResearchCenter developed a JRC_FPAR product basedon European vegetation conditions. The resolu-tion of the global JRC_FPAR product is 10 km,whereas the resolution of the European FAPARproduct is 2 km. The main algorithms for theMODIS LAI\FPAR and JRC_FPAR products areall based on the radiative transfer model withthe empirical alternative algorithms.

The radiative transfer model is a relativelymature and universal optical reflectance modelbased on physical optics and is widely used forlarge-scale FAPAR retrieval. The method estab-lishes a look-up table according to the canopystructure and the biological characteristics of thesoil and compares the observed bidirectionalreflectance factor (BRF) to that found in the

look-up table. When the discrepancy betweenthe observed BRF and the model BRF is less thana threshold, the LAI and FAPAR that are obtainedare a possible solution (Myneni et al., 1997,Knyazikhin et al., 1998, Tian et al., 2000). Takingthe MODIS LAI/FPAR and JRC_FPAR productalgorithms as examples, we will introduce themain principles and retrieval methods for calcu-lating FAPAR based on the radiative transfermodel.

12.5.1. MODIS Retrieval Algorithm

MODIS has a short revisit period and obtainsglobal integrated information every 1 to 2 days.MODIS has 36 spectral bands and accommo-dates three spatial resolutions: 250 m, 500 m,and 1000 m. It collects images every morningand afternoon. MODIS provides long-term Earthobservation data that help to monitor the globaldynamics and processes of the Earth’s surface. Italso provides atmospheric information (Kingand Greenstone, 1999). Global coverage, multi-spatial resolution, multispectral images, and itsproduct service policies have made MODIS themost powerful information acquisitions toolsfor studying atmospheric, oceanic, and terres-trial biochemical processes on a global scale.

The FAPAR values were retrieved via a three-dimensional radiative transfer equation, in whichthe canopy structure is the most important vari-able in thevegetation canopy.Different vegetationcanopies have different canopy structures. There-fore, three points must be carefully consideredwhen estimating canopy radiation: (1) the canopystructure of the individual plant or community; (2)the optical properties of the vegetation (leaves,stems) and the soil (the former depends on thephysiological state of the vegetation, e.g.,the water content and pigment content); and (3)the atmospheric conditions, which significantlyimpact instantaneous solar radiation. Based ontheir canopy structures, global terrestrial plantswere divided into six categories in the originalMODIS LAI/FPAR algorithm (see Table 12.2).

TABLE 12.1 Different FAPAR Algorithms Based on the Vegetation Index or LAI

Algorithm R2 Method Vegetation type Reference

FAPAR¼ 1.2 � NDVI-0.18 0.974 PARmeasurement

Spring wheat, growthstage

Hatfield et al., 1984

FAPAR¼ 0.6-(2.2 � NDVI)þ (2.9 � NDVI2)

- PARmeasurement

Corn, growth stage Gallo et al., 1985

FAPAR¼ 1.408 � NDVI-0.396 0.92 PARmeasurement

Alfalfa Pinter, 1993

FAPAR¼ 1.25 � NDVI-0.025 - Max/Min tropical rainforest/desert

Ruimy et al., 1994

FAPAR¼ 0.279 � SR-0.294 - Max/Min Winter Alaska/theoretical maximum

Heimann and Keeling, 1989

FAPAR¼ 0.171 � SR-0.186 - Max/Min High vegetation/desert Sellers et al., 1994

FAPAR¼ 0.248 � SR-0.268 - Max/Min Low vegetation/desert Sellers et al., 1994

FAPAR¼ 1.24 � NDVI-0.23 - 1D RT - Baret et al., 1989

FAPAR¼ 1.164 � NDVI-0.143 0.92 1D radiativetransferequation

- Myneni and Williams, 1994

FAPAR¼ 1.21 � NDVI-0.04 0.99 1D RT - Goward et al., 1994

FAPAR¼ 1.67 � NDVI-0.08 - 1D RT - Prince and Goward, 1995

FAPAR¼ 0.105-(0.323 � NDVI)þ (1.168 � NDVI2)

0.85 1D RT - Moreau and Li, 1996

FAPAR¼ 3.257 � SAVI-0.07 0.86 1D RT - Moreau and Li, 1996

FAPAR¼ 0.846 � NDVI-0.08 0.92 3D RT sparse vegetation Myneni et al., 1992

FAPAR¼ 1.723 � MSAVI-0.137 0.968 3D RT topical sparse grasslandvegetation

Begue and Myneni, 1996

FAPAR¼ 2.213 � (DMSAVI)** 0.931 3D RTequation

topical sparse grasslandvegetation


FAPAR¼ 1.71 � (DNDVI)** 0.931 3D radiativetransferequation

topical sparse grasslandvegetation


FAPAR¼ 1-e (LAI(-K)) - Beer-LamberLaw

- Gower et al., 1999

FAPAR¼min�

SR� SRmin

SRmax � SRmin; 0:95

�SR¼ (1þNDVI)/(1-NDVI)

- CASA model - Potter et al., 1993

** D Indicates the difference between pre-onset and post-onset vegetation index values.(by Yanhua Gao, doctoral dissertation, 2007).


