BOSTON UNIVERSITY GRADUATE SCHOOL OF ARTS AND SCIENCES. Dissertation ASSESSMENT AND REFINEMENT OF THE MISR LAI AND FPAR PRODUCT JIANNAN HU

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1 BOSTON UNIVERSITY GRADUATE SCHOOL OF ARTS AND SCIENCES Dissertation ASSESSMENT AND REFINEMENT OF THE MISR LAI AND FPAR PRODUCT by JIANNAN HU B.S., Northwestern Polytechnical University, 1993 M.S., Northern Jiaotong University, 1996 Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2005

2 Approved by First Reader Ranga B. Myneni, Ph.D. Professor of Geography Second Reader Yuri Knyazikhin, Ph.D. Research Professor of Geography Third Reader Curtis E. Woodcock, Ph.D. Professor of Geography

3 Acknowledgements I would like to take this opportunity to express my gratuity to my major advisor, Dr. Ranga B. Myneni, for giving me the opportunity to pursue PhD education in his Climate and Vegetation Research Group in the Department of Geography. His expertise in remote sensing studies, clearly formulated scientific questions, and well-organized research manner helped me in my research. I am lucky to work closely with my second advisor, Dr. Yuri Knyazikhin, an expert of radiative transfer theory, in MISR LAI/FPAR research. This dissertation benefits from his analytical skill and creative thoughts. I greatly appreciate their generous support and guidance during the five years of my studies. Thanks to my dissertation committee for their valuable insightful advice and significant input on advising my dissertation. I am greatly thankful to Dr. Jan Bogaert for bring land cover aggregation topic into my dissertation and advising me in my landcover aggregation research and spatial analysis. Many thanks to Dr. Curtis Woodcock for sharing his expertise in remote sensing, especially his insight in addressing the scale issue. Special thanks to Dr. Crystal Barker Schaaf for giving advice and discussing with me on land cover aggregation issues. I am honored to have all these great professors as members of my dissertation committee. I would like to say thanks to all the faculty of the Department of Geography, for their excellent lectures which build up my remote sensing background and beef up my research ability. Thanks the department administration staff for their patience in handling my logistic issues and computer problems. I am also grateful to my fellow students and iii

4 researchers for sharing their experience and knowledge with me, and also for their friendship which created a pleasant environment for my study and research. I dedicate this dissertation to my family, my wife and my daughter for their unceasing love, support and encouragement. iv

5 ASSESSMENT AND REFINEMENT OF THE MISR LAI AND FPAR PRODUCT (Order No. ) JIANNAN HU Boston University Graduate School of Arts and Sciences, 2005 Major Professor: Ranga B. Myneni, Professor of Geography ABSTRACT Land cover, vegetation green leaf area index (LAI) and the fraction of incident photosynthetically active radiation absorbed by vegetation (FPAR) govern the exchange of energy, momentum and mass (water and carbon dioxide, for example) between the Earth s surface and the atmosphere. These variables are operationally derived from measurements of the Multiangle Imaging SpectroRadiometer (MISR) aboard the NASA s Terra spacecraft, which was launched in December of The primary objectives of this research are to evaluate and refine the MISR LAI and FPAR algorithm in terms of retrieval quality, accuracy, spatial and temporal coverage. Further understanding and modeling of environmental processes requires land cover and land use maps at broad spatial scales. Therefore, a secondary objective is to develop a spatial aggregation algorithm that represents fine resolution land cover information from satellite data at coarser resolutions with minimal information loss for use in large scale modeling studies. A principal objective of the MISR LAI and FPAR retrieval algorithm is to retrieve LAI and FPAR without requiring a static, pre-specified global biome map. The spatial and temporal coverage of the MISR LAI and FPAR product are mainly limited by cloud v

6 contamination. The algorithm provides retrievals in percent of pixels with suitable input. Earlier versions of the algorithm overestimated LAI in grasses and broadleaf crops. Retrievals from the recalibrated algorithm show structural and phenological variability in agreement with field data. The product is accurate to within 0.5 units in herbaceous vegetation and savannas and overestimates LAI by about 1 unit in broadleaf forests. The land cover aggregation algorithm uses patterns in fine resolution images to preferentially aggregate blocks that show homogeneity, majority and adjacency. Disappearance of classes is avoided by predefining the number of pixels from each class that should be present in the coarser resolution data set. This technique conserves the complex patterns in the original image. Land cover maps generated using this aggregation method are found to be more similar to the original image than those created by random and majority aggregation and thus can better represent fine resolution land cover information for use in large scale modeling studies. vi

7 Table of Contents Acknowledgements...iii ABSTRACT... v Table of Contents... vii List of Tables... x List of Figures... xi List of Abbreviations... xvi Introduction Background Land Surface Processes Modeling MISR and Multiangular Remote Sensing MISR LAI and FPAR Algorithm Land Cover Aggregation Statement of the Research Problems Flow of the Research...9 Performance of the MISR LAI and FPAR algorithm: a case study in Africa Introduction MISR data Data analysis MISR LAI/FPAR algorithm Scaling of the algorithm Performance of the algorithm as a function of uncertainties Definition of uncertainties Optimal performance of the algorithm Impact of biome misidentification on LAI retrievals Test of physics...34 vii

8 2.9. Concluding remarks...36 Analysis of the MISR LAI/FPAR product for spatial and temporal coverage, accuracy and consistence Introduction Description of the MISR Surface Parameters Product Examples of MISR retrieval quality, uniqueness and consistency Angular signatures in spectral space LAI and FPAR retrievals over sparse vegetation Partitioning of solar radiation Obtaining new information on canopy structure from MISR products MISR Land Surface Products over validation sites Availability of MISR surface reflectance data LAI and FPAR retrievals Validation of MISR LAI product Validation of the LAI product at a cropland site in Alpilles Validation of MISR LAI product at other sites Conclusions...82 A rank based algorithm for aggregating land cover maps with minimal information loss Introduction Data set and methods MODIS land cover map Metrics to represent image information Aggregation algorithms Results and discussion Conclusions Concluding remarks Bibliography viii

9 Curriculum Vitae ix

10 List of Tables Table 2.1. Optimal values of relative uncertainties, ν A, in modeled and observed BHRs Table 2.2. Optimal values of relative uncertainties, ν r, in modeled and observed BRFs.39 Table 2.3. Disagreement between biome types assigned by the MISR algorithm and the six biome classification map used in the study for different values of QA Table 2.4. Mean values and standard deviations of the relative difference for different biome types and QAs Table 2.5. Most probable values of the relative difference and probabilities of < χ for different biome types, QAs and disagreement levels χ Table 3.1. Validation sites and availability of MISR BHR Table 3.2. MISR Retrieval Applicability Mask Table 4.1. Coverage of the 17 International Geosphere-Biosphere Programme (IGBP) classes in the North American data set shown in Figure Table 4.2. Images used to evaluate the aggregation procedures x

11 List of Figures Figure 2.1. Flow chart of the relationship between MISR LAI/FPAR algorithm and data Figure 2.2. Ratio of valid pixel number to total pixel number, in percentage Figure 2.3. Histograms of the difference between nominal and actual viewing angles. The maximum deviation is given for each camera Figure 2.4a. Distribution of pixel counts in the red and near-infrared DHR space for Broadleaf Forests Figure 2.4b. The mean and standard deviation of HDRFs in the perpendicular plane at red and NIR wavelengths derived from pixels around the data peak for Broadleaf Forests Figure 2.4c. The mean and standard deviation of HDRFs at red and NIR wavelengths derived from pixels around the data peak for Grasses & Cereal Crops Figure 2.4d. Mean and standard deviation of MISR BHR values from pixels near the data peak Figure 2.5. Histograms of the coefficient of variation (standard deviation/mean) of the MISR BHR from path 178 for 3 different days, orbit 6393 (Mar 1, 2001), 6626 (Mar 17, 2001) and orbit 6859 (April 2, 2001) Figure 2.6. Mean coefficient of variation of DHR at Red and NIR wavelengths derived from spatial and temporal analyses of MISR data Figure 2.7a. Fraction of energy, (1-DHR), absorbed by the vegetated surface at Red and NIR wavelengths by different cover types xi

12 Figure 2.7b. Adjusted single scattering albedos of different cover types used by the operational MISR LAI/FPAR software Figure 2.7c. Histogram of LAI values produced by the MISR algorithm using surface reflectances located around the data peak Figure 2.8a. Retrieval index as a function of biome type and Quality Assessment (QA) for optimal set of relative uncertainties Figure 2.8b. Biome Identification index (BI) as a function of biome type and QA for the optimal set of relative uncertainties Figure 2.8c. Performance Index (PI) as a function of biome type for the optimal set of relative uncertainties Figure 2.9. Histograms of the relative difference between reference and retrieved LAI values for different biome types and QAs Figure (a) NDVI-LAI and (b) NDVI-FPAR regression curves for Grasses & Cereal Crops and Broadleaf Forests Figure NDVI-LAI regression curves for (a) Grasses & Cereal Crops and (b) Broadleaf Forests for different values of QA Figure 3.1. Top Panel: Angular variation of BRF in red and NIR spectral bands for shrubs. Bottom Panel: Values of the BRF at red and NIR wavelengths as a function of the view zenith angle form a curve on the RED vs. NIR plane Figure 3.2. Angular signatures on the RED vs. NIR plane for five land covers xii

13 Figure 3.3. Temporal variation in the mean signature of a broadleaf forest located in the 2 by 2 degree area centered on the Harvard Forests EOS Core Validation Site Figure 3.4. Annual course of leaf area index (left panel) and fraction vegetation absorbed PAR (right panel), for year 2000, from MODIS and MISR data for the Walnut Gulch (San Pedro) site in Arizona Figure 3.5. Partitioning of the top-of-canopy PAR into its canopy and ground absorbed portions Figure 3.6. (a): Using MISR Level 2 Land Surface Data over Africa from 23 April 2002 (path 176, orbit 12480, blocks ), the negative logarithm of FGROUND is plotted against mean LAI normalized to the cosine of the solar zenith angle Figure 3.7. Statistical summary of the RAM flags for Agro and Harvard Forests sites Figure 3.8. Statistical summary of cases for which (i) a LAI/FPAR retrieval was not performed due to the absence of input; (ii) LAI/FPAR algorithm failed; and (iii) a successful LAI/FPAR retrieval was performed Figure 3.9. Temporal variation in the retrieval index for six validation sites Figure Annual profiles of the mean LAI temporal variation derived from MODIS (line) and MISR (symbols) data for Alpilles, Konza, Agro, Mongu, Harvard Forests and Ruokolahti sites Figure Annual profiles of the mean LAI temporal variation over biome 1 (grasses o o and cereal crops) and biome 3 (broadleaf crops) in 0.5 by 0.5 areas centered xiii

14 in Konza and Agro sites generated by the re-calibrated LAI and FPAR algorithm Figure Reference LAI maps at 30 m (left panel) and 1.1 km (right panel) resolutions over 16.5km 16.5km area containing the Alpilles site in the MISR Path 196 Space Oblique Mercator (SOM) projection Figure Distribution of the version 3.3 MISR LAI and reference LAI values at a resolution of 1.1 km Figure Linear regression models of MISR LAI with respect to the MODIS LAI for 4 validation sites Figure 4.1. MODIS land cover image for North America, at 1 km resolution in Lambert Azimutal equal area projection Figure 4.2. Illustration of the algorithms used in this paper Figure 4.3. Illustration of the 10 block types and the notation for the ranked aggregation algorithm Figure 4.4. Influence of spatial aggregation technique on class proportions Figure 4.5. Influence of spatial aggregation on image contagion Figure 4.6. Influence of spatial aggregation on class fragmentation by means of the Monmonier Fragmentation metric Figure 4.7. Influence of spatial aggregation on the mean probability of adjacency Figure 4.8. Analysis of pattern change due to spatial aggregation using similarity metrics Figure 4.9. Assessment of unpredictability to illustrate algorithm performance xiv

15 Figure Block assignment to a minority class as a parameter of algorithm performance Figure Accuracy of images aggregated using various aggregation algorithms xv

16 List of Abbreviations Nomenclature ASDC BHR BI BRF CART COVLAI DAAC DHR FPAR HDRF LAI LaRC LUT MISR MODIS NASA NDVI NIR PI QA Atmospheric Sciences Data Center Bi-Hemispherical Reflectance Biome Identification Index Bi-directional Reflectance Factor Canopy Architecture Radiative Transfer file Coefficient of Variation of LAI NASA Distributed Active Archive Centers Directional Hemispherical Reflectance Fraction of Photosynthetically Active Radiation absorbed by vegetation Hemispherical-Directional Reflectance Factors Leaf Area Index Langley Research Center Look-Up Table Multi-angle Imaging SpectroRadiometer Moderate Resolution Imaging Spectroradiometer National Aeronautics and Space Administration Normalized Difference Vegetation Index Near Infra-Red Performance Index Quality Assessment xvi

17 RI SOM Retrieval Index Space Oblique Mercator projection xvii

18 1 Chapter 1 Introduction 1.1 Background Land Surface Processes Modeling The terrestrial biosphere is a major component of the climate system that exhibits complex interactions of processes between the atmosphere, land and oceans. Exchanges of energy, mass, and momentum inside the climate system are controlled by plant canopies. A major research question in terrestrial biophysical science is how changes in land-surface processes/properties will interact with regional and global climate. To address this question, several types of modeling frameworks have been established: Land Surface Models (LSMs), which include the Biosphere-Atmosphere Transfer (BATS) model (Dickinson 1984), the Simple Biosphere (SiB) model (Sellers et al. 1986), and the Community Land Model (CLM) (Bonan, et al., 2002); ecosystem productivity models, which include the NASA - Carnegie Ames Stanford Approach (NASA-CASA) (Potter et al., 1993); and many other hydrology, biogeochemistry and ecology models. All land process models require a suite of land-surface variables, i.e., land cover, Leaf Area Index (LAI), Fraction of Photosynthetically Active Radiation absorbed by vegetation (FPAR), roughness length, and albedo. Several intensive regional scale field campaigns, such as the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE), the Hydrological-Atmospheric Pilot Experiment (HAPEX) and the Boreal Ecosystems Atmosphere Study (BOREAS), were launched to develop and test land process models. However, these observational campaigns have a limited temporal

19 2 and spatial coverage and can not fully address the problem of parameterization and evaluation of those models. Remote sensing is the only cost-effective means to regularly monitor the global land surface parameters. On December 18, 1999, in the framework of Earth Observing System (EOS), NASA launched the Terra platform on the Earth orbit with five state-of-the-art remote sensing instruments - ASTER, CERES, MISR, MODIS and MOPITT. These instruments deliver a comprehensive list of climate research parameters about atmosphere, land, and ocean. This dissertation addresses the progress of LAI, FPAR and land cover research in support of the MISR project MISR and Multiangular Remote Sensing The Multi-angle Imaging SpectroRadiometer (MISR) instrument is designed to provide global imagery at nine discrete viewing angles and four visible/near-infrared spectral bands. The nominal view angles of the nine cameras are: 0.0, +/- 26.1, +/- 45.6, +/ and +/ The four spectral bands are blue ( nm), green ( nm), red ( nm) and NIR ( nm). Measurements are taken at three spatial resolutions: 275m, 550m, and 1100m. The MISR data are in the format of path (swath) and orbit. The entire Earth is covered in 233 paths; each path is divided into 180 blocks measuring km (cross-track) by km (along track) area. The MISR data are processed and archived at the NASA Langley Atmospheric Sciences Data Center. The objective of the MISR mission is to characterize the angular heterogeneity of the Earth radiation regime, and to monitor physical properties of aerosol, clouds and land

20 3 vegetation (Martonchik et al., 1998a; Diner et al., 1998). MISR is one of the few space-borne instantaneous multiangular sensors that have been operationally implemented, e.g., the Along Track Scanning Radiometer (ATSR-2, two observational angles, at 1 km resolution) and the Polarization and Directionality of the Earth s Reflectances instrument (POLDER-1 and -2, up to 14 observational angles, at 6 km resolution) (Stricker et al., 1995; Deschamps et al., 1994; Diner et al., 1999a). Implementation of multiangular remote sensing techniques promises to improve the accuracy of various geophysical parameter retrievals by exploring the angular domain of data, as specified by Bidirectional Reflectance Distribution Function (BRDF) (Diner et al., 1999a, Zhang et al., 2000). BRDF, whose magnitude and angular shape are governed by the composition, density, and directional structure of the reflecting medium, depicts the relationship between surface reflectance and sun-view geometry (Nicodemus et al., 1977, Kimes, 1983). Conventionally single-angle observations, which are acquired at different times, are composited into a multi-angle observation to reconstruct the BRDF for a particular scene (Li, 1996; Cabot and Dedieu, 1997; d Entremont et al., 1999). For instance, the EOS MODerate Resolution Imaging Spectroradiometer (MODIS) uses 16 days worth of directional observations to reconstruct the directional patterns (Wanner et al. 1997; Lucht et al. 1998). However, changes in surface and atmospheric conditions during this time can add errors in the reconstruction of the BRDF. MISR measurements avoid the above and other limitations in single-angle remote sensing by making an instantaneous retrieval of the BRDF. Multi-angle information helps to differentiate atmospheric effects from surface

21 4 radiative effects. An atmospheric correction algorithm that accounts for surface anisotropy and heterogeneity has been developed by taking advantage of multi-angle information (Martonchik et al., 1998a, b). The MISR Level 2 land surface parameters product suite includes the spectral hemispherical-directional reflectance factors (HDRF) at the nine MISR view angles, bihemispherical reflectances (BHR), bidirectional reflectance factor (BRF) and the directional hemispherical reflectance (DHR). HDRF and BHR characterize the surface reflectance under ambient sky conditions, i.e., direct and diffused illumination. BRF and DHR are defined for the unique case when atmosphere is absent, that is, the black sky conditions. BHR, DHR and BRF are used to derive LAI and FPAR. The MISR LAI algorithm also produces a land cover product. This dissertation focuses on the MISR LAI product suite, which includes LAI, FPAR and land cover MISR LAI and FPAR Algorithm LAI, the Leaf Area Index, is defined as the one-sided green leaf area per unit ground area in broadleaf canopies and as the projected needle leaf area per unit ground area in coniferous canopies. FPAR, the Fraction of incident Photosynthetically Active Radiation ( nm) absorbed by vegetation canopy, is defined for ambient sky conditions, i.e., it accounts for both diffused and direct illumination. The first global maps of LAI and FPAR were produced from Advanced Very High Resolution Radiometer (AVHRR) data using empirical methods (Myneni et al., 1997, Sellers et al., 1996). Specifically, the empirical relationships between LAI, FPAR and Normalized Difference Vegetation Index (NDVI) were used (Nemani et al., 1993, Chen

22 5 et al., 1996). The accuracy of the generated LAI/FPAR maps was substantially limited by several factors, i.e., high uncertainties in AVHRR data, the limited ability of empirical methods to explain dependence of NDVI on view-illumination, variability in soil reflectances, and vegetation optical properties (Asrar et al., 1992; Friedl et al., 1995, 1996). The MISR LAI/FPAR research is targeted to improve the accuracy of LAI/FPAR retrievals based on advancements in remote sensing technology and the retrieval technique. The MISR LAI/FPAR algorithm uses a three-dimensional formulation of the radiative transfer model to establish relations between the vegetation-specific spectral and angular signatures of surface reflectances, and the structural and optical characteristics of vegetation canopies (Knyazikhin et al., 1998a). For the purpose of retrievals, global vegetation is stratified into six canopy architectural types or biomes: grasses and cereal crops (biome 1), shrubs (biome 2), broadleaf crops (biome 3), savannas (biome 4), broadleaf forests (biome 5) and needleleaf forests (biome 6) (Myneni et al., 1997). The LAI/FPAR retrieval technique is based on a Look-Up Table approach for efficiency in the execution of the algorithm, and all of the necessary radiative transfer parameters have been precomputed and stored in the Canopy Architecture Radiative Transfer (CART) file. The MISR algorithm retrieves LAI and FPAR values using a two-step process. The first step involves a comparison of the MISR BHR with those simulated with CART for a whole range of LAI, canopy structure and soil/understory patterns over all biomes. For each vegetation type, the algorithm identifies all LAI values and soil patterns for which modeled and observed BHR differ by an amount equivalent to or less than the combined

23 6 uncertainty in model and observations. FPAR is calculated for each such LAI and soil pattern. For the second test, this set is used to calculate the conditional mean LAI and FPAR and their dispersions. The conditional mean LAI and FPAR are defined as the LAI and FPAR averaged over all soil or understory models for a given biome type. The most probable LAI, FPAR and biome type are chosen, using the results from the biome which has the least coefficient of variation (dispersion divided by mean). The vegetation type, LAI and soil patterns that pass the first test are subject to the second test, which is a comparison of modeled and observed directional signatures. The conditional LAI values and their spread, as well as the most probable values of LAI and FPAR, are archived in the MISR surface parameters product. An additional goal of the MISR LAI/FPAR algorithm is the classification of vegetation in terms of the biome types described before, a parameter that is usually specified as an input to other algorithms that use single-angle observations. Based on the output archived, the following biome identification algorithm will be examined here. Assuming that more than one of the candidate biomes passes the second test (the comparison of retrieved and modeled directional reflectances), the biome type with the minimum coefficient of variation ( LAI 2 /LAI 2 ) of LAI (COVLAI) is chosen as the most representative of the observed vegetation type for that pixel. If the same minimum COVLAI is found for more than one biome type, then the biome type with the smallest mean LAI is chosen. If this process fails to identify a unique biome type, the retrieval is classified as unsuccessful (Hu et al., 2003).

