Rainfall-Runoff Modelling

Catchment Hydrology – Practical 2 Report Cobain Schofield
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Rainfall-Runoff Modelling in Chew Reservoir Catchment
Establishing Initial Parameters
Methods outlined in the Flood Studies Report were used to model the rainfall and run-off within the Chew
Reservoir catchment. The following equation was used to predict the time for rainfall to peak:
Tp = 46.4(MSL)0.14
∗ (S1085)−0.38
∗ (1 + URBAN)−1.99
∗ (RSMD)−0.4
The four parameters within this equation must be obtained. MSL (main stream length), S1085 (slope
between 10% and 85% of the stream’s MSL), and URBAN (fraction of urban development within the
catchment) are all variables which could be measured using an OS map. Figure 1 below shows Chew
reservoir on an OS map with annotations. RSMD was obtained from the map in Appendix A1.
Figure 1 – OS Map showing Chew Reservoir with measurement overlays
Values were obtained by measuring the length of the green line for MSL, and working out the area of each
of the twelve blue shapes in millimetres, then scaling the area values to kilometres. S1085 could then be
computed using the MSL value & the contours on the OS map, and URBAN could be gauged directly from
the OS map. Table 1 below shows the list of catchment properties obtained directly and indirectly from the
OS map.
Table 1 – Catchment properties parameters
Catchment Area (km2
) 2.98
MSL (km) 1.640
10% of MSL (km) 0.164
85% of MSL (km) 1.394
Height above sea level at 10% MSL (m) 530
Height above sea level at 85% MSL (m) 490
S1085 32.52
Red line – catchment outline
Green Line – main stream
Blue shapes – catchment area
measurement sectors

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The values in Table 1 were used to work out the time to peak (Tp) and peak discharge (Qp), before
subsequently deriving the synthetic unit hydrograph in Figure 2 after base time (TB) was calculated.
Q 𝑝 =
220
Tp
TB = 2.52 ∗ TP
- - - - - - -
Tp = 46.4(1.64)0.14
∗ (32.52)−0.38
∗ (1 + 0)−1.99
∗ (50)−0.4
Q 𝑝 =
220
2.77
TB = 2.52 ∗ 2.77
The data in Table 2 shows the values obtained from the equations above. The time to peak (Tp) and base
time (TB) values in Table 2 were each rounded to the nearest hour (3 and 7 hours, respectively), and these
were used as the basis of the synthetic unit hydrograph in Figure 2 below. Table 3 lists the discharge for
each hour of the storm.
Figure 2 – Synthetic Unit Hydrograph for Chew Reservoir catchment
Table 3 – Discharge (m3
/s per 10mm of rainfall) at each hour of the storm
Hour 1 2 3 4 5 6 7
Discharge (m3
/s per
10mm of rainfall) 0.75 1.45 2.18 1.68 1.15 0.55 0
The completed synthetic unit hydrograph can be used to predict the rainfall profile for a reference storm.
Predicting the Rainfall Profile for a Design Storm
The reference storm is a 2 day M5 storm, which is used by the Met Office as a base model from which to
scale up or down when computing a design storm. The following equation was used to calculate duration:
Duration (D) = 1 + (
𝑆𝐴𝑅𝑅
1000
) ∗ Tp
In the above equation, SARR refers to the standard average annual rainfall (mm) and Tp refers to the time
to peak which was calculated earlier while establishing initial parameters. The SARR value was obtained
from the map included in Appendix A2.
D = 1 + (
1600
1000
) ∗ 3
𝐷 = 7 (𝑟𝑜𝑢𝑛𝑑𝑒𝑑 𝑡𝑜 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟)
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6 7
Q(m3/secper10mmofrain)
Time (hours)
Table 2 – Catchment properties
computed parameter values
Tp (hours) 2.77
Qp (m3
/s per 10mm) 2.18
TB (hours) 6.97

