Hydrodynamically Constrained Unsupervised Learning of Multi-Source Data for Submarine Groundwater Discharge Identification

Submarine groundwater discharge (SGD) is an important pathway for water and solute exchange between coastal aquifers and the ocean, but its spatial detection remains challenging because field methods have limited coverage and remotely sensed anomalies may also reflect other coastal processes. This study developed a hydrodynamically constrained remote sensing framework for SGD identification by integrating optical and thermal indicators with hydrogeological constraints. Sentinel-2 imagery was used to derive the Normalized Difference Chlorophyll Index (NDCI) and Normalized Difference Turbidity Index (NDTI), while Landsat thermal data were used to quantify seasonal sea surface temperature variability using the 90th–10th percentile amplitude. These indicators were combined in a K-means clustering framework, and the classification results were further constrained using year-specific maximum offshore distances estimated from groundwater level observations with a Dupuit–Glover-based scaling approach and hydraulic time-lag correction. Applied to the north shore of Long Island, New York, the framework identified coherent nearshore SGD patches that were broadly consistent with field observation locations and showed both temporally persistent discharge zones and interannual variability in spatial extent. These results indicate that incorporating physically based constraints can improve the robustness and interpretability of remote sensing-based SGD detection.