Regional Frequency Analysis Research Articles

Regional frequency analysis of extreme rainfall in Sicily (Italy)

ABSTRACTExtreme rainfall events have large impacts on society and are likely to increase in intensity under climate change. For design and management decisions, particularly regarding hydraulic works, accurate estimates of precipitation magnitudes are needed at different durations. In this article, an objective approach of the regional frequency analysis (RFA) has been applied to precipitation data for the island of Sicily, Italy. Annual maximum series for rainfall with durations of 1, 3, 6, 12, and 24 h from about 130 rain gauges were used. The RFA has been implemented using principal component analysis (PCA) followed by a clustering analysis, through the k‐means algorithm, to identify statistically homogeneous groups of stations for the derivation of regional growth curves. Three regional probability distributions were identified as appropriate from an initial wider selection of distributions and were compared – the three‐parameter log‐normal distribution (LN3), the generalized extreme value (GEV) distribution, and the two component extreme value (TCEV) distribution. The regional parameters of these distributions were estimated using L‐moments and considering a hierarchical approach. Finally, assessment of the accuracy of the growth curves was achieved by means of the relative bias and relative root‐mean‐square error (RMSE) using a simulation analysis of regional L‐moments. Results highlight that for the lower return periods, all distributions showed the same accuracy while for higher return periods the LN3 distribution provided the best result. The study provides an updated resource for the estimation of extreme precipitation quantiles for Sicily through the derivation of growth curves needed to obtain depth–duration–frequency (DDF) curves.

Self-organizing map network-based precipitation regionalization for the Tibetan Plateau and regional precipitation variability

A precipitation-based regionalization for the Tibetan Plateau (TP) was investigated for regional precipitation trend analysis and frequency analysis using data from 1113 grid points covering the period 1900–2014. The results utilizing self-organizing map (SOM) network suggest that four clusters of precipitation coherent zones can be identified, including the southwestern edge, the southern edge, the southeastern region, and the north central region. Regionalization results of the SOM network satisfactorily represent the influences of the atmospheric circulation systems such as the East Asian summer monsoon, the south Asian summer monsoon, and the mid-latitude westerlies. Regionalization results also well display the direct impacts of physical geographical features of the TP such as orography, topography, and land-sea distribution. Regional-scale annual precipitation trend as well as regional differences of annual and seasonal total precipitation were investigated by precipitation index such as precipitation concentration index (PCI) and Standardized Anomaly Index (SAI). Results demonstrate significant negative long-term linear trends in southeastern TP and the north central part of the TP, indicating arid and semi-arid regions in the TP are getting drier. The empirical mode decomposition (EMD) method shows an evolution of the main cycle with 4 and 12 months for all the representative grids of four sub-regions. The cross-wavelet analysis suggests that predominant and effective period of Indian Ocean Dipole (IOD) on monthly precipitation is around ∼12 months, except for the representative grid of the northwestern region.

Regionalization of rainfall characteristics in India incorporating climatic variables and using self-organizing maps

Regionalization of rainfall or delineation of a region into areas having similar rainfall characteristics is useful for many hydrologic applications and water resources management. In this study, we aim to regionalize India into regions having similar rainfall and climatic characteristics using self-organizing maps (SOM), an artificial neural network algorithm derived clustering technique. The SOM algorithm is applied to observed gauge-based gridded Indian Meteorological Department (IMD) rainfall data (0.25° × 0.25°) for 34 years duration (1980–2013). Information about climatic variables like air temperature, specific humidity, geo-potential height, surface pressure, etc., which directly influence the rainfall characteristics is derived from the Modern Era-Retrospective Analysis for Research and Applications reanalysis data-set. Four cluster validity indices are used to identify the optimal number of clusters. While, 10 homogeneous regions are identified over India when accounting rainfall characteristics only, incorporation of climatic variables added more heterogeneity dividing India into 15 homogeneous rainfall regions. These 15 homogeneous rainfall zones effectively capture the spatial variability of rainfall and its spell-characteristics over India. Moreover, none of the 15 delineated regions are found to be heterogeneous when subjected to regional homogeneity test. The present study will aid in regional frequency analysis, forecasting and downscaling of rainfall, land-use management and agriculture planning.

