Bivariate Flood Frequency Analysis Using the Copula Archimedean Function (Gumbel–Hougaard)

Flood is a multivariate and complex phenomenon that has a random nature. In conventional methods of flood frequency analysis, only flood peak variable is important and it is assumed that the variable under consideration follows a particular parametric distribution function. In contrast to the Copula functions, it is capable of linking the marginal distributions of a variable different to each other and generating multivariate distributions. Analysis have been performed along with flood variables using the Copula functions that do not have the limitations of classical single distributions. The probability distribution and return periods of peak and volume flood variables in the AjiChay Basin in the province of East Azarbaijan have been investigated using of the Copula function of Gumbel–Hougaard for bivariate mathematical modeling. The results indicated that the use of the Copula functions of conditional cumulative distribution functions, as well as return periods of flood variables, is estimated with great accuracy with the average coefficient of NSE 0.745 and RMSE of 0.56. The estimated values of the peak flow and volume discharge from the bivariate analysis with univariate analysis with a 100-year return period were less than the observe amounts for all stations, which are influenced by the interaction of the two variables, peak flow and discharge volume. These values were 230 and 300.75 m3/s respectively, at Akhola Station, indicating that the use of the Copula function will economize the designs and reduce risk.