A new vector radiative transfer solution using Padé approximants

This paper solves the multi-layer multiple-scattering plane-parallel vector radiative transfer problem for solar and thermal sources. Efficient calculation of the Stokes vector for optically thin media is made possible by the method herein called VPARTM—"Vector Padé approximation radiative transfer method". The algorithm calculates the matrix exponential using the Padé approximation, with an accuracy prescribed by the user, from which the global reflection and transmission operators are obtained. In a multi-layer atmosphere, these operators can be combined using the adding method. Computational gain is enhanced by exploiting the symmetry inherent in the exponential solution and then exploiting the structure of this matrix to halve the order of the matrix solution. Computational efficiency is explored through a range of model configurations and the method is applied for two example cases, one for a range of wavelengths typically used to retrieve aerosol properties and one for an instrument similar to the GOSAT and OCO-2 0.76-μmO2 A-band spectrometers. -- Highlights: ► We present a multiple-scattering plane-parallel vector radiative transfer solution. ► The solution is based on the Pade approximation to the matrix exponential. ► Timing results indicate that our solution is efficient especially for thin media. ► Numerical results show that our solution is accurate to 10−4 % compared to VLIDORT