Analysis of the November 2009 Flood in the River Eden, Cumbria.

(Supervisor: Dr. James Bathurst)

By:

Syed Abbas Ali Mehdi.

MEng Civil Engineering

2016

Newcastle University, School of Civil Engineering & Geosciences CEG8099/cw2

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Module Details CEG8099 – Investigative Research Project

Student Syed Abbas Ali Mehdi

Supervisor Dr. James Bathurst

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Title: Analysis of November 2009 Flood in the River Eden, Cumbria

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Results 20 (15 –

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Abstract

The upscaling of peak discharge with catchment scale has been identified as a subject area that

needs more understanding. This study has analysed the November 2009 flood event in the Eden

catchment in Cumbria, UK. The flood event has been placed in the context of other notable floods

in the region, including the January 2005 and December 2015 floods. Note that these floods have

all occurred in the winter months, and therefore seasonal variability has not been accounted for

in this study. The flood has been analysed in three stages. Firstly, the rainfall distribution has been

analysed with respect to runoff. The results have shown that the cumulative runoff seemed to

exceed cumulative rainfall, which theoretically is not possible. This has been attributed to wind

induced undercatch, which would have resulted in raingauges recording less rainfall than actually

occurred, and a small number of available raingauges, which has affected the calculation of

catchment average rainfall. This highlights the need for better instrumentation and data

availability. The next stage of analysis was to observe the flood response and lag times as the

floodwave progressed through the catchment. The lag times for the two events varied greatly, and

upon closer inspection, this was found to be a result of interference between flows from

neighbouring catchments. Finally, the peak discharges and runoff values at the different gauging

stations have been plotted against the corresponding catchment areas, with power laws fitted to

them. The exponents obtained for the power laws have been found to match suggested values in

literature. However, it has previously been suggested that the scaling exponent decreases as the

return period of the event increases. This study did not find this to be the case. Instead, it was the

regression coefficient that increased as a result of the larger peak discharges. It was also found

that the peak runoff appeared to increase up to a certain scale before decreasing. This was

attributed to either a ponding effect at smaller catchment scales, or more likely, an error with the

rating curve at the gauging stations. Recommendations for future work have been suggested, and

include better instrumentation, piezometer records, and analysis of floods in summer months to

show the effects of seasonal variation.

ii

Acknowledgements

First and foremost, I would like to thank my supervisor, Dr. James Bathurst, for his exceptional

guidance, and uncanny ability to keep me on track. I would also like to thank Dr. Claire Walsh of

Newcastle University for her much needed aid with the creation of the rainfall maps exhibited in

this study. The data used within this study was obtained from numerous sources. These sources

include the Environment Agency, the CHASM project, Elizabeth Lewis and Mark Wilkinson. I

also extend my gratitude to Professor Hayley Fowler, Dr. Stephen Blenkinsop, and Michael

Pollock, for providing me with some insightful papers to help my literature review. I would also

like to show appreciation for the incessant banter provided by Jordan Crosland throughout the

project, for it certainly kept my spirits high. Lastly, I would like to thank my parents and my

brother for their relentless encouragement and good wishes.

iii

Abbreviations

AM – Annual Maximum.

CHASM – Catchment Hydrology And Sustainable Management.

EA – Environment Agency.

FARL – Flood Attenuation due to Reservoirs and Lakes.

FEH – Flood Estimation Handbook.

IDW – Inverse Distance Weighting.

POT – Peaks Over Threshold

QMED – Median Annual Maximum Flood.

SAAR – Standard Annual Average Rainfall.

