Nonstationary Frequency Analysis of Extreme Floods Using the Time-varying Two-component Mixture Distributions

The basic IID assumption of the traditional flood frequency analysis has been challenged by nonstationarity. The most popular practice for analyzing nonstationarity of flood series is to use a fixed single-type probability distribution incorporated with the time-varying moments. However, the type of probability distribution could be both complex because of distinct flood populations and time-varying under changing environments. To allow the investigation of this complex nature, the time-varying two-component mixture distributions (TTMD) method is proposed in this study by considering the time variations of not only the moments of its component distributions but also the weighting coefficients. Having identified the existence of mixed flood populations based on circular statistics, the proposed TTMD was applied to model the annual maximum flood series (AMFS) of two stations in the Weihe River basin (WRB), with the model parameters calibrated by the meta-heuristic maximum likelihood (MHML) method. The performance of TTMD was evaluated by different diagnostic plots and indexes and compared with stationary single-type distributions, stationary mixture distributions and time-varying single-type distributions. The results highlighted the advantages of using TTMD models and physically-based covariates in nonstationary flood frequency analysis. Besides, the optimal TTMD models were considered to be capable of settling the issue of nonstationarity and capturing the mixed flood populations satisfactorily. It is concluded that the TTMD model is a good alternative in the nonstationary frequency analysis and can be applied to other regions with mixed flood populations.