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Show R M R I QR„ - a„ H, • X X » W>! Xn + LLWi& i + e « A « < 51> r « lmsl r= l i « l where ast is an energy demand distribution factor, R is the total number of yield reliabilities, M is the total number of M& I demand areas, I, is the total number of irrigation demand areas, btm is the monthly demand fraction ( monthly demand/ annual demand) for month t and demand area m, jPmt is the reliability ( expressed as a probability) of M& I supply to area m at reliability level r, for month t, Cft is the monthly demand fraction ( monthly demand divided by annual demand) for month t and demand area i, qr^ t is the reliability ( expressed as a probability) of irrigation supply at reliability level r, in month t, to area i, es^ is an evaporation rate per unit area, and Ast is the surface area of reservoir s in month t. The demands are thus the sum of all required releases and evaporation losses. The sequent peak procedure determines the required storage capacity by accumulating deficits over time, and then indicating the required storage capacity as the maximum accumulated deficit over the operation period. Mathematically the procedure is stated as K„ = max { 0, K^, + QRa - QI„ } ( 5.2) where Kst is the required active storage capacity at site s to meet accumulated deficits at period t. The required active storage capacity Ss for the reservoir is then found by taking the largest of Kst> the required monthly active storage capacity. Ss - max { Kt t ) ( 5.3) The solution of equations ( 5.2) and ( 5.3) is a relatively straightforward procedure ( through simulation over the operation period), if the values for evaporation losses are known. Monthly evaporation is however a function of monthly surface area and hence of monthly storage, which is a function of the required storage capacity. Assuming that each reservoir is full at the start of the operation period expressions for monthly storage in the reservoir are developed as follows. The monthly active storage SJSf in the reservoir at the jth iteration of a recursive evaluation procedure can then be represented as the difference between the active storage capacity S3S and the accumulated deficit KJst upto that month. Sj 5t = Si - K*. ( 5.4) The surface area for evaporation AJS^ can then be computed as a function of the storage, where the total monthly storage STJS is defined at each iteration j , for each time period t at reservoir s, as: st - 1+ D.+ d4 « F « < 5- 5> where d4st is a ( 0,1) variable indicating whether or not flood storage is provided in month t at reservoir s. 107 |