24 7 Prior to the launch of MISR sensor, the MISR LAI/FPAR algorithm was prototyped with available POLDER data (Zhang et al., 2000). The MISR LAI/FPAR algorithm was operationally implemented and the MISR LAI/FPAR products have been generated at the Langley Atmospheric Sciences Data Center (ASDC) since October 2002 (Hu et al., 2003). At the current stage, three research directions in the development of the MISR LAI/FPAR products are most important: a) algorithm refinement; b) analysis of the product time series; c) product validation (Hu et al., 2003) Land Cover Aggregation In addition to LAI and FPAR, the MISR LAI/FPAR products also generate global land cover product. Land cover is also in high demand for land surface process modeling (Section 1.1.1). A theoretical basis for land cover mapping from MISR multiangular signatures of different vegetation types was developed (Zhang et al., 2002a,b). Driven by application needs, an important question has arisen now how to scale up or aggregate land cover from remote sensing observation resolution to the regional/global resolution for climate research. Coarsening the spatial resolution leads to a loss of spatial details and alteration of the statistical and spatial characteristics of the original data at a rate that depends on the spatial structure or heterogeneity of the landscape (Woodcock & Strahler, 1987; Townshend & Justice, 1988; Moody & Woodcock, 1994, 1995, 1996). Landscape patterns, as observed by digital images that are generated by remote sensing appear or disappear at different scales (Farina 1998). Rare land cover types are lost when resolution

25 8 becomes coarser; patchy arrangements disappear more rapidly with decrease in the resolution than contagious ones (Turner et al., 1989). This phenomenon is usually more pronounced when the elements which compose the spatial pattern (e.g., patches) are scattered and are as small as or smaller than a pixel of the aggregated image. Models that use aggregated data become scale-dependent, i.e., their predictions differ when input data of different resolutions are used (Bian & Butler, 1999). Although this effect is wellrecognized by the GIS, remote sensing, and other science communities that use spatial information (e.g., Moody & Woodcock, 1994, 1995; Marceau & Hay 1999; Milne & Cohen 1999), there are very few papers on the effects caused by different aggregation techniques. Studies that require aggregation often employ the most convenient method without taking all the effects into account. This may jeopardize the integrity of the studies as well as subsequent decision-making process Statement of the Research Problems This dissertation establishes a research basis to analyze and refine the MISR LAI/FPAR product suite and thus facilitate utilization in the environmental applications of the three MISR land products - LAI, FPAR and land cover. Specifically, the goals are to: 1) Analyze the uncertainties of the MISR LAI and FPAR products as a function of uncertainties in the MISR surface reflectances and land cover classification. This research provides a basis for transitioning the MISR LAI/FPAR products from beta to provisional status;

26 9 2) Investigate the spatial and temporal coverage, accuracy and consistency of the MISR LAI/FPAR product. This research provides a basis for transitioning the MISR LAI/FPAR products from provisional to validation stage 1 status; 3) Develop a rank-based algorithm for aggregating the retrieved MISR land cover from moderate resolution of remote sensing measurements to a coarse resolution of climate models with a minimal information loss by prototyping with the MODIS land cover product. The organization of the above is described below Flow of the Research Now that the MISR data has become publicly available, the major question is - what is the performance of the MISR LAI/FPAR retrievals? In general, the performance of the LAI/FPAR retrievals is restricted by two factors the uncertainties in the algorithm input and the uncertainties in the radiative transfer (RT) model. The input consists of the MISR surface reflectances. The model uncertainties correspond to the accuracy of a canopy radiation model to approximate the observed variability in surface reflectances. The accuracy of the LAI/FPAR retrievals is highly dependent on the specification of the above uncertainties in the algorithm. March 2000 MISR data over Africa is used to quantify: a) the uncertainties in the MISR surface reflectances; b) the impact of uncertainties in surface reflectances on the uncertainties in the retrieved LAI and FPAR fields; c) the impact of MISR biome misclassification on MISR LAI retrievals. This

27 10 research provides the basis for transitioning the MISR LAI/FPAR products from beta to provisional status. Detailed research is described in Chapter 2. Further study is focused on analysis of spatial and temporal coverage, accuracy and consistency of the MISR LAI/FPAR products. Lessons learned from the previous generation of global land imaging systems indicate that validation is an essential part in the development of biophysical product from satellite data (Justice & Townshend, 1994; Cihlar, Chen, & Li, 1997) and is required to quantify the reliability of satellite biophysical products (Baret et. al., 2004). Analysis conducted in this part of the research established the basis for transitioning the MISR LAI/FPAR products from provisional to stage 1 validated status, i.e., product accuracy has been estimated with a small number of independent ground truth measurements. To further evaluate the quality of the MISR LAI and FPAR products, spatial and temporal coverage of LAI retrievals over the above validation sites were analyzed. Also the consistency and complementarity between various MISR Level 2 land products derived from independent algorithms are assessed to demonstrate the potential utility in monitoring and modeling studies as well as to explore the potential for enhanced information retrieval through innovative manipulation of multiple products. These investigations are presented in Chapter 3. Finally, Chapter 4 describes the land cover aggregation research. Aggregation of moderate resolution land cover is required to meet climate research application requirements at coarse resolution. The widely used majority aggregation algorithm always loses the minority classes, especially the widely scattered minority classes at coarse resolution, and the spatial patterns will change. To keep the homogeneity, majority

28 11 and adjacency within an aggregate window and avoid missing minority classes, and thus conserve the information in the original image, a rank-based aggregation algorithm for aggregating land cover data sets to coarser resolutions with minimal change in information content is developed and compared to majority and random algorithms at continental scale. Patterns in a fine resolution image and the number of pixels of each class that should be present in the coarser resolution data set are predefined. Spatial pattern metrics quantifying class proportions, contagion, and fragmentation and similarity metrics such as Euclidean distance and Czekanowski coefficient are used to benchmark the ranked, random and majority aggregation algorithms in conserving the information in the original image.

29 12 Chapter 2 Performance of the MISR LAI and FPAR algorithm: a case study in Africa 2.1. Introduction The Multi-angle Imaging SpectroRadiometer (MISR) is an instrument on board the EOS-Terra platform. MISR collects observations of the Earth's surface at 1.1 km spatial resolution with the objective of providing atmospherically corrected reflectance properties of most of the land surface and the tropical ocean (Martonchik et al., 1998; Diner et al., 1998). The land surface reflectance parameters currently being generated at the NASA Langley Atmospheric Sciences Data Center (ASDC) include the spectral hemispherical-directional reflectance factors (HDRF) at the nine MISR view angles and the associated bihemispherical reflectances (BHR). The hemispherical directional reflectance factor (HDRF) and the bihemispherical reflectance (BHR) characterize the surface reflectance under ambient sky conditions, i.e., direct and diffuse illumination. The bidirectional reflectance factor (BRF) and the directional hemispherical reflectance (DHR) are defined for the unique case when the atmosphere is absent, that is, black sky conditions. An algorithm for the generation of vegetation green leaf area index (LAI) and the fraction of photosynthetically active radiation absorbed by vegetation (FPAR) from MISR BHR and BRF was implemented for operational processing in October 2002 (Knyazikhin et al., 1998a). An additional goal of the MISR LAI/FPAR algorithm is the classification of global vegetation into biome types; a parameter that is usually specified

30 13 as an input in certain algorithms that use single-angle observations for the retrieval of surface properties (Myneni et al., 2002). In this paper, we describe performance of the implemented version of the MISR LAI/FPAR algorithm with retrievals from Africa as a test case. The quality and spatial coverage of BHR and BRF determine the quality and spatial coverage of the LAI and FPAR products. Therefore, we start with a description of the MISR data and analyses of uncertainties in MISR surface reflectances, followed by a discussion of the spatial scaling issues associated with the MISR LAI/FPAR algorithm. At this initial stage, analyses that assess performance of the algorithm as a function of uncertainties in the MISR BHR and BRF data and the development of retrieval quality indicator flags are emphasized MISR data The MISR data distributed from the NASA Langley Atmospheric Sciences Data Center were used in this study. The MISR data are in the format of path (swath) and orbit. The entire earth surface is covered in 233 paths; each path is about 360 km wide from East to West. Each orbit corresponds to data acquired over a path for a particular date. Each path is divided into 180 blocks measuring km (cross-track) x km (along-track), that is 512 x 128 pixels. For a given path, a numbered block always contains the same geographic locations. The MISR Level 2 Surface Parameters Product contains information on land surface directional reflectance properties, albedos (both spectral and PAR integrated) and

31 14 associated radiation parameters. These data, in HDF format and at 1.1 km spatial resolution, are the source of BRFs, HDRFs, DHRs and BHRs (expansion of all abbreviations is given in a list at the beginning of this article). The view angles at the surface for each of the nine MISR cameras, as well as the incident solar angle at the surface, are contained in the MISR Geometric Parameters Product. This information is at a spatial resolution of 17.6 km, and is input to the LAI/FPAR algorithm. The latitude and longitude information is contained in the MISR Ancillary Geographic Product (MISR Data Products Specifications Document). A look-up table (LUT) approach is used to rapidly model the radiative transfer process of complex canopy/soil models to determine the matching modeled reflectances and the associated values of LAI and FPAR. For efficiency in execution of the algorithm, all necessary radiative transfer parameters have been precomputed and stored in the Canopy Architecture Radiative Transfer (CART) file. MISR data (version v2.2_i4) from Africa covering the vegetated surface between N and S were selected for this investigation as in situ LAI and FPAR measurements were available from several sites in Southern Africa (Tian et al., 2002a and 2002b). These field data, although collected in 2000, are useful for estimating certain algorithm parameters, as detailed elsewhere in this article. In particular, the analysis is focused on Southern Africa with MISR data from March 2001 the earliest period for which the MISR LAI/FPAR products are available. MISR has a ground track repeat cycle every 16 days and achieves global coverage every 9 days. However, in view of cloud cover, data from an entire month are required to

32 15 obtain full coverage of Southern Africa. Assembling the data set in this fashion meant an implicit assumption that vegetation changes were minimal in this one month composite period, introducing uncertainty into the derived results. This uncertainty will be assessed during the course of this investigation. The moderate spatial resolution, multispectral and multiangle aspects of the MISR instrument imply large data volumes and hence the need for analysis stratified by biome type. Raw data that were corrupted or with missing geometry information (flagged with fill values) were excluded from the analysis. Likewise, invalid reflectance data, for example, BHRs greater than 1, were ignored. A schematic chart of the data processing is shown in Figure 2.1. The ratio of pixels with valid data to the total number of vegetated pixels from path 162 to 203 is shown in Figure 2.2, separately for different biomes. The data from each path are from different days in March About 46% of the pixels contain valid data, useful as inputs to the algorithm. This number changes by date and by biome type, and may be as low as 31.5% in the case of tropical humid forests, where cloud cover is persistent Data analysis The nominal view angles for the nine cameras are 0.0, +/- 26.1, +/- 45.6, +/ and +/ (in degrees). The variations in actual view angles relative to the specification, for the fore and aft off-nadir sensors, are shown in Figure 2.3. The maximum deviation in view zenith angles is for camera A fore and aft (4.95 and 4.84 degrees, respectively). These deviations decrease with increasing view zenith angle. Most of the deviations are

33 16 positive. This is a geometric effect. The MISR data are in the Space Oblique Mercator (SOM) projection, in which the reference meridian nominally follows the spacecraft ground track. It maps the earth latitude and longitude to a SOM coordinate system that is approximately fit into MISR swath. The center of the block has the nominal view angles; since a block is 563 km wide, the view angle increases from the center to the edge of the block. The effect is most pronounced in the nadir camera, where the view angle is 0 degree at the center and 18 degrees at the edge of the block. While this problem can be avoided if one uses data from the center of the swath only, the MISR retrieval utilizes these large angle data. Even with the variations they still fall within the view angle bin limits in the CART file. Uncertainties in land surface reflectances determine the quality of retrieved LAI and FPAR values (Wang et al, 2001). The calibration and processing for atmospheric effects of the measured radiances induces uncertainties in surface reflectances. Land surface reflectance parameters, such as BRF and BHR, are inputs of the LAI/FPAR algorithm. Therefore, the uncertainties in MISR surface reflectance product are evaluated below, using two different methods, spatial and temporal. MISR surface reflectance data were first sorted according to the biome type. The atlaunch Moderate Resolution Imaging Spectroradiometer (MODIS) biome map was used to identify the pixel biome type (Lotsch et al., 2003). 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 & Cereal Crops (biome 1), Shrubs (biome 2), Broadleaf Crops (biome 3),

34 17 Savannas (biome 4), Broadleaf Forests (biome 5) and Needleleaf Forests (biome 6). The site-based accuracy of this map is 73% (Lotsch et al., 2003). The kappa coefficient (κ) (Cohen, 1960), which provides a correction for the proportion of chance agreement between reference and test data, is 0.68 (Lotsch et al., 2003). When compared to maps generated from the same data but classified using the International Geosphere Biosphere Program (IGBP) classes (Loveland et al., 1995; Hansen et al., 2000), the biomes were mapped with ~5% higher overall accuracy (Lotsch et al., 2003). It should be noted that this classification accuracy analysis is based on sites that are established as priori pure and therefore will not include errors due to sub-pixel mixing. The upper-left and bottomright latitude and longitude of the MISR data block were used as georeferences to reproject the at-launch MODIS biome map to the MISR SOM projection. Data density distribution functions, defined as the number of pixels per unit area in the red-nir space, were evaluated for each biome type. Pixels located around the data peak, i.e. the maximum pixel number, can be interpreted as the set of pixels representing the most probable pattern of canopy structure. As an example, the data density distribution function for Broadleaf Forests is shown in Figure 2.4a. Such pixels were selected for further analysis. The mean and standard deviation of the HDRFs and BHRs evaluated from pixels about the data peak (the spatial method) are shown in Figs. 4b-d, for different biomes. Uncertainties in HDRFs are larger at large view angles (except the A fore and aft camera), and greater in the near-infrared channel than the red channel, with one exception (standard deviations in the red channel for the nine view angles, from angle 1 to angle 9

35 18 are 0.031, 0.019, 0.015, 0.016, 0.016, 0.014, 0.013, 0.019, 0.042; standard deviations in the NIR channel for the nine view angles are 0.033, 0.026, 0.024, 0.023, 0.024, 0.019, 0.017, 0.022, 0.040). The uncertainties are generally similar in the fore and aft angles. The BHR magnitudes with respect to biome type, shown in Figure 2.4d, display expected behavior. In the red channel, Shrubs are brighter and the BHR magnitude decreases with increased tree cover. In the near-infrared, the opposite is seen. Although the uncertainties are generally comparable at both wavelengths, they are considerably larger in the red channel on a relative basis. The uncertainties in Figs. 4b-d may result from variations in view angles, sun angles, variation in vegetation canopy structure and atmospheric correction. Deviations from nominal view zenith angles were small (Figure 2.3). The angular signature of Broadleaf Forests which is in the 90 degree azimuth plane relative to sun is shown in Figure 2.4b. The solar zenith angle and azimuth are 23 ±2 and 288 ±9, respectively. For Grasses & Cereal Crops (Figure 2.4c), the solar zenith angle is 32 ±3, and solar azimuth is 232 ±5. Values of the difference between solar and view azimuth are 217 ±10 for forward cameras, and 37 ±10 for afterward cameras. Variations due to sun-view geometry differences, therefore, are small. Vegetation cover type mixture may also contribute to uncertainties in reflectance data. Variations in canopy structure due to biome mixtures are minimized by selecting pixels around the data peak. These pixels may be considered representative of a biome type with minimal mixing. Therefore, uncertainties due to biome mixture are unlikely to be the cause of variations seen in Figs. 4b-d.

