INTERNATIONAL HYDROLOGICAL DECADE / WORKING GROUP ON “THE INFLUENCE OF MAN ON THE HYDROLOGICAL CYCLE”

Abstract

Floods, as extreme hydrological phenomena, can be described by more than one correlated characteristic, such as peak, volume and duration. These characteristics should be jointly considered since they are generally not independent. For an ungauged site, univariate regional flood frequency analysis (FA) provides a limited assessment of flood events. A recent study proposed a procedure for regional FA in a multivariate framework. This procedure represents a multivariate version of the index-flood model and is based on copulas and multivariate quantiles. The performance of the proposed procedure was evaluated by simulation. However, the model was not tested on a real-world case study data. In the present paper, practical aspects are investigated jointly for flood peak (Q) and volume (V) of a dataset from the Côte-Nord region in the province of Quebec, Canada. The application of the proposed procedure requires the identification of the appropriate marginal distribution, the estimation of the index flood and the selection of an appropriate copula. The results of the case study show that the regional bivariate FA procedure performed well. This performance depends strongly on the performance of the two univariate models and, more specifically, the univariate model of Q. The results show also the impact of the homogeneity of the region on the performance of the univariate and bivariate models.

Editor D. Koutsoyiannis     

Asymmetric copula in multivariate flood frequency analysis

The univariate flood frequency analysis is widely used in hydrological studies. Often only flood peak or flood volume is statistically analyzed. For a more complete analysis the three main characteristics of a flood event i.e. peak, volume and duration are required. To fully understand these variables and their relationships, a multivariate statistical approach is necessary. The main aim of this paper is to define the trivariate probability density and cumulative distribution functions. When the joint distribution is known, it is possible to define the bivariate distribution of volume and duration conditioned on the peak discharge. Consequently volume–duration pairs, statistically linked to peak values, become available. The authors build trivariate joint distribution of flood event variables using the fully nested or asymmetric Archimedean copula functions. They describe properties of this copula class and perform extensive simulations to highlight differences with the well-known symmetric Archimedean copulas. They apply asymmetric distributions to observed flood data and compare the results those obtained using distributions built with symmetric copula and the standard Gumbel Logistic model.     

Regionalization of precipitation characteristics in the Canadian Prairie Provinces using large-scale atmospheric covariates and geophysical attributes

Observed data at most stations are often inadequate to obtain reliable estimates of many hydro-meteorological variables that not only define water availability across a region but also the vulnerability of social infrastructure to climatic extremes. To overcome this, data from neighboring sites with similar statistical characteristics are often pooled. The pooling process is based on partitioning of a larger region into smaller sub-regions with homogeneous features of interest. The established approaches rely heavily on statistics computed from observed precipitation data rather than the covariates that play a significant role in modulating the regional and local climate patterns at various temporal and spatial scales. In this study, a new approach for identifying homogeneous regions for regionalization of precipitation characteristics is proposed for the Canadian Prairie Provinces. This approach incorporates information about large-scale atmospheric covariates, teleconnection indices and geographical site attributes that impact spatial patterns of precipitation in order to delineate homogeneous precipitation regions through combined use of multivariate approaches—principal component analysis, canonical correlation analysis and fuzzy C-means clustering. Results of the analyses suggest that the study area can be partitioned into five homogeneous regions. These partitions are validated independently for homogeneity using statistics computed from monthly and seasonal precipitation totals, and seasonal extremes from a network of observation stations. Furthermore, based on the identified regions, precipitation magnitude-frequency relationships of warm and cold season single- and multi-day precipitation extremes, developed through regional frequency analysis, are mapped spatially. Such estimates are important for numerous water resources related activities.     

Homogeneity testing: How homogeneous do heterogeneous cross-correlated regions seem?

