Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: I. Recherche théorique

Abstract

Abstract The Gumbel distribution has been the prevailing model for quantifying risk associated with extreme rainfall. Several arguments including theoretical reasoning and empirical evidence are supposed to support the appropriateness of the Gumbel distribution. These arguments are examined thoroughly in this work and are put into question. Specifically, theoretical analyses show that the Gumbel distribution is quite unlikely to apply to hydrological extremes and its application may misjudge the risk, as it underestimates seriously the largest extreme rainfall amounts. Besides, it is shown that hydrological records of typical length (some decades) may display a distorted picture of the actual distribution, suggesting that the Gumbel distribution is an appropriate model for rainfall extremes while it is not. In addition, it is shown that the extreme value distribution of type II (EV2) is a more consistent alternative. Based on the theoretical analysis, in the second part of this study an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100–154 years of data. This verifies the inappropriateness of the Gumbel distribution and the appropriateness of EV2 distribution for rainfall extremes.     

Trends in frequency of precipitation extremes in the Yangtze River basin,China: 1960–2003 / Tendances d'évolution de la fréquence des précipitations extrêmes entre 1960 et 2003 dans le bassin versant du Fleuve Yangtze (Chine)

Abstract

The spatial distribution and trends in the frequency of precipitation extremes over the last 44 years (1960–2003), especially since 1990, have been analysed using daily precipitation data from 147 stations in the Yangtze River basin. The research results are as follows: (1) The 15 mm precipitation isohyet approximately divides the precipitation extremes (corresponding to the 95th percentile) of the stations in the middle and lower Yangtze reaches (higher) from those of the upper Yangtze reaches (lower). Also the starting time of the precipitation extremes in the middle and lower Yangtze reaches is earlier than of those in the upper Yangtze reaches. Precipitation extremes are concentrated mostly in June in the middle and lower Yangtze reaches, and July in the upper Yangtze reaches. (2) During the period 1960–2003, the first two decades had fewer precipitation extremes than the last two decades. There have been significant increasing trends and step changes in frequency of annual total precipitation extremes and precipitation extremes with a 1–5 day gap in the middle and lower Yangtze reaches. Precipitation extremes occur more frequently in shorter periods, separated by a few days. Precipitation extremes are also becoming more concentrated in the month with the highest frequency of extremes (June) in the middle and lower Yangtze reaches. In the upper Yangtze reaches, there is an upward tendency of extreme events in June. Increasing precipitation extremes in June for both the middle and lower, and the upper Yangtze reaches will increase the probability of flooding if the observed trends of the last 40 years continue into the future.     

Estimation of extreme floods of the River Meuse using a stochastic weather generator and a rainfall–runoff model / Estimation des crues extrêmes de la Meuse à l'aide d'un générateur stochastique de variables météorologiques et d'un modèle pluie–débit

Abstract

A stochastic weather generator has been developed to simulate long daily sequences of areal rainfall and station temperature for the Belgian and French sub-basins of the River Meuse. The weather generator is based on the principle of nearest-neighbour resampling. In this method rainfall and temperature data are sampled simultaneously from multiple historical records with replacement such that the temporal and spatial correlations are well preserved. Particular emphasis is given to the use of a small number of long station records in the resampling algorithm. The distribution of the 10-day winter maxima of basin-average rainfall is quite well reproduced. The generated sequences were used as input for hydrological simulations with the semi-distributed HBV rainfall–runoff model. Though this model is capable of reproducing the flood peaks of December 1993 and January 1995, it tends to underestimate the less extreme daily peak discharges. This underestimation does not show up in the 10-day average discharges. The hydrological simulations with the generated daily rainfall and temperature data reproduce the distribution of the winter maxima of the 10-day average discharges well. Resampling based on long station records leads to lower rainfall and discharge extremes than resampling from the data over a shorter period for which areal rainfall was available.