Bias correction in hydrologic GPD based extreme value analysis by means of a slowly varying function

Abstract

Exponential distributions (EXP) and generalized Pareto distributions (GPD) are frequently applied in hydrologic extreme value analysis. They are calibrated to peak-over-threshold (POT) or partial duration series (PDS) extremes extracted from time series of hydrologic variables above specific threshold levels. Based on the extreme value theory, extremes converge only asymptotically (towards infinitely high threshold levels) to the EXP or GPD distribution. Calibration of the distribution for limited thresholds considered in practical cases will therefore lead to a bias in the asymptotic properties of the calibrated extreme value distribution. The paper aims to bring this problem of bias to the attention of the statistical hydrologist and proposes a method for bias correction. The method is based on the calibration of a so-called slowly varying function, and is demonstrated for six rainfall-runoff or river flow series in four countries. Extremes are selected from the series on the basis of hydrologic independence criteria. Discrimination between EXP (normal tail) and GPD (heavy tail) and optimal threshold selection are based on regression in Q-Q plots (QQR method). It is found based on these methods that the bias and the slowly varying function strongly depend on the number of selected extremes or the independence level considered in the selection criteria. It is also shown that different independence levels can be considered and combined to decrease the variance in the calibration.