The homogeneity of the flood frequency regime for a given pooling-group of sites is a fundamental assumption for many regional flood frequency analysis techniques. Assessing regional homogeneity is a critical step, which may be complicated by the presence of cross-correlation among flood sequences. The scientific literature proposes a number of statistical homogeneity tests and documents that inter-site correlation of floods is normally not negligible, but does not specifically address the impact of cross-correlation on such statistical tests. This paper analyzes the effectiveness of a well-known homogeneity test proposed in the scientific literature in the presence of inter-site cross-correlation through a series of Monte Carlo experiments. The numerical experiments enable us to comment on a possible theoretical correction for the test and to identify an empirical tool that accounts for the impact of inter-site cross-correlation of floods.     

Fast and direct nonparametric procedures in the L-moment homogeneity test

Regional frequency analysis is an important tool to properly estimate hydrological characteristics at ungauged or partially gauged sites in order to prevent hydrological disasters. The delineation of homogeneous groups of sites is an important first step in order to transfer information and obtain accurate quantile estimates at the target site. The Hosking–Wallis homogeneity test is usually used to test the homogeneity of the selected sites. Despite its usefulness and good power, it presents some drawbacks including the subjective choice of a parametric distribution for the data and a poorly justified rejection threshold. The present paper addresses these drawbacks by integrating nonparametric procedures in the L-moment homogeneity test. To assess the rejection threshold, three resampling methods (permutation, bootstrap and Pólya resampling) are considered. Results indicate that permutation and bootstrap methods perform better than the parametric Hosking–Wallis test in terms of power as well as in time and procedure simplicity. A real-world case study shows that the nonparametric tests agree with the HW test concerning the homogeneity of the volume and the bivariate case while they disagree for the peak case, but that the assumptions of the HW test are not well respected.     

Regional frequency analysis of rainfall extremes in Southern Malawi using the index rainfall and L-moments approaches

Rainfall extremes often result in the occurrence of flood events with associated loss of life and infrastructure in Malawi. However, an understanding of the frequency of occurrence of such extreme events either for design or disaster planning purposes is often limited by data availability at the desired temporal and spatial scales. Regionalisation, which involves “trading time for space” by pooling together observations for stations with similar behavior, is an alternative approach for more accurate determination of extreme events even at ungauged areas or sites with short records. In this study, regional frequency analysis of rainfall extremes in Southern Malawi, large parts of which are flood prone, was undertaken. Observed 1-, 3-, 5- and 7-day annual maximum rainfall series for the period 1978–2007 at 23 selected rainfall stations in Southern Malawi were analysed. Cluster analysis using scaled at-site characteristics was used to determine homogeneous rainfall regions. L-moments were applied to derive regional index rainfall quantiles. The procedure also validated the three rainfall regions identified through homogeneity and heterogeneity tests based on Monte Carlo simulations with regional average L-moment ratios fitted to the Kappa distribution. Based on assessments of the accuracy of the derived index rainfall quantiles, it was concluded that the performance of this regional approach was satisfactory when validated for sites not included in the sample data. The study provides an estimate of the regional characteristics of rainfall extremes that can be useful in among others flood mitigation and engineering design.     

Dam risk assessment based on univariate versus bivariate statistical approaches: a case study for Argentina

Abstract

Considering floods as multivariate events allows a better statistical representation of their complexity. In this work the relevance of multivariate analysis of floods for designing or assessing the safety of hydraulic structures is discussed. A flood event is characterized by its peak flow and volume. The dependence between the variables is modelled with a copula. One thousand random pairs of variables are transformed to hydrographs, applying the Beta distribution function. Synthetic floods are routed through a reservoir to assess the risk of overtopping a dam. The resulting maximum water levels are compared to estimations considering the peak flow and volume separately. The analysis is performed using daily flows observed in the River Agrio in Neuquén Province, Argentina, a catchment area of 7300 km². The bivariate approach results in higher maximum water level values. Therefore the multivariate approach should be preferred for the estimation of design variables.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Synthetic regional flow duration curve for southern Taiwan

