BOSTON UNIVERSITY
GRADUATE SCHOOL OF ART AND SCIENCES
Dissertation
EVALUATION OF THE PERFORMANCE OF THE MODIS LAI
AND FPAR ALGORITHM WITH MULTIRESOLUTION
SATELLITE DATA
by
YUHONG TIAN
B.S., Nanjing Institute of Meteorology, 1992 M.S., Chinese Academy of Meteorological Science, 1995
Submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
2002
ii
Approved by
First Reader ________________________________________________
Ranga B. Myneni, Ph. D. Associate Professor of Geography
Second Reader ________________________________________________
Yuri Knyazikhin, Ph. D. Research Associate Professor of Geography
Third Reader ________________________________________________
Mark A. Friedl, Ph. D. Associate Professor of Geography
Fourth Reader ________________________________________________
Curtis E. Woodcock, Ph. D. Professor of Geography
Fifth Reader ________________________________________________
Alexander L. Marshak, Ph. D. Research Associate Professor DW-&(780%&
iii
Acknowledgments
I would first of all like to thank the members of my dissertation committee, Ranga
Myneni, Yuri Knyazikhin, Mark Friedl, Curtis Woodcock, and Alexander Marshak, for
their guidance and support during the past several years. I appreciate the help and
generous contributions of my committee members. My heartfelt thanks are due to my
advisors, Dr. Myneni and Dr. Knyazikhin, for their advice, academic encouragement and
trust in my research ability during my years at Boston University. Their insight to key
research questions inspired me to dig deeper and deeper. Countless discussions with them
about research and life had significant impact on my views about science and life. I thank
them for their patience, support, and mentoring.
I am grateful to Curtis Woodcock, who shared his knowledge of remote sensing,
geostatistics and validation. I thank him for providing tremendous guidance and
forthright comments on my research work. Many thanks to Jan Bogaert, whose
knowledge of spatial pattern metrics provided important insights on spatial processes and
enriched this dissertation. Special thanks to Jeff Privette and Jeff Morisette for providing
the opportunity to participate in the SAFARI 2000 wet season campaign in Botswana,
where I had wonderful experiences.
Thanks go to all members of the Geography Department, including the faculty, staff
and fellow students. Tony Soares helped with many computing problems. John Hodges
provided help with map projections. Mutlu Ozdogan with GIS software. Douglas McIver
kindly offered MODIS simulation codes. I am particularly grateful to Nikolay Shabanov,
for his talent and patient help with mathematics. It has been my pleasure to have Yu
Zhang and Yujie Wang as friends and colleagues. My knowledge of C programming is a
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result of their help and support. I also thank my friends in this department for sharing
many wonderful moments and fabulous conversations; they are Adeline Wong, Rongqian
Yang, Jiarui Dong, Wolfgang Buermann, Alex Lotsch, Jicheng Liu, Feng Gao, Conghe
Song, Yufang Jin, Xiangdong Song, Jiannan Hu, Junchang Ju and Gang Gong.
I am deeply in debt to my husband, Liming Zhou. His unceasing humor kept me
happy and refreshed. I thank him for his constant love, patience, encouragement and
strength during the four years of graduate study.
I thank my parents for encouraging my love of science. I dedicate this dissertation to
my parents and my husband; their encouragement and support enabled this work to come
to fruition.
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EVALUATION OF THE PERFORMANCE OF THE MODIS LAI
AND FPAR ALGORITHM WITH MULTIRESOLUTION
SATELLITE DATA
(Order No. )
YUHONG TIAN
Boston University Graduate School of Arts and Sciences, 2002
Major Professor: Ranga B. Myneni, Associate Professor of Geography
ABSTRACT
Green leaf area index (LAI) and fraction of photosynthetically active radiation absorbed
by vegetation (FPAR) are two key variables of vegetated surfaces because of the
important role they play in biosphere-atmosphere interactions. Accurate global estimates
of these parameters are essential for understanding and predicting the future state of the
climate and terrestrial ecosystems. The objective of this research is to evaluate the
performance of a LAI/FPAR algorithm designed for the Moderate Resolution Imaging
Spectroradiometer (MODIS) aboard the NASA TERRA spacecraft, with special
emphasis on the effects of scale, or spatial resolution. Results from prototyping exercises
prior to the launch of MODIS demonstrated the feasibility of physically valid retrievals
with the algorithm. It was found that land cover misclassifications between distinct
biomes could fatally impact the retrievals. A comparison of coarse (16 km) and fine (30
m) resolution retrievals highlighted the scale dependence of the algorithm. Investigation
of the effect of land cover mixtures within coarse resolution pixels shows that LAI
retrieval errors are inversely related to the proportion of the dominant land cover in a
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pixel. Errors are particularly large when forests are minority biomes in non-forest pixels.
A physically based theory for scaling with an explicit scale dependent radiative transfer
formulation was developed and successfully applied to scale the algorithm to various
resolutions of satellite data. Consistency between LAI retrievals from 30 m Landsat
Enhanced Thematic Mapper Plus (ETM+) data and field measurements from Maun
(Botswana) indicates good performance of the algorithm. LAI values for coarse
resolution data are underestimated if the resolution of the data is not considered in the
retrieval technique. Hierarchical variance analysis of data from Maun, Harvard Forest
(USA) and Ruokulahti Forest (Finland) indicates that LAI estimates derived from ETM+
data exhibit multiple characteristic scales of spatial variation. Isolating the effects
associated with different scales through variograms aids the development of a new
sampling strategy for validation of MODIS products.
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Table of Contents
Acknowledgments............................................................................................................ iii
Abstrace..............................................................................................................................v
Table of Contents............................................................................................................ vii
List of Tables.....................................................................................................................xi
List of Figures ................................................................................................................. xii
List of Abbreviations......................................................................................................xix
Chapter 1 Introduction .....................................................................................................1
1.1 Background ................................................................................................................1
1.2 LAI and FPAR Algorithms ........................................................................................3
1.2.1 Definition of LAI and FPAR ...............................................................................3
1.2.2 LAI/FPAR Algorithms ........................................................................................4
1.2.3 The MODIS LAI/FPAR Algorithm.....................................................................6
1.3 Statement of the Research Problems..........................................................................7
1.3.1 Quantification of the Physical Functionality and Performance of the MODIS
LAI/FPAR Algorithm...................................................................................................7
1.3.2 Scaling Effects on the MODIS LAI/FPAR Retrievals ........................................7
1.3.3 Validation.............................................................................................................9
1.4 Objectives and Organization of This Dissertation ...................................................11
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Chapter 2 Prototyping of MODIS LAI and FPAR Algorithm with LASUR and
LANDSAT Data...............................................................................................................13
2.1 Introduction ..............................................................................................................13
2.2 The Algorithm..........................................................................................................15
2.2.1 Statement of the Problem...................................................................................15
2.2.2 Radiation Transport in a Canopy.......................................................................16
2.2.3 Physical Meaning of Eq. (2.2) ...........................................................................19
2.2.4 Adjusting the LUT for Data Resolution ............................................................21
2.3 Data Analysis ...........................................................................................................22
2.3.1 Satellite Data......................................................................................................22
2.3.2 Spectral Signatures ............................................................................................24
2.4 Prototyping of The Algorithm..................................................................................26
2.4.1 Prototyping with LASUR Data..........................................................................26
2.4.2 Prototyping with Landsat Data ..........................................................................33
2.5 Conclusions ..............................................................................................................35
Chapter 3 Radiative Transfer Based Scaling of LAI/FPAR Retrievals From
Reflectance Data of Different Resolutions.....................................................................50
3.1 Introduction ..............................................................................................................50
3.2 Data and the LAI/FPAR Algorithm .........................................................................53
3.3 Data Analysis ...........................................................................................................55
3.3.1 Characterizing Land Cover Heterogeneity ........................................................55
3.3.2 Canopy Reflectances and Heterogeneity ...........................................................56
3.3.3 LAI Retrievals and Heterogeneity .....................................................................58
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3.4 Physically Based Theory for Scaling .......................................................................60
3.4.1 Definition and Background Information............................................................61
3.4.2 Scale Dependent Radiative Transfer Formulation.............................................62
3.4.3 Scaling of Reflection and Absorption Properties of Scattering Centers............67
3.4.4 Scaling of Surface Reflectances ........................................................................69
3.4.5 Scaling of LAI and FPAR Fields.......................................................................71
3.5 Concluding Remarks................................................................................................73
Chapter 4 Multiscale Analysis and Validation of the MODIS LAI Product over
Maun, Botswana ..............................................................................................................85
4.1 Introduction ..............................................................................................................85
4.2 SAFARI 2000 Wet Season KALAHARI Transect Campaign ................................88
4.2.1 Sampling Methods .............................................................................................89
4.2.2 LAI Measurements ............................................................................................90
4.3 Heterogeneity of Measured LAI at the SAFARI 2000 Sites....................................91
4.3.1 Statistical Analysis of Means.............................................................................91
4.3.2 Semivariance Analysis.......................................................................................92
4.4 Validation of MODIS LAI at MAUN......................................................................93
4.4.1 Selection of a 10 km by 10 km ETM+ Region..................................................94
4.4.2 Validation of 1 km by 1 km ETM+ LAI............................................................94
4.4.3 Resolution Effects on MODIS LAI Retrievals ..................................................98
4.5 Hierarchical Analysis of Multiscale Variation in LAI and NDVI Data.................102
4.5.1 Hierarchical Decomposition of Scene Variograms .........................................103
4.5.2 Satellite and Field Data....................................................................................105
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4.5.3 Variograms of Hierarchical Effects .................................................................106
4.6 Concluding Remarks..............................................................................................113
Chapter 5 Conclusions ..................................................................................................142
Appendix: Effect of Non-linearity and Pixel Mixture on LAI Retrievals ................147
List of Journal Abbreviations.......................................................................................152
References.......................................................................................................................153
CURRICULUM VITAE ...............................................................................................169
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List of Tables
Table 2.1. Spectral Statistics for LASUR Data and LANDSAT TM Data .......................47
Table 2.2. Retrieval Index (a) and Mean LAI (b) for Misclassified LASUR Data ..........48
Table 2.3. Comparison of the Results from LASUR LUT and LANDSAT LUT
Retrievals....................................................................................................................49
Table 3.1. Overall Percentage Function PF(j) at 8 km Resolution ...................................84
Table 4.1. Plant Height and LAI-2000 Measured Area...................................................137
Table 4.2. t-Test of the Means of the Transect and Grid LAI Measurements.................137
Table 4.3. t-Test of the LAI Means of Different Regions ...............................................138
Table 4.4. Means of Difference in LAI (DL) Retrievals Between Method 1 and
Method 2 from One Land Cover Type.....................................................................139
Table 4.5. Means of Difference in LAI (DL) Retrievals Between Method 1 and
Method 2 from Two Land Cover Types...................................................................139
Table 4.6. Hierarchical Model Results for the Maun Scenes ..........................................140
Table 4.7. Hierarchical Model Results for the Harvard Forest Scenes ...........................140
Table 4.8. Hierarchical Model Results for the Ruokolahti Forest Scenes.......................141
Table 4.9. Coefficients of Variation of NDVI and LAI from Different Biome Types
and Sites ...................................................................................................................141
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List of Figures
Figure 2.1. Statistical properties of canopy reflectances for global LASUR data in
July 1989. (a) Histogram of canopy reflectances at the RED band. (b) Histogram
of canopy reflectances at the NIR band. (c) Histogram of NDVI. (d) 25%
density contours in the RED-NIR space, which shows the location of points with
high density for different biomes. The straight line represents the place where
NDVI are equal to 0.68. Canopy structure varies considerably with the same
NDVI value. ...............................................................................................................38
Figure 2.2. Statistical properties of canopy reflectances for Landsat TM data of
Northwest U.S. in June 1987. (a) Histogram of canopy reflectances at the RED
band. (b) Histogram of canopy reflectances at the NIR band. (c) Histogram of
NDVI. (d) 25% density contours in the RED-NIR space, which shows the
location of points with high density for different biomes. The straight line
represents the place where NDVI are equal to 0.68. ..................................................39
Figure 2.3. Dependence of the retrieval index (RI) on uncertainties ε in
measurements and simulations...................................................................................40
Figure 2.4. (a), (c) Histograms of LAI/FPAR derived from the MODIS algorithm
with LASUR data. (b), (d) Histograms of LAI/FPAR derived from NDVI-based
algorithm with 10-year averaged AVHRR Pathfinder data (Myneni et al., 1997).
(e) Histogram of NDVI from retrieved pixels. (f) Histogram of NDVI from non-
retrieved pixels. The mean uncertainty ε is 0.20........................................................41
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Figure 2.5. For broadleaf forests in LASUR data, the scatter plot shows (a) the LAI-
NDVI relationship, (b) the NDVI-FPAR relationship, (c) retrieved pixels in the
RED-NIR space, and (d) non-retrieved pixels in the RED-NIR space. .....................42
Figure 2.6. (a) Histogram of LAI values retrieved under the condition of saturation.
Solid lines present the same histograms as Fig. 2.4(a). Dashed lines show the
ratio of the number of LAI values retrieved under the condition of saturation to
the total number of retrieved pixels. (b) Coefficient of variation (standard
deviation/mean) of retrieved LAI values (COVLAI) as a function of retrieved
LAI. ............................................................................................................................43
Figure 2.7. (a) Global LAI and (b) global FPAR fields derived from LASUR data in
July, 1989. For the non-retrieved pixels, the LAI-NDVI, NDVI-FPAR relations
were used to estimate LAI and FPAR. .......................................................................44
Figure 2.8. Retrievals from Landsat data as a function of spatial resolution-dependent
look-up table (LUT). Histograms of LAI from (a) Landsat LUT, (b) LASUR
LUT, histograms of FPAR from (c) Landsat LUT, and (d) LASUR LUT. ...............45
Figure 3.1. The overall purity PF(j) as a function of spatial resolution. ...........................75
Figure 3.2. Percentage of pixels in group 1 and group 3 as a function of spatial
resolution: (a) Group 1, biome purity ≥ 90%, (b) Group 3, biome purity < 50%. .....76
Figure 3.3. Contour plot of data density distribution in the spectral space of red and
near-infrared (RED-NIR) at (a) 1 km resolution, (b) 8 km resolution from group
1, and (c) 8 km resolution from group 3. Each contour line separates an area in
the spectral space with high data density containing 50% of the pixels from a
given biome. Groups 1 and 3 represent biome purities ≥ 90% and < 50%,
respectively.................................................................................................................77
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Figure 3.4. Mean red (RED) and near-infrared (NIR) reflectance as a function of
spatial resolution: (a) group 1 in RED, (b) group 1 in NIR, (c) group 3 in RED,
and (d) group 3 in NIR. Groups 1 and 3 represent biome purities ≥ 90% and <
50%, respectively. ......................................................................................................78
Figure 3.5. Average distance in spectral space between biome specific spectral
signature (R , N ) and pixels from (a) group 1, and (b) group 3, at different
spatial resolutions. Groups 1 and 3 represent biome purities ≥ 90% and < 50%,
respectively. The parameters R andN are mean red (RED) and near-infrared
(NIR) reflectance values of homogeneous pixels from group 1. See text for
further information. ....................................................................................................79
Figure 3.6. Contour plot of relative difference in LAI derived from unadjusted LAI
retrieval algorithm as a function of spatial resolution and pixel heterogeneity
(purity)........................................................................................................................80
Figure 3.7. NDVI-LAI relations derived from 4 km resolution pixels with purity ≥
90%.............................................................................................................................81
Figure 3.8. Relative difference in LAI retrievals as a function of the presence of the
minority biome: (a) Grasses and Cereal Crops, (b) Shrubs, (c) Broadleaf Crops,
(d) Savannas, (e) Broadleaf Forests, and (f) Needle Forests, in heterogeneous
pixels at 8 km resolution. See text for further information. .......................................82
Figure 3.9. Contour plot of relative difference in LAI derived from adjusted LAI
retrieval algorithm as a function of spatial resolution and pixel heterogeneity
(purity)........................................................................................................................83
Figure 4.1. Sampling scheme of SAFARI 2000 wet season Kalahari Transect (KT)
campaign. .................................................................................................................115
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Figure 4.2. Histograms of transect and grid LAI measurements at the four SAFARI
2000 wet season campaign sites: (a) Pandamatenga, (b) Maun, (c) Okwa, and (d)
Tshane. .....................................................................................................................116
Figure 4.3. Comparison between transect and grid LAI measurements at
Pandamatenga, Maun, Okwa, and Tshane. The dots and error bars represent
means and standard deviations, respectively............................................................117
Figure 4.4. Variograms of field measurements at (a) Pandamatenga, (b) Maun, (c)
Okwa, and (d) Tshane. .............................................................................................118
Figure 4.5. LAI measurements along the transects from the sample points located
375 meters west of the middle sample point to those located 375 meters east. (a)
Pandamatenga, (b) Maun..........................................................................................119
Figure 4.5. LAI measurements along the transects from the sample points located
375 meters west of the middle sample point to those located 375 meters east. (c)
Okwa, and (d) Tshane. .............................................................................................120
Figure 4.6. (a) Color RGB image from Bands 4, 3 and 2 of a 10 km by 10 km region
of the Maun site from an ETM+ image. (b) Vegetation classification map for the
10 km by 10 km region.............................................................................................121
Figure 4.7. Color RGB image from Bands 4, 3 and 2 of a 1 km by 1 km region of the
Maun site. Panel (a) is IKONOS data and panel (b) is ETM+ data. Yellow "+"
represents sampling points, and green "+" represents the positions where the
photos were taken.....................................................................................................122
Figure 4.8. Map of a 1 km by 1 km region at Maun using the segmentation procedure
described in the text. Patches 1, 2, 4, 7, 8, 9, 12, 13 and 15 are savannas. Patches
3, 5, 6, 10, 11, and 14 are shrubs..............................................................................123
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Figure 4.9. (a) Region by region comparison of field measurements and MODIS
algorithm based LAI from 30 m resolution ETM+ data at Maun. (b) Pixel by
pixel comparison of LAI retrievals from savanna and shrub look-up tables. (c)
Region by region comparison of LAI retrievals from savanna and shrub look-up
tables.........................................................................................................................124
Figure 4.10. Variations in the mean and standard deviation (SDT) of RED, NIR, and
NDVI as a function of spatial resolution: (a) mean of RED, (b) STD of RED, (c)
mean of NIR, (d) STD of NIR, (e) mean of NDVI, and (f) STD of NDVI..............125
Figure 4.11. Pixel by pixel comparison of LAI retrievals averaged at 30 m resolution
and retrieved directly from reflectance at resolution of (a) 250 m using shrub
look-up table (LUT) only, (b) 500 m using shrubs LUT only, (c) 1000 m using
shrubs LUT only, (d) 250 m using savannas LUT only, (e) 500 m using
savannas LUT only, and (f) 1000 m using savannas LUT only...............................126
Figure 4.12. Overall standard deviation as a function of the difference in LAI (DL)
between averages from 30 m resolution and retrievals directly from reflectance
at (a) 250 m, (b) 500 m, and (c) 1 km resolution. ....................................................127
Figure 4.13. Pixel by pixel comparison of LAI retrievals averaged from 30 m
resolution and retrieved directly from reflectance at resolution of (a) 250 m for
all pixels, (b) 500 m for all pixels, (c) 1000 m for all pixels, (d) 250 m for shrub
pixels only, (e) 500 m for shrub pixels only, (f) 1000 m for shrub pixels only, (g)
250 m for savanna pixels only, (h) 500 m for savanna pixels only, and (i) 1000
m for savanna pixels only.........................................................................................128
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Figure 4.14. (a) RBG image of a 15 km by 13 km region of Harvard Forests
produced from ETM+ Bands 4, 5, and 3. (b) Land cover classification map using
unsupervised classification procedure......................................................................129
Figure 4.15. (a) RBG image of a 10 km by 10 km region of Ruokolahti Forest
produced from ETM+ Bands 4, 5, and 3. (b) Land cover classification map using
unsupervised classification procedures. ...................................................................130
Figure 4.16. LAI images from (a) the Harvard Forest site and (b) the Ruokolahti
Forest site. ................................................................................................................131
Figure 4.17. Hierarchical decomposion of variograms for (a) NDVI and (b) LAI of
the Maun site. ...........................................................................................................132
Figure 4.18. Hierarchical decomposion of variograms for (a) NDVI and (b) LAI of
the Harvard Forest site. ............................................................................................133
Figure 4.19. Hierarchical decomposion of variograms for (a) NDVI and (b) LAI of
the Ruokolahti Forest site.........................................................................................134
Figure 4.20. The NDVI image from the Ruokolahti Forest site. The color from black
to white represents the range of NDVI values. The brighter the image, the larger
the NDVI value. .......................................................................................................135
Figure 4.21. Histograms of (a) NDVI, (b) RED, and (c) NIR for young, regular, and
dense forests at the Ruokolahti Forest site. ..............................................................136
Figure A.1. Relation between LAI and surface reflectance at 30 m resolution for (a)
savannas (solid line), (b) savannas (solid line) and shrubs (dash line), which
shows that the retrieved LAI from coarse resolution reflectance data is
underestimated for both savannas and shrubs, and (c) savannas (solid line) and
shrubs (dash line), which shows that the retrieved LAI from the coarse
xviii
resolution reflectance data is underestimated for shrubs and overestimated for
savannas. See Appendix for further clarification. ....................................................151
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List of Abbreviations
AVHRR Advanced Very High Resolution Radiometer
BATS Biosphere-Atmosphere Transfer Scheme
BCM Biome Classification Map
BRDF Bidirectional Reflectance Distribution Function
BU Boston University
CART Canopy Architecture Radiative Transfer
CLM Common Land Model
COV Coefficient of Variation
DL Difference in LAI
EOS Earth Observing System
ETM+ Enhanced Thematic Mapper Plus
FOV Field-Of-View
FPAR Fraction of Photosynthetically Active Radiation Absorbed by Vegetation
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GCM General Circulation Model
GO Geometrical Optics
GPS Global Positioning System
HDRF Hemispherical Directional Reflectance Factor
IGBP International Geosphere-Biosphere Program
LAI Leaf Area Index
LSAT Land-Surface Atmosphere Transfer
LUT Look-Up Table
MANOVA Multivariate Analysis of Variance
MISR Multiangle Imaging Spectroradiometer
MODIS Moderate Resolution Imaging Spectroradiometer
MVC Maximum Value Composite
NASA National Aeronautics and Space Administration
NDVI Normalized Difference Vegetation Index
NIR Near-Infrared
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NOAA National Oceanic and Atmospheric Administration
POLDER Polarization and Directionality of the Earth's Reflectance
RDL Relative Difference in LAI
RI Retrieval Index
RT Radiative Transfer
SiB Simple Biosphere
SDT Standard Deviation
TM Thematic Mapper
UMD University of Maryland
1
Chapter 1
Introduction
1.1 Background
The Earth’s land surface and its ecosystems play an important role in determining the
planet’s environment. Covering much of the Earth’s land surface, global vegetation has
been identified as one of the key constituents of the climate system due to its important
role in geosphere-biosphere-atmosphere interactions. As an important component of
terrestrial ecosystems, vegetation is influenced by and in turn influences the climate
system through biogeochemical processes that involve land-atmosphere exchanges of
radiatively active gases such as carbon dioxide, methane and nitrous oxide, and
biogeophysical processes that involve water and energy exchanges (Sellers et al., 1996).
Understanding these processes is essential for evaluating the future state of climate and
terrestrial ecosystems.
These exchanges of energy and materials are major components of the hydrologic
cycle, the carbon cycle, and the global and regional climate systems. Many hydrological,
ecological, and climate models use land surface properties such as the type of cover, leaf
area index (LAI), fraction of incident photosynthetically active radiation (0.4-0.7 µm)
absorbed by the vegetation canopy (FPAR), roughness length, and albedo as an essential
2
input (Asrar and Dozier, 1994; Sellers at al., 1996). Successful modeling of net primary
production, carbon storage, and trace gas emissions (e.g., methane, non-methane
hydrocarbons, nitrous oxide) requires an accurate model of the micrometeorological and
hydrological environment in addition to the traditional ecological emphasis on vegetation
and biogeochemical controls. Successful modeling of latent and sensible heat fluxes
requires an accurate description of the ecological state and biogeochemical controls in
addition to the traditional emphasis on the physical environment. Increasing realism in
land surface parameterizations has been shown to improve the representation of
interactions between soil, vegetation, and the atmosphere. It is recognized that the most
important properties of the land surface for climate modeling are those that determine
biogeochemical and biogeophysical processes (Townshend et al., 1994). However, many
of these land surface processes are only crudely represented in global climate models.
Satellite observations provide information of global extent at regular temporal
intervals, and thus have the capability to monitor the dynamics of the Earth’s surface and
to quantify the changes that take place. This information can undoubtedly improve the
accuracy of the quantitative treatment of these processes. Analysis of remotely sensed
data has revealed the possibility of using remote sensing techniques to characterize
vegetation properties, and much knowledge has been gained about the role of vegetation
in environmental and climate changes (Dickinson et al., 1993; Bonan, 1995; Sellers et al.,
1996; Myneni et al., 1998; Zhou et al., 2001).
Among the aforementioned biophysical parameters, LAI and FPAR are recognized
as two of the more important and commonly derived parameters from satellite data
because of their importance in estimation of canopy photosynthesis and transpiration. In
order to quantitatively and accurately model global vegetation dynamics and to
3
differentiate short-term from long-term trends, as well as to distinguish regional from
global phenomena, LAI and FPAR must be collected for a long period of time and should
represent every region of the Earth (Knyazikhin et al., 1998a,b). The Advanced Very
High Resolution Radiometer (AVHRR) has been until recently the only satellite sensor
able to observe the land surface activity at regional and global scales with high temporal
frequency. The first global maps of LAI and FPAR were produced from AVHRR data
with the use of biome-dependent semi-empirical and radiative transfer-based relations
between these quantities and a vegetation index (Sellers et al., 1996; Myneni et al., 1997).
New sensors with higher spectral and directional sampling, and more accurate signal in
terms of radiometric calibration, and improved quality of atmospheric and geometric
corrections are becoming available. High quality data acquired from the new generation
satellite sensors, such as the Moderate Resolution Imaging Spectroradiometer (MODIS)
and the Multi-angle Imaging Spectroradiometer (MISR) aboard the TERRA platform,
now provide a unique opportunity to improve the accuracy of LAI and FPAR retrievals.
