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16.5 hr (y) = 2.6550 which gives a value of T, the return period of 14 years.


7. The rarity of the SMD is assessed using the method described by Clark (2018). This is based on 20 years’ weighing lysimeter and open pan data gathered at CHRS and 142 years regional rainfall corrected using 30 years local rainfall. The result for a threshold SMD of 16mm over a time period of 142 years’ data = 2.15 years.


8. Thus the flood rarity = Rp ER x Rp SMDcrit where ER = effective rainfall after the SMD is


reduced to the critical value as determined from weighing lysimeter data at CHRS (Clark 2018). In the present case the critical SMD had already been attained so the effective rainfall is the storm rainfall.


9. Thus in the present case the return period of the flood = 14 x 2.15 = 30 years.


Results All the results of the previous section and the


estimates of the August 2019 flood are shown in Table 10, including the estimates of bankfull discharge which have a return period in the range 1.1-1.5 years (Williams, 1978, Edwards et al 2019). As noted above the return period of a flood event during the summer when the return period of critical SMD is more than 1.0 means that the rarity of the summer rainfall flood will be 2 x 2.15 = 4.6 years. The return period of the 1 in 10,000 and PMF must therefore be higher than the notional return periods of 104


and 106 years by a similar factor,


that is 2.15. However, there may be an early part of the design storm which would reduce that factor but determining its size is beyond the scope of the present work. Suffice to say that a critical test of these results is that they must form a Log linear relationship with the modified reduced variate. Figure 8 shows this to be the case. Also shown on Figure 8 are the results using the ReFH and the PMF as reported by Hughes (2020), which was calculated using FEH methods (IOH, 1999), including the FSR (1975) PMP. These alternative results have several problems. First the 1.1 year flood of 7.4 cumecs is far too high as is confirmed by the field survey. Second, as a result the growth curve of floods is much lower, all else being equal. Third the rate of increase of peak discharge with rarity does not fulfil the criteria for flood data, namely that the less rare floods must align themselves in a linear way on the modified Log Gumbel scale. Fourth, the July 2019 flood has a rarity in excess of 100 years but the storm has a rarity of less than 20 years. This implies a rarity of 1 in 5 years for the critical SMD which as we have seen is far too high. Fifth, the runoff rate for the PMF is midway between the normal maximum flood and the extreme catastrophic flood of Allard et al (1953). Thus historic floods have already exceeded the PMF at Todd Brook. Since the catchment is high, steep, and in an area of high rainfall the lower estimate of PMF is much too low. In fact the PMF at the dam site is 292 cumecs, over 100 cumecs higher than that reported by Hughes (2020). These observations are typical of other catchments at least in southern England such as the upper Brue dam site where the PMF was increased from 240 cumecs


www.waterpowermagazine.com | August 2022 | 19


Table 10 Estimates of index floods and the flood of 31/7/2019 at the survey site just above Todd Brook reservoir, CA = 15.41 km2


Bankfull discharge


2-year flood (winter rainfall) 2-year flood (summer rainfall) 31/8/2019 flood 1 in 10,000 flood PMF


Discharge (cumecs) Return period (years) 3.8


7.9


11.8 26


130 277


to 500 cumecs with subsequent improvement works in the interests of safety. At the other end of the scale the excessively high 1.1 year flood for the upper Stour at Bourton in Dorset was proven by current meter measurements (Clark, 2015a).


Reservoir flood routeing A useful test of the estimated hydrograph just


upstream of the reservoir is to route it through Toddbrook reservoir. The peak outflow discharge can then be compared with the calculated outflow based on the capacity of the bywash channel and the head above the auxiliary spillway. These structures have less uncertainty when it comes f


1.1 2


4.3 30


104 106


Figure 8: Flood frequency analysis


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