Regional Frequency Distribution Research Articles

Estimation of regional and at-site quantiles of extreme winds under flood index procedure

Extreme winds are becoming more common among environmental events with the most catastrophic societal consequences. A regional frequency analysis of Daily Annual Maximum Wind Speed (DAMWS) is necessary not only for a comprehensive understanding of wind hazards but also for infrastructure design and safety, wind energy potential, disaster risk reduction, insurance and risk assessment in a particular region of study. This study investigated regional frequency analysis of DAMWS of Baluchistan and Sindh provinces of Pakistan. L-moments regionalization techniques along with flood index procedure were applied to DAMWS records of 21 stations from 1990 to 2019 across the study area. We intended to find the regional frequency distribution for maximum winds and predict the returns for extreme winds events in the future. Only one station namely Lasbella was found to be discordant. With the help of cluster analysis, the remaining 20 stations were further divided into two homogeneous. Heterogeneity measures validate that both regions are homogenous with allotted stations. Regional quantiles for both regions are estimated through best-fit probability distribution among Generalized Normal (GNO), Generalized Logistic (GLO), Pearson Type 3 (P3), Generalized Pareto (GPA), and Generalized Extreme Value (GEV). Robustness of GLO distribution compared to GEV distribution is assessed through Monte Carlo simulations of relative bias and relative root mean square error. Findings clearly show that GLO distribution is the best for regional modeling. Furthermore, with the help of index flood procedure we determined at-site quantiles of all stations for various return periods. These estimated quantiles are of valuable information for various sectors, including infrastructure, energy, disaster management, and climate resilience, leading to improved planning, development, and risk reduction in the face of wind-related hazards in Sindh and Balochistan provinces of Pakistan.

Changing Characteristics of Regional and Site-based Frequency Distribution Under the Non-Stationary Process

Changing Characteristics of Regional and Site-based Frequency Distribution Under the Non-Stationary Process

Attribute analysis as a tool for determining the areas of the late diagenetic Main Dolomite deposits and assessing the stability of the seismic signal parameters

The results of the lithofacial analysis of data from the Moracz 3D seismic survey were among the main premises leading to the positioning of the new petroleum exploration well in that area. Unfortunately, the reservoir properties of the drilled part of the Main Dolomite carbonates differed significantly from those anticipated by the analysis of the amplitudes of the seismic signal recorded. Such surprisingly negative results impelled the reinterpretation of 3D seismic data. Hence, a number of analyses of the amplitudes, the frequencies, and the variability of phase shift were carried out in order to determine the influence of these parameters on the lithofacial interpretation of seismic data. The results revealed a fundamental error of amplitude with the extraction maps. It appeared that the distribution of amplitudes is not essentially controlled by the reservoir properties of the Main Dolomite carbonates but by the fault shadow effect coming from Mesozoic graben in the overburden. In addition, a large diversity of frequency spectra was found, which, combined with the small thickness of the exploration level, could have contributed to incorrect identification of seismic reflections. There was also a change in seismic signatures from the same reflection in different parts of the survey, raising doubts about the distribution of the phase rotation. In order to recognize phase rotation diversity, a new seismic data analysis was based upon the selected Triassic sediments of high impedance. The obtained maps demonstrated significant variability within the data volume due to attenuation. The reinterpreted data from the Moracz 3D seismic survey proved the uneven and unstable distribution of amplitudes, frequencies, and phase which resulted in erroneous conclusions of petroleum exploration. After modeling with the use of different frequency ranges, an analysis of the amplitude extraction of the horizons related to the Main Dolomite was performed. Then the amplitude ratio attribute was selected which eliminated the influence of the regional amplitude and frequency distribution and showed the distribution of dolomite properties more reliably than the amplitude extraction maps.