A novel fuzzy clustering approach to regionalise watersheds with an automatic determination of optimal number of clusters

Abstract One of the most important problems faced in hydrology is the estimation of flood magnitudes and frequencies in ungauged basins. Hydrological regionalisation is used to transfer information from gauged watersheds to ungauged watersheds. However, to obtain reliable results, the watersheds involved must have a similar hydrological behaviour. In this study, two different clustering approaches are used and compared to identify the hydrologically homogeneous regions. Fuzzy C-Means algorithm (FCM), which is widely used for regionalisation studies, needs the calculation of cluster validity indices in order to determine the optimal number of clusters. Fuzzy Minimals algorithm (FM), which presents an advantage compared with others fuzzy clustering algorithms, does not need to know a priori the number of clusters, so cluster validity indices are not used. Regional homogeneity test based on L-moments approach is used to check homogeneity of regions identified by both cluster analysis approaches. The validation of the FM algorithm in deriving homogeneous regions for flood frequency analysis is illustrated through its application to data from the watersheds in Alto Genil (South Spain). According to the results, FM algorithm is recommended for identifying the hydrologically homogeneous regions for regional frequency analysis.

A model-based site selection approach associated with regional frequency analysis for modeling extreme rainfall depths in Minas Gerais state, Southeast Brazil

Extreme rainfall data are usually scarce due to the low frequency of these events. However, prior knowledge of the precipitation depth and return period of a design event is crucial to water resource management and engineering. This study presents a model-based selection approach associated with regional frequency analysis to examine the lack of maximum daily rainfall data in Brazil. A generalized extreme values (GEV) distribution was hierarchically fitted using a Bayesian approach and data that were collected from rainfall gauge stations. The GEV model parameters were submitted to a model-based cluster analysis, resulting in regions of homogeneous rainfall regimes. Time-series data of the individual rainfall gauges belonging to each identified region were joined into a new dataset, which was divided into calibration and validation sets to estimate new GEV parameters and to evaluate model performance, respectively. The results identified two distinct rainfall regimes in the region: more and less intense rainfall extremes in the southeast and northwest regions, respectively. According to the goodness of fit measures that were used to evaluate the models, the aggregation level of the parameters in clustering influenced their performance.

Regional frequency analysis of extreme rainfall in Belgium based on radar estimates

Abstract. In Belgium, only rain gauge time series have been used so far to study extreme rainfall at a given location. In this paper, the potential of a 12-year quantitative precipitation estimation (QPE) from a single weather radar is evaluated. For the period 2005–2016, 1 and 24 h rainfall extremes from automatic rain gauges and collocated radar estimates are compared. The peak intensities are fitted to the exponential distribution using regression in Q-Q plots with a threshold rank which minimises the mean squared error. A basic radar product used as reference exhibits unrealistic high extremes and is not suitable for extreme value analysis. For 24 h rainfall extremes, which occur partly in winter, the radar-based QPE needs a bias correction. A few missing events are caused by the wind drift associated with convective cells and strong radar signal attenuation. Differences between radar and gauge rainfall values are caused by spatial and temporal sampling, gauge underestimations and radar errors. Nonetheless the fit to the QPE data is within the confidence interval of the gauge fit, which remains large due to the short study period. A regional frequency analysis for 1 h duration is performed at the locations of four gauges with 1965–2008 records using the spatially independent QPE data in a circle of 20 km. The confidence interval of the radar fit, which is small due to the sample size, contains the gauge fit for the two closest stations from the radar. In Brussels, the radar extremes are significantly higher than the gauge rainfall extremes, but similar to those observed by an automatic gauge during the same period. The extreme statistics exhibit slight variations related to topography. The radar-based extreme value analysis can be extended to other durations.

Homogeneity testing for skewed and cross-correlated data in regional flood frequency analysis

In regional flood frequency analysis the homogeneity of a group of stations is an essential assumption. A standard procedure in hydrology to evaluate this condition is the homogeneity measure of Hosking and Wallis, which applies L-moments. Disadvantages of it are the lack of power when analysing highly skewed data and the implicit assumption of spatial independence. To face these issues we generalize this procedure in two ways. Copulas are applied to model intersite dependence and trimmed L-moments as a more robust alternative to ordinary L-moments. The results of simulation studies are presented to discuss the influence of different copula models and different trimming parameters. The usage of asymmetrically trimmed L-moments improves the heterogeneity detection in skewed data. Simple copula models are sufficient to incorporate the dependence structure of the data in the procedure. Additionally, a more robust behaviour against extreme events at single stations is achieved with the use of trimmed L-moments. Strong intersite dependence and skewed data reveal the need of a modified procedure in a case study with data from Saxony, Germany.

