Trivariate generalized extreme value distribution in flood frequency analysis

Abstract

The multivariate extension of the logistic model with generalized extreme value (GEV) marginals is applied to provide a regional at-site flood estimate. The maximum likelihood estimators of the parameters were obtained numerically by using a multivariable constrained optimization algorithm. The asymptotic results were checked by distribution sampling techniques in order to establish whether or not those results can be utilized for small samples. A region in northern Mexico with 21 gauging stations was selected to apply the model. Results were compared with those obtained by the most popular univariate distributions, the bivariate approach of the logistic model and three regional methods: station-year, index flood and L-moments. These show that there is a reduction in the standard error of fit when estimating the parameters of the marginal distribution with the trivariate distribution instead of its univariate and bivariate counterpart, and differences between at-site and regional at-site design events can be significant as return period increases.     

Non-linear optimal multivariate spatial design using spatial vine copulas

A multivariate spatial sampling design that uses spatial vine copulas is presented that aims to simultaneously reduce the prediction uncertainty of multiple variables by selecting additional sampling locations based on the multivariate relationship between variables, the spatial configuration of existing locations and the values of the observations at those locations. Novel aspects of the methodology include the development of optimal designs that use spatial vine copulas to estimate prediction uncertainty and, additionally, use transformation methods for dimension reduction to model multivariate spatial dependence. Spatial vine copulas capture non-linear spatial dependence within variables, whilst a chained transformation that uses non-linear principal component analysis captures the non-linear multivariate dependence between variables. The proposed design methodology is applied to two environmental case studies. Performance of the proposed methodology is evaluated through partial redesigns of the original spatial designs. The first application is a soil contamination example that demonstrates the ability of the proposed methodology to address spatial non-linearity in the data. The second application is a forest biomass study that highlights the strength of the methodology in incorporating non-linear multivariate dependence into the design.     

A fully non-stationary linear coregionalization model for multivariate random fields

This paper introduces an extension of the traditional stationary linear coregionalization model to handle the lack of stationarity. Under the proposed model, coregionalization matrices are spatially dependent, and basic univariate spatial dependence structures are non-stationary. A parameter estimation procedure of the proposed non-stationary linear coregionalization model is developed under the local stationarity framework. The proposed estimation procedure is based on the method of moments and involves a matrix-valued local stationary variogram kernel estimator, a weighted local least squares method in combination with a kernel smoothing technique. Local parameter estimates are knitted together for prediction and simulation purposes. The proposed non-stationary multivariate spatial modeling approach is illustrated using two real bivariate data examples. Prediction performance comparison is carried out with the classical stationary multivariate spatial modeling approach. According to several criteria, the prediction performance of the proposed non-stationary multivariate spatial modeling approach appears to be significantly better.     

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     

Consequences of a freshwater canal discharge on the benthic community and its habitat on an exposed sandy beach

This paper analyses the spatial and temporal effects of a freshwater discharge (Canal Andreoni) on the macroinfauna community and its habitat in a sandy beach of Uruguay. Bimonthly, we examined 17 environmental variables plus macroinfauna abundance, biomass, richness, evenness and diversity of three sites: Andreoni, at the canal mouth, Coronilla, at 1 km, and Barra, at 13 km from the mouth. Both univariate and multivariate techniques showed an increasing degree of perturbation towards the canal. This was reflected by abiotic and biotic differences between sites and by a consistent two-dimensional ordination of the samples. A clear seasonal pattern was found, specially accentuated at Coronilla, where the effects of the canal were stronger in winter and weaker in summer. Multivariate linking between macroinfauna and its habitat highlighted the role of salinity as explanatory variable of the observed trends.     

