Regional Frequency Analysis Research Articles

Uncertainty Quantification in Rainfall Intensity Duration Frequency Curves Based on Historical Extreme Precipitation Quantiles

Intensity Duration Frequency (IDF) curves form the basis for quantifying the magnitude of rainfall events those are used in the design of a variety of civil infrastructure, especially in an urban environment. It is important that the capacity of urban infrastructure (e.g. storm sewers, culverts, and storm water management ponds) be appropriately sized to avoid overdesigned or underdesigned, which could lead to economic losses, increased property damage and possible increased risk of loss of life. Thus, obtaining high quality estimates of IDF curves is important. Uncertainty in IDF curves is usually disregarded in the view of difficulties associated in assigning a value to it. Latin Hypercube Sampling (LHS) and regional frequency analysis based on L-moments approach were utilized in order to estimate the uncertainty in the IDF curves based on historical extreme precipitation quantiles from different stations in the Langat River Basin. Uncertainties of the rainfall intensity in IDF curves were estimated with the bootstrap sampling method, and were described by a GEV distribution. Shape parameter, scale parameter, and location parameter, were modeled as the functions of rainfall duration and rainfall intensity using 103 LHS set samples for all the durations and return periods considered for each rainfall station.

Regional Frequency Analysis of Extreme Dry Spells during Rainy Season in the Wei River Basin, China

Our research analyzes the regional changes of extreme dry spell, represented by the annual maximum dry spell length (noted as AMDSL) during the rainy season in the Wei River Basin (WRB) of China for 1960–2014 using the L-moments method. The mean AMDSL values increase from the west to the east of the WRB, suggesting a high dry risk in the east compared to the west in the WRB. To investigate the regional frequency more reasonably, the WRB is clustered into four homogenous subregions via theK-means method and some subjective adjustments. The goodness-of-fit test shows that the GEV, PE3, and GLO distribution can be accepted as the “best-fit” model for subregions 1 and 4, subregion 2, and subregion 3, respectively. The quantiles of AMDSL under various return levels figure out a similar spatial distribution with mean AMDSL. We also find that the dry risk in subregion 2 and subregion 4 might be higher than that in subregion 1. The relationship between ENSO events and extreme dry spell events in the rainy season with cross wavelet analysis method proves that ENSO events play a critical role in triggering extreme dry events during rainy season in the WRB.

Regional extreme value index estimation and a test of tail homogeneity

This paper deals with inference on extremes of heavy‐tailed distributions. We assume distribution functions F of Pareto‐type, where the right‐tail behavior of F is characterized by a strictly positive parameter γ, the so‐called extreme value index (EVI). In some applications, observations from closely related variables are available, with possibly identical EVI γ. If these variables are observed for the same time period, a procedure called BEAR estimator has recently been proposed. We modify this approach allowing for different observation periods and pairwise extreme value dependence of the variables. In addition, we present a new test for equality of the EVI. As an application, we discuss regional flood frequency analysis, where we want to combine rather short sequences of univariate observations with very different lengths measured at many gauges for joint inference. We illustrate our findings on peak discharges from 18 river gauges located at the Mulde basin in Germany, which is known for its severe summer floods, and identify relevant heterogeneous tail behavior, which is not detected by other popular methods. Copyright © 2015 John Wiley & Sons, Ltd.

On the prediction of extreme flood quantiles at ungauged locations with spatial copula

The present study investigates the use of the spatial copula approach for predicting flood quantiles at ungauged basins. Spatial copulas are the formalization of traditional geostatistics by copulas. In regional flood frequency analysis (RFFA), the regression of flood quantiles is often carried out at the logarithmic scale. Consequently, traditional interpolation methods introduce a bias and provide suboptimal predictions. In this study, the copula framework is examined for offering proper corrections in this framework. Moreover, copula techniques separate the regional distribution of flood quantiles from spatial dependence. This provides a full probabilistic model that represents a more flexible framework where proper combinations of regional distribution and dependence can be adapted to various situations that are encountered in RFFA. The adequacy of the investigated methodology is evaluated on a real world case study involving hydrometric stations from southern Quebec, Canada. Results show that the spatial copula framework is able to deal with the problem of bias, is robust to the presence of problematic stations and may improve the quality of quantile predictions while reducing the level of complexity of the models used in RFFA.

