Regional Frequency Analysis Research Articles

Changing characteristics of precipitation for the contiguous United States

Using the US collection from the Global Historical Climatology Network Daily (GHCN-D) precipitation data for the contiguous United States (CONUS), this study examines the changing characteristics of precipitation during 1951–2013. In addition to mean precipitation, all precipitation events are divided into three categories: light, moderate, and heavy based on percentile thresholds. The historical trends are established for precipitation total, frequency and intensity, as well as for total and frequency of different intensity categories. Results show that from 1951 to 2013, mean precipitation increased at 1.66 % per decade, a higher rate than previous estimates. About one third of the increase is attributed to frequency change, whereas the other two thirds are attributed to an intensity increase. There was a slight decrease in light precipitation, a small increase in moderate precipitation, and much higher increase for heavy precipitation. Spatially, eastern and northern parts of the CONUS experienced higher rates of increase, whereas western regions experienced less increase. A statistically significant positive correlation exists between mean precipitation and precipitation change, suggesting the wet regions experienced more precipitation increase than dry regions. Seasonally, precipitation increased most for the fall, less in other seasons. Particularly, there were significant decreasing trends in summer precipitation for many parts of western and central CONUS. Regional frequency analysis is used to examine the change in extreme precipitation events with return intervals longer than a year. Results show that extreme precipitation events increased for most of the CONUS with the exception of the west region. These changes were a result of both a shift in the mean state and the shape of the precipitation data distribution.

Effect of Observed Discharge Data on Regional Flood Frequency Analysis in the Han River Basin

This study assessed the impact of uncertainties in flood data on the results of flood frequency analysis for Han river basin. To meet this aim, this study quantified assessment focused on the index flood and quantile by regional flood frequency analysis using the flood data from 17 water level gauges in Han river basin. We analysed the results categorized by three cases according to the characteristics of the measured data. Firstly, we analyzed the regional flood frequency for the water level gauge in the Pyungchang river basin to investigate the impact of water level data. The results has the error of 0.240 with respect to the mean flood. Secondly, we examined the impact of uncertainty in measurement data generated by the application of rating on the results of regional flood frequency analysis. We have compared the results by applying the rating estimated for each year to the one by the recently estimated rating. The results showed that the mean error has 0.246 in terms of the mean flood. Finally, we have inferred the regional flood frequency analysis results with the regulated flow in the downstream area of dams. The regulated specific discharge in the downstream area of dams controlled by dam operation showed a large difference to the estimated specific discharge in the downstream area of dams by extension of the natural specific discharge in the upstream area using the regionalization method.

Non-linear canonical correlation analysis in regional frequency analysis

Hydrological processes are complex non-linear phenomena. Canonical correlation analysis (CCA) is frequently used in regional frequency analysis (RFA) to delineate hydrological neighborhoods. Although non-linear CCA (NL-CCA) is widely used in several fields, it has not been used in hydrology, particularly in RFA. This paper presents an overview of techniques used to reproduce non-linear relationships between two sets of variables. The approaches considered in this work are based on NL-CCA using neural networks (CCA-NN), coupled to a log-linear regression model for flood quantile estimation. In order to demonstrate the usefulness of these approaches in RFA, a comparative study between the latter and linear CCA is performed using three different databases from North America. Results show that CCA-NN is more robust and can better reproduce the non-linear relationship structures between physiographical and hydrological variables. This reflects the high flexibility of this approach. Results indicate that for all three databases, it is more advantageous to proceed with the non-linear CCA approach.

The evaluation of regional frequency analyses methods for nonstationary data

Abstract. Regional frequency analysis is widely used to estimate more reliable quantiles of extreme hydro-meteorological events. The stationarity of data is required for its application. This assumption tends to be violated due to climate change. In this paper, four nonstationary index flood models were used to analyze the nonstationary regional data. Monte Carlo simulation was used to evaluate the performances of these models for the generalized extreme value distribution with linearly time varying location parameter and constant scale and shape parameters. As a results, it was found that the index flood model with time-invariant index flood and time-variant growth curve could yield more statistically efficient quantile when record is long enough to show significant nonstationarity.

