Joint probability analysis of storm surges and waves caused by tropical cyclones for the estimation of protection standard: a case study on the eastern coast of the Leizhou Peninsula and the island of Hainan in China

The impact of natural hazards such as storm surges and waves on coastal areas during extreme tropical cyclone (TC) events can be amplified by the cascading effects of multiple hazards. Quantitative estimation of the marginal distribution and joint probability distribution of storm surges and waves is essential to understanding and managing tropical cyclone disaster risks. In this study, the dependence between storm surges and waves is quantitatively assessed using the extreme value theory (EVT) and the copula function for the Leizhou Peninsula and the island of Hainan of China, based on numerically simulated surge heights (SHs) and significant wave heights (SWHs) for every 30 min from 1949 to 2013. The steps for determining coastal protection standards in scalar values are also demonstrated. It is found that the generalized extreme value (GEV) function and Gumbel copula function are suitable for fitting the marginal and joint distribution characteristics of the SHs and SWHs, respectively, in this study area. Secondly, the SHs show higher values as locations get closer to the coastline, and the SWHs become higher further from the coastline. Lastly, the optimal design values of SHs and SWHs under different joint return periods can be estimated using the nonlinear programming method. This study shows the effectiveness of the bivariate copula function in evaluating the probability for different scenarios, providing a valuable reference for optimizing the design of engineering protection standards.