Joint probability analysis of storm surge and wave caused by tropical cyclone for the estimation of protection standard: a case study on the eastern coast of the Leizhou Peninsula and Hainan Island of China

Abstract. Quantitatively estimating combined storm surge and wave hazards provides scientific guidance for disaster prevention, mitigation, and relief in coastal cities. The marginal and copula functions are preferred based on the Kolmogorov–Smirnov test pass rate, and the relationship between storm surge and wave is quantitatively evaluated using the optimal function, then the bivariate risk probabilities are estimated. The results show that the generalized extreme value function and Gumbel copula function are suitable for fitting the marginal and joint distribution characteristics of the surge height and significant wave height in this study area, respectively. Second, the surge height shows an increasing trend closer to the coastline, and the significant wave height is higher further from the coastline. Third, when one variable is constant, the simultaneous, joint, and conditional risk probability tends to decrease as the other variable increases. In actual engineering design, improving the protection standard can effectively reduce the bivariate risk probability. In addition, we can estimate the optimal design criteria for different joint return periods by the constraint condition and objective functions. This study shows that the bivariate copula function can effectively evaluate the risk probability for different scenarios, which provides a reference for optimizing engineering protection standards.