Copula based drought frequency analysis considering the spatio-temporal variability in Southwest China

Summary Drought frequency analysis is a prerequisite for drought resistance planning and drought risk management. Drought is a spatio-temporal dynamic process, usually characterized by its duration, spatial extent, and severity. Copula based multivariate frequency analysis has been widely used to calculate drought frequency. However, the spatial extent is scarcely considered in previous studies, due to the fact that drought event is usually identified either for a fixed spatial scale or for a fixed temporal scale. This study develops a regional drought frequency analysis model based on trivariate copulas by considering the spatio-temporal variations of drought events. Drought duration, drought affect area, and drought severity are identified first, and their trivariate joint distribution is constructed later. The model is applied for drought frequency analysis in Southwest China during 1961–2012. A variety of probability distribution functions and copula functions (including elliptical, symmetric and asymmetric Archimedean) are used as candidate choices, and the most appropriate ones are selected based on goodness of fit using different methods. The robustness of drought frequency analysis is then evaluated and discussed. The results show that drought frequency analysis needs to fully consider the three characteristic parameters (duration, affect area, and severity) reflecting drought spatio-temporal variability. And the drought return period estimated by the copula-based trivariate frequency analysis appropriately integrates the effects of drought duration, affect area and severity, which is a reliable drought statistical measurement. The 2009–2010 drought, which has a return period of about 94 years, is the most severe one in Southwest China during the period of 1961–2012. The Joe and Gumbel copulas are found to be more suitable to estimate the joint distribution of drought duration, affect area and severity, and the Asymmetric (nested) function forms perform better than the symmetric functions.

Comparison of two methods of regional flood frequency analysis by using L-moments

A regionalized relationship to estimate flood magnitudes for ungauged and poorly gauged catchments can be established using regional flood frequency analysis (RFFA). Comparison of index-flood and multiple-regression analyses based on L-moments was the main objective of this study. Factor analysis was applied to determine main variables influencing flood magnitude. Results showed that the main variables are perimeter, equivalent diameter, time of concentration, length of main waterway and area. The study area was divided into two regions based on the Ward’s method of clustering approach and site characteristics. The homogeneity test based on L-moments showed that two regions were acceptably homogeneous. Five distributions were fitted to the annual peak flood data of two homogeneous regions. Using the L-moment ratios and the Z-statistic criteria, generalized logistic (GLO) and generalized Pareto (GPA) distributions were identified for the first and second homogeneous regions respectively as the most robust distributions among five potential distributions. The relative root mean square error (RRMSE) measure was applied for evaluating the performance of the index-flood and the multiple-regression methods in comparison with the curve fitting (plotting position) method. In general, the index-flood method gives more reliable estimations for various flood magnitudes of different recurrence intervals.

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.

Comparing three methods to form regions for design rainfall statistics: Two case studies in Australia

One of the fundamental steps in regional rainfall frequency analysis is deciding the method by which rainfall stations are to be grouped together to form regions. This paper compares three methods of forming regions for use in estimating design rainfalls: a fixed region approach where all the available sites are included in a single region, a Region of Influence (ROI) approach based on geographical proximity and a hybrid approach where sites with similar topographic orientations are grouped together. The three region types were implemented in a Bayesian Generalized Least Squares Regression (BGLSR) framework which leads to regionalized regression equations that can be used to predict rainfall L-moments at ungauged sites. A leave-one-out cross validation approach was used to compare the relative accuracy, reliability and uncertainty of the derived rainfall statistics and resulting estimates of the rainfall quantiles. The study used data from two areas of Australia chosen for their highly varied topography and different climatic influences. It was found that all three methods provided good estimates of the L-moment statistics and the rainfall quantiles. The hybrid approach produced the smallest errors in the South-East Queensland region whilst for the Tasmanian region the fixed region approach was best. The results from this study show that although there is a slight benefit in using the proposed hybrid approach for BGLSR, these benefits were minor compared to maximizing the number of stations used to calibrate the BGLSR equations. This conclusion regarding the number of stations could be tested in future work by repeating the analyses in areas with sparser station density. Another test could be to simulate reduced station coverage in the current study areas by leaving stations out of the analyses. Finally it would be interesting to see if similar results are obtained by expanding the study area so that different climatological regimes are assessed.

