Application of Weibull distribution and stable energy concept for numerical solutions of random wave heights

Abstract

This study focuses on developing a new energy dissipation model and a corresponding solution for random wave height transformation based on stable energy theory and the Weibull distribution. Eight previously established breaking wave height formulas will be evaluated for compatibility with the new numerical solution in predicting wave height. A range of evaluation criteria (e.g., relative root-mean-square error (RRMSE), root-mean-square error (RMSE), mean absolute error (MAE), and standard deviation (ν)) will be applied to verify the reliability of the developed energy dissipation model alongside 13 existing models, using a large dataset of up to 6007 data points collected from 11 historical experiments. The results indicate that the NK1 solution for wave height transformation derived from the new energy dissipation model DB1 performs best in wave height prediction, with optimal shape and scale parameters of 1.53 and 0.83, respectively. The use of the DB1 model (or, equivalently, the NK1 solution) reduces errors compared to the 13 existing models by 8.1–69.4 % for RRMSE. For other evaluation criteria, DB1 also consistently outperforms the existing models. The findings further suggest that the stable energy concept is a feasible approach despite receiving limited attention from researchers. Additionally, the Weibull distribution is recommended for developing energy dissipation models or solutions for irregular wave height transformation. Therefore, the newly developed DB1 model and corresponding NK1 solution are strongly recommended for calculating random wave height transformation.