TABLE 12.2 The Vegetation Canopy Structure Distribution of Global Terrestrial Vegetationin the Radiative Transfer Model (Knyazikhin et al., 1999)

Grasses andcereal crops Shrubs

Broadleafcrops Savannas

BroadleafForests

NeedleForests

Horizontal heterogeneity no yes variable yes yes yes

Ground cover 100% 20-60% 10-100% 20-40% >70% >70%

Vertical heterogeneity(leaf optics and LAD)

no no no yes yes yes

Stems/trunks no no green stems yes yes yes

Understory no no no grasses yes yes

Foliage dispresion minimalclumping

random regular minimalclumping

clumped severeclumping

Grow shadowing no not mutual no no yes mutual yes mutual

Brightness of canopyground

medium bright dark medium dark dark


The MODIS algorithm describes the spectraland directional characteristics of the canopyusing a 3D radiative transfer (RT) model.Considering the particularities of radiativetransfer in canopies, the 3D RT model can bedivided into two submodels: (1) the radiationwhen the background is assumed to be a black-body (black soil); and (2) the radiation when thereflection is assumed to be anisotropic at thebottom of the canopy and when the canopyreflectance and absorption are viewed as theweighted average of both. Therefore, theformula for FAPAR at wavelength l can beexpressed by

alðU0Þ ¼ abs;lðU0Þ þ aS;lreffðlÞ

1� reffðlÞ$rS;ltbs;lðU0Þ

(12.8)

where alðU0Þ is the canopy absorption at l, U0 isthe incident direction of sun, abs;lðU0Þ andtbs;lðU0Þ are the canopy directional absorptionand directional transmission caused by blacksoil, asl and rsl are the canopy absorption andreflectance caused by the anisotropic emissionsource at the bottom of the canopy, and reff ðlÞis the effective reflectance of the surface at l.

The percentage of PAR that is instantaneouslyabsorbed by the vegetation canopy can be esti-mated using the following formula:

FPARðbio; pÞ ¼Z700nm

400nm

aheml ðU0ÞeðlÞdl

¼ Qbsðbio; LAI;U0ÞþQqðbio; p;U0Þ;

where

Qbsðbio; LAI;U0Þ ¼Z700nm

400nm

ahembs;lðU0ÞeðlÞdl

Qqðbio; p;U0Þ ¼Z700nm

400nm

aq;lðU0Þrq;eff ðlÞ

1� rq;eff ðlÞrq;l

� them;qbs;l eðlÞdl

¼Z700nm

400nm

aq;lðU0Þtq;lðU0Þ½A

wheml ðU0Þ

� rhembs;lðU0Þ�eðlÞdl


The Qbs term describes the absorption withinthe canopy for a black-soil condition, and Qq

term describes the additional absorption withinthe canopy due to the interaction between theground (soil and/or understory) and thecanopy. Here p˛Pbio; bio refers to the biomass,e is the ratio of the monochromatic flux incidentat the top surface of the canopy boundary to thetotal downward PAR flux which can beexpressed as

eðlÞ ¼ E0; l eheml ðU0ÞZ700nm400nm

E0;leheml ðU0Þdl

where E0;l is the solar irradiance spectrum that isknown for all wavelengths; eheml is the normal-ized incident irradiance defined as the ratio ofthe radiant incident on the surface to E0;l (Dineret al., 1998a). The mean over those p˛Pbio whichpassed the test DðpÞ � h is taken as the estimateof FPAR, that is,

FPARbio ¼ 1Np

XNp

k¼ 1

FPARðbio; pÞ

where NP is the number of canopy realizationsp˛Pbio passing this test. When there is no solu-tion (i.e., Fbio ¼ 0 ), the algorithm defaults toa NDVI-FPAR regression analysis to obtain anestimate of FPAR (Myneni et al, 1997b).

The flowchart for the MODIS LAI/FPARlook-up table algorithm is shown in Figure 12.12.

Tian et al. (2000) discussed the reasons whythe three-dimensional radiative transfer modelfails in different regions and situations. Theyfound that the retrieved LAI and FAPAR wereeffective only when the pixel spectral informa-tion fell into the spectral and angular rangeestablished by the look-up table algorithm. Thequality of the retrieval results can be measuredusing the saturation frequency and the coeffi-cient of variation (the standard deviationdivided by the average). The smaller the satura-tion frequency and coefficient of variation is, the

higher the quality of the results. For example, theforest has a high saturation rate, but its coeffi-cient of variation is small; therefore, the qualityof the data is sufficient.