Spatio-temporal characteristics of the extreme precipitation by L-moment-based index-flood method in the Yangtze River Delta region, China

The regionalization methods, which “trade space for time” by pooling information from different locations in the frequency analysis, are efficient tools to enhance the reliability of extreme quantile estimates. This paper aims at improving the understanding of the regional frequency of extreme precipitation by using regionalization methods, and providing scientific background and practical assistance in formulating the regional development strategies for water resources management in one of the most developed and flood-prone regions in China, the Yangtze River Delta (YRD) region. To achieve the main goals, L-moment-based index-flood (LMIF) method, one of the most popular regionalization methods, is used in the regional frequency analysis of extreme precipitation with special attention paid to inter-site dependence and its influence on the accuracy of quantile estimates, which has not been considered by most of the studies using LMIF method. Extensive data screening of stationarity, serial dependence, and inter-site dependence was carried out first. The entire YRD region was then categorized into four homogeneous regions through cluster analysis and homogenous analysis. Based on goodness-of-fit statistic and L-moment ratio diagrams, generalized extreme-value (GEV) and generalized normal (GNO) distributions were identified as the best fitted distributions for most of the sub-regions, and estimated quantiles for each region were obtained. Monte Carlo simulation was used to evaluate the accuracy of the quantile estimates taking inter-site dependence into consideration. The results showed that the root-mean-square errors (RMSEs) were bigger and the 90 % error bounds were wider with inter-site dependence than those without inter-site dependence for both the regional growth curve and quantile curve. The spatial patterns of extreme precipitation with a return period of 100 years were finally obtained which indicated that there are two regions with highest precipitation extremes and a large region with low precipitation extremes. However, the regions with low precipitation extremes are the most developed and densely populated regions of the country, and floods will cause great loss of human life and property damage due to the high vulnerability. The study methods and procedure demonstrated in this paper will provide useful reference for frequency analysis of precipitation extremes in large regions, and the findings of the paper will be beneficial in flood control and management in the study area.

Performance of regional flood frequency analysis methods in KwaZulu-Natal, South Africa

Estimates of design floods are required for the design of hydraulic structures and to quantify the risk of failure of the structures. Many international studies have shown that design floods estimated using a regionalised method result in more reliable estimates of design floods than values computed from a single site or from other methods. A number of regional flood frequency analysis (RFFA) methods have been developed, which cover all or parts of South Africa. These include methods developed by Van Bladeren (1993), Mkhandi et al. (2000), Görgens (2007) and Haile (2011). The performance of these methods has been assessed at selected flow-gauging sites in the province of KwaZulu-Natal (KZN), South Africa. It is recommended that the limitations of available flow records to estimate extreme flow events need to be urgently addressed. From the results for KZN the JPV method, with a regionalised GEV distribution with the veld zone regionalisation, generally gave the best performance when compared to design floods estimated from the annual maximum series extracted from the observed data. It is recommended that the performance of the various RFFA methods needs to be assessed at a national scale and that a more detailed regionalisation be used in the development of an updated RFFA method for South Africa.Keywords: regional flood frequency analysis, KwaZulu-Natal

On identifying relationships between the flood scaling exponent and basin attributes.

Floods are known to exhibit self-similarity and follow scaling laws that form the basis of regional flood frequency analysis. However, the relationship between basin attributes and the scaling behavior of floods is still not fully understood. Identifying these relationships is essential for drawing connections between hydrological processes in a basin and the flood response of the basin. The existing studies mostly rely on simulation models to draw these connections. This paper proposes a new methodology that draws connections between basin attributes and the flood scaling exponents by using observed data. In the proposed methodology, region-of-influence approach is used to delineate homogeneous regions for each gaging station. Ordinary least squares regression is then applied to estimate flood scaling exponents for each homogeneous region, and finally stepwise regression is used to identify basin attributes that affect flood scaling exponents. The effectiveness of the proposed methodology is tested by applying it to data from river basins in the United States. The results suggest that flood scaling exponent is small for regions having (i) large abstractions from precipitation in the form of large soil moisture storages and high evapotranspiration losses, and (ii) large fractions of overland flow compared to base flow, i.e., regions having fast-responding basins. Analysis of simple scaling and multiscaling of floods showed evidence of simple scaling for regions in which the snowfall dominates the total precipitation.

