Bivariate distributions of group height and length for ocean waves using Copula methods

• Both laboratory and field wave data are analyzed to investigate the bivariate distribution of the group height and group length.
• Strong dependence exists between smaller group height and length, whereas they become irrelevant with increasing values.
• An approach is set up to construct the joint distribution for the group height and length with bivariate copula function.
• The Clayton copula function-based distribution provides an excellent joint distribution of group height and group length.

We conduct laboratory experiments and numerical simulations, and analyze field wave data to investigate the bivariate distribution of two fundamental characteristics of wave groupiness, group height and group length. All data sets show strong dependence between the two characteristics when they are relatively small; however, gradually they become independent as the values increase. Based on the above findings, we propose a new approach to construct a joint distribution of the two characteristics through the use of the bivariate Clayton Copula function. Our result demonstrates that the Clayton Copula function-based distribution provides an excellent joint distribution of group height and group length. It shows significant improvement over the traditional method based on the total probability formula and three other Copula functions. The results can lead to a better understanding of a number of coastal engineering processes, including random ocean waves and the interactions between wave groups and marine structures.