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Table of Contents

Abstract ......................................................................................................................................... i

Acknowledgements ..................................................................................................................... ii

Abbreviations ............................................................................................................................. iii

Table of Contents ....................................................................................................................... iv

List of Figures and Tables ......................................................................................................... vi

1. Introduction ......................................................................................................................... 1

2. Aims and Objectives ........................................................................................................... 2

2.1 Aims .................................................................................................................................... 2

2.2 Objectives........................................................................................................................... 2

3. Literature Review ............................................................................................................... 3

3.1 Introduction ....................................................................................................................... 3

3.1.2 Notable Flood Events in Cumbria ............................................................................ 5

3.1.3 Sequence of Events Leading up to the November 2009 Flood ............................... 6

3.2 CHASM Initiative and the Eden Catchment .................................................................. 7

3.3 Instrumentation in the Upper Eden Catchment ............................................................ 9

3.3.1 Raingauge Errors ....................................................................................................... 9

3.4 Distribution of Precipitation .......................................................................................... 11

3.4.1 Interception and Depression Storage ..................................................................... 11

3.4.2 Infiltration and Overland Flow .............................................................................. 11

3.5 Flood Generation and Progression ................................................................................ 13

3.6 Spatial Scaling ................................................................................................................. 16

3.7 Conclusion ....................................................................................................................... 18

4. Methodology ...................................................................................................................... 19

4.1 Study Site ......................................................................................................................... 19

4.2 Data Origins .................................................................................................................... 20

4.3 Data Limitations and Corrections ................................................................................. 20

4.4 Identification of Storm Periods ...................................................................................... 22

4.5 Calculation of Runoff ..................................................................................................... 23

4.6 Calculation of Lag Times ............................................................................................... 23

4.7 Rainfall Map Generation using Inverse Distance Weighting ..................................... 24

4.8 Calculation of Catchment Average Rainfall ................................................................. 25

4.9 Return Periods ................................................................................................................ 27

4.10 Wave Speed Calculation ............................................................................................... 29

5. Results ................................................................................................................................ 30

5.1 November 2009 ................................................................................................................ 30

v

5.1.1 Rainfall ...................................................................................................................... 30

5.1.2 Discharge .................................................................................................................. 33

5.1.3 Wave Speed ............................................................................................................... 37

5.1.4 Catchment Average Rainfall versus Runoff .......................................................... 37

5.2 January 2005 ................................................................................................................... 38

5.2.1 Rainfall ...................................................................................................................... 38

5.2.2 Discharge .................................................................................................................. 40

5.2.3 Wave Speed ............................................................................................................... 43

5.2.4 Catchment Average Rainfall versus Runoff .......................................................... 43

6. Discussion........................................................................................................................... 45

6.1 Discussion of Rainfall ..................................................................................................... 45

6.2 Discussion of Flood Response and Lag Times .............................................................. 48

6.3 Discussion of Peak Discharge and Runoff .................................................................... 52

7. Conclusions ........................................................................................................................ 56

8. Recommendations ............................................................................................................. 58

9. References .......................................................................................................................... 59

10. Appendices ..................................................................................................................... 62

A. Project Management Statement .................................................................................. 62

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List of Figures and Tables

Figure 1: Predicted Energy Sources for 2020 demand. Reproduced from: (World Energy

Council, 2013)………………………………………………………………………………. 3

Figure 2: Map of Eden Valley Catchment (MAGIC, 2015)……………………………... 7

Figure 3: Translation and Attenuation of a Hydrograph (Shaw et al., 2011)…………. 14

Figure 4 – The Upper Eden sub-catchments (Mills and Bathurst, 2015)……………… 19

Figure 5- Rainfall at Aisgill used for identifying the storm period for the November 2009

event………………………………………………………………………………………... 22

Figure 6 – Rainfall at Aisgill used for identifying the storm period for the January 2005

event………………………………………………………………………………………... 23

Figure 7.a – Thiessen Polygons, January 2005………………………………………….. 26

Figure 7.b – Thiessen Polygons, November 2009……………………………………….. 26

Figure 8.a – Pooling group automatically generated by the software………………… 28

Figure 8.b- Check for heterogeneity…………………………………………………….. 28

Figure 9 – Return periods obtained from pooling group……………………………… 28

Figure 10 – Rainfall at each raingauge available for the November 2009 event……... 31

Figure 11 – Cumulative Rainfall at each raingauge over the November 2009 storm

period……………………………………………………………………………………... 32

Figure 12 – Rainfall map for the entire storm period created using the Inverse Distance

