Efficient computation of radiances for optically thin media by Padé approximants

This paper solves the multi-layer multiple-scattering plane-parallel radiative transfer problem for solar and thermal sources. Efficient calculation of radiances for optically thin media is made possible by the method herein called PARTM-“Padé approximation radiative transfer method”. The algorithm calculates the matrix exponential and the global reflection and transmission operators using Padé approximants with an accuracy prescribed by the user. 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. A range of numerical tests were performed that demonstrate the accuracy and speed of PARTM relative to widely used DISORT model. Finally, the method was applied for two example cases, one for a multispectral instrument such MODIS and one for an instrument similar to the 0.76‐μm GOSAT and OCO O2 A-band spectrometers.