On the Applicability of the Expected Waiting Time Method in Nonstationary Flood Design

Given a changing environment, estimating a flood magnitude corresponding to a desired return period considering nonstationarity is crucial for hydrological engineering designs. Four nonstationary design methods, namely expected waiting time (EWT), expected number of exceedances (ENE), equivalent reliability (ER), and average design life level (ADLL) have already been proposed in recent years. Among them, the EWT method needs to estimate design flood magnitudes by solving numerically. In addition, EWT requires estimating design quantiles for infinite lifespan, or extrapolation time (textra), to guarantee the convergence of the EWT solution under certain conditions. However, few studies have systematically evaluated pros and cons of the EWT method as to how to determine the textra and what kinds of misunderstandings on the applicability of the EWT method exist. In this study, we aim to provide the first investigation of various factors that influence the value of textra in the EWT method, and provide comprehensive comparison of the four methods from the perspectives of textra, design values and associated uncertainties. The annual maximum flood series (AMFS) of 25 hydrological stations, with increasing and decreasing trends, in Pearl River and Weihe River were chosen for illustrations. The results indicate that: (1) the textra of EWT is considerably affected by the trend of AMFS and the choice of extreme distributions. In other words, the textra of stations with increasing trends was significantly smaller than that of stations with decreasing trends, and the textra was also larger for distributions with heavier tail; (2) EWT produced larger design values than ENE for increasing trends, and both EWT and ENE yielded larger design values than ER and ADLL for higher return periods, while complete opposite results were obtained for decreasing trends.