Abstract
Severe flooding in coastal areas can result from the joint probability of oceanographic, hydrological, and meteorological factors, resulting in compound flooding (CF) events. Recently, copula functions have been used to enable a much more flexible environment in joint modelling. Incorporating a higher dimensional copula framework via symmetric 3-D Archimedean or elliptical copulas has statistical limits, and the preservation of all lower-level dependencies would be impossible. The heterogeneous dependency in CF events can be effectively modelled via a fully nested Archimedean (FNA) copula. Incorporating FNA under parametric settings is insufficiently flexible since it is restricted by the prior distributional assumption of the function type for both marginal density and copulas in parametric fittings. If the marginal density is of a specific parametric distribution, it could be problematic if underlying assumptions are violated. This study introduces a 3-D FNA copula simulation in a semiparametric setting by introducing nonparametric marginal distributions conjoined with parametric copula density. The derived semiparametric FNA copula is applied in the trivariate model in compounding the joint impact of rainfall, storm surge, and river discharge based on 46 years of observations on the west coast of Canada. The performance of the derived model has also been compared with the FNA copula constructed with parametric marginal density. It is concluded that the performance of FNA with nonparametric marginals outperforms the FNA copula built under parametric settings. The derived model is employed in multivariate analysis of flood risks in trivariate primary joint and conditional joint return periods. The trivariate hydrologic risk is analyzed using failure probability (FP) statistics. The investigation reveals that trivariate events produce a higher FP than bivariate (or univariate) events; thus, neglecting trivariate joint analysis results in FP being underestimated. Moreover, it indicates that trivariate hydrologic risk values increase with an increase in the service time of hydraulic facilities.
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Data Availability
Data used in the presented research are available at https://tides.gc.ca/eng/data (CWL data); https://wateroffice.ec.gc.ca/search/historical_e.html (daily streamflow discharge records); https://climate.weather.gc.ca/ (daily rainfall data).
References
Aas K, Berg D (2009) Models for construction of multivariate dependence—A comparison study. Eur J Finance 15:639–659
Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19(6):716–723
Adamowski K (1985) Nonparametric kernel estimation of flood frequencies. Water Resour Res 21(11):1885–1890
Adamowski K (1996) Nonparametric estimations of low-flow frequencies. J Hydraul Eng 122(1):46–49
Anderson TW, Darling DA (1954) A test of goodness of fit. J Am Stat Assoc 49(268):765–769
Atkinson DE, Forbes DL, James TS (2016) Dynamic coasts in a changing climate; in Canada's Marine Coasts in a Changing Climate, (ed.) D.S. Lemmen, F.J. Warren, T.S. James and C.S.L. Mercer Clarke; Government of Canada, Ottawa, Ontario, p. 27–68
Bardsley WE (1988) Toward a general procedure for analysis of extreme random events in the earth sciences. Math Geol 20(5):513–528
Bates PD, Dawson RJ, Hall JW, Horritt MS, Nicholls RJ, Wicks J, Hassan MAAM (2005) Simplified two-dimensional numerical modelling of coastal flooding and example applications. Coast Eng 52:793–810. https://doi.org/10.1016/j.coastaleng.2005.06.001
Bennett ND, Croke BFW, Guarios G, Guillaume JHA, Hamilton SH, Jakeman AJ, Marsili-Libeli S, Newham LTH, Norton JP, Perrin C, Pierce SA, Robson B, Seppelt R, Voinov AA, Fath BD (2013) Characterising performance of environmental models. Environ Model Softw 40:1–20
