Enhancing coastal bathymetric mapping with physics-informed recurrent neural networks synergizing Gaofen satellite imagery and ICESat-2 lidar data: A case in the South China Sea

Satellite-derived bathymetry (SDB) has emerged as a critical technique in response to the growing demand for large-scale coastal bathymetric mapping. However, high-resolution multispectral imagery from Gaofen satellites presents significant challenges owing to low signal-to-noise ratios (SNRs). This study aimed to enhance coastal bathymetric mapping by integrating high-resolution Gaofen satellite imagery with ICESat-2 lidar-derived bathymetry. The specific goals are to develop a novel physics-informed recurrent neural network (PI-RNN) for SDB that does not rely on prior information and assess its performance in terms of accuracy and robustness. We propose a physics-based RNN model that combines spectral and radiative transfer information from Gaofen satellite imagery with reference bathymetric data from ICESat-2. This methodology includes an adaptive ellipse density-based spatial clustering of applications with noise (AE-DBSCAN) algorithm for ICESat-2 data extraction, which surpasses standard DBSCAN in terms of accuracy. The RNN model was trained using various band combinations of Gaofen satellite data, and its performance was evaluated against in-situ measurements from Ganquan Island in the South China Sea. The physics-based RNN model achieved good bathymetric accuracy, with a coefficient of determination (R 2 ) value >0.93 and a root mean square error (RMSE) < 0.83 m when compared to in-situ measurements on Ganquan Island, indicating the model demonstrates high robustness even under low-SNR satellite imagery conditions. In addition, the inclusion of radiative transfer information in the band combination significantly improved the training accuracy of the model, with the average RMSE being 0.2 m lower and the average R 2 improving by 3 % compared to results without physical information. On Huaguang Reef, the model performance further improved with R 2 values ranging from 0.93 to 0.97 and RMSE between 0.55 and 0.66 m after applying atmospheric correction when compared to the ICESat-2 reference bathymetric data. Without atmospheric correction, the R 2 of the estimated depth was in the range of 0.85 to 0.94 and RMSE in the range of 0.62 to 0.71 m, indicating that although the model mitigated some atmospheric interference effects, atmospheric correction was still necessary to achieve higher accuracy under strong atmospheric conditions. This study demonstrates that a PI-RNN can significantly enhance SDB accuracy, even under challenging conditions. The integration of active and passive remote-sensing data provides a reliable and efficient tool for large-scale coastal bathymetric mapping. The unique contribution of this study lies in the development of a novel RNN model that leverages both spectral and physical information, offering a more accurate and generalised approach to SDB. Traditional methods for creating these maps are limited because of their high cost, time consumption, and reliance on favourable weather and sea conditions. To overcome these challenges, we integrated high-resolution images from China's Gaofen satellite with precise laser measurements obtained from NASA's ICESat-2 satellite. Using a physics-based recurrent neural network (RNN), we processed these data and generated detailed bathymetric maps without the need for onsite measurements. The key steps in our process included developing a new algorithm to extract accurate seafloor data from ICESat-2 laser measurements, and a neural network that incorporated both spectral information from satellite images and the physical principles of light interaction in water bodies. We tested our method in the South China Sea, where it produced highly accurate results with a coefficient of variation (R 2 ) value >0.93 and a root mean square error (RMSE) < 0.83 m when compared to actual measurements from an island in the area. This study demonstrates that our method not only achieves remarkable bathymetric accuracy but also simplifies the mapping process by eliminating the need for complex atmospheric corrections. This advancement is a significant step forwards in the field of coastal mapping and offers a more efficient and effective tool for managing and understanding coastal resources and the environment. • We synergised satellite imagery with lidar-derived bathymetry and diffuse attenuation, circumventing the traditional reliance on in-situ measurements. • Physics-based recurrent neural network (RNN) integration of spectral and radiative transfer information significantly enhanced model robustness. • Our study presents an adaptive DBSCAN algorithm for ICESat-2 data extraction that surpasses standard DBSCAN in accuracy without prior assumptions. • Our method achieved remarkable bathymetric accuracy even under conditions of low signal-to-noise (SNR) satellite imagery. • The effects with and without atmospheric correction on RNN satellite-derived bathymetry (SDB) are discussed.