Evaluating coastal safety using individual wave overtopping volumes: insights from evolutionary polynomial regression

Background: Wave overtopping threatens coastal safety and is expected to worsen with sea-level rise and stronger storms. Existing Weibull-based predictors require irregular sea states and offer limited insight for flume studies. This work seeks an interpretable, data-driven alternative to estimate maximum overtopping volumes under extremeevent conditions. Methods: A database of 316 tests from a 1:50-scale wave flume was analysed. Focused wave groups derived from NewWave theory replaced irregular spectra to target large overtopping events on shallow-water dikes with emergent toes. Hydraulic and structural inputs (wave height H, wave period T, crest freeboard Rc, local water depth h, and slope tan α) fed an Evolutionary Polynomial Regression algorithm with multi-objective genetic optimisation (EPR-MOGA) to identify compact predictive expressions. Results: the EPR models achieve coefficients of determination (CoD) up to 89.7% with simple expressions involving three to five key variables. Results show that wave period, wave height, structural freeboard, and local water depth at the dike toe are key factors influencing overtopping volumes. The group Tm􀀀 1;0=Rc alone accounts for 44.5% of variance in overtopping volumes, while the influence of focus phase, wave asymmetry and skewness is negligible. The model’s accuracy improves slightly when including the focus location, while other factors like focus phase, wave asymmetry, and wave skewness are less significant. Conclusion: EPR-based polynomial models provide accurate, transparent predictions of maximum overtopping volumes for experimental configurations where probabilistic Weibull methods are unsuitable. By relying on focused wave groups and a small set of readily measured variables, the approach offers a practical tool for design and risk assessment of shallow-water coastal dikes under extreme events.