Efficient Calculation of the Kirchhoff Integral for Predicting the Bistatic Normalized Radar Cross Section of Ocean-Like Surfaces

In recent years, several novel satellite platforms and sensors have been proposed for the Earth radiation budget (ERB). Simulating the sensor-measured signals could be helpful for optimizing the settings of sensors and exploring their potential in ERB. The anisotropic factor, depicting the anisotropy of Earth's radiation, is essential in the simulation. However, developing angular distribution models (ADMs) involves complex procedures of data preparation, processing, and modeling. This study, targeting at simplifying the procedure of simulating the signals of ERB sensors, proposed a suit of models for estimating the longwave anisotropic factors directly from the Earth's radiative fluxes. The models were developed with CERES/Terra data sensed in rotating azimuth plane (RAP) mode during 2000-2005 and the artificial neural network (ANN) algorithm and tested with 12 monthly of CERES/Terra data collected in RAP and cross-track (CT) mode during 2021-2022, respectively. Models were developed for ten scene types based on Earth's surface types and compared with the operational ANN ADMs. Results showed that the longwave anisotropic factors were accurately estimated with the correlation coefficient ( $r$ ) varying between 0.84 and 0.98 and mean absolute percentage error (MAPE) within 1.20% for the test dataset, and the approach proposed in this study had comparable performance with the ANN ADMs. With the estimated anisotropic factors, the sensor-measured radiances were accurately retrieved with $r$ = 1.00 and MAPE = 0.53%. Therefore, the proposed approach is promising in accurate and efficient simulations of novel ERB platforms and sensors like the Moon-based Earth Radiation.