Joint occurrence probability analysis of typhoon-induced storm surges and rainstorms using trivariate Archimedean copulas

In this paper, the trivariate frequency analysis method for joint probability assessment of typhoon-induced storm surges and rainstorms is presented. The proposed method includes three major processes. The first process is to the find the best fitted marginal cumulative distributions for wind speeds (W), storm surges (S) and rainstorms (R), respectively. It is found that the Lognormal distribution is more suitable for storm surges and rainstorms, and Weibull distribution is more suitable for wind speeds. The second process is to estimate the joint probability distributions of W, S and R using four trivariate copulas, namely, Gumbel, Clayton, Frank and AMH. It is found that the joint probability can be best modeled by Gumbel copula. The last process is to calculate the conditional joint distributions of typhoon-induced storm surges and rainstorms which is useful for government agencies for improving disaster system management during typhoon events. An effective Particle Swarm Optimization (PSO) is proposed for to estimate the parameters of marginal cumulative distributions and copula functions. Analysis results based on the maximum likelihood method (MLM) and log-likelihood function (LLF) demonstrate the effectiveness of the PSO.