Rainfall frequency analysis for ungauged sites using satellite precipitation products

The occurrence of extreme rainfall events and their impacts on hydrologic systems and society are critical considerations in the design and management of a large number of water resources projects. As precipitation records are often limited or unavailable at many sites, it is essential to develop better methods for regional estimation of extreme rainfall at these partially-gauged or ungauged sites. In this study, an innovative method for regional rainfall frequency analysis for ungauged sites is presented. The new method (hereafter, this is called the RRFA-S) is based on corrected annual maximum series obtained from a satellite precipitation product (e.g., PERSIANN-CDR). The probability matching method (PMM) is used here for bias correction to match the CDF of satellite-based precipitation data with the gauged data. The RRFA-S method was assessed through a comparative study with the traditional index flood method using the available annual maximum series of daily rainfall in two different regions in USA (11 sites in Colorado and 18 sites in California). The leave-one-out cross-validation technique was used to represent the ungauged site condition. Results of this numerical application have found that the quantile estimates obtained from the new approach are more accurate and more robust than those given by the traditional index flood method.

A regional extreme value analysis of ocean waves in a changing climate

This paper applies regional frequency analysis on extreme significant wave heights in the North Atlantic ocean for historical and projected ocean wave climates. Regional frequency analysis is applied in order to perform spatial extreme value analysis over a large ocean area. One of the main advantages of regional frequency analysis is that one borrows strength for nearby locations by site pooling in order to get more accurate and robust estimates of extreme significant wave heights. Moreover, a set of homogeneous regions are identified as ocean regions with similar characteristics. In this way, the effect of climate change on the ocean wave climate can be studied, both with regards to changes in extreme quantiles at certain location and to overall spatial changes. The results from the regional frequency analysis are presented in this paper. The results are generally found to be reasonable, suggesting that regional frequency analysis can be useful in the analysis of extreme ocean waves. In particular, regional frequency analysis yields narrower uncertainty bounds and hence more robust estimation of extreme quantiles, corresponding to long return periods.

The risks assessment via a regional approach using multivariate regional frequency clustering method

Conventional univariate drought frequency analysis should be replaced by the multivariate framework due to the correlated characteristics, such as duration, peak intensity, and severity. Compared to the bivariate case, trivariate analysis would be more considerable. Furthermore, the absence of historical records has a great impact on the reliability of statistical estimates. Multivariate regional frequency analysis approach would be a better choice for providing reliable information for risks assessment and management purpose. Standardized precipitation evapotranspiration index was used in this study to define and detect drought because of the global warming effect. A method based on the cubic spline interpolation was applied to derive drought samples. Applying the multivariate discordancy and homogeneity test, the Pearl River basin was divided into five homogeneous subregions. Regional distributions including marginal distribution and copula function were chosen based on the goodness-of-fit test. Finally, return periods were computed from a regional perspective to assess the different drought risks. The results indicate that high drought risks might exist in the Pearl River basin and the spatial distinction must be taken seriously. Due to the contradiction of water supply and requirement among different districts or provinces, policies needed to be made seriously and urgently to solve the unbalance between water resource and socioeconomic development.

Flood Frequency Analysis at Ungauged Sites Based on Regionally Estimated Streamflows

Abstract Estimation of flood events at ungauged sites is often performed through regional flood frequency analysis (RFFA). RFFA uses the available information at gauged sites to estimate the desired design events at the ungauged site. These regional methods are based on a prior aggregation of the hydrological information at the gauged sites, which implies loss of information. In the present study, a different approach or path for conducting RFFA is presented. First, the daily streamflow series at the ungauged site is regionally estimated from daily information at the gauged sites through a regional flow duration curve approach. Then, a local flood frequency analysis is performed on the extracted maximum peak flow series. The proposed approach, referred to as regional streamflow-based frequency analysis (RSBFA), is applied to a case study in the province of Quebec, Canada. Results indicate that the performance of the RSBFA approach is comparable to traditional methods. However, the proposed method has the advantages of being simple, flexible, and of providing the whole daily streamflow series at the ungauged site, which allows the direct estimation of a large number of other flow characteristics, such as low-flow features. The RSBFA approach also avoids performing a complete at-site flood frequency analysis at each gauged site. The fact that all the regional information is included in the regionally estimated daily streamflow series implies a number of benefits: annual or seasonal, absolute or specific, stationary or nonstationary, and univariate or multivariate flood quantiles corresponding to any return period may then be obtained through the estimated series without reconducting a regional analysis.