The primary purpose of this study is to develop the regional flow duration curves for southern Taiwan. To define homogeneous regions for developing regional flow duration curves, multivariate statistical analysis (principal component and cluster analysis) was applied to daily flow data from 34 stream-gauged stations in southern Taiwan. Two kinds of clustering variables, the dimensionless flow duration curve and specific flow duration curve, were compared in this study. It was found that three homogeneous regions delineated by specific flow duration curves as clustering variables have more reasonable results. The three homogeneous regions not only have well-defined geographical boundaries, but also correspond to the rainfall and geology characteristics of the regions. It seems that the technique of cluster analysis can reasonably define the homogeneous regions. In each homogeneous region, the synthetic regional flow duration curves were developed by a family of parametric duration curves. This approach has the advantage of being simple and needing only the basin area as an index. The performance of the regional flow duration curve was verified by the comparison of areas under the actual and synthetic flow duration curves; the latter were generated from the regional flow duration curve. Almost all the 34 stream-gauged stations had less than 25% absolute error.     

A regional Bayesian POT model for flood frequency analysis

Flood frequency analysis is usually based on the fitting of an extreme value distribution to the local streamflow series. However, when the local data series is short, frequency analysis results become unreliable. Regional frequency analysis is a convenient way to reduce the estimation uncertainty. In this work, we propose a regional Bayesian model for short record length sites. This model is less restrictive than the index flood model while preserving the formalism of “homogeneous regions”. The performance of the proposed model is assessed on a set of gauging stations in France. The accuracy of quantile estimates as a function of the degree of homogeneity of the pooling group is also analysed. The results indicate that the regional Bayesian model outperforms the index flood model and local estimators. Furthermore, it seems that working with relatively large and homogeneous regions may lead to more accurate results than working with smaller and highly homogeneous regions.     

A feature weighting and selection method for improving the homogeneity of regions in regionalization of watersheds

The method used for feature selection or feature weighting in regionalization of watersheds may affect the results of regionalization methods considerably. It can play a key role in forming hydrologically homogeneous regions for regional flood frequency analysis. In this study, a method based on exploring the nearest and farthest neighbours of data points is introduced for identifying salient features for regionalization of watersheds. The method includes options to relate watershed features to flood data records in order to increase the homogeneity of the regions. The nearest and farthest neighbours are identified based on the criteria such as the mutual information criterion and Spearman's rank correlation coefficient. Then, the watershed features more able to explain the relationships between the nearest and farthest neighbours are identified as salient features to form homogeneous features for regional flood frequency analysis. The results show that the optimum option of the proposed method improves the performances of the hard and fuzzy clustering algorithms in more than half of the cases based on the cluster validity indices. Furthermore, the results reveal that the optimum option can increase the number of the homogeneous regions formed by clustering algorithms to a great extent. By using the optimum option with 5 nearest and 5 farthest neighbours, longitude, drainage area, and run‐off coefficient are identified as the salient features to regionalize Sefidrud basin. The results show that the proposed method can be considered as an efficient method to form homogeneous regions for regional flood frequency analysis.     

Regionalisation of the parameters of the log‐Pearson 3 distribution: a case study for New South Wales,Australia

The index flood method is widely used in regional flood frequency analysis (RFFA) but explicitly relies on the identification of ‘acceptable homogeneous regions’. This paper presents an alternative RFFA method, which is particularly useful when ‘acceptably homogeneous regions’ cannot be identified. The new RFFA method is based on the region of influence (ROI) approach where a ‘local region’ can be formed to estimate statistics at the site of interest. The new method is applied here to regionalize the parameters of the log‐Pearson 3 (LP3) flood probability model using Bayesian generalized least squares (GLS) regression. The ROI approach is used to reduce model error arising from the heterogeneity unaccounted for by the predictor variables in the traditional fixed‐region GLS analysis. A case study was undertaken for 55 catchments located in eastern New South Wales, Australia. The selection of predictor variables was guided by minimizing model error. Using an approach similar to stepwise regression, the best model for the LP3 mean was found to use catchment area and 50‐year, 12‐h rainfall intensity as explanatory variables, whereas the models for the LP3 standard deviation and skewness only had a constant term for the derived ROIs. Diagnostics based on leave‐one‐out cross validation show that the regression model assumptions were not inconsistent with the data and, importantly, no genuine outlier sites were identified. Significantly, the ROI GLS approach produced more accurate and consistent results than a fixed‐region GLS model, highlighting the superior ability of the ROI approach to deal with heterogeneity. This method is particularly applicable to regions that show a high degree of regional heterogeneity. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessment of regional estimation error by canonical residual kriging