A ranking method for regionalization of watersheds

Identification of groups of watersheds with similar flood generation mechanisms and the same hydrological responses is an important step of regional flood frequency analysis which is called regionalization of watersheds. A group of watersheds with similar flood generation mechanisms and the same hydrological responses is called a homogeneous region. Theoretically, the homogeneity of regions is a requirement to fit the regional frequency distribution and estimate flood quantiles. However, it may be observed in some real-world cases that a regionalization with a more appropriate homogeneity condition results in less accurate estimates in comparison with a regionalization with lesszappropriate homogeneity. In this study, a ranking method is proposed to compare various regionalizations and select more suitable ones for regional flood frequency analysis. The proposed method is used to identify a suitable regionalization for regional flood frequency analysis by considering the homogeneity, quantile estimation accuracy, and average region size. The method was applied to Karun-e-bozorg basin in the southwest of Iran as a case study. The results show that the method has an acceptable performance in identifying a regionalization that provides suitable homogeneity, quantile estimation accuracy, and average region size. Also, the study results indicate that the ranking based on the homogeneity ratio is relatively compatible with the ranking based on the quantile estimation accuracy. In addition, according to the results, the most appropriate regionalization of 41 watersheds in the study area includes 3 regions provided by the combination of the clustering algorithms average-linkage and K-means.

Regional frequency analysis of daily maximum rainfall in Haryana

This paper is sets-out for the regional frequency analysis of daily maximum rainfall from the 27 rain gauge stations in Haryana using L-moments. As the distribution of rainfall varies spatially in Haryana, the 27 rain gauge stations are grouped into three clusters namely, cluster C1, C2 and C3 using Ward’s clustering method and homogeneity of clusters was confirmed using L-moments-based Heterogeneity measure (H). Using goodness-of-fit measure ( DIST Z ) and L-moment ratios diagram, suitable regional frequency distributions were selected among five candidate distributions;Generalized Logistic (GLO), Generalized Extreme Value (GEV),Generalized Normal (GNO), Generalized Pareto (GPA), and Pearson Type-3 (PE3) for each cluster. Results showed that PE3 and GNO were good fitted regional distribution for the cluster C1 and GEV, PE3 and GNO fitted for cluster C2 while for cluster C3; GLO and GEV were good fitted regional distribution. To select a robust distribution among good fitted distributions accuracy measures calculated using Monte Carlo simulations for each cluster. The simulation result showed that PE3 was the best choice for quantile estimation for cluster C1. For cluster C2, PE3 was the best choicefor a large return period and GEV was best for a small return period. For cluster C3, GEV was the most suitable distribution for quantile estimation. Using these robust distributions rainfall quantiles were estimated at each rain gauge station from 2 to 100 year return periods. These estimated rainfall quantiles may be rough guideline for planning and designing hydraulic structures by policy makers and structural engineers.

Frequency analysis of extreme precipitation in different regions of the Huaihe River Basin

AbstractAffected by climate change and human activities, the frequency and uncertainty of extreme precipitation have shown an increasing trend, which has brought great challenges to the prevention of flood disasters. The Huaihe River Basin (HRB) is located at the junction of northern and southern China and is more susceptible to climate change. In order to obtain the spatio‐temporal distribution characteristics of extreme precipitation in the HRB, in this study, the L‐moments method was used to analyse the regional frequency distribution of the annual precipitation (YP), the maximum one‐day rainfall (RM1day), the maximum five‐day rainfall (RM5day) and the maximum 15‐day rainfall (RM15day) in the HRB. The results show that the HRB can be divided into five sub‐zones on the basis of the division of natural sub‐basins to ensure regional consistency. The accuracy of quantile estimation will decrease as the return periods increase. When the return period is less than 100 years, the relative root mean square error (RMSE) can be guaranteed to be relatively small, and the cumulative RMSE is less than 0.3. However, after the return period is greater than 100 years, the 90% confidence interval of the quantile estimate increases rapidly, indicating that the estimated quantile error increased. The northwestern part of the HRB may experience extreme annual precipitation, which is different from the normal precipitation distribution. The extreme precipitation in Zone 1, Zone 2–2 and Zone 4 is not only strong but also has a large increase speed, making these areas the key focus zones for flood control and anti‐logging. This study can provide important reference for the prediction and prevention of extreme precipitation in the HRB.

