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Show time period t as B = B + E t t t ( 6.5) This representation of evaporation is only approximate, since the storage St is clearly changed upon consideration of E^. It is important to update Bt to include E^ prior to the computation of Bt + j . The resulting error in storage volumes is then small for most systems. If necessary, a recursion scheme ( similar to that used in the modified sequent peak algorithm in Chapter 5) to converge on the correct volumes could be adopted. 4. The stretched thread method search scheme then proceeds as before with the curve segments B^ Bj used in place of the line segments A^ Aj. As stated earlier, the stretched thread method is aimed at the satisfaction of the second physical objective for reservoir regulation - flow equalization, by minimizing the degree of reservoir spill and reservoir failure. Generalizations of the stretched thread method to policies for reservoir operation where yields for multiple purposes ( e. g. M& I use, Irrigation, Hydro- energy) with different lower and upper bounds and economic values are considered are not readily forthcoming. At best one can visualize, partitioning the active storage into sub- storages by purpose, and thereby developing joint allocation rules for the reservoir. Generalizations to multi- reservoir systems and/ or surface water - ground water use, with variable water treatment costs, evaporation and inflow characteristics, are also difficult to visualize unless the available storages in each reservoir are aggregated in some manner in the process of rule curve or yield development. Thus, while the method is efficient and utilitarian for simple situations, it is rather intractable for more complex situations. There is possible a good potential for the development of optimal operation rules in the more complex situations, if simulation models are utilized that exploit the basic principles exhibited by the stretched thread method - ( 1) dependence of the operation on only the cumulative volume of recent past and future inflows, and ( 2) dependence of operation only on the times at which the active storage is full or empty. The similarity in performance of the yield formulation ( Loucks et al, 1981, pp. 351- 355) to the stretched thread method is now described. It shall also be seen that the yield formulation addresses the shortcomings of the stretched thread method described in this paragraph. 6.2 The Stretched Thread Method and the Yield Model Loucks et al ( 1981, pp. 351- 355) consider annual yields y « for a certain purpose, at reliability level p, from the reservoir. A reliability level dpt is also considered for each of the secondary yields from the reservoir for each year t. The reliability level variables Opt may take the values 1 or 0 ( denoting whether or not the yield is supplied in a given year. If the stretched thread method indicates 4 different values of y0pt over the simulation period, then the equivalent situation is described by the yield model formulation, through a firm yield ypf and three ( incremental) secondary yields y « s with appropriate values of apt specified for each of the secondary yields. This relationship between the two models may be stated as 159 |