Uncertainty and variability in bivariate modeling of hydrological droughts

There are two kinds of uncertainty factors in modeling the bivariate distribution of hydrological droughts: the alteration of predefined critical ratios for pooling droughts and excluding minor droughts and the temporal variability of univariate and/or bivariate characteristics of droughts due to the impact of human activities. Daily flow data covering a period of 56 hydrological years from two gauging stations from a humid region in South China are used. The influences of alterations of threshold values of flow and critical ratios of pooling droughts and excluding minor droughts on drought properties are analyzed. Six conventional univariate models and three Archimedean copulas are employed to fit the marginal and joint distributions of drought properties, the Kolmogorov–Smirnov and Anderson–Darling methods are used for testing the goodness-of-fit of the univariate model, and the Cramer-von Mises method based on Rosenblatt’s transform is applied for the test of the bivariate model. The change point analysis of the copula parameter of bivariate distribution of droughts is first made. Results demonstrate that both the statistical characteristics of each drought property and their bivariate joint distributions are sensitive to the critical ratio of excluding minor droughts. A model can be selected to fit the marginal distribution for drought deficit volume or maximum deficit, but it is not determined for drought duration with the lower ratios of the pooling and excluding droughts. The statistical uncertainty of drought duration makes the modeling of bivariate joint distribution of drought duration and deficit volume or of drought duration and maximum deficit undermined. Change points significantly occurred in the period from the late 1970s to the middle 1980s for a single drought property and the copula parameter of their joint distribution due to the impact of human activities. The difference between two subseries separated by the change point is remarkable in the magnitudes of drought properties and the joint return periods. A copula function can be selected to optimally fit the bivariate distribution, provided that the critical ratios of pooling and excluding droughts are great enough such as the optimal value of 0.4 in the case study. It is valuable that the modeling and designing of the bivariate joint correlation and distribution of drought properties can be performed on the subseries separated by the change point of the copula parameter.     

Evaluating spatiotemporal variation in water chemistry of the upper Colorado River using longitudinal profiling

Stream water chemistry is traditionally measured as variation over time at fixed sites, with sparse sites providing a crude understanding of spatial heterogeneity. An alternative Lagrangian reference frame measures changes with respect to both space and time as water travels through a network. Here, we collected sensor-based measurements of water chemistry at high spatial resolution along nearly 500 km of the Upper Colorado River. Our objective was to understand sources of spatiotemporal heterogeneity across different solutes and determine whether longitudinal change manifests as smooth gradients as suggested by the River Continuum Concept (RCC) or as abrupt changes as suggested by the Serial Discontinuity Concept (SDC). Our results demonstrate that Lagrangian sampling integrates spatiotemporal variation, and profiles reflect processes that vary in both space and time and over different scales. Over each day of sampling, water temperature (T) and dissolved oxygen (DO) varied strongly in response to diel solar cycles, with most of the variation driven by sampling time rather than sampling location. Equilibration of T and DO with the atmosphere limited small scale spatial heterogeneity, with variation at the entire profile scale driven by regional climate gradients. As such, T and DO profiles more closely approximated the smooth gradients of the RCC (though including temporal sampling artefacts). Conversely, variation in specific conductance and nitrate (NO₃-N) was largely driven by spatial patterns of lateral inflows such as tributaries and groundwater. This resulted in discrete shifts in the profiles at or downstream of discontinuities, appearing as the profiles expected with the SDC. The concatenation of spatiotemporal variation that produces observed Lagrangian profiles presents interpretive challenges but also augments our understanding of where, how, and critically why water chemistry changes in time and space as it moves through river networks.     

