Regional Flood Frequency Analysis of North-Bank of the River Brahmaputra by Using LH-Moments

In this study LH-moment proposed by Wang (Water Resour Res 33(12):2841–2848, 1997) has been used for regional flood frequency analysis of the North-Bank region of the river Brahmaputra, India. Three probability distributions i.e. generalized extreme value (GEV), generalized logistic (GLO) and generalized Pareto (GPA) has been used for each level of LH-moments i.e. L, L₁, L₂, L₃ and L₄. The regional frequency analysis procedure proposed by Hosking and Wallis (Water Resour Res 29(2):271–281, 1993) for L-moments i.e. discordancy measure for screening the data, heterogeneity measure for formation of homogeneous region and goodness-of-fit test have been used for each level of LH-moments. Based on the LH-moment ratio diagram and ∣Z∣-statistic criteria, GEV distribution for level one LH-moment is identified as the robust distribution for the study area. For estimation of floods of various return periods for both gauged and ungauged catchments of the study area, regional flood frequency relationships have been developed by using the level one LH-moment based on GEV distribution. A comparative study has been performed between L-moments and LH-moments for the study area. It is observed from comparative study that the regional flood frequency analysis based on the GEV distribution by using level one LH-moment (L₁) is superior to the use of L-moments.     

基于广义极值分布和Metropolis-Hastings抽样算法的贝叶斯MCMC洪水频率分析方法

广义极值（GEV）分布是国内外洪水频率分析建模中广泛应用的一种概率分布。本文将水文频率分布线型的未知参数看作随机变量，通过基于Metropolis-Hastings抽样算法的贝叶斯MCMC方法估计GEV分布参数和设计时段洪量的后验分布，并据此进行极值洪水的频率分析。汉江流域丹江口水库年最大1日（3日、5日、7日）洪量频率分析的结果表明了本方法的有效性和实用性。主要结论包括：基于Metropolis-Hastings抽样的MCMC模拟在GEV分布参数的贝叶斯估计计算中行之有效；由于利用了与似然函数渐近性质无关的先验信息，贝叶斯估计方法得到的高分位数设计洪量的后验分布比经典统计方法得到的设计洪量能包含更多的信息，从而能表达由于参数不确定性而引起的预测不确定性。该方法能显著地通过分位数图、PPCC法、均方根误差法、K-S法等多种拟合优度检验方法，拟合效果不亚于其他常用的经典统计方法。     

Regional Frequency Analysis of Extreme Rainfalls in the West Coast of Peninsular Malaysia using Partial L-Moments

This study was to reinstate the development of regional frequency analysis using L-moments approach. The Partial L-moments (PL-moments) method was employed and a new relationship for homogeneity analysis is developed. For this study, the PL-moments for generalized logistic (GLO), generalized pareto (GPA) and generalized value (GEV) distributions were derived based on the formula defined by Wang (Water Resour Res 32:1767?C1771, 1996). The three distributions are used to develop the regional frequency analysis procedures. As a case of study, the Selangor catchment that consists of 30 sites which located on the west coast of Peninsular Malaysia has chosen as sample. Based on L-moment and PL-moment ratio diagrams as well as Z-test statistics, the GEV and GLO were identified as the best distributions to represent the statistical properties of extreme rainfalls in Selangor. Monte Carlo simulation shows that the method of PL-moments would outperform L-moments method for estimation of large returns period event.     

Regional Flood Frequency Analysis of the Seven Sites of Punjab, Pakistan, Using L-Moments

L-moments based regional flood frequency analysis has been carried out on the seven sites of Punjab, Pakistan. Discordancy measure in terms of L-moments has been used to screen the data on each of the seven sites. Homogeneity of the region has been tested using the L-moments based heterogeneity measure (H). H has been calculated using four parameter Kappa distribution with 500 simulations. In order to find the most suitable distribution for quantile estimates, a number of L-moments based frequency distributions, such as, generalized logistic (GLO), generalized extreme-value (GEV), generalized normal (GNO), Pearson type III (PE3), generalized Pareto (GPA) and five parameter Wakeby (WAK) distribution, have been used. Based on the L-moment ratio diagram and Z ^DIST statistic, three distributions; GNO, GPA and GEV have been identified as the suitable candidates for regional distribution. Accuracy measures for the estimated regional growth curves and quantiles have been calculated for the three candidate distributions, using Monte Carlo simulations. Simulations study showed that GNO distribution is the robust distribution with GPA as suitable alternative but GEV is not an appropriate distribution for the study area.     

