LIDORT and VLIDORT: Linearized pseudo-spherical scalar and vector discrete ordinate radiative transfer models for use in remote sensing retrieval problems

Abstract

The modern treatment of the radiative transfer equation (RTE) in plane-parallel media dates back to the pioneering work by Ambartsumian and Chandrasekhar in the 1940s (Chandrasekhar, 1960;Ambartsumian, 1961). Using a formulation in terms of the Stokes vector for polarized light, Chandrasekhar was able to solve completely the polarization problem for an atmosphere with Rayleigh scattering, and benchmark calculations from the 1950s are still appropriate today (Coulson et al., 1960). The scalar (intensity-only) and vector (with polarization) radiative transfer equations in one vertical dimension may be solved in a number of ways. These include the doubling-adding method, the discrete ordinates approach, the successive orders of scattering method, Gauss-Seidel iteration, and (not least) the Monte Carlo approach. For a review of solution methods, see for example (Lenoble, 1985). Most solution methods for scalar and vector RTEs divide into two camps: the doubling/adding approach and the discrete ordinate method. For descriptions of the former, see for example (Hansen and Travis, 1974;de Haan et al., 1987;Hovenier et al., 2004). The well-known scalar DISORT discrete ordinate model was developed in the 1980s and released for general use in plane-parallel multi-layer multiple scattering media (Stamnes et al., 1988a); this was extended to the vector model VDISORT in the 1990s (Schulz and Stamnes, 2000).