Application of L-moments for regional frequency analysis of maximum monthly rainfall in West Bengal, India

Application of L-moments for regional frequency analysis of maximum monthly rainfall in West Bengal, India

Qualitative and quantitative uncertainties in regional rainfall frequency analysis

Uncertainty exists widely in hydrological analysis, and this makes the process of uncertainty assessment very important for making robust decisions. In this study, uncertainty sources in regional rainfall frequency analysis are identified for the first time. The numeral unite spread assessment pedigree (NUSAP) method is introduced and is first employed to quantify qualitative uncertainty in regional rainfall frequency analysis. A pedigree matrix is particularly designed for regional rainfall frequency analysis, by which the qualitative uncertainty can be quantified. Finally, the qualitative and quantitative uncertainties are combined in an uncertainty diagnostic diagram, which makes the uncertainty evaluation results more intuitive. From the integrated diagnostic diagram, it can be determined that the uncertainty caused by the precipitation data is the smallest, and the uncertainty from different grouping methods is the largest. For the downstream sub-region, a generalized extreme value (GEV) distribution is better than a generalized logistic (GLO) distribution; for the south sub-region, a Pearson type III (PE3) distribution is the better choice; and for the north sub-region, GEV is more appropriate. 通过引进 NUSAP 方法量化区域降雨频率分析不确定性来源中质量方面的不确定性, 并结合数量方面的不确定性, 分析这些不确定性对降雨频率分析的影响, 为水资源风险决策和水利工程设计等提供更好的指导。 总结区域降雨频率分析中的不确定性来源, 并在区域频率分析中引进 NUSAP 方法用以量化其质量不确定性, 针对区域频率分析提出 Pedigree 矩阵。 1. 选取区域频率分析中三个主要不确定性来源, 即降雨测量不确定性、 水文分区不确定性和分布线型的不确定性; 2. 提出针对区域频率分析的评价依据 Pedigree 矩阵, 量化区域频率分析中的质量不确定性; 3. 将质量和数量两类不确定性结合在不确定性诊断图中, 综合评估区域频率分析中的质量不确定和数量不确定性。 NUSAP 方法可以有效地量化区域降雨频率分析中的质量不确定性, 并通过不确定性诊断图将质量不确定和数量不确定性很好地结合起来, 为水资源风险决策和水利工程设计等提供了直观的方案。

A hierarchicalBayesian regional model for nonstationary precipitation extremes inNorthernCalifornia conditioned on tropical moisture exports

AbstractWarm, moist, and longitudinally confined tropical air masses are being linked to some of the most extreme precipitation and flooding events in the midlatitudes. The interannual frequency and intensity of such atmospheric rivers (ARs), or tropical moisture exports (TMEs), are connected to the risk of extreme precipitation events in areas where moisture convergence occurs. This study presents a nonstationary, regional frequency analysis of precipitation extremes in Northern California that is conditioned on the interannual variability of TMEs entering the region. Parameters of a multisite peaks‐over‐threshold model are allowed to vary conditional on the integrated moisture delivery from TMEs over the area. Parameters are also related to time‐invariant, local characteristics to facilitate regionalization to ungaged sites. The model is developed and calibrated in a hierarchical Bayesian framework to support partial pooling and enhance regionalization skill. The model is cross validated along with two alternative, increasingly parsimonious formulations to assess the additional skill provided by the covariates. Climate diagnostics are also used to better understand the instances where TMEs fail to explain variations in rainfall extremes to provide a path forward for further model improvement. The modeling structure is designed to link seasonal forecasting and long‐term projections of TMEs directly to regional models of extremes used for risk estimation. Results suggest that the inclusion of TME‐based information greatly improves the characterization of extremes, particularly for their frequency of occurrence. Diagnostics indicate that the model could be further improved by considering an index for frontal systems as an additional covariate.

