Abstract
Statistical modeling of hydrological extremes is significant to the construction of hydraulic engineering. This paper, taking the Yingluoxia watershed as the study area, compares the annual maximum (AM) series and the peaks over a threshold (POT) series in order to study the hydrological extremes, examines the stationarity and independence assumptions for the two series, and discusses the estimations and uncertainties of return levels from the two series using the Generalized Extreme Value (GEV) and Generalized Pareto distribution (GPD) models. For comparison, the return levels from all threshold excesses with considering the extremal index are also estimated. For the POT series, the threshold is selected by examining the mean excess plot and the stability of the parameter estimates and by using common-sense. The serial correlation is reduced by filtering out a set of dependent threshold excesses. Results show that both series are approximately stationary and independent. The GEV model fits the AM series well and the GPD model fits the POT series well. The estimated return levels are fairly comparable for the AM series, the POT series, and all threshold excesses with considering the extremal index, with the difference being less than 10% for return periods longer than 10 years. The uncertainties of the estimated return levels are the highest for the AM series, and next for the POT series and then for all threshold excesses series in turn.
Highlights
A significant amount of attention has been paid to hydrological extreme events, which are likely to increase in frequency in most regions of the world [1,2,3]
Rao and Hamed [8] showed that the annual maximum series (AM) series is statistically more efficient than the peaks over a threshold (POT) series when λ is small ( λ ă 1.65 ), where λ is the mean number of peaks per year included in the POT series
This situation is avoided in the POT series where all peaks above a certain threshold value are considered, and more information about the extremes would be involved in the analysis [6]
Summary
A significant amount of attention has been paid to hydrological extreme events, which are likely to increase in frequency in most regions of the world [1,2,3]. The second or third peak within a year may be greater than the maximum flow in other years, and yet they are ignored [6] This situation is avoided in the POT series where all peaks above a certain threshold value are considered, and more information about the extremes would be involved in the analysis [6]. The POT series has some obvious disadvantages, and the major one is that the flood peaks might not form an independent time series, since some flood peaks may occur on the recession curves of the preceding flood peaks [10] Both series are used to indicate high flow extremes and compared to each other in this study
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