1.2 LAI and FPAR Algorithms
1.2.1 Definition of LAI and FPAR
Leaf area index is defined as the one-sided green leaf area per unit ground area. LAI for
conifer needles is defined as the projected needle leaf area per unit ground area in needle
canopies (Oker-Blom, 1988; Chen, 1996). FPAR is the fraction of incident
photosynthetically active radiation (0.4-0.7 µm) absorbed by the vegetation canopy. LAI
is a key variable for the evaluation of evapotranspiration and is used as an input in
mesoscale weather forecast and general atmospheric circulation models (Dickinson,
1984; Bonan, 1995). FPAR is one of the basic quantities (the other being the
4
photosynthetic efficiency) required for net primary production estimates (Sellers et al.,
1986). Quantitative and accurate values of LAI and FPAR at regional and global scales
with sufficient temporal frequency are important for quantifying the energy and water
fluxes at the atmosphere-biosphere interface and for characterizing and monitoring the
biosphere and its functioning. As such, there is considerable interest in developing
algorithms for the estimation of LAI/FPAR from satellite measurements of vegetation
reflectance (Knyazikhin et al., 1998a).
1.2.2 LAI/FPAR Algorithms
Two general classes of approaches have been used to infer LAI and FPAR from remote
sensing data; empirical approaches and inversion of physical models (Price, 1993; Hall et
al., 1995; Asner et al., 1998). Empirical approaches rely primarily on curve fitting to
correlate various measures of surface reflectance, including vegetation indices, to ground-
based measurements of LAI/FPAR (Tucker and Sellers, 1986; Peterson et al., 1987;
Verma et al., 1993). These approaches have applied various linear and nonlinear
combinations of spectral bands, which maximize sensitivity of the index to LAI/FPAR,
while minimizing the sensitivity to unknown and undesired canopy characteristics (e.g.,
background reflectance). Among the various vegetation indices, the normalized
difference vegetation index (NDVI) and the simple ratio (SR) are most frequently used to
derive LAI and FPAR from space-borne and air-borne data (Sellers et al., 1993; Myneni
et al., 1994; Chen and Cihlar, 1996). LAI is nonlinearly proportional to NDVI, while
FPAR is linearly related to NDVI (Myneni, 1997). Numerous studies have been reported
to relate vegetation indices to LAI of agricultural crops (Asrar et al., 1984). There have
also been several investigations with regard to this relationship in conifer stands from
Landsat Thematic Mapper (TM) and AVHRR data (Chen, 1996).
5
The limitations of these methods are well known. No unique relationship between
LAI/FPAR and the vegetation index is generally applicable everywhere because the
reflectances of plant canopies also depend on other factors, such as measurement
geometry and spatial resolution (Asrar et al., 1992; Price, 1993; Friedl et al, 1995; Friedl,
1996). These empirical relationships are therefore site- and sensor-specific, and are
consequently unsuitable for application to large areas or in different seasons (Gutman,
1991; Gobron et al., 1997). In addition, soil background, as well as sun-view angular and
atmospheric effects can have a big effect on the variation of vegetation indices (Huete,
1988 and 1989; Kaufman, 1989; Baret and Guyot, 1991; Yoshioka et al., 2000).
Therefore, a physically based model to describe the propagation of light in plant
canopies, and its use in retrieval of biophysical parameters, is the preferred alternative.
Physical models attempt to model the relationship between leaf, canopy, and stand-
level biophysical characteristics such as LAI/FPAR and reflected radiation. Generally,
these models are referred to as “canopy reflectance models”. They can be subdivided into
four general classes: (i) radiative transfer models (Myneni, 1991; Myneni et al., 1992;
Goel and Kuusk, 1992), (ii) geometric models (Li and Strahler, 1986 and 1992), (iii)
hybrid models (combinations of (i) and (ii)) (Li et al., 1995; Chen and LeBlanc, 1997; Ni
et al., 1999), and (iv) Monte Carlo and complex computer simulation models (Ross and
Marshak, 1988; Goel, 1991; Borel et al., 1991; North, 1996; Govaerts and Verstraete,
1998; Lewis, 1999). Once developed and tested, the understanding inferred from the
models can be used to develop algorithms to relate biophysical characteristics to
reflectance. As an alternative, the reflectance model can be used directly in a so-called
inversion, i.e., solved for the biophysical parameters (for example, LAI), given an input
of reflectance. The common technique used in inversion of the model is the look-up table
6
(LUT) method, which pre-calculates the reflectances from all possible combinations of
different parameters, as well as the geometrical combinations. Consequently, the satellite
measurements are compared with the entries of the LUT. Model inversion, which offers
many advantages over the empirical techniques, has been presented as the ultimate
approach for the estimation of LAI and FPAR, because it relies on fewer hypotheses and
is based on fundamental physical theories (Privette et al., 1994, Gobron et al., 1997).
1.2.3 The MODIS LAI/FPAR Algorithm
The MODIS LAI/FPAR algorithm for estimation of global LAI/FPAR was developed
and implemented for operational processing prior to the launch of Earth Observing
System (EOS) Terra. (Knyazikhin et al., 1998a, b). A three-dimensional (3-D)
formulation of the inverse problem underlies this algorithm in order to improve
description of natural variability of vegetation canopies. By accounting features specific
to radiation transfer in plant canopies, the Green’s function and adjoint formulation of the
problem were utilized to split a complicated 3-D radiative transfer problem into two
independent, simpler sub-problems. They can be expressed in terms of three basic
components of the energy conservation law: canopy transmittance, reflectance, and
absorptance. These components are the elements of the LUT, and the algorithm interacts
only with the elements of the LUT. In this manner, the most computationally expensive
aspect is independent of the inversion procedure, and the problem is reduced to searching
a LUT for the modeled reflectance set that most resembles the measured set. This
provides the independence of the retrieval algorithm to any particular canopy radiation
model. A detailed description of this algorithm is presented in Knyazikhin et al.
(1998a,b).
7
1.3 Statement of the Research Problems
The MODIS LAI/FPAR product has been operationally produced from day one of
science data processing and is available free of charge to the public. One key question is
to understand the performance of the algorithm in terms of the spatial domain. To answer
this question, several issues need to be addressed. The first is a quantification of the
physical functionality and performance of the algorithm. The second is an investigation
of the effects of spatial resolution on LAI/FPAR retrievals. The third is development of
appropriate ground-based validation techniques to assess uncertainties associated with
these products. These issues are discussed in the following subsections.
1.3.1 Quantification of the Physical Functionality and Performance of
the MODIS LAI/FPAR Algorithm
Prior to the launch of Terra, prototyping exercises were conducted to demonstrate the
physical functionality and performance of the algorithm, and the response to spatial
resolution of the data. Specifically, the questions that need to be addressed include: (1)
what is the effect of uncertainties in surface reflectances on the quality of retrieved
LAI/FPAR? (2) when and why does the algorithm fail? (3) how can an assessment of the
algorithm accuracy be made? and (4) what is the behavior of the algorithm as a function
of spatial resolution?
1.3.2 Scaling Effects on the MODIS LAI/FPAR Retrievals
Scaling-related issues have been investigated in a number of contexts. The meanings of
spatial scaling in remote sensing of the Earth surface are several and related to how
remote sensing data are used: (1) to examine how the statistical properties of image data
vary as a function of sensor spatial resolution, using statistical measures such as variance
8
and covariance (Jupp et al., 1988; Jupp et al., 1989; Woodcock et al., 1988a, b; Milne and
Cohen, 1999); (2) to derive surface parameters such as land cover, land cover change,
LAI/FPAR by using remote sensing measurements at various resolutions (Townshend
and Justice, 1990; Townshend and Justice, 1995; Aman et al., 1992; Friedl et al., 1995;
Pax-Lenney and Woodcock, 1997; Chen, 1999); scaling in this case requires knowledge
of surface heterogeneity and depends on the algorithms; (3) to estimate surface processes
such as gas and energy exchanges between the land surface and atmosphere using
remotely sensed parameters (Pierce and Running, 1995; Pierce et al., 1994; Turner et al.,
1999); scaling in this case depends not only on surface heterogeneity, but also on the
correlation between surface and atmospheric variables involved in the processes (Hall et
al., 1992).
This dissertation focuses on how the data resolution impacts the retrieval of
parameters, especially LAI. Information contained in a single pixel is usually a result of
several different components, which is especially the case for data acquired with sensors
such as AVHRR. It has been recognized that radiometric measurements of sparsely
vegetated regions such as arid and semi-arid areas or agricultural regions, is strongly
anisotropic (Qi et al., 1994). In such regions, no single component (soil or vegetation or
single type of crop) dominates the pixel response. The relative contribution to the signal
observed from space, varies depending on surface heterogeneity and variables of interest.
Heterogeneity and scaling issues greatly challenge the interpretation of information
contained in remote sensing measurements at regional to global scales.
There is conflicting information in the literature as to whether retrieval methods
based on NDVI are scale dependent or invariant (Hall et al., 1992; Friedl, 1996; Hu and
Islam, 1997). Of special interest are issues related to the use of retrieval methods based
9
on point scale physical models, applied to coarse scale data, which inevitably contain
land cover mixtures (Raffy, 1994; Gregoire and Raffy, 1994; Chen, 1999). In other
words, how can a physically based retrieval algorithm be made scale dependent, such that
scaling of the retrieved biophysical product is accomplished when the algorithm is
executed on data of multiple resolutions?
The problem addressed here, that of scale dependence of algorithms for the retrieval
of biophysical variables, arises in two contexts. The first is in the context of assembling
time series of biophysical variables with data from sensors of different spatial resolutions.
Satellite data collected during a long period of time can be used to produce a long time
series of LAI. A complicated issue that arises here is how a time series of a particular
biophysical product can be developed from data acquired from a series of sensors that
have different spatial resolutions. The second is in the validation of moderate resolution
(~ 1 km) sensor products such as MODIS and MISR LAI and FPAR. Validation here
means specification of the uncertainty in the products in relation to ground truth data. The
latter is often collected at resolutions much finer than the products for practical reasons.
Therefore, the retrieval algorithms must be scale dependent so that the products can be
validated through scaling, as defined above.
1.3.3 Validation
The Terra satellite was launched in December 1999 and first Earth views from MODIS
were taken in February 2000. As MODIS LAI and FPAR data become publicly available
through the EROS Data Center Data Active Archive Center (EDC DAAC), product
quality must be ensured through validation.
10
Validation is the process of assessing the uncertainty of satellite sensor derived
products (e.g. land cover, LAI) by analytical comparison to reference data, which is
presumed to represent the target value. During the past two decades, several large-area,
international field campaigns such as BOREAS, HAPEX-Sahel, FIFE, Grassland
PROVE, have provided important test-beds for land-product validation activities (Justice
et al., 2000). These campaigns have involved investigations where ground based
measurements are linked to flux towers (Running et al., 1999), atmospheric
characterization (Holben et al., 1998), models and methods for scaling (Cohen and
Justice, 1999), and algorithm development and testing (Strebel et al., 1998; Lucht et al.,
2000).
The MODIS land discipline team (MODLand) uses field and tower measurements,
fine resolution (less than 10 m Instantaneous Field of View, IFOV), and high resolution
(from 10-30 m IFOV) imagery from air-borne and satellite sensors, to compare with the
MODIS 1 km product. However, the uncertainty assessment of these products is not
straightforward. The 1 km resolution of the MODIS LAI product significantly exceeds
the plot size typically used for LAI/FPAR field measurements. Thus, a procedure is
needed to correlate the scale of the LAI measurements to the scale of the MODIS pixels
using high resolution imagery. Except for a few studies directly addressing validation
such as comparing albedo (Lutch et al., 2000; Stroeve et al., 2001), Bidirectional
Reflectance Distribution Function (BRDF) (Lewis et al., 1999; Hautecoeur and Leroy,
2000), and LAI (Weiss et al., 2001) with field data, there have been a limited number of
comparisons between ground-based and satellite-derived land variables. The paucity of
such work to date is an indication of the logistic and practical difficulties in the
11
comparison. Validation work still requires an accurate and efficient procedure to assess
the uncertainties of moderate resolution satellite products.
Another problem associated with validation is how to design a statistically valid and
logistically feasible field sampling. Woodcock et al. (1988 a, b) observed that image
variograms are diagnostic of scene structure. Curran (1988) suggested that variograms in
remote sensing could help selection of spatial resolution and design of sampling schemes.
Hierarchical decomposition of LAI images, coupled with analysis of the component
variograms, could reveal information about LAI variation over different scales, which in
turn aids in the formulation of sampling strategies for validation. Specifically, I would
like to know the dominant factor that influences the spatial distribution of LAI across the
landscape, and to provide guidance for field data collection and sampling strategies.
1.4 Objectives and Organization of This Dissertation
The overall objective of this research is to evaluate the performance of the MODIS
LAI/FPAR algorithm, with special emphasis on the effects of scale, or spatial resolution.
To approach this goal, some critical issues previously mentioned must be addressed. The
experimental objectives that this research seeks to implement are discussed below:
Objective 1: Conduct a comprehensive analysis to quantify the physical functionality
and performance of the algorithm through prototyping. Land Surface Reflectances
(LASUR) and Landsat TM data were used to prototype the MODIS LAI/FPAR
algorithm. I evaluated its performance as a function of spatial resolution, and
uncertainties in surface reflectance and the land cover map. I examined the cases when
12
the algorithm fails and tried to justify the use of algorithms based on radiative transfer,
rather NDVI-based methods. This study is presented in Chapter 2.
Objective 2: Investigate the effect of data resolution on the algorithm retrievals. The
study was focused on three aspects: (1) the relation between land cover heterogeneity and
spatial resolution, (2) the impact of heterogeneity on measured surface reflectances and
LAI/FPAR retrievals, (3) a physically based theory for scaling with explicit scale
dependent radiative transfer formulation. The effect of pixel heterogeneity on spectral
reflectances and LAI/FPAR retrievals was investigated with 1 km AVHRR data
aggregated to different coarse scale resolutions. This research is presented in Chapter 3.
Objective 3: Provide guidance for field data collection and sampling strategies, and
assess the uncertainty of the MODIS LAI product via comparisons with ground and high-
resolution satellite data. The ground LAI data were collected in Botswana during the
SAFARI 2000 wet season campaign. A patch by patch comparison method, which is
more realistically implemented on a routine basis for validation, was proposed. Multiple
scales can be identified with a hierarchical scene model by dividing an image into scale
of classes, regions and pixels. Hierarchical analysis of data from Maun, Harvard Forest,
and Ruokulahti Forest showed that the LAI estimated from ETM+ data exhibit multiple
characteristic scales of spatial variation. Isolating the effects associated with different
landscape scales through variograms helps in the evaluation of sampling strategies. This
research is presented in Chapter 4. Conclusions from these three studies are stated in
Chapter 5.
13
Chapter 2
Prototyping of MODIS LAI and FPAR Algorithm
with LASUR and LANDSAT Data
2.1 Introduction
The importance of vegetation in studies of global climate and biogeochemical cycles is
well recognized (Sellers et al., 1993). Presently, most ecosystem productivity models,
carbon budget models, and global models of climate, hydrology and biogeochemistry
require vegetation parameters to calculate land surface photosynthesis, evapotranspiration
and net primary production (Running and Coughlan, 1988; Prince, 1991; Running and
Gower, 1991; Potter et al., 1993; Sellers et al., 1997). Therefore, accurate estimates of
vegetation parameters are increasingly important in the carbon cycle, the energy balance
and environmental impact assessment studies. Two of these parameters are green leaf
area index (LAI), a canopy structural variable, and fraction of photosynthetically active
radiation (0.4–0.7 µm) absorbed by vegetation (FPAR), a radiometric variable. In order
to quantitatively and accurately model global vegetation dynamics and differentiate short-
term from long-term trends, as well as to distinguish regional from global phenomena,
these two parameters must be collected often for a long period of time and should
represent every region of the Earth’s lands (Knyazikhin et al., 1998a; 1998b).
14
These two parameters are estimated from remote sensing data using empirical
relationships between values of LAI/FPAR and vegetation indices which include near-
infrared (NIR) to red (RED) band ratios and the normalized difference vegetation index
(NDVI) (Asrar et al., 1984; Tucker and Sellers, 1986; Peterson et al., 1987; Verma et al.,
1993; Myneni and Williams, 1994; Chen, 1996; Chen and Cihlar, 1996). The limitations
of such methods are well known (Gutman, 1991; Asrar et al., 1992; Price, 1993). No
unique relationship between LAI/FPAR and vegetation index is applicable everywhere
and all the time (Friedl, et al., 1995; Friedl, 1996; Gobron et al., 1997) because the
reflectances of plant canopies depend on a number of other factors, such as, measurement
geometry and spatial resolution. These empirical relationships are site and sensor
specific, and are unsuitable for application to large areas or in different seasons (Gobron
et al., 1997). A physically based model to describe the propagation of light in plant
canopies and its use in retrieval of biophysical parameters is the preferred alternative. In
the context of the EOS, the land discipline group of the MODIS Science Team is
developing algorithms for the determination of land cover, LAI, albedo, etc. to be
operationally generated from data from one or more of satellites (Justice et al., 1998).
One of these algorithms is the synergistic algorithm for the estimation of global
LAI/FPAR from MODIS (Knyazikhin et al., 1998a). At the present time, the algorithm
has been developed and theoretically justified, but no evidence of its functionality has
been presented. The purpose of this chapter is to evaluate the physical functionality and
performance of the algorithm by prototyping with the land surface reflectances (LASUR)
data derived from AVHRR data and Landsat data. Specifically, I would like to know:
What is the effect of uncertainties in surface reflectances on the quality of retrieved
LAI/FPAR? When and why the algorithm does/does not retrieve a value of LAI/FPAR
15
from the reflectance data? How can an assessment of the algorithm accuracy be made?
What is the behavior of the algorithm as a function of spatial resolution? In this chapter,
first the concepts of the algorithm, the physical meaning of the bidirectional reflectance
distribution functions (BRDF) equation, and the method to adjust the look-up table
(LUT) were described. Then the spectral signatures of LASUR and Landsat were
analyzed, followed by a series of algorithm prototyping results discussed in the later
section.
Results from prototyping are a valuable means of testing the physics of the algorithm
and also constitute an important first step toward improving the algorithm. At the most
general level, this research contributes to an improved understanding of the algorithm
behavior. A more practical benefit is to provide a basis for improved retrieval of surface
parameters from satellite data.
2.2 The Algorithm
2.2.1 Statement of the Problem
The inverse problem of retrieving LAI and FPAR from atmospherically corrected BRDF
is formulated as follows. Given sun Ω0 and view Ωv view directions, vegetation type,
dk(Ω0,Ωv) at N spectral bands and their uncertainties δk(Ω0,Ωv) (k = 1, 2, …, N), find LAI
and FPAR. The retrievals are performed by comparing observed and modeled BRDF’s
for a suite of canopy structures and soil patterns that cover a range of expected natural
conditions. All canopy/soil patterns for which the magnitude of residuals in the
comparison does not exceed uncertainties in observed and modeled BRDF’s, i.e.,
16
1),(),,(1
2
1
00 ≤
−∑=
N
k k
vkvk dpr
N δΩΩΩΩ
, (2.1)
are treated as acceptable solutions to the inverse problem. Here rk(Ω0, Ωv, p),
k = 1, 2, …, N, are modeled BRDF’s, and p = [canopy, soil] denotes a canopy/soil
pattern, which is unknown and will be discussed later. For each acceptable solution, a
value of FPAR is also evaluated. Mean values of LAI and FPAR averaged over the set of
acceptable solutions are taken as solutions of the inverse problem. A mathematical
justification of this procedure is presented in Knyazikhin et al. (1998a). Its application to
the retrieval of LAI and FPAR from multi-angular observation is discussed in Zhang et
al. (2000).
2.2.2 Radiation Transport in a Canopy
For MODIS LAI/FPAR algorithm, a three-dimensional (3–D) radiative transfer model is
used to derive spectral and angular biome-specific signatures of vegetation canopies.
Taking into account features specific to the problem of radiative transfer in plant
canopies, powerful techniques developed in nuclear physics were utilized to split a
complicated 3-D radiative transfer problem into two independent, simpler subproblems.
The first subproblem describes the radiative regime within the vegetation canopy for the
case of a black surface underneath the medium (“black soil problem”). The second
subproblem is the radiation field in the vegetation canopy generated by anisotropic
heterogeneous wavelength-independent sources located at the canopy bottom (“S
problem”). In terms of this approach, the BRDF rk(Ω0, Ωv, p), of a heterogeneous canopy
at wavelength λ can be expressed as (Knyazikhin et al., 1998a; 1998b)
)()(1
)()(),( 0,
,,,0,,0 Ω
⋅−+Ω=ΩΩ λ
λλλλλλ λρ
λρbs
Seff
effSSbsbs t
rtwrwr . (2.2)
17
Here rbs,λ(Ω0) and tbs,λ(Ω0) are directional hemispherical reflectance (DHR) and canopy
transmittance for the black soil problem, and rS,λ and tS,λ are reflectance and transmittance
resulting from an anisotropic source located underneath the canopy. The weight wbs,λ is
the ratio of the BRDF for the black soil problem to rbs,λ(Ω0), and wS,λ is the ratio of the
canopy leaving radiance generated by anisotropic sources on the canopy bottom to tS,λ.
The weights wbs,λ and wS,λ are functions of sun-view geometry, wavelength, and LAI.
They are precomputed and stored in the LUT (Knyazikhin et al., 1998a).
The effective ground reflectance ρeff is the fraction of radiation reflected by the
canopy ground. It depends on the radiative regime at the canopy bottom. However, its
range of variations does not exceed the range of variations of the hemispherically
integrated bidirectional factor of the ground surface, which is independent of vegetation
(Knyazikhin et al., 1998a). Therefore, ρeff can be used as a parameter to characterize the
ground reflection. The set of various patterns of effective ground reflectances at the
MODIS spectral bands is a static table of the algorithm, i.e., the element of the LUT. The
present version of the LUT contains 29 patterns of ρeff ranging from bright to dark. They
were taken from the soil reflectance model developed by Jacquemoud et al. (1992), with
model inputs presented in Baret et al. (1993). These soil patterns include three soil types:
mixtures of clay, sand, and peat. Each soil type is characterized by three moisture levels
and three soil roughness types. In biomes with grounds of intermediate brightness, all soil
patterns are assigned. In biomes where the ground is bright, the first 16 bright soil
patterns are used.
Note that rbs,λ(Ω0) and rS,λ are not included in the LUT. Given canopy absorptance
(abs,λ(Ω0) and aS,λ) and transmittance (tbs,λ(Ω0) and tS,λ), they are evaluated via the law of
energy conservation as
18
1,,, =++ λλλ bsbsbs atr (2.3)
1,,, =++ λλλ SSS atr . (2.4)
This makes canopy reflectance sensitive to the within canopy radiation regime tbs,λ(Ω0),
abs,λ(Ω0), tS,λ and aS,λ.
The dependence of canopy absorptance on wavelength for the black soil problem
(subscript κ = “bs”) and S problem (κ = “S”) can be derived (Knyazikhin et al., 1998a) as
0,0
0,
)(1)(1
)(1)(1
λκκ
κλκ λω
λωλωλω
ap
pa
−−
−−= . (2.5)
Here ω(λ) is the leaf albedo (leaf reflectance leaf transmittance). It is a stable
characteristic of green leaves, although its magnitude can vary with leaf age and species.
In order to get accurate leaf albedos for the six biome types, I obtained leaf spectra data
from several sources. Mean leaf reflectance and transmittance values were calculated for
the six biome types at seven MODIS bands (645 nm, 859 nm, 469 nm, 555 nm, 1240 nm,
1640 nm, and 2130 nm). The mean albedos were stored in the LUT. Variable pκ is a
wavelength independent coefficient defined as (Knyazikhin et al., 1998a; Panferov et al.,
2001)
∫ ∫∫ ∫
ΩΩΩ
ΩΩΩ−=
V
Vb
drdrrI
drdrrIp
π ωκ
π κκ
σ
σ
4,
4,
),(),(
),(),(1 . (2.6)
Where Iκ,b and Iκ,ω are solutions of the black soil problem and S problem for black (ω = 0)
and white (ω = 1) leaves, and σ is the extinction coefficient (dependent on vegetation
types). V is a parallelepiped where vegetation canopies are located. Its height coincides
with the height of plants and its horizontal dimension coincides with the size of the
pixels. The coefficient pκ depends on canopy structure and V and is an element of the
19
LUT. Because the horizontal dimension of V coincides with the size of pixel, pκ is a
resolution dependent parameter. A precise derivation of Eq. (2.5) and (2.6) is given in
Knyazikhin et al. (1998a). Validation of relationships Eq. (2.6) with field measurements
is presented in Panferov et al. (2001). Similar relationships are also valid for canopy
transmittance (Knyazikhin et al., 1998a; Panferov et al., 2001).
Thus, given canopy absorptance and transmittance for the black soil problem and S
problem at a reference wavelength λ0, one can evaluate these variables at any other
wavelength λ. Therefore, instead of λκ ,a and λκ ,t , only canopy absorptances 0,λκa ,
transmittances 0,λκt , the coefficients pκ, and leaf albedo are stored in the LUT.
Reflectances rbs,λ(Ω0) and rS,λ can then be evaluated via the energy conservation law Eq.
(2.3) and Eq. (2.4) and inserted into Eq. (2.2).
Similar to Eq. (2.2), the fraction of radiation absorbed by vegetation, aλ(Ω0), at
wavelength λ can be expressed as (Knyazikhin et al., 1998a)
)()(1
)()()( 0,
,,0,0 Ω
⋅−+Ω=Ω λ
λλλλ λρ
λρbs
Seff
effSbs t
raaa . (2.7)
For each acceptable solution p = [canopy, soil], a value of FPAR can be explicitly
evaluated as the integral of Eq. (2.7) over the photosynthetically active region of the solar
spectrum (Knyazikhin et al., 1998a).
2.2.3 Physical Meaning of Eq. (2.2)
Any pixel can be depicted as a point in the spectral space. The spectral BRDF’s tend to
occupy certain well-localized space in the spectral space, depending upon the architecture
of the biome. Equation (2.2) is used here to explain this behavior in the RED-NIR plane
as follows:
20
1) If LAI = 0, then rbs,λ(Ω0) = rS,λ = 0, tbs,λ(Ω0) = tS,λ =1, and wS,λ coincides with
bidirectional surface reflectance factor (Knyazikhin et al., 1998a). The BRDF at
RED and NIR results from photon-ground interactions. The pixels are located on
the so-called soil line (around 1:1 line in the RED-NIR spectral space) (Huete,
1988; Baret et al., 1993). The spectral behavior for different soil types will
determine the exact location of the soil line. The bright soil pattern will generate
high reflectance in RED and NIR. The dark soil pattern will generate low
reflectance in RED and NIR.
2) A high value of LAI corresponds to a very dense canopy. Its transmittances
tbs,λ(Ω0) and tS,λ are close to zero and thus, the contribution of soil is minimal.
Pixels will occupy a narrow space near the NIR axis. Canopy reflectances at RED
and NIR wavelengths characterize exactly the spectral properties of vegetation,
that is, plants absorb radiation very efficiently throughout the visible regions and
strongly reflect and transmit at NIR. The type of vegetation and its phenology will
determine the precise location in the RED-NIR spectral space.
