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Abstract: 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 GOSAT and OCO O2 A-band spectrometers. [Copyright &y& Elsevier]

Abstract: The simplified M-1D algorithm (M stands for modified) for the calculation of horizontal distribution of reflected brightness coefficient in 2D regions with large homogeneous pixels is presented. This algorithm is based upon modified 3⁎ N−1 1D-transport equations (where N is the number of large pixels) instead of one 2D-transport equation, usually used in such problems. The method does not rely on empiric assumptions on both optical properties of atmosphere or diffuse radiation intensity. Numerical results demonstrating the accuracy of the presented algorithm for simulating brightening and shadowing effects in a vicinity of the jump of optical properties given. The accuracy of the M-1D approximation strongly depends on the geometry and illumination conditions. However, it remains below 15% and can reach 1% for all cases studied and is strongly higher than the accuracy of usually employed independent pixel approximation. Time reduction via replacing 2D problem via modified 1D problem is about 17 times for all cases considered in this paper. [Copyright &y& Elsevier]