Articles | Volume 21, issue 5
https://doi.org/10.5194/hess-21-2497-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/hess-21-2497-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Dealing with uncertainty in the probability of overtopping of a flood mitigation dam
Eleni Maria Michailidi
CORRESPONDING AUTHOR
DICATAM, Università degli Studi di Brescia, Via Branze 42, 25123 Brescia, Italy
Baldassare Bacchi
DICATAM, Università degli Studi di Brescia, Via Branze 42, 25123 Brescia, Italy
Related subject area
Subject: Engineering Hydrology | Techniques and Approaches: Stochastic approaches
Uncertainty estimation of regionalised depth–duration–frequency curves in Germany
FarmCan: a physical, statistical, and machine learning model to forecast crop water deficit for farms
Identifying sensitivities in flood frequency analyses using a stochastic hydrologic modeling system
Characteristics and process controls of statistical flood moments in Europe – a data-based analysis
Objective functions for information-theoretical monitoring network design: what is “optimal”?
Stochastic simulation of streamflow and spatial extremes: a continuous, wavelet-based approach
Numerical investigation on the power of parametric and nonparametric tests for trend detection in annual maximum series
Spatially dependent flood probabilities to support the design of civil infrastructure systems
Technical note: Stochastic simulation of streamflow time series using phase randomization
Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice
Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 1: theoretical development
Ensemble modeling of stochastic unsteady open-channel flow in terms of its time–space evolutionary probability distribution – Part 2: numerical application
Characterizing the spatial variations and correlations of large rainstorms for landslide study
Assessment of extreme flood events in a changing climate for a long-term planning of socio-economic infrastructure in the Russian Arctic
Flood frequency analysis of historical flood data under stationary and non-stationary modelling
Selection of intense rainfall events based on intensity thresholds and lightning data in Switzerland
Towards modelling flood protection investment as a coupled human and natural system
A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation
Examination of homogeneity of selected Irish pooling groups
Estimation of high return period flood quantiles using additional non-systematic information with upper bounded statistical models
Design flood hydrographs from the relationship between flood peak and volume
Introducing empirical and probabilistic regional envelope curves into a mixed bounded distribution function
HESS Opinions "A random walk on water"
Bora Shehu and Uwe Haberlandt
Hydrol. Earth Syst. Sci., 27, 2075–2097, https://doi.org/10.5194/hess-27-2075-2023, https://doi.org/10.5194/hess-27-2075-2023, 2023
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Design rainfall volumes at different duration and frequencies are necessary for the planning of water-related systems and facilities. As the procedure for deriving these values is subjected to different sources of uncertainty, here we explore different methods to estimate how precise these values are for different duration, locations and frequencies in Germany. Combining local and spatial simulations, we estimate tolerance ranges from approx. 10–60% for design rainfall volumes in Germany.
Sara Sadri, James S. Famiglietti, Ming Pan, Hylke E. Beck, Aaron Berg, and Eric F. Wood
Hydrol. Earth Syst. Sci., 26, 5373–5390, https://doi.org/10.5194/hess-26-5373-2022, https://doi.org/10.5194/hess-26-5373-2022, 2022
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A farm-scale hydroclimatic machine learning framework to advise farmers was developed. FarmCan uses remote sensing data and farmers' input to forecast crop water deficits. The 8 d composite variables are better than daily ones for forecasting water deficit. Evapotranspiration (ET) and potential ET are more effective than soil moisture at predicting crop water deficit. FarmCan uses a crop-specific schedule to use surface or root zone soil moisture.
Andrew J. Newman, Amanda G. Stone, Manabendra Saharia, Kathleen D. Holman, Nans Addor, and Martyn P. Clark
Hydrol. Earth Syst. Sci., 25, 5603–5621, https://doi.org/10.5194/hess-25-5603-2021, https://doi.org/10.5194/hess-25-5603-2021, 2021
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This study assesses methods that estimate flood return periods to identify when we would obtain a large flood return estimate change if the method or input data were changed (sensitivities). We include an examination of multiple flood-generating models, which is a novel addition to the flood estimation literature. We highlight the need to select appropriate flood models for the study watershed. These results will help operational water agencies develop more robust risk assessments.