Based on the results obtained using the RTalgorithm, the surface reflectance is not sensitiveto the LAI/FAPAR when LAI > 5 because of theLAI saturation. At this time, we can use only thisalgorithm. When the uncertainty of the inputreflectance data is too great or the BRF modelis incorrect, the three-dimensional radiativetransfer model algorithm fails, and the alterna-tive algorithm is used (the LAI/FAPAR-NDVIempirical relations).

The latest (Collection 5) LAI/FPAR productshave refined the algorithm to improve thequality of the LAI/FPAR retrieval. The originalvegetation type map for LAI/FPAR (C3, sixtypes of vegetation) has been replaced bya new one (C4, C5, eight types of vegetation).The broadleaf forest and needle forest typesare divided into two subclasses in C3: decid-uous forest and evergreen forest. The LUT algo-rithm for LAI/FPAR was also refined. Theinherent spatial heterogeneity of woody vege-tation and the canopy structure can be betterdemonstrated using the new random RTmodel.

The new LUT parameters will be set to retainthe consistency of the simulated and measuredsurface reflectance. It will minimize LAI retrievalanomalies (overestimation of LAI and failure ofthe retrieval algorithm in moderate or densevegetation) and inconsistencies in LAI andFPAR retrieval (in regions with sparse vegeta-tion, the LAI retrieval can be correct, while theFPAR values are overestimated).

12.5.2. JRC_FPAR Retrieval Algorithm

The JRC_FPAR retrieval algorithm was devel-oped by the European Commission JointResearch Center for European vegetation. Theresolution of the FAPAR product is 10 km forthe world and 2 km for Europe. The JRC_FPAR

FIGURE 12.12 The MODIS LAI/FPAR look-up table algorithm.


algorithm retrieves the FAPAR values based onthe physical model (Figure 12.13).

The algorithm was based on the continuousvegetation canopy model (Gobron et al., 1997)and the 6S model (Vermote et al., 1997).

The FAPAR algorithm includes two steps:First, an atmospheric correction is performed toeliminate the impact of the atmosphere and theangle. Second, mathematical methods are usedto calculate the FAPAR.

The JRC_FPAR algorithm calculates theFAPAR based on the adjusted spectral values.The equation is

g0ðrRred; rRnirÞ ¼l01 rRnir � l02 rRred � l03

ðl04 � rRredÞ2 þ ðl05 � rRnirÞ2 þ l06:

where the coefficients lom (m¼ 1,2,.6) of thepolynomial g0 have been optimized a priori toforce g0ðrRred; rRnirÞ to take on values as close aspossible to the FAPAR associated with the plantcanopy scenarios used in the training data set.Once the coefficients are optimized for a specificsensor, then the inputs of the algorithm are thebidirectional reflectance factors values in theblue, red, and near-infrared bands and the viewand illumination angles values.

θ vθS

gρ 0 gT ρ 20 g v,T θ λρ ρ

Soil single scattering

Canopy single scattering

FIGURE 12.14 Interactions of photons with canopy andsoil background.

FIGURE 12.13 Sketch of the remote-sensing retrieval forFPAR. (http://fapar.jrc.ec.europa.eu/WWW/Data/Pages/FAPAR_Algorithms/FAPAR_Algorithms_Fapar.php).


12.6. FAPAR RETRIEVAL METHODBASED ON THE HYBRID

VEGETATION SPECTRAL MODEL

The definition of FAPAR does not include inci-dent solar radiation reflected by the vegetation orsolar radiation absorbed by the background (in-cluding soil, lichen, and understory), but it doesinclude thepart that is reflectedby thebackgroundand then absorbed by vegetation. Thus, the inci-dent direction of the sun, the canopy structure,and the soil background should be consideredwhen describing the vegetation canopy FAPAR.

12.6.1. The Starting Equationof the FAPAR Model

Suppose that the sun illuminates the canopyfrom a zenith angle of qs, the sensor observationzenith angle of the sensor is qv, and the soilreflectance is rg. Along the light’s incomingpath, the photons can either directly penetratethe canopy and reach the soil or interact withleaves, in which case they are reflected, trans-mitted, or absorbed (Figure 12.14).

The probability of photons directly reachingthe soil represents the canopy transmittance:

T0 ¼ e�l0$Gsms$LAI (12.9)

where l0 is the Nilson parameter taking intoaccount the vegetation clumping effect, Gs isthe projection of leaves per ground area intothe plane perpendicular to the solar incidencedirection, ms is the cosine of the solar zenithangle, and LAI is the vegetation leaf areaindex. The canopy directional reflectance rqv,lalong the incoming path is expressed asfollows:

rqv;l ¼ rc;l

�1� e�l0

Gvmv$GðfÞ$LAI�

þ b$rc;l

264e�l0

Gvmv$GðfÞ$LAI � e�l0

Gvmv$LAI

375

(12.10)

where rc,l is the pure vegetation reflectance at

wavelength l, GðfÞ ¼ exp� �f

180� f

�, f is the

angle between the solar and viewing direction,and b is the ratio of scattering light. If we inte-grate qv into the 2p space, then rqv,l representsthe average single scattering along the incomingpath.