3) If LAI is between case 1) and case 2), neither rbs,λ(Ω0) nor transmittance will
equal zero, and gaps in the vegetation elements will cause photons to interact with
soil and canopies. The soil-canopy interactions will cause the canopy response,
with a hypothetical nonreflecting soil background, to shift toward the soil line
(RED reflectance will decrease, and changes in NIR reflectance will depend on
the soil brightness pattern under the canopy) (Huete, 1988). The location of pixels
will be between the soil line and NIR axis. The more gaps, the smaller the LAI
value and the closer the pixels are to the soil line.
21
To summarize, Eq. (2.2) shows how the location of a pixel in the spectral space is
related to LAI values. If a pixel is close to the soil line, its LAI value is small. Away from
the soil line toward the NIR axis, the contribution of soil to canopy leaving radiance
decreases as the product of tbs,λ(Ω0) and tS,λ, and thus, LAI values increase. The direction
of this movement in the spectral space results in different rates of LAI variations. Such a
representation of canopy reflectances is used in this algorithm to build and adjust the
LUT, and to interpret results presented in section 2.4.
2.2.4 Adjusting the LUT for Data Resolution
Before the configurable parameters of the LUT can be set, data of a specific spatial
resolution must be analyzed to locate the pixels in the spectral space (for example, the
RED-NIR space) according to the biome type. The data density distribution function was
evaluated as follows: specifying a fine grid cell in the spectral space, counting the
number of canopy reflectances in this cell, and then dividing this value by the total
number of pixels in the entire spectral space. The data density distribution function was
evaluated for each biome type. A location of high density (25% of all pixels) for each
biome in the RED-NIR space was plotted and used to adjust the LUT as follows. The
areas of 25% density can be interpreted as the sets of pixels representing the most
probable patterns of canopy structure. As an example, for biome 5 (broadleaf forests), the
25% density of this biome was localized in the spectral space during July, the green
season. Then the algorithm was run using only these pixels as input data and the
histogram of the retrieved LAI value was plotted. Based on previously reported results
(Myneni et al., 1997), the most probable canopy realization in this case has an LAI value
of about 5. It means that the peak of the histogram should be around five. The LUT was
adjusted by changing pκ to represent the corresponding data set so that the simulated
22
BRDF at RED and NIR wavelengths corresponding to LAI = 5 fall in the 25% density
plot. Given the location of the most probable realization of canopy structure, Eq. (2.2)
can be used to specify the location of pixels at other values of LAI and soil patterns. The
LUT was then adjusted for all biomes.
2.3 Data Analysis
Before MODIS data are available, data acquired by other instruments can be used to
prototype and test the functionality of the LAI-FPAR algorithm. The goal of this section
is to describe and analyze the surface reflectance data used to prototype the algorithm.
2.3.1 Satellite Data
LASUR refers to data acquired during 1989-1990 and processed at Centre d’Etudes
Spatiales de la Biosphere (CESBIO), Toulouse, France, from AVHRR onboard the
NOAA-11 satellite (Berthelot et al., 1994; Berthelot et al., 1997). LASUR is a
reprocessing of weekly global vegetation index data (Gutman et al, 1995). AVHRR is a
cross-track scanning system featuring one visible (RED, 572–698 nm), one NIR (716–
985 nm), one short wave infrared, and two thermal infrared channels. For LASUR
products, data from RED and NIR channels were used to estimate surface reflectances
and vegetation index, and data from the two thermal infrared channels were used to
estimate the surface temperature. LASUR data were calibrated and corrected for
atmospheric effects and filtered to eliminate residual noises and perturbations (Berthelot
et al., 1994; Berthelot et al., 1997). The data span is from 75° N to 55° S in latitude, and
180° W to 180° E in longitude. Each image has 904 rows and 2500 columns. The spatial
resolution is 1/7th of a degree. In this study, RED and NIR surface reflectances from July
23
1989 were used to prototype the MODIS LAI/FPAR algorithm. I created a monthly layer
based on maximum NDVI compositing of the four weekly layers in this month,
minimizing cloud contamination, off-nadir viewing effects, sun-angle effects and aerosol
and water vapor effects (Holben, 1986).
A biome classification map (BCM) that describes the global distribution of six
canopy structural types (biomes) was used as a prototype of the MODIS land cover
product, required by the MODIS LAI/FPAR algorithm. BCM was derived from the
AVHRR Pathfinder data set (Myneni et al., 1997) and is time independent. The six biome
types are: grasses and cereal crops (biome 1), shrubs (biome 2), broadleaf crops (biome
3), savannas (biome 4), broadleaf forests (biome 5), and needle forests (biome 6).
Landsat Thematic Mapper (TM) scene of Northwest U S. (Washington and Oregon)
from June 26, 1987 at 30 m resolution was also utilized to evaluate the algorithm’s
response to high resolution data. In this study, I used data from band 3 (RED, 630–690
nm) and band 4 (NIR, 760–900 nm). This image was geometrically registered to a
terrain-corrected image with an universal transverse Mercator (UTM) projection. The
dark object subtraction method was used to correct surface reflectance for the
atmospheric effect (Chavez and Jr., 1989; 1996). There was also a “sitemap” containing
polygons of known ground cover, associated with this data set. This sitemap
distinguished 17 different forest densities, based on the percentage of forest cover in a
forested pixel, and seven other types of miscellaneous landcover types. Using the
Bayesian maximum likelihood classification method, I separated this image into three
biomes, grasses and cereal crops, broadleaf forests and needle forests. Broadleaf forests
were attributed to all the pixels where hardwood forests make up more than 60% of the
pixel area. Needle forests consist of those pixels in which conifers make up more than
24
60% of the pixel area. The other landcover classes that do not belong to these three
biomes were defined as unknown class types. In total, grasses occupy 6.6% of the total
area, and broadleaf and needle forests occupy 4.8% and 10.3% of the total area.
2.3.2 Spectral Signatures
Although all the vegetation types have relatively similar spectral properties (large
absorption in RED and large reflectance in NIR), different biomes have special
characteristics depending on the canopy architecture. These characteristics can be
distinguished by comparing the spectral signatures. Fig. 2.1(a) and (b) present histograms
of canopy reflectances in RED and NIR spectral bands as a function of biome type
derived from LASUR data. In the RED band, canopy reflectances vary between 0.0 and
0.2. Broadleaf and needle forests have the strongest absorption features. On average, they
reflect only 3% and 4.5% (Table 2.1) of the incoming radiation. Grasses and broadleaf
crops are characterized as the brightest biomes. About 8% and 6.5% of the incoming
radiation is reflected. In the NIR band, reflectances vary between 0.1 and 0.5. Shrubs and
broadleaf crops represent two extremes. Their reflectances, on average, are 21% and
32%, respectively. The other biomes reflect nearly 25% of the incoming radiation and
have similar histograms.
Vegetation indices typically capture the absorption contrast across the 650-850 nm
wavelength interval through combinations of broadband RED and NIR reflectance. The
most widely used index in the processing of satellite data is NDVI, defined as (ρN -
ρR)/(ρN + ρR), where ρN and ρR are spectral reflectance at NIR and RED wavelengths,
respectively. It is a measure of chlorophyll abundance and energy absorption (Myneni et
al., 1995). Fig. 2.1(c) demonstrates the distribution of NDVI values derived from LASUR
25
data. In general, broadleaf forests have the highest NDVI values, around 0.813, followed
by needle forest, around 0.695 (Table 2.1). Broadleaf crops and savannas have similar
NDVI distributions, and their NDVI values are larger than those of grasses (0.515) and
shrubs (0.615). It would be difficult to distinguish broadleaf crops from savannas using
only NDVI.
The data density distribution function, introduced earlier in section 2.2, can be used
to indicate the location of a data peak in the spectral space. Fig. 2.1(d) shows the location
of points with high density for different biomes in the RED-NIR space. Each area
bounded by the contour represents an area containing the 25% density of the total pixels
from a given biome type. Each biome tends to cluster and occupy a well localized space.
Broadleaf forests are located at low RED and high NIR area, while grasses are at the high
RED and low NIR area. Broadleaf crops and savannas occupy different locations,
although their NDVI distributions are comparable. In general, the more unique a location,
the better the ability to distinguish each vegetation type. The influence of soil is also clear
from this panel. Grasses and shrubs are biomes located near the soil line. Broadleaf
forests are dense vegetation and located closest to the NIR axis.
Fig. 2.2 presents canopy reflectance features from Landsat data. On average, grasses,
broadleaf and needle forests reflect only 6.5%, 2%, and 1.3%, respectively, of the
incoming radiation in the RED band (Table 2.1). This is much less than that of LASUR
data. However, the NIR reflectance of grasses and broadleaf forest can be as high as 30%
and 34.8%, compared with 25% and 29% for the LASUR data. Needle forests are the
darkest among the three biomes, both at RED and NIR. The NDVI values for the three
biomes are 0.635, 0.881, 0.886, respectively (Table 2.1). The 25% density contours are
tightly clustered occupying a small but unique location in the spectral space. At the same
26
time, the clusters are away from the soil line, and closer to the NIR axis. The biomes are
well separated that they do not overlap even on the 75% density contour. Comparing the
results from the previous two data sets, I conclude that, as the spatial resolution increases
from LASUR data to Landsat data, the reflectance decreases in the RED band and
increases in the NIR band, and consequently, fewer biomes overlap in the RED-NIR
spectral space.
2.4 Prototyping of The Algorithm
2.4.1 Prototyping with LASUR Data
This section describes global LAI and FPAR fields derived with the MODIS LAI/FPAR
algorithm using the LASUR data. The objectives are to analyze these fields and situations
when the algorithm fails to retrieve a value of LAI/FPAR, to assess the influence of
uncertainties in surface reflectances and land cover map on the LAI/FPAR product
quality, and to justify the use of more complex algorithms, instead of NDVI-based
methods.
The algorithm was run pixel-by-pixel using LASUR data and land cover BCM on all
pixels with NDVI greater than 0.1. The following notions are used in discussion on
algorithm performance. First, a pixel for which the algorithm retrieves a value of LAI is a
“retrieved” pixel. Second, a pixel for which the algorithm cannot retrieve a value of LAI
is termed a “nonretrieved” pixel, and the algorithm is said to have failed for this pixel.
Third, the ratio of the number of retrieved pixels to the total number of pixels is the
retrieval index (RI).
27
2.4.1.1 Input Data
Atmospherically corrected surface reflectances and uncertainties in measurements and
simulations are inputs to the algorithm Eq. (2.1). However, LASUR reports no
information on reflectance uncertainties. Therefore, the uncertainties were simulated as
[ ] 2/122NIRREDNIRRED dd +== εδδ . (2.8)
Here, ε is the mean uncertainty and is assumed to be a constant in this study. Fig. 2.3
demonstrates the dependence of the RI on ε. The RI increases with increases in ε.
However, the quality of retrieved LAI/FPAR decreases with increases in ε. If ε is under-
estimated, the algorithm fails even though surface reflectances were reasonable. If ε is
overestimated, the algorithm can produce LAI/FPAR values for nonvegetated pixels.
Finding ε for which about 95% of nonretrieved pixels are nonvegetated is a solution to
the above problem, which was 0.2 for the LASUR data. The RI varies with biome types
at a constant ε. When ε is 0.2, the RI for biome 1 to biome 6 is 91.5%, 92.7%, 74.0%,
79.7%, 39.3%, and 54.5%. The reason that broadleaf and needle forests have low RI
could be due to dark soil patterns used to represent effective ground reflectance ρeff in Eq.
(2.2). If a pixel is bright, it will not be considered as a pure broadleaf or needle forest
pixel and, consequently, the algorithm will fail. Low values of RI are not necessarily an
indication of poor performance of the algorithm. For the coarse resolution data, such as
LASUR (1/7th of a degree), the vegetation in the pixel may be a case of mixture of
different land cover classes. Therefore, biome-specific spectral features may be lost. At
the present time, restricting the algorithm to pure vegetation types retains the ability to
discriminate biome types.
28
2.4.1.2 Histograms of LAI and FPAR
The histogram of the retrieved LAI/FPAR describes the value distribution of these fields
for various biomes. Fig. 2.4(a) presents the histogram of retrieved LAI using the LASUR
data. Broadleaf and needle forests have distributions distinct from the other four biomes.
The former have relatively high LAI values, concentrated about 4.0 to 6.0. For the latter,
the LAI values are generally less than 2.0. The differences among grasses, shrubs,
broadleaf crops, and savannas are seen in the peak and tail of the LAI histograms. The
highest frequency of LAI for broadleaf crops and savannas is around 1.25, for grasses
around 1.0, and for shrubs around 0.75 and 1.25. The distribution tail of broadleaf crops
and savannas contains at least 20% of the pixels whose LAI values are larger than 4.0.
The tail ends at about 4.0 for grasses and shrubs. Therefore, the mean LAI for broadleaf
crops and savannas are 2.1 and 2.2, for grasses and shrubs, only 1.2 and 1.4. Shrubs have
two obvious peaks that correspond to the two peaks in the NDVI histogram shown in Fig.
2.1(c). However, the retrieved LAI is not based on the NDVI.
The LAI distribution from a NDVI-based algorithm developed earlier by Myneni et
al. (1997) is shown in Fig. 2.4(b). The data used for this NDVI-based algorithm were
AVHRR Pathfinder data from July 1981 through June 1991. The average July retrievals
over the ten-year period are shown in this figure. There are many similarities between
Fig. 2.4(a) and (b). Broadleaf and needle forests have much higher LAI than the other
four biomes. The double peak in shrubs is also seen in Fig. 2.4(b). The similarity between
the two retrievals imbues confidence in the MODIS algorithm.
Fig. 2.4(e) and (f) show the NDVI histograms from retrieved and nonretrieved
pixels. Compared to Fig. 2.1(c), the NDVI histogram of retrieved pixels is similar to the
NDVI histogram of all pixels. Therefore, the algorithm identifies most of the features in
29
the observed data. Failures are typically two cases. First, NDVI is too high for a
particular biome. For example, the algorithm fails to retrieve information when the NDVI
of grasses is larger than 0.75. In the LUT, there is no information for grasses at such
values of NDVI. Second, for the same NDVI value, some of the pixels are retrieved
pixels, but the others are not. The failure of this type will be discussed later.
2.4.1.3 Test of Physics
There are many examples in published literature about the strong relation between NDVI
and LAI and FPAR (Asrar et al., 1984; Tucker and Sellers, 1986; Peterson et al., 1987;
Verma et al., 1994; Myneni and Williams, 1994; Chen, 1996; Chen and Cihlar, 1996).
This provides an opportunity to test the physics of the algorithm by comparing the LAI-
NDVI and FPAR-NDVI relationships derived from the algorithm with those reported
from field measurements. Fig. 2.5(a) and (b) shows the distributions of the retrieved
values of LAI and FPAR with respect to the NDVI of Broadleaf forests. LAI is
nonlinearly proportional to NDVI, while FPAR is linearly proportional to NDVI. This
corresponds to relations reported in the literature (Myneni et al., 1997; Clevers, 1989).
Note the NDVI in this plot is evaluated from measured RED and NIR reflectances, while
the retrieved quantities result from the algorithm that uses reflectances instead of NDVI.
The advantages of using the MODIS algorithm instead of NDVI relations are as follows.
First, NDVI–LAI relations are subject to changes in sun angle, background reflectance,
and view angle, while the MODIS algorithm actually uses these changes as sources of
information in the retrieval process. Second, NDVI is based on two spectral bands only,
while the algorithm can ingest 3, 4, or even MODIS 7 bands simultaneously to retrieve
LAI and FPAR.
30
Fig. 2.5(c) and (d) shows the scatter plot of data from retrieved and nonretrieved
pixels in the RED-NIR plane. This distribution provides insights into where and why the
algorithm failed. For retrieved pixels in the RED-NIR plane, canopy reflectances range
from 0.02 to 0.16 for the RED band and from 0.1 to 0.42 for the NIR band. This
reflectance space obviously overlaps the 25% density contour area. From Figs. 2.4(e),
2.4(f) and 2.5(c), 2.5(d), it appears that there are three regions where the algorithm fails:
RED reflectance less than 0.03 (NDVI is very large), large RED and NIR reflectances
(pixels are near the soil line and NDVI is very small), and RED and NIR are relatively
large and located between the first two regions. When the RED reflectance is very small,
the uncertainty is large, and the probability of retrieval decreases. When a pixel is near
the soil line, it is not a vegetated pixel, and the algorithm identifies it correctly. For the
third region, consider a line, on which NDVI is constant [Fig. 2.5(d)], in the RED-NIR
spectral space. For the same value of NDVI, some pixels result in retrievals, while others
do not. The algorithm is sensitive to canopy reflectances on a constant NDVI line, while
the NDVI-based algorithm is insensitive to these. It is clear that the algorithm uses
information on the canopy spectral properties instead of NDVI, especially, when there are
many spectral bands and multi-angle data. Only when a pixel falls within the specified
spectral and angular space in the LUT can it retrieve an LAI value. Otherwise, the
algorithm fails even if the NDVI is reasonable. Therefore, a correct LUT is a key factor
in algorithm performance.
2.4.1.4 Reliability of Retrieved LAI/FPAR
Equation (2.1) may admit a number of solutions, covering a wide range of LAI values.
When this happens, the canopy reflectances are said to belong to the saturation domain,
being insensitive to various parameter values characterizing the canopy. The algorithm
31
can recognize this situation. The frequency with which LAI values are retrieved under the
condition of saturation is termed saturation frequency. The accuracy of retrievals
decreases in the case of saturation, that is, the information conveyed about canopy
structure by canopy reflectances is small because a wide range of natural variations in
canopy structure and soil can result in the same value of remotely sensed signal
(Knyazikhin et al., 1998b). Therefore, the saturation frequency and threshold LAI value
of saturation are important criteria when assessing the accuracy of retrievals. For the six
biomes, the overall saturation frequencies are 0.38%, 2.5%, 16%, 15%, 48.5%, and
42.5%, respectively. Fig. 2.6(a) shows the histogram of LAI retrieved under the condition
of saturation for the six biomes. When the LAI is less than 4.0, the saturation frequency is
low for all biomes. But, when LAI is larger than 4.0, the saturation frequency drastically
increases. Nearly every pixel is retrieved under the condition of saturation when the LAI
is larger than 5.0.
Broadleaf and needle forests in general have high LAI values, and therefore, a high
saturation frequency. In order to assess the quality of retrieved LAI/FPAR values, I
examined the coefficient of variation of the retrieved LAI value (COVLAI) defined as the
ratio of LAI dispersion to mean LAI evaluated from the set of acceptable solutions. The
lower the COVLAI value, the more reliable and accurate the retrieval. Fig. 2.6(b)
demonstrates COVLAI as a function of retrieved LAI and biome types. The COVLAI
values vary around 0.2, while the standard deviations of the retrievals increase with LAI.
This is not surprising, because at high LAI values the reflectances belong to the
saturation domain and it is difficult to localize a single estimate. When LAI is larger than
3.0, broadleaf and needle forests have relatively lower COVLAI values than other biomes
at the same LAI value. Therefore, when LAI is large and saturation frequency is large,
32
the retrieval is not necessarily poor. COVLAI cannot be less than 0.2, because the mean
uncertainty in these runs is 0.2. The quality of the retrievals cannot be better than the
quality of the largest uncertainty in spectral reflectance data input to the algorithm.
Therefore, the availability of band specific uncertainties in atmospherically corrected
surface reflectances is critical to assess the quality of the LAI/FPAR product.
2.4.1.5 LAI and FPAR Images
The algorithm was run on the global LASUR data for the month of July 1989. For the
nonretrieved pixels, the averaged NDVI-LAI/NDVI-FPAR relations derived from all the
retrieved pixels were used to estimate LAI and FPAR. Fig. 2.7 shows color-coded images
of global LAI and FPAR. These compare well with the fields reported earlier by Myneni
et al. (1997). The comparison was done to assess if the algorithm captures the general
patterns of LAI and FPAR distribution at the global scale. Whether the retrievals are
accurate or not requires validation, which is the next step.
2.4.1.6 Biome Misclassification and LAI/FPAR Retrievals
The MODIS LAI/FPAR algorithm requires a land cover classification map provided by
the MODIS land cover product (Justice et al., 1998). It is important, therefore, to assess
the impact of biome misclassification on LAI/FPAR retrievals. The algorithm was run six
times per pixel, each time using a different biome’s LUT. This simulates the effects of
biome misclassification on LAI/FPAR retrievals. The results are shown in Table 2.2.
Typically, when pixels are misclassified, either the RI is low and/or the retrieved LAI
values are incorrect. When misclassification between distinct biomes occurs, the results
are predictable. For example, grasses and cereal crops (biome 1) and broadleaf forests
(biome 5) are distinct in their architecture and foliage optics. If biome 1 is misclassified
33
as biome 5, the RI is 27% compared to 91% without misclassification. Or, if biome 5 is
misclassified as biome 1, the retrieved LAI value decreases from 4 or 5 to 2.
Misclassification can be detected by the RI, mean LAI and the histogram of retrieved
LAI distribution in such cases. If misclassification happens between spectrally and
structurally similar biomes, perhaps, because of coarse spatial resolution, the impact on
LAI/FPAR retrievals is difficult to assess. As an example, consider shrubs (biome 2) and
savannas (biome 4). The RI and mean LAI do not vary greatly. The retrieved LAI/FPAR
values are acceptable, although the pixels have been misclassified. This example
indicates that various biome LUT’s share similar entries for certain combinations of
spectral reflectances.
2.4.2 Prototyping with Landsat Data
2.4.2.1 General Results
The MODIS LAI/FPAR algorithm was prototyped with Landsat data for three biomes:
grasses and cereal crops, broadleaf forests, needle forests. A fine resolution LUT was
used to retrieve LAI and FPAR because of the finer spatial resolution of Landsat data.
The RI’s for the three vegetation types are 90.7%, 53.9%, 57.9%, respectively, and the
mean LAI values are 1.87, 5.79, 4.11, respectively. Compared to LASUR data, the RI
increase for broadleaf and needle forests, and so do the mean LAI values. The saturation
frequencies at high LAI values for these biomes are comparable to those reported earlier
for LASUR data.
The following explains the dependency of the LUT on spatial resolution. Canopy
spectral properties are a function of spatial resolution (Figs. 2.1 and 2.2). In the RED-NIR
plane of 25% density contours, fine resolution data tend to cluster and occupy a small
34
region close to the NIR axis. Contours corresponding to different biome types do not
overlap either. As the resolution decreases, the spectral properties of each biome are
influenced by the presence of soil and water as well as the other vegetation types. In the
spectral space, the distance between the biomes decreases and the biomes become
similar. Therefore, the LUT should reflect these changes in vegetation canopy spectral
properties with changes in resolution. The parameters pκ, κ = “bs” or “S”, introduced by
Eq. (2.6) control the dependency of LUT on the spatial resolution of data. To further
investigate, the algorithm was performed on Landsat data with LASUR LUT, that is, fine
resolution data with coarse resolution LUT. Fig. 2.8 shows the histogram of LAI and
FPAR obtained from Landsat data with LASUR LUT and, also, Landsat data with
Landsat LUT. When Landsat data and Landsat LUT are used, the retrieved LAI values
vary from 0.0 to 2.5 for grasses, from 5.0 to 7.0 for broadleaf forest, and from 1.5 to 6.0
for needle forests (Table 2.3). When LASUR LUT is used with Landsat data, the
histograms of retrieved LAI and FPAR change greatly. For example, the LAI of
grasses/cereal crops can reach unrealistic values between 4.0 and 6.0. The LAI of needle
forests is concentrated between 1.5 to 4.0, a relatively small range for this biome. The RI
for the three biomes also decrease to 87.5%, 39.2%, 4.7%, respectively. When the
algorithm is run using LASUR data but with Landsat LUT (Fig. 2.9), the mean LAI for
all biomes decrease, and the differences between forests (high LAI) and other biomes
(low LAI) disappear. FPAR shows similar changes. This clearly indicates the dependency
between data resolution and the LUT.
2.4.2.2 Soil or Background Effects
As previously mentioned, in the design of the MODIS LAI/FPAR algorithm, the 3-D
radiative transfer problem can be represented as the sum of two components. The first
35
describes the radiation regime within the vegetation canopy with a completely absorbing
soil or background beneath the canopy. The second component describes additional
radiation due to interactions between the soil and vegetation. Therefore, the soil-
vegetation interaction is an important component controlling the spectral behavior of
vegetation canopies. At the fine resolution, the contribution of the soil-vegetation
interaction is negligible in the case of dense vegetation, such as forests. The algorithm
was executed only with the black soil problem on Landsat data to test this assumption.
The RI can be as high as 50.6% (broadleaf forest) and 54.3% (needle forest), compared to
53.7% and 57.9% if the contribution from the soil-vegetation interaction is added. The
histograms of retrieved LAI and FPAR do not change substantially. Therefore, the fine
resolution Landsat data represent pure and dense vegetation with minimal soil or
background effects in this instance. The RI are only 31% and 45% for broadleaf and
needle forests when only the black soil problem is used to retrieve LAI and FPAR for the
coarser resolution LASUR data. The soil-vegetation interaction is an important
component that controls the spectral behavior of vegetation canopies. Its effect becomes
large as the resolution decreases.
2.5 Conclusions
Results from the prototyping described in this chapter demonstrate the ability of the
algorithm to produce global LAI and FPAR fields. For global LASUR data in July, the
mean LAI of broadleaf and needle forest is around 4.0, broadleaf crops and savannas 2.1
and 2.2, shrubs 1.4 and grasses and cereal crops 1.2. The algorithm utilizes leaf spectral
properties and canopy structural attributes, instead of NDVI, in the retrieval process. An
LAI value can only be retrieved when a pixel falls within the specified spectral and
36
angular space in the LUT. The algorithm fails even if the NDVI value is reasonable. The
uncertainties in input data influence the RI. RI increases with increasing uncertainties.
However, the quality of retrieved LAI/FPAR decreases with increasing uncertainties. A
value of 0.2 was found optimal in this study. Quantitatively, the saturation frequency and
coefficient of variation (standard deviation/mean) of retrieved LAI values (COVLAI) are
two useful metrics to assess the quality of the retrieved field. The higher the saturation
frequency and COVLAI value, the lower the quality of the retrieval. On average, if LAI
is larger than 4.0, saturation problems begin to influence the retrieval. Forests have higher
saturation frequencies than other vegetation types. However, they have lower COVLAI
values than other biomes at the same LAI value, especially at high LAI values. Therefore,
the retrieval quality is not necessarily poor. COVLAI cannot be less than the total
uncertainty in the data and the LUT, because the quality of the retrievals cannot be better
than the quality of the largest uncertainty in spectral reflectance data input to the
algorithm. The effect of biome misclassification between distinct biomes on the
algorithm can be evaluated through the RI, mean LAI, and the histogram of the retrieved
LAI distribution. Misclassification can fatally impact the quality of the retrieval in this
case. The impact of biome misclassification between spectrally and structurally similar
biomes is negligible, particularly if the spatial resolution of the input data is coarse.