Weighting technique…………………………………………………………………….. 32

Figure 13 – Runoff hydrograph for the stations along Scandal Beck and Eden main

stem……………………………………………………………………………………….. 34

Figure 14 – Peak Runoff at all stations for which data was available………………... 34

Figure 15- Peak Discharge vs. Area for all stations with a power law fitted………… 35

Figure 16 – Peak Discharge vs. Area excluding Blind Beck, Helm Beck and

Ravenstonedale with a power law fitted………………………………………………… 35

Figure 17 – Lag time vs. Catchment area for all stations, with a power law fitted up to

Temple Sowerby………………………………………………………………………….. 36

Figure 18 – Lag time vs. Catchment area excluding Blind Beck and Helm Beck, with a

power law fitted up to Temple Sowerby………………………………………………... 36

Figure 19 – Catchment Average Rainfall calculated using Thiessen Polygons vs Runoff at

five different catchments scales………………………………………………………….. 37

Figure 20 – Cumulative Catchment Average Rainfall against Cumulative Runoff at five

different catchment scales……………………………………………………………..... 38

Figure 21 – Rainfall at all available raingauges for the January 2005 event………… 39

vii

Figure 22 – Cumulative Rainfall at each raingauge for the January 2005 event……….40

Figure 23 – Rainfall map for the January 2005 event generated using the IDW

technique…………………………………………………………………………………….40

Figure 24 – Peak Runoff at all stations in order of catchment area…………………….41

Figure 25 – Runoff Hydrographs for the EA stations for the January 2005 event…… 42

Figure 26 – Lag time vs. Catchment Area for January 2005 event, with a power law fitted

up to Temple Sowerby……………………………………………………………………. 42

Figure 27 – Peak Discharge vs. Catchment Area for the January 2005 event, with a power

law fitted to all stations…………………………………………………………………… 42

Figure 28 – Catchment Average Rainfall vs. Runoff at the three available stations in the

Upper Eden for the January 2005 event…………………………………………………44

Figure 29 – Cumulative Catchment Average Rainfall vs. Cumulative Runoff at the

available stations for the January 2005 event………………………………………….. 44

Figures 30.a-c – Rainfall during the three stages of the storm event, Stage 1-Stage 3 going

clockwise from the top left………………………………………………………………. 46

Figure 31 – Thiessen Polygons for the raingauges available for the November 2009 event.

The area of the polygon is represented as a percentage of the total catchment area…47

Figure 32 – Flood Response at Gais Gill with the rainfall at Aisgill, and Blind Beck with

the rainfall at Sykeside………………………………………………………………….. 48

Figure 33 – Lag times and calculated wave speeds at different stations for the November

2009 event………………………………………………………………………………... 49

Figure 34 – Lag times and calculated wave speeds at different stations for the January

2005 event………………………………………………………………………………... 50

Figure 35 – Lag times for both events with Power laws fitted to stations up to Temple

Sowerby. Great Corby is marked differently to highlight the differences due to inflows

from neighbouring catchments……………………………………………………….... 51

Figure 36 – Peak Discharge vs. Catchment Area with power laws fitted to the three

events…………………………………………………………………………………….. 52

Figure 37 – Peak Discharge vs. Catchment area for November 2009, with power laws

fitted to discharges at different catchment scales to investigate effect of increasing

catchment area………………………………………………………………………….. 53

Figure 38 – Peak Runoff vs. Catchment Area with power laws fitted to the three

events…………………………………………………………………………………….. 54

Figure 39 – Peak Runoff vs Catchment area with power laws fitted to six different events

taken from an earlier study on the Upper Eden Catchment (Wilkinson, 2009)……. 55

viii

Table 1- Flood Regime in the UK since 2000 (Met Office, 2015a)…………………………4

Table 2- Environment Agency Gauging Stations along the Eden………………………... 8

Table 3 – List of Upped Eden Catchments and corresponding number on Figure 4…... 19

Table 3 – Data used within the study……………………………………………………… 21

Table 4 – Example of a table used for locating the raingauges on the raster map…….. 24

