The Application of Mixture Distribution for the Estimation of Extreme Floods in Controlled Catchment Basins

Wiesław Szulczewski,Wojciech Jakubowski

doi:10.1007/s11269-018-2005-6

Wiesław Szulczewski, Wojciech Jakubowski

Open Access

https://doi.org/10.1007/s11269-018-2005-6

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Abstract

In the estimation of distribution of annual maximum flows it is a generally accepted assumption that the sequence of observations originates from a homogeneous population. This assumption, however, is rarely met. The observed annual maximum flow are only in part generated by flood events. The remaining ones are the result of the effect of other hydrological processes that do not have that character. For this reason, a new solution to this problem is proposed in the paper. It is assumed that the sought distribution is a mixture of two probability distributions: a three-parameter GEV distribution, describing flows generated by events with flood character, and a two-parameter gamma distribution, accounting for maximum annual flows that do not have such a character. The paper presents both the method of estimation of the mixture distribution and its application for gauging stations selected so as to take into account possible the most diverse conditions of meteorological, hydrological and geomorphological character. The area with such a high diversification, selected for the study, is the catchment basin of upper and central river Odra (South-West Poland). In the studied water gauge profiles the proposed mixture distribution indicates correct fit. Its advantages and limitations are presented through a comparative analysis with results obtained during estimation of distributions of maximum annual flows by means of standard methods.

Highlights

Observed flood flows have for years constituted the basis for the probability estimation of high flood quantiles or exceedance probabilities, values used in the design of hydrotechnical structures, and in the protection of river-side areas against floods
The mean absolute relative error (MARE) is determined between observed flows exceeding the value of the median and their equivalents calculated from the estimated MIX distribution
For maximum annual flows observed on a given water gauge the goodness-of-fit χ 2 tests were conducted for a predetermined and constant division into classes, irrespective of the tested distribution

Summary

Introduction

Observed flood flows have for years constituted the basis for the probability estimation of high flood quantiles or exceedance probabilities, values used in the design of hydrotechnical structures, and in the protection of river-side areas against floods. Starting from the nineties of the last century, from moment of publication of the Hosking (1990) paper on probability weighted moments, the number of publications in which distributions of maximum flows were estimated grew rapidly. Their extensive analysis, supported with numerous application examples, is described in papers from the turn of the 20th and 21st centuries. Subsequent studies devoted mainly to nonstationarity of annual maximum flows include significant introductions describing the applied methods of estimation of maximum flows Xiong et al (2015)

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Conclusion