Physics-Constrained Ensemble-Learning Modeling of Nonstationary Tidal Characteristics

This study addresses deviations between observed nonstationary tides and physical-model results caused by multiple indirectly observed factors. The S_TIDE framework performs well in estuaries by introducing time-varying nonequilibrium physical factors to represent tidal characteristics and is applicable to diverse nonstationary regimes. However, S_TIDE remains limited: even combined with the Enhanced Harmonic Analysis (EHA) scheme, which improves extraction of characteristic tidal levels, it still fails to capture differences between observed and harmonically analyzed tides driven by regional nonlinear processes, so tidal errors remain large. We develop a hybrid scheme coupling S_TIDE with an ensemble-learning model. The physically computed tide provides a constrained backbone; the observed–physical difference is formulated as a residual series, and the PELM ensemble learns regional tidal characteristics encoded in these residuals to provide targeted corrections. Using research-grade records from 528 tide-gauge stations of the University of Hawaii Sea Level Center (UHSLC), PELM increases tidal-simulation accuracy, yielding an average error-reduction of 45.63% across all stations; 66.10% of sites improve by more than 40%, and stations with large initial physical-tide errors improve on average by more than 65%. These results demonstrate that the Physics-Constrained Ensemble-Learning Method (PELM) scheme is highly effective and generalizable for extracting characteristic tidal levels and reducing tidal-simulation errors at the global scale.