David Lun, Alberto Viglione, Miriam Bertola, Jürgen Komma, Juraj Parajka, Peter Valent, and Günter Blöschl
Hydrol. Earth Syst. Sci., 25, 5535–5560, https://doi.org/10.5194/hess-25-5535-2021, https://doi.org/10.5194/hess-25-5535-2021, 2021
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We investigate statistical properties of observed flood series on a European scale. There are pronounced regional patterns, for instance: regions with strong Atlantic influence show less year-to-year variability in the magnitude of observed floods when compared with more arid regions of Europe. The hydrological controls on the patterns are quantified and discussed. On the European scale, climate seems to be the dominant driver for the observed patterns.
Hossein Foroozand and Steven V. Weijs
Hydrol. Earth Syst. Sci., 25, 831–850, https://doi.org/10.5194/hess-25-831-2021, https://doi.org/10.5194/hess-25-831-2021, 2021
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In monitoring network design, we have to decide what to measure, where to measure, and when to measure. In this paper, we focus on the question of where to measure. Past literature has used the concept of information to choose a selection of locations that provide maximally informative data. In this paper, we look in detail at the proper mathematical formulation of the information concept as an objective. We argue that previous proposals for this formulation have been needlessly complicated.
Manuela I. Brunner and Eric Gilleland
Hydrol. Earth Syst. Sci., 24, 3967–3982, https://doi.org/10.5194/hess-24-3967-2020, https://doi.org/10.5194/hess-24-3967-2020, 2020
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Stochastically generated streamflow time series are used for various water management and hazard estimation applications. They provide realizations of plausible but yet unobserved streamflow time series with the same characteristics as the observed data. We propose a stochastic simulation approach in the frequency domain instead of the time domain. Our evaluation results suggest that the flexible, continuous simulation approach is valuable for a diverse range of water management applications.
Vincenzo Totaro, Andrea Gioia, and Vito Iacobellis
Hydrol. Earth Syst. Sci., 24, 473–488, https://doi.org/10.5194/hess-24-473-2020, https://doi.org/10.5194/hess-24-473-2020, 2020
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We highlight the need for power evaluation in the application of null hypothesis significance tests for trend detection in extreme event analysis. In a wide range of conditions, depending on the underlying distribution of data, the test power may reach unacceptably low values. We propose the use of a parametric approach, based on model selection criteria, that allows one to choose the null hypothesis, to select the level of significance, and to check the test power using Monte Carlo experiments.
Phuong Dong Le, Michael Leonard, and Seth Westra
Hydrol. Earth Syst. Sci., 23, 4851–4867, https://doi.org/10.5194/hess-23-4851-2019, https://doi.org/10.5194/hess-23-4851-2019, 2019
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While conventional approaches focus on flood designs at individual locations, there are many situations requiring an understanding of spatial dependence of floods at multiple locations. This research describes a new framework for analyzing flood characteristics across civil infrastructure systems, including conditional and joint probabilities of floods. This work leads to a new flood estimation paradigm, which focuses on the risk of the entire system rather than each system element in isolation.
Manuela I. Brunner, András Bárdossy, and Reinhard Furrer
Hydrol. Earth Syst. Sci., 23, 3175–3187, https://doi.org/10.5194/hess-23-3175-2019, https://doi.org/10.5194/hess-23-3175-2019, 2019
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This study proposes a procedure for the generation of daily discharge data which considers temporal dependence both within short timescales and across different years. The simulation procedure can be applied to individual and multiple sites. It can be used for various applications such as the design of hydropower reservoirs, the assessment of flood risk or the assessment of drought persistence, and the estimation of the risk of multi-year droughts.