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Next, the 2DM5 storm rainfall depth for Chew Reservoir catchment was obtained from the map in Appendix
A3, and the percentage of rainfall that falls within the first hour of a 2DM5 storm was obtained from
Appendix A4. The rainfall depth was then estimated for a storm with duration 7 hours, as calculated earlier,
using the Table in Appendix B1. Table 4 below contains the values for these variables.
Now that the rainfall depth has been established for
the 2DM5 storm a growth factor can be applied to
obtain rainfall depth for a design storm of M10000; a 1-
in-10,000 year storm event. It is a storm of this calibre
that United Utilities must ensure that their dam walls
are capable of withstanding, with peak reservoir water
levels sitting at least 2m below the top of the dam wall.
The growth factor is listed in Appendix B2. In the case
of Chew Reservoir, and based on calculations made to this point, the growth factor to convert a M5 storm
to an M10,000 storm is 5.45. The growth factor is simply applied to the 2DM5 Rainfall amount by
multiplication:
M10,000 Rainfall Depth (P) = 2𝐷𝑀5 ∗ 𝐺𝑟𝑜𝑤𝑡ℎ 𝐹𝑎𝑐𝑡𝑜𝑟
P (mm) = 75 ∗ 5.45 = 𝟏𝟓𝟖. 𝟔𝟓
An areal reduction factor was then obtained from Appendix B3 of 0.965, which when multiplied with the
M10,000 rainfall depth, gave a catchment average rainfall of 152.65mm. Rainfall interception by vegetation
was accounted for in the standard percentage runoff (SPR) equation:
SPR = ((95.5 ∗ (SOIL)) + (0.12 ∗ (URBAN)))
In this equation, SOIL was equal to 0.5 (supplied value for an upland catchment), and URBAN remains
constant from the initial parameters as the catchment remains the same. Therefore:
SPR = ((95.5 ∗ (0.5)) + (0.12 ∗ (0)))
SPR = 47.8%
This equation suggests that 47.8% of rainfall within the Chew Reservoir catchment will result in run-off. The
Percentage Runoff equation was then used to put the run-off in context of the storm duration and rainfall
intensity:
PR = (SPR + (0.22 ∗ (CWI − 125)) + (0.1 ∗ (P − 10)))
Where CWI is catchment wetness index, obtained from the graph in Appendix A5 and based on SARR.
PR = (47.8 + (0.22 ∗ (125 − 125)) + (0.1 ∗ (158.65 − 10)))
PR = 62.1%
This states that 62.1% of all rainfall within the catchment will product run-off. The following equation
calculates the net rainfall:
Net rainfall = (
PR
100
) ∗ P
Net rainfall = (
62.1
100
) ∗ 152.65
Net rainfall (mm) = 94.75
The percentage of time per hour of rainfall was then calculated, giving a value of 14.3% per hour of rain:
% of time/hour of rain = (
1
D
) ∗ 100
Table 4 – Variable values for a design storm
SARR 2.77
2DM5 Tp (hours) 36
2DM5 Rainfall (mm) 75
2DM5 Ratio (%) 25
Rainfall Depth M5 Storm (mm) 29.03

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Table 5 shows rainfall depth changes throughout the storm.
Table 5 – Rainfall depth changes during the storm
% of duration 14.29 42.86 71.43 100.00
% of total rain 35.00 79.00 93.00 100.00
% increment 30.00 44.00 14.00 7.00
Increment per
hour (fraction)
0.30 0.22 0.07 0.03
Rainfall (mm) 28.4 20.8 6.60 3.30
The data in Table 5 can now be used to create the rainfall profile of the storm in Figure 3, with raw data
contained in Table 6. The data in Table 5 is extrapolated as the Flood Studies Report assumes a
symmetrical rainfall profile.
Figure 3 – Rainfall Profile for M10,000 design storm in Chew Reservoir catchment
Table 6 – Rainfall at each hour of the storm. Used to create the rainfall profile in Figure 3.
Hour 1 2 3 4 5 6 7
Rainfall (mm) 3.3 6.6 20.8 28.4 20.8 6.6 3.3
Estimating Discharge into Chew Reservoir
The discharge into Chew Reservoir is a function of rainfall and run-off in the catchment as well as duration
of the storm. The inflow is equal to the sum of the net rainfall from Figure 3 per hour, and the discharge
from the synthetic unit hydrograph in Figure 2 for the same hour. Figure 4 shows the resulting Hydrograph.
Figure 4 – Hydrograph for Chew Reservoir produced from a 7 hour M10,000 storm
0
5
10
15
20
25
30
1 2 3 4 5 6 7
Rainfall(mm)
Time (hours)
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12 14
Discharge(m3/s)
Time (hours)