36 19 Thus, uncertainties in BHR and HDRF remain even after accounting for minor uncertainties due to variations in view angles and cover type. The residual uncertainties may be due to atmospheric correction, and this is further investigated in the following temporal analysis. In this method, we assume the vegetation structure to remain unchanged during the month of March (a period of low vegetation activity at these African sites). The coefficients of variation (standard deviation divided by the mean) of the MISR BHR in Blue, Red, and NIR bands from three different days from path 178 are shown in Figure 2.5 for different biomes. The histograms are wide, especially in the blue band for both Grasses & Cereal Crops and Broadleaf Forests, which is likely due to correction for atmospheric effects. Likewise, the histograms are broad at the red band, especially in the case of Broadleaf Forests. The most probable value of the coefficient of variation is least for the NIR band (about 0.15 for Grasses & Cereal Crops and about 0.4 for Broadleaf Forests). Data from only three different days in March were available for this analysis and this sample is clearly insufficient. These uncertainties are considered as very rough estimates of the upper bounds of uncertainties in the MISR surface reflectances. At least in the case of Broadleaf Forests, the LAI does not change much during the peak green season. Therefore, variations in canopy structure can be excluded for this cover type. Coefficients of variation of solar zenith angle and azimuth did not exceed 0.07 for data shown in Figure 2.5 and thus the impact of the sun angular geometry on variation in the MISR

37 20 BHR is negligible. The large uncertainties here may be due to errors in pixel geolocation, or may be due to atmospheric correction. From the comparison presented in Figure 2.6 between uncertainties estimated from spatial (Figure 2.4) and temporal (Figure 2.5) analyses, it is obvious that uncertainties from the temporal analysis are greater than the uncertainties from spatial analysis for most biome types, with the exception of Shrubs, where both kinds of uncertainties are similar in both bands. The uncertainties of the temporal analysis are significant and they are taken as the upper bounds in the LAI/FPAR retrievals discussed in this article MISR LAI/FPAR algorithm As mentioned before, the MISR algorithm retrieves LAI and FPAR values using a two-step process. The first step involves a comparison of the MISR BHR with those determined from a suite of canopy models, which depend on biome type, canopy structure, and soil/understory reflectances. All canopy, soil and biome patterns for which the modeled and observed BHRs in the four spectral bands differ by an amount equivalent to or less than the uncertainty in model and observations are considered as acceptable solutions. FPAR is calculated for each acceptable solution. For each biome pattern bio, bio = 1, 2,..., 6, the algorithm then evaluates mean LAI 1 (bio) and FPAR 1 (bio) over acceptable solutions, their dispersions, LAI 1 (bio), FPAR 1 (bio), and number N sol,1 (bio) of acceptable solution. Equation (2.2) with overall uncertainties in modeled and observed BHRs is used to execute the first step. The biome, canopy, and soil patterns that pass this comparison test are subject to the second step, which is comparison of

38 21 directional signatures of modeled and observed BRFs. Again, for each biome type, mean LAI 2 (bio) over acceptable solutions, its dispersion, LAI 2 (bio) and number N sol,2 (bio) of acceptable solutions are evaluated. Equation (2.3) with appropriate overall uncertainties is used to execute the second test. For each 1.1 km MISR pixel within which the BHR/BRF retrieval was performed, LAI 1 (bio), LAI 1 (bio), N sol,1 (bio), LAI 2 (bio), LAI 2 (bio), and N sol,2 (bio), bio = 1, 2,..., 6, are archived in the MISR Aerosol/Surface Product. The FPAR is evaluated and archived for each 17.6 km region. An additional goal of the MISR LAI/FPAR algorithm is the classification of vegetation in terms of biome types described in the previous section, a parameter that is usually specified as an input to other algorithms that use single-angle observations. Based on the output archived, the following biome identification algorithm will be examined here. Assuming that more than one of the candidate biomes passes the second test (the comparison of retrieved and modeled directional reflectances), the biome type with the minimum coefficient of variation ( LAI 2 /LAI 2 ) of LAI (COVLAI) is chosen as being most representative of the observed vegetation type for that pixel. If the same minimum COVLAI is found for more than one biome type, then the biome type with the smallest mean LAI is chosen. If this process fails to identify a unique biome type, the retrieval is classified as unsuccessful Scaling of the algorithm In the MISR LAI/FPAR algorithm, the three-dimensional radiative transfer equation is used to simulate canopy reflectances as a function of biome type, sun-view geometry

39 22 and canopy/soil patterns (Kynazikhin et al., 1998a). Global vegetation is stratified into six canopy architectural types or biomes mentioned earlier. The structural attributes of these biomes are parameterized in terms of variables that the radiative transfer equation admits (Myneni et al., 1997). The radiative transfer equation was adjusted to model canopy reflectances of the six biome types at 30 m spatial resolution, which is taken as the reference resolution. However, when the spatial resolution of the imagery becomes significantly coarser than 30 m, both the degree of biome mixing within a pixel and the number of mixed pixels in the imagery increase. LAI retrieval errors increase as biome mixing in pixels increases if the within-pixel heterogeneity is not accounted for (Tian et al, 2002a and 2002b). Errors for the pixels in which forests are minority biomes in nonforest pixels are particularly larger than pixels within which forest biomes are mixed with one another. Thus, the retrieval algorithm must be scale-adjustable, to allow for spatial scale effects. Here we follow a technique developed by Tian et al (2001), which accounts for pixel heterogeneity by modifications to the single scattering albedo that the radiative transfer equation admits through the use of land cover fractions. To specify appropriate values for the single scattering albedo, the MISR DHRs corresponding to the peak green season are located in the red-nir spectral space for each of the biome types (Figure 2.4a). Pixels located around the data peak can be interpreted as the set of pixels representing the most probable pattern of canopy structure. Neglecting contribution of the surface underneath the canopy, the most probable value of DHR at wavelength λ is related to canopy transmittance and absorptance at this wavelength as (Knyazikhin et al., 1998a; Panferov et al, 2001; Shabanov et al., 2003; Zhang et al., 2002)

40 23 q 1 ω λ 1 DHR λ = + (1 q). (2.1) 1 ω p 1 ω p λ t λ i Here ω λ is the single scattering albedo defined as the ratio of energy scattered by the elementary volume formulated for the radiative transfer equation, to energy intercepted by this volume; q is the probability that a photon in the incident radiation will arrive at the bottom of the canopy without suffering a collision (uncollided radiation), ω λ p t and ω λ p i are portions of collided radiation in total radiation transmitted and intercepted by the vegetation canopy, respectively (Shabanov et al., 2003; Wang et al., 2003). The wavelength independent parameters q, p t, and p i are functions of LAI. (2.1) expresses the energy conservation law, namely, the radiation absorbed by a vegetated surface (the lefthand side) is the sum of radiant energy absorbed by the underlying surface and vegetation (the first and second terms on the right-hand side of equation (2.1), which are the canopy transmittance, tbs, λ, and absorption calculated for the case of a black surface underneath ρλ the canopy). In the case of a reflecting Lambertian surface, the term 1 ρ r t t s, λ bs, λ λ s, λ should be subtracted from the left-hand side of equation (2.1) to account for the contribution of the ground to the canopy leaving radiation (see equation (41) in Knyazikhin et al, 1998a). Here ρ λ is the reflectance of the underlying surface; t s, λ and rs, λ are fractions of radiation transmitted and reflected by the vegetation canopy if it were illuminated from below by an isotropic source (Knyazikhin et al, 1998a). Leaf area index values corresponding to the most probable canopy realization must be known in order to calibrate the algorithm, and this is usually accomplished through field

41 24 measurements. Given biome type and LAI, as well as measured DHR λ, and modeled q, pt and pi corresponding to this LAI value, the algorithm is then adjusted for data resolution by finding values of the single scattering albedo ω λ which provide the best agreement between the left and right sides of equation (2.1). Values of DHR for Africa, obtained from MISR retrievals (1-23 March 2001) and field measurements made during the SAFARI 2000 wet season campaign (3-18 March 2000) and the Operation Canopy La Makande 99 campaign (2-10 March 1999) (Panferov et al, 2001), were used to scale the LAI/FPAR algorithm to the MISR resolution. The MODIS biome classification map was used to sort the MISR DHR data into individual biome classes. The spectral ground reflectance ρ λ is assumed to vary within given biome-dependent ranges representative of reflective properties of the most probable surfaces underneath the canopy (Knyazikhin et al, 1998a). The above method was followed to scale the MISR LAI/FPAR algorithm. The most probable data, which have minimal variations in vegetation structure, are used as the input data. Figure 2.7a shows locations of the most probable values of (1 DHR λ ) at red and NIR wavelengths, for different biomes. The algorithm is adjusted for data resolution by finding values of the single scattering albedo which provide the best agreement between the retrieved and measured LAI values. The solutions to this problem are shown in Figure 2.7b. These single scattering albedos are used by the operational MISR LAI/FPAR software. Figure 2.7c shows histograms of LAI retrievals for Grasses & Cereal Crops and Broadleaf Forests, which are centered at about 1.5 and 5.0, respectively.

42 25 These mean values agree well with LAI measured in the field (Myneni et al, 2002; Privette et al, 2002) Performance of the algorithm as a function of uncertainties At least two types of uncertainties influence the quality of LAI/FPAR retrievals uncertainties in measured and modeled land surface reflectances. In general, these uncertainties set a limit to retrieval quality; that is, the retrieval accuracy cannot be better than summary accuracy in input data and the model. If uncertainties are ignored, it can result not only in the loss of information conveyed to the algorithm, but also in its destabilization (Wang et al., 2001). Thus, the use of uncertainty information in the retrieval technique can influence the quality of retrievals. An overall uncertainty in model and measurements is input to the MISR LAI/FPAR algorithm (Knyazikhin et al., 1998a). Our aim here is to evaluate an upper limit of acceptable uncertainties in data and observations which allow the algorithm to discriminate between pure biome types, to minimize the impact of biome misidentification on LAI retrievals, and to maximize the number of successful retrievals Definition of uncertainties Let A k and r k,i, k = 1, 2,,4, i = 1, 2,, 9, be atmospherically corrected BHRs at four spectral bands and BRFs at four spectral bands and in 9 MISR directions, respectively. We treat these values as independent random variables with finite variances σ A (k) 2 and σ r (k, i) 2, k = 1, 2,, 4, i=1, 2,, 9, and assume that the deviations

43 26 ε k = ( A A ) / σ ( k) and δ = r r ) / σ ( k, ) follow Gaussian distributions. Here k k A k, i ( k, i k, i r i A k and r, are the mathematical expectations of A k and r k,i which are treated as true k i values. The random variables, Nbands Nbands ( Ak Ak ) χ A = ε k =, (2.2) 2 σ ( k) k= 1 i= 1 k = 1 k= 1 A N view N bands N view N bands ( rk, i rk, i) χ r = δ k, i =, (2.3) 2 σ ( k, i) i= 1 k = 1 r characterizing the proximity of atmospherically corrected data to true values have chi square distributions. Here N bands and N view are the number of spectral bands and view directions for which MISR observations are available. Inequalities χ 2 A N bands and 2 χ r N bands N view indicate good accuracy in the atmospherically corrected surface reflectances with a high probability. Dispersions σa(k) and σ r (k, i) are uncertainties in the land surface reflectance product which are input to the MISR LAI/FPAR algorithm. Model uncertainties, σ A,m (k) and σ r,m (k, i) can be defined in a similar manner (Wang et al., 2001). Note that currently the MISR algorithm uses two spectral bands, red and NIR (N bands = 2) to retrieve the pixel LAI and FPAR values. Overall uncertainties in BHR, δ A (k), and BRF, δ r (k, i) which guarantee the convergence property of the retrieval technique (i.e., increasingly accurate retrievals with increasingly accurate inputs) can be represented as δ A (k) 2 = [σ A (k) 2 + σ A,m (k) 2 ]/θ 2 A, δ r (k, i) 2 = [σ(k, i) 2 + σ r,m (k, i) 2 ]/θ 2 r. Here, the stabilization parameters θ A and θ r vary between 0.5 and 1 (Wang et al., 2001). To evaluate proximity of observed to modeled surface

44 27 reflectances, true values A k, r,, and uncertainties in the surface reflectance product σ A (k) k i and σ r (k, i) that appear in equations (2.2) and (2.3) should be substituted with modeled reflectances and overall uncertainties (Wang et al., 2001). We assume that the model uncertainties do not exceed uncertainties in observations; that is, σ A,m (k)/σ A (k) < 1 and σ r,m (k, i)/σ(k, i) < 1. The overall uncertainties in BHR and BRF can be represented as δ A (k) = (α A /θ A )σ A (k) and δ r (k, i) = (α r /θ r )σ r (k, i), respectively. Here the coefficients α A and α r vary between 1 and 2. A correct specification of the ratios γ A = (α A /θ A ) and γ r = (α r /θ r ), each varying between 1 and 4, are required to achieve an optimal performance of the algorithm (Wang et al., 2001). Inequalities χ 2 A N bands and 2 χ r N bands N view with appropriate overall uncertainties are used to execute the first and second comparison tests (Section 4) Optimal performance of the algorithm The analysis presented earlier showed that uncertainties in surface reflectances can be quite high (Figs. 4 and 5). Figure 2.2 shows the availability of valid MISR surface reflectances which, on average, constitute 42% of the vegetated land for the selected paths. A subset of these surface reflectances whose uncertainties exceed a certain acceptable level will result in algorithm failure, reducing the number of successful LAI and FPAR retrievals. This number can be increased by setting the ratios γ A and γ r to higher values. The retrieval quality, however, will decrease in this case. A decrease in γ A and γ r will result in fewer successful retrievals. It should be emphasized that this does not

45 28 necessarily improve the retrieval quality. In general, the underestimation of the overall uncertainties can result in lower retrieval quality than their overestimation (Wang, 2001). Our aim here is to evaluate optimal values of γ A and γ r which allow the algorithm to discriminate between pure biome types, to minimize the impact of biome misidentification on LAI retrievals, and to maximize the number of successful retrievals. Two variables are used to characterize the algorithm performance as a function of uncertainties. The first, is the Retrieval Index (RI), defined as the ratio of the number of retrieved LAI values to the total number of pixels with valid surface reflectance data. This variable does not characterize retrieval quality, but shows the spatial coverage of the retrieved LAI and FPAR fields. In other words, (1 RI) is the probability that the algorithm will fail to retrieve LAI and FPAR and, as a result, return a fill value. The second, is the Biome Identification index (BI), the ratio of the number of cases for which the algorithm correctly identifies the biome type to the number of successfully retrieved pixels. The at-launch MODIS biome map (Section 3) was used as the reference biome classification map. The following procedure was executed to specify optimal values of the overall uncertainties. For each biome type, pixels located around the data peak were selected (Figure 2.4a). Given values of the ratios γ A and γ r for each biome type, the MISR LAI/FPAR algorithm was executed using these surface reflectances and the six-biome map described earlier. From the initial set, pixels that pass the first and/or second tests are selected. A Quality Assessment (QA) flag is assigned to each pixel, indicating that a retrieval resulted from both tests (QA = 0, highest quality), the first test only (QA = 1,

46 29 intermediate quality), or the second test only (QA = 2, low quality). The RI as a function of QA and biome type is also calculated. The biome identification algorithm is then applied and the BI as a function of QA is calculated. In this procedure, the RI is the conditional probability of retrieving a LAI value given biome type, while the BI is the probability of identifying the biome type. By calculating RI(γ A, γ r, bio, QA) and BI(γ A, γ r, bio, QA) for all possible combinations of the ratios γ A and γ r, we select those that result in the maximum of the Performance Index (PI), PI ( bio) = 2 QA= 0 RI( γ, γ, bio, QA) BI( γ, γ, bio, QA). (2.4) A r A r In this procedure, relative values ν A (k, bio) = δ A (k, bio)/a k and ν r (k, i, bio) = δ r (k, bio)/r k,i were used to parameterize the overall uncertainties in the model and observations. Given relative uncertainties, the MISR LAI/FPAR algorithm approximates actual overall uncertainties as δ A (k,bio) = ν A (k, bio)a k and δ r (k, i, bio) = ν r (k, i, bio)r k,i which are taken as the acceptable levels of uncertainties. Figures 8a-c show RI(bio, QA), BI(bio, QA) and PI(bio, QA) for the optimal set of relative overall uncertainties (values listed in Tables 1 and 2). With the exception of Broadleaf Crops, the algorithm retrieves LAI values with a very high probability, if information about the biome type is available and uncertainties in input do not exceed the threshold acceptable level. The probability of identifying pure biome types is quite high if both tests were successfully executed, again with the exception of Broadleaf Crops (Figure 2.8b, bars labeled "QA = 0"). If uncertainties in BRFs exceed the acceptable level and, as a consequence the second test fails, the probability of identifying Grasses &

47 30 Cereal Crops, Shrubs, Savannas and Broadleaf Forests based on BHRs only is greatly reduced (Figure 2.8b, bars labeled "QA = 1"). The first comparison test tends to extract information about canopy structure conveyed by the location of biome type in the spectral space. Although the locations of pure biome types in the spectral space are localized (Figure 2.4d), the uncertainties in BHRs do not allow the algorithm to take full advantages of this property. Their effect is most pronounced in the case of spectrally similar biomes like Broadleaf Crops and Savannas (Figure 2.4d). Thus, the inclusion of additional angular information compensates for the loss of information due to uncertainties in input surface reflectances. Values of the BI corresponding to QA = 2 are higher compared to those derived from the first test only, with the exception of Broadleaf Crops and Savannas (QA = 1). This suggests that the angular signature of vegetation conveys more information about the canopy structure than the location of BHRs in the spectral space, at least, for the data investigated here. However, as will be shown later in this paper, the use of BRFs only results in a lower retrieval quality, as compared to when the first test only or both tests are triggered to retrieve LAI values. This is because an increase in the amount of angular information not only increases the information content but also decreases the overall accuracy in the data. The former enhances quality of the retrievals, while the latter suppresses it. A failure of the algorithm to execute the first test indicates high uncertainties in BHR which, propagating through the surface retrieval algorithm, result in a poor quality of BRF and, as a consequence, LAI retrievals. At the Langley ASDC, the operational version of the algorithm generates LAI and FPAR

48 31 products only for the conditions of QA = 0 and QA = 1, i.e., the first or both comparison tests must be successful Impact of biome misidentification on LAI retrievals Figure 2.8c shows the PI for six biome types. On average, for only about 20% of pixels, both LAI and biome type can be simultaneously specified at the optimal level of uncertainties. This means that the majority of LAI values are retrieved using incorrect information about biome type. Table 2.3 summarizes disagreement between the biome types derived from the MISR LAI/FPAR algorithm and the six-biome map described earlier, as a function of QA. For a given vegetation type, the distribution of biomes assigned by the MISR algorithm is shown in rows. The aim of this section is to analyze the impact of biome misidentification on LAI retrievals. To address this issue we compare two LAI fields. The first, produced by the algorithm using the biome map as input, is taken as the reference field. The second LAI field was obtained by applying the MISR LAI/FPAR algorithm to the same data without using the biome map. For pixels in which both retrievals were available, a relative difference,, was calculated between reference values, LAI ref, and retrieved values, LAI MISR, i.e., LAI ref LAI MISR =. (2.5) LAI ref Pixels located around the data peaks (Figure 2.4a) were used to generate these values. Figure 2.9 shows histograms of as a function of QA for different biome types. Mean

49 32 values and standard deviations of are shown in Table 2.4. With the exception of Broadleaf Crops and Savannas, the impact of biome misidentification on LAI retrievals is minimal if both comparison tests were executed (Table 2.4). The histogram of for Shrubs corresponding to QA = 1 has two local minimums at = 0 and =-0.7 (Figure 2.9). This biome was mainly misclassified as Broadleaf Forests and Needleleaf Forests (Table 2.3). The reference and retrieved LAI values for which the relative difference was close to -0.7 varied between 0.2 and 0.34, respectively. Shrubs exhibit lateral spatial heterogeneity, low to intermediate vegetation ground cover, and have a bright background. The information conveyed about the canopy structure is small and a wide range of natural variation in ground cover and soil brightness can result in the same value of the BHR. Broadleaf and Needleleaf Forests with a very low ground cover and bright (green) understory can result in similar values of surface reflectances at 1.1 km resolution. The effect of biome misclassification on the retrievals, therefore, is maximal if retrievals are from the first test only (curve "QA = 1" in Figure 2.9b). The availability of additional angular information results in a reduced disagreement between reference and retrieved LAI values (curve "QA = 0" in Figure 2.9b). Note that the probability of identifying Shrubs using angular information only (QA = 2) is very high (Figure 2.8b and Table 2.3). However, the inclusion of LAI retrievals corresponding to QA = 2 has no significant effect on the PI (Eq. (4) and Figure 2.8a). Note that the failure of the algorithm to execute the first test (QA = 2) indicates high uncertainties in BHR which, propagating through the surface retrieval algorithm, result in poor quality BRFs, and, as a consequence, LAI retrievals.