Leaf canopy spectral properties differ with spatial resolution. Each vegetation type in
Landsat data tends to cluster and occupy a small region close to the NIR axis in the
spectral space, while biomes become spectrally similar in the case of coarse resolution
LASUR data. The algorithm is dependent on the spatial resolution of the data through the
use of the LUT. Landsat LUT cannot be used to retrieve LASUR LAI/FPAR and vice
37
versa. By evaluating the data density distribution function, the algorithm can be adjusted
for data resolution and can be utilized with data from other sensors.
38
(a) Histogram of RED Band
0.00 0.05 0.10 0.15 0.20Reflectance
0
10
20
30
40
50
Freq
uenc
y (%
)
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannaSavannaSavannaSavannaSavannaBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b) Histogram of NIR Band
0.10 0.20 0.30 0.40 0.50Reflectance
0
5
10
15
20
25
Freq
uenc
y (%
) Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannaSavannaSavannaSavannaSavannaBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(c) Histogram of NDVI
0.0 0.2 0.4 0.6 0.8 1.0NDVI
0
5
10
15
20
Freq
uenc
y (%
)
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannaSavannaSavannaSavannaSavannaBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(d) 25% Density contours
0.00 0.05 0.10 0.15 0.20RED
0.00
0.10
0.20
0.30
0.40
NIR
Grassland and Cereal CropsShrubslandsBroadleaf CropsSavannasBroadleaf ForestsNeedle Forests
ND
VI=
0.68
Figure 2.1. Statistical properties of canopy reflectances for global LASUR data in July 1989. (a) Histogram of canopy reflectances at the RED band. (b) Histogram of canopy reflectances at the NIR band. (c) Histogram of NDVI. (d) 25% density contours in the RED-NIR space, which shows the location of points with high density for different biomes. The straight line represents the place where NDVI are equal to 0.68. Canopy structure varies considerably with the same NDVI value.
39
(a) Histogram of RED Band
0.00 0.05 0.10 0.15 0.20Reflectance
0
20
40
60
80
100
Freq
uenc
y %
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b) Histogram of NIR Band
0.10 0.20 0.30 0.40 0.50Reflectance
0
10
20
30
40
Freq
uenc
y %
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(c) Histogram of NDVI
0.0 0.2 0.4 0.6 0.8 1.0NDVI
0
10
20
30
40
Freq
uenc
y %
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(d) 25% Density contours
0.00 0.05 0.10 0.15 0.20RED
0.00
0.10
0.20
0.30
0.40
NIR
Grassland and Cereal CropsBroadleaf ForestsNeedle Forests
ND
VI=
0.68
Figure 2.2. Statistical properties of canopy reflectances for Landsat TM data of Northwest U.S. in June 1987. (a) Histogram of canopy reflectances at the RED band. (b) Histogram of canopy reflectances at the NIR band. (c) Histogram of NDVI. (d) 25% density contours in the RED-NIR space, which shows the location of points with high density for different biomes. The straight line represents the place where NDVI are equal to 0.68.
40
0.05 0.10 0.20 0.30 0.40 0Epsilon
0
20
40
60
80
100R
etri
eval
Ind
ex (
%)
Grasses and Cereal Crops
Shrubs
Broadleaf Crops
Savannas
Broadleaf Forests
Needle Forests
Figure 2.3. Dependence of the retrieval index (RI) on uncertainties ε in measurements and simulations.
41
(a) LAI of retrieved pixels
0 2 4 6 8LAI
0
10
20
30Fr
eque
ncy
(%) Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal Crops
ShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b) LAI From Myneni et al., 1997
0 2 4 6 8LAI
0
10
20
30
Freq
uenc
y (%
) Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(c) FPAR of retrieved pixels
0.0 0.2 0.4 0.6 0.8 1.0FPAR
0
10
20
30
40
Freq
uenc
y (%
)
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(d) FPAR From Myneni et al., 1997
0.0 0.2 0.4 0.6 0.8 1.0FPAR
0
10
20
30
40
Freq
uenc
y (%
)Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(e) NDVI of retrieved pixels
0.0 0.2 0.4 0.6 0.8 1.0NDVI
0
5
10
15
20
Freq
uenc
y (%
)
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(f) NDVI of nonretrieved pixels
0.0 0.2 0.4 0.6 0.8 1.0NDVI
0
5
10
15
20
Freq
uenc
y (%
)
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 2.4. (a), (c) Histograms of LAI/FPAR derived from the MODIS algorithm with LASUR data. (b), (d) Histograms of LAI/FPAR derived from NDVI-based algorithm with 10-year averaged AVHRR Pathfinder data (Myneni et al., 1997). (e) Histogram of NDVI from retrieved pixels. (f) Histogram of NDVI from non-retrieved pixels. The mean uncertainty ε is 0.20.
42
(a)
0 2 4 6 8LAI
0.0
0.2
0.4
0.6
0.8
1.0N
DV
I(b)
0.0 0.2 0.4 0.6 0.8 1.0NDVI
0.0
0.2
0.4
0.6
0.8
1.0
FPA
R
(c)
0.0 0.2 0.4 0.6 0.8 1.0RED
0.0
0.2
0.4
0.6
0.8
1.0
NIR
(d)
0.0 0.2 0.4 0.6 0.8 1.0RED
0.0
0.2
0.4
0.6
0.8
1.0
NIR
from retrieved pixels from nonretrieved pixelsN
DV
I=0.
58
Figure 2.5. For broadleaf forests in LASUR data, the scatter plot shows (a) the LAI-NDVI relationship, (b) the NDVI-FPAR relationship, (c) retrieved pixels in the RED-NIR space, and (d) non-retrieved pixels in the RED-NIR space.
43
(a)
0 2 4 6 8LAI
0
5
10
15
20Fr
eque
ncy
% Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b)
0 2 4 6 8LAI
0.0
0.2
0.4
0.6
0.8
1.0
CO
VL
AI Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal Crops
ShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 2.6. (a) Histogram of LAI values retrieved under the condition of saturation. Solid lines present the same histograms as Fig. 2.4(a). Dashed lines show the ratio of the number of LAI values retrieved under the condition of saturation to the total number of retrieved pixels. (b) Coefficient of variation (standard deviation/mean) of retrieved LAI values (COVLAI) as a function of retrieved LAI.
44
Figure 2.7. (a) Global LAI and (b) global FPAR fields derived from LASUR data in July, 1989. For the non-retrieved pixels, the LAI-NDVI, NDVI-FPAR relations were used to estimate LAI and FPAR.
45
(a) LASUR LUT
0 2 4 6 8LAI
0
10
20
30Fr
eque
ncy
(%) Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal Crops
ShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b) LANDSAT LUT
0 2 4 6 8LAI
0
10
20
30
Freq
uenc
y (%
) Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(c) LASUR LUT
0.0 0.2 0.4 0.6 0.8 1.0FPAR
0
10
20
30
40
Freq
uenc
y (%
)
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(d) LANDSAT LUT
0.0 0.2 0.4 0.6 0.8 1.0FPAR
0
10
20
30
40
Freq
uenc
y (%
)Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 2.8. Retrievals from Landsat data as a function of spatial resolution-dependent look-up table (LUT). Histograms of LAI from (a) Landsat LUT, (b) LASUR LUT, histograms of FPAR from (c) Landsat LUT, and (d) LASUR LUT.
46
(a)
0 2 4 6 8LAI
0
10
20
30Fr
eque
ncy
(%) Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal Crops
ShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b)
0.0 0.2 0.4 0.6 0.8 1.0FPAR
0
10
20
30
40
Freq
uenc
y (%
)
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 2.9. Retrievals from LASUR data using Landsat look-up table (LUT). Histograms of (a) LAI; (b) FPAR.
47
Table 2.1. Spectral Statistics for LASUR Data and LANDSAT TM Data
LASUR Data
Biome Type Mean Red Mean NIR Mean NDVI
Grasses and cereal crops 0.080 0.25 0.515
Shrubs 0.050 0.21 0.615
Broadleaf crops 0.065 0.32 0.662
Savanna 0.050 0.23 0.645
Broadleaf forests 0.030 0.29 0.813
Needle forests 0.045 0.25 0.695
LANDSAT Data
Biome Type Mean Red Mean NIR Mean NDVI
Grasses and cereal crops 0.065 0.304 0.635
Broadleaf forests 0.022 0.348 0.881
Needle forests 0.013 0.200 0.886
48
Table 2.2. Retrieval Index (a) and Mean LAI (b) for Misclassified LASUR Data
(a)
Misclassified Biome Type
BCM Biome Type Grasses and cereal crops
Shrubs
Broadleaf Crops
Savanna
Broadleaf forests
Needle forests
Grasses and cereal crops 91.53 88.54 89.60 88.68 27.63 29.00
Shrubs 87.67 92.66 91.53 91.73 47.34 46.37
Broadleaf crops 87.93 70.33 74.03 71.29 14.80 19.52
Savanna 78.02 79.91 80.25 79.65 41.31 44.33
Broadleaf forests 55.02 63.23 61.4 61.32 39.30 33.59
Needle forests 76.75 85.74 84.92 84.78 46.38 54.54
(b)
Misclassified Biome Type
BCM Biome Type Grasses and cereal crops
Shrubs
Broadleaf Crops
Savanna
Broadleaf forests
Needle forests
Grasses and cereal crops 1.197 1.245 1.401 1.363 1.293 2.011
Shrubs 1.026 1.408 1.542 1.514 1.505 1.987
Broadleaf crops 1.845 1.833 2.097 2.044 2.424 3.710
Savanna 1.508 2.079 2.286 2.250 2.221 2.953
Broadleaf forests 1.921 3.299 3.439 3.451 4.014 4.649
Needle forests 1.640 2.916 3.205 3.179 2.976 3.996
49
Table 2.3. Comparison of the Results from LASUR LUT and LANDSAT LUT Retrievals
LASUR Data
LASUR LUT LANDSAT LUT
Biome Type Retrieval Index
Mean LAI Retrieval Index
Mean LAI
Grasses and cereal crops 91.53 1.20 91.6 1.07
Shrubs 92.66 1.41 96.4 0.92
Broadleaf crops 74.03 2.09 80.1 1.17
Savanna 79.65 2.25 85.4 1.61
Broadleaf forests 39.30 4.01 41.8 2.62
Needle forests 54.54 3.99 41.8 1.66
LANDSAT Data
LANDSAT LUT LASUR LUT
Biome Type Retrieval Index
Mean LAI Retrieval Index
Mean LAI
Grasses and cereal crops 90.7 1.87 87.5 3.62
Broadleaf forests 53.9 5.79 39.2 6.21
Needle forests 57.9 4.11 4.7 3.39
50
Chapter 3
Radiative Transfer Based Scaling of LAI/FPAR
Retrievals From Reflectance Data of Different
Resolutions
3.1 Introduction
Vegetation-atmosphere interactions can be conveniently grouped into biogeophysical
(energy and water exchanges) and biogeochemical (carbon and volatile organic
compound exchanges) themes (Sellers et al., 1997). Models of these processes, e.g., land
surface parameterizations in climate models, are key tools for evaluating the role of
vegetation in the context of global climate change and variability (Running et al., 1999).
The utility of such models is significantly enhanced when they can be either forced or
tested with satellite data products, in view of the coverage, repeativity and consistency of
remote sensing products.
One of the key state variables in land surface models is the vegetation green leaf area
index (LAI), defined as the one-sided green leaf area per unit ground area. Vegetation
leaf area index governs net radiation and its expenditure (energy balance), net primary
production (carbon fixation), evapotranspiration and canopy interception (water budget).
51
As such, there is considerable interest in developing algorithms for the estimation of LAI
from satellite measurements of vegetation reflectance (Knyazikhin et al., 1998a and
1998b), and also to assemble time series of LAI data from the archive of almost two
decades of AVHRR data to study interannual global vegetation dynamics (Myneni et al.,
1998).
Several complicated issues arise when one attempts to assemble a consistent time
series of LAI and other biophysical products with data from different instruments. One
needs to account for varying radiometric integrity, spectral band widths, calibration,
geometry of acquisition, etc. A key issue in this context is the possiblity of varying
spatial resolution of the data from different instruments. This problem may be posed as,
how can a time series of a particular biophysical product be developed from data acquired
from a series of sensors that have different spatial resolutions?
The issue of spatial resolution of image data has been addressed previously, usually
depending on the application. For instance, Nelson and Holben (1986) reported that a 1.1
km or higher resolution data are required to identify forested areas. Woodcock and
Strahler (1987) argued that a spatial resolution at which the local variance reaches its
maximum should be taken as the characteristic scale of scene variation. Other
investigators used the concept of entropy to evaluate the feasibility of detecting land
cover changes in coarse resolution data (Townshend and Justice, 1988).
This chapter is focused on how the data resolution impacts the retrieval of
biophysical parameters, especially LAI. There is conflicting information in the literature
as to whether retrieval methods based on the normalized difference vegetation index
(NDVI) are scale dependent or invariant (Hall et al., 1992; Friedl, 1996; Hu and Islam,
1997). Of special interest are issues related to the use of retrieval methods based on point
52
scale physical models, applied to coarse scale data, which inevitably contain land cover
mixtures (Raffy, 1994; Gregoire and Raffy, 1994; Chen, 1999). In other words, how can
a physically based retrieval algorithm be made scale dependent, such that scaling of the
retrieved biophysical product is accomplished when the algorithm is executed on data of
multiple resolutions?
The goal of scaling is defined here, as a process by which it is established that values
of a certain biophysical product, LAI in this case, derived from coarse resolution sensor
data should equal the arithmetic average of values derived independently from fine
resolution sensor data. Specifically, this chapter addresses the problem of LAI retrievals
with 1 km AVHRR data aggregated to different resolutions, in support of the MODIS and
MISR LAI and FPAR algorithm research. MODIS and MISR refer to the Moderate
Resolution Imaging Spectroradiometer and Multi-angle Imaging Spectroradiometer
aboard the TERRA platform launched by National Aeronautics and Space Administration
(NASA) in December 1999.
The problem addressed here, that of scale dependence of algorithms for the retrieval
of biophysical variables, arises in two contexts. The first, as previously mentioned, is in
the context of assembling time series of biophysical variables with data from sensors of
different spatial resolution. The second is in the validation of moderate resolution (~ 1
km) sensor products such as MODIS and MISR LAI and FPAR. Validation means
specification of the uncertainty in the products in relation to ground truth data. The latter
are often collected at resolutions much finer that the products for practical reasons.
Therefore, the retrieval algorithms must be scale dependent so that the products can be
validated through scaling, as defined above.
53
The organization of this chapter is as follows. I begin with a brief description of the
data and the LAI/FPAR retrieval algorithm used in this study. Then I focus on data
analysis, where the relation between land cover heterogeneity and spatial resolution, and
the impact of heterogeneity on measured surface reflectances and LAI/FPAR retrievals
are demonstrated. Then I present a physically based theory for scaling with explicit scale
dependent radiative transfer formulation. I conclude by providing illustrative results that
highlight scaling of LAI with the MODIS LAI/FPAR algorithm.
3.2 Data and the LAI/FPAR Algorithm
Land surface reflectances at 1 km resolution from AVHRR over North America for July
1995 are used in this study. The data consist of channels 1 (580-680 nm) and 2 (725-1100
nm) reflectances, that is, the red and near-infrared bands, respectively. The data
processing included radiometric calibration, partial atmospheric corrections, geometric
registration and the production of 10-day maximum NDVI value composites (Eidenshink
et al., 1998). A monthly layer based on the maximum NDVI composite of the three 10-
day layers was generated for further analysis.
An important ancillary data layer required for this study is the six biome North
American land cover map, which was previously developed from 1 km AVHRR
normalized difference vegetation index (NDVI) data of 1995 and 1996, and ancillary data
sources (Lotsch et al., 2001). This map segregates global vegetation into six major biome
types depending on vegetation structure and optical properties, and background
characteristics (Myneni et al., 1997). The six biomes include: Grasses and Cereal Crops
(biome 1), Shrubs (biome 2), Broadleaf Crops (biome 3), Savannas (biome 4), Broadleaf
Forests (biome 5) and Needle Forests (biome 6). Bare land, which is considered as cover
54
type 7 in this study, and water-bodies are also included in this map. The site-based
accuracy of this map is 73%. When compared to maps generated from the same data but
classified using the International Geosphere Biosphere Program (IGBP) classes (e.g.,
Loveland et al. (1995), and Hansen et al. (2000)), the biomes were mapped with ~5%
higher overall accuracy (Lotsch et al., 2001).
The structural attributes of these biomes can be parameterized in terms of variables
that radiative transfer models admit (Myneni et al., 1997). Numerical solutions of the
three-dimensional radiative transfer equation are used to model the Bi-directional
Reflectance Factors (BRF) of the biomes for varying sun-view geometry and canopy/soil
patterns (Knyazikhin et al., 1998a and 1998b). The retrieval of LAI and FPAR is done by
comparing the observed and modeled BRFs for a suite of canopy structures and soil
patterns. All canopy and soil patterns for which the magnitude of the residuals in the
comparison does not exceed uncertainties in observed and modeled BRFs are treated as
acceptable solutions. For each acceptable solution, a value of FPAR is also evaluated.
The mean values of LAI and FPAR averaged over all acceptable values and their
dispersions are taken as the retrievals and their accuracy (Knyazikhin et al., 1998a and
1998b). This algorithm was prototyped with POLDER, LASUR, Landsat Thematic
Mapper (TM), and SeaWiFS data (Tian et al., 2000; Zhang et al., 2000; Wang et al.,
2000). Its theoretical basis was validated with field measurements (Panferov et al., 2001).
The algorithm has been implemented for operational production of LAI and FPAR from
MODIS data.
55
3.3 Data Analysis
3.3.1 Characterizing Land Cover Heterogeneity
The 1 km AVHRR reflectance data were aggregated to 4, 8, 16, 32 and 64 km resolutions
in this study. The 1 km pixel is denoted as the “sub-pixel”, and the aggregated coarse
resolution pixel is denoted as the “pixel” for the remainder of this chapter. Each sub-pixel
is assumed to contain only one biome type, in view of the 1 km resolution of the biome
map. The biome type of a pixel is assigned based on the dominant biome fraction. Water-
bodies were not accounted because there is no reflectance data for water in the AVHRR
data set. Therefore, all aggregations were based on 7 land cover types - biomes 1 through
6, and bareland, also denoted as land covers 1 through 7. When a pixel contains only one
cover type, it is defined as "homogeneous". Otherwise, it is heterogeneous. Thus,
heterogeneity in this study only indicates that pixels at coarse resolution contain more
than one land cover type.
I introduce the percentage function (pf) to quantify the heterogeneity of a vegetated
pixel. For a pixel, pfl (l = 1, …, 7), is the percent of sub-pixels land cover type l in the
pixel of a given resolution. Note that %100pf7
1ll∑
== . The index pfj, which corresponds to
the percent occupation of the dominant cover type j within the pixel, can also be defined
as the "purity" or homogeneity of that pixel. Pixels with low pfj value are more
heterogeneous than those having high values of pfj.
The overall percentage function, PF(j), is defined as the average of pfj over the total
number of biome j pixels in North America at a given resolution. The index PF(j) is
called the overall purity of biome j at that resolution. If PF(j) value is higher, on average,
biome j is more homogeneously resolved at that resolution.
56
The overall percentage functions PF(j) at 8 km resolution are given in Table 3.1.
Eight kilometer resolution pixels denoted as biome 1 have, on average, about 63.32% of
sub-pixels containing biome 1. That is, the overall biome 1 purity at 8 km resolution is
63.32%. Shrubs (biome 2) are in general more homogeneously distributed, with about
85.2% of coverage. On the other extreme, broadleaf crops (biome 3) are most
heterogeneous. The overall purities PF(j) are shown in Fig. 3.1 as a function of
resolution. The purities decrease with decrease in resolution. Shrubs tend to be most
homogeneously resolved at all resolutions followed by broadleaf and needle forests,
which is possibly indicative of the natural, that is, undisturbed, state of these biomes.
Biome j pixels are divided into three categories for further analysis. The first group
consists of pixels with pfj ≥ 90%; these are assumed to represent homogeneous pixels.
The second group consists of nominally heterogeneous pixels with 50% ≤ pfj < 90%. The
last group contains the rest, that is, heterogeneous pixels with pfj < 50%. Figure 3.2(a)
shows that the percentage of pixels belonging to group 1 decreases in a nonlinear fashion
with decreasing spatial resolution, in all biomes. Similarly, the percentage of pixels
belonging to group 3 increases with decreasing spatial resolution (Fig. 3.2b). This is to be
expected in view of increasing mixtures with increase in pixel area. I concluded that the
overall purity PF(j) decreases with decreasing spatial resolution.
3.3.2 Canopy Reflectances and Heterogeneity
The data density distribution function was evaluated for each biome as follows: specify a
fine grid cell in the spectral space of red and near-infrared reflectances (RED-NIR), count
the number of canopy reflectances in this cell, divide this value by the total number of
pixels in the entire spectral space (Tian et al., 2000). The location of high density data
57
(50% of all pixels) for each biome in the RED-NIR space is then plotted (Fig. 3.3). These
can be interpreted as the set of pixels representing the most probable patterns of canopy
structure for each of the biomes. For instance, broadleaf forests and crops are situated at
high near-infrared and low red reflectance locations. Likewise, needle forests and shrubs
are located uniquely in the spectral space. The other biomes, however, have considerable
overlap. The 50% data density contours at 1 and 8 km resolution are identical. However,
the density contours from pixels with pfj ≥ 90%, shown in Fig. 3.3b, indicate that the
biomes have distinct locations in the spectral space. Broadleaf forests have higher near-
infrared reflectance that broadleaf crops, and thus, separate better. Likewise, grasses and
savannas also occupy distinct locations. Thus, it is important to observe homogeneous
patches of vegetation types to deduce their reflectance signatures. And, it is possible to
identify such homogeneous patches at any resolution, provided a finer resolution land
cover map is available. This point is further illustrated, in Fig. 3.3c, where the biome
density contours of heterogeneous pixels (pfj < 50%) are shown to have considerable
overlap in the spectral space.
The mean red and near-infrared reflectances of homogeneous and heterogeneous
pixels are shown in Fig. 3.4 as a function of spatial resolution. The reflectance
magnitudes of both kinds of pixels do not change much with changing resolution.
However, the contrast between the biomes decreases with increasing heterogeneity. This
is observed in both spectral bands. It appears cover mixture, rather than spatial resolution,
that is critical to determining the spectral signature of a pixel. Also note that decreasing
pixel resolution does not necessarily lead to increasing cover type heterogeneity.
An important issue is the degree of spectral variation in reflectance data from pixels
of the same biome type, and how this changes with resolution and pixel heterogeneity.
58
First, I assume that the mean red ( R ) and near-infrared ( N ) reflectance values of
homogeneous pixels (group 1; pfj ≥ 90%) represent the correct biome spectral
characteristics. Second, I evaluate the average distance between pixels from group i (i =
1, 2, 3) and point ( R , N ), which can be understood as the deviation from representative
biome spectral features,
∑=
−+−=iK
k
ikik
ii
N
NN
R
RR
KD
1
2,2, )()(1
. (3.1)
Here Ki is the total number of pixels in group i, Rk,i and Nk,i are the red and near-infrared
reflectance of the kth pixels in group i. Variables R and N are used in Eq. (3.1) in order
to equally weight the two spectral bands. The resulting distance values are shown in Fig.
3.5 as a function of resolution and biome type. The distance values increase with
increasing heterogeneity, as expected. Shrubs have a large distance value compared to
other biomes at a given level of homogeneity and resolution, indicating that these are
spectrally heterogeneous media. This spectral variation within a biome type can also lead
to misclassification if the training data set is not representative of the full range of
spectral variations.
3.3.3 LAI Retrievals and Heterogeneity
Let Lt denote vegetation LAI values at resolutions 4, 8, 16, 32 and 64 km, obtained by
averaging 1 km LAI retrievals. Let Lc denote LAI retrievals obtained directly from 4, 8,
16, 32 and 64 km surface reflectance data. The discrepancy between Lt and Lc defines the
response of the LAI retrieval algorithm to heterogeneity of the medium. Therefore, I
propose the following to quantify the scaling effect on the algorithm,
.Lt/LcLtRDL −= (3.2)
59
In the above, RDL denotes LAI error incurred by first averaging reflectances and then
performing LAI retrievals. The average value of RDL for a given biome is termed here as
the “overall RDL”. Likewise, RDFPAR denotes the discrepancy in FPAR between coarse
and fine resolution retrievals. In general, both RDL and RDFPAR increase with
decreasing resolution because of the nonlinear relation between reflectances and
LAI/FPAR (Fig. 3.6; RDFPAR results are not shown for brevity), as noted previously by
Weiss et al. (2000). The contour plots further highlight the importance of cover
heterogeneity (Fig. 3.6), that is, the degree of pixel heterogeneity determines the
discrepancy between coarse and fine resolution retrievals, and thus, the dependence of the
algorithm on the spatial resolution of the data.
It is noted that RDL values in the case of needle forests are in general higher
compared to other biomes. This is possibly due to the unique reflectance features of
needle leaf canopies. Here, the role of canopy architecture is paramount, and when these
canopies are mixed with other biome types, the pixel reflectances are significantly
altered, thus, resulting in larger RDL values. As an example, the NDVI vs. LAI relation
for needle forests is compared to that of shrubs and grasses in Fig. 3.7. These relations
show NDVI values computed from red and near-infrared reflectances input to the
algorithm and the corresponding LAI retrievals. These relations demonstrate how
differently the input reflectance data were translated to LAI by the algorithm in these
biomes. From Table 3.1, it is noted that among the biomes, grasses are most commonly
mixed with needle forests. Hence, large RDL values in the case of needle leaf forests.
The LAI/FPAR retrieval algorithm utilizes a look-up table (LUT) of the dominant
biome of a pixel in the course of retrieval. The presence of other biomes in the case of
heterogeneous pixels leads to error in LAI and FPAR retrievals. Thus, it is of interest to
60
evaluate the impact of minority biome presence on LAI retrievals of heterogeneous
pixels. This is illustrated in Fig. 3.8, where for each of the biomes, the relative differences
in LAI are shown as a function of increasing fractions of minority biome type at 8 km
resolution. It appears that larger LAI errors are incurred when forests are minority biomes
in non-forest pixels compared to when forest biomes are mixed with one another.
Likewise, larger LAI errors are incurred when non-forest biomes are a minority biome in
forest pixels compared to when non-forest biomes are mixed with one another. This is in
a way not surprising considering the differences in architecture, such as, the presence of
woody biomass, clumping and structural heterogeneity, between forest and non-forest
biomes.
