Evaluation of Return Period and Risk in Bivariate Non-Stationary Flood Frequency Analysis

The concept of a traditional return period has long been questioned in non-stationary studies, and the risk of failure was recommended to evaluate the design events in flood modeling. However, few studies have been done in terms of multivariate cases. To investigate the impact of non-stationarity on the streamflow series, the Yichang station in the Yangtze River was taken as a case study. A time varying copula model was constructed for bivariate modeling of flood peak and 7-day flood volume, and the non-stationary return period and risk of failure were applied to compare the results between stationary and non-stationary models. The results demonstrated that the streamflow series at the Yichang station showed significant non-stationary properties. The flood peak and volume series presented decreasing trends in their location parameters and the dependence structure between them also weakened over time. The conclusions of the bivariate non-stationary return period and risk of failure were different depending on the design flood event. In the event that both flood peak and volume are exceeding, the flood risk is smaller with the non-stationary model, which is a joint effect of the time varying marginal distribution and copula function. While in the event that either flood peak or volume exceed, the effect of non-stationary properties is almost negligible. As for the design values, the non-stationary model is characterized by a higher flood peak and lower flood volume. These conclusions may be helpful in long-term decision making in the Yangtze River basin under non-stationary conditions.