Inhomogeneous atmospheres – On transforming conservative multiple scattering to non-conservative multiple pseudo-scattering

Abstract

The F- and K-integrals are used to transform the zeroth azimuthal Fourier component of the radiative transfer equation for conservative multiple scattering of polarized light in vertically inhomogeneous plane atmospheres into an equivalent transfer equation with a modified phase matrix corresponding to non-conservative pseudo-scattering. With symmetry properties of the original phase matrix to be retained, the modification generally includes two arbitrary scalar functions depending on optical depth. It is shown that the surface Green׳s function matrices for conservative scattering can be expressed in terms of surface Green׳s function matrices for non-conservative pseudo-scattering. Linear constraints are obtained for surface Green׳s functions for conservative scattering as well as for particular forms of non-conservative pseudo-scattering.Explicit formulae are derived for retrieving the solutions of standard problems like diffuse reflection and transmission, and also for Milne׳s problem, for conservative inhomogeneous atmospheres by means of appropriate solutions for non-conservative multiple pseudo-scattering. Numerical experiments performed by solving the nonlinear integral equations for the diffuse reflection functions of homogeneous semi-infinite atmospheres demonstrate that an acceleration of iterations by orders of magnitude can be achieved when the transformation to equivalent multiple pseudo-scattering is applied.