Bevacqua E, Maraun D, Hobæk Haff I, Widmann M, Vrac M (2017) Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy). Hydrol Earth Syst Sci 21:2701–2723
Bisht DS, Chatterjee C, Raghuwanshi NS, Sridhar V (2017) Spatio-temporal trends of rainfall across Indian River basins. Theor Appl Climatol 80:1–18
Brunner MI, Favre A, Seibert J (2016) Bivariate return periods and their importance for flood peak and volume estimations. Wiley Interdiscip Rev Water 3(6):819–833. https://doi.org/10.1002/wat2.1173
Capéraà P, Fougères AL, Genest C (1997) A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika 84(3):567–577
Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)? Arguments against avoiding RMSE in the literature. Geosci Model Dev 7:1247–1250
Charpentier A, Fermanian J, Scaillet O (2006) Copulas: from theory to application in finance, 1st edn. Risk Books, Torquay, UK, chap The Estimation of Copulas: Theory and Practice
Chen S (2015) Optimal bandwidth selection for kernel density functionals estimation. J Probab Stat 2015:1–21. https://doi.org/10.1155/2015/242683
Church JA, Clark PU, Cazenave A, Gregory JM, Jevrejeva S, Levermann A, Merrifield MA, Milne GA, Nerem RS, Nunn PD, Payne AJ, Pfeffer WT, Stammer D, Unnikrishnan AS (2013) Sea Level Change. In Climate ChangeIn Climate Change 2013: The Physical Science Basis, Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental, Panel on Climate Change edited by: Stocker, T. F., Qin, D., Plattner, G.-K., Tignor, M., Allen, S. K., Boschung, J., Nauels, A., Xia, Y., Bex, V., and Midgley, P. M., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 2013
Coles S, Heffernan J, Tawn J (1999) Dependence measures for extreme value analyses. Extremes 2(4):339–365
Coles SG (2001) An introduction to statistical modelling of extreme values. Springer, London
Couasnon A, Eilander D, Muis S, Veldkamp TIE, Haigh ID, Wahl T, Ward PJ (2020) Measuring compound flood potential from river discharge and storm surge extremes at the global scale. Nat Hazards Earth Syst Sci 20(2):489–504. https://doi.org/10.5194/nhess-20-489-2020
Cramér H (1928) On the composition of elementary errors. Scand Actuar J 1928(1):13–74. https://doi.org/10.1080/03461238.1928.10416862
Daneshkhan A, Remesan R, Omid C, Holman IP (2016) Probabilistic modelling of food characteristics with parametric and minimum information pair-copula model. J Hydrol 540:469–487
Efromovich S (1999) Nonparametric curve estimation: Methods. Springer-Verlag, New York, NY, Theory and Applications
Fan L, Zheng Q (2016) Probabilistic modelling of flood events using the entropy copula. Adv Water Resour 97:233–240. https://doi.org/10.1016/2Fj.advwatres.2016.09.016
Farrel PJ, Stewart KR (2006) Comprehensive study of tests for normality and symmetry: Extending the Spiegelhalter test. J Stat Comput Simul 76:803–816. https://doi.org/10.1080/10629360500109023
Frahm G, Junker M, Schmidt R (2005) Estimating the tail-dependence coefficient: Properties and pitfalls. Insur Math Econ 37(1):80–100. https://doi.org/10.1016/j.insmatheco.2005.05.008
Genest C, Favre AC, Beliveau J, Jacques C (2007) Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resour Res 43:W09401. https://doi.org/10.1029/2006WR005275
Genest C, Rémillard B (2008) Validity of the parametric bootstrap for goodness-of-ft testing in semiparametric models. Ann l’Inst Henri Poincare Prob Stat 44:1096–1127
Genest C, Rémillard B, Beaudoin D (2009) Goodness-of-fit tests for copulas: A review and a power study. Insur Math Econ 44(2):199–213. https://doi.org/10.1016/j.insmatheco.2007.10.005
Ghanbari M, Arabi M, Kao S, Obeysekera J, Sweet W (2021) Climate change and changes in compound coastal-riverine flooding hazard along the U.S. coasts. Earth’s Future 9(5). https://doi.org/10.1029/2021ef002055
