| Projects Table 7 Extract of the convolution for delayed flow Time (hours)
Del Q (mm)
0.83 0.65 1.62 2.16 1.69 1.30 2.03 1.82 1.47 0.26
0.024 2.3 0.0290 2.8
0.0774 0.0290
3.3
0.1258 0.0774 0.0290
3.8
0.1742 0.1258 0.0774 0.0290
4.3
0.1899 0.1742 0.1258 0.0774 0.0290
4.8
0.1840 0.1899 0.1742 0.1258 0.0774 0.0290
5.3
0.1782 0.1840 0.1899 0.1742 0.1258 0.0774 0.0290
5.8
0.1726 0.1782 0.1840 0.1899 0.1742 0.1258 0.0774 0.0290
6.3
0.1672 0.1726 0.1782 0.1840 0.1899 0.1742 0.1258 0.0774 0.0290
0.083 0.201 0.414
non-linear processes, and agree with direct observations made during the historic floods of 1979 and 1982 on the upper Brue: slow rise to begin with, then rapidly increasing and finally reaching peak discharge at a slower rate of change. The falling limb repeats these changes but at a slower rate. The temporal distribution of rainfall will determine the shape of the unit hydrograph. The depth of quickflow and delayed flow runoff is calculated using the sine of catchment slope, the Ksat relationship, leaving the remaining rainfall as delayed flow. This part of the flow model has remained unchanged since it was first put into operational use in 2004.
Results Table 6 is an extract from the calculation of
quickflow and delayed flow. The data are 0.5 hour interval and the rainfall mm. Slope runoff = rainfall x sin α where α is the average catchment slope. The delayed flow ordinates are calculated via the function:
0.3896 [Catchment area / catchment area U. Brue]
The delayed flow starts after a time period related to the mainstream channel length and the time to peak being the same time period as per the Upper Brue. The decay constant for delayed flow is via the function:
k = 0.0247 Log A + 0.909
where A = catchment area. Table 7 shows an extract of the convolution of the delayed flow discharge, where the values are ordinates not discharges. Calculation of quickflow is in two stages. The first is the calculations of Tp TB and Qp are shown in Table 8. The second is the convolution of the ordinates at each stage of the storm. Values of the ordinates for the rising and falling
limb are then calculated and there must be a perfect match between the time to peak and data interval for the time to peak of the highest rainfall
0.690 0.998 1.323 1.635
intensity. In this case it is 2.8 hours. Hence with a time interval of 0.5 hr the times become 0.3, 0.8, 1.3, 1.8, 2.3, 2.8, 3.3….. The convolution of the unit hydrograph takes
place in the normal way except that the values in the body of the Table 9 are ordinates not discharges. The total discharge for each time step is the sum of the products of quickflow which is the sum of slope runoff and Ksat runoff, and the ordinates. Table 9 gives an extract from this process. Time (hr) abscissa, ordinates total quickflow (mm). Total flow is quickflow x Scf + delayed flow, where Scf is the slope correction factor. This factor f
Table 8 Parameters of the non-linear flow model CA = 15.41 km2 MSL = 7.952. TB = 2.52 Tp Tp
mm 0.5 hr 1.18 1.00 2.69 4.03 2.86 2.01 3.70 3.19 2.35 0.33 3.36 4.03 0.17 1.68 0.84 8.90 9.24 3.02 2.52
TB
3.978 4.092 3.458 3.228 3.422 3.634 3.276 3.359 3.538 4.940 3.330 3.228 5.530 3.746 4.215 2.822 2.804 3.391 3.497
10.026 10.312 8.715 8.136 8.625 9.158 8.255 8.466 8.918
12.451 8.392 8.136
13.937 9.441
10.622 7.111 7.066 8.545 8.812
1.923 2.169 6.8
0.1620 0.1672 0.1726 0.1782 0.1840 0.1899 0.1742 0.1258 0.0774 0.0290
0.85(TB-Tp) 5.141 5.287 4.469 4.172 4.422 4.695 4.232 4.341 4.573 6.384 4.302 4.172 7.146 4.841 5.446 3.646 3.623 3.381 4.518
Qp
1.278 1.242 1.470 1.575 1.486 1.399 1.552 1.513 1.437 1.029 1.527 1.575 0.919 1.357 1.206 1.802 1.813 1.499 1.454
www.waterpowermagazine.com | August 2022 | 17
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