Projects |
Table 4 Estimated discharge at CS1 and CS2 CS1
Channel Floodplain CS2
Area 11.48
11.88 12.28 1 component method * Jarrett (1987)
f The 2-year and PMP depth are then regressed against the modified Gumbel scale (Rakhecha & Clark, 1999, Clark, 2015, 2019):
y = [-ln ln(1 -1/T) – 3.3842 x 1.09348 T -0.046518
] + 3.3842 [1]
where T = return period (years) y = modified Gumbel reduced variate. Note that the return period of PMP is taken as 106
(Lowing and Law, 1995,
Rakhecha & Clark, 1999, Clark, 2015, 2019). Rainfall is partitioned into slope runoff and quickflow with the remaining rainfall becoming delayed flow. The unit hydrograph time to peak is related to rainfall intensity and a measure of the saturated soil hydraulic conductivity as measured in the field:
Tp = c (R-0.17 ) MSL catch/ MSL Brue
where Tp = time to peak (hr) of the UH; MSL catch = mainstream channel length; MSL Brue = mainstream channel length of the upper Brue (9.0 km); c = a function of the percentage runoff at a rainfall intensity of 10 mm hr-1
. Over 2500
measurements covering nearly 70 soil Associations have been made. The 1:250,000 maps of the Soil Survey of England and Wales (Mackney et al 1983)
Table 5 Hydraulic conductivity of Todd Brook catchment soils Association
SSEW code
Rivington/Neath Belmont
Winter Hill Hafren
Wilcocks 1 Brickfield 3
Catchment % runoff
541g/h 651a
1011b 654a 721c 713g
% cover
46 10 8
18 8
10 100
Wetted perimeter
8.8 21.8 12.1 n
0.0801 0.082*
Total discharge = 30.31m3 0.0531
/sec 0.0128 26.47 S
0.0128 0.0128
Q cumecs 19.38
10.93
are detailed enough to allow the application of data gathered elsewhere from areas with the same soil associations. To make sure that a given catchment conforms to this expectation a local survey should be carried out. In the present case the Brown Earths Rivington 2 (541g) and Neath (541h), which cover 46% of the area were tested in the field and shown to be almost identical in hydraulic conductivity at low and moderate rainfall intensities but more responsive at higher intensities. The catchment soils and their percentage runoff are given in Table 5. The percentage runoff for a given rainfall intensity using the following formula:
% runoff = [ Σ (R – Mid value R-Ksat) A ] / R
where R = rainfall intensity; Mid value R-Ksat = mid value of each Ksat class (0-5, 5-10…) of conductivity; A = proportion of catchment covered by each soil association. Values of % runoff are summed for each conductivity class until the mid value equals or exceeds the value of R. The UH ordinates of overland or quickflow are non-linear using an alternative growth curve of the form for the rising limb:
Y = [INVLOG 2(t – 0.7Tp) / 1 + INVLOG 2(t – 0.7Tp)] Qp
where Tp = time to peak; Qp = peak runoff rate = 330/Tp) 0.001 CA where CA = catchment area. For the falling limb:
Y = [INVLOG (t1 -0.85(TB-Tp)) / 1 + INVLOG(t1
-0.85(TB-Tp))] Qp where TB = time base = 2.52Tp, t1
= TB- t where t =
time since start of storm. These equations have been found to mimic the hydraulics of overland flow which are themselves
5
18 26 50 33 24 40 27
% runoff at rainfall intensity (mm hr1) 10 30 42 66 54 42 62 43
20 52 58 84 73 62 78 62
80 83 77 95 92 80 94 86
150 92 81 97 95 86 96 92
Table 6 The partition of rainfall into slope runoff and Ksat runoff 1.18
Rainfall mm hr-1
Slope Ksat Total Del
0.26 0.09 0.35 0.83
1.00 0.22 0.13 0.35 0.65
2.69 0.61 0.46 1.07 1.62
4.03 0.91 0.96 1.87 2.16
2.86 0.65 0.52 1.17 1.69
2.01 0.45 0.26 0.71 1.30
3.70 0.84 0.83 1.67 2.03
3.19 0.72 0.65 1.37 1.82
2.35 0.53 0.35 0.88 1.47
0.33 0.07 0.00 0.07 0.26
3.36 0.76 0.71 1.47 1.89
16 | August 2022 |
www.waterpowermagazine.com
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