History and Perspectives of Hydrologic Frequency Analysis in Japan (original) (raw)
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Weighted estimate of extreme quantile: an application to the estimation of high flood return periods
Stochastic Environmental Research and Risk Assessment, 2013
ABSTRACT Parametric models are commonly used in frequency analysis of extreme hydrological events. To estimate extreme quantiles associated to high return periods, these models are not always appropriate. Therefore, estimators based on extreme value theory (EVT) are proposed in the literature. The Weissman estimator is one of the popular EVT-based semi-parametric estimators of extreme quantiles. In the present paper we propose a new family of EVT-based semi-parametric estimators of extreme quantiles. To built this new family of estimators, the basic idea consists in assigning the weights to the k observations being used. Numerical experiments on simulated data are performed and a case study is presented. Results show that the proposed estimators are smooth, stable, less sensitive, and less biased than Weissman estimator.
Future climatic conditions likely will not satisfy stationarity assumption. To address this concern, this study applied three methods to analyze non-stationarity in hydrologic conditions. Based on the principle of identifying distribution and trends (IDT) with time-varying moments, we employed the parametric weighted least squares (WLS) estimation in conjunction with the non-parametric discrete wavelet transform (DWT) and ensemble empirical mode decomposition (EEMD). Our aim was to evaluate the applicability of non-parameter approaches, compared with traditional parameter-based methods. In contrast to most previous studies, which analyzed the non-stationarity of first moments, we incorporated second-moment analysis. Through the estimation of long-term risk, we were able to examine the behavior of return periods under two different definitions: the reciprocal of the exceedance probability of occurrence and the expected recurrence time. The proposed framework represents an improvement over stationary frequency analysis for the design of hydraulic systems. A case study was performed using precipitation data from major climate stations in Taiwan to evaluate the non-stationarity of annual maximum daily precipitation. The results demonstrate the applicability of these three methods in the identification of non-stationarity. For most cases, no significant differences were observed with regard to the trends identified using WLS, DWT, and EEMD. According to the results, a linear model should be able to capture time-variance in either the first or second moment while parabolic trends should be used with caution due to their characteristic rapid increases. It is also observed that local variations in precipitation tend to be overemphasized by DWT and EEMD. The two definitions provided for the concept of return period allows for ambiguous interpretation. With the consideration of non-stationarity, the return period is relatively small under the definition of expected recurrence time comparing to the estimation using the reciprocal of the exceedance probability of occurrence. However, the calculation of expected recurrence time is based on the assumption of perfect knowledge of long-term risk, which involves high uncertainty. When the risk is decreasing with time, the expected recurrence time will lead to the divergence of return period and make this definition inapplicable for engineering purposes.
This study examines the joint impact of sample variability and rating curve imprecision in regional instantaneous flood frequency analysis based on L-moments. A parametric bootstrap methodology is developed for this purpose, assuming (1) a power-law model for the stage-discharge measurements, (2) a generalised extreme value (GEV) model for the annual maximum discharges and (3) no intersite correlation. The bootstrap framework is applied to data from eight gauging stations located in the southwest of Norway. The application shows that rating curve imprecision can have a major impact on the accuracy of regionally-based T-year flood estimates. The coefficients of variations for 25-and 50-year flood return level estimates at two of the eight stations are used as case-studies. The main findings is that when more stations are added to the regional analysis, the effect of sample variability decreases rapidly before stagnating, whereas the uncertainty due to rating curve imprecision fluctua...
This paper reviews the distribution functions suitable for hydrological extreme values and analyses on probability distributions for the Yodo River Basin, Japan and Kuala Lumpur, Malaysia. The proposed distribution functions are the Normal, Log Normal 3 parameter (LN3), Extreme Value I (EVI), Extreme Value II (EVII), Extreme value III (EVIII), Gamma 3 parameter (Gamma 3p) and Log-Pearson Type III (LP3). Modified distributions suggested for hydrological extreme value are also presented. They include the transformed extreme value (TDF) distribution, log normal 4-parameter (LN4) distribution, and extreme value distribution with lower and upper bounds (EVLUB or EV4). Data includes more than 100 years daily precipitation data of 3 stations in the Yodo river basin and 40 years of daily precipitation data of several stations in Kuala Lumpur, Malaysia. The SLSC goodness of fit criterion was used to test for the best fit distribution functions against the datasets. Results show that both the...