Reservoir Management and Capacity for Zarqa River Basin Using the Linear Decision Rule (LDR) in Reservoir Management and Design

The LDR model was analyzed for monthly flow problem and seasonal flow problem. The results showed that the monthly operation requires smaller reservoir capacity of 42.24 Million Cubic meter (MCM) than the seasonal operation of 84.59 MCM. The seasonal operation, however, has the advantage of determining the release commitment before the beginning of the following period, thus allowing farmers and decision makers to determine their priorities without risking a lower monthly commitment. The Zarqa River Basin comprises an area of approximately 3931 km, with 92% of this area representing the catchment area of King Talal Dam, which has a total capacity of 86 Million Cubic meter (MCM). The dam was constructed by the ENERGOPROJEKT engineering company and raised by the Harza overseas company. The original design of the dam was determined according to the irrigation requirements of the Jordan Valley, but inadequate data at that time prohibited the establishment of optimal reservoir capacity and operation for Zarqa River Basin. The objective of this study is to screen the optimal reservoir operation and capacity using the Linear Decision Rule (LDR) model. The LDR model is used to make release commitment depending on the existing storage and decision parameter that represents the portion of the current inflow needed to honor the release commitment. The results and discussion presented here are based on the work of Rahbeh (1996) in his master thesis. The Linear Decision Rule (LDR) model has been developed by Revelle et al. (1969) as a chance constraint linear programming model. The model structure is formulated as probabilistic constraints of minimum and maximum releases, storage, and freeboard capacity, which are thereafter converted into linear programming problem. The LDR has the advantage of implementation because it determines the release commitment at the beginning of the period and eliminates mathematical difficulties in formulating the chance constraint. However, it has two main limitations: the reservoir capacities are overestimated, leading to conservative results, and the LDR result is not guaranteed to be optimal, as it considers each flow in each period to be critical. Several enhancements and modifications have been introduced to the original LDR model. These modifications fall under three general aspects: extending the original LDR to include new objective functions, developing the LDR model to include the solution for multireservoir systems, and incorporating the stochastic nature of the stream flow process into the LDR model. The multiple LDR model, which incorporates explicitly the stochastic nature of the stream process, specifies significantly smaller reservoir capacities than the single LDR model. However, this advantage appears to decrease with increasing the number of seasons or decision periods. The Linear Decision Rule (LDR) in Reservoir Management and Design is a simple and effective method for determining release commitment. The simplest form of the LDR is given by the equation: X = S + b, where X is the release commitment, S is the storage at the end of the previous period, and b is the decision parameter to be determined. The decision parameter can be positive or negative, with a negative decision parameter indicating a release commitment made less than the current storage, and a positive decision parameter indicating a release commitment made greater than the current storage. The continuity equation, which implies no shortage or spill, is given by the equation: S = S + R - X, where S is the storage during the period of operation, R is the random inflow during the operation period, and X is the release commitment during the period of operation. By substituting the fundamental equation of the linear decision rule into the continuity equation, the solution of the LDR method is subjected to several engineering constraints.