50 33 For the other biome types, the disagreement between reference and retrieved LAI values is maximal for QA = 2 (Table 2.4). If retrievals are from the first or both comparison tests, the biome misidentification, on average, involves an overestimation of LAI for Grasses & Cereal Crops and Shrubs, and an underestimation in the case of Broadleaf Crops, Savannas and Broadleaf Forests (Figure 2.9 and Table 2.4). In general, misclassification between distinct biomes has a significant effect on LAI retrieval. For example, Shrubs are mainly misclassified as Broadleaf or Needleleaf Forests (Table 2.3, QA = 1). The mean relative difference is 0.37 compared to 0.14 when the probability of such a misidentification is much lower (Tables 4, QA = 0). What is the probability that biome misidentification has no impact on LAI retrieval? To address this question, we introduce the most probable relative difference as values of at which the histogram exhibits local maxima. Many of histograms have two local maxima (Figure 2.9), however, all biomes have a local maximum around = 0. Table 2.5 lists the most probable values of and probabilities of χ for different biome types, QA values and disagreement levels χ. For Grasses & Cereal Crops, Shrubs, Savannas and Broadleaf Forests, the disagreement between reference and high quality retrievals (QA = 0) does not exceed 15% with probabilities 97%, 68%, 71% and 100%, respectively (Table 2.5). For 81% of Savannas, the relative difference corresponding to QA = 0 and =0 is about 25%. With the exception of Shrubs, more than 70% of intermediate quality retrievals agree with reference values to within 25%. For these retrievals, however, probabilities of 0. 25

51 34 are reduced. On average, with a probability of 70% and higher, the high and intermediate quality retrievals agree with true values to within 25% uncertainties, which is close to the overall uncertainty in model and observations (Tables 1 and 2). Thus, the optimal performance of the algorithm minimizes biome misclassification when it has a significant effect on LAI retrievals. With a very high probability, uncertainties due to the biome misclassification do not exceed uncertainties in model and observations. Note that cover type information is an important input to LAI/FPAR algorithms that use single-angle observations. The typical overall accuracy in most biome maps is about 70% (Lotsch et al., 2003). Thus about 30% of LAI retrievals should be treated as unreliable. The use of angular and spectral information of vegetations, instead of biome maps, results in comparable accuracy in LAI and also facilitates assignment of quality flags to retrievals. It should also be noted that uncertainties in the reference LAI field are unknown and thus the above analysis does not characterize uncertainties in retrievals. However, the proximity of retrieved and reference LAI fields indicates that MISR angular and spectral information is sufficient for LAI/FPAR retrievals without using land cover maps as input Test of physics The measured spectral reflectance data are usually compressed into vegetation indexes. More than a dozen such indexes are reported in the literature and shown to correlate well with vegetation amount (Tucker, 1979), the fraction of absorbed photosynthetically active radiation (Asrar et al., 1984), unstressed vegetation conductance

52 35 and photosynthetic capacity (Sellers et al., 1992), and seasonal atmospheric carbon dioxide variations (Tucker et al., 1986). There are some theoretical investigations to explain these empirical regularities (Vygodskaya and Gorshkova, 1987; Myneni et al., 1995; Knyazikhin et al., 1998b). Such relationships provide a method to test the physics of retrievals. Here we test relationships between the normalized difference vegetation index (NDVI), LAI and FPAR. NDVI values were regressed against both LAI and FPAR to ascertain whether the proper relationships were obtained. The NDVI values were computed using the MISR nadir view HDRF values in the red and NIR bands. It should be emphasized that the LAI values were obtained from the MISR LAI/FPAR algorithm with MISR surface reflectances as inputs and not NDVI values. Figure 2.10 shows the NDVI-LAI and NDVI-FPAR regression curves for Grasses & Cereal Crops and Broadleaf Forests. The high quality retrievals (QA = 0) were used to derive these curves. The biome specific relationships between the retrieved LAI/FPAR and the measured NDVI values conform to both theoretical and empirical results. Figure 2.11 shows NDVI- LAI relationships for Grasses & Cereal Crops and Broadleaf Forests corresponding to different values of QA. One can see that curves corresponding to QA = 2 do not follow regularities expected from physics and are mainly outside of the error bars of curves the NDVI-LAI relationships derived from high quality retrievals. A failure of the algorithm to execute the first test (QA = 2) indicates high uncertainties in BHR which, propagating through the surface retrieval algorithm, result in a poor quality of BRF, and, as a consequence, LAI retrievals. At the Langley ASDC, the operational version of the

53 36 algorithm will generate LAI and FPAR products only for the condition of QA = 0 and QA = Concluding remarks An algorithm for the retrieval of LAI, FPAR, and biome type from MISR BHR and BRF data has been in operational processing at the Langley ASDC since October This paper describes the research basis for transitioning the MISR LAI/FPAR product from beta to provisional status. The quality and spatial coverage of MISR surface reflectances input to the algorithm determine the quality and spatial coverage of the LAI and FPAR products. Therefore, our primary objective was to establish the convergence property of the MISR LAI/FPAR algorithm, namely, that the reliability and accuracy of the retrievals increase with increased input information content and accuracy. The uncertainties in modeling the physics of the problem and measurements of surface reflectances are input to the MISR LAI/FPAR algorithm. An upper limit for these uncertainties that allows the algorithm to discriminate between pure biome types, minimizes the impact of biome misidentification on LAI retrievals, and maximizes the spatial coverage of retrievals was empirically evaluated from MISR data over Africa. Our analysis indicates that uncertainties in MISR BHR values over dense vegetation can substantially exceed the acceptable level of 20%, resulting in failure of the LAI/FPAR algorithm.

54 37 The performance of the MISR LAI/FPAR algorithm evaluated on a limited set of MISR data from Africa can be stated as resulting in valid LAI values and correct biome identification in about 20% of the pixels, on an average, given the current level of uncertainties in the MISR surface reflectance product. About 80% of LAI values are retrieved using incorrect information about biome type. We document that the LAI/FPAR algorithm minimizes biome misclassification when it has a significant effect on LAI retrievals. Finally, with a probability of about 70%, uncertainties in LAI retrievals due to biome misclassification do not exceed uncertainties in observations. These metrics will significantly improve as the quality of MISR surface reflectances improves. In fact, the surface reflectances used in this article are already outdated, as the upstream algorithms and products, related to aerosol optical depth retrieval and atmospheric correction, have been significantly improved. Considerable attention was also paid to characterizing the quality of the LAI/FPAR fields and this information is available to the users as quality assessment flags accompanying the product. A Quality Assessment (QA), as defined in this study, takes on values between 0 and 2, indicating that a retrieval passed both comparison tests (QA = 0, highest quality), the first test only (QA = 1, intermediate quality), or the second test only (QA = 2, low quality). Analyses presented in this paper indicate that, with a high probability, the quality indicator correctly reflects retrieval quality. Based on our investigation, one can conclude that the LAI/FPAR algorithm realizes the stated convergence goal, namely, that the reliability and accuracy of the retrievals increase with increased input information content and accuracy. Therefore, the increasing quality of the

55 38 MISR surface reflectances will lead to better quality LAI and FPAR retrievals in the near future.

56 39 Biome Type Grass and Cereal Shrubs Broadleaf Crops Savanna Broadleaf Forests Crops Red NIR Table 2.1. Optimal values of relative uncertainties, ν A, in modeled and observed BHRs. View Angle Nadir Aa, Af Ba, Bf Ca, Cf Da, Df Spectral band Grass and Cereal Crops Shrubs Broadleaf Crops Savanna Broadleaf Forests Red NIR Red NIR Red NIR Red NIR Red NIR Table 2.2. Optimal values of relative uncertainties, ν r, in modeled and observed BRFs.

57 40 Landcover Type Grasses & Cereal Crops Shrubs Broadleaf Crops Savannas Broadleaf Forests QA Landcover Type assigned by MISR algorithm, % Grasses & Shrubs Broadleaf Savannas Broadleaf Needleleaf Failure Cereal Crops Crops Forests Forests n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a Table 2.3. Disagreement between biome types assigned by the MISR algorithm and the six biome classification map used in the study for different values of QA.

58 41 Mean Standard Deviation QA=0 QA=1 QA=2 QA=0 QA=1 QA=2 Grasses & Cereal Crops Shrubs Broadleaf Crops n/a n/a Savannas n/a n/a Broadleaf Forests Table 2.4. Mean values and standard deviations of the relative difference for different biome types and QAs. Most Probable Value Prob ( < χ) QA=0 QA=1 QA=2 QA=0 QA=1 QA=2 χ = 0.15 χ = 0.25 χ = 0.15 χ = 0.25 χ = 0.15 χ = 0.25 Grasses & Cereal Crops Shrubs Broadleaf Crops Savannas Broadleaf Forests Table 2.5. Most probable values of the relative difference and probabilities of < χ for different biome types, QAs and disagreement levels χ.

59 42 CART canopy/soil model parameters MISR Level 2 Surface Parameters BHR, DHR BRF MISR LAI/FPAR LAI MISR Geometric Parameters Sun Angle View Angle Algorithm FPAR Figure 2.1. Flow chart of the relationship between MISR LAI/FPAR algorithm and data. The inputs, BHR, DHR and BRF are from the MISR Level 2 Surface Parameters Product, the sun and view angles from the MISR Geometric Parameters Product and canopy/soil model parameters from the Canopy Architecture Radiative Transfer (CART) file.

60 43 Percentage of Valid Pixels (%) (a) All biomes Total Number of Pixels = Average=45.6% Path Number Percentage of Valid Pixels (%) (b) Grasses/Cereal Crops Total Number of Pixels = Average=47% Path Number Percentage of Valid Pixels (%) (c) Shrubs Total Number of Pixels = Average=47% Path Number Percentage of Valid Pixels (%) (d) Broadleaf Crops Total Number of Pixels = Average=39.6% Path Number Percentage of Valid Pixels (%) (e) Savannas Total Number of Pixels = Average=44.7% Path Number Percentage of Valid Pixels (%) (f) Broadleaf Forests Total Number of Pixels = Average=31.5% Path Number Figure 2.2. Ratio of valid pixel number to total pixel number, in percentage. (a) All biomes, (b) Grasses and Cereal Crops, (c) Shrubs, (d) Broadleaf Crops, (e) Savannas, (f) Broadleaf Forests. There is no significant presence of Needleleaf Forests in Africa. The average ratio is shown in these plots as a dashed line. The maximum percentage of valid pixels is for Shrubs (47%), and the minimum is 31.5% for Broadleaf Forests.

61 44 Figure 2.3. Histograms of the difference between nominal and actual viewing angles. The maximum deviation is given for each camera. Number of Pixels * Maximum Deviation = 1.01 degree Fore D Camera View Zenith Angle Number of Pixels * Maximum Deviation = 0.83 degree Aft D Camera View Zenith Angle Number of Pixels * Maximum Deviation = 1.54 degree Fore C Camera View Zenith Angle Number of Pixels * Maximum Deviation = 1.32 degree Aft C Camera View Zenith Angle Number of Pixels * Maximum Deviation = 2.43 degree Fore B Camera View Zenith Angle Number of Pixels * Maximum Deviation = 2.25 degree Aft B Camera View Zenith Angle

62 45 Figure 2.3. Number of Pixels * Maximum Deviation = 4.95 degree Fore A Camera View Zenith Angle Number of Pixels * Maximum Deviation = 4.84 degree Aft A Camera View Zenith Angle

63 46 Figure 2.4a. Distribution of pixel counts in the red and near-infrared DHR space for Broadleaf Forests. Pixels located around data peak (0.02, 0.36), may be interpreted as pixels characteristic of Broadleaf Forests. Figure 2.4b. The mean and standard deviation of HDRFs in the perpendicular plane at red and NIR wavelengths derived from pixels around the data peak for Broadleaf Forests. The solar zenith angle and azimuth are 23 ±2 and 288 ±9, respectively. Figure 2.4c. The mean and standard deviation of HDRFs at red and NIR wavelengths derived from pixels around the data peak for Grasses & Cereal Crops. The solar zenith angle and azimuth are 32 ±3 and 232 ±5, respectively. Values of the difference between solar and view azimuth are 217 ±10 for forward cameras, and 37 ±10 for afterward cameras. Figure 2.4d. Mean and standard deviation of MISR BHR values from pixels near the data peak (there is no appreciable Needleleaf Forests presence in Africa).

64 47 Figure 2.4 (a) Red Reflectance Near-Infrared Reflectance (b) Broadleaf Forests 0.3 HDRF NIR NIR Red HDRF Red f 60.0f 45.6f 26.1f a 45.6a 60.0a 70.5a Camera Angle (degrees) 0

65 48 Figure (c) Grasses&Cereal Crops HDRF NIR Red f 60.0f 45.6f 26.1f a 45.6a 60.0a 70.5a Camera Angle (degrees) 0.4 (d) BHR NIR Grasses/Cereal Crops Shrubs Broadleaf Crops Savannas Broadleaf Forests BHR Red

66 49 Number of Pixels Grasses & Cereal Crops Blue Number of Pixels Broadleaf Forests Blue Coefficient of Variation Coefficient of Variation Number of Pixels Grasses & Cereal Crops Red Number of Pixels Broadleaf Forests Red Coefficient of Variation Coefficient of Variation Number of Pixels Grasses & Cereal Crops NIR Number of Pixels Broadleaf Forests NIR Coefficient of Variation Coefficient of Variation Figure 2.5. Histograms of the coefficient of variation (standard deviation/mean) of the MISR BHR from path 178 for 3 different days, orbit 6393 (Mar 1, 2001), 6626 (Mar 17, 2001) and orbit 6859 (April 2, 2001). Coefficients of variation of the solar zenith angle and azimuth do not exceed 0.07 for data used. The plots are for Grasses & Cereal Crops and Broadleaf Forests at Blue, Red and NIR bands.

67 50 Coefficient of Variation TR TN SR SN 0.0 Grasses&Cereal Shrubs Crops Broadleaf Crops Savannas Broadleaf Forests Figure 2.6. Mean coefficient of variation of DHR at Red and NIR wavelengths derived from spatial and temporal analyses of MISR data. The data described in Figs. 2.4d and 2.5 were used to derive spatial and temporal variation in MISR surface reflectance. Labels TN and TR refer to the temporal, and SR and SN refer to the spatial coefficients of variation at Red and NIR spectral bands.

68 51 Figure 2.7a. Fraction of energy, (1-DHR), absorbed by the vegetated surface at Red and NIR wavelengths by different cover types. Pixels located around the data peak (see Figure 2.4a) were used to derive values of (1-DHR). Figure 2.7b. Adjusted single scattering albedos of different cover types used by the operational MISR LAI/FPAR software. Figure 2.7c. Histogram of LAI values produced by the MISR algorithm using surface reflectances located around the data peak (see Figure 2.4a). Single scattering albedos shown in Figure 2.7b were used. Uncertainties in MISR BHRs and BRFs were set to 0.2 based on analysis presented in Figs. 2.4 to 2.6. The left curve is for Grasses & Cereal Crops with peak probability at LAI = 1.5 (mean LAI = 1.27) and the right curve is for Broadleaf Forests with peak probability at LAI = 5.0.

69 52 Figure (a) Grasses & Cereal Crops Broadleaf Crops Broadleaf Forests Shrubs Savannas (1-DHR) at NIR (1-DHR) at Red Near-Infrared Reflectance (b) Grasses & Cereal Crops Shrubs Broadleaf Crops Savannas Broadleaf Forests Red Reflectance

70 53 Figure 2.7 Probability (c) Grasses & Cereal Crops Broadleaf LAI

71 54 Figure 2.8a. Retrieval index as a function of biome type and Quality Assessment (QA) for optimal set of relative uncertainties listed in Tables 1 and 2. Pixels located around the data peak and the six-biome map were used to derive values of the retrieval index. In this case, the retrieval index is the conditional probability of retrieving LAI value given the biome type. Figure 2.8b. Biome Identification index (BI) as a function of biome type and QA for the optimal set of relative uncertainties. Pixels for which the MISR algorithm retrieved LAI values using the six-biome map and surface reflectance located around data peaks were used to evaluate the BI. Figure 2.8c. Performance Index (PI) as a function of biome type for the optimal set of relative uncertainties.

72 55 Figure 2.8 (a) Grasses&Cereal Crops Shrubs Broadleaf Crops Savannas Broadleaf Forests Retrieval Index QA=0 QA=1 QA=2 (b) Grasses&Cereal Crops Shrubs Broadleaf Crops Savannas Broadleaf Forests Biome Identification Index QA=0 QA=1 QA=2 Average= Grasses&Cereal Crops Shrubs Broadleaf Crops Savannas Broadleaf Forests Performance Index

73 Grasses & Cereal Crops QA=0 QA=1 QA= Shrubs QA=0 QA=1 QA=2 Probability Probability Delta Delta Broadleaf Crops QA=0 QA=1 QA= Savannas QA=0 QA=1 QA=2 Probability Probability Delta Delta Broadleaf Forests QA=0 QA=1 QA=2 Probability Delta Figure 2.9. Histograms of the relative difference between reference and retrieved LAI values for different biome types and QAs.

74 57 (a) 1.0 NDVI(nadir) Grasses & Cereal Crops Broadleaf Forests LAI (b) NDVI(nadir) Grasses & Cereal Crops Broadleaf Forests FPAR Figure (a) NDVI-LAI and (b) NDVI-FPAR regression curves for Grasses & Cereal Crops and Broadleaf Forests, based on the MISR data. High quality retrievals (QA=0) were used to derive these curves.

75 58 (a) NDVI(nadir) Grasses & Cereal Crops QA=0 QA=1 QA= LAI (b) NDVI(nadir) Broadleaf Forests QA=0 QA=1 QA= LAI Figure NDVI-LAI regression curves for (a) Grasses & Cereal Crops and (b) Broadleaf Forests for different values of QA.

76 59 Chapter 3 Analysis of the MISR LAI/FPAR product for spatial and temporal coverage, accuracy and consistence 3.1. Introduction The multiangle imaging spectroradiometer (MISR) instrument is designed to provide global imagery at nine discrete viewing angles and four visible/near-infrared spectral bands. The MISR team is responsible for development and validation of algorithms and for producing a series of products which include vegetation green Leaf Area Index (LAI) and Fraction of Photosynthetically Active Radiation ( nm) absorbed by vegetation (FPAR). These products are required to describe the exchange of fluxes of energy, mass (e.g., water and CO 2 ) and momentum between the surface and atmosphere (Sellers et al., 1997). MISR LAI/FPAR research has three major components - algorithm development, product analysis and validation. Algorithm development includes the development of the at-launch algorithm (Knyazikhin et al., 1998a and 1998b), prototyping of the algorithm prior to the launch of Terra platform (Zhang et al., 2000), and algorithm refinement (Hu et al., 2003). Product analysis includes assessment of the overall algorithm performance at global scale and assessment of the accuracy and quality of the product at regional scales with emphasis on understanding how input data uncertainties impact retrieval quality (Hu et al., 2003). This paper describes the research basis for transitioning the MISR LAI/FPAR product from provisional to stage 1 validated status, i.e., an estimation of product accuracy has

77 60 been made using a small number of independent measurements from selected locations and time periods through ground-truth/field program efforts (WWW1). An infrastructure presently exists that accumulates resources required for validation of satellite products (Morisette et al., 2005). At most of the sites included in this structure, there is a long-term measurement program to support in situ measurements that can be used to assess the quality of satellite products. Data available through the existing infrastructure are used in this research to establish the stage-1 validation status of MISR LAI/FPAR products. The assessment of the quality of satellite-derived parameters should include not only validation but also a comprehensive analysis of relationships, consistency and complementarity between various products derived from independent algorithms. Such an analysis is valuable to establishing product accuracies and demonstrating their utility for monitoring and modeling studies. This aspect of product quality assessment is also discussed in this paper. The paper is organized as follows. Section 2 provides background information on the MISR Level 2 surface parameters product relevant to further discussion. The information content of MISR surface parameters, their consistency and complementarity, as well as their utility for monitoring and modeling studies are analyzed in section 3. The spatial and temporal coverage of the MISR Level 2 surface product over different validation sites is examined in section 4. The validation results from five vegetation sites are presented in section 5. Finally, the concluding remarks are summarized in section 6.

