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Ranga B. Myneni received his Ph.D. degree in biology from the University of Antwerp, Antwerp, Belgium, in 1985. He has been with Kansas State University, Manhattan, the University of Gottingen, Gottingen, Germany, and NASA\'s Goddard Space Flight Center, Greenbelt, MD. He is now an Associate Professor in the Department of Geography, Boston University, Boston, MA. He is also a Member of the MODIS and MISR science teams. His research interests are radiative transfer, remote sensing of vegetation, and climate-vegetation dynamics.
The basic physical principle underlying our MODIS synergistic Leaf Area Index (LAI) & Fraction Photosynthetically Active Radiation (FPAR) algorithm is the law of energy conservation. However, a rather wide family of canopy radiation models conflict with this law. Therefore, the three-dimensional transport equation which includes a non-physical internal source is taken as the starting point for the derivation of the algorithm.
We distinguished six biome types, each representing a pattern of the architecture of an individual tree (leaf normal orientation; stem, trunk, and branch area fractions; leaf and crown size) and the entire canopy (trunk distribution, topography), as well as patterns of spectral reflectance and transmittance of vegetation elements. The soil and/or understory type are also characteristic of the biome, which can vary continuously within given biome-dependent ranges. The distribution of leaves is described by the leaf area density distribution function which also depends on some continuous parameters.
A technique developed in atmospheric optics is utilized to parameterize the radiative field in terms of reflectance properties of the canopy and ground, as well as to split the radiative transfer problem into two independent sub-problems, each of which is expressed in terms of three basic components of the energy conservation law - canopy transmittance, reflectance and absorptance. These components are elements of the Look-up-Table (LUT), and the algorithm interacts only with the elements of the LUT. This provides the required independence of the retrieval algorithm to a particular canopy radiation model.
The next important step is to specify the dependence of canopy transmittance, reflectance and absorptance on wavelength. This dependence is described by a simple function which depends on the unique positive eigen value of the transport equation. The eigen value relates optical properties of individual leaves to canopy structure. This result allows not only a significant reduction in the size of the LUT, but also relates canopy spectral reflectance with spectral properties of individual leaves, which is a rather stable characteristic of green leaves.
In spite of the considerable simplification in canopy characterization by using a vegetation cover classification, the inverse problem still allows for multiple solutions. A method to estimate the most probable LAI and FPAR, accounting for specific features of the MODIS instrument, and providing convergence of the algorithm was developed.
The maximum positive eigen value and the unique positive eigen vector corresponding to this eigen value express the law of energy conservation in a compact form. This results allow us to relate the Normalized Difference Vegetation Index (NDVI) to this fundamental physical principle. Relationships between FPAR and NDVI are used in our algorithm as a back-up to the LUT approach.