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Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil SurfacesWe describe a simple and highly efficient and accurate radiative transfer technique for computing bidirectional reflectance of a macroscopically flat scattering layer composed of nonabsorbing or weakly absorbing, arbitrarily shaped, randomly oriented and randomly distributed particles. The layer is assumed to be homogeneous and optically semi-infinite, and the bidirectional reflection function (BRF) is found by a simple iterative solution of the Ambartsumian's nonlinear integral equation. As an exact Solution of the radiative transfer equation, the reflection function thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. Since this technique bypasses the computation of the internal radiation field, it is by far the fastest numerical approach available and can be used as an ideal input for Monte Carlo procedures calculating BRFs of scattering layers with macroscopically rough surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web at http://ww,, and can be applied to a wide range of remote sensing, engineering, and biophysical problems. We also examine the potential effect of ice crystal shape on the bidirectional reflectance of flat snow surfaces and the applicability of the Henyey-Greenstein phase function and the 6-Eddington approximation in calculations for soil surfaces.
Document ID
Document Type
Preprint (Draft being sent to journal)
Mishchenko, Michael I. (NASA Goddard Inst. for Space Studies New York, NY United States)
Dlugach, Janna M. (Main Astronomical Observatory Kiev, Ukraine)
Yanovitsku, Edgard G. (Main Astronomical Observatory Kiev, Ukraine)
Zakharova, Nadia T. (Science Systems and Applications, Inc. New York, NY United States)
Date Acquired
September 6, 2013
Publication Date
January 1, 1999
Subject Category
Report/Patent Number
Distribution Limits
Work of the US Gov. Public Use Permitted.

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NameType 19990103079.pdf STI