Markov chain formalism for vector radiative transfer in a plane-parallel atmosphere overlying a polarizing surface

We report on a way of building bidirectional surface reflectivity into the Markov chain formalism for polarized radiative transfer through a vertically inhomogeneous atmosphere. Numerical results are compared to those obtained by the Monte Carlo method, showing the accuracy of the Markov chain method when 90 streams are used to compute the radiation from a Rayleigh-plus-aerosol atmosphere that overlies a surface with a bidirectional reflection function consisting of both depolarizing and polarizing parts.