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.     

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.     

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.     

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.     

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.     

Regional Flood Frequency Analysis Using L-Moments for the West Mediterranean Region of Turkey

The aim of this study is to investigate and determine hydrologically homogeneous regions and to derive regional flood frequency estimates for 47 gauged sites in the West Mediterranean River Basins in Turkey, using an index flood method with L-moments parameter estimation. Screening of the data of the gauged site is carried out based on a discordancy measure in terms of the L-moments. Initial candidate regions are established by the cluster analysis of first five L-moment statistics, using k-means method. Homogeneity of the basins is tested using simulation with a four-parameter Kappa distribution and an L-moments based heterogeneity measure. Three subregions are defined, namely the Antalya subregion, the Lower West Mediterranean subregion, and the Upper West Mediterranean subregion. Comparative regional flood frequency estimates are made for each subregion using various distributions, namely the generalized logistic, general extreme value, generalized normal, Pearson type III, generalized Pareto, kappa, and Wakeby distributions. Based on an L-moments goodness-of-fit statistic, the Pearson type III distribution is identified as the best-fit distribution for the Antalya and Lower-West Mediterranean subregions, and the Generalized Logistic for the Upper-West Mediterranean subregion. Monte Carlo simulation is used to evaluate the accuracy of the quantile estimates on the basis of the relative root-mean-square error and relative bias.     

Comparison of Frequency Calculation Methods for Precipitation Series Containing Zero Values

The Muskingum-based (MK-based) distributions and their probability weighted moments (PWMs) have been used for frequency calculation of hydrological data that contain zero values. However, the performance of different MK-based distributions have not been compared and evaluated. Moreover, the partial L-moments (PLMs), which are used for analyzing censored samples, have not been used for frequency calculation of such hydrological data. To obtain the most effective method, this study compares and evaluates the performance of four MK-based distributions by fitting 64 monthly precipitation series and using the ordinary least square (OLS) criterion, Akaike information criterion (AIC), residual square sum criterion (RSS), and the Quasi-optimal Deterministic coefficient (QD). The distributions include ?exponential distribution combines with Dirac delta function (M-like), two-parameter gamma distribution (GA2) combines with Dirac delta function (DGA2), two-parameter generalized Pareto distribution combines with Dirac delta function (DGP2), and two-parameter Weibull distribution (WB2) combines with Dirac delta function (DWB2). The applicability of PLMs were also tested and PLMs of four traditional distributions, including GA2, WB2, generalized extreme value distribution (GEV) and three-parameter generalized Pareto distribution (GP3) were used in application. Results showed that the PLMs are feasible for frequency calculation of hydrological data with zeros. The DGP2 and GP3 are superior to the other MK-based distributions and traditional distributions, respectively. The DGP2 distribution is the optimal choice in most cases and is more universal than the other distributions.

     

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.     

Comparison of Artificial Neural Network Methods with L-moments for Estimating Flood Flow at Ungauged Sites: the Case of East Mediterranean River Basin, Turkey

A regional flood frequency analysis based on the index flood method is applied using probability distributions commonly utilized for this purpose. The distribution parameters are calculated by the method of L-moments with the data of the annual flood peaks series recorded at gauging sections of 13 unregulated natural streams in the East Mediterranean River Basin in Turkey. The artificial neural networks (ANNs) models of (1) the multi-layer perceptrons (MLP) neural networks, (2) radial basis function based neural networks (RBNN), and (3) generalized regression neural networks (GRNN) are developed as alternatives to the L-moments method. Multiple-linear and multiple-nonlinear regression models (MLR and MNLR) are also used in the study. The L-moments analysis on these 13 annual flood peaks series indicates that the East Mediterranean River Basin is hydrologically homogeneous as a whole. Among the tried distributions which are the Generalized Logistic, Generalized Extreme Vaules, Generalized Normal, Pearson Type III, Wakeby, and Generalized Pareto, the Generalized Logistic and Generalized Extreme Values distributions pass the Z statistic goodness-of-fit test of the L-moments method for the East Mediterranean River Basin, the former performing yet better than the latter. Hence, as the outcome of the L-moments method applied by the Generalized Logistic distribution, two equations are developed to estimate flood peaks of any return periods for any un-gauged site in the study region. The ANNs, MLR and MNLR models are trained and tested using the data of these 13 gauged sites. The results show that the predicting performance of the MLP model is superior to the others. The application of the MLP model is performed by a special Matlab code, which yields logarithm of the flood peak, Ln(Q_T), versus a desired return period, T.     

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.