Development of Regional Flood Frequency Relationships Using L-moments for Middle Ganga Plains Subzone 1(f) of India

In this study, screening of the data has been carried out basedon the discordancy measure (D _i) in terms of the L-moments. Homogeneity of the region has been tested using the L-moments based heterogeneity measure, H. For computing the heterogeneity measure H, 500 simulations were carried out using the four parameter Kappa distribution. Based on this test, it has been observed that the data of 8 out of 11 bridge sites constitute ahomogeneous region. Hence, the data of these 8 sites have been used in this study. Catchment areas of these 8 sites vary from 32.89 to 447.76 km² and their mean annual peak floods varyfrom 24.29 to 555.21 m³ s^-1. Comparative regional floodfrequency analysis studies have been carried out using the various L-moments based frequency distributions viz. Extreme value (EV1), General extreme value (GEV), Logistic (LOS), Generalized logistic (GLO), Normal (NOR), Generalized normal (GNO), Uniform (UNF), Pearson Type-III (PE3), Exponential (EXP),Generalized Pareto (GPA), Kappa (KAP), and five parameter Wakeby(WAK). Based on the L-moment ratio diagram and Z _i ^dist –statistic criteria, GEV distribution has been identified as the robust distribution for the study area. For estimation of floods of various return periods for gauged catchments of the study area, regional flood frequency relationship has been developed using the L-moments based GEV distribution. Also, for estimation of floods of desiredreturn periods for ungauged catchments, regional flood frequencyrelationship has been developed by coupling the regional flood frequency relationship with the regional relationship between mean annual maximum peak flood and catchment area.     

Use of L-Moments Approach for Regional Flood Frequency Analysis in Sicily, Italy

Extremely great floods are among environmental events with the most disastrous consequences for the entire world. Estimates of their return periods and design values are of great importance in hydrologic modeling, engineering practice for water resources and reservoirs design and management, planning for weather-related emergencies, etc. Regional flood frequency analysis resolves the problem of estimating the extreme flood events for catchments having short data records or ungauged catchments. This paper analyzes annual maximum peak flood discharge data recorded from more than 50 stream flow gauging sites in Sicily, Italy, in order to derive regional flood frequency curves. First these data are analyzed to point out some problems concerning the homogeneity of the single time series. On the basis of the L-moments and using cluster analysis techniques, the entire region is subdivided in five subregions whose homogeneity is tested using the L-moments based heterogeneity measure. Comparative regional flood frequency analysis studies are carried out employing the L-moments based commonly used frequency distributions. Based on the L-moment ratio diagram and other statistic criteria, generalized extreme value (GEV) distribution is identified as the robust distribution for the study area. Regional flood frequency relationships are developed to estimate floods at various return periods for gauged and ungauged catchments in different subregions of the Sicily. These relationships have been implemented using the L-moment based GEV distribution and a regional relation between mean annual peak flood and some geomorphologic and climatic parameters of catchments.     

Effect of Extraordinary Large Floods on at-site Flood Frequency

The peak flow of extraordinary large floods that occur during a period of systematic record is a controversial problem for flood frequency analysis (FFA) using traditional methods. The present study suggests that such floods be treated as historic flood data even though their historical period is unknown. In this paper, the extraordinary large flood peak was first identified using statistical outlier tests and normal probability plots. FFA was then applied with and without the extraordinary large floods. In this step, two goodness-of-fit tests including mean absolute relative deviation and mean squared relative deviation were used to identify the best-fit probability distributions. Next, the generalized extreme value (GEV), three-parameter lognormal (LN3), log-Pearson type III (LP3), and Wakeby (WAK) probability distributions were used to incorporate and adjust the extraordinary large floods with other systematic data. Finally, procedures with and without historical adjustment were compared for the extraordinary large floods in terms of goodness-of-fit and flood return-period quantiles. The results of this comparison indicate that historical adjustment from an operational perspective was more viable than without adjustment procedure. Furthermore, the results without adjustment were unreasonable (subject to over- and under-estimation) and produced physically unrealistic estimates that were not compatible with the study area. The proposed approach substantially improved the probability estimation of rare floods for efficient design of hydraulic structures, risk analysis, and floodplain management.     

