THE PICARD ITERATIVE APPROXIMATION TO THE SOLUTION OF THE INTEGRAL-EQUATION OF RADIATIVE-TRANSFER .1. THE PLANE-PARALLEL CASE

The present Picard Iterative (PI) approach is designed to be a compromise between the generality of Monto Carlo techniques and the numerical efficiency of the existing analytical approaches. The PI method, like the Successive Orders of Scattering approach, begins with the integral equation form of the radiative transfer equation (RTE). Starting with an approximate radiance field, the PI performs a fixed-point iteration. The solution converges in approx. 10 iterations for Cl water cloud phase functions and in approx. 20 iterations for highly peaked cirrus-type phase functions. The PI iteration (1) is unaffected by vertical inhomogeneities; (2) converges even for highly peaked phase functions; and (3) can be extended to 3-D geometries. However, it is less efficient for (1) optically thick, but homogeneous, media; and (2) media with a weakly peaked scattering phase function.