3.4 Physically Based Theory for Scaling
Most of the algorithms that estimate surface biophysical parameters from remote sensing
data use vegetation maps as a priori information to constrain the parameter space. A
common problem with land cover characterization is one of mixture. The designated
biome type may be just the dominant biome type, and other biomes can exist within the
coarse resolution pixel. Pixel heterogeneity is an important factor causing variations in
surface reflectance data (Fig. 3.3). This information should therefore be taken into
account in algorithms in order to correctly interpret data of different resolutions. In this
section, a related but wider problem, i.e., fusion of biophysical parameters derived from
data acquired by spectroradiometers of different spectral bands and different resolutions,
is considered.
61
3.4.1 Definition and Background Information
Consider two hypothetical spectroradiometers of resolutions, say, 8 km and 1 km, which
measure at different wavelength bands. Let R(λ) be the surface reflectances of a 8 km by
8 km vegetated pixel at wavelength λ = λ1, λ2, …λn provided by the first instrument
(instrument 1). Let the same pixel be sensed by the second instrument (instrument 2) and
ri(β), i = 1, 2, … , 64 be surface reflectances at wavelength β = β1, β2 … βm at 1 km
resolution covering the 8 km by 8 km pixel. Suppose that one uses instrument 1 and
instrument 2 reflectance data independently to produce biophysical parameters at 8 km
and 1 km resolution. The fusion (or scaling, if only the spatial dimension is considered) is
said to be accomplished if the biophysical variable at 8 km resolution is equal to the mean
value of the 1 km resolution retrievals.
The three-dimensional radiation field in a scattering and absorbing medium bounded
at the bottom by a reflecting surface can be expressed in terms of the reflectance
properties of the background surface and solutions of two sub-problems: the radiation
field in the medium calculated for a black or completely absorbing background, and the
radiation field in the same medium generated by anisotropic sources located at the bottom
(Knyazikhin et al., 1998a and 1998b; Knyazikhin and Marshak, 2000). Thus, to quantify
photon interactions between the vegetation canopy and its background (soil and/or
understory), it is important to specify those variables that determine the radiation regime
in vegetation canopies when reflection from the background back into the canopy is zero.
Such variables include information on intrinsic canopy properties. It was theoretically
derived (Knyazikhin et al., 1998a and 1998b) and verified with field measurements
(Panferov et al., 2001) that, in the case of a black background, some simple algebraic
combinations of leaf and canopy spectral transmittances and reflectances eliminate their
62
dependencies on wavelength through the specification of two canopy-specific wavelength
independent variables. These variables and leaf optical properties govern the law of
energy conservation in vegetation canopies at any given wavelength of the solar
spectrum. These results constitute the basis for the approach to scaling, or more broadly,
fusion, in the sense of the definition given previously.
3.4.2 Scale Dependent Radiative Transfer Formulation
Solar radiation scattered from a vegetation canopy and measured by satellite-borne
sensors results from interaction of photons traversing through the foliage medium,
bounded at the bottom by a radiatively participating surface. Therefore, to estimate the
canopy reflectance, three important variables must be carefully formulated: the
architecture of the canopy, the optical properties of foliage elements, and the background
surface reflectance properties. Specification of the first two variables depends on the
definition of the foliage element or scattering center. An individual leaf, for example,
should be taken as the basic foliage element to describe photon transport in a vegetation
canopy of a small area (about 0.1-0.3 ha) (Knyazikhin et al., 1997). Optical properties of
tree crowns and their distribution in the canopy space can be used to estimate the
radiation regime in an extended canopy. In both cases, the three-dimensional transport
equation relates properties of the scattering centers to the radiative regime of the medium.
The former allows estimation of the radiation field at the leaf scale, while the latter
describes the interaction of photons with trees, which is appropriate for interpretation of
reflectances at coarse resolution. The reflective properties of the tree crown are
determined by its leaf optical properties and architecture. Therefore, solutions of the
transport equation that describe canopy radiation regime at the leaf and crown scales are
not independent. This allows us to relate these solutions to the biophysical parameters
63
defined at different scales. The major issue is, of course, how the coefficients appearing
in the transport equation vary with resolution.
Let the domain in which the vegetation canopy is located be a parallelepiped P.
Assume that its horizontal and vertical dimensions coincide with the area of the pixel and
the tallest tree, respectively. This parallelepiped P is termed as a 3D pixel, or simply,
pixel. To approximate the canopy structure, a spatial mesh is introduced by dividing P
into fine grid cells. The ratio R, the total number of cells in P to the volume of P, is
termed as the resolution of the model, or a scale at which photon transport and interaction
are formulated. This parameter determines the accuracy in the modeled mean radiation
quantities of the pixel (Knyazikhin et al., 1997).
Photons interact with scattering centers that reside in these cells. Let us assume that,
for a cell containing M scattering centers, the intensity scattered by the cell is the sum of
intensities scattered by the individual scattering centers. That is, photons experience only
a single interaction with the scattering centers inside the cell. This assumption allows the
use of the radiative transfer equation to describe photon interactions with scattering
centers. Thus, the total interaction and differential scattering cross-sections that appear in
the transport equation are cell averages of the cross-sections calculated for individual
scattering centers. The solution of the transport equation provides mean intensity over the
cell around the spatial point r in direction Ω (Ross, 1981, pp. 144).
The specification of the scattering centers and scale R must be consistent in order to
predict correct canopy reflectance for the pixel. For example, in the case of a coniferous
forest (Picea abies(L.) Karst) of domain P = 25 m × 30 m × 29 m, a model resolution of
R = 8 (or cell size of 50 cm × 50 cm × 50 cm) and a one-year shoot of size 5-7 cm as the
scattering center guarantees accurate evaluation of mean canopy reflectance over a
64
horizontal area of about 10 m2 (Knyazikhin et al., 1997). It should be emphasized that the
scattering properties of the shoot must be known in order to formulate the differential
scattering cross-section. At this scale, a single needle can not be taken as the scattering
center because photons undergo multiple interactions within the shoot, and thus, the
above assumption is violated for a cell of 50 cm × 50 cm × 50 cm.
In this manner, three spatial attributes of the medium, namely, pixel size, scale, and
scattering centers to describe its radiative behavior, are introduced. Under the consistency
assumption, the radiation regime in this medium can be described by the three-
dimensional transport equation (Ross, 1981; Myneni, 1991; Knyazikhin et al., 1997)
Ω′Ω′Ω→Ω′=ΩΩ+Ω∇•Ω ∫ drRIrRrRIrRrRI ),,(),,(),,(),,(),,(4
S,
πλλλλ σσ . (3.3)
Here, “•” denotes scalar product of two unit vectors. The total interaction cross-sections,
σ, and the differential scattering cross-sections, σS,λ, depend on the scale R and the
definition of the scattering centers. The reflectance measured by satellite-borne sensors is
the solution to the above transport equation averaged over the pixel. By definition, the
total interaction cross-section σ ds is the probability that a photon, while traveling a
distance ds, hits a scattering center. Because the photon interacts with leaves at any
wavelength, this probability is wavelength independent. A precise description of the
cross-sections can be found in Ross (1981) and Myneni (1991). Below, the formulation
of Myneni (1991) is adopted.
The magnitude of scattering per volume unit is described using the single scattering
albedo
65
),,(
),,(
),,( 4
,S
Ω
Ω′Ω′→Ω=Ω
∫rR
drR
rRσ
σω π
λ
λ . (3.4)
Let gλ(R, r, Ω → Ω′) be the differential scattering cross-section normalized by the single
scattering albedo, i.e., σS,λ(R, r, Ω → Ω′) = ωλ(R, r, Ω)gλ(R, r, Ω → Ω′). For simplicity,
the single scattering albedo is assumed constant with respect to spatial, r, and directional,
Ω, variables, and g is independent of wavelength. In this case, the solution Iλ depends on
values of the spectral leaf albedo, which in turn depends on wavelength. This allows its
parameterization in terms of single scattering albedo rather than wavelength. Therefore,
wavelength dependence will be suppressed in further notations. The value of the single
scattering albedo ω will be added to the argument list of the solution of Eq. (3.3).
Consider an extended vegetation canopy contained in a parallelepiped P. Let V ⊂ P
be another parallelepiped contained in P. The top, δVT, base, δVB, and lateral surfaces,
δVL, of the parallelepiped V form its boundary δV = δVT + δVB + δVL. Integration of Eq.
(3.3) over V and the full solid angle 4π leads to the law of energy conservation of the
form (Titov, 1998)
)()()()()()()( LLBTBT ωωωωωωω +−−−++ −++=++ FFFFFFA , (3.5)
where A is radiant energy absorbed by V; ±TF , ±
BF and ±LF are radiant fluxes penetrating
into (sign "−") and exiting (sign "+") the canopy through the top (subscript "T"), base
(subscript "B") and lateral sides (subscript "L") of the parallelepiped V, i.e.,
∫∫>•Ω±
± •ΩΩ=0)(
)(),,()(rV
rrRIdSFn
nωδ
χχ
ω , χ = T, B, or L. (3.6)
66
Here, n(r) is the outward normal at points r ∈ δV, and Iω(R, r, Ω) is the solution of Eq.
(3.3). As mentioned previously, the discussion here can be restricted to the case of a
completely absorbing background beneath the canopy, i.e., 0B =−F .
Titov (1998) introduced horizontal transport of radiant energy as E = +− − LL FF . It
follows from Eq. (3.5) that the amount of energy absorbed ( −T/ FA ), reflected ( _
TT / FF + ),
and transmitted ( _TB / FF + ) by the volume V is not necessarily equal to 1; it can be greater
or less than 1, depending on the sign of E. The magnitude of horizontal transport depends
on mean length, l, of photon lateral migration in the medium (Titov, 1998). If the
horizontal sizes, xV and yV, of V are substantially greater than l, the horizontal transport
1/ _T <<FE . This condition is fulfilled for horizontally homogeneous medium. If xV,
yV ∼ l, the average of Eq. (3.5) over number NxNy of pixels, such that NxxV >> l,
NyyV >> l, results in 0/ _T ≈FE (Titov, 1998). This property is used to adjust the radiative
transfer equation [Eq. (3.3)] to simulate surface reflectances at a given resolution by
choosing an appropriate model resolution R and definition of the scattering center
(Knyazikhin et al., 1997). It means that the definition of scattering centers and model
resolution should be chosen such that the horizontal size of the fine cell is comparable to
l. This allows us to account for horizontal transport within the pixel. The transport
equation at this scale can be extended to evaluate surface reflectances of horizontally
homogeneous coarse pixels. The reflectance of a heterogeneous coarse pixel, however,
cannot be taken as the average of reflectances calculated for fine resolution pixels
because this technique does not account for the radiative properties of neighboring pixels.
Neglecting horizontal transport can lead to uncontrollable errors in the interpretation of
measured data (Titov, 1978). The transport equation, therefore, should be adjusted for the
resolution of data.
67
3.4.3 Scaling of Reflection and Absorption Properties of Scattering
Centers
Consider a volume V that can be taken as the scattering center. The radiative response of
V at a point r ∈ V to a point mono-directional source located at a point r0 on the boundary
δV of the volume V is the Green’s function, G(r0, r, Ω0 → Ω), where Ω0 and Ω are
directions of the incident and reflected radiation streams, respectively (Case and Zweifel,
1967). The volume Green’s function satisfies Eq. (3.3) and the boundary condition
G(r0, rV, Ω0 → Ω) = δ(rV − r0)δ(Ω − Ω0), rV ∈ δV. (3.7)
The extinction coefficient σ, the single scattering albedo ωλ, and the normalized
differential scattering cross-section g which characterize properties of the volume V at the
fine scale R0 are assumed known. Properties of Green's function are investigated using
operator theory (Vladimirov, 1963; Richtmyer, 1978) by introducing the differential, L,
and integral, S, operators,
),(),,( 0 ΩΩ+∇•Ω= rIrRILI σ ; Ω′Ω′Ω→Ω′= ∫ drIrRgSI ),(),,(4
0
π
. (3.8)
It should be emphasized that the differential and integral operators are wavelength
independent. In terms of these notations, the equation for the Green's function can be
rewritten as LG = ωSG. Its solution Gω can be represented as the sum, i.e., Gω = Q + ϕω.
Here, the wavelength independent function Q is the probability density that a photon in
the direct beam will arrive at r along the direction of incident radiation without suffering
a collision. It satisfies the equation LQ = 0 and the boundary conditions specified by Eq.
(3.7). The second term, ϕω, describes photons scattered in the volume V. It satisfies
Lϕω = ωSϕω + ωSQ and zero boundary conditions. By stating T = L−1S, the transfer
equation for ϕω can be transformed to
68
ϕω = ωTϕω + ωTQ. (3.9)
Substituting ϕω = Gω − Q into this equation results in an integral equation for Gω
(Vladimirov, 1963; Bell and Glasstone, 1970)
Gω − ωTGω = Q. (3.10)
It follows from Eq. (3.10) that Gω − ωTGω does not depend on ω, and involves the
validity of the following relationship
Gω − ωTGω = Gα − αTGα = Q, (3.11)
where Gω and Gα are Green’s functions corresponding to single scattering albedos ω and
α, respectively.
Let i(V, ω) be volume absorption a(V, ω) normalized by 1 − ω, i.e.,
i(V, ω) = a(V, ω)/(1 − ω). This variable is the average number of photon interactions with
the scattering centers in V before either being absorbed or exiting V. It can be expressed
via Green’s function as
00000
4
)(/),,(),,(),( Ω•Ω′→ΩΩΩ′= ∫∫ rrrGrRdrdVV
ni ωπ
σω . (3.12)
Multiplying Eq. (3.3) by the extinction coefficient σ and integrating over V and all
directions Ω results in
i(V, ω) − ωpi(ω)i(V, ω) = i(V, ω) − αpi(α)i(V, ω) = q(V) . (3.13)
Here
00
4
00
)()(
),,(),,(
)(Ω•
ΩΩΩ=
∫∫r
drRrRdr
p V
nii ω
ψσω π
ω
, (3.14a)
69
00
00
4
)(
),(),,(
)(Ω•
ΩΩΩ=
∫∫r
rQrRdrd
Vq V
n
σπ , (3.14b)
where ψω = TGω. It was theoretically shown (Knyazikhin et al., 1998a and 1998b) and
confirmed with field measurements (Panferov et al., 2001) that the coefficient
pi(ω) equals p0(V), where p0(V) is the positive eigenvalue of the operator T (Knyazikhin
et al., 1998a and 1998b). This implies that the ratio [Eq. (3.14a)] is invariant with respect
to the single scattering albedo, and the value of p0(V) is determined by intrinsic structural
properties of V. Equation (3.13) expresses the energy conservation law for the volume V.
The coefficient q(V) is the probability that a photon entering V along Ω0 will undergo
one interaction with scattering centers defined at the scale R0. Given q(V), one can derive
the extinction coefficient for another volume consisting of scattering centers V. The
absorption and reflection properties of this coarse volume are determined by
a(V, ω) = q(V)[1 − ω]/[1 − p0(V)ω] and Green’s function Gω . These coefficients describe
photon interactions with vegetation at coarse scale R that, in turn, are determined by
photon transport at the fine scale R0 .
3.4.4 Scaling of Surface Reflectances
Consider an extended vegetation canopy that occupies a parallelepiped P of horizontal
dimensions XP and YP. The pixel P consists of N fine resolution pixels Pk ; that is,
∑ == N
k kPP1
. Let R0 be the scale of Pk . Attenuation and scattering of photons within the
fine resolution pixel Pk is given by the total interaction cross-section σk and the single
scattering albedo ωk . These variables are assumed to be constant with respect to the
spatial variable r within Pk and take on a zero value outside the pixel Pk . This allows us
70
to express the total interaction cross-section σ and the single scattering albedo ω for the
coarse pixel P at the scale R0 as
∑=
Ω=ΩN
kk RrR
100 ),(),,( σσ , ∑
==
N
kk RrR
100 )(),( ωω . (3.15)
Note that the single scattering albedo for the pixel P depends on the spatial variable
r. Let a parallel beam of unit intensity be incident on the upper boundary of P along Ω0.
Multiplying Eq. (3.3) by the extinction coefficient σ and integrating over P and all
directions Ω and normalizing by XPYPµ0, where µ0 = |n0•Ω0|, and n0 is the outward
normal to the upper boundary of P, one obtains
)()(1
PqPN
kPkk k =>Ψ<− ∑
=σωi . (3.16)
Here Ψ = TI, and < ⋅ >Pk denotes integration over Pk and the full solid angle 4π
normalized by XPYPµ0.
Let p0(P) be the positive eigenvalue of the operator T corresponding to the scale R0
(Knyazikhin et al., 1998a and 1998b). Integrating Eq. (3.12) over the upper boundary of
P and accounting for Eq. (3.13) results in p0(P) = < σΨ >P/i(P). This involves
)()()()(
0 PpPPP P
PkPkPk
kkk ii
i >Ψ<>Ψ<=>Ψ<=>Ψ<
σσσσ . (3.17)
The latter allows us to rewrite Eq. (3.16) as
)()()()( 0 PqPPpP =− ii ϖ , (3.18)
where
71
∑= >Ψ<
>Ψ<=N
k P
Pkk
k
1 σσωϖ (3.19)
is the single scattering albedo at a scale that accounts for photon interaction with sub-
pixels Pk. The solution of the transport equation corresponding to the single scattering
albedo ϖ satisfies the energy conservation relationship specified by Eq. (3.18). This
shows that a re-evaluation of the single scattering albedo is required to force the transport
equation formulated at scale R0 to simulate coarse pixel reflectances without violating the
energy conservation law. It also means that the single scattering albedo is the basic
parameter of the transport equation that describes variations in surface reflectance due to
changing spatial resolution.
3.4.5 Scaling of LAI and FPAR Fields
The transport equation was adjusted as described above to simulate the radiation regime
in vegetation canopies bounded by a parallelepiped P0 of horizontal dimensions 30 m ×
30 m with an uncertainty of 20% (Knyazikhin et al., 1997). The model resolution is
R0 = 8. A single leaf and a one-year shoot of size 5-7 cm were taken as scattering centers
in broadleaf and needle forests, respectively. The single scattering albedo coincides with
leaf albedo in this case, which is defined as the fraction of incident radiation flux density
that the leaf transmits and reflects. The leaf albedo is a measurable parameter. A data
bank of leaf optical properties was assembled from various sources, and analyzed to
obtain the mean and variance spectrum as a function of biome type. This information is
used to model canopy reflectance at 30 m resolution.
For the purpose of LAI and FPAR retrieval, global vegetation is stratified into six
architectural types or biomes (Myneni et al., 1997) as mentioned previously. Each biome
is represented by wavelength independent eigenvalues of the operator T that quantify
72
canopy structures, wavelength dependent patterns of ground reflectances and one single
pattern of leaf spectral albedo per biome. The solution of the transport equation can be
expressed explicitly in terms of these variables (Knyazikhin et al., 1998a and 1998b).
Thus, surface reflectances can be simulated as a function of resolution and wavelength
bands of the spectroradiometer.
It follows from the parameterization of global vegetation, that Eq. (3.19) contains six
different values of the single scattering albedo. Therefore,
∑∑== >Ψ<
>Ψ<=lk
k
P
Pk
ll
ωω σσωϖ
6
1
. (3.20)
A simple estimation of Eq. (3.20) can be performed as follows. One replaces the
solution I in the definition of Ψ by the normalized positive eigenvector ek of the operator
T defined on Pk . This yields
||
)(||
),()(
)(00
4
µµ
σσσ π
PP
k
PP
P
kkk
PkkkkPkkYX
Pp
YX
drredPp
ePpTe kkk
=
ΩΩ
==∫∫
. (3.21)
The eigenvector p(Pk) is determined by the intrinsic structural properties of Pk and takes
on values between 0 and 1. Assuming that the structure of a given biome type has equal
probability of occurrence, the average value of p(Pk) over biome type is 0.5. Let Nk and
Nveg be the number of pixels Pk belonging to biome k and the total number of vegetated
pixels Pk, respectively. Taking into account σk = 0 for non-vegetated pixel, one obtains
7veg pf1pf−
==>Ψ<>Ψ<∑
=
ll
P
Pk
N
N
lk
k
ωω σσ
. (3.22)
Substituting Eq. (3.22) into Eq. (3.20) results in
73
∑=−
=6
17pf
pf11
lllωϖ . (3.23)
Thus, given the percentage function pfl (l = 1, …, 7) of each coarse resolution pixel, one
can redefine the single scattering albedo according to Eq. (3.23). Solution of the transport
Eq. (3.3) with this single scattering albedo provides a correct partition of incoming solar
radiation between canopy reflection, transmission and absorption.
The realization of this radiative transfer based scaling theory is illustrated in Fig. 3.9,
where the relative discrepancy in retrieved LAI (RDL; Eq. (3.2)) is shown as a function
of spatial resolution and pixel heterogeneity for the six biomes. Note that the RDL does
not exceed the uncertainty in the model used simulate radiation regime in vegetation
canopies at the scale R0 = 8. This figure is similar to Fig. 3.6, except that the look-up
tables of the LAI/FPAR estimation algorithm have been tuned based on theoretical
considerations given above. There is a dramatic decrease in RDL in all cases, including
the case of large pixels with significant heterogeneity. Based on the definition of RDL,
which is the difference between Lt and Lc (Eq. (3.2)), tuning of the look-up tables by
adjusting the single scattering albedo as per Eq. (3.23) to minimize RDL, constitutes the
physics based approach to scaling. And this is consistent with the definition of scaling,
given earlier as, the process by which it is established that values of a certain biophysical
product, LAI in this instance, derived from coarse resolution sensor data equal the
arithmetic average of values derived independently from fine resolution sensor data.
3.5 Concluding Remarks
The effect of spatial resolution of reflectance data on retrievals of LAI and FPAR is
addressed in this chapter. Problems related to data resolution arise in the context of
74
assembling time series of biophysical variables with data from sensors of different spatial
resolution, fusion of data of different instruments and in the validation of moderate
resolution sensor products. The goal of scaling is defined as the process by which it is
established that values of a certain biophysical product, LAI in this instance, derived
from coarse resolution sensor data equal the arithmetic average of values derived
independently from fine resolution sensor data. Pixel heterogeneity is defined in terms of
fractional presence of different land covers, for purposes of scaling. The effect of pixel
heterogeneity on spectral reflectances and LAI/FPAR retrievals is investigated with 1 km
AVHRR data aggregated to different coarse scale resolutions. Pixel heterogeneity is
shown to increase as the resolution of the data decreases. LAI retrieval errors at coarse
resolution are inversely related to the proportion of the dominant land cover in such pixel.
Further, large errors in LAI retrievals are shown to occur when forests are minority
biomes in non-forest pixels compared to when forest biomes are mixed with one another,
and vice-versa. A physically based theory for scaling with explicit scale dependent
radiative transfer formulation was developed. The mean length of photon lateral
migration in the medium, which characterizes the magnitude of horizontal transport, is
used to imbue scale dependence to the radiative transfer equation. Scale dependence of
absorption and reflection properties of the scattering centers is accomplished via the use
of a Green’s function formulation. Pixel heterogeneity is accounted by modifications to
the single scattering albedo that the transfer equation admits through the use of land cover
fractions. The successful application of this theory to scaling LAI retrievals from
AVHRR data of different resolutions demonstrates a capability to validate moderate
resolution (~ 1 km) LAI and FPAR products from MODIS and MISR.
75
0 20 40 60 80Spatial Resolution (km)
20
40
60
80
100
Ove
rall
Puri
ty
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal Crops
ShrubsShrubsShrubsShrubsShrubs
Broadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf Crops
SavannasSavannasSavannasSavannasSavannas
Broadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf Forests
Needle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 3.1. The overall purity PF(j) as a function of spatial resolution.
76
(a) Group 1, Biome Purity >= 90%
0 20 40 60 80Spatial Resolution (km)
0
20
40
60
80
Perc
enta
ge o
f Pi
xels
in G
roup
1
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b) Group 3, Biome Purity < 50%
0 20 40 60 80Spatial Resolution (km)
0
20
40
60
80
Perc
enta
ge o
f Pi
xels
in G
roup
3
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 3.2. Percentage of pixels in group 1 and group 3 as a function of spatial resolution: (a) Group 1, biome purity ≥ 90%, (b) Group 3, biome purity < 50%.
77
(a) 1 km Resolution Data
0.00 0.05 0.10 0.15 0.20RED Reflectance
0.10
0.20
0.30
0.40
0.50
NIR
Ref
lect
ance Grassland and Cereal Crops
ShrubslandsBroadleaf CropsSavannasBroadleaf ForestsNeedle Forests
(b) Group 1, 8 km Resolution Data
0.00 0.05 0.10 0.15 0.20RED Reflectance
0.10
0.20
0.30
0.40
0.50
NIR
Ref
lect
ance Grassland and Cereal Crops
ShrubslandsBroadleaf CropsSavannasBroadleaf ForestsNeedle Forests
(c) Group 3, 8 km Resolution Data
0.00 0.05 0.10 0.15 0.20RED Reflectance
0.10
0.20
0.30
0.40
0.50
NIR
Ref
lect
ance Grassland and Cereal Crops
ShrubslandsBroadleaf CropsSavannasBroadleaf ForestsNeedle Forests
Figure 3.3. Contour plot of data density distribution in the spectral space of red and near-infrared (RED-NIR) at (a) 1 km resolution, (b) 8 km resolution from group 1, and (c) 8 km resolution from group 3. Each contour line separates an area in the spectral space with high data density containing 50% of the pixels from a given biome. Groups 1 and 3 represent biome purities ≥ 90% and < 50%, respectively.
78
(a) Group 1, Biome Purity >= 90%
0 20 40 60 80Spatial Resolution (km)
0.00
0.05
0.10
0.15
0.20R
ED
Ref
lect
ance
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b) Group 1, Biome Purity >= 90%
0 20 40 60 80Spatial Resolution (km)
0.00
0.10
0.20
0.30
0.40
NIR
Ref
lect
ance
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(c) Group 3, Biome Purity < 50%
0 20 40 60 80Spatial Resolution (km)
0.00
0.05
0.10
0.15
0.20
RE
D R
efle
ctan
ce
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(d) group 3, Biome Purity < 50%
0 20 40 60 80Spatial Resolution (km)
0.00
0.10
0.20
0.30
0.40
NIR
Ref
lect
ance
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 3.4. Mean red (RED) and near-infrared (NIR) reflectance as a function of spatial resolution: (a) group 1 in RED, (b) group 1 in NIR, (c) group 3 in RED, and (d) group 3 in NIR. Groups 1 and 3 represent biome purities ≥ 90% and < 50%, respectively.