Cong Jiang, Lihua Xiong, Lei Yan, Jianfan Dong, and Chong-Yu Xu
Hydrol. Earth Syst. Sci., 23, 1683–1704, https://doi.org/10.5194/hess-23-1683-2019, https://doi.org/10.5194/hess-23-1683-2019, 2019
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We present the methods addressing the multivariate hydrologic design applied to the engineering practice under nonstationary conditions. A dynamic C-vine copula allowing for both time-varying marginal distributions and a time-varying dependence structure is developed to capture the nonstationarities of multivariate flood distribution. Then, the multivariate hydrologic design under nonstationary conditions is estimated through specifying the design criterion by average annual reliability.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 1993–2005, https://doi.org/10.5194/hess-22-1993-2018, https://doi.org/10.5194/hess-22-1993-2018, 2018
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A new method is proposed to solve the stochastic unsteady open-channel flow system in only one single simulation, as opposed to the many simulations usually done in the popular Monte Carlo approach. The derivation of this new method gave a deterministic and linear Fokker–Planck equation whose solution provided a powerful and effective approach for quantifying the ensemble behavior and variability of such a stochastic system, regardless of the number of parameters causing its uncertainty.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 2007–2021, https://doi.org/10.5194/hess-22-2007-2018, https://doi.org/10.5194/hess-22-2007-2018, 2018
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A newly proposed method is applied to solve a stochastic unsteady open-channel flow system (with an uncertain roughness coefficient) in only one simulation. After comparing its results to those of the Monte Carlo simulations, the new method was found to adequately predict the temporal and spatial evolution of the probability density of the flow variables of the system. This revealed the effectiveness, strength, and time efficiency of this new method as compared to other popular approaches.
Liang Gao, Limin Zhang, and Mengqian Lu
Hydrol. Earth Syst. Sci., 21, 4573–4589, https://doi.org/10.5194/hess-21-4573-2017, https://doi.org/10.5194/hess-21-4573-2017, 2017
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Rainfall is the primary trigger of landslides. However, the rainfall intensity is not uniform in space, which causes more landslides in the area of intense rainfall. The primary objective of this paper is to quantify spatial correlation characteristics of three landslide-triggering large storms in Hong Kong. The spatial maximum rolling rainfall is represented by a trend surface and a random field of residuals. The scales of fluctuation of the residuals are found between 5 km and 30 km.
Elena Shevnina, Ekaterina Kourzeneva, Viktor Kovalenko, and Timo Vihma
Hydrol. Earth Syst. Sci., 21, 2559–2578, https://doi.org/10.5194/hess-21-2559-2017, https://doi.org/10.5194/hess-21-2559-2017, 2017
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This paper presents the probabilistic approach to evaluate design floods in a changing climate, adapted in this case to the northern territories. For the Russian Arctic, the regions are delineated, where it is suggested to correct engineering hydrological calculations to account for climate change. An example of the calculation of a maximal discharge of 1 % exceedance probability for the Nadym River at Nadym is provided.
M. J. Machado, B. A. Botero, J. López, F. Francés, A. Díez-Herrero, and G. Benito
Hydrol. Earth Syst. Sci., 19, 2561–2576, https://doi.org/10.5194/hess-19-2561-2015, https://doi.org/10.5194/hess-19-2561-2015, 2015
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A flood frequency analysis using a 400-year historical flood record was carried out using a stationary model (based on maximum likelihood estimators) and a non-stationary model that incorporates external covariates (climatic and environmental). The stationary model was successful in providing an average discharge around which value flood quantiles estimated by non-stationary models fluctuate through time.