An analog period method for gap-filling of latent heat flux measurements

Practically all records of eddy-covariance flux measurements are affected by gaps, caused by several reasons. In this work, we propose analog period (AP) methods for gap-filling, and test them for filling gaps of latent heat flux at five AmeriFlux sites. The essence of the methods is to look for periods in the record that bear a strong resemblance, in the variable to be filled, to the periods immediately before and after the gap. Similarity between periods is gauged by the coefficient of determination, and the search for similar periods and their ranking is straightforward. The methods are developed in a univariate version (that uses only the latent heat flux data series itself) and several multivariate ones, that incorporate sensible heat flux, ground heat flux and net radiation data. For each set of independent variables used for gap-filling, the methods are tested against an existing gap-filling procedure with similar data requirements. Thus, the univariate version is tested against the mean diurnal variation method, and the multivariate versions are tested against corresponding simple and multiple linear regression techniques that use energy-budget data, and in one case the evaporative fraction as well. In our tests, the proposed univariate version performs better than the mean diurnal variation method, and the multivariate versions perform better than simple/multiple linear regression methods. An often used available computer package, REddyProc, was also tested as a basis of comparison. In general, the proposed methods (in univariate and multivariate versions) and simple/multiple linear regressions performed better than REddyProc. For the datasets analysed, gap filling via the evaporative fraction method performed poorly.     

Morphometric analysis and tectonic interpretation of digital terrain data: a case study

Tectonic movement along faults is often re?ected by characteristic geomorphological features such as linear valleys, ridgelines and slope‐breaks, steep slopes of uniform aspect, regional anisotropy and tilt of terrain. Analysis of digital elevation models, by means of numerical geomorphology, provides a means of recognizing fractures and characterizing the tectonics of an area in a quantitative way. The objective of this study is to investigate the use of numerical geomorphometric methods for tectonic geomorphology through a case study. The methodology is based on general geomorphometry. In this study, the basic geometric attributes (elevation, slope, aspect and curvatures) are complemented with the automatic extraction of ridge and valley lines and surface speci?c points. Evans' univariate and bivariate methodology of general geomorphometry is extended with texture (spatial) analysis methods, such as trend, autocorrelation, spectral, and network analysis. Terrain modelling is implemented with the integrated use of: (1) numerical differential geometry; (2) digital drainage network analysis; (3) digital image processing; and (4) statistical and geostatistical analysis. Application of digital drainage network analysis is emphasized. A simple shear model with principal displacement zone with an NE–SW orientation can account for most of the the morphotectonic features found in the basin by geological and digital tectonic geomorphology analyses. Copyright © 2003 John Wiley & Sons, Ltd.     

Synoptic sampling reveals spatial stability in flow and chemistry patterns despite large seasonal variability in a subarctic mountain catchment

Seasonality plays a critical role in cold mountain regions as variation in air temperature, ground thermal status, and precipitation phase alter the rate, timing and magnitude of hydrological and chemical transport. Additionally, cold mountain catchments can have highly variable topography, geology, permafrost, and landcover, which intrinsically add to this irregularity. Understanding how external and internal variability act to control mass fluxes requires sampling at a high spatial resolution over time, which rarely occurs in cold remote regions. In this work, we conduct five snapshot sampling surveys across 34 subcatchments during the ice-free period in Wolf Creek Research Basin (a mesoscale montane subarctic catchment) and two additional winter surveys across a subset of sites to assess the drivers of variability in stream chemistry and discharge. We sampled for specific conductance (SpC), major ions, and dissolved organic carbon (DOC) and used statistical metrics and Bayesian mixing analysis to quantify patterns of flow and chemistry across space and time. Our results indicate patterns in both flow and chemistry remain largely consistent across seasons for all solutes. However, there was weaker correlation of chemistry between sites, suggesting asynchronous behaviour within the catchment. There was evidence of increasing production of ions and DOC along the stream network during high spring flows but not during low flows. Although concentrations and flows exhibit high seasonality in subarctic mountains, this seasonal variability does not alter spatial patterns that arise from highly variable catchment characteristics.     

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.     

