A Physics-Assisted Convolutional Neural Network for Bathymetric Mapping Using ICESat-2 and Sentinel-2 Data

Machine learning methods for water depth estimation using remote sensing require accurate prior depth measurements. The successful operation of the ICESat-2 mission provides depth in shallow water directly; however, its spatial coverage is limited. Machine learning has been used to link optical remote sensing images and ICESat-2 data for bathymetric mapping. Compared with other machine learning models, convolutional neural network (CNN) models utilize the local spatial correlation between adjacent pixels and can thus reduce the effect of environmental noise. However, existing CNN and other machine learning models rely on data mining to build a general relationship between water depth and spectral information, and they ignore the known physical law. In this paper, we propose a physics-assisted convolutional neural network (PACNN) model. This model incorporates knowledge from radiative transfer theory into a normal CNN model by building a series of spectral feature input layers. In the PACNN model, the spectral information, which is directly related to water depth, is emphasized. Multitemporal ICESat-2 data and Sentinel-2 images were used to validate the model. In experiments with data from three study areas, the PACNN model outperformed the existing CNN model, achieving an accuracy of over 98%. The proposed method can effectively solve the underestimation in deeper water (20–30 m) and reduce the variance of estimates. The superiority of the PACNN model demonstrates how a machine learning model can be assisted by physics theory.