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I I I I I I I I I L.ll'J"\I I U '0000 1 <> 1 I ~ 1000 ~ 1 *'" 1 .s ;: 1 0 1 u: "'" <II '" i 11. 100 1 j j 1 I I 10 , 2 Inflow frequency curve Joint probability results Fitted outflow frequency curve OUfJow at median drawdown ~, 1II1 I I IIII! I I u......." VI - .........., 'eu'....'I ...., LGUY'='~"" ....^......""". ,............. II1III I I lillll I I Illilll I I 0.5 0.2 0.1 0.05 0.01 0.001 Annual Exceedance Probability (%) 0.00001 0.0001 Figure 17 Outflow frequency curves obtained using joint probability analysis and a median level of drawdown, Annual Exceedance Probabir Oesian Quantiles Bivariate I -Normal Estimates Concurrent tributa flood Standardised Mainstream Flood Tributary Flood Mainstream Flood Trib""" Flood Flood AEP (1inY) (%) Norm. Variate (m'/s) log(m'/.) (m'/s) log(m'/s) log(m'/s) (m'/s) log(m'/s) (m'/s) log(m'/s) (m'/s) (1 inY) 111 '" {31 {41 ~ (51 '" m (8) (9) (10) (11) I12J (13) 1141 SO 2.000 2.054 344 2.537 'OS 2.020 2,540 341 2.024 106 1.638 43 7 100 1.000 2.326 443 2.646 135 2.130 2.639 43S 2.121 134 1.689 49 6 500 O.1J(lO ,al. 103 2.847 2.~9 S9ll Z.334 2'6 .1.1S~ e2 13 1000 0.100 3.090 .26 2.917 2.916 623 2.414 ZSS 1.833 6. 16 2000 0.050 3.290 969 2.986 2.986 973 2.489 30. 1.870 14 20 10000 ,0.010 3.719 1351 3.131 3.144 1392 2.651 441 1.951 89 32 50000 0.002 4.101 1860 3.270 3.262 1913 2.794 622 2.023 'OS SO 500000 0.0002 ~4.606 2910 3.484 3.465 2918 2.984 964 2.118 '31 94 22.0000 4.39E-05 - ~4.913 389. 3.591 3.576 3769 3.099 1257 2.175 'SO '43 10000000- 0.0ll0r>r '519& 1"610 "'07 '.680 4788 3.W 1i11 2.2!ll no 2\4 Average (1ntercept) = 1.796 1.251 p= 0.5 Std Oev (slope) = 0.362 0.376 I I I I I I I I I I using the CRC-FORGE procedure in combination with the pre-burst temporal patterns, as described in Section 6.3.4. Floods flows in the tributary are assumed to be minor compared to that in the mainstream, and it may be assumed that preliminary design flood estimates were derived using the procedures described in Section 4.7.1. Tributary flood estimates were only obtained for AEPs of 1 in 50, 1 in 100 and 1 in 10', and these are shown in column 6, Table 22. (b) Fitting of log-Normal distribution In order to calculate the parameters of the marginal log- Normal distributions, the flow data are flrst converted into the logarithmic domain (columns 5 and 7), and the AEPs are linearised by calculating the corresponding standard normal deviates (column 3). The latter can be obtained from normal probability tables, or else using the in-built functions available in spreadsheet software (note that the standardised normal variate obtained using some spreadsheet software may be incorrect at very low probabilities; correct values should be checked against Table 22 Calculation of concurrent tributary flows. published information e.g. Abramowitz and Stegun, 1964, 1974). The parameters of the log-Normal distribution can then most easily be calculated by simply fitting a linear regression line through the transformed data (i.e. columns 3 and 5, and columns 3 and 7). The intercept of the fitted line is equivalent to the mean of the distribution (as the standardised variate of the mean of a log-Normal distribution is zero), and the slope is equivalent to the standard deviation. The fltted parameters are listed below columns 5 and 7, and may be obtained either graphically, or by using standard spreadsheet functions. The design flood estimates and the fitted log-Normal distributions are shown in Figure 18. The log-Normal estimate (x) may be calculated from the relevant sample mean (m), standard deviation (s), and standardised variate (z) as follows: x ;:: m+s.z For example, to calculate the 1 in 100 AEP design flood in the mainstream: x 1.796 + 0.362 x 2.326 = . Note: the standardised normal variates for low probabilities were obtained using. Abramowitz and Stegun, 1964, 1974.