Regional frequency analysis of daily maximum rainfall in Haryana

This paper is sets-out for the regional frequency analysis of daily maximum rainfall from the 27 rain gauge stations in Haryana using L-moments. As the distribution of rainfall varies spatially in Haryana, the 27 rain gauge stations are grouped into three clusters namely, cluster C1, C2 and C3 using Ward’s clustering method and homogeneity of clusters was confirmed using L-moments-based Heterogeneity measure (H). Using goodness-of-fit measure ( ) and L-moment ratios diagram, suitable regional frequency distributions were selected among five candidate distributions; Generalized Logistic (GLO), Generalized Extreme Value (GEV),Generalized Normal (GNO), Generalized Pareto (GPA), and Pearson Type-3 (PE3) for each cluster. Results showed that PE3 and GNO were good fitted regional distribution for the cluster C1 and GEV, PE3 and GNO fitted for cluster C2 while for cluster C3; GLO and GEV were good fitted regional distribution. To select a robust distribution among good fitted distributions accuracy measures calculated using Monte Carlo simulations for each cluster. The simulation result showed that PE3 was the best choice for quantile estimation for cluster C1. For cluster C2, PE3 was the best choicefor a large return period and GEV was best for a small return period. For cluster C3, GEV was the most suitable distribution for quantile estimation. Using these robust distributions rainfall quantiles were estimated at each rain gauge station from 2 to 100 year return periods. These estimated rainfall quantiles may be rough guideline for planning and designing hydraulic structures by policy makers and structural engineers.

Regional extreme rainfall estimation in Middle Black Sea Region, Turkey

The occurrence probabilities of heavy rainfalls brought about flood events have an essential role in designing water-related structures and water resource management. In many cases, data for analysis are either not available or are insufficient for reliable design of water-related structures. Regional frequency analysis is frequently preferred to provide design information at sites with especially inadequate data available. Our study implemented L-moment procedures to annual maximum rainfall series from 70 gauging stations in the Middle Black Sea Region (MBSR) in Turkey to estimate regional rainfall quantiles. The first attempt for regionalization was to evaluate the entire area as an only homogeneous region. The sub-regions were initially defined with the ward’s clustering algorithm due to the presence of discordant sites under a presumption of a single homogeneous region. In compliance with the results of the discordancy and heterogeneity measures, the most promising classification was achieved with 6 clusters (sub-regions). The sub-regions have satisfied the homogeneity condition as “acceptably homogeneous.” The GEV and GLO distributions in five sub-regions, GNO distribution in four sub-regions, and PE3 distribution in three sub-regions were decided to be acceptable as a regional frequency distribution. In comparison, GPA is a candidate distribution in none of six sub-regions.

Regional Frequency Analysis of Maximum Monthly Rainfall in Haryana State of India Using L-Moments

The paper aims to select the appropriate regional frequency distribution for the maximum monthly rainfall and estimation of quantiles using L-moments for the 27 rain gauge stations in Haryana. These 27 rain gauge stations were grouped into three homogeneous regions (Region-1, Region-2, and Region-3) using Ward’s method of cluster analysis. To confirm the homogeneity of each region, L-moments based measure of heterogeneity was used. For each homogeneous region, a regional distribution was selected with the help of the L-moments ratio diagram and goodness-of-fit test. Results of the goodness-of-fit test and L-moments ratio diagram indicated that Generalized Logistic and Generalized Extreme Value distributions were best- fitted regional frequency distributions for the Region-1 and Region-2 respectively while for Region-3, Pearson Type-3) was best-fitted distribution. The quantiles for each region were calculated and the regional growth curves were developed. The accuracy measurements were determined using Monte Carlo simulations for the regional quantiles. Results of simulations showed that uncertainty in regional quantiles measured by Root Mean Square Error value and 90 percent error limits were small when the return period was low but uncertainty in quantiles increases as the return period increases.