Consider that the leaf reflectance valuesapproximate transmittance. The canopy absorp-tion along the incoming path is:

FAPARqv;l;0 ¼ 1� T0 � 2rqv;l (12.11)

12.6. FAPAR RETRIEVAL METHOD BASED ON THE HYBRID VEGETATION SPECTRAL MODEL 401

We express the absorption of the canopyalong the outgoing path of the photons reflectedfrom the background as:

FAPAR1qv;l ¼ T0rg � T0rgTqv � 2T0rgrqv;l

¼ T0rgð1� Tqv � 2rqv;lÞ

Canopy absorption in a single direction ona single wavelength is:

FAPARtqv;l ¼ ð1� T0 � 2rqv;lÞ

þ ð1� Tqv � 2rqv;lÞT0rg

1� rgrqv;l

Let a ¼ 1� Tqv � 2rqv;l1� T0 � 2rqv;l

; which is simplified:

FAPARtqv;l ¼ FAPARqv;l;0

1þ a $

T0rg

1� rgrqv;l

!

(12.12)

The so-called instantaneous FAPAR is theintegral in the 2p space from 400 to 700 nm:

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FAPA

R

FIGURE 12.15 FAPAR an

FAPARt ¼Z

0:4�0:7

dlZ2p

FAPARtqv;l dUv (12.13)

It is a function of the Nilson parameter (l0), Gfunction (Gs, Gv), solar zenith angle (qs), leaf areaindex (LAI), background reflectance (rg), anddirectional reflectance (rqv,l) of the canopy.

The daily average FAPAR is the integral ofinstantaneous FAPAR with the cosine of solarzenith angle:

FAPARd ¼RFAPARt$cos q dqR

cos q dq(12.14)

12.6.2. Validation of the Model withMonte Carlo Simulations

We conducted the Monte Carlo simulations ofthe FAPAR and compared the results achievedusing the model with those achieved usingthe simulations. The FAPAR for different LAIvalues (Figure 12.15), the solar zenith angle(Figure 12.16), the soil reflectance (Figure 12.17),

5 6 7 8 9

LAI

MC value

Model value

d LAI for MC and model.

0 10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sun zenith angle(°)

FAPA

R

MC valueModel value

FIGURE 12.16 FAPAR and sun zenith angle for MC and model.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

supposed soil reflectance

FAPA

R

MC value

Model value

FIGURE 12.17 The relationships between FAPAR and the assumed soil reflectance in MC and the model.


TABLE 12.3 A Comparison of the MC and ModelFAPAR for Different LAD when LAIis Large

MCFAPAR

ModelFAPAR

ModelFAPAR*

Error(%)

Error*(%)

Planophile 0.9080 0.8940 0.8822 1.547 2.837

Spherical 0.8511 0.8321 0.8191 2.239 3.764

Erectophile 0.8297 0.8157 0.8011 1.685 3.445

* Represents the model FAPAR value when the canopy absorption alongthe outgoing path of photons reflected from the background is omitted.The results are obtained when LAI¼ 3.5, qs¼ 30�, rg¼ 0.1181.

TABLE 12.4 A Comparison of MC and Model FAPARfor Different LAD when LAI is Low

MCFAPAR

ModelFAPAR

ModelFAPAR*

Error(%)

Error*(%)

Planophile 0.5517 0.5416 0.5212 1.834 5.526

Spherical 0.4495 0.4458 0.4175 0.819 7.123

Erectophile 0.4440 0.4242 0.3961 4.448 10.780

* Represents the model FAPAR value when the canopy absorption alongthe outgoing path of photons reflected from the background is omitted.The results are obtained when LAI¼ 1, qs¼ 30�, rg¼ 0.1181.


and the leaf angle distribution (LAD) (Tables12.3 and 12.4) were calculated using the modeland simulated using the MC method.

The relationships between the FAPAR andLAI in the MC simulation and the model areshown in Figure 12.15. In both cases, the FAPARincreases with the LAI, but the rate graduallyslows. The value saturates after LAI¼ 5. Themodel value is slightly lower than the MC valuebecause the model does not consider themultiple scattering of photons in the canopy,while the MC value does. Because multiple scat-tering increases with the LAI, it is understand-able that the difference between the model andMC results increases. However, the differenceis limited to a small range (less than 3%) whenthe LAI is maximized.

Figure 12.16 shows that the FAPAR increaseswith the sun zenith angle. The physical reason isthe elongation of the photon path in the canopyand, hence, the higher probability of collisionsbetween the photons and leaves. Due to theomission of multiple scattering, the model valueis also smaller.