Various regional flood frequency analysis procedures are used in hydrology to estimate hydrological variables at ungauged or partially gauged sites. Relatively few studies have been conducted to evaluate the accuracy of these procedures and estimate the error induced in regional flood frequency estimation models. The objective of this paper is to assess the overall error induced in the residual kriging (RK) regional flood frequency estimation model. The two main error sources in specific flood quantile estimation using RK are the error induced in the quantiles local estimation procedure and the error resulting from the regional quantile estimation process. Therefore, for an overall error assessment, the corresponding errors associated with these two steps must be quantified. Results show that the main source of error in RK is the error induced into the regional quantile estimation method. Results also indicate that the accuracy of the regional estimates increases with decreasing return periods. Copyright © 2010 John Wiley & Sons, Ltd.     

Multivariate analysis of flood characteristics in a climate change context of the watershed of the Baskatong reservoir,Province of Québec,Canada

The analysis of the impact of climate change (CC) on flood peaks has been the subject of several studies. However, a flood is characterized not only by its peak, but also by other characteristics such as its volume and duration. Little effort has been directed towards the study of the impact of CC on these characteristics. The aim of the present study is to evaluate and compare flood characteristics in a CC context, in the watershed of the Baskatong reservoir (Province of Québec, Canada). Comparisons are based on observed flow data and simulated flow series obtained from hydrological models using meteorological data from a regional climate model for a reference period (1971–2000) and a future period (2041–2070). To this end, two hydrological models HSAMI and HYDROTEL are considered. Correlations, stationarity, change‐points, and the multivariate behaviour of flood series were studied. The results show that, at various levels, all flood characteristics could be affected by CC. Copyright © 2011 John Wiley & Sons, Ltd.     

Regional flood frequency and spatial patterns analysis in the Pearl River Delta region using L-moments approach

The Pearl River Delta (PRD) has one of the most complicated deltaic drainage systems with probably the highest density of crisscross-river network in the world. This article presents a regional flood frequency analysis and recognition of spatial patterns for flood-frequency variations in the PRD region using the well-known index flood L-moments approach together with some advanced statistical test and spatial analysis methods. Results indicate that: (1) the whole PRD region is definitely heterogeneous according to the heterogeneity test and can be divided into three homogeneous regions; (2) the spatial maps for annual maximum flood stage corresponding to different return periods in the PRD region suggest that the flood stage decreases gradually from the riverine system to the tide dominated costal areas; (3) from a regional perspective, the spatial patterns of flood-frequency variations demonstrate the most serious flood-risk in the coastal region because it is extremely prone to the emerging flood hazards, typhoons, storm surges and well-evidenced sea-level rising. Excessive rainfall in the upstream basins will lead to moderate floods in the upper and middle PRD region. The flood risks of rest parts are identified as the lowest in entire PRD. In order to obtain more reliable estimates, the stationarity and serial-independence are tested prior to frequency analysis. The characterization of the spatial patterns of flood-frequency variations is conducted to reveal the potential influences of climate change and intensified human activities. These findings will definitely contribute to formulating the regional development strategies for policymakers and stakeholders in water resource management against the menaces of frequently emerged floods and well-evidenced sea level rising.     

