A nonstationary bivariate design flood estimation approach coupled with the most likely and expectation combination strategies

In this study, a framework is proposed to estimate the nonstationary bivariate design flood, which includes three key steps. First, a nonstationary copula model was constructed to analyze the temporal variation in the bivariate joint distribution. Second, the equivalent reliability method was used to calculate the design value of the dominant variable for a return period and the design lifespan length under non-stationarity. Third, the design value of the secondary variable that was conditioned on the design value of the dominant variable, was calculated using the conditional most likely combination and conditional expectation combination strategies. Through the above three steps, the typical design value combination of the nonstationary bivariate was obtained for a specific design standard. A case study, based on the nonstationary annual maximum 1-day (AM1) and 15-day (AM15) flood volume at the Yichang station, was conducted to illustrate the framework. The results indicate that the joint distribution of the AM1 and AM15 flood volumes varied over time. For a specific design standard, the design values of the AM15 and AM1 flood volumes decreased with an increase in the design lifespan length. Moreover, the conditional most likely estimation of the design value for the AM1 flood volume that was conditioned on the design value for the AM15 flood volume was greater than its conditional expectation estimation.

Automated summary

A framework is proposed to estimate the nonstationary bivariate design flood, which includes constructing a nonstationary copula model, using the equivalent reliability method to calculate design values and design lifespan length, and calculating the design value of the secondary variable using conditional most likely combination and conditional expectation combination strategies. A case study shows the design value combination of the nonstationary bivariate and its temporal variation.