Spatial distribution,fractionation and ecological risk assessment of potentially toxic metals in bottom sediments of the Zarivar freshwater Lake (Northwestern Iran)

Freshwater lakes are one of the most vulnerable ecosystems to environmental contamination. This study was initiated to assess the spatial distribution, fractionation, ecological risk of selected potentially toxic metals (Pb, Zn, Cu, Cr, and Ni) in bottom sediments of the Zarivar lake, the second largest freshwater lake in Iran. The results revealed that Pb, Zn and Cu had the high spatial variability (coefficient of variation >50) across the sampling sites and their maximum concentrations (197.5 for Pb, 198.7 for Zn and 185.6 mg/kg for Cu) were observed in sampling sites from the northern, western and eastern margins of the lake. Cr and Ni with average concentrations of 28.3 and 31.38 mg/kg respectively, exhibited low spatial variability (coefficient of variation <20) and their concentrations did not vary significantly among the sampling sites. Based on the redundancy analysis (RDA), sediment organic matter was strongly correlated with Pb, Zn and Cu while Fe₂O₃ and Al₂O₃ showed a positive correlation with Ni and Cr. The calculated average enrichment factor (EF) and geoaccumulation index (I_geo) showed that the contamination level of metals can be arranged in the following order of Pb> Cu > Zn > Cr > Ni. Results from the modified five-step sequential extraction analysis indicated that 40 % of total Pb and Zn were associated with the reducible fraction, 45 % of Cu with the oxidizable fraction and more than 80 % of total Ni and Cr were retrieved from the residual fraction. It was also noticed that Pb, Zn and Cu were more incorporated into the non-residual fractions in the sites with a higher total concentration of these metals, suggesting that both total concentration and fractionation behavior of metals were influenced by their potential sources in the study area. Ecological risk assessment using the potential ecological risk index (PERI) and the modified potential ecological risk index (MPERI) showed that sediments from the eight sampling sites pose a moderate to considerable risk whereas the other sites had low ecological risk level. In comparison to sediment quality guidelines (SQGs), the effects range low (ERL) and probable effect level (PEL) values for Pb, Cu and Zn were exceeded at some sampling sites while Ni and Cr concentrations were found to be below or close to their SQGs values at all the sampling sites. Pb was generally identified as the contaminant of most concern in the study area. Taking into account the results obtained from the fractionation study and the source contribution estimate, it can be inferred that the Pb, Zn and Cu with the average contribution of 79, 54 and 64 % respectively, were mainly derived from anthropogenic sources whereas Ni and Cr with the estimated contribution of 80 and 89 % were predominately from the lithogenic source.     

Spatial variability in specific discharge and streamwater chemistry during low flows: Results from snapshot sampling campaigns in eleven Swiss catchments

Catchments consist of distinct landforms that affect the storage and release of subsurface water. Certain landforms may be the main contributors to streamflow during extended dry periods, and these may vary for different catchments in a given region. We present a unique dataset from snapshot field campaigns during low‐flow conditions in 11 catchments across Switzerland to illustrate this. The catchments differed in size (10 to 110 km²), varied from predominantly agricultural lowlands to Alpine areas, and covered a range of physical characteristics. During each snapshot campaign, we jointly measured streamflow and collected water samples for the analysis of major ions and stable water isotopes. For every sampling location (basin), we determined several landscape characteristics from national geo‐datasets, including drainage area, elevation, slope, flowpath length, dominant land use, and geological and geomorphological characteristics, such as the lithology and fraction of quaternary deposits. The results demonstrate very large spatial variability in specific low‐flow discharge and water chemistry: Neighboring sampling locations could differ significantly in their specific discharge, isotopic composition, and ion concentrations, indicating that different sources contribute to streamflow during extended dry periods. However, none of the landscape characteristics that we analysed could explain the spatial variability in specific discharge or streamwater chemistry in multiple catchments. This suggests that local features determine the spatial differences in discharge and water chemistry during low‐flow conditions and that this variability cannot be assessed a priori from available geodata and statistical relations to landscape characteristics. The results furthermore suggest that measurements at the catchment outlet during low‐flow conditions do not reflect the heterogeneity of the different source areas in the catchment that contribute to streamflow.     

