Hydrology 2 - Report

Catchment Hydrology – Practical 2 Report Cobain Schofield

1 | Page

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


2 | Page

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.

Q𝑝 =220

Tp TB = 2.52 ∗ TP

- - - - - - -

Tp = 46.4(1.64)0.14 ∗ (32.52)−0.38 ∗ (1 + 0)−1.99 ∗ (50)−0.4

Q𝑝 =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 7Q (

m3/s

ec p

er

10m

m o

f ra

in)

Time (hours)

Table 2 – Catchment properties computed parameter values

Tp (hours) 2.77

Qp (m3/s per 10mm) 2.18

TB (hours) 6.97


3 | Page

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


4 | Page

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

Rain

fall (

mm

)

Time (hours)

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14

Dis

ch

arg

e (

m3/s

)

Time (hours)


5 | Page

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


6 | Page

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

Rain

fall (

mm

) an

d In

flo

w Q

(m

3/s

)

Reserv

oir

Ele

vati

on

(m

)

Time from start of storm (hours)

Reservoir Elevation

Rainfall

Inflow

Dam wall height

Safety limit (2m below wall)


7 | Page

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


8 | Page

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/s

ec p

er

10m

m)

Time (hours)

0

5

10

15

20

25

30

1 2 3 4 5

Rain

fall (

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

Dis

ch

arg

e (

m3/s

)

Time (hours)

265

270

275

280

285

290

295

300

305

0 1 2 3 4 5 6 7 8 9 10

Ele

vati

on

(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


11 | Page

Appendix A1 – RSMD Map


12 | Page

Appendix A2 – SARR Map


13 | Page

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 Hydrograph (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

0.2475 0.4785

0.7194

0.5544

0.3795

0.1815 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

Documents

Hydrology 2 - Report