You are here:
A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters
Citation:
Sokoletsky, L., O. Nikolaeva, V. Budak, L. Bass, R. S. LUNETTA, V. Kuznetsov, AND A. Kokhanovsky. A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo of Natural Waters. Journal of Quantitative Spectroscopy & Radiative Transfer. ELSEVIER, AMSTERDAM, Holland, 110(13):1132-1146, (2009).
Impact/Purpose:
Healthy Communities and Ecosystems - by providing new approaches to characterize landscape features, conditions, and change.
Description:
Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different variants of the discrete ordinate method (DOM). Parameters for these algorithms (single-scattering albedo ω0 and solar zenith angle) were selected across all possible ranges, but with a special emphasis on natural waters. All computations were made for two scattering phase functions; which included an almost isotropic Rayleigh phase function and double-peaked Fournier-Forand-Mobley phase function. Models were validated using quasi-single-scattering (QSSA) and exponential approximations to represent the extreme cases of ω0 > 0 and ω0 > 1, respectively. All methods yielded relative differences within 1.8% for modeled natural waters. However, a combination of DOM with a modified spherical harmonics method (MSH) provided both high accuracy and minimal computational complexity. An analysis of plane albedo behavior resulted in the development of a new extended QSSA approximation, which when applied in conjunction with the extended Hapke approximation gives a maximum relative error of 2.7%. The study results demonstrated that for practical applications, the estimation of inherent optical properties from observed reflectance can best be achieved using an extended Hapke approximation.