Multivariate drought frequency estimation using copula method in Southwest China

Drought over Southwest China occurs frequently and has an obvious seasonal characteristic. Proper management of regional droughts requires knowledge of the expected frequency or probability of specific climate information. This study utilized k-means classification and copulas to demonstrate the regional drought occurrence probability and return period based on trivariate drought properties, i.e., drought duration, severity, and peak. A drought event in this study was defined when 3-month Standardized Precipitation Evapotranspiration Index (SPEI) was less than −0.99 according to the regional climate characteristic. Then, the next step was to classify the region into six clusters by k-means method based on annual and seasonal precipitation and temperature and to establish marginal probabilistic distributions for each drought property in each sub-region. Several copula types were selected to test the best fit distribution, and Student t copula was recognized as the best one to integrate drought duration, severity, and peak. The results indicated that a proper classification was important for a regional drought frequency analysis, and copulas were useful tools in exploring the associations of the correlated drought variables and analyzing drought frequency. Student t copula was a robust and proper function for drought joint probability and return period analysis, which is important for analyzing and predicting the regional drought risks.

Mixture Distribution Fitting and Modeling for Regional Frequency Analysis of Maximum Wind Speed Over South Korea

본 연구에서는, L-moments와 Harmony Search 파라미터 추정법을 사용하여 지역빈도해석을 통한 한국 68개소의 설계풍속을 도출하는 연구를 실시하였다. 기존에 일반적으로 풍속 산정에 적용된 Generalized Logistic (GLOG), General Extreme Value (GEV), Generalized Pareto (GPAR), Weibull의 분포형에 적용하여 설계 풍속값을 산정하였을 뿐만 아니라 Gamma와 Gumbel의 분포를 조합시킨 혼합분포형을 이용하여서도 설계값을 산정하였다. 산정결과, 한국에서는 Weibull분포가 가장 적절한 분포모형임을 알 수 있었다. 기존에 적용되지 않았던 새로운 혼합형 분포형도 특정지역에서 충분히 사용가능한 분포형이 될 수 있음을 알 수 있었다. In this study, we tried to determine and investigate meteorologically homogeneous regions and to derive regional wind frequency estimates for 68 gauged sites in South Korea using an index wind method with L-moments and harmony search parameter estimation. Comparative regional wind frequency estimates were made for the tested region using various distributions, namely the Generalized Logistic (GLOG), General Extreme Value (GEV), Generalized Pareto (GPAR), Weibull. Furthermore, we applied three types of two-component mixture distributions, built by combination of Gumbel and Gamma distributions with five-parameters such as Gumbel-Gumbel (GumGum), Gamma-Gamma (GamGam), and Gamma-Gumbel (GamGum) distribution models. Their parameters are estimated by harmony search method (HS). The results of the current study showed that the Weibull distribution is identified as the bestfit distribution in Korea. In other words, Weibull as a suitable distribution with three parameters for other Korean stations.

Regional flood frequency analysis method for Tasmania, Australia: a case study on the comparison of fixed region and region-of-influence approaches

A new regional flood frequency analysis method for Tasmania is developed using data from 53 gauged catchments. The Bayesian generalized least squares regression (BGLSR) approach is used to developing prediction equations for selected flood quantiles using a quantile regression technique (QRT) and the first three moments of the log Pearson Type 3 distribution by means of a parameter regression technique (PRT). Regions are formed in three ways: (a) a fixed-region approach is examined in which all the sites in Tasmania are assumed to form one region; (b) a region of influence (ROI) approach is investigated in which a region is formed around each of the sites based on the criterion of minimum model error variance; and (c) the state of Tasmania is divided into two fixed regions (east Tasmania and west Tasmania) based on their distinct rainfall regimes. Independent testing showed that the BGLSR-ROI approach can deal quite well with the uncertainty in the regional estimation, as shown by the various regression diagnostics. Furthermore, the PRT-ROI approach was found to provide quantile estimates that are generally more accurate and consistent than the QRT. Generally, the ROI approach outperformed the fixed-region approach for Tasmania.