78 Description of the MISR Surface Parameters Product The MISR instrument on the Earth Observing System (EOS) Terra platform orbits the Earth about 15 times each day. There are 233 distinct orbits, called paths, which are repeated every 16 days, and since the paths overlap, near global coverage is obtained in 9 days. The MISR instrument views symmetrically about the nadir in forward and aftward directions along the spacecraft flight track. Image data are acquired with nominal view zenith angles relative to the surface reference ellipsoid of 0.0 o, 26.1 o, 45.6 o, 60.0 o and 70.5 o in four spectral bands (446, 558, 672, and 866 nm). The MISR data are distributed from the NASA Langley Atmospheric Sciences Data Center (WWW2). The MISR products are archived for each path and orbit. The orbit number corresponds to data acquired over a path for a particular date. Each path is about 360 km wide from East to West which, in turn, is divided into 180 blocks measuring km (cross-track) x km (along-track), that is, 512 x 128 pixels. For a given path, a numbered block always contains the same geographic locations. The MISR Level 2 Surface Parameters Product is at a spatial resolution of 1.1 km and includes spectral hemispherical-directional reflectance factors (HDRF) at the nine MISR view angles and the associated bihemispherical reflectance (BHR). The HDRF is the ratio of the directionally reflected radiance from the surface to the reflected radiance from an ideal lambertian target under identical illumination conditions as the surface. The BHR is the HDRF integrated over all reflection angles in the upward hemisphere, i.e., it is the surface spectral albedo under ambient atmospheric illumination. Related MISR surface parameters, also being generated and archived within the Land Surface Product, are the

79 62 spectral bidirectional reflectance factor (BRF) at the nine MISR view angles and the directional-hemispherical reflectance (DHR). The BRF and the DHR characterize the surface in the same way as the HDRF and BHR, respectively, but are defined for the condition of direct illumination only. In addition to these spectral products, the BHR and DHR, integrated over the wavelength region of photosynthetically active radiation (PAR) ( µm), are also computed. The details of the retrieval methodologies used to derive these products have been described by Martonchik et al. (1998b). The MISR Land Surface Products include vegetation green leaf area index (LAI) and the fractional amount of vegetation absorbed photosynthetically active radiation (FPAR). The LAI is defined as the one-sided green leaf area per unit ground area in broadleaf canopies and as the projected needle leaf area per unit ground area in coniferous canopies. The FPAR is defined for ambient sky conditions, i.e., it accounts for both diffuse and direct illumination. In the MISR approach to LAI/FPAR retrievals, global vegetation is stratified into six canopy architectural types or biomes (Myneni et al., 1997). The six biomes are grasses and cereal crops (biome 1), shrubs (biome 2), broadleaf crops (biome 3), savannas (biome 4), broadleaf forests (biome 5) and needle leaf forests (biome 6). For each biome, the LAI/FPAR algorithm identifies all LAI values and soil or understory reflectances for which modeled and observed BHR and BRF differ by an amount equivalent to or less than the combined uncertainty in model and observations. FPAR is calculated for each such LAI and soil or understoty reflectance. From this set, conditional mean LAI and FPAR and their dispersions are calculated. The conditional mean LAI and FPAR are defined as the LAI and FPAR averaged over all soil or understory models for a

80 63 given biome type. The most probable LAI, FPAR and biome type are chosen, using the results from the biome which has the least coefficient of variation (dispersion divided by mean). The conditional LAI values, their spread as well as the most probable values of LAI and FPAR are archived in the MISR Surface Parameters Product for each 1.1 km MISR pixel within which the BHR/BRF retrieval was performed. The details of the retrieval methodologies used to derive these products can be found in (Knyazikhin et al., 1998a and 1998b; Hu et al., 2003). Here we shall restrict our consideration to the conditional LAI parameter. The most probable values of LAI and FPAR are analyzed in (Hu et al., 2003) Examples of MISR retrieval quality, uniqueness and consistency Product assessment should include, in addition to validation efforts, a comprehensive analysis of the relationships, consistency and complementarity between various parameters derived from independent algorithms. Such an analysis highlights the utility of these parameters for studies on monitoring and modeling as well as for exploring the potential for enhanced information retrieval through innovative manipulation of multiple parameters. Here, a select number of retrieval cases are presented to showcase the information content of surface directional reflectances, consistency and complementarity between the various parameters of the MISR surface product suite.

81 Angular signatures in spectral space A vegetated surface scatters shortwave radiation into an angular reflectance pattern, the magnitude and shape of which is governed by the composition, density, optical properties and geometric structure of the vegetation canopy and its underlying surface. Zhang et al. (2002a and 2002b) have shown that the angular signatures at different spectral bands are not independent and their correlation conveys information about canopy structure. The correlation, e.g., can be seen if one depicts variation in the BRF at red and near-infrared (NIR) wavelengths with the view angle (Fig. 3.1). Points corresponding to different view angles form a curve an angular signature in spectral space (Zhang et al., 2002a). The signature can be characterized by three metrics: (i) its location in the spectral space, which is mainly determined by the biome type; the DHR at red and NIR wavelengths is used to specify the location; (ii) inclination (slope and intercept) of the signature, which is determined by leaf and soil optical properties, and the structure of the canopy; and (iii) the length of the signature, which describes spectral variation in the shape of the BRF. Here we follow a methodology to interpret multiangle data proposed by Zhang et al. (2002a and 2002b). The mean signatures of 2 by 2 degree areas representative of five biomes and corresponding to the greenest seasons are shown in Fig. 2. The selected areas are centered on the following EOS Core Validation Cites (WWW1, see also Table 1): KONZ, Konza Prairie Biological Station, Manhattan, Kansas, USA ( N, W); AGRO, a cropland site in Illinois, USA ( N, W); HARV, a temperate mixed forest site in Massachusetts, USA ( N, W); Walnut Gulch (San Pedro), a

82 65 shrubland/grassland mixture site in Arizona, USA (31.74 N, W); and Ruokolahti, a needleleaf forest site in Finland, (61.32 N, E). The location of reflectance data in the spectral space is the basic source of information about the vegetation canopy conveyed by single-angle multi-spectral satellite data. In our example, the locations of broadleaf crops, broadleaf and needleleaf forests, shrubs, and to some extent grasses and cereal crops are distinct in the red-nir space. Needle forests appear darkest in these plots. Multiple photon-needle interactions within shoots are primarily responsible for this phenomenon (Smolander and Stenberg, 2003, 2005; Rautiainen and Stenberg, 2005). The length of the signature is another type of information provided by multiangle data about canopy structure. It measures the degree of anisotropy in the reflected radiation field which is dependent on the heterogeneity of the medium. For the case of a homogeneous medium, defined as an isotropic reflector, the length is zero because the angular signature in spectral space is a point. One can see that shrubs have the highest length values relative to other biomes, thus indicating a high degree of both lateral and vertical heterogeneity. The forest biomes exhibit larger length magnitudes compared to grasses and crops. This indicates a higher degree of vertical heterogeneity in the case of forests (Zhang et al., 2002a). In terms of the inclination of the signature, forest biomes tend to have steeper slopes and smaller intercept values. Shrubs, on the other hand, show the lowest slope and a large intercept. In the case of dense vegetation canopies, the ratio between BRFs at near infrared and red spectral bands, or the simple ratio (SR), is nearly independent of view

83 66 directions, indicating a low impact of canopy background on the BRF (Kaufmann et al., 2000). The fact that sparse vegetations tend to have a non-zero intercept indicates a sensitivity of the simple ratio to view and sun angle variations. This is because the surface reflectance results from nonlinear combinations of radiation reflected by vegetation (e.g., shrub) and ground. The temporal movement of data in the spectral space characterizes changes in canopy properties (Shabanov et al., 2002). Fig. 3.3 shows the seasonal change in the mean signature of a broadleaf forest located in a 2 by 2 degree area centered on the Harvard Forests (Massachusetts) EOS Core Validation site (Table 3.1). In April, the trees are leafless and hence LAI is equal to zero. The corresponding signature is mainly determined by the reflectance and anisotropy of a bare background. A non-zero intercept and a low value of the slope make the simple ratio sensitive to view angle. As LAI increases from May to July, the signature moves in the spectral space away from its location in April. This movement is accompanied by a sharp decrease in the red and an increase in the NIR reflectance. The slope jumps from 2.4 in May to its maximum value of about 7.7 in July and August. In these summer months, the simple ratio is insensitive to the view angle. The length reaches its minimum value, indicating the lowest degree of the horizontal heterogeneity. The location corresponding to the greenest seasons depends mainly on the leaf optical properties (Zhang et al., 2002b). The September signature still has a steep slope. It occupies approximately the same space on the RED vs. NIR plane as in July and August. These two features suggest a low impact of background on canopy reflectance (Zhang et al., 2002b). However, changes in the leaf optics result in an

84 67 increased value of the signature length. The decrease in the slope and increase in the length from October to November indicate a stronger impact of the background on reflected radiation and, consequently, a lower LAI value LAI and FPAR retrievals over sparse vegetation Shrubs have low vegetation cover over a bright background and exhibit lateral spatial heterogeneity. This biome constitutes about 25% of global vegetation. Fig. 3.4 shows the annual course of LAI and FPAR derived from MODIS and MISR data for a 2 by 2 degree area centered on the Walnut Gulch (San Pedro) site in Arizona (WWW1). The MISR product exhibits seasonality while the MODIS product does not. This seasonality is consistent with precipitation in this region, which is bi-modally distributed with about 50 to 60% of the annual total of about 76 cm (30 inches) falling in the summer monsoon season, and 21% to 35% occurring in the winter months. The MODIS and MISR algorithms both perform retrievals by comparing observed and modeled radiances for a suite of canopy structure and soil patterns that covers a range of expected natural conditions (Knyazikhin et al., 1998a, 1998b). The set of all canopy and soil patterns for which the magnitude of the residuals in the comparison does not exceed uncertainties in observed radiances are treated as acceptable solutions. FPAR is calculated for each such LAI and soil or understory reflectance. The mean LAI and FPAR over all acceptable LAI values are taken as a retrieved LAI and FPAR values. The information conveyed about canopy structure is small in the case of a single-angle instrument whose footprint does not spatially resolve individual scene elements.

85 68 Therefore, a wide range of natural variation in LAI and soil or understory reflectance can result in the same value of the remotely sensed signal. This results in a higher uncertainty in retrieved values of LAI and FPAR. Since the interaction of photons with canopy structure determines the directional reflectance distribution, the use of multiangle information results in fewer solutions that are consistent with the observations. The retrieval uncertainty in MISR LAI is therefore low. A comparison of MODIS and MISR LAI retrievals with field data supports this inference (section 3.5.2). This example demonstrates the advantage of multiangle data for retrievals in arid land marginal ecosystems that are dynamic and being subject to anthropogenic pressures Partitioning of solar radiation LAI and FPAR are parameters that are descriptive of vegetation canopy structure and its energy absorption capacity, and are key state variables in most ecosystem productivity models and in global models of climate, hydrology, and ecology (Sellers et al., 1997). For example, Buermann et al. (2001) reported that the use of satellite LAI reduces the model biases in near-surface air temperature in comparison to observations. The model was the NCAR Community Climate Model 3 (Kiehl, et al., 1996, 1998). The analysis showed how the use of satellite LAI fields allowed a more realistic partitioning of incoming solar radiation between the canopy and the ground below the canopy, thus resulting in improved model predictions of near-surface climate. This also highlighted the need for independent estimates of vegetation and ground absorption of solar radiation to describe the energy balance correctly.

86 69 The MISR surface product includes bihemispherical reflectance integrated over the photosynthetically active spectral region (BHRPAR), the broadband visible albedo. From energy conservation, the fraction of PAR absorbed by the ground beneath the canopy is given by the formula FGROUND = 1 BHRPAR FPAR. Fig. 3.5 shows examples of the MISR standard surface product suite that includes LAI, FPAR and BHRPAR and the new parameter, FGROUND, derived from these standard products. In this example, BHRPAR is nearly homogeneous spatially. Thus the amount of PAR absorbed by the surface is also homogeneous. However, its partitioning between the vegetation and ground can be dramatically different. For example, from the LAI panel we note considerable spatial variation in LAI. Not surprisingly, FPAR is also spatially variable and, consequently, the energy absorbed by the ground. This example suggests that the BHRPAR, or generally the albedo, alone does not convey adequate information in many cases Obtaining new information on canopy structure from MISR products Given LAI and FGROUND fields (Fig. 3.5), two types of regression curves can be derived. The first one, the best possible prediction of LAI given a realized value of FGROUND, LAI=F 1 (f), is the expectation of observed LAI under the condition that the FGROUND takes a given value f (Bronshtein and Semendyayev 1985, pp ). Similarly, the best possible prediction of FGROUND given a LAI value L, i.e., FROUND=F 2 (L), can be obtained by averaging FGROUND values over pixels for which LAIs fall in a sufficiently narrow interval around a given value L. If there is a one-to-one

87 70 relationship between LAI and FGROUND the functions F 1 and F 2 are reciprocally related; that is, 1 F2 ( L) = F1 ( L). Fig. 3.6a shows the relationship between the negative logarithms of FGROUND and mean LAI normalized by the cosine of the solar zenith angle. The predicted LAI and FGROUND are related as FGROUND = F 1 1 (LAI) =0.95 exp[ 0.61 LAI/cos(θ0)] where θ 0 =35 0 is the solar zenith angle. Panel (b) shows the distribution of points [F 1 (f), f] and [L, F 2 (L)] on the FGROUND vs. LAI plane. Their joint distribution can be well approximated by the exponential function shown in Fig. 3.6a. This indicates a strong relationship between LAI and FGROUND at the resolution of MISR products. These results can be interpreted as follows. The fraction of PAR absorbed by the ground is the downward PAR flux density, F, times the soil absorptance, 1 α, where α is the reflectance of the canopy background. The downward flux, in turn, can be expressed via the downward flux density, F BS, calculated for a vegetation canopy bounded by a non-reflecting surface as F = FBS /(1 α r * ) where r * is the probability that photon entering through the lower canopy boundary will be reflected back by the vegetated layer (Knyazikhin and Marshak, 2000; Wang et al., 2003). Since green leaves usually absorb 85% 90% of intercepted radiation in the photosynthetically active region of the solar spectrum, F BS can be approximated by the fraction of direct incident PAR that the vegetation canopy transmits. This fraction follows Beer s law, given by exp[ G( θ 0 ) LAI/cos( θ 0 )], where θ 0 is the

88 71 solar zenith angle, and G(θ 0 ) is a geometric factor defined as the projection of unit leaf area onto a plane perpendicular to the illumination direction (Ross 1981). Thus, 1 α FGROUND = exp[ G( θ 0 )LAI/ cos( θ 0 )]. (1) * 1 α r The relationship between LAI and FGROUND derived from MISR data (Fig. 3.6) follows this equation with (1 α)/(1 αr * )=0.95 and G(35 ο )=0.61. The following new canopy structure information can be obtained from this equation. According to de Wit s (1965) classification (see also Ross 1981, pp. 92 and ), the value G(θ 0 )=0.61 at SZA=35 corresponds to a canopy with leaves between a planophile (mostly horizontal leaves) and plagophile (mostly leaves at 45 ) type of orientation. Given a model of leaf normal orientation, one can estimate the gap fraction as exp( G(0)LAI). Thus, the fraction of PAR absorbed by the ground together with independent estimates of LAI can potentially be used to derive at least three measures of canopy structure (1) extinction coefficient, G/ cos( θ 0), for use in ecological models, which typically use the Beer s law or two-stream approximation to model radiation, (2) derive estimates of mean leaf inclination and (3) the gap fraction along the near-nadir direction which is related to vegetation ground cover. It should be noted that the BHRPAR and FPAR are derived from two independent algorithms using different input information. The broadband visible albedo is directly obtained from the spectral BHR by integrating this product over the photosynthetically active spectral region (Diner et al., 1999). In the MISR approach to FPAR retrieval, BHR and BRF in the red and NIR spectral bands alone are used to estimate LAI and canopy

89 72 absorptance at the red spectral wavelength. The latter then is extrapolated from one spectral point to the entire PAR region using the canopy spectral invariant (Knyazikhin et al., 1998b, Panferov et al., 2001, Wang et al., 2003; Smolander and Stenberg, 2003, 2005; Rautiainen and Stenberg, 2005). Thus BHRPAR and FPAR can be treated somewhat as independent estimates of canopy reflective and absorptive properties, and thus the canopy structure information can also be retrieved. The analyses presented here, therefore, suggests the consistency and complementarity of the MISR surface product suite that includes LAI, FPAR and BHRPAR MISR Land Surface Products over validation sites The EOS land community provides the infrastructure to accumulate resources required for validation of satellite products by linking multiple field programs (Morisette et al., 2005). At most of the sites included in this structure, there is a long-term measurement program to support in situ measurements that can be used to assess the quality of satellite products. We selected five validation sites to analyze the MISR Level 2 Surface Parameters Product at local scales. The selected sites are shown in Table 3.1. MISR data from year 2000 were selected for this investigation as in situ LAI measurements were available from most of these sites for this period Availability of MISR surface reflectance data A successful retrieval of the BHR in the red band is necessary to perform LAI/FPAR retrievals. Therefore, we examine the availability of the red band BHR

90 73 product at local scales by evaluating the ratio of pixels with valid (non-fill) BHR values to the total number of pixels. The analysis was performed for 2 o by 2 o areas centered on the validation sites. For each area, the ratio was calculated using pixels from all paths that overlapped with the 2 o by 2 o area and all orbits from Year The availability of MISR BHR changes with site and varies between 7% and 40% (Table 3.1). On average, input valid for LAI/FPAR retrievals was successfully generated for about 25% of the pixels. A significant portion of pixels with invalid input appeared to be cloud contaminated as the following analysis will demonstrate. Inputs to the MISR surface retrieval algorithm include several atmospheric parameters from the MISR Aerosol Product. A successful retrieval must be done as a prerequisite to performing any type of surface retrieval (Martonchik et al., 1998a; 2002). A Stage 1 aerosol retrieval algorithm (Diner et al., 2001) generates a Retrieval Applicability Mask (RAM) which contains flags indicating either a pixel is acceptable for the aerosol retrieval process or the name of the test which resulted in an unusable or contaminated designation. If data are not available in all 36 (angular and spectral) channels of MISR, the tests are skipped and the flag is set to 253. A complete list of flag values is presented in Table 3.2. Their precise definitions can be found in (Diner et al., 2001). A statistical summary of the RAM flags for two validation sites that exhibit minimum data availability is shown in Fig The failure results are mainly generated by the angle-to-angle correlation test (40%-48%). The failure of the angle-to-angle smoothness test is the second factor (about 9%) preventing the aerosol retrieval process. The angle-to-

91 74 angle correlation test and the angle-to-angle smoothness test capture clouds at any angles that escape the cloud screening. Results from the remaining tests average between 7% and 17%. The percentage of pixels with flag value 253 varies between 13% and 21%. Distributions of the RAM flags for other sites exhibit similar behavior (Hu et al., 2004). These results can be interpreted as follows. The imagery is first put through a cloud-screening process before any aerosol retrievals are performed using MISR data (Martonchik et al., 2002). A number of tests (Table 3.2) are then performed to identify all areas in a scene that are considered not suitable for aerosol retrieval. Note that the radiance angle-to-angle smoothness (# 9) and the image angle-to-angle correlation (#10) tests are performed using multiangle imagery that has been radiometrically calibrated, coregistered, and geolocated to the terrain. As such, if there are any clouds remaining within a scene, they will appear to be misregistered because of parallax. Since these two tests are designed to detect any such misregistrations, they provide a measure of cloud screening. Currently, these tests frequently override a flag value "optically thick atmosphere" generated by the cloud decision matrix. This explains the absence of flag value #7 in Fig. 3.7 that indicates cloudy. To summarize, (1) cloud contamination is the main reason why a limited number of valid data are available for LAI/FPAR retrievals. In about 48%-56% of the cases examined, failure of the radiance angle-to-angle smoothness (# 9) and the image angleto-angle correlation (#10) tests prevented aerosol retrieval. (2) The absence of data in all 36 channels of MISR (flag value 253 ) is responsible for about 13%-21% of invalid