Regional Frequency Distribution Type of Low Flow in North of Iran by L-moments

A regional low flow frequency analysis in the north of Iran using L-moments was carried out. Low flow events have been represented by the 7-day annual minimum series and the L-moments approach was used to assign these data into homogenous regions. According to the homogeneity measure and climatic properties, two subdivisions were found – one in the west of the study area having a homogenous assemblage of sites, and one in the east in which the sites were found to be heterogeneous. The regional low flow frequency distribution was derived for the western division using L-moments and goodness of fit tests were used to evaluate which of a number of possible distributions best represented this. The evaluation suggested that the Generalized Logistic distribution gives the best overall result. For heterogeneous subdivision, the performance of the 2-parameter distribution such as 2-parameter Log Normal, Normal and Gamma distributions gave the best result for the majority of sites. Regional and at-site frequency curves were also compared for the western division, which showed that the quantile estimates could be very different in the upper and lower tails of the distribution. The influence on flow regime and watershed properties on the type of the best fit distribution was investigated which showed that the 2 and 3 parameter distributions do not have a clear relationship with climatic and physiographic characteristics of the watersheds except the watershed area. This may result in simple scaling laws of low flows.     

At-Site Flood Frequency Analysis Coupled with Multiparameter Probability Distributions

The proper design of hydraulic structures as well as river basin management are directly dependent on adequate estimates of maximum streamflow, preferably obtained from long historical series. However, the scarce hydrological monitoring, recurrent in developing countries and the need for estimates associated with high return periods (RPs) have led to the use of estimation methods based statistical procedures, such as at-site flood frequency analysis. This study presents a framework for at-site flood frequency analysis coupled with multiparameter probability distribution functions (PDFs) (GEV, LN3, PE3, GLO, GPA, KAP and WAK), in which all the statistical procedures are derived from L-moments, in order to investigate the applicability of these PDFs in comparison to those of 2-parameters (EV1, LN2 and Gamma). The modeling framework was evaluated considering 106 maximum annual streamflow (MAS) series for the Rio Grande do Sul State - Brazil. PDFs’ goodness-of-fit was studied in accordance with the Anderson-Darling test. It can be concluded that: i) the multiparameter distributions, especially KAP and WAK, had performance superior to the traditional 2-parameter distributions, providing a greater number of historical series better adjusted by such multiparameter PDFs; ii) shorter series were usually better represented by GEV when compared to the other PDFs, which is an important characteristic when long historical series are not frequently available; and iii) the quantile estimates derived from multiparameter PDFs presented lower Relative Absolute Error, thus emphasizing the importance of using such PDFs in water resources management and engineering projects.     

L-Moment-Based Regional Frequency Analysis of Annual Extreme Precipitation and its Uncertainty Analysis

Estimation of precipitation amounts associated with different return periods is an important task for the planning and design of many types of infrastructures. In this study, regional frequency analysis based on L-moments is proposed to estimate the annual maximum daily precipitation quantiles in the Taihu basin, China. The Generalized Extreme Value (GEV) distribution is used to describe the frequency distributions of extreme rainfall events. At-site frequency analysis results based on L-moments are compared with those obtained from regional analysis. The 95% confidence intervals of estimated precipitation quantiles are calculated using Monte Carlo simulations (MCS). Uncertainty assessment results indicate that regional analysis is more robust and more accurate than at-site analysis. Furthermore, when conducting regional frequency analysis, the estimation of precipitation quantile confidence intervals can be simplified by assuming normality for the MCS results. The variation of the precipitation quantiles’ sample statistics for different return periods is expressed as a function of the return period. The proposed methods are useful for the Taihu Basin and are recommended for other regions.     