Application of distribution-free nonstationary regional frequency analysis based on L-moments

Regional frequency analysis (RFA) based on L-moments is widely used in the analysis of hydrological process. However, L-moments are defined by order statistics from a stationary distribution and thus theoretically good properties of RFA do not hold under a nonstationary distribution. In this study, a procedure was proposed for an RFA based on L-moments for nonstationary hydrological processes. The proposed method uses a distribution-free de-trended method to apply the conventional RFA based on L-moments. The conventional and the proposed RFAs for annual maximum precipitation in South Korea were compared, and the simulation results indicated that the proposed RFA could provide proper information regarding heterogeneity in a nonstationary distribution. The estimated results of return levels, the median in the nonstationary RFA, were higher than in the conventional RFA.

L‐moment homogeneity test in trivariate regional frequency analysis of extreme precipitation events

ABSTRACTIdentification of homogeneous regions is a key task in regional frequency analysis to obtain accurate estimates of a given event. Homogeneity testing based on multivariate L‐moments has recently been proposed and all studies dealing with application of the methodology using real‐world data still focus on the bivariate case. The practical aspects of the trivariate homogeneity tests for maximum annual 1, 3 and 7 day precipitation totals measured at stations in the Czech Republic are investigated. A trivariate model of the precipitation amounts for simulating synthetic homogeneous regions in parametric testing was determined by goodness‐of‐fit tests based on the Cramér–von Mises and Vuong statistics and Akaike and Bayesian information criteria while considering selected trivariate exchangeable Archimedean, fully nested Archimedean and mixed C‐vine copulas in the copula model test space. Each of the regions into which the area of the Czech Republic is divided meets the homogeneity condition when using both the parametric and non‐parametric L‐moment homogeneity tests and considering three mixed C‐vine copula models given by the bivariate Gumbel copula for two unconditional pair‐copulas and normal, Frank or Plackett copula families for the conditional pair‐copula for simulating synthetic homogeneous regions.

The estimation of flood quantiles in ungauged sites using teaching-learning based optimization and artificial bee colony algorithms

In this study, a regional flood frequency analysis (RFFA) was applied to 33 stream gauging stations in the Eastern Black Sea Basin, Turkey. Homogeneity of the region was determined by discordancy (Di) and heterogeneity measures (Hi) based on L-moments. Generalized extreme-value, lognormal, Pearson type III, and generalized logistic distributions were fitted to the flood data of the homogeneous region. Based on the appreciate distribution for the region, flood quantiles were estimated for return periods of T=5, 10, 25, 50, 100, and 500 years. A non linear regression model was then developed to determine the relationship between flood discharges and meteorological and hydrological characteristics of the catchment. In order to compare with regression analysis, artificial bee colony algorithm (ABC) and teaching-learning based optimization (TLBO) models were developed. The equations were obtained by using the ABC and TLBO algorithms for the estimation of flood discharges for different return periods. The analysis showed that the TLBO and ABC results were superior to the regression analysis. Error values indicated that TLBO method yielded better results for estimation of flood quantiles for different independent variables.

Homogeneity testing for spatially correlated data in multivariate regional frequency analysis

AbstractIdentification of homogeneous regions is a key task in regional frequency analysis (RFA) to obtain adequate quantile estimates for an event of interest. Recently, the frequently used univariate Hosking‐Wallis L‐moment homogeneity test was extended to the multivariate case. Multivariate L‐moments are used as a tool to define the test statistic and copula models to describe the statistical behavior of the analyzed dependent variables. To avoid drawbacks in fitting a parametric joint distribution to the data and a rejection threshold which is based on simulations, its nonparametric alternatives were also proposed. Although the simulation studies performed demonstrated the usefulness of both the parametric and nonparametric tests, the powers obtained were valid only for regions without intersite dependence. Examples from practice nevertheless demonstrate that intersite correlation may be expected for some kinds of data. To overcome the problem of cross correlation between stations, the parametric testing procedure is generalized using D‐vine copulas to model intersite dependence when generating synthetic homogeneous regions during the testing procedure. Monte Carlo simulations were performed and illustrate how intersite dependence negatively impacts the multivariate L‐moment homogeneity tests by significantly reducing their powers. The results of simulations also demonstrate the superiority of the proposed modification over both the original parametric and nonparametric procedures inasmuch as it improves the heterogeneity detection and avoids miscategorization of a region. The modified test is also applied in a case study for meteorological data in the Czech Republic.