Grimaldi S, Serinaldi F (2006) Asymmetric copula in multivariate flood frequency analysis. Adv Water Resour 29:1155–1167. https://doi.org/10.1016/j.advwatres.2005.09.005
Gringorten II (1963) A plotting rule of extreme probability paper. J Geophys Res 68(3):813–814
Hannan EJ, Quinn BG (1979) The determination of the order of an autoregression. J R Stat Soc Ser B Methodol 41(2):190–195. Portico. https://doi.org/10.1111/j.2517-6161.1979.tb01072.x
Hardle W (1991) Kernel density estimation. In: Smoothing techniques. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4432-5_2
Haylock M, Nicholls N (2015) Trends in extreme rainfall indices for an updated high quality data set for Australia, 1910–1998. Int J Climatol 20(13):1533–1541
Hendry A, Haigh ID, Nicholls RJ, Winter H, Neal R, Wahl T, Joly-Laugel A, Darby SE (2019) Assessing the characteristics and drivers of compound flooding events around the UK coast. Hydrol Earth Syst Sci 23:3117–3139. https://doi.org/10.5194/hess-23-3117-2019
Hofert M, Pham D (2013) Densities of nested Archimedean copulas. J Multivar Anal 118:37–52
Huang Q, Chen Z (2015) Multivariate flood risk assessment based on the secondary return period. J Lake Sci 27(2):352–360. https://doi.org/10.18307/2015.0221
James TS, Henton JA, Leonard LJ, Darlington A, Forbes DL, Craymer M (2014) Relative sealevel projections in Canada and the adjacent Mainland United States. Geological Survey of Canada Open File 7737:72. https://doi.org/10.4095/295574
Joe H (1997) Multivariate models and dependence concept. CRC Press, Boca Raton, FL, USA
Kao S, Govindaraju R (2008) Trivariate statistical analysis of extreme rainfall events via the Plackett family copulas. Water Resour Res 44. https://doi.org/10.1029/2007WR006261.
Karmakar S, Simonovic SP (2009) Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions. J Flood Risk Manag 2(1):32–44. https://doi.org/10.1111/j.1753-318x.2009.01020.x
Kendall MG (1975) Rank correlation methods, 4th edn. Charles Griffn, London, p 1975
Kim KD, Heo JH (2002) Comparative study of flood quantiles estimation by nonparametric models. J Hydrol 260:176–193
Kim TW, Valdes JB, Yoo C (2006) Nonparametric approach for bivariate drought characterization using Palmer drought index. J Hydrol Eng 11(2):134–143
Klein B, Schumann AH, Pahlow M (2011) Copulas-New risk assessment methodology for dam safety, food risk assessment and management. Springer, pp 149–185
Kojadinovic I, Yan J (2010) Modeling multivariate distributions with continuous margins using the copula R package. J Stat Softw 34(9):1–20
Krstanovic PF, Singh VP (1987) A multivariate stochastic flood analysis using entropy. Hydrologic Frequency Modeling 515–539. https://doi.org/10.1007/978-94-009-3953-0_37
Kurowicka D, Cooke R (2006) Uncertainty analysis with high dimensional dependence modelling. John Wiley
Latif S, Mustafa F (2020) A nonparametric copula distribution framework for bivariate joint distribution analysis of flood characteristics for the Kelantan River basin in Malaysia. AIMS Geosci 6(2):171–198. https://doi.org/10.3934/geosci.2020012
Latif S, Mustafa F (2021) Bivariate joint distribution analysis of the flood characteristics under semiparametric copula distribution framework for the Kelantan River basin in Malaysia. J Ocean Eng Sci 6(2):128–145. https://doi.org/10.1016/j.joes.2020.06.003
Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241
Lian JJ, Xu K, Ma C (2013) Joint impact of rainfall and tidal level on flood risk in a coastal city with a complex river network: a case study of Fuzhou City, China. Hydrol Earth Syst Sci 17(679–689):2013. https://doi.org/10.5194/hess-17-679-2013
Ljung GM, Box GEP (1978) On a measure of lack of ft in time series models. Biometrika 65:297–303
