Optimal allocation of reservoir water: A case study of Lake Tenkiller

Scope and Method of Study. The purpose of this research study is to determine the optimal allocation of reservoir water among consumptive and non-consumptive uses. Hydroelectric power generation benefits and lake recreational benefits (nonconsumptive uses) and urban and rural water supply benefits (consumptive uses) are implicitly considered in this study. Recreational benefits depend explicitly on the summer lake levels, while the flood control capacity of the reservoir is maintained through upper bounds on the lake level. An optimization model using non-linear programming is developed to optimally allocate reservoir water among competing uses. General Algebraic Modeling System (GAMS) with MINOS solver is used to solve this model. Lake Tenkiller and its surrounding area of northeastern Oklahoma are considered for this study. A mass balance equation is used to determine the level and volume of water in the lake for each month over twelve month period. This paper compares different water management scenarios, (recreational benefits are and are not included in the objective function) while managing Lake Tenkiller.;Findings and Conclusions. The results of this study showed that the total benefits arising from the use of Lake Tenkiller water will increase under the optimization model compare to the benefits obtained under historical releases. It was also found that when recreational benefits are included within in the objective function then the total benefits will be greater than when the recreational benefits are not included in the objective function. The results also showed that for Lake Tenkiller maintaining lake level around the normal lake level of 632 feet during summer months and shifting the releases for hydropower generation to other months increased overall benefits including recreational benefits with only a slight reduction in hydropower generation values. Therefore for Lake Tenkiller, it is beneficial to maintain lake levels near the normal pool of 632 feet during the summer months in order to maximize the net social benefits. It was shown that for Lake Tenkiller an optimal allocation of water between competing uses requires that the marginal price of water at the lake in each month must be same for the last unit of water used for hydropower, recreation or urban and rural water uses.