Introducing empirical and probabilistic regional envelope curves into a mixed bounded distribution function

B Guse,Th Hofherr,B Merz

doi:10.5194/hess-14-2465-2010

Abstract

Abstract. A novel approach to consider additional spatial information in flood frequency analyses, especially for the estimation of discharges with recurrence intervals larger than 100 years, is presented. For this purpose, large flood quantiles, i.e. pairs of a discharge and its corresponding recurrence interval, as well as an upper bound discharge, are combined within a mixed bounded distribution function. The large flood quantiles are derived using probabilistic regional envelope curves (PRECs) for all sites of a pooling group. These PREC flood quantiles are introduced into an at-site flood frequency analysis by assuming that they are representative for the range of recurrence intervals which is covered by PREC flood quantiles. For recurrence intervals above a certain inflection point, a Generalised Extreme Value (GEV) distribution function with a positive shape parameter is used. This GEV asymptotically approaches an upper bound derived from an empirical envelope curve. The resulting mixed distribution function is composed of two distribution functions which are connected at the inflection point. This method is applied to 83 streamflow gauges in Saxony/Germany. Our analysis illustrates that the presented mixed bounded distribution function adequately considers PREC flood quantiles as well as an upper bound discharge. The introduction of both into an at-site flood frequency analysis improves the quantile estimation. A sensitivity analysis reveals that, for the target recurrence interval of 1000 years, the flood quantile estimation is less sensitive to the selection of an empirical envelope curve than to the selection of PREC discharges and of the inflection point between the mixed bounded distribution function.

Highlights

Flood frequency analysis provides flood quantiles, i.e. discharges and their corresponding recurrence intervals
The integration of the probabilistic regional envelope curves (PRECs) flood quantiles leads to a higher k and a lower skewness of GEVsim−prec compared to GEVsim
Large flood quantiles were derived by probabilistic regional envelope curves (PREC)

Summary

Introduction

Flood frequency analysis provides flood quantiles, i.e. discharges and their corresponding recurrence intervals. To reduce the estimation uncertainty of an at-site flood frequency analysis, it is recommended to use more information than the observed flood series Hosking and Wallis, 1986a; Stedinger and Cohn, 1986; Merz and Bloschl, 2008a,b; Merz and Thieken, 2009). Since the quantile estimates become less precise with higher recurrence intervals, additional information becomes increasingly important in these cases Additional information can be classified into three groups: causal, temporal (historic floods) and spatial (flood regionalisation) information (Merz and Bloschl, 2008a,b). Process understanding can be incorporated as causal information into a flood frequency analysis. Merz and Bloschl (2008a) illustrated that an investigation of event runoff coefficients helps to explain the generation processes

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