We also analyzed the contribution of the back-ground to the canopy FAPAR. With the increasein soil reflectance, the canopy absorption alongthe outgoing path of the photons reflected fromthe background also increases. Thus, the resultof greater soil reflectance is a larger FAPARvalue for the vegetation. The model value issignificantly lower than the MC value whenthe soil reflectance is assumed to be greaterthan 0.6. Because the real soil reflectance is oftenless than 0.4 in the PAR region from 400 to 700nm, the error for the model is actually low. Theresults imply that the canopy absorption alongthe outgoing path cannot be neglected.

Comparisons of the model and MC results fordifferent LAD values are listed in Table 12.3 forLAI¼ 3.5 and in Table 12.4 for LAI¼ 1. Due tothe small sun zenith angle (<45�), the largestFAPAR value is found for the planophilecanopy; the spherical and erectophile valuesare the second and third, respectively. Themodel

value is slightly smaller, and the error is approx-imately 2%, as shown in column 4. The FAPARmodel values when the canopy absorption alongthe outgoing path is omitted are listed in column3, with the corresponding error in the lastcolumn. It is clear that the average error is larger;it exceeds 7% when the LAI is low. By contrast,our model considers this contribution, and theerror is approximately 2% when we compareour results with those of the MC simulation.

12.6.3. The Field Validation

We further validated the algorithm using dailyFAPAR values for wheat. The winter wheat sitewas located at 38� 51’ 26’’ N, 100� 24’ 38’’E inZhangye, Gansu Province, China. The PAR data


were measured using a SunScan v1.01 probe athalf-hour intervals from 8 AM to 8 PM on June16, 2008. In every instance, we measuredthe incoming solar flux IYTOC, the flux to theground IYGround, the flux from the ground I[Ground,and the outgoing solar flux I[TOC. The APAR valuewas calculated using the following formula:

APAR ¼ IYTOC � IYGround þ I[Ground � I[TOC

(12.15)

The daily change in APAR is depicted inFigure 12.18. The curve resembles a sine curve,reaching a peak at approximately 1 PM. Thecurve is also similar to a cosine curve, witha trough at approximately 1 PM. Figure 12.19also depicts the MC and model results. Theywere simulated or calculated based on the corre-sponding leaf reflectance, transmittance, and soilreflectance data as well as the LAI and LAD

8 10 12 140

200

400

600

800

1000

1200

1400

1600

1800

APA

R

FIGURE 12.18 The dai

values. The results show that the algorithm, theMC method data, and the field data share thesame daily trend and a similar scale. The degreeof error is small and acceptable, demonstratingthe feasibility of the proposed model.

12.6.4. The Retrieval Algorithmof FAPAR

According to the FAPAR equation in Section12.1, the FAPAR input parameters include thefollowing: leaf area index (LAI), clumping index,G function (Gs, Gv), leaf reflectance (rc;l), soilbackground reflectance (rg), solar zenith angle(qs), and the sun-target-sensor angle (f). TheFAPAR is expressed by

FAPAR ¼ FðLAI; l0;Gs;Gv; rc;l; rg; qs;fÞ:

The LAI is the basic canopy parameter. It isobtained from the reflectance image retrieval

16 18 20 22hour

ly change in the APAR.

FIGURE 12.19 The daily change in the FAPAR for the field, MC, and model.


process. l0, Gs, Gv depend on the vegetation type.They are obtained from prior ground measure-ments. rc,l and rg can be extracted from the data-base of measured spectra or can be replaced withpurepixel spectra. qs can be calculatedusing astro-nomical software by inputting the time and place.fdependson theanglebetween the sunand lineofsight and the LAD of the canopy as obtained fromthe image retrieval.

The solid angle integral in 2p space can besplit into the double integral of the zenith andazimuth, and the integrated FAPAR averagecan be obtained in 2p space, that is,

FPAR2p;l ¼ 1p

ZFPARqv;l cos q dU

¼ 1p

Z2p0

Zp=20

FPARqv; l cos q sin q dq d4:

(12.16)

Here,

FPARqv;l ¼ FPARqv;l;0

1þ a$

T0rg

1� rgrqv;l

!

¼ ð1� T0 � 2rqv;lÞ 1þ a$

T0rg

1� rgrqv;l

!

a ¼ 1� Tqv � 2rqv;l1� T0 � 2rqv;l

; T0;qv ¼ e�l0

Gs;qvms;qv

$LAI

rqv;l ¼ rc;l

�1� e�l0

Gvmv$GðfÞ$LAI

�

þ b$rc;l

�e�l0

Gvmv$GðfÞ$LAI � e�l0

Gvmv$LAI

�

GðfÞ ¼ exp�� f

p� f

�


The integrated wavelength is calculated.When the number of single-band FAPARelements in the 400e700 nm range is large, thefollowing formula is used:

FAPARt ¼ 1700� 400

24 Pn�1

i¼ 1

FAPARliþ1 þ FAPARli

2ðliþ1 � liÞ

þFAPARl1ðl1 � 400Þ þ FAPARlnð700� lnÞ

35: (12.17)

Here, n is the number of bands. and FAPARt isthe final integral of the FAPAR in the 400e700nm range. FAPARli is the FAPAR for band i. liis the central wavelength for band i. The unitsare nm. If the central wavelengths of the startingand ending bands are not between 400 nm and700 nm, then the last two items in squarebrackets are the correction terms.