L. Gaál, P. Molnar, and J. Szolgay
Hydrol. Earth Syst. Sci., 18, 1561–1573, https://doi.org/10.5194/hess-18-1561-2014, https://doi.org/10.5194/hess-18-1561-2014, 2014
P. E. O'Connell and G. O'Donnell
Hydrol. Earth Syst. Sci., 18, 155–171, https://doi.org/10.5194/hess-18-155-2014, https://doi.org/10.5194/hess-18-155-2014, 2014
A. I. Requena, L. Mediero, and L. Garrote
Hydrol. Earth Syst. Sci., 17, 3023–3038, https://doi.org/10.5194/hess-17-3023-2013, https://doi.org/10.5194/hess-17-3023-2013, 2013
S. Das and C. Cunnane
Hydrol. Earth Syst. Sci., 15, 819–830, https://doi.org/10.5194/hess-15-819-2011, https://doi.org/10.5194/hess-15-819-2011, 2011
B. A. Botero and F. Francés
Hydrol. Earth Syst. Sci., 14, 2617–2628, https://doi.org/10.5194/hess-14-2617-2010, https://doi.org/10.5194/hess-14-2617-2010, 2010
L. Mediero, A. Jiménez-Álvarez, and L. Garrote
Hydrol. Earth Syst. Sci., 14, 2495–2505, https://doi.org/10.5194/hess-14-2495-2010, https://doi.org/10.5194/hess-14-2495-2010, 2010
B. Guse, Th. Hofherr, and B. Merz
Hydrol. Earth Syst. Sci., 14, 2465–2478, https://doi.org/10.5194/hess-14-2465-2010, https://doi.org/10.5194/hess-14-2465-2010, 2010
D. Koutsoyiannis
Hydrol. Earth Syst. Sci., 14, 585–601, https://doi.org/10.5194/hess-14-585-2010, https://doi.org/10.5194/hess-14-585-2010, 2010
Cited articles
Ariff, N. M., Jemain, A. A., Ibrahim, K., and Wan Zin, W. Z.: IDF relationships using bivariate copula for storm events in Peninsular Malaysia, J. Hydrol., 470–471, 158–171, https://doi.org/10.1016/j.jhydrol.2012.08.045, 2012.
Aronica, G. T., Candela, A., Fabio, P., and Santoro, M.: Estimation of flood inundation probabilities using global hazard indexes based on hydrodynamic variables, Phys. Chem. Earth A/B/C, 42–44, 119–129, https://doi.org/10.1016/j.pce.2011.04.001, 2012.
Asquith, W.: lmomco – L-moments, censored L-moments, trimmed L-moments, L-comoments, and many distributions, r package version 2.1.4, http://www.cran.r-project.org/package=lmomco (last access: 10 May 2017), 2015.
Autorità di bacino del fiume Po: Caratteristiche del bacino del fiume Po e primo esame dell'impatto ambientale delle attività umane sulle risorse idriche, Report, Parma, Italy, 2006.
Balistrocchi, M. and Bacchi, B.: Modelling the statistical dependence of rainfall event variables through copula functions, Hydrol. Earth Syst. Sci., 15, 1959–1977, https://doi.org/10.5194/hess-15-1959-2011, 2011.
Balistrocchi, M., Ranzi, R., and Bacchi, B.: Multivariate Statistical Analysis of Flood Variables by Copulas: Two Italian Case Studies, in: 3rd IAHR Europe Congress, 14–16 April 2014, Porto, Portugal, 2014.
Brechmann, E. C. and Schepsmeier, U.: Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine, J. Stat. Softw., 52, 1–27, https://doi.org/10.18637/jss.v052.i03, 2013.
Burnham, K. P. and Anderson, D. R.: Multimodel inference understanding AIC and BIC in model selection, Sociolog. Meth. Res., 33.2, 261–304, 2004.
Candela, A., Brigandì, G., and Aronica, G. T.: Estimation of synthetic flood design hydrographs using a distributed rainfall–runoff model coupled with a copula-based single storm rainfall generator, Nat. Hazards Earth Syst. Sci., 14, 1819–1833, https://doi.org/10.5194/nhess-14-1819-2014, 2014.
