| OCR Text |
Show probabilities can be determined. Yields Y « with a given probability p, refer to releases ( taken from the stream or reservoir) that have a high reliability ( probability) of being equalled or exceeded in future periods. As an example, say 2 yields are desired, one ( Yo. 95) 95% reliable and the other ( Y0.75) 75% reliable ( i. e. an annual demand of water of that magnitude can be met 75% of the time). Then the first case ( Y0.95) * s analogous to a statement of ' firm yield', while a secondary incremental yield may be defined as ( Y0.95" Y0.75), or the magnitude of the supply in excess of firm yield', that is 75% reliable. A number of such yields can be simultaneously considered. Reservoir storage is allocated as over- the- year and within- year storage, and procedures for the incorporation of evaporation, precipitation and flood control storage are indicated. No consideration of hydropower is presented. Reservoir operation is considered over the critical period and procedures for the joint critical period of a set of streams are identified. Reservoirs are operated on an annual basis over the critical period for the determination of over the year storage capacities, and are operated monthly/ seasonally over the lowest flow (' failure') years in the critical period for the determination of within year storage capacities. The example application presented by Stedinger et al ( 1983) is a simplified version of the basic formulation - a single yield is considered, only water supply operation is considered, evaporation, precipitation and seepage loss effects are ignored and only reservoirs in parallel are considered with no constraints on instream flow values. Based on the comparisons in Stedinger et al ( 1983) and on the modeling criteria delineated earlier, it was felt that the implicitly stochastic models, specifically the linear programming based yield models of Loucks et al ( 1981) were the most promising foundations for our study. This conclusion was based particularly on their superior performance relative to some explicitly stochastic and deterministic techniques, the ability to use historical ( or synthetic), critical period data, satisfy supply reliability and their flexibility in terms of ease of modification and subsequent application. The model formulation in this chapter extends the yield model concept to include hydropower generation, multiple uses for water and recreation. The linear programming model of Loucks et al ( 1981) is recast as a hierarchical, nonlinear programming ( NLP) model which is significantly more compact and efficient. The NLP formulation also allows for a much greater exploitation of the problem's mathematical and physical structure without a significant increase in problem size. Real world example applications of the model developed are also presented. 5.3 Model Formulation: The model formulated is presented first for a single, multi- purpose reservoir, and then generalized to the multi- reservoir case. Yields for Municipal and Industrial ( M& I), Irrigation and Hydropower generation are considered from the reservoir to one or more demand areas. The yield definitions correspond to those used by Loucks et al ( 1981) for their ' yield model'. In addition, provision of conservation storage for recreation and augmentation of available head for hydropower generation, as well as flood storage are also considered. These decision variables are symbolically defined as: Ds - Dead ( conservation) storage at site s NFsm - Annual M& I Yield with reliability r from s to m Fsi - Annual Irrigation Yield with reliability r from s to i 105 |