Application of the Regional Flood Frequency Analysis to the Upper and Lower Basins of the Indus River,Pakistan

The paper presents results of an application of the L-moments based regional flood frequency analysis to annual maximum peak (AMP) flows observed at seven stations (Tarbela, Kalabagh, Chashma, Taunsa, Guddu, Sukkur and Kotri) located on the main stream of the Indus River, Pakistan. The results of Run-test and lag-1 correlation coefficient showed that the data series at given sites is random and has no serious serial correlations respectively. Furthermore, the results of Grubbs and Beck test illustrated that there are no irregularities (abrupt variations) except low outlier(s) in the data series at various sites. To avoid their undue influence, these low outliers have been discarded and the sample information has been re-summarized using the idea of left censored type A ^′ partial probability weighted moments. L-moments based regional heterogeneity measure (H) showed that the region, defined by seven stations, is heterogeneous; therefore, it has been sub-divided into two homogeneous regions (Region 1 and Region 2 consist of four (Tarbela, Kalabagh, Chashma and Taunsa) and three sites (Guddu, Sukkur and Kotri, respectively) using Ward’s clustering method based on the site characteristics only. The results of various goodness-of-fit measures (L-moment ratio diagram, average weighted distance and Z ^DIST measures) showed that Region 1 has four candidates: generalized normal (GNO), generalized logistic (GLO), generalized extreme-value (GEV) and Pearson type III (PE3), while Region 2 has only one candidate; GLO, as regional distribution. Based on the results of different accuracy measures (regional average absolute relative bias, relative bias and relative root mean square error) of the estimated regional growth curves and quantiles, obtained from simulation experiments, PE3 is the robust distribution for Region 1, while for Region 2, GLO distribution can be used for the estimation of flood quantiles. Moreover, the results of the simulations study have been extended to obtain standard errors of the estimated quantiles at each site of the sub-divided homogeneous regions.     

Possible Regional Probability Distribution Type of Canadian Annual Streamflow by L-moments

For effective planning, design, and management of water resources engineering, the probability distribution of annual streamflow is necessary. The method of L-moments is applied to identify the probability distribution type of annual streamflow in different climatic regions of Canada. In the Pacific and southern British Columbia mountains (regions 1 and 2), the generalized extreme value (GEV) distribution fits the observations best with the 3-parameter lognormal (LN3) and log Pearson type III (LP3) as potential candidates. In Yukon and northern British Columbia (region 3), the LN3 distribution corresponds to observations best with the LP3 and P3 as potential candidates. In the northwestern forest (region 5), the LP3 distribution matches observations best with the P3 and GEV as potential candidates. In Arctic Tundra (region 10), the 3-parameter Weibull (W3) is the best one with the LN3 and P3 as potential candidates. The P3 distribution provides a best-fit to observations in the Prairies (region 4), northeastern forest (region 6), great Lakes and St. Lawrence (region 7), Atlantic (region 8), and Mackenzie (region 9) with the LN3, LP3, and GEV as potential candidates.     

淮河上游紫罗山流域枯水频率及退水规律分析

应用枯季径流退水规律预报枯季径流总量和径流过程是枯季径流预报最常用、有效的方法。但目前,尚未有一种通用的分布可以很好地模拟所有枯水径流。以淮河上游紫罗山流域为研究对象,以1952～2010年各年最小7 d平均流量作为枯季径流统计特征序列,采用P-Ⅲ,LP-Ⅲ,GLO,GPA,LN3和GEV 6种分布,利用适线法、矩法等进行参数估计,推求经验频率对应的理论线型计算值。利用概率点据相关系数、四阶线性矩系数、确定性系数,均方根误差和平均绝对误差5个特征统计量,比较各分布线型拟合情况,确定该流域枯水频率最优拟合线型为P-Ⅲ分布。此外,利用退水曲线法推求各年份退水系数与多年综合退水系数。结果表明:流域年退水系数在0.007～0.200范围内波动,其变化与降水无关,随着最小7 d平均流量的变小而增大,流域多年综合退水系数为0.08。研究成果对合理开发利用水资源、保护河流生态系统平衡具有现实意义。     

基于地区线性矩法对四川省水文频率分析的研究

为了促进地区线性矩法在水文频率分析领域的研究与应用并改进我国传统水文频率分析的研究成果,为四川省的防洪工作提供一定的参考,根据地区线性矩法的基本思想和原理,对四川省共计150个国家自动气象站点的年最大日降雨序列进行分析,对四川省进行水文气象一致性区域划分,并确定各区域的最优频率分布线型。根据各个一致性区域的最优频率分布线型,估算出各个站点不同重现期下的设计值。此外,还把地区线性矩法与传统水文频率分析法估算的结果进行比较分析。结果表明:四川省可以划分为9个水文气象一致性区域;水文气象一致性区域1区、2区、3区、5区、6区、7区、8区、9区的最优频率分布线型均为广义逻辑斯蒂分布(GLO),4区的最优频率分布线型为广义极值分布(GEV);水文气象一致性区域3区、4区、6区为主要暴雨区。随着重现期增大,利用传统方法得到的设计值总体偏低。     