79
(a) Group 1, Biome Purity >= 90%
0 20 40 60 80Spatial Resolution (km)
0.0
0.2
0.4
0.6
0.8
1.0
Dis
tanc
e fr
om P
ure
Veg
etat
ion
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b) Group 3, Biome Purity < 50%
0 20 40 60 80Spatial Resolution (km)
0.0
0.2
0.4
0.6
0.8
1.0
Dis
tanc
e fr
om P
ure
Veg
etat
ion
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 3.5. Average distance in spectral space between biome specific spectral signature ( R , N ) and pixels from (a) group 1, and (b) group 3, at different spatial resolutions. Groups 1 and 3 represent biome purities ≥ 90% and < 50%, respectively. The parameters R and N are mean red (RED) and near-infrared (NIR) reflectance values of homogeneous pixels from group 1. See text for further information.
80
Grasses and Cereal Crops
Spatial Resolution (km)
0.10
0.20
44
44
44
88
88
88
1616
1616
1616
3232
3232
3232
6464
6464
6464
20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%H
eter
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Shrubs
Spatial Resolution (km)
0.10
0.20
44
44
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88
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88
1616
1616
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3232
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6464
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20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%H
eter
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Broadleaf Crops
Spatial Resolution (km)
0.10
44
44
44
88
88
88
1616
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3232
3232
3232
6464
6464
6464
20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
Het
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Savannas
Spatial Resolution (km)
0.10
0.10
44
44
44
88
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88
1616
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1616
3232
3232
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6464
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20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
Het
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Broadleaf Forests
Spatial Resolution (km)
0.10
0.20
0.30
0.40
44
44
44
88
88
88
1616
1616
1616
3232
3232
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6464
6464
646420% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
Het
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Needle Forests
Spatial Resolution (km)
0.20
0.30
0.40
44
44
44
88
88
88
1616
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3232
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6464
6464
646420% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
Het
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Figure 3.6. Contour plot of relative difference in LAI derived from unadjusted LAI retrieval algorithm as a function of spatial resolution and pixel heterogeneity (purity).
81
0 2 4 6 8LAI
0.0
0.2
0.4
0.6
0.8
1.0
ND
VI
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal Crops
ShrubsShrubsShrubsShrubsShrubs
Needle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 3.7. NDVI-LAI relations derived from 4 km resolution pixels with purity ≥ 90%.
82
(a)
0.00 0.10 0.20 0.30 0.40 0.50Percent of Grasses and Cereal Crops
0.0
0.2
0.4
0.6R
elat
ive
Dif
fere
nce
in L
AI
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(b)
0.00 0.10 0.20 0.30 0.40 0.50Percent of Shrubs
0.0
0.2
0.4
0.6
Rel
ativ
e D
iffe
renc
e in
LA
I
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(c)
0.00 0.10 0.20 0.30 0.40 0.50Percent of Broadleaf Crops
0.0
0.2
0.4
0.6
Rel
ativ
e D
iffe
renc
e in
LA
I
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(d)
0.00 0.10 0.20 0.30 0.40 0.50Percent of Savannas
0.0
0.2
0.4
0.6
Rel
ativ
e D
iffe
renc
e in
LA
IGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(e)
0.00 0.10 0.20 0.30 0.40 0.50Percent of Broadleaf Forests
0.0
0.2
0.4
0.6
Rel
ativ
e D
iffe
renc
e in
LA
I
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
(f)
0.00 0.10 0.20 0.30 0.40 0.50Percent of Needle Forests
0.0
0.2
0.4
0.6
Rel
ativ
e D
iffe
renc
e in
LA
I
Grasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsGrasses and Cereal CropsShrubsShrubsShrubsShrubsShrubsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsBroadleaf CropsSavannasSavannasSavannasSavannasSavannasBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsBroadleaf ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle ForestsNeedle Forests
Figure 3.8. Relative difference in LAI retrievals as a function of the presence of the minority biome: (a) Grasses and Cereal Crops, (b) Shrubs, (c) Broadleaf Crops, (d) Savannas, (e) Broadleaf Forests, and (f) Needle Forests, in heterogeneous pixels at 8 km resolution. See text for further information.
83
Grasses and Cereal Crops
Spatial Resolution (km)
0.10
0.2044
44
44
88
88
88
1616
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3232
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6464
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20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%H
eter
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Shrubs
Spatial Resolution (km)
0.10
0.20
44
44
44
88
88
88
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20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%H
eter
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Broadleaf Crops
Spatial Resolution (km)
0.10
44
44
44
88
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88
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20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
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Savannas
Spatial Resolution (km)
0.10
44
44
44
88
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88
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20% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
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Broadleaf Forests
Spatial Resolution (km)
0.10
0.200.20
44
44
44
88
88
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1616
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3232
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646420% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
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Needle Forests
Spatial Resolution (km)
0.20
0.20
0.30
44
44
44
88
88
88
1616
1616
1616
3232
3232
3232
6464
6464
646420% 20%20% 20%20% 20%
30% 30%30% 30%30% 30%
40% 40%40% 40%40% 40%
50% 50%50% 50%50% 50%
60% 60%60% 60%60% 60%
70% 70%70% 70%70% 70%
80% 80%80% 80%80% 80%
90% 90%90% 90%90% 90%
100% 100%100% 100%100% 100%
Het
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Figure 3.9. Contour plot of relative difference in LAI derived from adjusted LAI retrieval algorithm as a function of spatial resolution and pixel heterogeneity (purity).
84
Table 3.1. Overall Percentage Function PF(j) at 8 km Resolution
Sub-pixel landcover type Dominant land cover
type Biome 1 Biome 2 Biome 3 Biome 4 Biome 5 Biome 6 Bare-land
Biome 1 63.32 4.63 5.80 7.12 3.56 11.04 4.54
Biome 2 3.77 85.20 0.50 2.45 1.00 2.59 4.50
Biome 3 12.28 1.92 61.30 9.24 6.09 6.51 2.65
Biome 4 10.62 5.66 5.99 62.34 4.89 6.86 3.64
Biome 5 8.50 2.16 3.97 4.44 72.37 7.33 1.22
Biome 6 9.02 2.96 3.84 3.80 3.52 74.93 1.93
85
Chapter 4
Multiscale Analysis and Validation of the MODIS
LAI Product over Maun, Botswana
4.1 Introduction
Leaf area index (LAI), the projected green leaf area per unit ground surface, is a key
biophysical variable influencing vegetation photosynthesis, transpiration, and the energy
balance of the land surface (Running, 1990; Bonan, 1995). LAI is not only an important
driver of most ecosystem productivity models operating at landscape to global scales
(Running et al., 1989; Turner et al., 2000), but also an interaction component of some
general circulation models (Chase et al., 1996). LAI, together with other biophysical
variables, plays an important role in measurement and monitoring of land surface
characteristics and in the development of earth-system models that potentially can predict
large scale changes accurately enough to assist policy makers in making decisions
concerning the management of our environment (Cohen and Justice, 2000). In view of
this need, LAI is a standard product to be delivered from data acquired by the MODIS
aboard the EOS Terra platform. As MODIS LAI data products begin to be available to
the public through the EROS Data Center Data Active Archive Center (EDC DAAC), a
sustained validation program is needed to provide timely feedback to algorithm
86
developers so that through iterative improvements, superior products will result (Privette
et al., 2000).
"Validation" is the process of assessing by independent means the accuracy of data
products (Justice et al., 2000; Privette et al., 2000). In general, validation refers to
assessing the uncertainty of satellite derived products by analytical comparison to
reference data (e.g., in situ, aircraft, and high-resolution satellite sensor data), which are
presumed to represent the target values (Justice, et al., 2000).
Validation of satellite products comes at a time when international agencies and the
global change research community are evaluating their needs for long-term space-borne
measurements (Justice et al., 2000). In the coming years, several moderate and coarse
spatial resolution satellite sensors such as AVHRR, GLI, MERIS, MISR, MODIS,
POLDER, VEGETATION, etc. will concurrently fly providing valuable multiple views
daily of the Earth surface. These sensors will provide similar land products, such as
vegetation indices, LAI, FPAR, albedo, and land cover. Establishing standard methods
and protocols for validation of these products will enable broad participation in validation
campaigns. As a result, high-quality and consistent data sets of known accuracy with
product continuity between instruments and missions will foster product standardization
and synergy from these sensors (Justice et al., 2000).
However, uncertainty assessment for these coarse spatial resolution products is not
straightforward and presents a challenge to the remote sensing community because
ground-based measurements cannot be easily compared to coarse resolution satellite
sensor data. Development of appropriate ground-based validation techniques is critical to
assessing the uncertainties associated with such data products. The main challenge in
land satellite data validation is to attain adequate ground sampling of observed
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biophysical variables, which exhibit spatial and temporal variance, at the spatial scale of
a satellite sensor (Lucht et al., 2000).
NASA developed certain validation protocols and organized several pre- and post-
launch validation campaigns. The “BigFoot” program is one such protocol designed for
the validation of MODIS LAI/FPAR and NPP products, providing guidance for field data
collection, sampling strategy, and scaling algorithms to compare to the ground, airborne
and satellite sensor data (Cohen and Justice, 2000). The Prototype Validation Exercises
(PROVE) were designed and carried out as a prototype of EOS episodic validation
campaigns (Privette et al., 2000). The Southern Africa Regional Science Initiative 2000
(SAFARI 2000) took place during 1999 and 2000 in Southern African as an extensive
validation component associated with EOS Terra and Landsat 7. Internationally, the
VALidation of European Remote sensing Instruments (VALERI) project is designed to
provide coordinated ground measurements of LAI, FPAR, albedo and similar variables
for developing and testing new generation algorithms and validating biophysical variable
products. Rather than being aimed at a specific sensor program, this project allows the
inter-comparison between sensors and algorithms (Weiss et al. 2001).
There is a large body of research that needs to be undertaken before land product
validation can become operational (Justice et al., 2000). For LAI/FPAR product
validation activities, challenges include designing statistically valid and logistically
feasible field sampling, assessing the accuracy of reference data, and correlating coarse
and fine resolution satellite sensor data.
Large-scale validation should rely on methods that avoid time-consuming procedures
while preserving accuracy. The primary objectives of this chapter are to provide guidance
for field data collection and sampling strategies, and assess the uncertainty of the MODIS
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LAI product via comparisons with ground and high-resolution satellite data. Specifically,
A region by region comparison method that is more realistically implemented on a
routine basis is proposed, and the issue of spatially scaling ground-based point
measurements to the spatial scale of satellite observations is addressed. In lieu of using
MODIS data, 30 m ETM+ LAI retrievals are compared to those derived from the 250 m,
500 m and 1 km resolutions of simulated MODIS data (MODIS data were largely
unavailable during the period of campaigns for various reasons). Validation of SAFARI
2000 wet season data is the main task in this chapter. Data from campaigns at the
Harvard Forest (USA) and Ruokulahti Forest (Finland) were also used to analyze
multiscale variations in the LAI data.
4.2 SAFARI 2000 Wet Season KALAHARI Transect
Campaign
SAFARI 2000 is an organizational umbrella for various studies, which together should
improve understanding of the sources, transformations, dynamics, sinks and impacts of
atmospheric aerosols in Southern Africa (Swap and Annegarn, 1999). A major
component of SAFARI 2000 is remote sensing research and validation with NASA EOS
data products (Privette et al., 2001). An international group of researchers completed an
intensive field campaign in Botswana and Zambia between February 28 and March 18,
2000. These dates coincided with the first weeks of MODIS Earth views because of the
launch delay. The activity was the second of four planned intensive campaigns of
SAFARI 2000. The field sites are located along the International Geosphere-Biosphere
Program (IGBP) Kalahari Transect (KT). The KT extends over a large rainfall gradient
(200 to 1000 mm/year mean annual rainfall) in an area of uniform soils, the Kalahari
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sands, albeit with some local variation associated with pans and subsurface duricrusts.
The vegetation extends from equatorial forest to subtropical, arid shrubland of the
Kakahari desert (Dowty et al., 2000).
Field data were collected to validate the MODIS LAI algorithm. Ground
measurements of LAI, leaf hemispherical reflectance and transmittance, and canopy
transmittance were taken using the LAI-2000 plant canopy analyzer, AccuPAR
ceptometer, LI-1800 portable spectroradiometer and ASD handheld spectroradiometer
during the period from March 3 to March 18, 2000, in Botswana. LAI was intensively
measured at four different sites, Pandamatenga, Maun, Okwa and Tshane (from north to
south in Botswana), where the vegetation ranged from moist closed woodland to arid
grasslands with scattered shrubs.
4.2.1 Sampling Methods
At each of the four sites, data were collected within a 1 km by 1 km region on three
transects of 750 m and on a 250 m by 300 m grid (Fig. 4.1). For the transects,
measurements were made along three straight, parallel lines, “B”, “A”, and “N” from
south to north, each of 750 m in length. LAI measurements were taken at 25 m intervals
from west to east, for a total of 31 sample points on each 750 m transect. Each sample
point was labeled as A375W, A00, A375E … and so on. “A00” represents the middle
sample point on the line “A”, and “A375W” represents the sample point located 375 m
west of A00. On the grid, measurements were taken at a 50 m by 50 m resolution in a
rectangular area, located at the southwest corner of the 1 km2 site. There were 6 east-west
oriented lines (300 m in length) and 7 south-north oriented lines (250 m in length) for a
total of 42 sample points.
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Another 34 measurements were taken around the scaffolding tower (19.91641°S,
23.5594°E), set up by the Max Plank Institute. This tower was located at 1 km northwest
of the Maun site. The sampling method was similar to the grid measurement. The
vegetation type is savanna. This site was labeled as T (tower). The mean and standard
deviation of measured LAI is 1.04, and 0.59, respectively.
4.2.2 LAI Measurements
LAI was measured using the LAI-2000 plant canopy analyzer, which consists of a LAI-
2070 control unit and a LAI-2050 sensor head. The control unit has connectors for two
sensor heads, two connectors for other LI-COR sensors, and a connector for RS-232
communication. The sensor head projects the image of its nearly hemispheric view onto
five detectors arranged in concentric rings (approximately 0-13, 16-28, 32-43, 47-58, 61-
74 degrees). Radiation above 490 nm is not measured (LI-COR, 1991).
Three LAI-2000 units were used in this campaign, two in the field, and the other in
an open space as a reference for incident radiation. The two sample units were calibrated
against the reference unit under overcast conditions or shortly before sunset, prior to field
measurements. The calibration procedures are given in the LAI-2000 Plant Canopy
Analyzer Instruction Manual, Chapter 4-1 (LI-COR, 1991). The reference unit was set in
remote logging mode at a sampling frequency of one sample per 60 seconds.
The LAI-2000 measures attenuation of diffuse sky radiation at five zenith angles
simultaneously. LAI measurements were done mostly shortly before and after sunset.
Some measurements in Pandamatenga and Maun were taken during dawn. In Tshane, one
set of measurements was taken in the afternoon under overcast conditions.
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All the measurements were taken by holding the sensors (three) opposite to the
direction of sunlight. A 90-degree mask was used in Pandamatenga and Maun to prevent
interference caused by the operator’s presence. A 270-degree mask was used in Okwa
and Tshane because of the heterogeneous distribution of shrubs and trees on the
grassland. The same mask was used for the reference sensor as well.
From beneath a canopy, the sensor’s potential field of view resembles an inverted
cone whose radius (r) is roughly 3 times the canopy height. The sensor’s view limit is
74°, and the tangent of which is 3.48. However, 3 serves as a working number, because
of the reduced probability that foliage at the edge of the sensor’s field of view will be
significant (LI-COR, 1991). Therefore, the measured resolution (area) of each site is
Area = 22 )h3(r ππ = , (4.1)
where h is the tree/plant height. The woody plant height on the Kalahari Transect was
measured by Scholes et al. (2001) during this campaign. The averaged plant height at the
four sites (Scholes et al., 2001) is in listed Table 4.1. A 90-degree mask was used in
Pandamatenga and Maun and a 270-degree mask was used in Okwa and Tshane as
mentioned before. The actual measured area was: three fourths of the total area in Panda
and Maun, and one fourth in Okwa and Tshane. The percentage overlap between two
adjacent measurements is also listed in Table 4.1.
4.3 Heterogeneity of Measured LAI at the SAFARI 2000 Sites
4.3.1 Statistical Analysis of Means
Histograms of measured LAI along the transects and the grid are shown in Fig. 4.2. The
mean and standard deviation are given in Fig. 4.3. One immediate question concerns the
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similarity of the grid and transect measurements. Are they sampling the same population?
A t statistic was used to test the null hypothesis that the mean values of two groups are
equal. The t-test results (Table 4.2) indicate that the means of the transect and grid
measurements are statistically different in Maun and Okwa at p<0.05 and Pandamatenga
at p<0.10. Tshane, on the other hand, shows a very high probability of equal means.
These results indicate that LAI in three of the four sites is not spatially uniform.
4.3.2 Semivariance Analysis
The spatial heterogeneity of measured LAI can also be quantitatively described by
estimating the spatial dependence of LAI within each site. A useful measure of spatial
variation in the values of a variable Z is the semivariance, which is half the average
squared difference in Z values between pairs of the sample points. For a stationary and
isotropic spatial process, the semivariance γ in Z values between all the pairs of points
Z(x) and Z(x+h) separated by distance h (referred to as “lag”) can be estimated from the
sample data,
∑ −+=)(
2)]()([)(2
1)(
hN
xZhxZhN
hγ , (4.2)
where N is the number of pairs of sample points (x, x+h) separated by distance h.
The key to investigation of the semivariance is the construction of a variogram,
which is a plot of semivariance, )(hγ , as a function of distance, h. There are several
important features worth noting in the sample variogram. At relatively short distance h,
the semivariance is small, but increases with distance between pairs of sample points. At
a distance referred to as “range”, the semivariance levels off to a relatively constant value
referred to as the “sill”. This implies that beyond this range, Z values are no longer
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spatially correlated. Within this range, Z values are more similar when the pairs of sample
points are closer together. The variograms of LAI (Fig. 4.4) at the four sites show a
similar structure, with a small range, less than 50 m. This means that the LAI values
between the sample points are not spatially related, indicating a high level of
heterogeneity in the spatial distribution of LAI. This can be proved by the transect LAI
measurements (Fig. 4.5) which are instructive. I conclude that there are large variance
within these sites and little spatial structure.
4.4 Validation of MODIS LAI at MAUN
The objective here is to validate the 1 km2 LAI values derived from MODIS data through
comparing with field measurements. The first challenge is how to validate coarse
resolution MODIS LAI with fine resolution measurements from the 1 km2 sites, each
with an area equivalent to only one MODIS pixel. In total, there are only four pairs of
pixels at 1 km2 resolution between field measurements and MODIS data. In addition, if
the spatial registration is not accurate, some of the field measurements may fall out of the
1 km2 MODIS pixel, and this makes the comparison more difficult and unreliable.
Therefore, I propose first to validate and produce a LAI map of a 10 by 10 km region
from ETM+ data based on the field measurements. Using this ETM+ LAI map, I validate
the MODIS LAI product. In view of the large amount of work associated with field and
satellite data processing, classification, atmospheric correction, geo-registration, etc., data
from the Maun site is used only to illustrate the strategy for validation of the MODIS LAI
product.
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4.4.1 Selection of a 10 km by 10 km ETM+ Region
A subset of a Landsat ETM+ scene from April 3, 2000 (Fig. 6(a)) and a subset of
IKONOS scene from March 30, 2000 were selected, with the point A00 of the Maun site
as the central point. The ETM+ (IKONOS) subset has a resolution of 30 m (4 m) and
covers a 10 km by 10 km (about 11 km by 11 km) region. Both images were in the
Universal Transverse Mercator (UTM) projection and were corrected for atmospheric
effects (Rahman and Didieu, 1994; Hame et al., 2001). The IKONOS image was mainly
used to help identify features and regions. In addition, I have 33 photographs with Global
Positioning System (GPS) navigation readings in this site. They were also used to help
identify features. The ETM+ subset was classified into two vegetation classes, shrubs and
savannas (Fig. 4.6(b)), using an unsupervised classification approach, with the aid of field
photographs and an IKONOS image. Savannas and shrubs occupy 65% and 35% of the
total area, respectively.
4.4.2 Validation of 1 km by 1 km ETM+ LAI
Let focus on a 1 km by 1 km area in the ETM+ subset, with the point A00 as the central
point. This region corresponds to where the field measurements were taken in Maun. The
MODIS LAI algorithm was executed using ETM+ surface reflectances to produce ETM+
LAI fields, and the retrieved fields were compared with in situ measurements at 30 m
resolution.
4.4.2.1 Image Segmentation
The problem is how to compare the field and ETM+ LAI data? A pixel by pixel
comparison is not feasible for several reasons. First, the MODIS algorithm was designed
to estimate the LAI value in a region (or stand) on the basis of attributes of the pixels in
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the region (or stand). Theoretically it is possible that not a single pixel of MODIS LAI
estimated accurately, but that at the level of multiple retrievals within a site, the algorithm
accurately represents the mean value. The goal of validation is to provide product
uncertainty at patch level instead of pixel level. To validate the algorithm, it is essential
to identify multi-pixel patches in the image data. Second, the GPS readings are not
accurate. The measurements and photographs did not give the same GPS readings (only
four months after the campaign, accurate GPS estimates were possible). Third, the area
measured with LAI-2000 is smaller than the resolution of the ETM+. Fourth, because of
the high variance of LAI value over short distances, there are some errors associated with
field measurements and mismatch of pixels between the measurements and the image.
In the analysis of remotely sensed imagery, pixels are assumed to be representative
samples of objects in the scene. When pixels are large relative to ground objects,
individual pixels often cover parts of two or more objects, resulting in mixed pixels, and
the effectiveness of analysis is undermined (MacDonald and Hall, 1980). Similarly, when
pixels are small relative to the objects, internal variance of the objects adversely affects
the analysis (Markham and Townshend, 1981). The ideal situation is when the elements
of analysis in the image correspond to the objects in the scene (Woodcock and Harward,
1992). The objective of image segmentation is to partition the image into a set of regions,
which correspond to objects in the ground scene and will serve as the basis of further
analysis (Beaulieu and Goldberg, 1989). Therefore, the spectral attributes of regions
defined via segmentation may more accurately be grouped into categories than the pixels
comprising the region when taken singly (Woodcock and Harward, 1992).
A segmentation procedure was used to generate patches of vegetation to serve as the
basis of validation of the MODIS LAI algorithm as opposed to the more conventional
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per-pixel kinds of analyses. Fig. 4.7(a) displays the IKONOS image, combined with
Bands 4, 3, and 2. Fig. 4.7(b) shows the same area but with the coarser resolution ETM+
image, of which individual pixels are visible. The sampling points of measurements
(yellow "+") and the positions where pictures (green "+") were taken are also shown in
Fig. 4.7. It is apparent that the landscape is heterogeneous and patchy, and the LAI
measurements were made on different patches. A segmentation algorithm was used to
group pixels into patches based primarily on their spectral similarity and adjacency, with
Bands 3, 4 and 5 of the ETM+ image as inputs. The resulting map (Fig. 4.8) yields
patches corresponding to identifiable features in the landscape. There are 15 patches in
total. Most of the measurements fall in patches 3, 5, 6, 7, 8, 9 10, and 12. According to
the land cover map (Fig. 4.6), patches 3, 5, 6 and 10 are mostly shrubs, and patches 7, 8,
9, 12 are mostly savannas. The LAI measurements were grouped by patch, excluding
points located at patch boundaries whose patch membership was ambiguous. Patches 7
and 8 were merged into one patch, because most of the measurements on the line “A” are
located at the edge of patches 7 and 8, both of which savannas. There is one more
savanna patch “T”, as mentioned before. Therefore, there are 8 groups (patches) of LAI
measurements in total, with four of savannas and four of shrubs. The mean LAI for each
group was calculated, and the t statistic was used to test whether the means of any two
patches are equal. Results (Table 4.3) show that groups from the same land cover class
generally have a higher probability of equal mean LAI value than those of different
classes, which are always significantly different, except for group 6 and group 12. Image
segmentation thus helps in regrouping the measurements.
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4.4.2.2 Validation of the MODIS LAI Algorithm at 30 m Resolution
To validate the MODIS LAI algorithm at 30 m resolution, the algorithm was executed
(Knyazikhin et al., 1998a, b) for each pixel in the ETM+ image with Band 4 (NIR) and
Band 3 (RED) reflectance data and the patch map defining biome type as input. Pixels
from patches 3, 5, 6,10 were retrieved with the shrub look-up table (LUT), and pixels
from patches 7, 8, 9, 12 with the savanna LUT. The mean values of the retrieved and
measured LAI of each patch are shown in Fig. 4.9(a). Most of these are along the 1:1
diagonal line. The savannas have LAI values lower than the shrubs. The consistency
between LAI retrievals and field measurements indicates good performance of the
algorithm.
To investigate the effect of misclassification on LAI retrievals, the LAI of all pixels
were also estimated using the savanna LUT only and the shrub LUT only. Fig. 4.9(b) is
the scatter plot of these retrievals. For a pixel with the same surface reflectance, the
savanna LUT generally gives a higher LAI value than the shrub LUT. The difference is
small for pixels with LAI values less than 2, but larger for higher values. In this case,
most pixels have LAI values less than 2, with a mean of 1.32 for shrub LUT retrievals
and 1.45 for savanna LUT retrievals. Consequently, the effect of misclassification on LAI
retrievals is not large. For an individual patch, however, the misclassification effect can
be large. Fig. 4.9(c) shows the comparison of patch mean LAI of the measurements and
retrievals using the different LUTs. If the shrub pixels are retrieved using the savanna
LUT, the patch mean LAI will be higher than the measurements. The difference can be as
high as 0.5 LAI for patches 5 and 10. Therefore, it is essential to identify the cover type
accurately for validation and operational mapping of LAI.
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4.4.3 Resolution Effects on MODIS LAI Retrievals
A common approach to study of the effects of resolution between fine and coarse
resolution results is to compare data from sensors with varying resolutions or to
aggregate fine resolution data to larger cell sizes (Pax-Lenney et al., 1997; Chen, 1996;
Tian et al, 2001). The SAFARI 2000 wet season campaign was conducted two months
after Terra was launched. Unfortunately, this campaign period was during the first weeks
of MODIS operation, and there are no MODIS surface reflectance data and MODIS LAI
product over that period. Therefore, coarse resolution data were created from the 30 m
resolution ETM+ data. The ETM+ data from Bands 3 and 4 in the 10 km by 10 km study
area were spatially degraded to generate data of resolution 240 m, 480 m, and 960 m. The
program used to degrade the ETM+ image was developed as part of an effort to simulate
the spatial resolution of MODIS-N sensor from ETM+ imagery using a convolution
algorithm developed by Barker et al. (1992). The ETM+ data are forward Fourier
transformed, multiplied by the transfer function of a Gaussian blur filter and then inverse
Fourier transformed. The resulting output array is reduced to the appropriate size through
nearest neighbor re-sampling. The aggregated 240 m, 480 m, and 960 m resolutions
correspond closely to the proposed MODIS resolutions of 250 m, 500 m, and 1000 m.