Actually, a multispectral image usually hasthree or four bands, so FAPARt can be calculatedas follows:

FAPARt ¼ 1n

Xni¼ 1

FAPARli

FAPAR0

FAPAR0li

: (12.18)

Here, FAPAR’ is the integrated FAPAR referencevalue in the 400e700 nm range, and FAPAR0

liis

the reference value of the FAPAR band i.The basic process of FAPAR retrieval is

shown below.

ρ

v

0.4 0.7 2

tFAPAR d d

FAPAR

π

λ−

= Ω∫ ∫ ...

{ }0...1g e ...LAIλρ ρ −= +

[ ] msv 04

m Iωρ

μ μ= ...

This section presents a new FAPARmodel thatis basedonahybridvegetationmodel. It considersthe solar incident direction, canopy structure, soilbackground, and the multiscattering inside the

canopy or between the canopy and soil. Thenumerical simulation and field validation wereperformed, and the retrieved process wasestablished.

12.7. CASE STUDY

12.7.1. Study Region and Dataset

The study region is an oasis situated inZhangye City in the middle of the Heihe RiverBasin (37�450w42�400N, 97�420w102�040E), thesecond largest inland river basin in China. It isone of the most arid areas in the country. Thetype and distribution of the landscapes and plantcommunities in the region can be found athttp://heihe.westgis.ac.cn/. The crops sowed inthe oasis includemaize, wheat, barley, and benne;growing these crops always requires irrigation.The Watershed Allied Telemetry ExperimentResearch (WATER) remote-sensing experimentwas conducted in the Heihe River Basin in 2008.Our field experiment was one part of WATER.

12.7.2. FAPAR Retrieval Usinga Hyperspectral Multiangle Image

12.7.2.1. Preprocessing of CHRIS Data

After verifying the reliability of the model,PROBE-CHRIS hyperspectral multiangle imagesobtained on June 4, 2008 (Figure 12.20) wereselected for retrieving the FAPAR. On October22, 2001, PROBA (Project On-Board Autonomy)was launched as a technology demonstrationwithin ESA’s general support technologyprogram. CHRIS (compact high-resolutionimaging spectrometer), the prime instrument of

FIGURE 12.20 A CHRIS image covering the study area with 4 view angles, after geometric correction (the view anglesfrom left to right are 55� and -36�).

12.7. CASE STUDY 407

the PROBA mission, is a hyperspectral sensor. Itis intended to collect BRDF (bidirectional reflec-tance distribution function) data for a betterunderstanding of spectral reflectance. CHRISacquires a set of images with five view angles(e55�, e36�, 0�, 36�, and 55�) for each targetduring its 2.5-min acquisition sequence (Verrelstet al., 2008; CHRIS/PROBA Website), and the62-band images are collected in the visible andnear-infrared regions (from 400 nm to 1050 nm).

The CHRIS sensor includes 18 bands (thecentral wavelengths are 442 nm, 490 nm, 530nm, 551 nm, 570 nm, 631 nm, 661 nm, 674 nm,697 nm, 706 nm, 712 nm, 741 nm, 751 nm, 780nm, 872 nm, 895 nm, 905 nm, and 1018 nm).The geometric image correction, radiation correc-tion, atmospheric correction, and noise removalmethod are described elsewhere (Fan et al., 2010).

An atmospheric correction is an essential partof the preprocessing for hyperspectral images. Inthis study, the atmospheric correction of theCHRIS image products obtains the surfacereflectance using the ACORN 1.5 model andthe atmospheric sounding data. ACORN is anatmospheric correction software for quantitativehyperspectral images. It can accurately eliminatethe blurring effect caused by the atmosphere,and it can be used to obtain the spectral reflec-tance of the hyperspectral image. Figure 12.21shows the spectrums before and after atmo-spheric correction.

The integrated filter method is used in thischapter. This method combines space-dimen-sional filtering with spectral filtering. First,a minimum noise fraction (MNF) transformationis performed to remove the noise from the spatialdimension. Then, the noise in the spectral dimen-sion is removed by a fast Fourier transform(FFT), and spectral filtering is conducted in thefrequency dimension. The spectrum analysis ofthe information and noise shows that the usefulinformation tends to be low frequency but thatthe noise is mainly high frequency; therefore,the noise can be removed by applying low-passfiltering to the actual hyperspectral data. TheButterworth low-pass filter was chosen.