Spatial mapping of drought in Zambia using regional frequency analysis

ABSTRACTRegional frequency analysis based on L-moments was applied to assess the spatial extent of meteorological droughts in tandem with their return periods in Zambia. Weather station monthly rainfall data were screened to form homogeneous sub-regions-, validated by a homogeneity criterion and fitted by a generalized extreme value distribution using goodness-of-fit test statistics. Predictor equations at regional scale for L-moment ratios and mean annual precipitation were developed to generate spatial maps of meteorological drought recurrences. The 80% of normal rainfall level and two thresholds of 60% and 70% were synonymous with moderate and severe droughts, respectively. Droughts were more severe in the south than in the north of Zambia. The return periods for severe and moderate droughts showed an overlapping pattern in their occurrence at many locations, indicating that in certain years droughts can affect the entire country. The extreme south of Zambia is the most prone to drought.

Multivariate regional frequency analysis: Two new methods to increase the accuracy of measures

The accurate detection of discordant sites in a heterogeneous region and the estimation of the regional parameters of a statistical distribution are two important issues in multivariate regional frequency analysis. In this study, two new methods are proposed for increasing the accuracy of the multivariate l-moment approach. The first one, the optimization-based method (OBM) is utilized to estimate the best distribution parameters. The second one is the rank-based method (RBM), which is used in the robust discordancy measure for identifying discordant sites. In order to assess the performance of the proposed approaches on the heterogeneity measure, real and simulated regions of drought characteristics are considered. The results confirm the usefulness of the new methods in comparison with some well-established techniques.

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.

Regional frequency analysis for consecutive hour rainfall using L-moments approach in Jeju Island, Korea

BackgroundExtreme rainfall events are enormously frequent and abrupt in tropical areas like the Jeju Island of South Korea, impacting the hydrological functions as well as the social and economic situation. Rainfall magnitude and frequency distribution related information are essential for water system design, water resources management and hydro-meteorological emergencies. This study therefore has investigated the use of L-moments approach for hourly regional rainfall frequency estimation so as to ensure better accuracy and efficiency of the estimation process from the usually limited data sets.ResultsThe Hancheon catchment was considered as the primary study domain and several best fitted statistical tools were used to analyze consecutive hour rainfall data from five hydro-meteorological stations (Jeju, Ara, Eorimok, Witsaeorum and Jindallaebat) adjacent to the area. The cluster analysis and discordancy measure categorized the Hancheon catchment in three regions (1, 2 and 3). Based on the L-moments heterogeneity and goodness-of-fit measure, Gumbel and generalized extreme value (GEV) distribution were identified as robust distributions for the study area. The RMSE ratios for the catchment were found as 0.014 to 0.237 for Gumbel and 0.115 to 0.301 for GEV distribution. The linear regression analysis of the different rainfall quantiles inferred r-square values from 0.842 to 0.974.ConclusionsThe L-moments and other statistical information derived from the study can be useful for important hydrological design considerations in connection with flood risk management, mitigation and safety; whereas the methodological framework of the study may be suitable for other small scaled catchment areas with high slope.

On the use of a four-parameter kappa distribution in regional frequency analysis

ABSTRACTNew developments are presented enabling the using a four-parameter kappa distribution with the widely used regional goodness-of-fit methods as part of an index flood regional frequency analysis based on the method of L-moments. The framework was successfully applied to 564 pooling groups and was found to significantly improve the probabilistic description of British flood flow compared to existing procedures. Based on results from an extensive data analysis it is argued that the successful application of the kappa distribution renders the use of the traditional three-parameter distributions such as the generalized extreme value (GEV) and generalized logistic (GLO) distributions obsolete, except for large and relatively dry catchments. The importance of these findings is discussed in terms of the sensitivity of design floods to distribution choice.