Assessment of Regional Floods Using L-Moments Approach: The Case of The River Nile

In this study, a regional flood frequency analysis has been carried out, using the index flood L-moments approach. Annual maximum stream flood data observed at 14 gauged sites on the Nile River tributaries (Blue Nile, White Nile, and Atbara River) are investigated. The aim of the study is to investigate and derive hydrologically homogeneous region or regions and to identify and establish the regional statistical distribution. To this end, five distribution functions are used, namely: generalized pareto, generalized extreme-value, generalized logistic, generalized normal, and Pearson type-3 distributions. Analyses have shown that 8 sites form a hydrologically homogeneous region, and this region follows a generalized logistic (GLO) distribution. Furthermore, the other remaining two regions (possibly heterogeneous and definitely heterogeneous) are also defined. Regional dimensionless growth curves for the identified three regions are derived. Results are assessed on the basis of relative RMSE% and relative BIAS% through the use of Monte Carlo simulation.     

极端条件下堆石坝溃坝风险及应急预案

考虑洪水漫顶条件下的溃决模式,拟定汛限水位、校核洪水位与校核洪水流量、多年平均入库流量的极端组合方式,采用DB-IWHR模型计算堆石坝溃坝洪水过程;利用MIKE 21模拟洪水演进过程,取支流历史最大洪水过程并使其与干支流洪峰遭遇,评估洪水对下游的淹没风险.以涔天河大坝为例,根据库容、堆石材料参数等确定不同入库洪水组合方...     

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.     

分布式水文模型结合雷达测雨用于三峡区间的洪水预报

长江三峡区间因暴雨形成的洪水峰高量大, 对三峡水库防洪安全和运行调度的影响不容忽视。依据三峡地区的地形地貌特征,采用基于 GIS的分布式水文模型来模拟区间洪水过程,以尽量减小洪水预报中的不确定性。研究表明 ,降雨信息缺失是洪水预报不确定性的主要来源,尤其是在雨量站稀疏的山区,雨量站观测 的降雨信息难以充分表征降雨空间变化。为此,进一步尝试利用雷达测雨数据作为分布式水 文模型的输入,通过对2个小流域的示例研究,结果表明雷达测雨能捕获降雨的空间分布, 它与分布式水文模型相结合,是提高洪水预报精度的有效途径之一。     

Modeling nonstationary extreme wave heights in present and future climates of Greek Seas

In this study the generalized extreme value(GEV) distribution function was used to assess nonstationarity in annual maximum wave heights for selected locations in the Greek Seas, both in the present and future climates. The available significant wave height data were divided into groups corresponding to the present period(1951e2000), a first future period(2001e2050), and a second future period(2051e2100). For each time period, the parameters of the GEV distribution were specified as functions of time-varying covariates and estimated using the conditional density network(CDN). For each location and selected time period, a total number of 29 linear and nonlinear models were fitted to the wave data, for a given combination of covariates. The covariates used in the GEV-CDN models consisted of wind fields resulting from the Regional Climate Model version 3(RegC M3) developed by the International Center for Theoretical Physics(ICTP) with a spatial resolution of 10 km 10 km, after being processed using principal component analysis(PCA). The results obtained from the best fitted models in the present and future periods for each location were compared, revealing different patterns of relationships between wind components and extreme wave height quantiles in different parts of the Greek Seas and different periods. The analysis demonstrates an increase of extreme wave heights in the first future period as compared with the present period, causing a significant threat to Greek coastal areas in the North Aegean Sea and the Ionian Sea.     

陕北地区年降水量频率分布参数估算研究

以陕北地区年降水量系列为基础资料,选取12种概率分布模型,分别按矩法、极大似然法估计参数,并参照离差平方和最小准则OLS进行了参数优选,最终优选出在OLS准则下的最佳分布模型、参数计算方法以及最优分布不同频率下的设计值.结果表明:在OLS准则下,对数正态分布(LN2)或广义极值分布(GEV)拟合效果好.文中计算结果可以为水利工程的规划设计与运行以及水资源管理提供依据.