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I UI""V'\I I U LlVVro. VI - i::~LUII':U1VII VI '-Cll\;:le' lV l::.Alle'llle' I IVVV~ Table 21 Transition probabilities between reservoir inflow and outflow classes. Inflow class Outflow Outflow interv!. (m'/s) <550 700 1000 1300 1700 2200 3000 4000 class cumulative Inflow class probab. probability probab. (%) 99.51341 0.28355 0.15983 0.03106 0.00896 0.00234 0.00068 0.00013 (%J (%) 0 99.999969 100.0000 78.4716 69.3027 54.2430 47.9156 41.6945 34.4040 27.1748 99.869080 350 0.130893 21.5284 2.3793 2.2986 1.0037 0.8095 0.9611 0.5138 0.065678 380 0.065216 2.9773 3.4824 1.6977 1.3187 1.0253 0.7559 0.006031 420 0.059185 2.6210 4.5351 1.8148 1.4459 0.7783 1.0328 0.005801 480 0.053384 3.1509 4.3690 2.0795 1.5345 1.3152 1.4447 0.006626 530 0.046758 19.5688 4.1312 4.5458 2.0523 1.4027 1.9820 0.033027 600 0.013730 U; 2.4953 4.0726 2.2000 0.7413 1.7640 0.001199 n- 670 0.012531 .s 2.9152 5.4847 1.8765 1.0761 1.5613 0.001450 (ii 750 0.011081 1: 21.5302 4.6796 4.3988 2.0627 1.2286 0.007226 2 850 0.003855 .5 2.8491 4.9704 1.8965 2.0188 0.000387 <Il 950 0.003468 <Il III 3.2690 5.6700 3.0500 0.9686 0.000448 13 1060 0.003021 " 20.5878 5.0081 3.2303 1.4521 0.001986 0 '" 1190 0.001035 :; 0 3.5337 4.9378 2.3873 0.000119 1340 0.000916 4.5897 6.8184 3.5258 0.000158 1500 0.000757 18.8973 7.8759 4.1623 0.000501 1890 0.000256 4.5785 6.3883 0.000039 1890 0.000217 23.8459 9.1470 0.000174 2120 0.000043 7.3367 0.000010 2380 0.000033 5.5530 0.000007 2670 0.000026 19.6024 0.000026 3000 0.000000 I I I I I I I I I I I I I I I I I I storage volume is (37.4-29.5=) 7.9%. Thus the probability that a peak inflow between 2200 m'ls to 3000 m'/s would lead to an outflow between 1500 m'ls to 1690 m'/s is 7.9%. This value is inserted in the appropriate position in the table and other values are computed in a similar manner. (c) Outflow frequency curve The distribution of peak outflows is evaluated by multiplying each element of the table by the corresponding probability of occurrence of the inflow interval, and the resulting products are summed horizontally (and divided by 100) to give the values in the second last column of Table 21. For example, the outflow element corresponding to the outflow range of 1500 m'/s to 1690 m'ts is obtained from the following calculation: (18.8973xO.00234 + 7.8759xO.00068 + 4.1623xO.00013)/100 = 0.000501% Finally, the vahles are added for aU Outfl0W intervals which exceed the outflow magnitude of interest to give the probabilities of exceedance, as listed in the last column. For this example, the AEP of Q = 1500 m'ls is found to be 0.000757% or about 1 in 130000. The calculale<1 outflow points from Table 21 are plotted and a curve fitted to define the frequency distribution of peak outflows, as shown in Figure 17. Note that if a sufficient number of intervals are used to discretise the inflow and outflow frequency curves then it is probably not necessary to fit a curve as the points generally follow a smooth curve in the log-Normal domain. For comparison purposes, outflows are also derived for an initial storage volume fixed at the median level of drawdown, which is 81.3% of the full supply storage (Figure 16). The corresponding outflow curve is plotted in Figure '17, and it is seen that this simplistic approach yields an outflow frequency curve that is signifICantly lower than that obtained using the more accurate joint probability approach. 6.5 Estimation of Concurrent Flows For this example it is assumed that it is required to derive the concurrent tributary inflows originating from a 60 km' catchment located just downstream of the reservoir. A township is located below the confluence and the concurrent tributary inflows are required to help determine the component of incremental damages that could be attributed to dam failure. (a) Basic flood data The design floods for the point on the mainstream are shown for a range of AEPs in Table 22 (columns 1 and 4), where flood estimates for the mainstream were derived