Abstract
Historically, severe floods have caused great human and financial losses. Therefore, the flood frequency analysis based on the flood multiple variables including flood peak, volume and duration poses more motivation for hydrologists to study. The main goal of this paper is conducting a tri-variate flood frequency analysis through simultaneously processing the three main variables of any flood event. In addition to this analysis, three bi-variate flood frequency analyses are also performed considering the variables pairwise. Meanwhile, the Archimedean copula functions are employed to conduct such analyses, and finally compared based on their performance in estimating the accurate and reliable flood frequencies. Bivariate and trivariate flood frequency analysis and modeling using Archimedean copula functions is focused. For this purpose, the annual flood data over a 55-year historical period recorded at the Dez Dam hydrometric station were used. According to the goodness-of-fit criteria along with the analytical tail dependence results based on the extreme value theory, the Frank function built upon the couple of the flood peak-volume and the couple of the flood peak-duration as well as the Clayton function built upon the flood volume-duration were identified 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 flood 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.
Highlights
Flood is one of the most important natural disasters annually causing many financial and human losses in different parts of the world, its analysis and forecasting are required to control its possibly acute damages
One of the traditional methods for multivariate flood frequency analysis is the use of classical multivariate distribution functions, such as normal, log normal, Gamma, etc..; the main problem hindering employing these methods is that these functions face limitations that either reduce the accuracy of the analysis or make it essentially impossible to be conducted
The correlation coefficients between the variables were calculated and according to the results shown in Table 2, there is a significant and direct correlation between the flood peak and volume and between the flood volume and duration while there is an inverse correlation between flood peak and duration
Summary
Flood is one of the most important natural disasters annually causing many financial and human losses in different parts of the world, its analysis and forecasting are required to control its possibly acute damages. To predict floods in a certain area, it is necessary to understand the three important characteristics of flood namely flood peak, flood volume and flood duration, to perform a joint analysis of the flood data occurring in the past in the area. One of the traditional methods for multivariate flood frequency analysis is the use of classical multivariate distribution functions, such as normal, log normal, Gamma, etc..; the main problem hindering employing these methods is that these functions face limitations that either reduce the accuracy of the analysis or make it essentially impossible to be conducted. One of the most important limitations to use these functions is the need to specify the parameters of the distribution functions of marginal variables and their uniformity.
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