Mann HB (1945) Nonparametric test against trend. Econometrics 13:245–259
Masina M, Lamberti A, Archetti R (2015) Coastal flooding: A copula based approach for estimating the joint probability of water levels and waves. Coast Eng 97:37–52. https://doi.org/10.1016/j.coastaleng.2014.12.010
Milly PCD, Wetherald RT, Dunne KA, Delworth TL (2002) Increasing risk of great floods in a changing climate. Nature 415(6871):514–517
Mirabbasi R, Kakheri-Fard A, Dinpashoh Y (2012) Bivariate drought frequency analysis using the copula method. Theor Appl Climatol 108:191–206. https://doi.org/10.1007/s00704-011-0524-7
Moftakhari H, Schubert JE, AghaKouchak A, Matthew RA, Sanders BF (2019) Linking statistical and hydrodynamic modeling for compound flood hazard assessment in tidal channels and estuaries. Adv Water Resour 128:28–38. https://doi.org/10.1016/j.advwatres.2019.04.009
Moftakhari HR, Salvadori G, AghaKouchak A, Sanders BF, Matthew RA (2017) Compounding effects of sea level rise and fluvial flooding. Proc Natl Acad Sci 114(37):9785–9790. https://doi.org/10.1073/pnas.1620325114
Moon Y-I, Lall U (1993) A kernel quantile function estimator for flood frequency analysis. Rep Pap 194. https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1193&context=water_rep. Accessed 16 Mar 2022
Moon Y-I, Lall U (1994) Kernel function estimator for flood frequency analysis. Water Resour Res 30(11):3095–3103
Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900
Nash J, Sutcliffe J (1970) River flow forecasting through conceptual models part I a discussion of principles. J Hydrol 10(3):282e290
Nelsen RB (2006) An introduction to copulas. Springer, New York
Okhrin O (2020) https://cran.r-project.org/web/packages/HAC/HAC.pdf. Accessed 19 Apr 2022
Okhrin O, Ristig A (2014) Hierarchical Archimedean copulae: The HAC package. J Stat Softw 58(4):1–20. https://www.jstatsoft.org/v58/i04/. Accessed 6 Mar 2022
Okhrin O, Ristig A, Sheen J, Trueck S (2015) Conditional systemic risk with penalized copula, SFB 649 discussion paper 2015–038, sonderforschungsbereich 649. Humboldt University, Germany
Owen CEB (2008) Parameter estimation for the beta distribution. All Thesis and Disertation 1614. https://scholarsarchive.byu.edu/etd/1614. Accessed 10 Feb 2022
Padgett J, DesRoches R, Nielson B, Yashinsky M, Kwon O-S, Burdette N, Tavera E (2008) Bridge damage and repair costs from hurricane Katrina. J Bridge Eng 13:6–14. https://doi.org/10.1061/(ASCE)1084-0702(2008)13:1(6)
Paprotny D, Vousdoukas MI, Morales-Nápoles O, Jonkman SN, Feyen L (2018) Compound flood potential in Europe. Hydrol Earth Syst Sci Discuss. https://doi.org/10.5194/hess-2018-132
Pirani FJ, Najafi MR (2020) Recent trends in individual and multivariate flood drivers in Canada's Coasts. Water Resour Res 56(8). https://doi.org/10.1029/2020WR027785
Poulin A, Huard D, Favre AC, Pugin S (2007) Importance of tail dependence in bivariate frequency analysis. J Hydrol Eng 12(4):394–403. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(394)
Public Safety Canada (2022) Adapting to rising flood risk: An analysis of insurance solutions for Canada is a report by Canada’s task force on flood insurance and relocation (2022-2023). ISBN: 978-0-660-43841-2. https://www.publicsafety.gc.ca/cnt/rsrcs/pblctns/dptng-rsng-fld-rsk-2022/index-en.aspx]
Rauf AUF, Zeephongsekul P (2014) Analysis of Rainfall Severity and Duration in Victoria, Australia using Nonparametric Copulas and Marginal Distributions. Water Resour Manage 28(13):4835–4856. https://doi.org/10.1007/s11269-014-0779-8
Read LK, Vogel RM (2015) Reliability, return periods, and risk under nonstationarity. Water Resour Res 51(8):6381–6398. https://doi.org/10.1002/2015wr017089