Assessment of extreme waves in the North Atlantic Ocean by regional frequency analysis

Regional frequency analysis is applied to North Atlantic Ocean wave data to determine the regions that can be considered homogenous from the point of view of extreme distributions and to obtain the extreme regional frequency distributions able to characterize those regions. The entire information is used on a regional scale to obtain an accurate estimation of the probability of occurrence of extreme events at a given location. Regional frequency analysis is implemented using 43 years (1958-2000) of hindcast data extracted from the HIPOCAS database. The domain of this area covers the latitudes 20.0∘N to 68.0∘N and the longitudes -50.0∘W to - 4.0∘W, with a grid resolution of 1∘ x 1∘. This approach can identify sites that lie close to each other but belong to different regions and in this way defines the areas in which the North Atlantic Ocean can be divided from a statistical point of view.

Regional flood frequency analysis for flood index estimation in hydrologic regions with limited flood data

The objective of this study is to establish a regional relationship between mean annual peak flood and the catchment area based on the annual peak flood frequency analysis. Annual peak flood time series for various gauging sites of six basins in north part of Iraq are used in analysis. The procedure of analysis is approached by scaling a regional flood frequency distribution (index-flood of catchment) which is defined here as the mean annual maximum flood discharge and estimated by linear regression using physiographic and climatic catchment properties. The index-flood method was found to have slightly better prediction accuracies over the direct-regression method. The coefficient of determination R2 between reference and estimated index-floods is relatively high in most cases for all the gauging stations. All regions give very high R 2 correlation and the best model is the model (2), which is also associated with minimum value of RMSE.

Regional Flood Frequency Analysis for a Poorly Gauged Basin Using the Simulated Flood Data and L-Moment Method

The design of hydraulic structures and the assessment of flood control measures require the estimation of flood quantiles. Since observed flood data are rarely available at the specific location, flood estimation in un-gauged or poorly gauged basins is a common problem in engineering hydrology. We investigated the flood estimation method in a poorly gauged basin. The flood estimation method applied the combination of rainfall-runoff model simulation and regional flood frequency analysis (RFFA). The L-moment based index flood method was performed using the annual maximum flood (AMF) data simulated by the rainfall-runoff model. The regional flood frequency distribution with 90% error bounds was derived in the Chungju dam basin of Korea, which has a drainage area of 6648 km2. The flood quantile estimates based on the simulated AMF data were consistent with the flood quantile estimates based on the observed AMF data. The widths of error bounds of regional flood frequency distribution increased sharply as the return period increased. The results suggest that the flood estimation approach applied in this study has the potential to estimate flood quantiles when the hourly rainfall measurements during major storms are widely available and the observed flood data are limited.

A modified regional L-moment method for regional extreme precipitation frequency analysis in the Songliao River Basin of China

The regional frequency analysis (RFA) is a widely used method in analyzing the changes of extreme precipitation (EP). The uncertainties in the identification of homogeneous subregions and the selection of optimal regional frequency distributions can largely influence the results of the RFA. In this study, the fuzzy c-means method combined with the extended Xie-Benn index (FCXB) is used to help determine the optimal division of subregions. In addition, we introduce a new comprehensive index (CI) to overcome the shortcomings of present measures and reduce the uncertainty in regional frequency distribution selection. The changes of EP at 93 meteorological stations in the Songliao River Basin (SRB) during 1960 to 2016 is analyzed. The main results show that: (1) FCXB can effectively identify the optimum number of homogeneous subregions automatically, and the corresponding subregion division is proven to be reasonable and reliable; (2) compared with the single goodness-of-fit measure, the developed CI can reduce the uncertainties in distribution selection and determine the optimal regional distribution in a reliable way; (3) the estimated EP under different return periods both decrease from the south to the north of the SRB, which indicates the risk of high-intensity EP events in the southern SRB is relatively higher. These findings can provide technical support for local policymakers to formulate effective measures to lessen the damages of the EP on ecosystem and society.

