Abstract
Abstract. This paper proposes the estimation of high return period quantiles using upper bounded distribution functions with Systematic and additional Non-Systematic information. The aim of the developed methodology is to reduce the estimation uncertainty of these quantiles, assuming the upper bound parameter of these distribution functions as a statistical estimator of the Probable Maximum Flood (PMF). Three upper bounded distribution functions, firstly used in Hydrology in the 90's (referred to in this work as TDF, LN4 and EV4), were applied at the Jucar River in Spain. Different methods to estimate the upper limit of these distribution functions have been merged with the Maximum Likelihood (ML) method. Results show that it is possible to obtain a statistical estimate of the PMF value and to establish its associated uncertainty. The behaviour for high return period quantiles is different for the three evaluated distributions and, for the case study, the EV4 gave better descriptive results. With enough information, the associated estimation uncertainty for very high return period quantiles is considered acceptable, even for the PMF estimate. From the robustness analysis, the EV4 distribution function appears to be more robust than the GEV and TCEV unbounded distribution functions in a typical Mediterranean river and Non-Systematic information availability scenario. In this scenario and if there is an upper limit, the GEV quantile estimates are clearly unacceptable.
Highlights
Flood frequency analysis is one of the most common methods to estimate the design flood for hydraulic structures and for flood hazard/risk mitigation programs
The gestimated by models type distribution function (TDF)/Maximum Likelihood (ML)-GE (93 100 m3 s−1) and LN4/ML-C (99 300 m3 s−1) are approximately three times G, which are unreasonable values, whereas the gestimated with EV4/ML-GE is 18 100 m3 s−1, almost half of G value and about 40% above the maximum observed value in two centuries, which is more reasonable
Once the EV4 distribution function has been selected for the Jucar River case study, an uncertainty analysis has been made in order to establish the reliability of the quantiles and Probable Maximum Flood (PMF), estimated with this distribution function and using the different parameter estimation methods (ML-C, ML-GE and MLPG)
Summary
Flood frequency analysis is one of the most common methods to estimate the design flood for hydraulic structures and for flood hazard/risk mitigation programs. Some distribution functions incorporate an additional parameter, which is the upper limit to the random variable This class of functions has been applied to the extreme frequency analysis of annual maximum daily precipitation by Elıasson (1994 and 1997), Takara and Loebis (1996) and Takara and Tosa (1999) and in frequency analysis of annual maximum flood by Takara and Tosa (1999). All these authors concluded that upper bounded distribution functions fit properly to extreme data and improve the quantile estimates. The PMF can be estimated as one of the parameters of the statistical model, using in this paper additional Non-Systematic information, called temporal information expansion, in terms of Merz and Bloschl (2008) to obtain enough estimation reliability
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