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The table in Appendix C1 shows the calculations used to work out inflow for Figure 4.
Estimating the Change in Volume of Chew Reservoir
In order to test whether or not the reservoir meets safety regulations, the volume of the reservoir at base
level must be known. Firstly, the surface area of the reservoir needed to be calculated at OS map base
height and at the next highest contour line. The surface area was calculated in the same way as the
catchment area and the areas of each shape were added together (see Figure 5 below). Table 7 shows the
given parameters relating to estimating reservoir change in volume.
The equation used to work out the change in reservoir
volume between base level and the next contour is:
∆V = (
H
3
) ∗ (A1 + A2 + √A1 ∗ A2)
Where H is equal to the difference in height between the base
level and the next contour (m), and A1 & A2 are equal to the
surface area of the reservoir at base level and next contour
levels, respectively. Therefore, the equation can be populated
as:
∆V = (
0.6
3
) ∗ (53100 + 82700 + √53100 ∗ 82700
∆V = 121240.45m3
The change in volume figure can now be divided by H to give the volume of water per meter of water level
change within the reservoir:
V per m of water height =
121240.45
1.8
V per m of water height = 67355.80m3
Now that this value is known, the inflow discharge can be used to estimate the change in reservoir height
with time. This data is displayed in Table 8 below.
Table 8 – Calculating the change in reservoir level throughout the M10,000 storm
Time (hours) Inflow Q (m3
/s) Delta V (m3
) Delta H (m) Elevation (m)
0 0.25 891.00 0.01 488.20
1 0.97 3504.60 0.05 488.25
2 3.24 11651.04 0.17 488.43
3 7.14 25701.12 0.38 488.81
4 11.70 42122.52 0.63 489.43
5 14.14 50893.56 0.76 490.19
6 13.27 47754.36 0.71 490.90
7 9.82 35358.12 0.52 491.42
8 5.78 20815.92 0.31 491.73
9 2.46 8846.64 0.13 491.86
10 0.74 2673.00 0.04 491.90
11 0.18 653.40 0.01 491.91
12 0.00 0.00 0.00 491.91
Table 7 – Given parameters relating to reservoir
volume changes
Resr Base Level (m) 488.20
Resr next contour (m) 490.00
Resr wall height (m) 491.02
Figure 5 – OS Map of Chew Reservoir
showing base-level surface area
measurement sectors and the base-level
reservoir perimeter
Reservoir perimeter Surface area
measurement
sectors