The spectral variation in the vegetation canopy(which consists mostly of corn, wheat, and othercrops) is caused mainly by the variation in thechlorophyll content and leaf area index in thevisible and near-infrared bands (400e900 nm).To identify the frequency range accurately, thecanopy reflectance spectrum without noise mustbe selected as a reference spectrum. Thus, thedata simulated using the PROSAIL model werechosen. Assuming that the analog spectrumcontains nonoise, the vegetation canopy spectrumcan be obtained by changing the correspondingparameters under different conditions. Aftera Fourier transform of the canopy spectrum, thehigh cut-off frequency is determined accordingto the frequency range affected by the spectral

400 500 600 700 800 900 1000 11000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Wavelength (nm)

Ref

lect

anc

Soil spectrum before correction

Soil spectrum after correction

Canopy spectrum before correction

Canopy spectrum after correction

FIGURE 12.21 The soil and vegetation spectrum of the CHRIS image before and after the atmospheric correction.


change. Todemonstrate the spectral intensity vari-ations of the CHRIS image pixels, the spectralamplitude of the image pixels was comparedwith that of the simulated data. However, theCHRIS data contain only 18 channels; therefore,the 18 channels should be interpolated into 180channels before using the FFT.

We selected the Butterworth low-passfilter andset the minimum value of the Butterworth func-tion to 0.01283, according to the high-frequencyinformation from the Fourier analog data spec-trum. The CHRIS images of the study area beforeand after the filtering are shown in Figure 12.22.

12.7.2.2. FAPAR Retrieval

The FAPAR retrieval parameters include theLAI, clumping index, G function, leaf reflectance,soil reflectance, solar zenith angle, observationzenith angle, and GðfÞ. Given this informationand the prior knowledge from the groundmeasurements, Gv ¼ 0:6 and l0 ¼ 0:6 in themaize canopy, and Gv ¼ 0:1 and l0 ¼ 0:97 inthe wheat canopy. The measured reflectance of

the pure soil and pure vegetation and the vegeta-tion reflectance of the image are shown inFigure 12.23. The solar zenith angle (qs) and thesolar azimuth (4s) of the scanning time arecomputed using astronomical software, resultingin qs ¼ 24.97� and 4s ¼ 137.00�. Wheat and maizeare isolated after the classification of the CHRISdata; then, the LAI of the multispectral imagesis retrieved using the least-squares method(LSE) and GðfÞ is obtained synchronously.

First, the FAPAR of the single band and singleangle is calculated using Formula (12.12). Then,the FAPAR of the single-band done zenith angleintegral can be calculated using Formula (12.17).The CHRIS data have a high spectral resolution,and nine bands exist in the 400e700 nm range;therefore, FAPAR can be retrieved using Formula(12.18). The results are shown in Figure 12.24.

12.7.2.3. Validation of Retrieval Results

We measured the PAR of the wheat a fewminutes before and after imaging, as shown inTable 12.5. The measurement site is located at

(a) (b)

FIGURE 12.22 A comparison of the CHRIS image of the study region area before and after the filtering (a) before;(b) after.

12.7. CASE STUDY 409

38 � 51 ’27.59’’N, 100 � 24’ 35.39’’E. The retrievedLAI is 6, and the measured LAI is 6.1. Theretrieved FAPAR is 0.90063, and the measuredFAPAR is 0.8605. The retrieved values andmeasured values are close, indicating that thisalgorithm is effective.

12.7.3. FAPAR Retrieval Usingthe Multispectral Image

The visible and near-infrared band data arethe most popular data used to retrieve FAPAR.In this section, multiband SPOT data were usedto retrieve the FAPAR. Unlike the CHRISimages, the SPOT data only have three bandsthat are observed from one direction. Therefore,the FAPAR of the three bands can be inverted,and the FAPAR of the canopy can be calculatedby integrating the band and the direction.

The images were acquired on July 4, 2008, at4:23:26 GMT. They included SPOT 2.5mpanchromatic images and 10 m multispectralimages. The images cover the central plain ofLinze County, Zhangye City, Gansu Province,and the latitude and longitude are 39�6 ’-39�22’N, 99�53 ’-100�18 ’E.

The SPOT-5 data indicate the 1A product.Therefore, geometric correction, atmospheric

correction, radiometric calibration, and cross-radiation correction should be performed. TheFAPAR can be retrieved after preprocessing.

The radiance can be calculated after the cali-bration by

L ¼ X=Aþ B;

where L is the radiance calculated from the pixelsor the equivalent radiance (its units are W$m-2 $sr-1$mm-1); parameter A is the product of Ak,Gm, g, and g, and is known as the absolute cali-bration of the radiometrically corrected image(its unit are W-1$m2$sr$mm); and parameterB is the calibration bias (its units are W$m-2$sr-1$mm-1). The radiometric calibration parame-ters for the SPOT-5 images are listed in Table 12.6.