Reddy MJ, Ganguli P (2012) Bivariate flood frequency analysis of upper Godavari River flows using archimedean copulas. Water Resour Manag. https://doi.org/10.1007/s11269-012-0124-z
Reddy MJ, Ganguli P (2013) Probabilistic assessments of flood risks using trivariate copulas. Theor Appl Climatol 111:341–360. https://doi.org/10.1007/s00704-012-0664-4
Resio DT, Westerink JJ (2008) Modeling the physics of storm surges. Phys Today 61(9). https://doi.org/10.1063/1.2982120
Saklar A (1959) Functions de repartition n dimensions et leurs marges. Publications De L’institut De Statistique De L’université De Paris 8:229–231
Salvadori G (2004) Bivariate return periods via-2 copulas. J R Stat Soc Ser B 1:129–144
Salvadori G, De Michele C (2004) Frequency analysis via copulas: theoretical aspects and applications to hydrological events. Water Resour Res 40:W12511. https://doi.org/10.1029/2004WR003133
Salvadori G, De Michele C (2010) Multivariate multiparameters extreme value models and return periods: a copula approach. Water Resour Res. https://doi.org/10.1029/2009WR009040
Salvadori G, De Michele C, Durante F (2011) Multivariate design via copulas. Hydrol Earth Sys Sci Discuss 8(3):5523–5558. https://doi.org/10.5194/hessd-8-5523-2011
Santhosh D, Srinivas VV (2013) Bivariate frequency analysis of flood using a diffusion kernel density estimators. Water Resour Res 49:8328–8343. https://doi.org/10.1002/2011WR0100777
Savu C, Trede M (2010) Hierarchies of Archimedean copulas. Quant. Finance 10(3):295–304. https://doi.org/10.1080/14697680902821733
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2). https://doi.org/10.1214/aos/1176344136
Scott DW, Terrell GR (1987) Biased and unbiased cross-validation in density estimation. J Am Stat Assoc 82(400):1131–1146. https://doi.org/10.1080/01621459.1987.10478550
Seneviratne S, Nicholls N, Easterling D, Goodess C, Kanae S, Kossin J, Luo Y, Marengo J, McInnes K, Rahimi M, Reichstein M, Sorteberg A, Vera C, Zhang X (2012) Changes in climate extremes and their impacts on the natural physical environment. Manag Risk Extrem Events Disasters Adv Clim Chang Adapt 109–230. Available at: https://www.ipcc.ch/pdf/special-reports/srex/SREX-Chap3_FINAL.pdf
Serinaldi F (2015) Dismissing return periods! Stoch Environ Res Risk Assess 29(4):1179–1189
Serinaldi F, Grimaldi S (2007) Fully nested 3-copula procedure and application on hydrological data. J Hydrol Eng 12(4):420–430. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(420)
Sevat E, Dezetter A (1991) Selection of calibration objective functions in the context of rainfall-runoff modeling in a sudanese savannah area. Hydrol Sci J 36(4):307–330
Sharma A, Lall U, Tarboton DG (1998) Kernel bandwidth selection for a first order nonparametric streamflow simulation model. Stoch Hydrol Hydraul 12:33–52
Sheather SJ, Jones MC (1991) A reliable data-based bandwidth selection method for kernel density estimation. J Roy Stat Soc B 53:683–690
Shiau JT (2003) Return period of bivariate distributed hydrological events. Stoch Environ Res Risk Assess 17(1–2):42–57. https://doi.org/10.1007/s00477-003-0125-9
Shiau JT (2006) Fitting drought duration and severity with two dimensional copulas. Water Resour Manag 20(5):795–815. https://doi.org/10.1007/s11269-005-9008-9
Silverman BW (1986) Density estimation for statistics and data analysis, 1st edn. Chapman and Hall, London
Singh J, Knapp HV, Demissie M (2004) Hydrologic modeling of the Iroquois River watershed using HSPF and SWAT. ISWS CR 2004–08. Champaign, Ill.: Illinois State Water Survey. Available at: www.sws.uiuc.edu/pubdoc/CR/ISWSCR2004-08.pdf. Accessed 8 Sept 2005
Svensson C, Jones DA (2002) Dependence between extreme sea surge, river flow and precipitation in eastern Britain. Int J Climatol 22:1149–1168. https://doi.org/10.1002/joc.794
