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RTE numerical solution methods: Successive orders of scattering - Overview

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Successive orders of scattering (SOS) method is one of the oldest and conceptually simplest solutions to the multiple scattering problem in layered turbid media, such as the atmosphere (Hansen JE and Travis 1974). In this method, the atmosphere is divided into a number of layers and the RTE is solved for each layer by iterations. The radiance is successively computed for photons scattered once, twice, three times, etc., and the total radiance is obtained as the sum of contributions from all scattering orders. In practice, the summation is truncated once a given convergence criterion is satisfied. Numerical integration is typically performed by using the decomposition of radiance into a Fourier series to handle its azimuthal dependence, expansion of the aerosol phase function in Legendre polynomials, and discretization of the cosine of the zenith angle in gaussian quadratures

In the case of vector RTE, the calculation of unpolarized radiance is replaced by the calculation of the four components of the Stokes vector, S = [I, Q, U, V], also referred to as the Stokes parameters (for example, Liou KN 1980). The first component (I ) of that vector describes the unpolarized irradiance, while the other three components characterize the polarized irradiance.

The SOS method has several advantages. First, being conceptually simple, it nevertheless provides an accurate solution to the multiple scattering problem. Second, it is applicable to both homogeneous (for example, Wauben WMF et al 1993) and vertically inhomogeneous atmospheres (for example, Kotchenova SY et al 2008). Third, the SOS method allows one to correct for the spherical geometry of the atmosphere. Fourth, it is computationally fast for atmospheres not contaminated by clouds (calculation time is measured in seconds).

The main disadvantage of the SOS method is a significant computation time for a medium with a large single scattering albedo and optical thickness. Various approaches have been developed to speed up the SOS method in such cases (for example, Zhai PW et al 2009, Duan M and Min 2005).

See also radiative transfer equation, solution methods, numerical, successive orders of scattering for additional references.

CITATION: Kotchenova S. Y. 2009. RTE numerical solution methods: Successive orders of scattering - Overview. (www.tpdsci.com/Tpc/RTESolNumSos1.php) In: Radiative transfer equation (RTE): Numerical solution methods. Kokhanovsky A. A. (ed.) (www.tpdsci.com/Tpc/RTESolNumIntro.php). Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 12-Jan-2010 Modified: 24-Dec-2009 Peer-reviewed: 04-Aug-2009

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