Application of bivariate frequency analysis to the derivation of rainfall–frequency curves

Bivariate distributions have been recently employed in hydrologic frequency analysis to analyze the joint probabilistic characteristics of multivariate storm events. This study aims to derive practical solutions of application for the bivariate distribution to estimate design rainfalls corresponding to the desired return periods. Using the Gumbel mixed model, this study constructed rainfall–frequency curves at sample stations in Korea which provide joint relationships between amount, duration, and frequency of storm events. Based on comparisons and analyses of the rainfall–frequency curves derived from univariate and bivariate storm frequency analyses, this study found that conditional frequency analysis provides more appropriate estimates of design rainfalls as it more accurately represents the natural relationship between storm properties than the conventional univariate storm frequency analysis.     

Application of multivariate statistical procedures to the hydrochemical study of a coastal aquifer: an example from Crete,Greece

A variety of multivariate statistical procedures were applied to three separate sets of quantitative analytical data from a coastal aquifer located in Malia, Crete (Greece), in order to identify the major hydrochemical processes affecting the groundwater quality and to investigate the evolution of groundwater composition in three different sampling periods. Two of them were carried out on October 2001 and September 2002 at the end of the dry season and the third on April 2002 at the end of the wet period. Two factors were found that explained major hydrochemical processes in the aquifer. These factors reveal the existence of an intensive intrusion of seawater and mechanisms of nitrate contamination of groundwater. Bivariate plots of the scores of the two main factors showed that the seawater intrusion and nitrate pollution processes are maintained through three surveys and that the process of nitrate pollution increases from the first to the second dry survey. Q‐mode factor analysis and discriminant analysis of the three sampling periods clearly showed a seasonal variation of the whole chemistry of groundwater samples. This seasonal variation can be attributed to the freshwater recharge and seawater intrusion that affect the groundwater quality of the Malia aquifer. The results of trend surface analysis are in agreement with those of factor analysis. Moreover, the fourth‐order trend surfaces of EC, Cl^? and NO₃^? showed that the salinization process is more intensive during the first dry period and the spatial variation of NO₃^? maxima plumes are strongly affected by the flow regime of the Malia aquifer. Copyright © 2007 John Wiley & Sons, Ltd.     

Multivariate homogeneity testing in a northern case study in the province of Quebec,Canada

In regional frequency analysis, the examination of the regional homogeneity represents an important step of the procedure. Flood events possess multivariate characteristics which can not be handled by classical univariate regional procedures. For instance, classical procedures do not allow to assess regional homogeneity while taking into consideration flood peak, volume and duration. Chebana and Ouarda proposed multivariate discordancy and homogeneity tests. They carried out a simulation study to evaluate the performance of these tests. In the present paper, practical aspects are investigated jointly on flood peak and flood volume of a data set from the Côte‐Nord region in the province of Quebec, Canada. It is shown that, after removing the discordant sites, the remaining ones constitute a homogeneous region for the volumes and heterogeneous region for the peaks. However, if both variables are jointly considered, the obtained region is possibly homogeneous. Furthermore, the results demonstrate the usefulness of the bivariate test to take into account the dependence structure between the variables representing the event, and to take advantage of more information from the hydrograph. Copyright © 2009 John Wiley & Sons, Ltd.     

Modeling short duration extreme precipitation patterns using copula and generalized maximum pseudo-likelihood estimation with censoring

The paper aims to develop researches on the spatial variability of heavy rainfall events estimation using spatial copula analysis. To demonstrate the methodology, short time resolution rainfall time series from Stuttgart region are analyzed. They are constituted by rainfall observations on continuous 30 min time scale recorded over a network composed by 17 raingages for the period July 1989–July 2004. The analysis is performed aggregating the observations from 30 min up to 24 h. Two parametric bivariate extreme copula models, the Husler–Reiss model and the Gumbel model are investigated. Both involve a single parameter to be estimated. Thus, model fitting is operated for every pair of stations for a giving time resolution. A rainfall threshold value representing a fixed rainfall quantile is adopted for model inference. Generalized maximum pseudo-likelihood estimation is adopted with censoring by analogy with methods of univariate estimation combining historical and paleoflood information with systematic data. Only pairs of observations greater than the threshold are assumed as systematic data. Using the estimated copula parameter, a synthetic copula field is randomly generated and helps evaluating model adequacy which is achieved using Kolmogorov Smirnov distance test. In order to assess dependence or independence in the upper tail, the extremal coefficient which characterises the tail of the joint bivariate distribution is adopted. Hence, the extremal coefficient is reported as a function of the interdistance between stations. If it is less than 1.7, stations are interpreted as dependent in the extremes. The analysis of the fitted extremal coefficients with respect to stations inter distance highlights two regimes with different dependence structures: a short spatial extent regime linked to short duration intervals (from 30 min to 6 h) with an extent of about 8 km and a large spatial extent regime related to longer rainfall intervals (from 12 h to 24 h) with an extent of 34 to 38 km.     

