Non-Stationary Frequency Analysis of Extreme Water Level: Application of Annual Maximum Series and Peak-over Threshold Approaches

Abstract

A great challenge has been appeared on if the assumption of data stationary for flood frequency analysis is justifiable. Results for frequency analysis (FA) could be substantially different if non-stationarity is incorporated in the data analysis. In this study, extreme water levels (annual maximum and daily instantaneous maximum) in a coastal part of New York City were considered for FA. Annual maximum series (AMS) and peak-over threshold (POT) approaches were applied to build data timeseries. The resulted timeseries were checked for potential trend and stationarity using statistical tests including Man-Kendall, Augmented Dickey–Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS). Akaike information criterion (AIC) was utilized to select the most appropriate probability distribution models. Generalized Extreme Value (GEV) distribution and Generalized Pareto Distribution (GPD) were then applied as the probability distribution functions on the selected data based on AMS and POT methods under non-stationary assumption. Two methods of maximum likelihood and penalized maximum likelihood were applied and compared for the estimation of the distributions’ parameters. Results showed that by incorporating non-stationarity in FA, design values of extreme water levels were significantly different from those obtained under the assumption of stationarity. Moreover, in the non-stationary FA, consideration of time-dependency for the distribution parameters resulted in a range of variation for design floods. The findings of this study emphasize on the importance of FA under the assumptions of data stationarity and non-stationarity, and taking into account the worst case flooding scenarios for future planning of the watershed against the probable flood events. There is a need to update models developed for stationary flood risk assessment for more robust and resilient hydrologic predictions. Applying non-stationary FA provides an advanced method to extrapolate return levels up to the desired future time perspectives.