Machine Learning-Based Atmospheric Radiation Calculation Incorporating Earth Curvature

Plane-parallel atmospheric radiative transfer models neglect the Earth’s curvature, resulting in substantial optical path errors at large zenith angles and limiting the accuracy of satellite remote sensing retrievals. Fully spherical Monte Carlo models can accurately represent curvature and multiple-scattering effects, but their high computational cost limits their application in rapid or operational calculations. Pseudo-spherical approximations offer greater computational efficiency but generally retain plane-parallel assumptions for multiple scattering, which may reduce their accuracy in aerosol- and cloud-laden atmospheres. To address these limitations, this study develops a physics-guided, data-driven framework for efficient spherical radiance estimation. Reference spherical radiances were generated using a Monte Carlo radiative transfer model for representative clear-sky, aerosol-laden, and cloudy atmospheric scenarios. An extreme gradient boosting (XGBoost) model was then trained to map plane-parallel radiances to their spherical counterparts at wavelengths of 450, 550, and 650 nm. The predictors included wavelength, solar zenith angle (SZA), viewing zenith angle, azimuth angle, asymmetry factor, surface albedo, optical depth, single scattering albedo, the central height of a single aerosol or cloud layer and plane-parallel radiance. On the independent test set, the XGBoost model achieved a mean absolute percentage error (MAPE) of 5.71%. For the common clear-sky subset used to compare all three methods, the corresponding MAPEs of the plane-parallel and pseudo-spherical models were 29.61% and 19.65%, respectively. These results indicate that the proposed model can substantially reduce curvature-related radiance errors while retaining high computational efficiency across the atmospheric scenarios considered in this study.