Selection of an Optimal Distribution Curve for Non-Stationary Flood Series

Abstract

The stationarity assumption of hydrological processes has long been compromised by human disturbances in river basins. The traditional hydrological extreme-value analysis method, i.e., “extreme value theory” which assumes stationarity of the time series, needs to be amended in order to adapt to these changes. In this paper, taking the East River basin, south China as a case study, a framework was put forward for selection of a suitable distribution curve for non-stationary flood series by using the time-varying moments (TVM). Data used for this study are the annual maximum daily flow of 1954–2009 at the Longchuan, Heyuan and Boluo Stations in the study basin. Five types of distribution curves and eight kinds of trend models, for a combination of 40 models, were evaluated and compared. The results showed that the flood series and optimal distribution curves in the East River basin have been significantly impacted by a continuously changing environment. With the increase of the degree of human influence, the thinner tails of distributions are more suitable for fitting the observed flow data, and the trend models are changed from CP (mean and standard deviation fitted by parabolic trend model) to CL (mean and standard deviation fitted by linear trend model) from upstream to downstream of the catchment. The design flood flow corresponding to a return period of more than 10 years at the Longchuan, Heyuan and Boluo Stations was overestimated by more than 28.36%, 53.24% and 26.06%, respectively if the non-stationarity of series is not considered and the traditional method is still used for calculation. The study reveals that in a changing environment, more advanced statistical methods that explicitly account for the non-stationarity of extreme flood characteristics are required.

Keywords

• time-varying statistical parameters
• frequency analysis
• probability distribution function
• extreme value flow
• non-stationarity