Modified L-distributions method for atmospheric remote sensing problems

Many applications involving atmospheric radiation need radiative transfer codes with an appropriate combination of accuracy, speed, and spectral coverage. In this paper, a new formulation, to our knowledge, of the L-distributions (LD) method is developed for modeling infrared sensor transmittances and radiances in inhomogeneous thermodynamic atmospheres containing a mixture of absorbing gases with variable concentrations. The formulation, called the modified L-distributions (MLD) method, overcomes the limitations of the LD method and establishes a balance between speed and accuracy. The atmosphere is considered a plane-parallel medium, limited at the top by the vacuum, while the kernel bidirectional reflectance distribution function is used to describe the anisotropy of the ground surface. The vertical structure of the plane-parallel atmosphere is subdivided into homogeneous layers of constant or variable discretization steps. It is demonstrated that the transmittance in an inhomogeneous atmosphere using the MLD method requires solving an equivalent homogeneous problem with the absorption coefficient equal to the weighted sum of absorption coefficients of all layers (above or below the observation point) and with thickness equal to the highest discretization step. The weighting factor is the ratio of the layer height to the highest discretization step. Compared to the standard version of the LD method, the MLD formulation is shown to be (1) independent of the direction of propagation along a non-uniform path, (2) more accurate, and (3) more computationally economic and efficient. The line-by-line (LBL) results are used as a benchmark for the comparison of the atmospheric transmittance. Daytime and nighttime top-of-atmosphere (TOA) radiances for a Lambertian ground surface are plotted and compared with the atmospheric radiative transfer code MATISSE outputs. The MLD method results match well with the MATISSE ones. Four locations with anisotropic surface configurations are also studied, and the daytime and nighttime TOA irradiance and albedo are estimated. For the atmospheres studied in this work, the MLD method yields absolute errors less than 1.1% transmittance with a CPU time of 0.2 s on an Intel Xeon W1250P 4.10 GHz computer. This means that the MLD method is about 2.5 times more accurate and 30 times faster than the standard LD method.