Analytical algorithm for modeling polarized solar radiation transfer through the atmosphere for application in processing complex lidar and radiometer measurements

•We create an analytical algorithm and code to solve direct atmospheric task.•Data-out include a Stokes vector of scattered Sun light in a homogeneous atmosphere.•Solution for radiance involves several rather accurate approximations of scalar theory.•Errors of radiance estimates at the atmosphere bottom are within 10-15%.

Inversion algorithms and program packages recently created for processing data of the ground-based radiometer spectral measurements along with lidar multi-wavelength measurements are extremely multiparametric. Therefore, it is very important to develop an efficient program module for computations of functions modeling measurements by a sun-radiometer in the inversion procedure. In this paper, we present the analytical version of such efficient algorithm and analytical code on C++ designed for performance of algorithm testing. The code computes multiple scattering of the Sun light in the atmosphere. Data output are the radiance and linear polarization parameters angular patterns at a preselected altitude. The atmosphere model with mixed aerosol and molecular scattering is given approximately as the homogeneous atmosphere model. The algorithm testing has been carried out by comparison of computed data with accurate data obtained on the base of the discrete-ordinate code. Errors of estimates of downward radiance above the Earth surface turned out to be within 10%-15%.. The analytical solution construction concept has taken from the scalar task of solar radiation transfer in the atmosphere where an approximate analytical solution was developed. Taking into account the fact that aerosol phase functions are highly forward elongated, the multi-component method of solving vector transfer equations and small-angle approximation have been used. Generalization of the scalar approach to the polarization parameters is described.