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In Table 8, the data for the Inflow Q column is taken from Appendix C1. The Delta V column is equal Inflow
Q multiplied by 3600 (seconds) to show the volume of water entering the reservoir each hour. The Delta H
column is calculated using the Delta V divided by ‘V per m’ value (67355.8m3
) to give the new cumulative
height of the reservoir at each hour. The Elevation column is then simply the cumulative elevation added to
the Delta H, using base level as the initial elevation. The Elevation column is highlighted with green to show
that the water height is a safe distance from the top of the dam wall, and red to show that it is within 2m.
Numbers in bold show that water has overtopped the dam. Figure 6 shows how the reservoir elevation
changes with rainfall and inflow discharge over time.
Figure 6 – Changes in Rainfall and Reservoir Elevation throughout the storm event
Discussion and Recommendations
The purpose of this report is to establish whether or not the dam wall at Chew Reservoir is capable of
withstanding a 1-in-10,000 year storm event. The method employed was purely hypothetical, based on a
predictable 1-in-5 year storm which was then scaled up based on findings in the Flood Studies Report. The
calculations used to model the reference storm and the design storm are also based on a number of
assumptions, such as uniformity in slope, vegetation cover, rainfall intensity and run-off to name but a few.
There are however elements of the equations which aim to mitigate the impact of these assumptions, such
as CWI (catchment wetness index), which attempts to factor in the usual wetness of the catchment so as to
reflect a more accurate run-off value rather than a generic run-off number. However, given the scale of the
design storm, and the uncertainties surrounding its intensity & duration in real terms, it is therefore
unavoidable to make assumptions when modelling. When making assumptions it is best to remain
conservative so as not to underestimate the calibre of the storm as this could lead to unprecedented
impacts. Dales and Reed, (1989) states that “the risk of a design exceedance occurring is shown to be
about a sixth of that calculated”, suggesting that the method used does perhaps show a worst-case
scenario. It then goes on to say “it exposes the presumption of those who argue that UK reservoir flood
standard are unnecessarily high, purely on the basis that there have been no recent major design
exceedances”. This is speculation given that the true effects of the modelled storm are not known, and this
is simply a ‘best-guess’ as to what might happen, based on measurements and observations from a smaller
time-frame. It is therefore reasonable to assume based on the methods employed, the calculations used,
and the parameters outlined in this report that the dam wall at Chew Reservoir does not comply with
current safety regulations set out by the Environment Agency, and a recommendation is made to United
Utilities to increase the height of the dam wall by at least 2.9m to ensure that it can withstand an M10,000
storm. Figure 6 shows that the safety limit is breached in under 4 hours, and the dam wall is overtopped
0
5
10
15
20
25
30
488.0
488.5
489.0
489.5
490.0
490.5
491.0
491.5
492.0
492.5
0 2 4 6 8 10 12
Rainfall(mm)andInflowQ(m3/s)
ReservoirElevation(m)
Time from start of storm (hours)
Reservoir Elevation
Rainfall
Inflow
Dam wall height
Safety limit (2m below wall)

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just over 2 hours later, which coincides with peak run-off. The water level then continues to rise for another
4 hours before reaching its peak elevation at 491.91m, a full 0.89m above the dam wall.
Kinder Reservoir
Kinder reservoir is located approximately 14km south of Chew Reservoir and 24km south east of
Manchester (Figure 7).
Figure 7 – A map showing relative locations of Manchester, Chew Reservoir and Kinder Reservoir
Given the close proximity of each reservoir, the rainfall and soil conditions are similar between the two.
However, the two catchments are different sizes, with different slopes.
Figure 8 – OS map showing the Kinder Reservoir catchment, with coloured overlays showing catchment
perimeter, reservoir base-height perimeter and the main stream
Kinder
Reservoir
Chew
Reservoir
Catchment perimeter
Main stream
Reservoir Perimeter
Reservoir surface area measurement
sectors

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The catchment at Kinder (Figure 8) is much steeper than Chew (Figure 1). The Chew catchment had a
maximum change in elevation of 70m, whereas Kinder has a change in elevation of around 340m, with
closely compacted contour lines all around detailing the steepness of the slopes. Steep slopes are usually
sparsely vegetated and may have a lot of rocky outcrops, increasing run-off. The infiltration capacity of the
soil will also be lower given that water is not able to pool on its surface to infiltrate. It is therefore highly
likely that the run-off will be much higher and will peak much faster for an identical storm as that described
in this report for Chew reservoir. This will therefore cause the inflow into the reservoir to increase over a
shorter time in Kinder than Chew, having a much greater impact on the changing water level of the
reservoir.
If it is assumed that a storm with the same characteristics as the M10,000 storm at Chew hits Kinder, then
the only data which must be changed in the model is the catchment area, main stream length, S1085,
reservoir area (base-level and next contour) and the dam wall.
The same model was run but with this new data which was obtained through the same means as described
in the ‘Estimating initial parameters’ section of this report, and the model outputted the following graphs in
Figures 9, 10 and 11.
Figure 9 – Synthetic unit hydrograph for Kinder Reservoir catchment
Figure 10 – Rainfall Profile for Kinder catchment
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6
Q(m3/secper10mm)
Time (hours)
0
5
10
15
20
25
30
1 2 3 4 5
Rainfall(mm)
Time (hours)

