A General Multilayer Analytical Radiative Transfer-Based Model for Reflectance Over Shallow Water

Shallow waters hold ecological and economic importance. Traditional reflectance forward models, such as Hydrolight and Monte Carlo (MC), are difficult to access or time-consuming. Two-stream models show great performance in radiative transfer simulation, but most of them are applied in other mediums, or ignore the asymmetry scattering characteristic of shallow water. In this paper, we propose a general multilayer analytical radiative transfer-based (GMART) model considering the realistic volume scattering function of water body, which is theoretically applicable for various shallow waters. GMART results are validated against Hydrolight and MC. The mean absolute percentage error (MAPE) of GMART and Hydrolight remote sensing reflectance ( R_rs ) among different combinations of the bottom depth, solar zenith angle and wind speed spans in ranges of 5.37%-28.86%, 3.37%-39.28%,and 4.91%-26.73%, with root mean square error (RMSE) values from 1.73×10 ^-4 -4.49×10 ^-3 , 2.68×10 ^-4 -1.85×10 ^-2 and 1.59×10 ^-4 -2.92×10 ^-3 sr ^-1 , respectively, for the coral, sand, and seagrass bottom. Comparisons of the bidirectional reflectance function with Hydrolight and MC indicate the capacity of GMART to compute bidirectional reflectance. Additionally, a comparison with field measurements is carried out. The minimum MAPE and RMSE between the modeled and measured normalized R_rs among several stations in the Sanya coastal area are 13.99%, and 0.061, respectively. The mean MAPE and RMSE among 6 stations are 21.38% and 0.083, respectively. The field validation underscores the feasibility of the model in shallow water radiative transfer. Compared with MC, the computational efficiency of GMART is much higher. The new model is shown to be an alternative and efficient tool capable of addressing shallow water-related challenges across diverse environmental conditions.