Tarboton DG, Sharma A, Lall U (1998) Disaggregation procedures for stochastic hydrology based on nonparametric density estimation. Water Resour Res 34(1):107–119. Portico. https://doi.org/10.1029/97wr02429
von Mises RE (1928) Wahrscheinlichkeit, Statistik und Wahrheit. Julius Springer
Wahl T, Jain S, Bender J, Meyers SD, Luther ME (2015) Increasing risk of compound flooding from storm surge and rainfall for major US cities. Nat Clim Change 5(12):1093–1097. https://doi.org/10.1038/nclimate2736
Wand MP, Jones MC (1995) Kernel Smoothing. Chapman and Hall, London, UK
Whelan N (2004) Sampling from Archimedean copulas. Quant. Finance 4(3):339–352
Willmott C, Matsuura K (2005) Advantage of the Mean Absolute Error (MAE) OVER THE Root Mean Square Error (RMSE) in assessing average model performance. Clim Res 30:79–82
Wong G, Lambert MF, Leonard M, Metcalfe AV (2010) Drought analysis using trivariate copulas conditional on climatic states. J Hydrol Eng 15(2):129–141. https://doi.org/10.1061/(asce)he.1943-5584.0000169
Xu K, Ma C, Lian J, Bin L (2014) Joint probability analysis of extreme precipitation and storm tide in a coastal city under changing environment. PLoS ONE 9(10):e109341–e109341
Xu H, Xu K, Lian J, Ma C (2019) Compound effects of rainfall and storm tides on coastal flooding risk. Stoch Env Res Risk Assess 33:1249–1261
Xu Y, Huang G, Fan Y (2015) Multivariate Flood Risk Analysis for Wei River. Stoch Env Res Risk Assess 31(1):225–242. https://doi.org/10.1007/s00477-015-1196-0
Yue S (1999) Applying the bivariate normal distribution to flood frequency analysis. Water Int 24(3):248–252
Yue S (2001) A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Process 15:1033–1045
Yue S, Rasmussen P (2002) Bivariate frequency analysis: discussion of some useful concepts in hydrological applications. Hydrol Process 16:2881–2898
Zellou B, Rahali H (2019) Assessment of the joint impact of extreme rainfall and storm surge on the risk of flooding in a coastal area. J Hydrol 569:647–665. https://doi.org/10.1016/j.jhydrol.2018.12.028
Zhang L, Singh VP (2007) Trivariate flood frequency analysis using the Gumbel-Hougaard copula. J Hydrol Eng 12(4):431–439. https://doi.org/10.1061/(ASCE)1084-0699(2007)12:4(431)
Zheng F, Seth W, Michael L, Sisson SA (2014) Modeling dependence between extreme rainfall and storm surge to estimate coastal flooding risk. Water Resour Res 50(3):2050–2071
Zheng F, Westra S, Sisson SA (2013) Quantifying the between extreme rainfall and storm surge in the coastal zone. J Hydrol 505:172–187
Acknowledgements
We are thankful to Fisheries and Ocean Canada for providing the coastal water level observations and Environment and Climate Change Canada for daily streamflow discharge records. Special thanks to Canadian Hydrographic Service for providing tide data. We are special thanks for the funding provided by NSERC and ICLR.
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This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) collaborative grant with the Institute for Catastrophic Loss Reduction (ICLR) to the second author (Slobodan P. Simonovic).
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Shahid Latif (SL): Conceptualization, Methodology, Software, Visualization, Investigation, Validation, Writing-Original draft preparation. Slobodan P. Simonovic (SPS): Supervision. Conceptualization, Writing- Reviewing and Editing.
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Latif, S., Simonovic, S.P. Trivariate Probabilistic Assessments of the Compound Flooding Events Using the 3-D Fully Nested Archimedean (FNA) Copula in the Semiparametric Distribution Setting. Water Resour Manage 37, 1641–1693 (2023). https://doi.org/10.1007/s11269-023-03448-6
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DOI: https://doi.org/10.1007/s11269-023-03448-6