Delignette-Muller, M. L. and Dutang, C.: fitdistrplus: An R Package for Fitting Distributions, J. Stat. Softw., 64, 1–34, https://doi.org/10.18637/jss.v064.i04, 2015.
De Michele, C. and Rosso, R.: A multi-level approach to flood frequency regionalisation, Hydrol. Earth Syst. Sci., 6, 185–194, https://doi.org/10.5194/hess-6-185-2002, 2002.
De Michele, C. and Salvadori, G.: A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-Copulas, J. Geophys. Res.-Atmos., 108, 4067, https://doi.org/10.1029/2002JD002534, 2003.
De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., and Rosso, R.: Bivariate Statistical Approach to Check Adequacy of Dam Spillway, J. Hydrol. Eng., 10, 50–57, https://doi.org/10.1061/(ASCE)1084-0699(2005)10:1(50), 2005.
Domeneghetti, A., Vorogushyn, S., Castellarin, A., Merz, B., and Brath, A.: Probabilistic flood hazard mapping: effects of uncertain boundary conditions, Hydrol. Earth Syst. Sci., 17, 3127–3140, https://doi.org/10.5194/hess-17-3127-2013, 2013.
Dung, N. V., Merz, B., Bárdossy, A., and Apel, H.: Handling uncertainty in bivariate quantile estimation – An application to flood hazard analysis in the Mekong Delta, J. Hydrol., 527, 704–717, https://doi.org/10.1016/j.jhydrol.2015.05.033, 2015.
Duong, T.: ks: Kernel Smoothing, r package version 1.10.4, http://CRAN.R-project.org/package=ks (last access: 10 May 2017), 2016.
Durante, F. and Sempi, C.: Principles of copula theory, CRC Press, Boca Raton, Florida, 2015.
Dyck, S. and Peschke, G.: Grundlagen der Hydrologie, Verlag für Bauwesen, Berlin, 1995.
Faraway, J., Marsaglia, G., Marsaglia, J., and Baddeley, A.: goftest: Classical Goodness-of-Fit Tests for Univariate Distributions, r package version 1.0-3, http://CRAN.R-project.org/package=goftest (last access: 10 May 2017), 2015.
Fellows, I.: wordcloud: Word Clouds, r package version 2.5, http://CRAN.R-project.org/package=wordcloud (last access: 10 May 2017), 2014.
Frahm, G., Junker, M., and Schmidt, R.: Estimating the tail-dependence coefficient: Properties and pitfalls, Insur. Math. Econ., 37, 80–100, https://doi.org/10.1016/j.insmatheco.2005.05.008, 2005.
Gambarelli, P., Moretti, G., and Orlandini, S.: Sviluppo di un Modello Matematico del Funzionamento Idraulico della Cassa di Espansione sul Fiume Panaro, Thesis, Università degli Studi di Modena e Reggio Emilia, Modena, Italy, 2009.
Ganguli, P. and Reddy, M. J.: Probabilistic assessment of flood risks using trivariate copulas, Theor. Appl. Climatol., 111, 341–360, https://doi.org/10.1007/s00704-012-0664-4, 2013.
Gaume, E., Gaál, L., Viglione, A., Szolgay, J., Kohnová, S., and Blöschl, G.: Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites, J. Hydrol., 394, 101–117, https://doi.org/10.1016/j.jhydrol.2010.01.008, 2010.
Genest, C. and Favre, A.: Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask, J. Hydrol. Eng., 12, 347–368, https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347), 2007.
Gräler, B., van den Berg, M. J., Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B., and Verhoest, N. E. C.: Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation, Hydrol. Earth Syst. Sci., 17, 1281–1296, https://doi.org/10.5194/hess-17-1281-2013, 2013.
Halbert, K., Nguyen, C. C., Payrastre, O., and Gaume, E.: Reducing uncertainty in flood frequency analyses: A comparison of local and regional approaches involving information on extreme historical floods, J. Hydrol., 541, 90–98, https://doi.org/10.1016/j.jhydrol.2016.01.017, 2016.
