Data-driven parameterisation of representative wave heights and periods over coastal bathymetry

Accurate representation of wave conditions is essential in the design of coastal infrastructure and requires reliable estimates of representative wave heights and periods across variable bathymetric conditions. This study develops data-driven predictive formulations for the evolution of these parameters using an extensive numerical data set generated with the Simulating WAves till SHore (SWASH) model comprising over 2 million individual waves simulated across 21 sea-states and five bed slopes. The data set enables a detailed evaluation of existing models commonly used in engineering practice, highlighting their limitations in capturing non-linear transformations of wave statistics in coastal waters. Building on physical insights into wave evolution, new formulations are derived for the root-mean-squared wave height, explicitly accounting for sea-state steepness and bed slope. Furthermore, a new expression for the mean energy period is introduced that incorporates the influence of infragravity energy through the local slope gradient. These results are extended to propose updated relationships for the mean spectral and mean zero-crossing periods. The proposed parameterisations provide improved accuracy and physical consistency for representing nearshore wave conditions, offering a practical tool for the design and assessment of coastal infrastructure.