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“An Introduction to Copulas.” Springer Series in Statistics (2006). “A Generalized Pareto Intensity-Duration Model of Storm Rainfall Exploiting 2-Copulas.” Journal of Geophysical Research 108, no. "Fonctions de repartition an dimensions et leurs marges." Publ. “Probabilistic Assessment of Flood Risks Using Trivariate Copulas.” Theoretical and Applied Climatology 111, no. “Bivariate Return Periods via 2-Copulas.” Statistical Methodology 1, no. “Multivariate Return Periods in Hydrology: a Critical and Practical Review Focusing on Synthetic Design Hydrograph Estimation.” Hydrology and Earth System Sciences 17, no. “Joint Modeling of Flood Peak Discharges, Volume and Duration: a Case Study of the Danube River in Bratislava.” Journal of Hydrology and Hydromechanics 62, no. “A Comparison of Two Bivariate Extreme Value Distributions.” Stochastic Environmental Research and Risk Assessment (SERRA) 18, no. “The Gumbel Mixed Model for Flood Frequency Analysis.” Journal of Hydrology 226, no. Yue, S, T.B.M.J Ouarda, B Bobée, P Legendre, and P Bruneau. “Bivariate Flood Frequency Analysis Using the Copula Function: a Case Study of the Litija Station on the Sava River.” Hydrological Processes 29, no. Sraj, Mojca, Nejc Bezak, and Mitja Brilly. “Trivariate Flood Frequency Analysis Using the Gumbel–Hougaard Copula.” Journal of Hydrologic Engineering 12, no. “Bivariate Frequency Analysis: Discussion of Some Useful Concepts in Hydrological Application.” Hydrological Processes 16, no. Doctoral dissertation, Beijing Normal University (2005).
“Multivariate hydrological frequency analysis and risk mapping”. "The bivariate lognormal distribution to model a multivariate flood episode." Hydrological Processes 14, no. “Multivariate Modeling of Flood Flows.” Journal of Hydraulic Engineering 124, no. “Bivariate Flood Frequency Analysis of Upper Godavari River Flows Using Archimedean Copulas.” Water Resources Management 26, no. “A Compilation of Data on European Flash Floods.” Journal of Hydrology 367, no. Gaume, Eric, Valerie Bain, Pietro Bernardara, Olivier Newinger, Mihai Barbuc, Allen Bateman, Lotta Blaškovičová, et al. “Increasing Risk of Great Floods in a Changing Climate.” Nature 415, no. Overall, this study could provide a basis for making an appropriate flood defence plan and long-lasting infrastructure designs. Investigation revealed that the value of bivariate hydrologic risk statistics incrementally increases over the project lifetime (i.e., 30, 50, and 100 years) service time, and at the same time, it incrementally decreases in the return period of flood volume and duration. Similarly, the variations in bivariate hydrologic risk with the changes of flood peak in the different synthetic flood volume and duration series (i.e., 5, 10, 20, 50 and 100 years return periods) under different service lifetimes are demonstrated. In addition, we found that ignoring the mutual dependency can underestimate the failure probabilities where the univariate events produced a lower failure probability than the bivariate events. The bivariate hydrologic risks of flood peak flow and volume pair, and flood peak flow and duration pair in different return periods (i.e., 5, 10, 20, 50 and 100 years) were estimated and revealed that the risk statistics incrementally increase in the service lifetime and, at the same instant, incrementally decrease in return periods. The Gaussian copula was recognized as the best-fitted distribution for capturing the dependence structure of the flood peak-volume and peak-duration pairs based on goodness-of-fit test statistics and was further employed to derive the joint return periods.
The copula dependence parameters are estimated using the method-of-moment estimation procedure. Both the Archimedean and Gaussian copula family were introduced and tested as possible candidate functions. This study incorporated the copula-based methodology in deriving the joint distribution analysis of the annual flood characteristics and the failure probability for assessing the bivariate hydrologic risk. Flood episodes are usually thoroughly characterized by flood peak discharge flow, volume and duration series. Floods are becoming the most severe and challenging hydrologic issue at the Kelantan River basin in Malaysia.
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