Identification of homogeneous rainfall regions using a genetic algorithm involving multi-criteria decision making techniques

Abstract The detection of appropriate homogeneous regions is an important step in regional frequency analysis with the determination of homogeneity depending to a great extent on the type of method used in grouping. So, the study considers a genetic-algorithm-based clustering method to identify homogeneous precipitation regions for 39 gauge stations of the north-eastern region of India. The performance evaluation is done using six cluster validation measures. Further, considering all the six indices together, selection for the optimum cluster is modelled as a multi-criteria decision making (MCDM) problem. Three MCDM methods, namely TOPSIS, WASPAS and VIKOR, are applied to obtain ranked clusters which are then subjected to a heterogeneity test using the L-moments approach. The results suggested the stations to be grouped into three homogeneous regions. Comparison with the k-means method indicated relatively better performance for genetic-algorithm-based clustering. Finally, an L-moment ratio diagram and goodness-of-fit measures were conducted to select regional frequency distributions for the identified homogeneous regions.

Regional frequency analysis of extreme waves in a coastal area

This study analysed the wave data from several locations in a coastal region to identify the areas with comparable wave height statistics and to estimate regional extreme significant wave heights of designated return periods. The regional frequency analysis algorithm executed in this work utilised the significant wave height data from 35 sites (35°–45°N, -6.5°–-11.0°W) in a coastal grid (0.25° × 0.25°) off Portugal in the North Atlantic Ocean, extracted from 44 years HIPOCAS hindcast wave database. Regional frequency analysis algorithms based on L-moments identified the discordant sites (discordant site statistics are substantially diffused from the group of sites statistics), assisted in the formation of homogeneous regions by cluster analyses (data vectors include site characteristics and site statistics) and consequently selected appropriate regional frequency distributions by Z goodness-of-fit test statistic at 90% level of significance to estimate regional extreme significant wave height quantiles of designated return periods. The regional frequency analysis algorithm recognised in certain cases, neighbouring sites as members of diverse regions, revealing that geographical proximity of sites are not ascertaining factors to form homogeneous regions. At-site analyses along with regional frequency analysis enabled to apprehend the precision of the regional extreme quantile as genuine feature of its at-site extreme quantiles.

A framework of integrated hydrological and hydrodynamic models using synthetic rainfall for flash flood hazard mapping of ungauged catchments in tropical zones

Abstract. Flash flood hazard maps provide a scientific support to mitigate flash flood risk. The present study develops a practical framework with the help of integrated hydrological and hydrodynamic modelling in order to estimate the potential flash floods. We selected a small pilot catchment which has already suffered from flash floods in the past. This catchment is located in the Nan River basin, northern Thailand. Reliable meteorological and hydrometric data are missing in the catchment. Consequently, the entire upper basin of the main river was modelled with the help of the hydrological modelling system PANTA RHEI. In this basin, three monitoring stations are located along the main river. PANTA RHEI was calibrated and validated with the extreme flood events in June 2011 and July 2008, respectively. The results show a good agreement with the observed discharge data. In order to create potential flash flood scenarios, synthetic rainfall series were derived from temporal rainfall patterns based on the radar-rainfall observation and different rainfall depths from regional rainfall frequency analysis. The temporal rainfall patterns were characterized by catchment-averaged rainfall series selected from 13 rainstorms in 2008 and 2011 within the region. For regional rainfall frequency analysis, the well-known L-moments approach and related criteria were used to examine extremely climatic homogeneity of the region. According to the L-moments approach, Generalized Pareto distribution was recognized as the regional frequency distribution. The synthetic rainfall series were fed into the PANTA RHEI model. The simulated results from PANTA RHEI were provided to a 2-D hydrodynamic model (MEADFLOW), and various simulations were performed. Results from the integrated modelling framework are used in the ongoing study to regionalize and map the spatial distribution of flash flood hazards with four levels of flood severities. As an overall outcome, the presented framework can be applied in areas with inadequate runoff records.

