Learning unresolved coastal dynamics in hydrodynamic models

Thomas Carey Monahan , Jeff Polton, Silvia Innocenti, Pascal Matte, Mahmoud Ayyad, Krijn Saman, Thomas A.A. Adcock

Coastal hydrodynamic models play a vital role in understanding and predicting flooding, but practical computational constraints and uncertainties in boundary conditions and bathymetry lead to systematic errors in local sea level. We show that much of this error is not random but reflects a stable, site-specific response that can be learned from model output and observations. We develop a time-invariant response operator combining linear memory and bilinear interactions to approximate unresolved shallow-water dynamics. In idealized experiments, the operator recovers overtide generation, tide–surge interaction, and fluvial coupling. The approach yields substantial improvements across regional and operational models of water level and currents, and the correction substantially reduces errors in coarse-resolution simulations, yielding skill comparable to higher-resolution models. Applied globally to a GTSM reanalysis, it reduces a 0.14 m negative bias in 100-year return levels to 0.02 m across 199 GESLA4 gauges, with mean absolute error reductions of 48%, 26%, and 20% for 10-, 50-, and 100-year return periods. These results show that a significant component of coastal model error, including extremes, stems from tidal processes and is locally learnable, offering a practical way to improve skill without modifying underlying models or increasing computational cost.