Concerning the various effects of climate change on intensifying extreme weather phenomena all around the world, studying its possible consequences in the following years has attracted the attention of researchers. As the drought characteristics identified by drought indices are highly significant in investigating the possible future drought, the Copula function is employed in many studies. In this study, the two-and three-variable Copula functions were employed for calculating the return period of drought events for the historical, the near future, and the far future periods. The results of considering the two-and three-variable Copula functions were separately compared with the results of the calculated Due to the high correlation between drought characteristics, bivariate and trivariate of Copula functions were applied to evaluate the return periods of the drought.The most severe historical drought was selected as the benchmark, and the drought zoning map for the GCM models was drawn. The results showed that severe droughts can be experienced, especially in the upper area of the basin where the primary water resource is located. Also, the nature of the drought duration plays a decisive role in the results of calculating the return periods of drought events.

This study contributes to emerging computationally efficient methods to account for multi-purpose reservoir operations at the dam design stage. In many cases, the water supply reliability objective introduces binary variables into an otherwise simpler linear programming (LP) formulation. This has led to widespread use of evolutionary methods such as particle swarm optimisation (PSO). Combining the branch and bound (BB) method with a hybrid PSO–LP, this study presents a new BB–PSO–LP algorithm to solve the joint design and operations problem. The proposed BB–PSO–LP algorithm was benchmarked against classical versions of the BB algorithm and PSO–LP. Superiority of the BB–PSO–LP algorithm was demonstrated by finding slightly better solutions in a shorter time. That said, PSO–LP also led to acceptable results in a similar time. Although the BB algorithm was found to be efficient in problem solving, under certain conditions it is difficult for the BB method to find a feasible solution.

Concerning the various effects of climate change on intensifying extreme weather phenomena all around the world, studying its possible consequences in the following years has attracted the attention of researchers. As the drought characteristics identified by drought indices are highly significant in investigating the possible future drought, the Copula function is employed in many studies. In this study, the two- and three-variable Copula functions were employed for calculating the return period of drought events for the historical, the near future, and the far future periods. The results of considering the two- and three-variable Copula functions were separately compared with the results of the calculated Due to the high correlation between drought characteristics, bivariate and trivariate of Copula functions were applied to evaluate the return periods of the drought. The most severe historical drought was selected as the benchmark, and the drought zoning map for the GCM models was drawn. The results showed that severe droughts can be experienced, especially in the upper area of the basin where the primary water resource is located. Also, the nature of the drought duration plays a decisive role in the results of calculating the return periods of drought events.

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