Comparison of regional and at-site frequency analysis methods for the estimation of southern Alberta extreme rainfall

At least one national meteorological organization has updated their rainfall intensity–duration–frequency (IDF) estimates using a regional frequency analysis approach. In this study, the regional frequency analysis L-moments approach was applied to data from 12 rain gauge sites in southern Alberta, for rainfall durations from 1 hour to 24 hours. Five candidate frequency distributions were tested, and the best-fit regional frequency distribution was used to estimate rainfall quantiles for return periods up to 1:1000 years. The quantiles were compared to the quantiles from the conventional at-site Gumbel approach. The results showed that the conventional approach tends to underestimate the quantiles relative to the regional approach, mainly for the sub-daily rainfall durations. The accuracy of the two approaches was tested using Monte Carlo simulations, and the results showed that the root mean square error (RMSE) using the conventional approach is approximately 2–2.5 times greater than the error using the regional approach, for the 1:100-year return period. The full benefits of regional frequency analysis have not yet been realized in Canada, which could benefit from a national program to update rainfall IDF estimates using these more statistically robust approaches.

Evaluation of the Index-Flood Approach Related Regional Frequency Analysis Procedures

AbstractIndex-flood related regional frequency analysis (RFA) procedures are in use by hydrologists to estimate design quantiles of hydrological extreme events at data sparse/ungauged locations in river basins. There is a dearth of attempts to establish which among those procedures is better for RFA in the L-moment framework. This paper evaluates the performance of the conventional index flood (CIF), the logarithmic index flood (LIF), and two variants of the population index flood (PIF) procedures in estimating flood quantiles for ungauged locations by Monte Carlo simulation experiments and a case study on watersheds in Indiana in the U.S. To evaluate the PIF procedure, L-moment formulations are developed for implementing the procedure in situations where the regional frequency distribution (RFD) is the generalized logistic (GLO), generalized Pareto (GPA), generalized normal (GNO) or Pearson type III (PE3), as those formulations are unavailable. Results indicate that one of the variants of the PIF procedu...

A More Efficient Rainfall Intensity-Duration-Frequency Relationship by Using an “at-site” Regional Frequency Analysis: Application at Mediterranean Climate Locations

Intensity-duration-frequency (IDF) relationships are the tools for obtaining design rainfall estimation. Their calculation requires rainfall data not commonly available in time. The scarce spatial information makes it difficult to perform a Regional Frequency Analysis (RFA). The objective of this paper was to establish a new method to obtain more efficient IDF relationships than those traditionally applied, by using at-site regional frequency analysis. An application to rainfall datasets from two Mediterranean climate locations (Spain and Chile) has been set up. Nine annual maximum rainfall data series (AMS) of duration from 10 min to 24 h were analyzed. The tests of Mann–Whitney for homogeneity, Wald-Wolfowitz for independence and Mann-Kendall for stationarity, were conducted to test the underlying assumptions in frequency analyses. The RFA tests identified the nine considered datasets from each location as a homogeneous region, and the suitable regional frequency distribution to establish the regional growth curves. Considering the regional index flood model, the regional growth curves were used to obtain the rainfall quantiles for the return periods and durations considered at each location Their combination with the equations obtained after correlating the mean values from the AMS and their durations permitted the obtainment of the new power-type IDF relationships.. The efficiency of the new model was evaluated by using several efficiency indexes, being more efficient and giving a better performance compared to traditional IDF models. The proposed method offers great application possibilities in Mediterranean climate areas located in the Mediterranean Catchment, California, Mexico, Central Chile, Australia and South Africa.

A bivariate extension of theHosking andWallis goodness‐of‐fit measure for regional distributions

AbstractThis study presents a bivariate extension of the goodness‐of‐fit measure for regional frequency distributions developed by Hosking and Wallis (1993) for use with the method of L‐moments. Utilizing the approximate joint normal distribution of the regional L‐skewness and L‐kurtosis, a graphical representation of the confidence region on the L‐moment diagram can be constructed as an ellipsoid. Candidate distributions can then be accepted where the corresponding theoretical relationship between the L‐skewness and L‐kurtosis intersects the confidence region, and the chosen distribution would be the one that minimizes the Mahalanobis distance measure. Based on a set of Monte Carlo simulations, it is demonstrated that the new bivariate measure generally selects the true population distribution more frequently than the original method. Results are presented to show that the new measure remains robust when applied to regions where the level of intersite correlation is at a level found in real world regions. Finally the method is applied to two different case studies involving annual maximum peak flow data from Italian and British catchments to identify suitable regional frequency distributions.