Hyndman, R. J.: Computing and Graphing Highest Density Regions, Am. Statist., 50, 120–126, https://doi.org/10.2307/2684423, 1996.
Joe, H.: Dependence modeling with copulas, Chapman and Hall/CRC Press, London, 2014.
Kojadinovic, I. and Yan, J.: Modeling Multivariate Distributions with Continuous Margins Using the copula R Package, J. Stat. Softw., 34, 1–20, https://doi.org/10.18637/jss.v034.i09, 2010.
Merz, R. and Blöschl, G.: Flood frequency hydrology: 1. Temporal, spatial, and causal expansion of information, Water Resour. Res., 44, W08432, https://doi.org/10.1029/2007WR006744, 2008.
Nelsen, R. B.: An introduction to copulas, in: vol. 139, Springer Science & Business Media, New York, 2006.
Nora, E. and Ghinoi, A.: Alluvioni e terremoti: Principali rischi naturali di Modena nel Novecento, http://www.comune.modena.it/lecittasostenibili/documenti-cittasostenibili/annale-900-citt-ambiente/alluvioni-e-terremoti (last access: 10 May 2017), 2009.
Ouarda, T. B. M. J. and El-Adlouni, S.: Bayesian Nonstationary Frequency Analysis of Hydrological Variables, J. Am. Water Resour. Assoc., 47, 496–505, https://doi.org/10.1111/j.1752-1688.2011.00544.x, 2011.
Parent, E. and Bernier, J.: Encoding prior experts judgments to improve risk analysis of extreme hydrological events via POT modeling, J. Hydrol., 283, 1–18, https://doi.org/10.1016/S0022-1694(03)00080-5, 2003.
Parkes, B. and Demeritt, D.: Defining the hundred year flood: A Bayesian approach for using historic data to reduce uncertainty in flood frequency estimates, J. Hydrol., 540, 1189–1208, https://doi.org/10.1016/j.jhydrol.2016.07.025, 2016.
R Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/ (last access: 10 May 2017), 2015.
Reis Jr., D. S. and Stedinger, J. R.: Bayesian MCMC flood frequency analysis with historical information, J. Hydrol., 313, 97–116, https://doi.org/10.1016/j.jhydrol.2005.02.028, 2005.
Requena, A. I., Mediero, L., and Garrote, L.: A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation, Hydrol. Earth Syst. Sci., 17, 3023–3038, https://doi.org/10.5194/hess-17-3023-2013, 2013.
Rob J Hyndman with contributions from Jochen Einbeck and Matt Wand: hdrcde: Highest density regions and conditional density estimation, r package version 3.1, http://CRAN.R-project.org/package=hdrcde (last access: 10 May 2017), 2013.
Salvadori, G. and De Michele, C.: On the Use of Copulas in Hydrology: Theory and Practice, J. Hydrol. Eng., 12, https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(369), 2007.
Salvadori, G., De Michele, C., Kottegoda, N., and Rosso, R.: Extremes in Nature: An Approach Using Copulas, Water Science and Technology Library, 1st Edn., Springer Netherlands, https://doi.org/10.1007/1-4020-4415-1, 2007.
Salvadori, G., Durante, F., Tomasicchio, G. R., and D'Alessandro, F.: Practical guidelines for the multivariate assessment of the structural risk in coastal and off-shore engineering, Coast. Eng., 95, 77–83, https://doi.org/10.1016/j.coastaleng.2014.09.007, 2015.
Schmidt, R. and Stadtmüller, U.: Non-parametric Estimation of Tail Dependence, Scand. J. Stat., 33, 307–335, https://doi.org/10.1111/j.1467-9469.2005.00483.x, 2006.
Serinaldi, F.: An uncertain journey around the tails of multivariate hydrological distributions, Water Resour. Res., 49, 6527–6547, https://doi.org/10.1002/wrcr.20531, 2013.
