Nonstationary flood frequency analysis using univariate and bivariate time-varying models based on GAMLSS

Abstract

With the changing environment, a number of researches have revealed that the assumption of stationarity of flood sequences is questionable. In this paper, we established univariate and bivariate models to investigate nonstationary flood frequency with distribution parameters changing over time. Flood peak Q and one-day flood volume W1 of the Wangkuai Reservoir catchment were used as basic data. In the univariate model, the log-normal distribution performed best and tended to describe the nonstationarity in both flood peak and volume sequences reasonably well. In the bivariate model, the optimal log-normal distributions were taken as marginal distributions, and copula functions were addressed to construct the dependence structure of Q and W1. The results showed that the Gumbel-Hougaard copula offered the best joint distribution. The most likely events had an undulating behavior similar to the univariate models, and the combination values of flood peak and volume under the same OR-joint and AND-joint exceedance probability both displayed a decreasing trend. Before 1970, the most likely combination values considering the variation of distribution parameters over time were larger than fixed parameters (stationary), while it became the opposite after 1980. The results highlight the necessity of nonstationary flood frequency analysis.