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Modern methods of remote sensing of the atmosphere and the surface are based on minimizing the difference between simulated and measured reflectances. An iterative process to specify the model of the atmosphere is used, and the direct problems to the radiative transfer equation (RTE) are solved on each iteration loop. These direct problems have to be solved quickly for realistic models of the atmosphere under peaked-forward scattering by aerosol particles, water droplets, and ice crystals. Accurate and fast algorithms to solve the RTE under these conditions are in great demand. A method based upon the new version of small angle approximation to the singular component of the solution is presented. Numerical results in the problem on reflection of the visible light by aerosol and cloud layers are presented. Calculation time reduction due to the small angular technique is shown. [ABSTRACT FROM AUTHOR]

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]