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Klaho, M.H., Safavi, H.R., Golmohammadi, M.H., Alkntar, M. (2022). Comparison between bivariate and trivariate flood frequency analysis using the Archimedean copula functions, a case study of the Karun River in Iran. Natural Hazards, 112(2), 1589-1610.

Comparison between bivariate and trivariate food frequency analysis using the Archimedean copula functions, a case study of the Karun River in Iran


Historically, severe foods have caused great human and fnancial losses. Therefore, the food frequency analysis based on the food multiple variables including food peak, volume and duration poses more motivation for hydrologists to study. The main goal of this paper is conducting a tri-variate food frequency analysis through simultaneously processing the three main variables of any food event. In addition to this analysis, three bivariate food frequency analyses are also performed considering the variables pairwise. Meanwhile, the Archimedean copula functions are employed to conduct such analyses, and fnally compared based on their performance in estimating the accurate and reliable food frequencies. Bivariate and trivariate food frequency analysis and modeling using Archimedean copula functions is focused. For this purpose, the annual food data over a 55-year historical period recorded at the Dez Dam hydrometric station were used. According to the goodness-of-ft criteria along with the analytical tail dependence results based on the extreme value theory, the Frank function built upon the couple of the food peak-volume and the couple of the food peak-duration as well as the Clayton function built upon the food volume-duration were identifed to be the best copula families to be adopted. The trivariate analysis was conducted and the Clayton family was chosen as the best copula function. Thereafter, the common and conditional cumulative probability distribution functions were built and analyzed to determine the periodic "and", "or" and "conditional" bivariate and trivariate food return periods. The results suggest that the bivariate conditional return period obtained for short-term periods is more reliable than the trivariate conditional return period. Additionally, the trivariate conditional return period calculated for long-term periods is more reliable than the bivariate conditional return period.


Flood frequency; Copula functions; Archimedean; Hierarchical; Return period.

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