Joint probability of storm surge and wave along Hainan Island based on bi-variate copulas analysis

Tropical cyclones (TCs) often bring multiple hazards to offshore and onshore areas, including wind, rainfall, riverine flood, wave and storm surge. These hazards usually interact with each other and cause greater amplified hazard intensity. In the coastal areas, wave may damage coastal defense system like sea walls and dykes, and overtopping storm surge could hence become severe flooding due to the breach of the dykes. The probability distributions of wave and surge, as univariate respectively, have been studies and used in the design in various research. However, far less investigations on their joint probability distribution have been carried out in the past.

In this study, the dataset of hourly surge height, and significant wave height of 89 TC events impacting along Hainan Island during 1949~2013 was obtained, which are simulated numerically with ADCIRC and SWAN respectively. Following that, 4 types of probability distributions for univariate were used to fit the marginal distribution of storm surge and wave. Secondly, Frank, Clayton and Gumbel Copula were tried to construct the joint probability distribution of wave and surge, and the optimal Copula was determined by K-S test and AIC, BIC criteria. Based on the optimal Copula selected for each area of interest, the joint return period of wave and surge was estimated.

The results show that, 1) the annual maximum value of the storm surge height and significant wave height of Hainan Island has a relatively obvious geographical distribution regularity. 2) GEV and Gumbel are the most optimal distribution for storm surge height and significant wave height respectively. 3) Clayton Copula is the best model for fitting joint probability of storm surge and wave. The estimated joining probability distribution can help the determination of design standard, and typical TC disaster scenario development.