The 6S (the Second Simulation of SatelliteSignal in the Solar Spectrum), version 4.1(Vermote et al., 1997) model was used for theatmospheric correction. The Wiener filter (Liuzhengjun, 2004) was chosen to remove thecross-radiance.

The supervised classification was performedusing maximum likelihood estimation. Thesurface features of the image include maize,wheat, and other vegetation; roads; cities; waterbodies; canals; and desert. The purpose of theclassification process is to distinguish the

400 500 600 700 800 900 1000 11000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Wavelength (nm)

Ref

lect

ance

Vegetation

Soil

Pixel

FIGURE 12.23 A comparison of the reflectance of pure vegetation, pure soil, and vegetation in the image.

TABLE 12.5 The Measured Surface Data and Calculated FAPAR

Time Upper light*Canopyreflectance* Lower light* Spread

Surfacereflectance* APAR* FAPAR

11:51:40 1711.6 56.9 191.7 1.13 9.8 1472.8 0.8604814

* The units for Upper light, Canopy reflectance, Lower light, Surface reflectance and APAR are mmol/(m2*s).

(a) (b)

FIGURE 12.24 Retrieval results of LAI and FAPAR.


(b)(a)

FIGURE 12.25 SPOT-5 images (a) panchromatic 2.5-m image (b) multispectral 10-m image (near-infrared, red, green).

12.8. SUMMARY 411

vegetation from the background in remote-sensing images. The SPOT panchromatic imagewith 2.5-m resolution only has one band; it isnot easy to classify. Thus, this image should firstbe fused with the SPOT-5 multispectral image(10 m resolution); here, the Gram-Schmidtspectral enhancement method was used. Theimage has multispectral information; therefore,the vegetation and background can be properlydistinguished using near-infrared bands.

12.7.3.1. FAPAR Retrieval

The FAPAR retrieval parameters include thefollowing: the LAI, clumping index, G function,leaf reflectance, soil reflectance, solar zenithangle, observation zenith angle, and GðfÞ. Basedon prior information from groundmeasurements,Gv ¼ 0:6 and l0 ¼ 0:6 in the maize canopy, andGv ¼ 0:1 and l0 ¼ 0:97 in the wheat canopy.The solar zenith angle (qs) and solarazimuth (4s) are computed at scanning time usingSUN_ELEVATION and SUN_AZIMUTH in theMETADATA.DIM file, that is, qs ¼ 24.97� and

TABLE 12.6 The Radiometric Calibration Parameters for t

Band Green Red

Gain (W-1$m2$sr$mm) 1.677074 1.22502

Bias (W$m-2$sr-1$mm-1) 0 0

4s ¼ 137.00�. The wheat and maize are isolatedafter the supervised classification of the SPOT-5data, and then the LAI is retrieved using theleast-squares method (LSE). GðfÞ is obtainedsynchronously. The FAPAR can then be obtainedusing Equations (12.17) and (12.19).

The results of the FAPAR retrieval processusing the SPOT data are shown in Figure 12.26.

12.8. SUMMARY

This chapter describes the instruments andfield measurement methods, the MC simula-tions, the empirical models, and the quantitativemodel and retrieval methods based on the radi-ative transfer model for FAPAR retrieval.Finally, we use the Heihe River Basin as anexample and present a FAPAR retrieval casestudy using a physically based model.

As described above, FAPAR retrieval hasachieved remarkable advances, and manymature remote-sensing products can currently

he SPOT-5 Images

Near infrared Shortwave infrared Pan

1.73855 6.332 1.388448

0 0 0

(a) (b)

FIGURE 12.26 The FAPAR retrieval results for the multisource data (a) 2.5 m SPOT, (b) 10 m SPOT.


be acquired. This empirical retrieval algorithmserves as an example for generating sucha product, but its applications are limited. Thephysically based retrieval method considersmultiple scattering in the canopy using the radi-ative transfer mechanism; therefore, it is moreuniversal and useful.

To accurately calculate key parameters, suchas light energy utilization, and to provide inputparameters for the land-surface process models,the FAPAR should also be obtained undercloudy conditions. Solar radiation is dividedinto direct and diffuse after atmospheric trans-mission. The directions of the direct and diffuseradiation reaching the surface are different, asare the directions in which they are transmittedwithin the vegetation. The expressions usedwill differ when describing the FAPAR usingradiative transfer models. Most FAPAR retrievalalgorithms have not separated direct solar radia-tion from diffused radiation, which will result inthe impact of scattered radiation on the APARbeing underestimated. Because the proportionof scattered radiation increases under cloudyconditions, modeling direct and diffuse radia-tion separately is necessary to improve retrievalaccuracy. This topic is a future direction forFAPAR retrieval research.

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