92 75 input to the LAI and FPAR algorithm. (3) The failure rate of other tests (Table 3.2) for the selected areas is about 7%-16%. (4) When a successful aerosol retrieval is performed, there is a 95% probability of successful surface reflectance retrieval (Martonchik, personal communication) LAI and FPAR retrievals The availability of LAI and FPAR products was performed for each 2 o by 2 o area centered on the validation sites. For each area, pixels from all paths that overlapped with the 2 o by 2 o area and all orbits from Year 2000 were separated into three categories where (i) LAI/FPAR retrievals were not performed due to unavailability of BHR in the red and NIR spectral bands; (ii) LAI/FPAR algorithm failed and (iii) successful LAI/FPAR retrievals were performed. The first category, in turn, was broken down into unavailability of input due to clouds and due to other reasons. Fig. 3.8 shows a statistical summary of these cases. On average, about 25% of the pixels contain valid input to the LAI/FPAR algorithm. This number changes by site and may be as low as 14%. The LAI/FPAR algorithm performance can be further assessed by analyzing the seasonal course of the Retrieval Index (RI) defined as the ratio of the number of pixels with successful LAI/FPAR retrievals to the total number of pixels with valid input (Fig. 3.9). This index does not indicate retrieval quality but rather the success rate of the algorithm. The low number of algorithm retrievals during the winter time is due to snow

93 76 conditions and/or the absence of green leaves. The retrieval index varies between 50% and 80% during the summer time. Fig shows the temporal variation in mean LAI values over 2 o by 2 o areas. Such a large area was required to accumulate sufficient statistics needed to derive mean temporal trajectories in view of the poor spatial coverage of the product. To reduce the impact of biome heterogeneity, mean LAI at a given validation site was derived from pixels with the correct biome type (Table 3.1). Visual inspection of Fig indicates a significant overestimation of LAI in cases of biomes 1 (grasses and cereal crops) and 3 (broadleaf crops). The problem was traced to the calibration of the algorithm. The calibration procedure was performed by deriving global biome-dependent patterns of surface reflectance first and then adjusting a number of configurable parameters in the algorithm to match observations and simulations (Tian et al., 2003; Hu et al., 2003). The at-launch land cover map based on AVHHR data was used to select biome dependent surface reflectances. It was found (Yang et al., 2005) that this land cover map has significant misclassification between grasses (biome 1) and broadleaf crops (biome 3), resulting in the mismatch between simulated and actual observations of the surface reflectance. The algorithm was recalibrated with the Collection 3 MODIS Land Cover Product and integrated into version 3.3 operational MISR LAI/FPAR software. Fig shows temporal profiles of mean LAI generated by the recalibrated algorithm. The LAI trajectories show expected seasonal variations with the exception of needleleaf forests. The strong LAI seasonality in needleleaf forests is spurious and must be treated as an artifact resulting from too few reliable winter time retrievals (Fig. 3.8). It

94 77 should also be noted that there are few reliable measurements in the high northern latitudes during the winter period because of low sun angles and weak illumination conditions, which further amplify the problem of reliably estimating LAI in these regions during the winter months Validation of MISR LAI product Validation results are a key source of information to users on product accuracy and also serve as the basis for further algorithm and product refinement research. Product validation refers to assessment of product accuracy through comparisons to ground measurements that are scaled to the product resolution (Morisette et al., 2002). Significant efforts have already been made by multiple international teams to validate the Terra MODIS LAI product (Yang et al., 2005). Part of those validation activities were carried out at some of the same validation sites used in this study (Table 3.1). For most of the sites, the validation procedure includes generation of a fine LAI resolution map, typically 7 by 7 km, from ground measurements and high-resolution satellite imagery according to a specific algorithm. This map is then degraded to a moderate resolution which is used as a reference to assess the quality of satellite products. We detail this same validation strategy for MISR data over Alpilles site in France and summarize validation results from other sites.

95 Validation of the LAI product at a cropland site in Alpilles A field campaign over a 3 x 3 km agricultural area near Alpilles in France ( N, E) was performed from February 26 to March 15 in year 2001 (Baret et al., 2004). More than 95% of this site was composed of young and mature wheat and grasses (biome 1). Leaf area index was measured with a LAI-2000 Plant Canopy Analyzer. Data were collected on two transects of about 1 km at 50 m intervals and at 15 locations scattered throughout the site. Measurements at the 15 locations were performed at 4 m intervals on two 20 m lines which formed a regularly shaped cross. The average of 12 measurements was assigned as the LAI value at each of these locations and the standard deviations were taken as the precision of field measured LAI. A subset of an ETM+ image from March 15, 2001 (path 196, row 90) containing the Alpilles site was selected for the purpose of generating a fine resolution LAI map of the site. The image was atmospherically corrected using the 6S radiative transfer code (Vermote et al., 1997). Various techniques, including an empirical regression based on the Simple Ratio and the fine resolution MODIS LAI/FPAR algorithm, were evaluated to identify the most accurate method for generating the fine resolution LAI maps. The fine resolution MODIS algorithm and the SR relationship were the best candidates for this site and thus were used to generate a 30m LAI map of a km area centered on the Alpilles site (Tan et al., 2005). This map was re-projected from UTM WGS84 projection into the Space Oblique Mercator (SOM) projection using the ENVI (version 4) software (WWW3) first and then degraded to a 1.1 km resolution reference map (Fig. 3.12). Biome 1 pixels were selected for further analysis.

96 79 The MISR data from path 196, orbit 6598 (March 15, 2001) were used to validate the version 3.3 MISR LAI product. A km area (15 15 MISR pixels) which coincided with the reference map was extracted from this path. There were 125 biome 1 pixels in the reference map. The MISR LAI/FPAR algorithm successfully retrieved LAI values for 65 of these pixels. Fig shows distributions of the version 3.3 MISR LAI product and the reference LAI. Mean LAIs derived from the MISR and reference maps are 0.84 (std=0.3) and 0.96 (std=0.29), respectively. This result suggests that the MISR LAI product for this site is accurate to within an accuracy of about 0.2LAI with a precision of 0.3. This statement refers to an area consisting of about 156 MISR pixels (about km) Validation of MISR LAI product at other sites An analysis of the availability of MISR observations over the remaining sites showed that 0.5 o by 0.5 o or larger areas around the sites were required to accumulate statistically stable LAI retrievals needed for the analysis described at Alpilles. The validation reference maps of such large sizes were not available. Therefore, the validated Collection 4 MODIS LAI product with known accuracy and precision, was taken as the reference (Yang et al., 2005). The assessment of the MISR product was accomplished via analyses of linear regression models Y = βx + α of MISR LAI (dependent variable Y) with respect to the MODIS LAI (independent variable X). Several complicated issues arise when one attempts to implement this strategy. For example, the actual spatial location of the corresponding pixels in the two product maps

97 80 may not match well because of geolocation uncertainties as well as reprojection and resampling procedures. Also, satellite derived products themselves have a certain accuracy and precision, for example, due to incomplete atmospheric correction. Therefore, the LAI value assigned to a single pixel may be unreliable, but the mean LAI of multiple pixels may be valid (Wang et al., 2004). Thus, it is preferable to perform comparisons at multi-pixel (patch) scale, where the LAI product is statistically stable. Analyses of MISR and MODIS LAI were performed for the 0.5 o by 0.5 o areas centered on the validation sites. For each 8-day MODIS composite period, mean MODIS and MISR LAI values were accumulated over MISR paths that overlay the 0.5 o by 0.5 o area and whose orbits fall within the MODIS compositing period. These mean values were then used to build linear regression models of MISR LAI with respect to the MODIS LAI. The relationships between the MISR conditional LAI and MODIS LAI values for four biome types are shown in Fig The BigFoot team (WWW4) performed validation of MODIS LAI products at AGRO (a cropland site in Illinois, USA), KONZ (Konza Prairie Biological Station, Manhattan, Kansas, USA), and HARV (a temperate mixed forest site in Massachusetts, USA) sites (Cohen et al., 2003). At KONZ and AGRO, Collection 4 MODIS LAI was close to BigFoot field measurements scaled to MODIS resolution. MODIS and MISR LAI products agree sufficiently well at the KONZ site (Fig. 3.14). Together with the Alpilles results described earlier, this suggests good agreement between MISR LAI retrievals and ground measurements. The correlation between MISR and MODIS LAIs is stronger at the AGRO site (R 2 =0.88), where the slope is 1 and the offset is 0.4. The MISR product

98 81 underestimates MODIS LAI by about 0.4 LAI which is still within the product accuracy specification of 0.5 LAI. The MISR product underestimates MODIS LAI by 0.9 LAI at HARV site. This result may indicate better MISR retrievals since MODIS tends to overestimate ground measurements at this site(cohen et al., 2003). The spatial and temporal variation of the MODIS LAI product in southern Africa was validated by Privette et al. (2002) and Huemmrich et al. (2005) along the International Geosphere Biosphere Programme s (IGBP) Kalahari Transect. Mongu in Zambia was one of five sites incorporated in this large-scale transect. At this site, field data were collected from March through December The TRAC instrument was used to sample the vegetation overstory LAI along three 750-m transects separated by 250 m. The length and spacing of transects were chosen to sample an area large enough to be representative of a 1-km MODIS pixel. The direct outcome of TRAC, plant area index, was adjusted with ancillary stem area index data to estimate the LAI. The results indicate that the MODIS LAI product correctly captured the temporal phenology including the wet season peak (April), senescence (May through July), peak dry season (September) and green-up (November). The MISR product also captures this behavior (Fig. 3.10). MODIS and MISR LAIs are well correlated, R 2 =0.7 (Fig. 3.14). However, the MODIS LAIs exhibit a smaller range of variation compared to MISR LAIs. This is because MODIS overestimates LAI values by about 0.4 LAI during the dry season (see Fig. 3.8 in Privette et al., 2002). This results in an increased value of the slope in the regression model (β=1.4). If one corrects overestimated values by 0.4, the slope and intercept become 1 and 0.1, respectively, suggesting that the MISR provides a more accurate

99 82 estimate of LAI during the dry seasons at this site and coincides with MODIS values during other periods. This is consistent with the example discussed in section Conclusions An algorithm for the retrieval of LAI and FPAR from MISR surface reflectance data has been in operational processing at the Langley ASDC since October This paper describes the research basis for transitioning the MISR LAI/FPAR product from provisional to stage 1 validated status, i.e., an estimation of product accuracy has been made using a small number of independent measurements from selected locations and time periods and ground-truth/field program effort. In our approach, a comprehensive analysis of relationships, consistency and complementarity between various MISR surface products derived from independent algorithms is also included to demonstrate the potential utility of these MISR products in monitoring and modeling studies as well as to explore the potential for enhanced information retrieval through innovative manipulation of multiple products. At the present time, most of the validation efforts are limited to LAI, and only a few FPAR measurements are available over select locations. Therefore, most of the material in this paper is focused on the LAI product. The location of reflectance data in the spectral space is the basic source of information about the vegetation canopy conveyed by single angle multispectral satellite data. The inclusion of multiangular data (in addition to spectral sampling) provides additional information on land cover type, heterogeneity of vegetation canopies and brightness of their background. The use of this information results in reduced ambiguity

100 83 and error in the retrieved LAI and FPAR fields in arid lands. The consistency and complimentarity of the parameters in the MISR surface product suite that includes LAI, FPAR and BHRPAR is demonstrated here in the derivation of the canopy extinction coefficient, mean leaf angle inclination and the gap fraction. The spatial coverage of the MISR LAI/FPAR product is limited by the availability of atmospherically corrected surface reflectance data that are input to the algorithm. Cloud contamination is the principal reason limiting the availability of reflectance data. Failure of the radiance angle-to-angle smoothness and the image angle-to-angle correlation tests prevented aerosol retrieval in about 48-56% of the cases examined. The absence of data in all 36 channels of MISR is responsible for about 13-21% of invalid input to the LAI and FPAR algorithm. These pixels are mainly located near the path edges where the deviation of MISR view angles from their nominal values is maximal. The failure rate due to other reasons is about 7-17%. Validation of the early versions of the MISR LAI product suggests the algorithm overestimates LAI values in grasses and broadleaf crops. The algorithm was recalibrated and incorporated into the version 3.3 operational MISR software. Validation of this version suggests the MISR LAI product to correctly accommodate structural and phenological variability. The product is accurate to within 0.5 LAI in herbaceous vegetation and savannas and is an overestimate by about 1 LAI in broadleaf forests.

101 84 Site Konza Agro Mongu Lat/Lon (degree) 39.08N/96.56W Grasses 40.01N/88.29W Biome Type Broadleaf Crops Harv Forest 42.54N/72.17W Broadleaf Forests 15.43S/23.25E Savannas MISR BHR Availability 23% 20.30% 14.50% 40% Alpilles 43.81N/4.75E Cropland 29.80% Feb 26-Mar 15, 2001 Date Sampling Field LAI Extrapolated LAI Area Mean STD Area mean LAI Jun, x7 km 2.0~2.9 Aug, x25 m Jul, 2001 plots Jul, x7 km 2.5~3.6 Aug, Jun, x7 km 4.3 Aug, Jul, Apr 20, x750m Sep 02, x3 km n/a 10x10 km n/a Reference Cohen et. al, 2003 Privette et. al, 2002 ~0.9 Bin et. al, 2005 Table 3.1. Validation sites and availability of MISR BHR.

102 85 Flag Flag Description/Test Name 0 clear 1 missing data 2 poor quality 3 glitter contamination test 4 topography obscuration test 5 topography shadow test 6 topographic complexity evaluation 7 cloudy 8 cloud shadow masking 9 angle-to-angle smoothness evaluation 10 angle-to-angle correlation evaluation 11 region not suitable 253 fill value Table 3.2. MISR Retrieval Applicability Mask.

103 Red NIR BRF Red View zenith angle (Degree) BRF DHR length NIR 0.2 location 0.1 slope intercept Red Figure 3.1. Top Panel: Angular variation of BRF in red and NIR spectral bands for shrubs. Bottom Panel: Values of the BRF at red and NIR wavelengths as a function of the view zenith angle form a curve on the RED vs. NIR plane, or, angular signature in spectral space (Zhang et al., 2002a). The signature is characterized by three metrics: (i) its location in the spectral space which is determined by the directional hemispherical reflectance (DHR), (ii) inclination (slope and intercept) of the signature, and (iii) the length of the signature, which describes spectral variation in the shape of the BRDF.

104 87 Figure 3.2. Angular signatures on the RED vs. NIR plane for five land covers. The solar zenith angle and the azimuth angle of the BRFs measured from the principal plane are 19 o ±1 o and 51 o ±10 o for Grasses and Cereal Crops; 25 o ±3 o and 50 o ±10 o for Shrubs, 24 o ±1 o and 60 o ±15 o for Broadleaf Crops; 33 o ±2 o and 40 o ±8 o for Broadleaf Forests; 42 o ±3 o and 60 o ±10 o for Needleleaf Forests. The locations, or DHRs in red and NIR spectral bands, are depicted as stars. The solid symbol on each curve indicates the 70.5 o afterward camera.

105 June: y = 5.8x + 0.0;R 2 = July: y = 7.7x - 0.0; R 2 = Aug: y = 7.8x + 0.0; R 2 = Sep: y = 5.8x + 0.1; R 2 = NIR Oct: y = 3.7x + 0.0; R 2 = Apr: y = 0.8x + 0.1; R 2 = Nov: y = 2.4x - 0.0; R 2 = May: y = 2.4x R 2 = Red April May June July August September October November Figure 3.3. Temporal variation in the mean signature of a broadleaf forest located in the 2 by 2 degree area centered on the Harvard Forests EOS Core Validation Site ( N, W). The MISR data acquired from March to November, 2000 were used to derive these signatures.

106 89 3 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec MODIS MISR Path LAI Day (Year 2000) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec MODIS MISR Path FPAR Day (Year 2000) Figure 3.4. Annual course of leaf area index (left panel) and fraction vegetation absorbed PAR (right panel), for year 2000, from MODIS and MISR data for the Walnut Gulch (San Pedro) site in Arizona, (31.74N, W). Symbols in the MISR LAI and FPAR profiles correspond to mean values over different paths overlapped with 2 o by 2 o areas centered on the flux tower site. The most probable LAI and FPAR are used.

107 90 Figure 3.5. Partitioning of the top-of-canopy PAR into its canopy and ground absorbed portions. The MISR Land Surface Product includes leaf area index (LAI), fraction of photosynthetically active radiation absorbed by vegetation (FPAR) and bihemispherical reflectance integrated over the photosynthetically active spectral region (BHRPAR). From these products, the fraction of PAR absorbed by the ground can be estimated as 1 BHRPAR FPAR. MISR Level 2 Land Surface Data over North America from 15 August 2003 (path 32, orbit 19461, blocks 54-60) are shown here. The most probable LAI and FPAR are used.

108 91 -LN(FGROUND) y = x R 2 = (a) FGROUND (b) Best prediction of GFROUND given LAI Best prediction of LAI given FGROUND 0.95 EXP(-0.61 LAI/cos(SZA)) LAI/COS(SZA) LAI Figure 3.6. (a): Using MISR Level 2 Land Surface Data over Africa from 23 April 2002 (path 176, orbit 12480, blocks ), the negative logarithm of FGROUND is plotted against mean LAI normalized to the cosine of the solar zenith angle. The linear relation shows that mean LAI and FGROUND follows Beer s law. (b) Distribution of points [F1(f), f] and [l, F2(l)] on the FGROUND vs. LAI plane. Here LAI=F 1 (f) is the best possible prediction of LAI given a realized value, f, of FGROUND; FROUND=F 2 (l) is the best possible prediction of FGROUND given a value, l, of LAI. The most probable LAI and FPAR are used.

109 92 60 Agro Percentage (%) Retrieval Applicability Mask 50 Harvard Forests 40 Percentage (%) Retrieval Applicability Mask Figure 3.7. Statistical summary of the RAM flags for Agro and Harvard Forests sites.

110 93 Figure 3.8. Statistical summary of cases for which (i) a LAI/FPAR retrieval was not performed due to the absence of input; (ii) LAI/FPAR algorithm failed; and (iii) a successful LAI/FPAR retrieval was performed. The first case is broken down into two sub-categories: Input is unavailable due to clouds and Input is unavailable due to other reasons.

111 Alpilles Feb Apr Jun Aug Oct Dec 100 Konza Feb Apr Jun Aug Oct Dec Retrieval Index Retrieval Index Day (Year 2000) Day (Year 2000) 100 Agro Feb Apr Jun Aug Oct Dec 100 Mongu Feb Apr Jun Aug Oct Dec Retrieval Index Retrieval Index Day (Year 2000) Day (Year 2000) 100 Harvard Forests Feb Apr Jun Aug Oct Dec 100 Ruokolahti Feb Apr Jun Aug Oct Dec Retrieval Index Retrieval Index Day (Year 2000) Day (Year 2000) Figure 3.9. Temporal variation in the retrieval index for six validation sites.

112 95 LAI Konza Feb Apr Jun Aug Oct Dec MISR Path MODIS Day (Year 2000) LAI Alpilles Feb Apr Jun Aug Oct Dec MISR Path MODIS Day (Year 2000) LAI MISR Path MODIS Agro Feb Apr Jun Aug Oct Dec Day (Year 2000) LAI Mongu Feb Apr Jun Aug Oct Dec MISR Path MODIS Day (Year 2000) LAI Harvard Forests Feb Apr Jun Aug Oct Dec 7 MISR Path MODIS Day (Year 2000) LAI Ruokolahti Feb Apr Jun Aug Oct Dec MISR Path / MODIS Day (Year 2000) Figure Annual profiles of the mean LAI temporal variation derived from MODIS (line) and MISR (symbols) data for Alpilles, Konza, Agro, Mongu, Harvard Forests and Ruokolahti sites. Symbols in the MISR LAI profile corresponds mean values over different paths overlapped with 2 o by 2 o areas centered on the validation site.

