Gated fusion neural network Met-SDB for satellite-derived bathymetry incorporating synchronous meteorological data

Satellite-derived bathymetry (SDB) based on spectral inversion is susceptible to atmospheric and sea-surface perturbations that vary across acquisition scenes. We present Met-SDB, a gated fusion neural network that incorporates synchronous meteorological covariates obtained from ERA5-Land reanalysis to dynamically modulate Sentinel-2 spectral features during depth inversion. A dual-stream encoder processes spectral and meteorological inputs independently, and a sigmoid-gated modulation unit fuses them by generating channel-wise weights conditioned on the environmental context. The model is trained with ICESat-2 ATL03 photon-derived depths and a physics-informed monotonicity loss. Experiments on a single Sentinel-2 acquisition (28 February 2023) in a representative shallow-water study area around Culebra Island, Puerto Rico show that Met-SDB achieves R=0.98 and RMSE=0.62m, reducing RMSE by 24% relative to an equivalent spectral-only network and by 46% relative to the classical Stumpf log-ratio model. Ablation experiments confirm that wind speed and cloud cover are the most influential covariates and that the gated fusion strategy outperforms concatenation-based alternatives. These results demonstrate that freely available environmental data can substantially improve SDB accuracy without additional in-situ survey costs.