A bivariate gamma distribution for use in multivariate flood frequency analysis

A gamma distribution is one of the most frequently selected distribution types for hydrological frequency analysis. The bivariate gamma distribution with gamma marginals may be useful for analysing multivariate hydrological events. This study investigates the applicability of a bivariate gamma model with five parameters for describing the joint probability behavior of multivariate flood events. The parameters are proposed to be estimated from the marginal distributions by the method of moments. The joint distribution, the conditional distribution, and the associated return periods are derived from marginals. The usefulness of the model is demonstrated by representing the joint probabilistic behaviour between correlated flood peak and flood volume and between correlated flood volume and flood duration in the Madawask River basin in the province of Quebec, Canada. Copyright © 2001 John Wiley & Sons, Ltd.     

Implications of heterogeneous flood‐frequency distributions on traditional stream‐discharge prediction techniques

Traditional flood‐frequency analysis involves the assumption of homogeneity of the flood distribution. However, floods are often generated by heterogeneous distributions composed of a mixture of two or more populations. Differences between the populations may be the result of a number of factors, including seasonal variations in the flood‐producing mechanisms, changes in weather patterns resulting from low‐frequency climate shifts and/or El Niño/La Nina oscillations, changes in channel routing owing to the dominance of within‐channel or floodplain flow, and basin variability resulting from changes in antecedent soil moisture. Not recognizing these physical processes in conventional flood‐frequency analysis probably is the main reason that many frequency distributions do not provide an acceptable fit to flood data. In this paper, we use long‐term hydroclimatic records from the Gila River basin of south‐east and central Arizona in the USA to explore the extent and significance of mixed populations. First, we discuss the probable causes of heterogeneity in the frequency distribution of annual flood and present evidence of its occurrence. Second, we investigate the implications of using various popular homogeneous distributions for predicting peak flows for basins that exhibit mixed population characteristics. Third, we demonstrate how alternative frequency models that explicitly account for floods generated by a mixture of two or more populations are both hydrologically and statistically more appropriate. We illustrate how the selection of the most plausible distribution for flood‐frequency analysis also should be based on hydrological reasoning as opposed to the sole application of the traditional statistical goodness‐of‐fit tests. Copyright © 2002 John Wiley & Sons, Ltd.     

Formation of homogeneous regions for regional frequency analysis of extreme precipitation events in the Czech Republic

Extreme high precipitation amounts are among environmental events with the most disastrous consequences for human society. This paper deals with the identification of ‘homogeneous regions’ according to statistical characteristics of precipitation extremes in the Czech Republic, i.e. the basic and most important step toward the regional frequency analysis. Precipitation totals measured at 78 stations over 1961–2000 are used as an input dataset. Preliminary candidate regions are formed by the cluster analysis of site characteristics, using the average-linkage clustering and Ward’s method. Several statistical tests for regional homogeneity are utilized, based on the 10-yr event and the variation of L-moment statistics. In compliance with results of the tests, the area of the Czech Republic has been divided into four homogeneous regions. The findings are supported by simulation experiments proposed to evaluate stability of the test results. Since the regions formed reflect also climatological differences in precipitation regimes and synoptic patterns causing high precipitation amounts, their future application may not be limited to the frequency analysis of extremes.     

Return period of bivariate distributed extreme hydrological events

 Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either separate single random variables or two joint random variables. In the latter case, the return periods can be defined using one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical models and observed flood data. The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this work.     

Timescale-based flood typing to estimate temporal changes in flood frequencies

ABSTRACT

The flood peak is the dominating characteristic in nearly all flood-statistical analyses. Contrary to the general assumptions of design flood estimation, the peak is not closely related to other flood characteristics. Differentiation of floods into types provides a more realistic view. Often different parts of the probability distribution function of annual flood peaks are dominated by different flood types, which raises the question how shifts in flood regimes would modify the statistics of annual maxima. To answer this, a distinction into five flood types is proposed; then, temporal changes in flood-type frequencies are investigated. We show that the frequency of floods caused by heavy rain has increased significantly in recent years. A statistical model is developed that simulates peaks for each event type by type-specific peak–volume relationships. In a simulation study, we show how changes in frequency of flood event type lead to changes in the quantiles of annual maximum series.