113 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Konza Agro 5 Conditional LAI Day (Year 2000) Figure Annual profiles of the mean LAI temporal variation over biome 1 (grasses and cereal crops) and biome 3 (broadleaf crops) in 0.5 o by 0.5 o areas centered in Konza and Agro sites generated by the re-calibrated LAI and FPAR algorithm.

114 Non-biome1 Figure Reference LAI maps at 30 m (left panel) and 1.1 km (right panel) resolutions over 16.5km 16.5km area containing the Alpilles site in the MISR Path 196 Space Oblique Mercator (SOM) projection.

115 MISR LAI Reference LAI Percentage (%) LAI Figure Distribution of the version 3.3 MISR LAI and reference LAI values at a resolution of 1.1 km.

116 99 MISR Conditional LAI Konza y = x R 2 = MODIS LAI MISR Conditional LAI Agro y = x R 2 = MODIS LAI MISR Conditional LAI Mongu y = x R 2 = MODIS LAI MISR Conditional LAI Harvard Forests y = x R 2 = MODIS LAI Figure Linear regression models of MISR LAI with respect to the MODIS LAI for 4 validation sites.

117 100 Chapter 4 A rank based algorithm for aggregating land cover maps with minimal information loss 4.1. Introduction The understanding and modeling of natural and anthropogenic processes which affect the Earth s environment require the production of land cover and land use maps at broad spatial scales (Mayaux & Lambin, 1995). For global scale research, data aggregation is primarily practiced for scaling up environmental analysis or models from local to landscape, regional, or global scales (Moody & Woodcock, 1996). Satellite data typically available at fine resolutions need to be coarsened to represent the spatial characteristics (spatial pattern, spatial autocorrelation, etc.) at scales used by global models. The scale of data is associated with its resolution, which is defined as the area represented by one single pixel (DeMers, 1997), or more generally, as the degree to which small objects are distinguishable (Forman & Godron, 1986; Forman, 1997). The scale is often expressed in terms of grain and extent, describing the minimum spatial resolution of the data and the width of the study area, respectively (Milne, 1991; McGarigal & Marks, 1995; Hargis et al., 1998). The grain then determines the lower limit of what can be studied. Coarsening the spatial resolution leads to a loss of spatial details at a rate that depends on the spatial structure or heterogeneity of the landscape (Woodcock & Strahler, 1987; Townshend & Justice, 1988; Moody & Woodcock, 1994, 1995, 1996). Landscape patterns, as observed by digital images generated by remote

118 101 sensing appear or disappear at different scales (Farina 1998). Rare land cover types are lost when resolution becomes coarser; patchy arrangements disappear more rapidly with decrease in the resolution than contagious ones (Turner et al., 1989). This phenomenon is usually more pronounced when the elements composing the spatial pattern (e.g., patches) are scattered and are as small as or smaller than a pixel of the aggregated image. As a result, the use of coarse resolution images poses divergent problems in the estimation of cover type areas and the assessment of its accuracy. Aggregating data to a coarser resolution is often preferred because certain spatial patterns will not be revealed until the data are displayed at a coarser scale (e.g. Seyfried & Wilcox, 1995). It is well recognized that any aggregation method causes the loss of certain spatial details. However some methods retain statistical characteristics of the data better than others (Bian & Butler, 1999). A question then arises as to how these aggregation effects can be evaluated. Aggregation reduces the number of pixels in the image for a fixed spatial extent. Each pixel consequently represents a larger area. This effect can alter the statistical and spatial characteristics of the data. Models that use aggregated data become scale-dependent, i.e., their predictions differ when input data of different resolutions are used (Bian & Butler, 1999). Although this effect is well-recognized by the GIS, remote sensing, and other science communities that use spatial information (e.g., Moody & Woodcock, 1994, 1995; Marceau & Hay 1999; Milne & Cohen 1999), there are very few papers on the effects caused by different aggregation techniques. Studies that require aggregation often employ the most convenient method without taking all the effects into account. This may

119 102 jeopardize the integrity of studies as well as subsequent decision-making process. The goal of this study is to develop and test an algorithm that generates coarse resolution land cover maps at the continental scale but minimizes changes relative to the original image. A series of 1 km and coarser maps of North American land cover are generated. The algorithm performance is quantified in terms of spatial metrics commonly used in landscape ecology. This approach has two justifications. First, it was reported that class spatial pattern influences information change during aggregation (Moody & Woodcock, 1994, 1995). Second, it is accepted that land cover pattern is related to landscape function, a central hypothesis of landscape ecology, known as the pattern/process paradigm (Coulson et al., 1999). Using spatial metrics, we can document the way different algorithms alter or conserve certain characteristics of the spatial information presented in the original image. The objectives of this investigation are: (a) to develop a new spatial aggregation algorithm that represents fine resolution data at a coarser resolution with minimal information loss, and (b) to evaluate the new algorithm through comparison to the random aggregation algorithm and the most widely used majority aggregation algorithm; this evaluation is performed through spatial metrics and parameters describing the predictability and accuracy of the aggregation results.

120 Data set and methods MODIS land cover map The International Geopsphere-Biosphere Programme (IGBP) set of 17 land cover classes (Belward et al., 1999) are provided by the MODIS land cover product. Figure 1. 1 shows an image of the Northern American data set used in this paper. Table shows the percentage of each class in the image. The water class dominates the image making up 68% of the total number of pixels. The areal percentage of other classes varies between 0.001% and 7%. The large size of the image allows us to have more minority classes in the original image and to evaluate the ability of the aggregation algorithms to keep the class properties of the original image at coarser resolutions. The number of coarse pixels in each row and column as a function of the image resolution is given in Table Metrics to represent image information Characteristics of landscape patterns are usually expressed in terms of connectedness (e.g. contagion, fragmentation), diversity (e.g. Shannon diversity, Simpson index), and image heterogeneity (e.g., class area evenness). How these characteristics change with resolution and algorithm was examined by calculating a series of metrics that measure these properties. The landscape pattern metrics selected for this study quantify the relative percentage of different land cover classes, their spatial adjacencies, and represent overall image properties. Most metrics used here are from landscape ecology. Pattern differences between the aggregated images and the original 1 km data are expressed as

121 104 R M M M r 1 = (4.1) 1 where are the metrics of aggregated image at spatial resolution r and M is that of M r 1 original image at 1 km spatial resolution Metrics based on class proportions The distribution of patterns and their areas are important characteristics of any image. Conservation of areas in the aggregation procedure is consequently a prerequisite to limit pattern change since pattern can be defined as spatial distribution of area. We use the concept of class area evenness to quantify the presence of classes relative to each other. The length of the Lorenz curve (L) is used to assess the degree of evenness (Lorenz 1905; Rousseau et al., 1999), which is calculated as follows. The class areas are replaced with relative values which are then ranked in ascending order. Let ( p i p ) pi i 1 represents the relative area of i-th class and z be the total number of classes. The cumulative function of area distribution is given by * p i = p j i j= 1 (4.2) The set of pairs ( * p i, i/z), i = 1, 2,, z, is termed the Lorenz curve. To construct it, values of * p i are plotted on the ordinate against its rank number normalized by the total number of classes on the abscissa. The length of the Lorenz curve L can be calculated from the graph as (Bogaert et al., 2000b),

122 105 L = z i= z + z * * 2 1 ( pi pi 1 ) = + ( pi ) 2 i= 1 z 2 (4.3) In case of perfect evenness, i.e. i, j z : p i = p, the curve coincides with the diagonal (1:1 line) and L = 2 j. For a series in which a certain class dominates over others, i j : p >> p, L 2. Evenness can be interpreted as a partial order (Rousseau i j et al., 1999) and thus adequately represented by a Lorenz curve (Taillie 1979). Note that curves can cross each other in which case evenness can not be used for they can generate identical L values (Bogaert et al., 2000b). We use the Shannon ( ) (Shannon & Weaver, 1949) and Simpson diversity ( characterize the diversity of the classes. These are defined as H z 1 = p i p i ) i= 1 z i= 1 H 2 H 1 ) (Simpson 1949) indices to ln( (4.4) 2 H 2 = ln p i (4.5) The higher their values the more diverse the image is. The diversity metrics depend on two variables the richness component shows the number of classes present and the evenness component quantifies the distribution of the image pixels over the classes. The Shannon index is more sensitive to the richness component while the Simpson index is relatively less sensitive to richness and places more weight on the common classes (McGarigal & Marks 1995). These indices, therefore, can show considerable variation in response to changes in landscape richness and evenness.

123 106 The proportion estimation error ( E i ) is used as a fourth descriptor. This metric shows whether an aggregation procedure results in an over- or underestimation of class areas. This variable is defined as (Moody & Woodcock, 1994) E i pci p fi = (4.6) p fi where p and p are relative areas of class i at the coarse and fine resolutions. An ci fi overall effect of the aggregation procedure of class proportion is given by the mean error over classes and its standard deviation Contagion metric Contagion (C) measures the degree to which the image is composed of a few large or several small patches (O Neill et al., 1988). It ranges between 0 and 1. High values indicate that the image is clumped into a few large patches. The metric accounts for adjacency and is expressed in terms of conditional probabilities p i, j of class i given that one of its neighboring pixels belongs to class j( i j) as z z 1 C = 1 + p i, j ln( pi, j ) (4.7) 2ln( z) i= 1 j= 1 where z is the number of classes in the image. Contagion measures both class interspersion (intermixing of classes) as well as class dispersion (the spatial distribution of the class). It is one of the most frequently applied and commented landscape metrics in landscape ecology to characterize landscape pattern (e.g., Schumaker 1996; Hargis et al., 1998; O Neill et al., 1999).

124 Monmonier fragmentation metric Fragmentation describes the spatial scatter of pixels. Measurement of class fragmentation is still a subject of debate (Bogaert et al., 2002; Bogaert 2003) but a tendency towards simpler metrics quantifying components of complex spatial patterns was suggested (Giles & Trani, 1999). Therefore, a simple fragmentation metric (F) based on the grouping of adjacent pixels of the same class into patches is used in this study (Monmonier 1974; Johnsson 1995), m1 1 F = (4.8) m 1 2 where and m are numbers of patches and pixels, respectively. This metric varies m1 2 between two extremes, 0 and 1. If all pixels are grouped into a single patch, F = 0. For maximum fragmentation, m 1 = m2 and F = 1. To calculate F, aggregation of pixels into patches based on pixel neighborships for each class is required. Two pixels are grouped in one patch if they are orthogonal neighbors (nearest neighbors) and if they belong to the same class (Bogaert et al., 2000a). Orthogonal neighbors are also denoted as adjacent. Patch mosaics constitute another level of structural composition of the image. Patches are treated as spatially homogeneous entities and relationships between patches can consequently be studied (Fortin 1999). The conversion of pixel-format into patchformat data can be performed using standard software. We will calculate F two ways. First, Eq. (4.8) is calculated for the entire image. Second, we evaluate F for each class and then calculate the average over the classes.

125 Probability of adjacency We measured the conditional probability of adjacency (p c ), that is, given a pixel of class of interest, the nearest neighbor is also a pixel of the class of interest (Riiters et al., 2000). This measure is considered an alternative assessment of fragmentation and is calculated as n n 2 p c = (4.9) 1 with n 1 the number of pixel pairs that include at least one pixel of the class of interest and n 2 the number of pixel pairs of which both pixels belong to the class of interest. The measure p c is calculated in a 3 3 template window. Diagonally adjacent pixels are not considered as pixel pairs. The measure p c equals zero if none of the pairs includes pixels of interest; p c equals one if all pixels in the template are pixels of the class of interest. The average probability per class can be determined using the distribution of the template values Similarity metrics We use similarity metrics to quantify changes in image as a function of resolution. Such metrics combine the information provided by every separate pattern component and express the extent to which the coarse resolution image is similar to the original one. The Euclidean distance ED i, j, between two images i and j, is denoted as

126 109 ED n 2 i, j = xm, i xm, j ) m= 1 ( (4.10) where and are the metrics values, observed in images i and j, respectively. The x m, i x m, j larger ED i, j is, the less similar two images are. The Euclidean distance is the length of the distance between two images by accounting for the 7 metrics we calculated. For F, the average class data were used to determine similarity. A second similarity index known as the Czekanowski coefficient (Motyka et al., 1950; Legendre et al., 1979) expresses the percentage of similarity ( PS i, j ) between two images and is calculated as 2w PS i, j = 100 (4.11) t + r Here w, t and r are w = t = n m= 1 n x m i m= 1 min( x m x (4.12), i, m, j ) n x m j m= 1, and r =, (4.13) For two identical images, PS i, j = 100% Accuracy metric Accuracy assessment is used to quantify product quality. We applied accuracy assessment in evaluating coarse landcover maps aggregated by different aggregation algorithms and different approaches (consecutive and non-consecutive). For a given land cover map, factors such as resolution, aggregation algorithm, and approach can affect

127 110 accuracy. The reference data used in the accuracy assessment is the 1km IGBP land cover map. In this paper, aggregation accuracy is defined as the average percent fraction of labeled class of all pixels in the original 1km IGBP landcover map, ACCU n pi i= = 1 (4.14) n For a specified aggregated map, n is the total pixel number, p i is the accuracy of pixel i. For example, consider an aggregated 2km coarse-resolution map and a pixel labeled as grassland. Let 3 out of the 4 subpixels in the 1km map belong to the grassland class and one subpixel is labeled savanna. The accuracy of the pixel in the 2 km image is then given by the proportion of the subpixel numbers that belong to the same class as the pixel in the coarse resolution image, i.e., 3/4 = It should be noted that different aggregation algorithms and approaches could have different classes at the coarse resolution and thus have different accuracy values. In this case, aggregation accuracy reflects the agreement between coarse resolution class and subpixel land cover in the original IGBP map (Latifovica & Olthof, 2004) Aggregation algorithms Numerous aggregation methods have been reported in remote sensing literature. The most widely used procedures are averaging over all pixels, nearest neighbor resampling, or choosing the dominant value (Turner 1989; Bian 1997; Gardner 1998). In the following description, we denote pixels of the original image as subpixels, and the aggregated coarse resolution pixels as the pixels. The aggregation window (in the

128 111 following sections is always a 2 2 subpixel window) is denoted as a block. Figure 1. 2 shows the algorithms considered in this study. Only non-overlapping blocks are considered in this study. For random and majority aggregations, both consecutive and non-consecutive approaches are used. In the non-consecutive approach, every coarse image is aggregated from the original 1km image directly. In the consecutive approach, a fixed aggregation window of 2 2 subpixels is used, which means that an image with resolution z serves as the input for an image with resolution 2z Majority aggregation This is the most widely used aggregation procedure. It uses a line by line scanning sequence, generally starting at the upper left corner of the image and ending at the bottom right corner, and every cluster of subpixels is aggregated independently. This technique attributes a pixel to a class based on the dominant subpixel class in the block. If several classes are present with the same fraction, a random class selection is made. The number of blocks with randomly selected classes will account for uncertainty or lack of predictability in the aggregated images (Figure 1.2). This algorithm is not areaconservative, i.e., classes that have large contiguous patches will stay in the aggregated image while classes showing scattered small patches may disappear. This characteristic should be avoided Random aggregation With random aggregation, the image is aggregated line-by-line and every

129 112 aggregation action is independent of the preceding actions. A random selection is made among the subpixels in the block. Classes with majority patterns will be favored due to an enhanced probability of being selected. Nevertheless, this does not exclude the assignment of pixels to a class that was dominated by another one in the block. With this approach, and except for homogeneous patterns in which all four subpixels belong to the same class, every aggregation step involves a random selection. The initial proportions of the classes are likely to be conserved due to this randomization effect (Gardner 1998). This will decrease the degree of predictability of the aggregated map product which may be considered as a negative characteristic of this technique Ranked aggregation A new aggregation procedure is proposed which is more conservative with regard to class area and spatial pattern, that is, the proportional area of every class in the aggregated image remains similar to that in the original image. Metrics describing the spatial pattern in the original image are conserved maximally. In the proposed algorithm, the original image is not scanned line by line, but crisscross movements across the image are made. Some blocks are preferentially aggregated. This irregular selection of blocks is governed by well-defined rules given below. Aggregation of subpixels into pixels are not independent events, i.e., the aggregation result of the i-th block is determined by earlier aggregations, e.g., the ( i 1)th pixel, in the same image. Blocks could be assigned to the minority class instead of the dominant class. These two features constitute the main difference of this new algorithm.

130 113 Consider an image I m m with m m subpixels. This image is aggregated using 2 2 non-overlapping aggregation windows or blocks into I, with n = m / 2. Every 4 subpixels in are replaced by one single pixel in. Consider z classes in of areas a, a2,,. Given class j, the a subpixels exhibit a particular spatial pattern in I m m I m m 1 K a z j ; if the blocks are superimposed on the original image, 10 different block types can be observed (Figure 1.3): (1) Blocks composed of 4 subpixels of class j and denoted as {4, 0, 0, 0}. This is a homogeneous block type with complete dominance of class j. (2) Blocks containing 3 subpixels of class j and one subpixel from another class denoted as {3, 1, 0, 0}. This is a heterogeneous block type with dominance of class j. (3) Blocks containing 2 adjacent subpixels of class j next to 2 subpixels from two other classes with notation {2, 1, 1, 0}a. This is a heterogeneous block type with dominance of class j. (4) Blocks containing 2 diagonally placed subpixels of class j and 2 subpixels from two other classes with block type notation {2, 1, 1, 0}d. This is a heterogeneous block type with dominance of class j. (5) Blocks containing 2 adjacent subpixels of class j and 2 adjacent subpixels from another class denoted as {2, 2, 0, 0}a. This is a heterogeneous block type with evenness between the 2 classes presented. (6) Blocks containing 2 diagonally placed subpixels of class j next to 2 diagonally I n n n n I m m

131 114 placed subpixels from another class which is denoted as {2, 2, 0, 0}d. This is a heterogeneous block type with evenness between the 2 classes presented. (7) Blocks containing 4 subpixels from 4 different classes which is denoted as {1, 1, 1, 1}. This is a heterogeneous block type with evenness between the 4 classes presented. (8) Blocks containing 1 subpixel of class j and 3 subpixels from two other classes. If the two subpixels belonging to the same class are diagonally placed this block type is denoted as {1, 1, 2, 0}d. This is a heterogeneous block type in which class j is dominated by another class. (9) Blocks containing 1 class j subpixel next to 3 subpixels from two other classes. If the two subpixels belonging to the same class are adjacent this block type is denoted as {1, 1, 2, 0}a. This is a heterogeneous block type in which class j is dominated by another class. (10) Blocks containing 1 subpixel of class j next to 3 subpixels from another class which is denoted as {1, 3, 0, 0}. This is a heterogeneous block type in which class j is dominated by another class. Consider the areas of the z classes in the aggregated image, i.e., a, a2,, a 1 K. In the z ideal case, the relationship between a j and a j is then given by a j = 4 a j (4.15) j Let N be the number of blocks of a particular type of class j with BlockType the BlockType block type notation. A remotely sensed image of a landscape exhibits hierarchical