A simple model for spatial rainfall fields

Spatial rainfall amounts accumulated over short to medium periods of time, say a few days, tend to have a probabilistic structure with very distinctive features. Some of these that are specially relevant for the purpose of spatial modeling are the presence of mixed sampling distributions, right skewed distributions conditional on rainfall occurrence, and a complex spatial association structure. The goal of this work is to construct a family for the bivariate distributions of spatial rainfall fields that incorporates these distinctive features. It is based on the separate modeling of spatial occurrence of rainfall and the spatial distribution of positive rainfalls. The main properties of the bivariate distributions are derived, and some properties of the random field realizations are illustrated through simulation. Some limitations of the proposed model are also discussed.     

Economics of Sample Compositing as a Screening Tool in Ground Water Quality Monitoring

Recent advances in high throughput/automated compositing with robotics/field-screening methods offer seldom-tapped opportunities for achieving cost-reduction in ground water quality monitoring programs. An economic framework is presented in this paper for the evaluation of sample compositing as a screening tool in ground water quality monitoring. When the likelihood of occurrence of a contaminant in a well is very small, the use of sample compositing instead of routine exhaustive sampling will lead to reduction in analytical efforts. Such reduction will be maximum when there are no contaminated wells in the network. An N-fold reduction will result when none of the wells in a network of N wells are contaminated. When 25 percent or more wells in a network are contaminated, the use of sample compositing will require, at the most, an additional 50 percent analytical effort compared to exhaustive sampling. A quantitative measure of the cost-effectiveness of sample compositing as a screening tool is shown to be dependent on two factors: a ratio (f1) of laboratory analytical cost to that of well installation and field sampling costs and a ratio (f2) of the expected number of contaminated wells to that of the total number of wells in the network. Several useful mathematical results of primary interest are derived and illustrated with case examples in the paper. Selected areas for further research are also outlined.     

Hydrological risk analysis of dam overtopping using bivariate statistical approach: a case study from Geheyan Reservoir,China

Hydrological risk analysis is essential and provides useful information for dam safety management and decision-making. This study presents the application of bivariate flood frequency analysis to risk analysis of dam overtopping for Geheyan Reservoir in China. The dependence between the flood peak and volume is modelled with the copula function. A Monte Carlo procedure is conducted to generate 100,000 random flood peak-volume pairs, which are subsequently transformed to corresponding design flood hydrographs (DFHs) by amplifying the selected annual maximum flood hydrographs (AMFHs). These synthetic DFHs are routed through the reservoir to obtain the frequency curve of maximum water level and assess the risk of dam overtopping. Sensitive analysis is performed to investigate the influence of different AMFH shapes and correlation coefficients of flood peak and volume on estimated overtopping risks. The results show that synthetic DFH with AMFH shape characterized by a delayed time to peak results in higher risk, and therefore highlight the importance of including a range of possible AMFH shapes in the dam risk analysis. It is also demonstrated that the overtopping risk is increased as the correlation coefficient of flood peak and volume increases and underestimated in the independence case (i.e. traditional univariate approach), while overestimated in the full dependence case. The bivariate statistical approach based on copulas can effectively capture the actual dependence between flood peak and volume, which should be preferred in the dam risk analysis practice.