Application of Artificial Neural Networks and regression analysis to L-moments based regional frequency analysis in the Eastern Black Sea Basin, Turkey

This study presents the use of L-moments based regression analysis and Artificial Neural Networks (ANN) for forecasting maximum annual flows of Eastern Black Sea Basin, Turkey. Homogeneity of the region is determined by discordancy (Di) and heterogeneity (Hi) measures based on L-moments. Several distributions are fitted to the data of the 33 stream gauging stations. Return periods (T) corresponding to each flow rates are calculated using the probability density functions of best fit distribution of the region. Using these T values and also drainage area, main stream slope, elevation, stream density, and mean annual rainfall values as independent variables, regression and ANN models are adopted to the data. Mean relative error, mean absolute error and root mean square error are applied for evaluating the performance of the models. Error values indicate that ANN method yields better results for estimation of maximum flows.

High-resolution analysis of 1 day extreme precipitation in Sicily

Abstract. Sicily, a major Mediterranean island, has experienced several exceptional precipitation episodes and floods during the last century, with serious damage to human life and the environment. Long-term, rational planning of urban development is indispensable to protect the population and to avoid huge economic losses in the future. This requires a thorough knowledge of the distributional features of extreme precipitation over the complex territory of Sicily. In this study, we perform a detailed investigation of observed 1 day precipitation extremes and their frequency distribution, based on a dense data set of high-quality, homogenized station records in 1921–2005. We estimate very high quantiles (return levels) corresponding to 10-, 50- and 100-year return periods, as predicted by a generalized extreme value distribution. Return level estimates are produced on a regular high-resolution grid (30 arcsec) using a variant of regional frequency analysis combined with regression techniques. Results clearly reflect the complexity of this region, and show the high vulnerability of its eastern and northeastern parts as those prone to the most intense and potentially damaging events.

Reply to discussion of “Extreme streamflow drought in the Karkheh river basin (Iran): probabilistic and regional analyses”

In our original paper (Nat Hazards 76:327–346, 2015. doi:10.1007/s11069-014-1492-x), we analyzed hydrological droughts based on the minimum values of the streamflow drought index at different time scales using L-moments. In this paper, we highlight the importance of the magnitude and type of selected drought index for regional frequency analysis and discuss the validity of results only for station clusters considered in response to the commentary by Bahmani and Khorsandi (Nat Hazards, 2015. doi:10.1007/s11069-015-1830-7).

Flood analysis and flood projections under climate change in New Brunswick

Floods events are a key component in river engineering including the design and risk assessment of various projects. In this study, a flood frequency analysis was carried out to determine flood characteristics in New Brunswick under present and future climate. For current flood characteristics, an analysis was carried out using 56 hydrometric stations across the province using the Generalized Extreme Value (GEV) distribution and the three-parameter lognormal distribution function. A regional flood frequency analysis was also carried out using regression equations. Results showed that current regional flood equations were very consistent among distribution functions. Results were also consistent with previous studies. To study floods under climate change, seven catchments were selected within the province and these catchments were further analyzed using artificial neural network (ANN) models for two climate scenarios. As such, future climate data were extracted from the third-generation Coupled Climate Model (CGCM3.1) under the greenhouse gas emission scenarios B1 and A2. The climate variables (temperature and precipitation) were downscaled using the delta change approach, and future river discharges were predicted. A frequency analysis was then carried out on these seven stations using the GEV distribution function. Results showed that for the period 2010–2100, average temperatures are projected to increase between 2.9°C (B1) and 5.2°C (A2) in New Brunswick. As for precipitation, the mean annual precipitation showed an increase of 9 to 12% compared to current conditions. Results also showed an increase in flood flows. The increase in low-return floods (e.g. 2-year) was generally higher than the increase of higher return floods (e.g. 100-year). Depending on the scenario and the future time period, the increase in low-return floods was about 30%, and about 15% for higher return floods. A Regional Climate Index (RCI) was used to links floods to their frequency under future climate scenarios.