132 115 j j patterns. It can be accepted that generally and will compose the majority j j j class pattern features of class j, while, for example,, and will form the minority class pattern components. N {4,0,0,0} N {3,1,0,0} N {1,1,1,1 } The starting point in the aggregation procedures is, first, all aggregated. By doing this, a part of the of the j N {4,0,0,0} N {1,1,2,0 }d j N {4,0,0,0} N {1,3,0,0} block types are a j pixels are already specified. Pixel assignment blocks does not involve any information loss because of the homogeneity of the pixels. The total area of pixels generated in this way is denoted asα, and is related to a j as j a = α + β (4.16) j j j with β j class j pixels in the aggregated image that result from heterogeneous blocks without loss. It should be noted that generally a > α. Only if β = 0, the aggregation procedure is complete after this initial step which is executed first for all z classes. It can even be concluded that the original map contained redundant information by presenting j j j the data at a resolution finer than required when β = 0 j. After this step, 4 k i= 1 N i {4,0,0,0} subpixels are aggregated. All remaining pixels have to be assigned for every class except for the case of β = 0. These pixels have to be selected from those blocks containing at least one single pixel of class j. The aggregation at each step is based on the ranking of the block types: { 3,1,0,0} {2,1,1,0} a {2,1,1,0} d {2,2,0,0} a {2,2,0,0 } d j

133 116 { 1,1,1,1} {1,1,2,0} d {1,1,2,0} a {1,3,0,0} (4.17) with indicating the order of aggregation. Within a class all blocks of type {3,1,0,0} have to be first aggregated followed by blocks types {2,1,1,0}a, {2,1,1,0}d, {2,2,0,0}a, {2,2,0,0}d, {1,1,1,1}, {1,1,2,0}d, {1,1,2,0}a, and {1,3,0,0}. This is repeated until β j blocks are aggregated. If different blocks of a certain pattern type are present in the I m m image, for example, in the initial phase of the aggregation, a random selection is made among them. The rank in Eq. (4.17) is based on the principles of subpixel majority and subpixel connectivity. In the heterogeneous blocks with type {3,1,0,0}, {2,1,1,0}a and {2,1,1,0}d, class j is dominant, with the latter two showing less dominance than the first. In configurations {2,2,0,0}a, {2,2,0,0}d and {1,1,1,1}, none of the classes dominate, but the former two configurations have a higher priority because more subpixels of the class of interest are present. In {1,1,2,0}a, {1,1,2,0}d and {1,3,0,0}, class j is dominated by other classes, but the dominance in configurations {1,1,2,0}a and {1,1,2,0}d is less pronounced than in {1,3,0,0}. The principle of connectivity indicates that, in case of equality, {2,2,0,0}a prevails over {2,2,0,0}d. When class j is dominant, {2,1,1,0}a types will be aggregated before {2,1,1,0}d. The same principle explains why {1,1,2,0}d blocks are chosen, and if this type is not available any more for class j, type {1,1,2,0}a will be aggregated. This procedure is not executed class by class. Subpixels of more than one class are replaced by only one class in the coarse pixel image in the case of aggregating a heterogeneous block. If a class-by-class aggregation were executed, it is possible that

134 117 when the last class had to be aggregated all the blocks containing subpixels of this class were already assigned to other classes with which they have these blocks in common. Therefore, to determine the sequence of block aggregation, a ratio is defined as γ j ( β j ) r = (4.18) ( ζ ) j r with (β ) the number of blocks to be assigned to class j, and j r (ζ ) j r the number of remaining blocks containing a subpixel of class j. The subscript r indicates remaining, and both (β ) and j r (ζ ) j r have to be recalculated after a block is assigned to a particular class. Classes with low values of (ζ have a higher probability that not enough blocks ) j r are available relative to the required number (β. Therefore, a class with the highest γ - values is aggregated first according to the above mentioned rule of rank (Eq. (4.18)). After this assignment, all γ values are recalculated, and the procedure repeated. A class with the lowest (ζ is chosen in the case of equal of γ -values. This procedure hence ) j r ) j r avoids ( β ) > ( ζ. A random selection is made among the classes involved in the case j r j ) r of identical (ζ values. ) j r The novelty and added value of this aggregation technique are in Eqs. (4.17) and (4.18). Eq. (4.17) describes the rank of the block types, giving preference to those types that contain a majority of the class of interest and to pattern connectivity (adjacent patterns prevail on diagonal and vice versa in the case where the class of interest is a minority). Eq. (4.18) describes how this rank is optimized for all classes and avoids disappearance of classes due to their initial scattered pattern. Neither line by line

135 118 sequence nor a class by class sequence is used when the image is aggregated. The selection to which class a block is assigned and where this block is located in the image is not fixed unlike the other techniques. Instead, it is determined only by the spatial pattern of all classes at each stage. The non-consecutive approach was unrealizable for the ranked aggregation technique due to exponentially increasing number of block type patterns for block with dimensions greater than Results and discussion Investigation of how the relative presence of classes changes with resolution is a first step towards assessing the algorithm performance. Four variables quantify these changes the Shannon and Simpson indices which measure the diversity of proportions, the Lorenz Curve Length which characterizes the evenness of these proportions, and the proportional errors. Figure 4.4(a) shows the relative values of the Lorenz Curve Length compared to that in the original image. Ranked aggregation does not change evenness proportion up to a resolution level of 128 km. Changes can be clearly seen at 2 km resolution in the case of consecutive and nonconsecutive majority aggregations, which indicates the appearance of class dominance. For example, deciduous needleleaf forests, urban and built-up areas (data not shown) are not present anymore in the coarse resolution images. Majority aggregation will favor classes with a large extent. Consequently, large classes extend and smaller ones disappear. The increasingly negative value of the metric signifies a decreasing length of the Lorenz curve with aggregation, reflecting more proportional evenness.

136 119 Non-consecutive random aggregation closely follows the tendency in ranked aggregation up to a resolution of 32 km and then shows a positive deviation which indicates less evenness at 64 km resolution. The other techniques do not provide better results. The diversity of total class area (Figures 1.4(b) and 1.4(c)) is clearly altered by aggregation in the case of random and majority algorithms. This is especially true of the majority algorithm; the deviation is large for both consecutive and non-consecutive approaches and appears already after the first aggregation (2 km level). Ranked aggregation conserves the diversity of the class areas almost perfectly for both diversity metrics, especially at coarse resolutions (32 to 128 km). The proportional error expresses the extent to which the proportion of each class in the image changes with resolution (Figure 4.4(d)). Both majority aggregation algorithms have bigger proportional errors than other aggregation techniques and the increasingly negative trend of the curve indicates smaller proportions with aggregation. However, since an average value is used to reflect the image information content and the sum of the proportions at every scale level has to equal unity, this trend indicates that certain classes will have a smaller proportion due to aggregation (12 out of 19 classes), while the others show an increase (3 classes) or an irregular trend (4 classes). Ranked aggregation is the most effective in conserving the relative proportion of every class. Random aggregation techniques generate patterns similar to the original image at fine to moderate resolutions (2 to 16 km). Contagion expresses the extent to which pixels of different classes are adjacent. It quantifies interspersion of classes and combines two features fragmentation of classes

137 120 and their spatial mixing. Contagion is calculated for the entire image and therefore reflects a characteristic of the overall spatial pattern. Contagion is based on the determination of the probability that a certain class is neighboring another one and accounts for the size differences between classes. Nevertheless, small classes remain more sensitive to the disappearance of one single pixel than large ones, which will likely alter the observed probability considerably at coarse resolutions. Ranked aggregation conserves the degree of contagion almost perfectly, with a deviation not exceeding 1% at fine to moderate resolutions (Figure 4.5). At coarser resolutions, majority aggregation, both in the consecutive and non-consecutive mode, performs better although the contagion for all techniques shows a clear trend deviating from the horizontal reference line of no change. Random aggregation clearly does not conserve contagion and the choice between a consecutive or a non-consecutive way of generating the image series has no impact. All three techniques show a decreasing trend for contagion indicating a tendency towards smaller patches which is due to the smaller number of pixels available to represent pattern information. It should be noted that contagion is based only on pixel counts regardless of the area represented by them. The difference between random aggregation and majority/ranked aggregation is likely due to the fact that the former does not account for spatial relationships between pixels while the latter techniques favor conservation of pixels that are spatially grouped. Figure 4. 6 shows evolution of the Monmonier fragmentation index F for the 19 classes pooled. Fragmentation is measured by expressing the number of patches observed relative to the number of pixels. F tends to zero in the absence of fragmentation while F

138 121 values equal to unity indicate patches composed of a single pixel only. A general tendency of increasing fragmentation is observed with aggregation. A nearly linear increase of the fragmentation metric is seen for random aggregation, which results from the presence of more singular pixels at coarse resolutions. Figure 4.6(a) suggests a steady change in the spatial pattern of all classes pooled. No clear influence of the choice of input data (non-consecutive versus consecutive aggregation) is observed. The difference between the original and aggregated images increases with every aggregation step reflecting an increase in patches of single pixel. This tendency is not observed for ranked aggregation and majority aggregation. Both ranked and majority aggregations show less deviation from the original image and the change is not continuously increasing at every aggregation level. Ranked aggregation must be preferred over majority aggregation for this specific image as the relative differences are smaller. The upward trend in both curves reflects the representation of larger number of single pixel patterns. It should be noted that the Monmonier fragmentation metric does not account for pixel area and is only based on pixel counts, like the contagion metric. Figure 4.6(b) uses class-based data to evaluate pattern change due to aggregation. While for random aggregation the aggregated pattern becomes rapidly more fragmented relative to the starting image, majority and ranked aggregation show less deviation from the original pattern at coarser resolution, especially when standard errors are taken into account. Except at 64 and 128 km, ranked aggregation is the most conservative towards pattern as quantified here by its degree of fragmentation. It should be noted that data series based on different aggregation rules are not fully comparable, especially at coarse

139 122 resolutions, due to class disappearance with majority aggregation. This general trend where majority and ranked aggregation perform better than random aggregation with regard to fragmentation is partially confirmed by separate analysis of every class (details not presented for brevity). The probability of adjacency expresses the probability that if a pixel belongs to a certain class, its neighbor also represents that class. This probability is a measure of spatial dispersion of pixels of a class (class fragmentation) and quantifies the spatial mixing and connectivity of the classes. An overall view on pattern change with changing resolution is obtained by expressing this pattern characteristic using the average of the probabilities observed for every class. Figure 4.7 shows the evolution of the average probability of adjacency for the three aggregation techniques. Random aggregation (both consecutive and non-consecutive) influences class dispersion (lower probabilities in coarse resolution images) and large deviations (~50% for non-consecutive random aggregation) are observed at coarse resolution. Nevertheless, the value obtained by consecutive random aggregation is closest to the original for the first aggregation step (2 km), while the other techniques immediately report a deviation of greater than 8% relative to the probability of adjacency in the original image. The average probability of adjacency decreases more rapidly with decreasing resolution for random aggregation compared to the other techniques. This decreasing trend is a direct consequence of the fact that subpixel groups present at fine resolution are replaced by more isolated pixels at coarser resolutions. Consecutive majority aggregation conserves the probability more thoroughly at fine to moderate

140 123 resolutions (2-32 km). Ranked aggregation is more reliable at coarse resolutions. Note that non-consecutive majority aggregation never performs better than the ranked technique. It should be noted that both consecutive majority and ranked aggregation have nearly coinciding curves for the range 2 to 32 km, which is also observed for 12 out of 19 classes (data not shown). We calculated (dis)similarity metrics to assess change in image information relative to the original image. These metrics summarize the results described in detail above. Figure 4.8(a) shows evolution of the Euclidean distance with decreasing resolution. All techniques show a partially upward trend indicating persistent information change with aggregation. This can hardly be avoided as less information units are available in the coarse resolution images to represent the pattern complexity present in the original image. This was already observed from the preceding metrics individually. Their separate effects are superimposed in these similarity metrics. Ranked aggregation has clearly the smallest Euclidean distances (~0.05) at every resolution up to a resolution of 64 km. For consecutive majority aggregation, the Euclidean distance exceeds the distance measured by ranked aggregation, and for the non-consecutive majority rule, the difference is even higher. Consecutive random aggregation takes an intermediate position between both techniques and changes almost linearly with decreasing resolution. The Czekanowski coefficient expresses the degree of similarity between the original and the aggregated images (Figure 4.8(b)). The decreasing trends therefore indicate an increasing degree of pattern difference between the images. Majority aggregation is clearly less pattern conservative than ranked aggregation. The latter does not show a

141 124 distinct pattern change up to 64 km, and the drop observed at 128 km does not pass the ~95% level, which is remarkable after that many aggregation steps. Consecutive random aggregation takes an intermediate position between consecutive majority and ranked aggregation also for the Czekanowski coefficient, except at 32 km, where it performs worse than consecutive majority aggregation. The use of non-consecutive approach does not enhance the similarity between the high and low resolution images. The results presented in Figs. 4 to 8 express pattern changes with decreasing resolution which are indicative of algorithm performance. A complementary approach analyzes the decision processes of the various algorithms. When the predictability of the aggregation result is high and when the number of subpixels selected belonging to a minority class in the block is low, the aggregation result is more reliable, predictable, and closer to the information present in the original image. This tendency should be favored in developing aggregation algorithms. Figure 4.9 shows the degree of unpredictability of the three aggregation algorithms. Unpredictability occurs when a class has to be selected randomly in the case of equal γ- values (Eq. (4.18)) for the ranked aggregation. Equal γ-values have only been observed for block type {3,1,0,0} during the aggregation. The associated unpredictability at every resolution is calculated as the ratio between the number of blocks randomly selected to the total number of blocks used to create the aggregated image (Figure 4.9(a)). Low unpredictability levels ( 0.5%) are observed except at 64km. Nevertheless, the unpredictability (~ 1.5%) observed at this particular resolution is still relatively low. A higher degree of unpredictability is observed for the majority aggregation rule (Figure

142 (b)) and in particular for the consecutive mode, where the unpredictability ranges from 3.5% to 6 %. Unpredictability is introduced when the block types {2,2,0,0}a, {2,2,0,0}d, and {1,1,1,1} are present for this aggregation technique. Unpredictability is calculated as the ratio of the number these three block types to the total number of blocks. Note that unpredictability decreases sharply after the 4km resolution level for the non-consecutive approach. This is perhaps because class evenness in large aggregation blocks is improbable. Non-consecutive random aggregation (Figure 4.9(c)) generates the largest degree of unpredictability, which increases with decreasing resolution from ~15% to ~45%. Note that the consecutive approach generates less predicable results than its nonconsecutive counterpart. Unpredictability is present in this aggregation algorithm every time when a heterogeneous block is encountered. The number of subpixel minority classes to which a pixel is assigned is another indicator of algorithm performance. It is evident that this never occurs for majority aggregation. For ranked aggregation, the percentage of assigned minority classes, observed for block types {1,1,2,0} a, {1,1,2,0} d, and {1,3,0,0}, increases with resolution, but never passes the 0.2% level (Figure 4.10), which means that it remains a marginal event. The results of the accuracy assessment are presented in Figure All techniques show a decreasing trend indicating more subpixel heterogeneity. Majority aggregation performs slightly better than ranked aggregation but the tendencies are similar and the absolute differences between the curves are negligible. This is likely because both techniques favor pixel majority and adjacency. The marginally lower accuracy of the

143 126 ranked aggregation technique is because it enables minority class assignment and conserves proportional class area at the same time. Random aggregation generates less accurate results as may be expected by its randomizing effect Conclusions Multi-scalar land cover data are needed to model and quantify ecosystem processes at different spatial scales. This motivates the development of reliable aggregation algorithms which enable resolution coarsening with minimal information loss. We propose a new aggregation technique which maintains class evenness, diversity, proportion and patch diversity of the original image. The method uses spatial patterns in the fine resolution image as the starting point. Non-overlapping square-shaped aggregation windows or blocks containing four subpixels are parameterized in terms of adjacency, majority, and ambiguity which determine the type of the block. The blocks are then ranked with respect to their content. The frequency of the types per class determines the class to which a block is assigned to and the order in which blocks are processed. Well-defined rules to assign a class to the block minimize changes in the class proportions and overall characteristics of the original spatial patterns in the aggregated image. This is achieved by (i) aggregating homogeneous blocks which contains one single class, (ii) avoiding class disappearance through a step-by-step monitoring of subpixel loss per class (Eq. (4.18)), and (iii) giving aggregation preference to blocks showing majority and adjacency of subpixels. We used class proportion-based metrics in addition to image contagion and the Monmonier fragmentation metrics to characterize

144 127 spatial patterns. We show that the ranked aggregation technique better conserves the complex patterns in the original image. Some information changes are likely unavoidable as fewer pixels are available to represent information at coarser resolutions. Also, images generated with ranked aggregation are found to be more similar to the original image than those created by random or majority aggregation. Our conclusions are based on analyses of several predictability and accuracy parameters.

145 128 Class Coverage (%) Evergreen broadleaf forest Evergreen needleleaf forest Deciduous needleleaf forest Deciduous broadleaf forest Mixed forests Closed shrublands Open shrublands Woody Savannas Savannas Grasslands Permanent wetlands Croplands Urban and built-up Cropland/Natural vegetation mosaic Snow and ice 2.81 Barren or sparsely vegetated Water Unclassified Fill value Table 4.1. Coverage of the 17 International Geosphere-Biosphere Programme (IGBP) classes in the North American data set shown in Figure 4.1.

146 129 Spatial resolution (km) Rows Columns 1 (IGBP original image) Table 4.2. Images used to evaluate the aggregation procedures. The original image is the MODIS land cover map, i.e. the pixel image with a spatial resolution of 1 km. This image serves as the input to the 2 km image, which is generated using a 2 2 window.

147 130 Evergreen Needleleaf Forest Evergreen Broadleaf Forest Deciduous Needleleaf Forest Deciduous Broadleaf Forest Mixed Forests Closed Shrublands Open Shrublands Woody Savannas Savannas Grasslands Permanent Wetlands Croplands Urban and Built-Up Mixed Forests Cropland/Natural Vegetation Mosaic Snow and Ice Water Unclassified & Fill Value Figure 4.1. MODIS land cover image for North America, at 1 km resolution in Lambert Azimutal equal area projection. The central meridian is located at 100 W and the central parallel at 50 N.

148 131 Figure 4.2. Illustration of the algorithms used in this paper. In (a) the original image (4 4) is given, composed of 16 subpixels and 4 classes. This image will be aggregated into an image with 2 2 pixels. In (b) the image resulting from majority aggregation is shown. The pixels correspond to classes represented by a majority of subpixels in the aggregation windows. In case of equity (e.g. presence of two biomes with two subpixels or presence of four biomes), a random selection is made. In this example, this random selection for the bottom right aggregation window can result in four different results. The image is aggregated line by line, starting in the upper left position of the image. In (c), the image created by random aggregation is given. The classes of the pixels are determined by a random selection among the subpixels in each aggregation window. Note that due to this random selection, 24 different results can be generated. Also random aggregation uses a line-by-line aggregation sequence. In (d), the result using the ranked aggregation algorithm is shown. The sequence of the aggregation is given in (e), hence no line-by-line aggregation is observed. Only one random selection (between the two classes represented by a hatched fill pattern) was needed during the application of the latter technique, to determine the last pixel class, which implies a higher predictability as compared to the other techniques. The reader will notice that the aggregation results shown in (d) is the closest to the original set shown in (a) from visual perception, and that is the only case has one of the classes represented by striped pattern.

149 132 Figure 4.3. Illustration of the 10 block types and the notation for the ranked aggregation algorithm. The class represented by the black pixel is the class of interest. Pattern (a) is denoted as homogeneous, while the others are heterogeneous. In patterns (a) - (d), the selected subpixel has a majority in the aggregation window, while in patterns (h) - (j) the selected subpixel belongs to the minority in the block. In patterns (e) - (g), none of the classes is dominant. The a, and d labels indicate that subpixels of the class of interest are adjacent and diagonally placed respectively. The numbers represent the subpixel number for each class.