Serinaldi, F.: Can we tell more than we can know? The limits of bivariate drought analyses in the United States, Stoch. Environ. Res. Risk A., 30, 1691–1704, https://doi.org/10.1007/s00477-015-1124-3, 2016.
Serinaldi, F., Bárdossy, A., and Kilsby, C. G.: Upper tail dependence in rainfall extremes: would we know it if we saw it?, Stoch. Environ. Res. Risk A., 29, 1211–1233, https://doi.org/10.1007/s00477-014-0946-8, 2015.
Servizio Idrografico Italiano: Dati Caratteristici dei Corsi d'Aqcua Italiani, Ministero dei Lavori Pubblici, Istituto Poligrafico dello Stato, Roma, 1939, 1953.
Singh, V. P.: Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph, Hydrol. Process., 11, 1649–1669, https://doi.org/10.1002/(SICI)1099-1085(19971015)11:12<1649::AID-HYP495>3.0.CO;2-1, 1997.
Singh, V. P. and Zhang, L.: IDF Curves Using the Frank Archimedean Copula, J. Hydrol. Eng., 12, 651–662, https://doi.org/10.1061/(ASCE)1084-0699(2007)12:6(651), 2007.
Sklar, M.: Fonctions de répartition à n dimensions et leurs marges, Université Paris 8, Paris, 1959.
Smyth, G., Hu, Y., Dunn, P., Phipson, B., and Chen, Y.: statmod: Statistical Modeling, r package version 1.4.21, http://CRAN.R-project.org/package=statmod (last access: 10 May 2017), 2015.
Statisticat, LLC: LaplacesDemon: Complete Environment for Bayesian Inference, r package version 16.0.1, https://cran.r-project.org/web/packages/LaplacesDemon/ (last access: 10 May 2017), 2016.
Urbanek, S. and Horner, J.: Cairo: R graphics device using cairo graphics library for creating high-quality bitmap (PNG, JPEG, TIFF), vector (PDF, SVG, PostScript) and display (X11 and Win32) output, r package version 1.5-9, http://CRAN.R-project.org/package=Cairo (last access: 10 May 2017), 2015.
Viglione, A., Merz, R., Salinas, J. L., and Blöschl, G.: Flood frequency hydrology: 3. A Bayesian analysis, Water Resour. Res., 49, 675–692, https://doi.org/10.1029/2011WR010782, 2013.
Volpi, E. and Fiori, A.: Hydraulic structures subject to bivariate hydrological loads: Return period, design, and risk assessment, Water Resour. Res., 50, 885–897, https://doi.org/10.1002/2013WR014214, 2014.
Yan, J.: Enjoy the Joy of Copulas: With a Package copula, J. Stat. Softw., 21, 1–21, https://doi.org/10.18637/jss.v021.i04, 2007.
Yee, T. W.: The VGAM Package for Categorical Data Analysis, J. Stat. Softw., 32, 1–34, https://doi.org/10.18637/jss.v032.i10, 2010.
Zhang, L. and Singh, V. P.: Bivariate rainfall frequency distributions using Archimedean copulas, J. Hydrol., 332, 93–109, https://doi.org/10.1016/j.jhydrol.2006.06.033, 2007.
Zhang, Q., Xiao, M., and Singh, V. P.: Uncertainty evaluation of copula analysis of hydrological droughts in the East River basin, China, Global Planet. Change, 129, 1–9, https://doi.org/10.1016/j.gloplacha.2015.03.001, 2015.
Short summary
In this research, we explored how the sampling uncertainty of flood variables (flood peak, volume, etc.) can reflect on a structural variable, which in our case was the maximum water level (MWL) of a reservoir controlled by a dam. Next, we incorporated additional information from different sources for a better estimation of the uncertainty in the probability of exceedance of the MWL. Results showed the importance of providing confidence intervals in the risk assessment of a structure.
In this research, we explored how the sampling uncertainty of flood variables (flood peak,...