Determining return water levels at ungauged coastal sites: a case study for northern Germany

We estimate return periods and levels of extreme still water levels for the highly vulnerable and historically and culturally important small marsh islands known as the Halligen, located in the Wadden Sea offshore of the coast of northern Germany. This is a challenging task as only few water level records are available for this region, and they are currently too short to apply traditional extreme value analysis methods. Therefore, we use the Regional Frequency Analysis (RFA) approach. This originates from hydrology but has been used before in several coastal studies and is also currently applied by the local federal administration responsible for coastal protection in the study area. The RFA enables us to indirectly estimate return levels by transferring hydrological information from gauged to related ungauged sites. Our analyses highlight that this methodology has some drawbacks and may over- or underestimate return levels compared to direct analyses using station data. To overcome these issues, we present an alternative approach, combining numerical and statistical models. First, we produced a numerical multidecadal model hindcast of water levels for the entire North Sea. Predicted water levels from the hindcast are bias corrected using the information from the available tide gauge records. Hence, the simulated water levels agree well with the measured water levels at gauged sites. The bias correction is then interpolated spatially to obtain correction functions for the simulated water levels at each coastal and island model grid point in the study area. Using a recommended procedure to conduct extreme value analyses from a companion study, return water levels suitable for coastal infrastructure design are estimated continuously along the entire coastline of the study area, including the offshore islands. A similar methodology can be applied in other regions of the world where tide gauge observations are sparse.

Potential impact of climate change on intensity duration frequency curves of central Alberta

Under the effect of climate change, warming likely means that there will be more water vapour in the atmosphere and extreme storms are expected to occur more frequently and with greater severity, resulting in municipal Intensity-Duration-Frequency (IDF) curves with higher intensities and shorter return periods. A regional climate model, MM5 (the Pennsylvania State University / National Center for Atmospheric Research numerical model), was set up in a one-way, three-domain nested framework to simulate future summer (May to August) precipitation of central Alberta. MM5 is forced with climate data of four Global Climate Models, CGCM3, ECHAM5, CCSM3, and MIROC3.2, for the baseline 1971–2000 and 2011–2100 based on the Special Report on Emissions Scenarios A2, A1B, and B1 of Intergovernmental Panel on Climate Change. Due to the bias of MM5’s simulations, a quantile-quantile bias correction method and a regional frequency analysis is applied to derive projected grid-based IDF curves for central Alberta. In addition, future trends of air temperature and precipitable water, which affect storm pattern and intensity, are investigated. Future IDF curves show a wide range of increased intensities especially for storms of short durations (≤1-h). Conversely, future IDF curves are expected to shift upward because of increased air temperature and precipitable water which are projected to be about 2.9 °C and 29 % in average by 2071–2100, respectively. Our results imply that the impact of climate change could increase the future risk of flooding in central Alberta.

Analytical approach to quantile estimation in regional frequency analysis based on fuzzy framework

Regional frequency analysis is widely used for estimating quantiles of hydrological extreme events at sparsely gauged/ungauged target sites in river basins. It involves identification of a region (group of watersheds) resembling watershed of the target site, and use of information pooled from the region to estimate quantile for the target site. In the analysis, watershed of the target site is assumed to completely resemble watersheds in the identified region in terms of mechanism underlying generation of extreme event. In reality, it is rare to find watersheds that completely resemble each other. Fuzzy clustering approach can account for partial resemblance of watersheds and yield region(s) for the target site. Formation of regions and quantile estimation requires discerning information from fuzzy-membership matrix obtained based on the approach. Practitioners often defuzzify the matrix to form disjoint clusters (regions) and use them as the basis for quantile estimation. The defuzzification approach (DFA) results in loss of information discerned on partial resemblance of watersheds. The lost information cannot be utilized in quantile estimation, owing to which the estimates could have significant error. To avert the loss of information, a threshold strategy (TS) was considered in some prior studies. In this study, it is analytically shown that the strategy results in under-prediction of quantiles. To address this, a mathematical approach is proposed in this study and its effectiveness in estimating flood quantiles relative to DFA and TS is demonstrated through Monte-Carlo simulation experiments and case study on Mid-Atlantic water resources region, USA.