The spatially degraded data for each band however retain the ETM+ spectral bandwidths.
4.4.3.1 Relation Between Changes in Reflectance and Spatial Resolution
To investigate the effect of changes in resolution on MODIS LAI retrievals, an
understanding of the relation between changes in reflectance and spatial resolution is
needed. Figure 4.10 shows variations in the mean and standard deviation (SDT) of RED
and NIR reflectances, and NDVI as a function of spatial resolution. NDVI is calculated
directly from coarse resolution reflectance data.
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Without consideration of the land cover type, the overall mean values (RED, NIR,
NDVI) of the image show little or no change with resolution. However, the mean values
for different classes change quickly. For a class with a higher (lower) mean value, its
mean value decreases (increases) as resolution decreases, with the overall mean value
remaining invariant. That is, the difference in the mean values between savannas and
shrubs becomes smaller. The decrease in the STD with coarser resolution is obvious. I
conclude that spatial aggregation results in a decrease in the variance of the data and a
smaller discrepancy in mean reflectance between different classes. This is because the
number of mixed pixels in the image and the degree of spatial mixture within pixels
increases as the spatial resolution becomes coarser. As a result, there will be some loss of
spectral separability between the land cover classes defined at finer spatial scale.
4.4.3.2 Non-linearity in LAI Retrievals from One Land Cover Type
The goal of scaling is defined as the process, by which it is established that values of a
LAI product derived from coarse resolution sensor data equal the arithmetic average of
values derived independently from fine resolution sensor data (Tian et al., 2001).
Therefore, coarse resolution LAI can be derived by two different methods. First, LAI
values are generated from ETM+ reflectance data using the MODIS algorithm at 30 m
resolution, and then averaged over space to estimate LAI at coarse resolutions (method
1). This is the correct way. Second, LAI values are generated directly from the simulated
coarse resolution reflectance data using the same MODIS algorithm (method 2). The
following equation measures the difference in LAI (DL) retrievals between method 1 and
method 2 for each of the coarse resolution pixels
100)LAI/)LAILAI(( 121 ⋅−= methodmethodmethodDL . (4.3)
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If DL is positive, method 2 underestimates the LAI value; otherwise, method 2
overestimates the LAI value. Theoretically, any algorithm will not over- or underestimate
the LAI value if the input data are homogeneous, or if the algorithm is a linear model
with respect to surface reflectance data. Otherwise, a non-linear algorithm will
systematically over- or underestimate LAI values from coarse resolution data.
For simplicity, assume that there is only one land cover type in the 10 km by 10 km
image, either savannas or shrubs. This assumption eliminates the effect of mixture of land
cover types. The overall mean reflectance and NDVI do not change appreciably as the
resolution decreases, as illustrated in Fig. 4.10. Does the overall mean LAI not change
either? Figure 4.11 and Table 4.4 compare the LAI retrievals from method 1 and method
2. The mean DL values are always positive, that is, the LAI values are underestimated
when retrieved with coarse resolution data. The algorithm underestimates more in the
case of savannas than in shrubs given the same reflectance values. The underestimation is
larger as spatial resolution decreases.
One interesting result is that there are some pixels where method 2 overestimates
LAI values. This could be possibly noise. Let the overall standard deviation of each
coarse resolution pixel’s reflectance be (Wang et al., 2001),
NIRREDNIRRED
⋅⋅= σσσ . (4.4)
Here, RED ( NIR ) and REDσ ( NIRσ ) are the mean and standard deviation of sub-pixel
level reflectance of band 3 (band 4) of coarse resolution pixels, respectively. Pixels that
contain homogeneous sub-pixels of reflectance will have a small σ , and vise versa.
Figure 4.12 shows σ as a function of DL. The σ value increases as DL increases.
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Negative DL values always correspond to the smallest σ value. Therefore, the
overestimated values are mainly from pixels with the most homogeneous sub-pixel
reflectance. It is possible that the overestimated value is either due to limitations of the
algorithm or due to measurement errors. For savannas, the mean overestimated DL value
is -5.03, -6.61 and -2.52, at 250 m, 500 m and 1000 m, respectively. These values are
much smaller than the mean underestimated DL values (14.34, 14.14, and 14.28,
respectively). Therefore, the overestimated value may be considered as noise.
The MODIS LAI algorithm being non-linear will always underestimate the retrieved
LAI from coarse resolution reflectance data, even though the overall mean reflectance
and NDVI of the image do not change with resolutions. The more heterogeneous the
reflectances at fine resolution, the larger the underestimated LAI value will be. As spatial
resolution decreases, the underestimation becomes larger. The magnitude of
underestimation is dependent on the vegetation type. At 1 km resolution, the algorithm
underestimated the LAI values by about 8% and 12% for shrubs and savannas at the
Maun site, respectively, if the resolution of the data is not considered in the retrieval
technique. Therefore, it is necessary to scale the algorithm to resolutions of satellite data
(Tian et al., 2000; 2001). It should be noted that the MODIS LAI/FPAR operational
algorithm is scale-dependent and has been adjusted for 1 km resolution of the data.
4.4.3.3 Non-linearity and Pixel Mixture in LAI Retrievals from Two Land Cover
Types
When resolution decreases from 30 m to 1000 m, coarse resolution pixels may contain
fractions of different land cover types. The coarse resolution LAI values will be
influenced by both the non-linearity of the algorithm and pixel mixture. In this study, LAI
values over the 10 by 10 km area were estimated from the coarse resolution reflectance
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by considering the real land cover type. Table 4.5 lists the mean DL values for savannas
and shrubs, and the overall estimation (shrubs + savannas). Figure 4.13 shows a pixel by
pixel comparison between LAI from method 1 and method 2. Shrubs have higher DL
values compared with Table 4.4, which means that the underestimation becomes larger
when both the non-linearity and pixel mixture influence the retrievals. Savannas, on the
other hand, show much smaller DL values. This should be interpreted cautiously - LAI
from shrubs will always be underestimated, but LAI from savannas could be over- or
underestimated depending on the value of the sub-pixel reflectance at the fine resolution
(see Appendix). Results from this analysis indicate that the MODIS algorithm will
underestimate LAI values by about 5%.
4.5 Hierarchical Analysis of Multiscale Variation in LAI and
NDVI Data
A key to scaling process in remote sensing is understanding the magnitude of the effects
resulting from processes acting at different scales in the landscape (Woodcock et al.,
1997). Nested-hierarchical models can determine variance in an image at different levels.
In a hierarchical model of landscapes, each level in the hierarchy corresponds to a
different scale. In a forested landscape, for example, the most fundamental element might
be individual trees. The next level might be patches or stands of trees. All patches of the
same kind would combine to form forest classes, which would be a third level in the
hierarchy. These different forest types might then combine to form a general class of
forest, which exists with other classes at this level, such as grassland, water, savannas.
Therefore, each successive level in the hierarchy is more general and is formed by
combining elements from the level below (Woodcock et al, 1997).
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4.5.1 Hierarchical Decomposition of Scene Variograms
A nested-hierarchical model of spatial data is provided by Moellering & Tobler (1972)
and is elaborated by Woodcock et al., (1997) and Collins and Woodcock (2000). Under
this theory, the hierarchical model describes the image as being composed of a number of
land cover classes, Di, which are defined as disjoint subsets of the entire image D. Each
class Di is in turn composed of a number of regions (Dij). Note that “region” as defined
here has the same meaning as “patch,” mentioned in the previous sections. Regions are
composed of pixels, denoted Dijk (Woodcock et al., 1997, Collins and Woodcock, 2000).
The mean of the entire image is µ(D), the mean of a class at the first level of the
hierarchy is µ(Di), and so on. Under this assumption, the observed pixel values may be
defined as
ijkijk Dx = . (4.5)
A new set of images that are derivatives of the original image can be created and these
images contain only the effects associated with an individual scale. Values from these
new images at each pixel can be calculated for the entire image (I), and for scales of
classes (C), regions (R), and pixels (P), respectively, as
)D(I µ= , (4.6)
)D()D(C ii µ−µ= , (4.7)
)D()D(R iijij µ−µ= , (4.8)
)D(xP ijijkijk µ−= . (4.9)
Here I is the image effect, iC is the effect associated with class i, ijR is the effect
associated with region j of class i, and ijkP is the residual or pixel effect associated with
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pixel k of region j of class i. Adding the above four equations indicates that an observed
pixel value is equal to the sum of the effects of all levels of the hierarchy:
ijkijiijk PRCIx +++= . (4.10)
According to Woodcock et al. (1997), this ordering of levels by area size can be
taken as a surrogate for scale or resolution. Data at different levels of the hierarchy thus
correspond to different geographical scales. Squaring both sides of Eq. (4.10) and taking
the mathematical expectation leads to the basic result of the hierarchical Analysis of
Variance (ANOVA) model,
2222PRC σσσσ ++= . (4.11)
Here, 2σ is the overall data variance, and 2iσ (I = C, R, P) is the variance of the effect of
level class, region, and pixel, respectively. The total variance of the data is the sum of the
variances of the individual effects. Equation (4.11) indicates how the total variance is
partitioned into components corresponding to each of these scales. To apply this model,
data must first be divided hierarchically.
Equation (4.2) can be used to calculate the semivariance for any image, including the
original image, I, and the new images related to effects associated with classes C, regions
R and pixels P to create separate variograms for each I , C , R , and P . According to
Collins and Woodcock (2000), the semivariance for these scenes can be decomposed as
)(2)(2)(2)()()() hhhhhhh RPCPCRPRC +++++= , (4.12)
where the subscripts are the same as Eq. (4.11). Symbols with single subscripts are
variograms, and symbols with two subscripts are cross-variograms. The cross-variograms
between hierarchical effects are usually small (Collins and Woodcock, 2000) and are
105
ignored here. As is well known, validation efforts can be undertaken at a broad range of
observation scales. Efforts will likely be successful when the observation scales are
chosen to capture the variation at the characteristic scale of interest.
4.5.2 Satellite and Field Data
In this study, the 30 m LAI fields retrieved from ETM+ data are used. The corresponding
ETM+ data are related to three field sites as described below. The three sites are savannas
in Maun, Botswana; broadleaf forests in the Harvard Forest, USA; and needle forests in
the Ruokolahti Forest, Finland. The Harvard Forest research site is located at 42.5382°N,
72.1714°W. It includes mixed hardwood and conifer forests, ponds, extensive spruce and
maple swamps, with pine and hemlock, and conifer plantations. The Ruokolahti Forest
site is a typical northern needle leaf forest (61.5263°N, 28.7103°E), mixed with large and
small body of lakes.
Following the procedures described previously that utilized 10 km by 10 km ETM+
data to validate the MODIS LAI algorithm in Maun, a 15 km by 13 km (10 km by 10 km)
ETM+ image, acquired on August 31, 1999 (June 10, 2000), was used to validate the
algorithm at 30 m resolution in the Harvard (Ruokolahti) Forest site (Fig. 4.14(a) and Fig.
4.15(a)). First, the raw data of Band 3 (red) and Band 4 (NIR) from both sites were
atmospherically corrected using the Dark Object Subtraction (DOS) approach (Chavez
and Jr., 1989; 1996), and then converted to surface reflectances. Second, the ETM+
images were classified to produce a classification map. Using an IKONOS image and 1
m resolution black and white digital orthophotos from the Massachusetts Geographic
Information System (Massgis, http://www.state.ma.us/mgis/masgis.htm), the 15 km by
13 km Harvard Forest image was classified into broadleaf forest, needle forest, grass,
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shrub, bare land, and water using a supervised classification procedure (Fig. 4.14(b)).
With help of an IKONOS image and a CCD image from an aircraft, the 10 km by 10 km
Ruokolahti Forest image was classified into young, regular and dense needle forest, grass
and water (Fig. 4.15(b)). The three different needle forests were then merged into one
biome type, needle forests. Third, an automated image segmentation procedure
(Woodcock and Harward, 1992) was used to produce a region map of each image. For
the Harvard Forest site, the minimum region size of 8 ETM+ pixels was used to define
regions. Following the definition of regions in the region map, the classification map was
overlaid on the region map and each region was assigned a class label. For the Ruokolahti
Forest site, the regions mainly represented the three different forest classes. Finally, the
algorithm was executed to produce LAI over the whole ETM+ images at 30 m resolution
(Fig. 16).
4.5.3 Variograms of Hierarchical Effects
To generate a set of data layers corresponding to the three hierarchical levels for each site
using Eqs. (4.6)-(4.9), the LAI data retrieved from ETM+ reflectances at 30 m resolution
were decomposed into a nested hierarchy of classes, regions and pixels. The
semivariances were calculated according to Eq. (4.2) for each of the decomposed
components. NDVI was also included in this analysis in view of its widespread use in
vegetation remote sensing.
4.5.3.1 Maun
Following the Eq. (4.11), Table 4.6 lists the distribution of global variance at the class,
region and pixel level for the site at Maun. Most of the NDVI variance occurs at the class
(47%) and pixel scales (35%). For the LAI data, the majority of variation is at the pixel
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(55%), and class scales (32%). Therefore, most of the observed spatial variation of LAI at
the Maun site is due to the effect of classes and pixels rather than regions, implying for
example, that shrubs and savannas behave differently from each other (class effect) and
there is lots of internal variability within those two classes, but that variability exists at
the pixel rather than the patch scale.
While Hierarchical ANOVA quantifies the scale decomposition of variance,
examining the variograms can aid understanding of the spatial structure. Figures 4.17(a)
and (b) show the variograms of the NDVI and LAI data. Sill heights are close
approximations of data variance, so these figures provide a graphic illustration of the
information contained in Table 4.6. The semivariance of the original image, Iγ (h),
exhibits the highest sill, and therefore contains the effects of all scales. It initially
increases quickly as a function of lag and later gradually throughout the remainder of the
graph.
The variograms of the class, region and pixel scales are different. For both the NDVI
and LAI data, the pixel effect reaches a sill within 300 m (range), and remains flat at
larger lags. The class effect reaches the sill at about 500 m, and still increases slowly,
which indicates that there are objects larger in size than the 3000 m range. This
interpretation is supported by Fig. 4.5, which shows that savannas exceed this size in the
upper left corner. The range is related to the size of objects in the image. Therefore, these
plots give an indication of the spatial structure of the effects, in addition to partitioning of
the variance.
There is a stronger pixel effect on the LAI than NDVI, which indicates that there is
less difference between vegetation classes in the mean value of LAI than NDVI. The
large variance and small range (200 m) at the pixel scale are consistent with field
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measurements that indicate that most LAI changes in Maun occur at distances smaller
than vegetation stands. This result is also consistent with results from the previous
section. The reason for the differing effect of classes on NDVI and LAI is for the same
input reflectance, that is, the same NDVI, savannas result in a higher LAI value than
shrubs. Generally, shrubs have higher NDVI values than savannas in the ETM+ images.
Thus, smaller differences in mean LAI values of savannas and shrubs result from the
MODIS LAI algorithm.
These results indicate that the dominant factor influencing the spatial distribution of
LAI across the landscape in Maun is variability within land cover types as opposed to
differences between land cover types. The strong spatial heterogeneity observed in the
field LAI measurements indicate that for validation at the pixel level, individual field
measurements must have GPS readings accurate to within meters, and the accuracy of
geo-registration of ETM+ images should be within half a pixel.
The variance of LAI retrieved from ETM+ data is much smaller than the field
measurements (Fig. 4.4 and Fig. 4.17), which indicates that the resolution of the LAI-
2000 is not larger than 30 m. Several measurements in one 30 m resolution pixel are
needed for a pixel by pixel comparison. These requirements, that is, accurate GPS
readings and geo-registration and a large number of measurements within each pixel,
make pixel by pixel validation risky if the spatial accuracies of GPS and image
registration are not achieved. A region by region (or patch by patch) comparison is a
more conservative alternative with less risk.
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4.5.3.2 Harvard Forest
The decomposition of variance for the Harvard Forest site is listed in Table 4.7, and the
variograms of the three-level hierarchy are shown in Fig. 4.18. The majority of variation,
59.66% in the NDVI data and 76.55% in the LAI data, is at the scale of classes. Both the
region and pixel effect are relatively small. For both the NDVI and LAI data, the pixel
variograms reach their sill at about 60 m and remain flat for all larger lags. The range for
the class effect is about 500 m, which is roughly twice that of the region scale.
The class effect contributes more variance (76.55%) in the LAI data than the NDVI
data (59.66%). The variance of the region effect decreases to 11% in the LAI data,
compared with 26.17% in the NDVI data. The relatively higher variance of the class
effect indicates that there are large differences between the means of different land cover
types. For example, broadleaf forests have mean LAI values as large as 5, compared to
zero LAI values for water or bare land. Thus, the LAI values at this site depend heavily
on the land cover types to which the pixels belong. Within a vegetation type, the LAI
variation among pixels is only about 23.45%. Hence LAI at the Harvard Forest site is
relatively homogeneous within classes, but varies strongly among classes.
4.5.3.3 Ruokolahti Forest
At the Ruokolahti site, the class effect contributes the most (93.56%) to the total NDVI
variance (Table 4.8). Of the total LAI variance, the class, region and pixel effects explain
47.78%, 14.41%, and 37.7%, respectively. The pixel variogram reaches its sill at roughly
300 m, while the range for the region effect is about 400-500 m (Fig. 4.19). The class
effect reaches the sill at about 1000 m, and still increases slowly. The NDVI spatial
variation is almost completely determined by the class effect. The LAI spatial structure,
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however, is determined not only by the class effect, but also by the pixel effect, as at
Maun.
The very small region scale variation in both NDVI and LAI data is unexpected,
because individual patches associated with harvesting and subsequent plantations can be
easily distinguished in a RGB image of bands 4, 5 and 3. In the NDVI image (Fig. 20),
however, these features are blurred, possibly for two reasons. First, histograms of NDVI
from young, regular and dense forests (Fig. 4.21) indicate that the NDVI of regular and
dense needle forests are not very different. Smaller values of both RED and NIR
reflectance of the dense forests result in NDVI similar to the regular forests. Second,
although variations in the NDVI data among regions are small, they are large within
regions, especially in the case of young and regular forests, which is also seen in the CCD
aircraft photographs. This possibly explains the dominance of the pixel effects.
The algorithm retrievals compare well in the case of dense and regular forests, but
not in young forests. This could be a reason that the region effect does not contribute
much to the spatial variation in the LAI data. Improvements to the algorithm are therefore
necessary.
4.5.3.4 Comparison of LAI Data Between Sites
There are very different patterns of LAI variance with respect to the three levels of
landscape organization. At Maun, the pixel effect is dominant, while at the Harvard
Forest site the class effect contributes most to the variance. At the Ruokulahti Forest site,
both the class and pixel effect are equally important in determining the spatial variation
of LAI. A question of some importance is, under what circumstances the spatial
distribution of LAI across the landscape is due to variations within land cover types as
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opposed to differences between land cover types? The coefficients of variation (standard
deviation/mean, COV) of NDVI and LAI at the three sites are listed in Table 4.9. The
NDVI data from Maun and Ruokolahti show a similarity; the COV within classes is
relatively larger than that from the Harvard Forest, especially for the dominant class type
(savannas in Maun, broadleaf forests in the Harvard Forest, and needle forests in the
Ruokolahti Forest). Although most spatial variation occurs at the class scale in the NDVI
data, the large COV within classes results in a large spatial variation within classes in the
LAI retrievals. As a result, the majority of spatial variation is first at the scale of pixels in
the LAI data. On the other hand, the Harvard Forest exhibits smaller COV in NDVI, thus,
less spatial variation at the pixel scale in the LAI data. Thus, whether the spatial
distribution of LAI across the landscape is due to variations within land cover types or
not depend on the homogeneity of the land cover, especially the dominant class type. The
validation of homogeneous broadleaf forests will be relative easier than savannas or
needle forests. The latter require more accurate GPS readings and scientific sampling
strategy, in order to capture the LAI spatial variations.
The range of variograms is often related to the size of the largest elements (objects)
in the scale that characterize the correlation structure. The < 500 m range in the class
effect at Maun and Harvard Forest sites indicates that landscape variations occur over
relative small areas. Land cover generally varies beyond 500 m. This also indicates that
the 1 km MODIS pixels are generally mixed pixels. Ranges in the pixel scale effect from
the three sites suggest that no variation at scales finer than regions could be detected at
resolutions coarser than 200 m. Therefore, validation needs to be performed in small
regions (< 500 m).
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Results from Table 4.6, 4.7, and 4.8 indicate that the region effect always contributes
10-15% of spatial variation in the LAI data. This is why one could and should use the
segmentation procedure to compare field data with fine resolution satellite retrievals,
especially at the Harvard Forest and Ruokulahti Forest sites, where the pixel scale
variation is small.
The decomposition of variograms according to the hierarchical model shows the
relative contribution of different characteristic scales to the overall variation. This method
also displays the spatial structure of the effects at different scales. Knowledge gained
from these analyses can influence data collection practices. For a homogeneous (within
class) site such as broadleaf forests of the Harvard Forest, where the class and region
effect account for 90% of the spatial variation, a sampling strategy should focus more on
using accurate land cover maps and selection of regions. However, for a heterogeneous
(within class) site such as needle forests of the Ruokulahti Forest or savannas of Maun,
accurate point measurements within GPS readings are needed. The fine resolution of
LAI-2000 makes it difficult to quantify the relation between field measurements and
satellite retrievals. Therefore, either the number of point measurements at 30 m resolution
should be increased, or a region by region comparison should be attempted.
The absolute magnitudes of variance vary significantly across the three sites. The
overall variance in the LAI data is only 0.2 in Maun, compared to 2.5 at Harvard Forest;
even the pixel effect variance here is larger than the total variance in Maun. Higher
variance is equivalent to higher information content. The Harvard Forest site contains
more spatial information than Maun.
In this study, it is found that the spatial structure of NDVI is not similar to that of
LAI, due to the non-linear relation between NDVI and LAI. It may also be due to certain
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limitations of the LAI/FPAR algorithm. It should be noted that the algorithm does not use
NDVI-LAI relations for LAI retrievals.
4.6 Concluding Remarks
Validation of global data products is crucial, both to establish the accuracy of the
products for the science-user community and to provide feedback to improve the data
processing algorithms. The validation efforts here are aimed not only at testing the
accuracy of the LAI product, but also to gain an understanding of the causes of errors,
and thus provide feedback for potential improvement in second-generation MODIS
products (Cohen and Justice, 2000).
In this chapter, the LAI retrievals from 30 m resolution ETM+ data were first
compared with field measurements from the SAFARI 2000 wet season campaign, and
then the validated LAI fields were compared with those retrieved from MODIS data (250
m, 500 m, and 1 km) simulated from ETM+. Consistency between LAI retrievals from 30
m ETM+ data and field measurements indicates good performance of the algorithm. LAI
values for coarse resolution data are underestimated if the resolution of the data is not
considered in the retrieval technique.
This chapter also attempts to define sampling strategies based on comparison
between ground measurements and fine spatial resolution remote sensing data.
Hierarchical analysis of data from Maun, Harvard Forest and Ruokulahti Forest sites
shows that the MODIS algorithm based LAI retrievals from ETM+ data exhibit multiple
characteristic scales of spatial variation. These scales can be identified with a hierarchical
scene model by dividing the image into scales of classes, regions and pixels. Isolating the
114
effects associated with different landscape scales through variograms helps in the
evaluation of sampling strategies. I find that (1) within the three sites, patterns of variance
in the class, region, and pixel scale are different with respect to the importance of the
three levels of landscape organization; (2) the spatial structure in LAI shows similarity
across the three sites, that is, sills are reached a lag (distance) less than 1000 m; (3)
validation needs to be performed over smaller areas, with more field measurements and
smaller intervals; (4) the spatial structure of the NDVI is not the same as that of LAI; and
(5) the absolute magnitudes of variance vary significantly across the three sites. These
results imply that for the validation activity, knowledge about basing the sample scale on
the underlying spatial structure of the scene (as understood through hierarchical
decomposition of variograms) is necessary and in general, patches are better than
individual pixels unless sample and registration accuracy are outstanding.
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Figure 4.1. Sampling scheme of SAFARI 2000 wet season Kalahari Transect (KT) campaign.
1000 m
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(a) Pandamatenga
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Figure 4.2. Histograms of transect and grid LAI measurements at the four SAFARI 2000 wet season campaign sites: (a) Pandamatenga, (b) Maun, (c) Okwa, and (d) Tshane.
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0.0 0.5 1.0 1.5 2.0 2.5 3.0Transect Mean LAI
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Gri
d M
ean
LA
I
PandamatengaMaunOkwaTshane
Figure 4.3. Comparison between transect and grid LAI measurements at Pandamatenga, Maun, Okwa, and Tshane. The dots and error bars represent means and standard deviations, respectively.
118
(a) Pandamatenga
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Figure 4.4. Variograms of field measurements at (a) Pandamatenga, (b) Maun, (c) Okwa, and (d) Tshane.
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(a)
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Figure 4.5. LAI measurements along the transects from the sample points located 375 meters west of the middle sample point to those located 375 meters east. (a) Pandamatenga, (b) Maun.
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(c)
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Figure 4.5. LAI measurements along the transects from the sample points located 375 meters west of the middle sample point to those located 375 meters east. (c) Okwa, and (d) Tshane.
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(a)
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Figure 4.6. (a) Color RGB image from Bands 4, 3 and 2 of a 10 km by 10 km region of the Maun site from an ETM+ image. (b) Vegetation classification map for the 10 km by 10 km region.
Shrub
Savannas
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(a)
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Figure 4.7. Color RGB image from Bands 4, 3 and 2 of a 1 km by 1 km region of the Maun site. Panel (a) is IKONOS data and panel (b) is ETM+ data. Yellow "+" represents sampling points, and green "+" represents the positions where the photos were taken.
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Figure 4.8. Map of a 1 km by 1 km region at Maun using the segmentation procedure described in the text. Patches 1, 2, 4, 7, 8, 9, 12, 13 and 15 are savannas. Patches 3, 5, 6, 10, 11, and 14 are shrubs.
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(a)
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Figure 4.9. (a) Region by region comparison of field measurements and MODIS algorithm based LAI from 30 m resolution ETM+ data at Maun. (b) Pixel by pixel comparison of LAI retrievals from savanna and shrub look-up tables. (c) Region by region comparison of LAI retrievals from savanna and shrub look-up tables.
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Figure 4.10. Variations in the mean and standard deviation (SDT) of RED, NIR, and NDVI as a function of spatial resolution: (a) mean of RED, (b) STD of RED, (c) mean of NIR, (d) STD of NIR, (e) mean of NDVI, and (f) STD of NDVI.