Regional frequency analysis at ungauged sites using a two-stage resampling generalized ensemble framework

Regional frequency analysis (RFA) deals with the estimation of hydrological characteristics at sites where little or no data is available. Recently, machine learning applications to RFA have received considerable attention in terms of their flexibility in modeling as well as superior generalization ability compared to conventional approaches. The proper application of machine learning techniques, however, requires good understanding of the available information about system's dynamics, i.e. system variables. This paper presents two contributions to the literature. First, novel ensemble architecture, using a unique two-stage resampling approach, is proposed. The objective of the proposed ensemble model is to promote diversity within the individual learners and reduce over fitting. Second, the application of the proposed model is demonstrated in RFA case study to obtain improved regional flood quantile estimates at ungauged sites. A jackknife validation procedure is used for the evaluation of the model's performance. The method is applied to data from the province of Quebec, Canada. The model showed similar performance and generalization compared to major ensemble models in the literature, which were investigated in previous studies using the same data set. The proposed model confirmed the diversity requirement in ensemble modeling and, in the same time, validated the proposed model adherence to ensemble learning theory.

A recursive multi-scaling approach to regional flood frequency analysis

Summary Scaling approaches are widely used by hydrologists for Regional Frequency Analysis (RFA) of floods at ungauged/sparsely gauged site(s) in river basins. This paper proposes a Recursive Multi-scaling (RMS) approach to RFA that overcomes limitations of conventional simple- and multi-scaling approaches. The approach involves identification of a separate set of attributes corresponding to each of the sites (being considered in the study area/region) in a recursive manner according to their importance, and utilizing those attributes to construct effective regional regression relationships to estimate statistical raw moments (SMs) of peak flows. The SMs are then utilized to arrive at parameters of flood frequency distribution and quantile estimate(s) corresponding to target return period(s). Effectiveness of the RMS approach in arriving at flood quantile estimates for ungauged sites is demonstrated through leave-one-out cross-validation experiment on watersheds in Indiana State, USA. Results indicate that the approach outperforms index-flood based Region-of-Influence approach, simple- and multi-scaling approaches and a multiple linear regression method.

Process-based design flood estimation in ungauged basins by conditioning model parameters on regional hydrological signatures

The use of rainfall–runoff models constitutes an alternative to statistical approaches (such as at-site or regional flood frequency analysis) for design flood estimation and represents an answer to the increasing need for synthetic design hydrographs associated with a specific return period. Nevertheless, the lack of streamflow observations and the consequent high uncertainty associated with parameters estimation usually pose serious limitations to the use of process-based approaches in ungauged catchments, which in contrast represent the majority in practical applications. This work presents a Bayesian procedure that, for a predefined rainfall–runoff model, allows for the assessment of posterior parameters distribution, using limited and uncertain information available about the response of ungauged catchments, i.e. the regionalized first three L-moments of annual streamflow maxima. The methodology is tested for a catchment located in southern Italy and used within a Monte Carlo scheme to obtain design flood values and simulation uncertainty bands through both event-based and continuous simulation approaches. The obtained results highlight the relevant reduction in uncertainty bands associated with simulated peak discharges compared to those obtained considering a prior uniform distribution for model parameters. A direct impact of uncertainty in regional estimates of hydrological signatures on posterior parameters distribution is also evident. For the selected case study, continuous simulation, generally, better matches the estimates of the statistical flood frequency analysis.

