Local and regional flood frequency analysis based on hierarchical Bayesian model in Dongting Lake Basin,China

This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV)distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC)method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.

THE TRANSFORMED NONPARAMETRIC FLOOD FREQUENCY ANALYSIS

The nonparametric kernel estimation of probability density function (PDF) pro-vides a uniform and accurate estimate of flood frequency-magnitude relationship.However, the kernel estimate has the disadvantage that the smoothing factor h is estimate empirically and is not locally adjusted, thus possibly resulting in deteri oration of density estimate when PDF is not smooth and is heavy-tailed. Such a problem can be alleviate by estimating the density of a transformed random vari able, and then taking the inverse transform. A new and efficient circular transform is proposed and investigated in this paper

A 249-Year Record of Floods at Appleby in Westmorland, UK

An analysis of nearly 250 years of flood records on the river Eden at Appleby-in-Westmorland has enabled a flood frequency relationship to be established. The most severe floods were in the late 18th and early 19th century. With such a long history of flooding, some remedial measures would have been expected but the local people have, to some extent, adapted to the flood hazard by means of temporary and permanent flood proofing methods such as a cemented board across a doorway and removable flood boards. These measures were overwhelmed during the 2015 flood, as were the flood gates installed by the Environment Agency in 1998. A higher level of protection from floods at Appleby is called for.

Flood Risk for Embanked Rivers

Flood frequency analysis (FFA) concentrates on peak flows of flood hydrographs. However, floods that last years devastated large parts of Poland lead us to revision of the views on the assessment of flood risk in Poland. It turned out that it is the prolonged exposure to high water on levees that causes floods, not only the water overflowing the levee crest. This is because, the levees are weakened by water and their disruption occurs when it seems that the danger is over, i.e. after passing culmination. Two main causes of inundation of embanked rivers, namely over-crest flow and wash out of the levees, are combined to assess the total risk of inundation. Therefore the risk of inundation is the total of risk of exceeding embankment crest by flood peak and risk of washout of levees. Hence, while modeling the flood events in addition to the maximum flow one should consider also the duration of high water in a river channel, Analysis of the frequency of annual peak flows based on annual maxima and peaks over threshold is the subject of countless publications. Therefore we will here mainly modeling the duration of high water levels. In the paper the two-component model of flood hydrograph shape i.e. “duration of flooding-discharge- probability of nonexceedance” (DqF), with the methodology of its parameters estimation for stationary case was developed as a completion to the classical FFA with possible extension to non stationary flood regime. The model combined with the technical evaluation of probability of levees breach due to the d-days duration of flow above alarm stage gives the annual probability of inundation caused by the embankment breaking. The results of theoretical research were supplemented by a practical example of the model application to the series for daily flow in the Vistula River in Szczucin. Regardless promising results, this method is still in its infancy despite its great cognitive potential and practical importance. Therefore, we would like to point to the usefulness and necessity of the DqF models to the one-dimensional analysis of the peak flood hydrographs and to flood risk analysis. This approach constitutes a new direction in FFA for embanked rivers.

On Return Periodof the Largest Historical Flood

The use of nonsystematic flood data for statistical purposes depends on reliability of assessment both flood magnitudes and their return period. The earliest known extreme flood year is usually the beginning of the historical record. Even though the magnitudes of historic floods are properly assessed, a problem of their retun periods remains unsolved. Only largest flood (XM) is known during whole historical period and its occurrence carves the mark of the beginning of the historical period and defines its length (L). So, it is a common practice of using the earliest known flood year as the beginning of the record. It means that the L value selected is an empirical estimate of the lower bound on the effective historical length M. The estimation of the return period of XM based on its occurrence, i.e. , gives the severe upward bias. Problem is to estimate the time period (M) representative of the largest observed flood XM. From the discrete uniform distribution with support of the probability of the L position of XM one gets ?which has been taken as the return period of XM and as the effective historical record length. The efficiency of using the largest historical flood (XM) for large quantile estimation (i.e. one with return period T = 100 years) has been assessed using maximum likelihood (ML) method with various length of systematic record (N) and various estimates of historical period length ?com- paring accuracy with the case when only systematic records alone (N) are used. The i-th simula- tion procedure incorporates systematic record and one largest historic flood (XMi) in the period M which appeared in the Li year backward from the end of historical period. The simulation result for selected distributions, values of their parameters, different N and M values are presented in terms of bias (B) and root mean square error (RMSE) of the quantile of interest and widely discussed.

Uncertainty Quantification for Multivariate Eco-Hydrological Risk in the Xiangxi River within the Three Gorges Reservoir Area in China

This study develops a multivariate eco-hydrological risk-assessment framework based on the multivari-ate copula method in order to evaluate the occurrence of extreme eco-hydrological events for the Xiangxi River within the Three Gorges Reservoir （TGR） area in China. Parameter uncertainties in marginal distri-butions and dependence structure are quantified by a Markov chain Monte Carlo （MCMC） algorithm. Uncertainties in the joint return periods are evaluated based on the posterior distributions. The proba- bilistic features of bivariate and multivariate hydrological risk are also characterized. The results show that the obtained predictive intervals bracketed the observations well, especially for flood duration. The uncertainty for the joint return period in ＂AND＂ case increases with an increase in the return period for univariate flood variables. Furthermore, a low design discharge and high service time may lead to high bivariate hydrological risk with great uncertainty.