9 | Page
Figure 11 – Design storm hydrograph for Kinder 5 hour M10,000 storm
The base level of the reservoir was taken as 268m, with the next contour as 270m and the dam wall as
274m. The change in volume was calculated as 46,739m3
with the volume per meter being 23369m3
.
The model re-run found Kinder reservoir to overtop it’s dam by 27.49m, with the dam wall clearly being of
insufficient height to withstand the water. Figure 12 shows how within 2 hours the water level was over the
maximum safety limit, and that the dam wall was over topped approximately 2.5 hours after the storm
began.
Figure 12 – Change in reservoir elevation throughout the storm
Although an over-topping of 27.49m seems extraordinary and unlikely, it is highly likely that the peak inflow
will occur faster in Kinder than in Chew, and that the effects of the storm will be felt more at Kinder than at
Chew because of the differences in the catchment’s physical properties. Therefore, it is recommended that
Kinder reservoir does not comply with Environment Agency regulations, based on the data used to run this
model.
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9 10
Discharge(m3/s)
Time (hours)
265
270
275
280
285
290
295
300
305
0 1 2 3 4 5 6 7 8 9 10
Elevation(m)
Time from start of storm (hours)
Dam wall height
Safety Limit (2m below wall)

10 | Page
References
M.Y. Dales, D.W. Reed. (1989). Regional Flood and Storm Hazard Management. Available:
http://www.ceh.ac.uk/products/publications/documents/ih102floodandstormassessment.pdf. Last accessed
9th November 2014.
Appendices
 A1 – RSMD Map
 A2 – SARR Map
 A3 - 2DM5 storm rainfall map
 A4 – Ratio Percentage Rainfall Map
 A5 – CWI Graph
 B1 – Percentage of Rainfall within Durations of 2DM5 Storm
 B2 – 2DM5 Storm Growth Factors
 B3 – ARF
 C1 – Table showing estimate of discharge into reservoir

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Appendix A1 – RSMD Map

12 | Page
Appendix A2 – SARR Map

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Appendix A3 – 2DM5 Storm Rainfall Map

14 | Page
Appendix A4 – Ratio Percentage Rainfall Map

15 | Page
Appendix A5 – Catchment Wetness Index Graph
Appendix B1 – Percentage of Rainfall within Durations of 2DM5 Storm

16 | Page
Appendix B2 - 2DM5 Storm Growth Factors
Appendix B3 – ARF

17 | Page
Appendix C1 - Table showing estimate of discharge into reservoir
Times (hrs) 1 2 3 4 5 6 7 8 9 10 11 12 13
Unit
Hydrograp
h (m^3/s
per 10mm) 0.75 1.45 2.18 1.68 1.15 0.55 0
Time
(hrs)
Net Rainfall
(cm)
1 0.33 0.25 0.48 0.72 0.55 0.38 0.18 0.00 0.00 0.00 0.00 0.00 0.00 0.00
2 0.66
0.49
5
0.95
7
1.438
8
1.108
8 0.759 0.363 0 0 0 0 0 0
3 2.08 1.56 3.016
4.534
4
3.494
4 2.392 1.144 0 0 0 0 0
4 2.84 2.13 4.118
6.191
2
4.771
2 3.266 1.562 0 0 0 0
5 2.08 1.56 3.016
4.534
4 3.4944 2.392 1.144 0 0 0
6 0.66 0.495 0.957 1.4388
1.108
8 0.759 0.363 0 0
7 0.33
0.247
5 0.4785
0.719
4
0.554
4
0.379
5
0.181
5 0
INFLOW
(M^3/S) 0.25 0.97 3.24 7.14 11.70 14.14 13.27 9.82 5.78 2.46 0.74 0.18 0.00

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