A Nonlinear Approach to Regional Flood Frequency Analysis Using Projection Pursuit Regression

AbstractThis paper presents an approach for regional flood frequency analysis (RFFA) in the presence of nonlinearity and problematic stations, which require adapted methodologies. To this end, the projection pursuit regression (PPR) is proposed. The PPR is a family of regression models that applies smooth functions on intermediate predictors to fit complex patterns. The PPR approach can be seen as a hybrid method between the generalized additive model (GAM) and the artificial neural network (ANN), which combines the advantages of both methods. Indeed, the PPR approach has the structure of a GAM to describe nonlinear relations between hydrological variables and other basin characteristics. On the other hand, PPR can consider interactions between basin characteristics to improve the predictive capabilities in a similar way to ANN, but simpler. The methodology developed in the present study is applied to a case study represented by hydrometric stations from southern Québec, Canada. It is shown that flood quantiles are mostly associated with a dominant intermediate predictor, which provides a parsimonious representation of the nonlinearity in the flood-generating processes. The model performance is compared to eight other methods available in the literature for the same dataset, including GAM and ANN. When using the same basin characteristics, the results indicate that the simpler structure of PPR does not affect the global performance and that PPR is competitive with the best existing methods in RFFA. Particular attention is also given to the performance resulting from the choice of the basin characteristics and the presence of problematic stations.

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.

Delimiting homogeneous regions using the multifractal properties of validated rainfall data series

Summary In this work, a regional frequency analysis of extreme annual rainfall data in Malaga (Southern Spain) has been performed. Rainfall records have been validated, applying various quality control tests as a pre-requisite before their use, ensuring their reliability and discarding anomalous data. For grouping the stations into potential homogeneous regions, the multifractal properties of daily rainfall data series recorded at 72 locations have been studied. The scaling of the rainfall moments has been analyzed and the empirical moments scaling exponent functions have been obtained. The corresponding multifractal values have been used to group stations into regions, resulting some of them homogeneous.

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...

Flood outlier detection using PCA and effect of how to deal with them in regional flood frequency analysis via L-moment method

Regional flood frequency analysis (RFFA) is the major instrument for studying of the flood regime at locations where little or no information is available. Outliers have an important effect on the flood frequency analysis and the existence of them in hydrologic data sets affects the regional flood frequency analysis. Outlier analysis is composed of two steps, outlier detection and outlier treatment. After detecting outlier, one should determine how to deal with it. This has the particular role in outlier analysis. In this research, flood frequency analysis was done for the Dez River basin located in south-western Iran. First of all, the studied basin was separated in two hydrological homogeneous regions according their physiographical, climatic and vegetation characteristics. Then, outliers were detected in each region by using Principal component analysis method (PCA). We considered two approaches to survey and compare the effect of the outliers in RFFA. In the first approach outliers were retained, while in the second approach frequency analysis was done after removal the years which contain outliers. Result of RFFA via L-moment method showed that the estimated quantiles in two approaches, particularly in highly return period have a lot of difference. These results illustrate that dealing with the outliers in flood frequency analysis is of the special importance.

The relationship between Monte Carlo estimators of heterogeneity and error for daily to monthly time steps in a small Minnesota precipitation gauge network

AbstractPrecipitation quantile estimates are used in engineering, agriculture, and a variety of other disciplines. Index flood regional frequency methods pool normalized gauge data in the case of homogeneity among the constituent gauges of the region. Unitless regional quantile estimates are outputted and rescaled at each gauge. Because violation of the homogeneity hypothesis is a major component of quantile estimation error in regional frequency analysis, heterogeneity estimators should be “reasonable proxies” of the error of quantile estimation. In this study, three Monte Carlo heterogeneity statistics tested in Hosking and Wallis (1997) are plotted against Monte Carlo estimates of quantile error for all five‐or‐more‐gauge regionalizations in a 12 gauge network in the Twin Cities region of Minnesota. Upper‐tail quantiles with nonexceedance probabilities of 0.75 and above are examined at time steps ranging from daily to monthly. A linear relationship between heterogeneity and error estimates is found and quantified using Pearson's r score. Two of Hosking and Wallis's (1997) heterogeneity measures, incorporating the coefficient of variation in one case and additionally the skewness in the other, are found to be reasonable proxies for quantile error at the L‐moment ratio values characterizing these data. This result, in addition to confirming the utility of a commonly used coefficient of variation‐based heterogeneity statistic, provides evidence for the utility of a heterogeneity measure that incorporates skewness information.