Machine learning-based intelligent parameterization of source functions in numerical wave model

Abstract

In recent years, although the application of machine learning in parameterizing complex marine physical processes has gradually become widespread, most of the existing studies rely on statistically correlated parameter selection methods for neural network construction and lack physical support. This study proposed a physics-guided neural network parameterization method combining physical feature selection and data-driven modeling. By integrating source function parameterization equations (wind input, wave breaking dissipation, wave-wave nonlinear interactions) from the MASNUM-WAM physical framework into the feature engineering of a backpropagation neural network (BPNN), a physically guided parameterization model was developed. The experiments show that the three major source functions exhibit excellent prediction performance (R²>0.95, RMSE<0.09, BIAS between -0.02 and 0.05), with stable results across multi-test points. Then, a new directional wave spectra prediction model was developed using the prediction results. Directional wave spectra predictions show strong consistency with MASNUM-WAM (COR>0.92, RMSE<0.09 m²s, |BIAS|≤0.03 m²s). Spectral integration parameters achieve high accuracy: significant wave height (RMSE≤0.477 m), mean wave direction (RMSE≤1.010°), and mean wave period (0.203 s≤RMSE≤0.247 s). Feature importance analysis reveals that wave breaking dissipation contributes most substantially to directional wave spectra prediction accuracy, while initial conditions, wave-wave nonlinear interaction, wind field components exhibit variable influence, and wind input term maintains a minor but consistent role. This physics-guided approach retains data-driven advantages while enhancing model reliability and computational efficiency, offering a new pathway for parametric research in ocean wave simulation.