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lect
ance
(f) 1000m Resolution, Savannas
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 1
000m
Ref
lect
ance
Figure 4.11. Pixel by pixel comparison of LAI retrievals averaged at 30 m resolution and retrieved directly from reflectance at resolution of (a) 250 m using shrub look-up table (LUT) only, (b) 500 m using shrubs LUT only, (c) 1000 m using shrubs LUT only, (d) 250 m using savannas LUT only, (e) 500 m using savannas LUT only, and (f) 1000 m using savannas LUT only.
127
(a) 250m Resolution
-0.4 -0.2 0.0 0.2 0.4DL
0.00
0.05
0.10
0.15
0.20
SDT
SavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrub
(b) 500m Resolution
-0.4 -0.2 0.0 0.2 0.4DL
0.00
0.05
0.10
0.15
0.20
SDT
SavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrub
(c) 1000m Resolution
-0.4 -0.2 0.0 0.2 0.4DL
0.00
0.05
0.10
0.15
0.20
SDT
SavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasSavannasShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrubShrub
Figure 4.12. Overall standard deviation as a function of the difference in LAI (DL) between averages from 30 m resolution and retrievals directly from reflectance at (a) 250 m, (b) 500 m, and (c) 1 km resolution.
128
(a) 250m Resolution, All Pixels
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 2
50m
Ref
lect
ance
(b) 500m Resolution, All Pixels
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 5
00m
Ref
lect
ance
(c) 1000m Resolution, All Pixels
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 1
000m
Ref
lect
ance
(d) 250m Resolution, Shrubs
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 2
50m
Ref
lect
ance
(e) 500m Resolution, Shrubs
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 5
00m
Ref
lect
ance
(f) 1000m Resolution, Shrubs
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 1
000m
Ref
lect
ance
(g) 250m Resolution, Savannas
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 2
50m
Ref
lect
ance
(h) 500m Resolution, Savannas
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 5
00m
Ref
lect
ance
(i) 1000m Resolution, Savannas
0 1 2 3 4Averaged LAI from 30m Resolution
0
1
2
3
4
LA
I R
etri
eved
fro
m 1
000m
Ref
lect
ance
Figure 4.13. Pixel by pixel comparison of LAI retrievals averaged from 30 m resolution and retrieved directly from reflectance at resolution of (a) 250 m for all pixels, (b) 500 m for all pixels, (c) 1000 m for all pixels, (d) 250 m for shrub pixels only, (e) 500 m for shrub pixels only, (f) 1000 m for shrub pixels only, (g) 250 m for savanna pixels only, (h) 500 m for savanna pixels only, and (i) 1000 m for savanna pixels only.
129
(a)
(b)
Figure 4.14. (a) RBG image of a 15 km by 13 km region of Harvard Forests produced from ETM+ Bands 4, 5, and 3. (b) Land cover classification map using unsupervised classification procedure.
Water
Glasses
Shrubs
Broadleaf Forests
Needle Forests
Bare Land
130
(a)
(b)
Figure 4.15. (a) RBG image of a 10 km by 10 km region of Ruokolahti Forest produced from ETM+ Bands 4, 5, and 3. (b) Land cover classification map using unsupervised classification procedures.
Water
Grasses
Young Forests
Regular Forests
Dense Forests
131
(a)
(b)
Figure 4.16. LAI images from (a) the Harvard Forest site and (b) the Ruokolahti Forest site.
132
(a) NDVI
0 500 1000 1500 2000 2500 3000Distance (m)
0.000
0.002
0.004
0.006
0.008
Sem
ivar
ianc
e
Entire ImageEntire ImageEntire ImageEntire ImageEntire ImageClass EffectClass EffectClass EffectClass EffectClass EffectRegion EffectRegion EffectRegion EffectRegion EffectRegion EffectPixel EffectPixel EffectPixel EffectPixel EffectPixel Effect
(b) LAI
0 500 1000 1500 2000 2500 3000Distance (m)
0.00
0.05
0.10
0.15
0.20
Sem
ivar
ianc
e
Figure 4.17. Hierarchical decomposion of variograms for (a) NDVI and (b) LAI of the Maun site.
133
(a) NDVI
0 500 1000 1500 2000 2500 3000Distance (m)
0.000
0.002
0.004
0.006
0.008
0.010Se
miv
aria
nce
Entire ImageEntire ImageEntire ImageEntire ImageEntire ImageClass EffectClass EffectClass EffectClass EffectClass EffectRegion EffectRegion EffectRegion EffectRegion EffectRegion EffectPixel EffectPixel EffectPixel EffectPixel EffectPixel Effect
(b) LAI
0 500 1000 1500 2000 2500 3000Distance (m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Sem
ivar
ianc
e
Figure 4.18. Hierarchical decomposion of variograms for (a) NDVI and (b) LAI of the Harvard Forest site.
134
(a) NDVI
0 500 1000 1500 2000 2500 3000Distance (m)
0.00
0.02
0.04
0.06
0.08
Sem
ivar
ianc
e
Entire ImageEntire ImageEntire ImageEntire ImageEntire ImageClass EffectClass EffectClass EffectClass EffectClass EffectRegion EffectRegion EffectRegion EffectRegion EffectRegion EffectPixel EffectPixel EffectPixel EffectPixel EffectPixel Effect
(b) LAI
0 500 1000 1500 2000 2500 3000Distance (m)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Sem
ivar
ianc
e
Figure 4.19. Hierarchical decomposion of variograms for (a) NDVI and (b) LAI of the Ruokolahti Forest site.
135
Figure 4.20. The NDVI image from the Ruokolahti Forest site. The color from black to white represents the range of NDVI values. The brighter the image, the larger the NDVI value.
136
(a) NDVI
0.2 0.4 0.6 0.8 1.0NDVI
0
10
20
30
40
50
Freq
uenc
y %
Young ForestsYoung ForestsYoung ForestsYoung ForestsYoung ForestsRegular ForestsRegular ForestsRegular ForestsRegular ForestsRegular ForestsDense ForestsDense ForestsDense ForestsDense ForestsDense Forests
(b) RED
0.00 0.05 0.10 0.15 0.20RED
0
20
40
60
80
100
Freq
uenc
y %
(c) NIR
0.0 0.1 0.2 0.3 0.4NIR
0
20
40
60
80
100
Freq
uenc
y %
Figure 4.21. Histograms of (a) NDVI, (b) RED, and (c) NIR for young, regular, and dense forests at the Ruokolahti Forest site.
137
Table 4.1. Plant Height and LAI-2000 Measured Area
Site Height
m
Radius
m
Total area
m2
Actual area
m2
Overlap at
transect (%)
Overlap at
grid (%)
Pandamatenga 11.4 34.2 3674.53 2755.89 39.36 0
Maun 6.0 18 1017.88 763.41 0 0
Okwa 2.2 6.6 136.85 34.21 0 0
Tshane 3.7 11.1 387.07 96.77 0 0
Table 4.2. t-Test of the Means of the Transect and Grid LAI Measurements
Site Name
Pandamatenga Maun Okwa Tshane
0.0725 0.0269 0.0023 0.9952
The null hypothesis is that the LAI means of the two groups are equal. Here, p values are given.
138
Table 4.3. t-Test of the LAI Means of Different Regions
Region Number Region
Number 3 5 6 10 7+8 9 12 Tower
3 1.0000
5 0.3614 1.0000
6 0.4108 0.0108 1.0000
10 0.7928 0.4862 0.2412 1.0000
7+8 0.0241 0.0003 0.0713 0.0050 1.0000
9 0.0993 0.0035 0.2539 0.0349 0.5922 1.0000
12 0.2747 0.0220 0.7243 0.1259 0.1722 0.4569 1.0000
Tower 0.0085 0.0001 0.0382 0.0010 0.8112 0.4309 0.0901 1.0000
The null hypothesis is that the LAI means of the two regions are equal. Here, p values are given.
139
Table 4.4. Means of Difference in LAI (DL) Retrievals Between Method 1 and Method 2 from One Land Cover Type
Resolution
Land cover 250m 500m 1000m
Shrubs 5.6 6.39 7.63
Savannas 8.6 10.09 11.9
Table 4.5. Means of Difference in LAI (DL) Retrievals Between Method 1 and Method 2 from Two Land Cover Types
Resolution
Land cover 250m 500m 1000m
Shrubs 15.1 16.8 16.3
Savannas 0.3 3.4 2.6
shrubs+savannas 4.3 4.6 5.1
140
Table 4.6. Hierarchical Model Results for the Maun Scenes
Scene Image Variance Percentage of Variance (%)
Original image 0.006956 100
Class effect 0.003263 46.52
Region effect 0.001257 18.07
NDVI
Pixel effect 0.002436 35.02
Original image 0.18936 100
Class effect 0.06044 31.92
Region effect 0.02502 13.21
LAI
Pixel effect 0.10391 54.87
Table 4.7. Hierarchical Model Results for the Harvard Forest Scenes
Scene Image Variance Percentage of Variance (%)
Original image 0.008365 100
Class effect 0.004991 59.66
Region effect 0.002189 26.17
NDVI
Pixel effect 0.001185 14.17
Original image 2.7476 100
Class effect 2.1032 76.55
Region effect 0.3147 11.45
LAI
Pixel effect 0.3296 11.99
141
Table 4.8. Hierarchical Model Results for the Ruokolahti Forest Scenes
Scene Image Variance Percentage of Variance (%)
Original image 0.068958 100
Class effect 0.006452 93.56
Region effect 0.001422 2.62
NDVI
Pixel effect 0.003016 4.37
Original image 1.11046 100
Class effect 0.53058 47.78
Region effect 0.16002 14.41
LAI
Pixel effect 0.41985 37.7
Table 4.9. Coefficients of Variation of NDVI and LAI from Different Biome Types and Sites
Site Name Biome Type NDVI LAI
Maun Shrubs 0.0953 0.3596
Savanns 0.1314 0.4622
Farvard Forest Grasses 0.1104 0.2438
Shrubs 0.0601 0.1474
Broadleaf Forests 0.0260 0.1423
Needle Forests 0.0561 0.2756
Ruokolahti Forest Grasses 0.1502 0.2566
Total Needle Forests 0.1066 0.4306
Sparse Needle Forests 0.1187 0.4357
Regular Needle Forests 0.1230 0.5271
Dense Needle Forests 0.0806 0.3181
142
Chapter 5
Conclusions
Analysis of global vegetation dynamics is of importance in studies of ecology and
climatology in view of biosphere-atmosphere interactions of energy, momentum and
mass. Accurate characterization of biophysical parameters of vegetation, spatially and
temporally, is therefore required in studies of the carbon cycle, the energy balance,
environmental impact assessment studies, and evaluating the future state of climate and
terrestrial ecosystems.
The MODIS products, leaf area index (LAI) and fraction of photosynthetically active
radiation absorbed by vegetation (FPAR), are two of the key vegetation parameters in the
aforementioned studies. They have been operationally produced and available free of
charge for public use. This dissertation is one of many studies that detail the MODIS
LAI/FPAR algorithm’s functionality, accuracy, and validation. My emphasis is on
interpreting the performance of the algorithm in the spatial domain.
Three specific themes are addressed in this dissertation. The first is regarding
prototyping of the algorithm using Land Surface Reflectance (LASUR) and Landsat data.
The objectives are to evaluate the performance of the algorithm as a function of spatial
resolution, and uncertainties in surface reflectance and land cover data. Results from
prototyping exercises prior to the launch of MODIS indicated correctly the physical
143
relationships between surface reflectances and biophysical parameters and demonstrated
the feasibility of physically valid retrievals with the algorithm. Retrieval quality is found
to depend on the quality of the most uncertain input, if uncertainties in spectral canopy
reflectances are not available. Land cover misclassifications between distinct biomes are
found to fatally impact the retrievals. Retrievals are evaluated with metrics such as
retrieval index (RI), mean LAI, and the histogram of the retrieved LAI distribution. Land
cover misclassifications between spectrally and structurally similar biomes are negligible,
particularly if the spatial resolution of the input data is coarse. Canopy spectral properties
are found to differ with spatial resolution. Each vegetation type in Landsat data tends to
cluster and occupy a small region close to the near-infrared axis in the spectral space,
while biomes become spectrally similar in the case of coarse resolution LASUR data. A
comparison of coarse (16 km) and fine (30 m) resolution retrievals highlighted the scale
dependence of the algorithm. The algorithm should be adjusted for data resolution in
order to get accurate retrievals.
The second theme addresses how the spatial resolution of reflectance data impacts
retrievals of vegetation LAI and FPAR. The goal of scaling was defined in this study as
the process by which it is established that LAI and FPAR values derived from coarse
resolution sensor data equal the arithmetic average of values derived independently from
fine resolution sensor data. The increasing probability of land cover mixtures with
decreasing resolution is defined as heterogeneity, which is a key concept in scaling
studies. The effect of pixel heterogeneity within coarse resolution pixels on LAI/FPAR
retrievals was investigated with 1 km AVHRR data aggregated to various coarse scale
resolutions. It is shown that LAI retrieval errors are inversely related to the proportion of
the dominant land cover in a pixel. Errors are particularly large when broadleaf and
144
needle forests are minority biomes in non-forest pixels compared to when these two
forest biomes are mixed with one another, and vice-versa. A physically based theory for
scaling with explicit scale dependent radiative transfer formulation was developed. The
successful application of this theory to scaling LAI retrievals from AVHRR data of
different resolutions was demonstrated. These principles underlie the approach to
production and validation of LAI and FPAR products from the MODIS and MISR data.
The third topic of investigation is validation of the MODIS LAI/FPAR product with
field measurements. The development of appropriate ground-based validation techniques
is critical to assessing uncertainties associated with satellite data derived products. In this
study, patch by patch LAI retrievals from 30 m resolution ETM+ data were compared
with field measurements from the SAFARI 2000 wet season campaign. The consistency
between LAI retrievals and field measurements speaks favorably about the performance
of the algorithm. The comparison between the 30 m resolution LAI fields and those
retrieved from MODIS data (250 m, 500 m, and 1 km) simulated from ETM+ indicated
that LAI values estimated from coarse resolution data are underestimated if the resolution
of the data is not considered in the retrieval technique.
This dissertation also provides insight related to sampling strategies. Hierarchical
analysis of data from Maun, Harvard Forest (USA) and Ruokulahti Forest (Finland)
indicates that the LAI retrievals from ETM+ data exhibit multiple characteristic scales of
spatial variation. These scales can be identified with a hierarchical scene model by
dividing the image into classes, regions and pixels. Isolating the effects associated with
different landscape scales through variograms aids in formulation of sampling strategies.
I find that (1) patterns of variance at the class, region, and pixel scale are different with
respect to the importance of the three levels of landscape organization; (2) the spatial
145
structure of LAI shows similarity across the three sites, that is, sills are reached at a lag
(distance) less than 1000 m; (3) validation needs to be performed over smaller regions,
with numerous accurate field measurements; (4) the spatial structure of NDVI is not the
same as that of LAI; (5) the absolute magnitudes of variance vary significantly across the
three sites. Based on these results, a strategy for ground sampling is proposed for
validation of moderate resolution satellite sensor biophysical products.
This research aims at not only testing the validity and performance of the MODIS
LAI/FPAR algorithm, but also gaining an understanding of the causes of errors and thus
providing feedback for potential improvement in second-generation MODIS products. In
addition, these efforts help establish a quantitative estimate of uncertainty in surface
biophysical parameters for vegetation monitoring at regional to global scales in an
operational mode. The MODIS, Landsat 7, and AVHRR in orbit over the next few years
will provide a unique set of remote sensing measurements suitable for vegetation
monitoring because of their unique spectral and spatial configurations. The high temporal
frequency will facilitate timely update of the vegetation status for short term change
detection and long term interannual variability monitoring. The data to be acquired with
these instruments will improve quantitative estimation of the physical and biophysical
parameters for environmental change studies.
In the future, I will apply global satellite data in General Circulation Model (GCM)
studies on the role of vegetation dynamics on interannual variability in near surface
climate and carbon dynamics. It has been well recognized that the most important
properties of the land surface for climate and carbon modeling are those that determine
biogeochemical and biogeophysical processes. Using satellite observations can
undoubtedly improve the accuracy of the quantitative treatment of these processes.
146
However, there are many reasons that currently most models of land surface
biogeophysics and biogeochemistry do not use satellite products. Chief amongst these
are: (1) model structures do not permit ingestion of satellite products, (2) various
products of important variables are not compatible with one-another and, (3) the products
have not been validated and therefore their accuracy is unknown. In order to remedy this
situation, the development of land surface products must be an integral part of climate
and carbon modeling studies. The model structure formulations that ensure compatibility
between satellite products and land surface processes need to be developed. These
activities will make coupling of satellite data products to land surface models compatible
and logical. Research is planned with the Common Land Model (CLM) coupled to GCM
to assess if simulation of the near surface climate improves with improved model
structures linked to accurate land surface products from MODIS. Specifically, I intend to
extend my current research on three fronts by working on the following: (1) to understand
the difference between climate model treatment of LAI and FPAR and those used for
MODIS standard products, and to work with MODIS LAI/FPAR products to improve the
boundary condition related to the global vegetation of the GCM models; (2) to study the
influence of vegetation heterogeneity on land surface energy balance, land surface
hydrological balance, and atmospheric boundary layer development, by taking into
account the variation in canopy architecture and fractional vegetation cover; and (3) to
monitor and quantify climate change based on the new generation of remotely sensed
data (e.g. ETM+, MODIS and MISR), and the new generation of CLM system.
147
Appendix: Effect of Non-linearity and Pixel Mixture on LAI Retrievals
Coarse resolution LAI can be derived by two different methods: LAI derived from
arithmetic averaging of LAI values retrieved from fine resolution data (method 1) and
LAI retrieved from coarse resolution sensor data directly (method 2). It is clear that the
LAI value from method 1 is the correct value. In this appendix, I discuss situations under
which the LAI values from method 2 will be under- or overestimated.
The MODIS LAI algorithm is a non-linear and biome type dependent model. Let us
assume that f represents the relation between LAI and surface reflectances derived from
fine resolution data, i.e., LAIi= fi(reflectance). Here, i represents the land cover type (1 to
6). For a coarse resolution pixel, it could be a pure pixel, or a mixed pixel that consists of
sub-pixels with other land cover types. For simplicity, let us assume that there are only
two sub-pixels, of reflectance of r1 and r2, respectively, in a coarse resolution pixel.
Obviously, the two sub-pixels are either the same land cover type or two different cover
types. I discuss this below separately.
A.1 One Land Cover Type
If the two sub-pixels are from the same land cover type, for example, savannas, we have
)(LAI 11 rf= , (A.1)
)(LAI 22 rf= . (A.2)
The mean LAI of the coarse resolution pixel in method 1 is
148
2
)()(
2
LAILAILAI 2121
1method
rfrf +=+= . (A.3)
In method 2, the reflectance of the coarse resolution pixel is r=(r1+r2)/2. If the
function f is used to retrieve the LAI value, then
)2
()(LAI 21method2
rrfrf
+== . (A.4)
Figure A.1(a) shows the relation between LAI and reflectance at 30 m resolution for
savannas (solid line). It is clear that LAImethod1 is larger than LAImethod2. Therefore, the
retrieved LAI from coarse resolution data underestimates the LAI value.
A.2 Two Different Land Cover Types
If the two sub-pixels are of two different land cover types, class 1 and class 2, two
different functions f1 and f2 are needed to represent the relation between LAI and
reflectance at the fine resolution. Thus
)(LAI 111 rf= , (A.5)
)(LAI 222 rf= . (A.6)
The mean LAI for the coarse resolution pixel in method 1 is
2
)()(
2
LAILAILAI 221121
1method
rfrf +=+= . (A.7)
In method 2, the retrieved LAI value of the coarse resolution pixel is dependent on
which function, f1 and f2, is used. It is either
)2
()(LAI 21111method2,
rrfrf class
+== , (A.8)
149
if defined as class 1, or
)2
()(LAI 2122class2 method2,
rrfrf
+== , (A.9)
if defined as class 2.
Figures A.1(b) and A.1(c) show the relation between LAI and reflectance, f1, for
class 1 (savannas, solid line), and f2, for class 2 (shrubs, dash line), at 30 m resolution.
Whether the retrieved LAI from the coarse resolution data is under- or overestimated
depends on the location of reflectance of class 1 and class 2 in the reflectance-LAI space
at the fine resolution. There are two possible cases:
A.2.1 Case A
If the location of the reflectance of class 1 and class 2 is distributed as shown in Fig.
A.1(b), then
class2 method2,class1 method2,method1 LAI LAILAI >> . (A.10)
This means that the retrieved LAI for the coarse resolution pixel is underestimated
irrespective of the biome classification.
A.2.2 Case B
If the location of the reflectance of class 1 and class 2 is distributed as shown in Fig.
A.1(c), then
class2 method2,method11method2 LAI LAILAI >>, class . (A.11)
This means that the retrieved LAI for the coarse resolution pixel is underestimated if it is
defined as class 2 or overestimated if it is defined class 1.
150
These results indicate that class 2 (shrubs) is always underestimated while class 1
(savannas) could be under- or overestimated.
151
(a) 30m Resolution
0 1 2 3 4 5LAI
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8R
efle
ctan
ce(b) 30m Resolution
0 1 2 3 4 5LAI
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Ref
lect
ance
(c) 30m Resolution
0 1 2 3 4 5LAI
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Ref
lect
ance
Figure A.1. Relation between LAI and surface reflectance at 30 m resolution for (a) savannas (solid line), (b) savannas (solid line) and shrubs (dash line), which shows that the retrieved LAI from coarse resolution reflectance data is underestimated for both savannas and shrubs, and (c) savannas (solid line) and shrubs (dash line), which shows that the retrieved LAI from the coarse resolution reflectance data is underestimated for shrubs and overestimated for savannas. See Appendix for further clarification.
152
List of Journal Abbreviations
Agric. For. Meteorol. Agricultural and Forests Meteorology
American Meteorol. Soc. American Meteorology Society
Ecol. Model. Ecological Modelling
Geophys. Res. Lett. Geophysical Research Letters
Global Biochem. Cycles Global Biochemical Cycles
Int. J. Remote Sens. International Journal of Remote Sensing
IEEE Trans. Geosci. IEEE Transactions on Geoscience and
Remote Sens. Remote Sensing
J. Appl. Meteorol. Journal of Applied Meteorology
J. Atmos. Sci. Journal of the Atmospheric Sciences
J. Clim. Appl. Met. Journal of Climate and Applied meteorology
J. Geophys. Res. Journal of Geophysical Research
Quant. Spectrosc. Radiat. Journal of Quantitative Spectroscopy
Transfer and Radiative Transfer
Remote Sens. Rev. Remote Sensing Review
Remote Sens. Environ. Remote Sensing of Environment
153
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publication).
Zhang, Y., Tian, Y., Knyazikhin, Y., Martonchick, J. V., Diner, D. J., Leroy, M., and
Myneni, R. B. (2000), Prototyping of MISR LAI and FPAR algorithm with
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169
CURRICULUM VITAE
Yuhong Tian
14 Buswell St., Apt. 405, Boston, MA 02215, USA
Tel: (617) 266-0974 Email: [email protected]
EDUCATION
• Ph.D. in Geography specialization in Remote Sensing.
Boston University, Boston, MA 2002
• M.S. (honors) in Meteorology.
Chinese Academy of Meteorological Science, Beijing, China 1995
• B.S. in Meteorology.
Nanjing Institute of Meteorology, Nanjing, China 1992
EXPERIENCE
• Doctoral Research Assistant
Department of Geography
Boston University, Boston, MA, 1998 – 2001
• Research Assistant
Open Lab for Climate Study
National Climate Center, Beijing, China 1995 – 1998
170
• Master Research Assistant
Chinese Academy of Meteorological Science
Beijing, China, 1992 – 1995
PUBLICATIONS
First Author
• Tian, Y., Woodcock, C. E., Wang, Y., Privette, J. L., Shabanov, N. V., Zhou, L.,
Buermann, W., Dong, J., Veikkanen, B., Hame, T., Ozdogan, M., Knyazikhin, Y.,
and Myneni, R. B. (2001), Multiscale Analysis and Validation of MODIS LAI
Product over Maun, Botswana, Remote Sens. Environ. (submitted in October 2001).
• Tian, Y., Wang, Y., Zhang, Y., Knyazikhin, Y., Bogaert, J., and Myneni, R. B.
(2001), Radiative transfer based scaling of LAI/FPAR retrievals from reflectance
data of different resolutions. Remote Sens. Environ. (in review).
• Tian, Y., Zhang, Y., Knyazikhin, Y., Myneni, R. B., Glassy, J. M., Dedieu, D., and
Running, S. W. (2000), Prototyping of MODIS LAI and FPAR algorithm with
LASUR and LANDSAT data. IEEE Trans. Geosci. Remote Sens. 38(5):2,387-
2,401.
Co-author
• Zhang, Y., Tian, Y., Myneni, R. B., Knyazikhin, Y., Woodcock, C. E., (2001).
Required consistency between biome definitions and signatures with the physics
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of remote sensing. Part I: Empirical arguments. Remote Sens. Environ. (Accepted
in August 2001).
• Wang, Y., Tian, Y., Zhang, Y., El-Saleous, N., Knyazikhin, Y., Vermote, E.,
Myneni, R.B. (2001), Investigation of product accuracy as a function of input and
model uncertainties: Case study with SeaWiFS and MODIS LAI/FPAR
Algorithm. Remote Sens. Environ. (Accepted in January 2001).
• Lotsch, A., Tian, Y., Friedl, M. A., and Myneni, R. B. (2001), Land cover mapping
in support of LAI/FPAR retrievals from EOS-MODOS and MISR: classification
methods and sensitivities to errors. Int. J. Remote Sens. (in review).
• Myneni, R. B., Knyazikhin, Y., Privette, J. L., Glassy, J., Tian, Y., Wang, Y.,
Hoffman, S., Song, X., Zhang, Y., Smith, G. R., Lotsch, A., Friedl, M., Morisette, J.
T., Votava, P., Nemani, R. R., and Running, S. W. (2001), Global products of
vegetation leaf area and fraction of absorbed PAR from year one of MODIS
data. Remote Sens. Environ. (in review).
• Privette, J. L., Tian, Y., Roberts, G., Scholes, R. J., Wang, Y., Caylor, K. C., Frost,
P., and Mukelabai, M., (2001), Structural characteristics and relationships of
Kalahari woodlands and savannas. Global Change Biology (submitted in May
2001).
• Privette, J. L., Myneni, R. B., Knyazikhin, Y., Mukufute, M., Roberts, G., Tian, Y.,
Wang, Y., and Leblanc, S. G., (2001), Early spatial and temporal validation of
MODIS LAI product in Africa. Remote Sens. Environ. (Submitted in February
2001).
• Zhang, Y., Tian, Y., Knyazikhin, Y., Martonchick, J. V., Diner, D. J., Leroy, M., and
Myneni, R. B. (2000), Prototyping of MISR LAI and FPAR algorithm with
POLDER data over Africa. IEEE Trans. Geosci. Remote Sens. 38(5):2,402-2,418.
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