Abstract
Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03.
Highlights
Introduction and overviewThe polarization state of atmospheric radiation potentially contains abundant information about aerosol properties
The Markov chain formalism is presented for the vertically inhomogeneous atmosphere in the current paper, by setting the Mueller matrix P(cosΘ,n) and single scattering albedo ω0(n) to be constant for all sublayers, the formalism reduces to its counterpart for the homogeneous atmosphere [1]
Even when polarization is not a focus of the mission, it needs to be accounted for to keep the accuracy of the forward radiative transfer modeling at par with instrument precision
Summary
The polarization state of atmospheric radiation potentially contains abundant information about aerosol properties. The Markov chain method retains (i) the advantage of the adding/doubling method of easy physical interpretation and high numerical accuracy in calculating the atmosphere of large optical depth, (ii) the advantage of the successive orders of scattering method in separating the contribution of a specific scattering order numerically [5,6,7] or analytically [8], and (iii) the advantage of the discrete source method [9,10,11] for the internal radiation field calculation These merits form the motivation of the current research to extend the Markov chain method to polarized radiative transfer in a vertically inhomogeneous atmosphere.
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