Design flood estimation in ungauged catchments using genetic algorithm-based artificial neural network (GAANN) technique for Australia

This paper focuses on the development and testing of the genetic algorithm (GA)-based regional flood frequency analysis (RFFA) models for eastern parts of Australia. The GA-based techniques do not impose a fixed model structure on the data and can better deal with nonlinearity of the input and output relationship. These nonlinear techniques have been applied successfully in many hydrologic problems; however, there have been only limited applications of these techniques in RFFA problems, particularly in Australia. A data set comprising of 452 stations is used to test the GA for artificial neural networks (ANN) optimization known as GAANN. The results from GAANN were compared with the results from back-propagation for ANN optimization known as BPANN. An independent testing shows that both the GAANN and BPANN methods are quite successful in RFFA and can be used as alternative methods to check the validity of the traditional linear models such as quantile regression technique.

An intercomparison of regional and at-site rainfall extreme value analyses in southern British Columbia, Canada

Rainfall extreme value estimates in Canada have historically been based on fitting the Gumbel distribution to annual maxima at individual sites by the method of moments (MOM). Studies have, however, shown that regional frequency analyses (RFA) may perform better than at-site methods. Also, the Fréchet rather than Gumbel form of the generalized extreme value (GEV) distribution may better describe the distribution of annual extremes. In this study, at-site Gumbel MOM and GEV extreme value analyses based on L-moment, maximum likelihood (MLE), and generalized maximum likelihood (GML) estimators are compared against RFA with L-moment methods at stations in southern British Columbia, Canada via cross-validation and Monte Carlo simulations. While GEV shape parameter estimates are predominately negative, qualitatively showing weak evidence for the Fréchet form of the GEV distribution, field significant differences from the Gumbel distribution in the region are not found. Regional frequency analysis leads to substantial reductions in error relative to at-site methods, especially for the GEV distribution and small samples. While Gumbel estimators exhibit lower variance than GEV estimators, they are also more biased, underestimating 100 year return levels. Of the at-site GEV estimators, GML tended to perform better than the L-moment estimator, in some cases nearing performance of RFA. Maximum likelihood performed worst, especially for small samples sizes.

Regional frequency analysis of daily rainfall extremes using L-moments approach

Daily extreme precipitation values are among environmental events with the most disastrous consequences for human society. Information on the magnitudes and frequencies of extreme precipitations is essential for sustainable water resources management, planning for weather-related emergencies, and design of hydraulic structures. In the present study, regional frequency analysis of maximum daily rainfalls was investigated for Golestan province located in the northeastern Iran. This study aimed to find appropriate regional frequency distributions for maximum daily rainfalls and predict the return values of extreme rainfall events (design rainfall depths) for the future. L-moment regionalization procedures coupled with an index rainfall methodwere applied to maximum rainfall records of 47 stations across the study area. Due to complex geographicand hydro-climatological characteristics of the region, an important research issue focused on breaking downthe large area into homogeneous and coherent sub-regions. The study area was divided into five homogeneousregions, based on the cluster analysis of site characteristics and tests for the regional homogeneity.The goodness-of-fit results indicated that the best fitting distribution is different for individual homogeneousregions. The difference may be a result of the distinctive climatic and geographic conditions. The estimatedregional quantiles and their accuracy measures produced by Monte Carlo simulations demonstrate that theestimation uncertainty as measured by the RMSE values and 90% error bounds is relatively low when returnperiods are less than 100 years. But, for higher return periods, rainfall estimates should be treated withcaution. More station years, either from longer records or more stations in the regions, would be required forrainfall estimates above T=100 years. It was found from the analyses that, the index rainfall (at-site averagemaximum rainfall) can be estimated reasonably well as a function of mean annual precipitation in Golestanprovince. Index rainfalls combined with the regional growth curves, can be used to estimate design rainfallsat ungauged sites. Overall, it was found that cluster analysis together with the L-moments based regional frequencyanalysis technique could be applied successfully in deriving design rainfall estimates for northeasternIran. The approach utilized in this study and the findings are of great scientific and practical merit, particularlyfor the purpose of planning for weather-related emergencies and design of hydraulic engineering structures