OCR Text |
Show found, the optimal yield is described by AQAJ. Otherwise determine the point Aj ( t= i) that lies on Xf at a maximum distance above ArjAj, and the point Aj ( t= j) that lies on Xe at a maximum distance below AQAJ. Define k= min( j4), and l= max( j4). 4. The point Afc at time k is then regarded as an end point of the shortest path in the period ( 0, k). 5. Steps 2 through 4 are repeated with k replacing T. 6. If no additional corner points are found in the interval ( 0, k) the line AQAJ^ represents the first segment of the shortest path, and the optimal yield, and the search moves to the interval ( k, l). If an additional corner point m is found in the interval ( 0, k), the search moves to the interval ( 0, m). 7. The search moves forward sequentially, only after the shortest path in a time interval ( k, l) is found without infraction of Xe or Xf, where k and 1 are updated as one proceeds from initial to later comer points. Indices of all corner points found in the search process are maintained in ascending order, and the search proceeds pairwise between these indices. Klemes ( 1979) does not indicate procedures for treating evaporation losses and periodically varying ( within year) outflows. These extensions are however easily developed and incorporated in the numerical, sequential search procedure presented by Klemes ( 1979). These extensions were developed and tested with data from City Creek in the Jordan River Basin. The modifications to Klemes's algorithm for this purpose are really quite minor. These are summarized as follows. 1. The analysis is monthly rather than annual. Periodic variability of demand in the within year period is considered through monthly demand fractions of the annual yield. The line A^ Aj is first constructed for the search period ( k, l) as described earlier. A modified cumulative demand curve B^ Bj is then constructed as ( BrBJ* 12* bt B< " BM + ( 1- k) ( 6 ' 2) where Bt is the ordinate of the cumulative outflow curve at time t, t lies in the interval ( k, l), and b( is the monthly demand fraction for the yield in month t. 2. Evaporation volumes Ej are then computed on a monthly basis, by determining end of month reservoir storages St. These computations are represented as S.- XJ.- B, ( 6.3) E, = e. A, ( 6.4) where At is the surface area of the reservoir in month t, corresponding to storage S(, et is a net evaporation rate per unit area and Xelt is the ordinate of Xe at time t. 3 . Modify the cumulative demand ( outflow) curve to include net evaporation for the 158 |