Flooding from the Indus river and its tributaries has regularly influenced the region of Pakistan. Therefore, in order to limit the misfortune brought about by these inevitable happenings, it requires taking measures to estimate the occurrence and effects of these events. The current study uses flood frequency analysis for the forecast of floods along the Indus river of Pakistan (Tarbela). The peak and volume are the characteristics of a flood that commonly depend on one another. For progressively proficient hazard investigation, a bivariate copula method is used to measure the peak and volume. A univariate analysis of flood data fails to capture the multivariate nature of these data. Copula is the most common technique used for a multivariate analysis of flood data. In this paper, four Archimedean copulas have been tried using the available information, and in light of graphical and measurable tests, the Gumbel Hougaard copula was found to be most appropriate for the data used in this paper. The primary (T^AND, T^OR), conditional and Kendall return periods have been also determined. The copula method was found to be a powerful method for the distribution of marginal variables. It also gives the Kendall return period for the multivariate analysis the consequences of flooding.

Pakistan is considered a great natural reservoir of fresh water from the River Indus. When the river is in flood it causes immense damage. Flood frequency analysis provides guidance related to the behavior of anticipated flood flows using historical flow records. Flood frequency analysis usually focuses on the annual maximum peak discharge (flood peak) values, which is insufficient to solve many problems related to hydrological engineering design, management and planning. Therefore, the values of flood peak are not considered the only flood characteristic to assess the flood event. Flood durations and volumes are also associated with the flood frequency distributions as the characteristics of a flood event for authenticated results. The application of Gumbel mixed model on the recorded flood flows is proposed in this paper to analyze the joint probability distribution of flood volumes and peaks as well as flood durations and volumes, which are mutually correlated. Gumbel mixed model is a bivariate extreme value distribution with marginal distributions of two random variables by which the joint probability distributions, the conditional probability functions and the related return periods are obtained. Application of the suggested model on the observed data of Tarbela dam in Pakistan reveals that the model is appropriate for representing the joint probability distribution of flood volumes and peaks, and the joint probability distribution of flood durations and volumes. Hence, it is concluded that a bivariate probability distribution provides detailed information regarding future floods, whereas the univariate probability distribution is insufficient in providing extensive information regarding future flows.