Table 5- Example of a table used to create a layer to be used with the Inverse Distance

Weighting technique…………………………………………………………………....… 25

Table 6 – Areas of the Thiessen Polygons generated for the two events……………….. 27

Table 7 – Distances between stations taken from Wilkinson (2009)…………………... 29

Table 9- Raingauges, elevation and rainfall totals for November 2009……………..… 30

Table 10 – Gauging stations, peak discharges, and lag times calculated from Aisgill for

November 2009 event…………………………………………………………………...... 33

Table 11 – Calculated wave speeds for the November 2009 event……………...…….. 37

Table 12 – Raingauges and Total Rainfall – January 2005………………………........ 38

Table 13 – Peak Discharges and Lag Times for the January 2005 event…………...... 41

Table 14 – Wave speeds at the available stations for the January 2005 event…...….. 43

1

1. Introduction

An extensive literature review has found that climate change is an ever present issue, and with a

projected increase in population, it is going to continue to be an issue. Subsequently, the frequency

and intensity of precipitation events during the winter is predicted to increase in the UK

(Intergovernmental Panel on Climate Change, 2014). This can lead to fluvial floods. The past 15

years in the UK (2000-2015) has been a flood rich period. However, whilst floods occur regularly,

they are still complex phenomena which have not been understood fully. One of the main

complexities of floods are ‘scale issues’, which involve the upscaling of peak discharge with

respect to catchment area. To increase understanding, data is needed.

An opportunity for obtaining data has presented itself in the form of the Upper Eden catchment

in Cumbria, UK. This catchment includes numerous sub-catchments ranging from micro-scale to

meso-scale, and an extensive hydrological monitoring network. In recent years, the catchment has

experienced numerous flooding events of varying magnitudes. Out of these events, the one of

interest is the November 2009 flood of the River Eden. The data for this event has been obtained

from the Catchment Hydrology And Sustainable Management Initiative (CHASM) and the

Environment Agency (EA). To provide some context, data was also obtained for the January 2005

event. From the literature review, various ways of presenting and analysing rainfall and discharge

data have been uncovered, which will be utilised in this study. Firstly, hyetographs will be created

wherever possible to show the rainfall pattern with respect to time. Secondly, rainfall maps will

be generated using the Inverse Distance Weighting tool in ArcMap to show the spatial distribution

of rainfall. Next, discharge hydrographs will be created in terms of runoff to allow comparison

with the catchment average rainfall. The catchment average rainfall will be calculated using

Thiessen polygons, which can also be created in ArcMap. Further to this, the flood response will

be observed at different catchment elevations, and the lag times and wave speeds will be

calculated. Data from Great Corby, which is a station outside the Upper Eden will also be

included. The reasoning behind this is to show the variation in lag times at a catchment scale

where major inflows from other catchments are present. Lastly, and most importantly, the peak

discharges will be studied with respect to catchment area. The idea behind this is to fit power laws

to the data and compare the calculated values for the exponents to values present in literature.

The outcomes of this study will aim to show how the flood behaved as it progressed through the

catchment. They will also hopefully highlight the impact of spatial variability of rainfall on flood

response. Finally, it is anticipated that the study sheds some light on the scale issues, and the

findings provide guidance to potential areas of further research.

2

2. Aims and Objectives

2.1 Aims

This project will investigate and analyse the November 2009 Flood in the Eden Valley whilst

placing it in the context of other notable floods in the region. The data will be provided from the

unusually dense CHASM instrument network and the Environment Agency. The key aim will be

to advance the understanding of flood generation and progression for a single event across a range

of catchment scales.

2.2 Objectives

Undertake a thorough literature review to develop expertise in the area.

Key reading material will include how precipitation is distributed and how runoff is generated.

Previous studies on floodwave generation, progression, and spatial scaling will be analysed.

Assemble the necessary dataset and exhibit the rainfall distribution and the river response

variation during the event.

Data will be obtained from the Environment Agency and the CHASM gauging stations. Rainfall

maps will be constructed to describe the spatial pattern and variability. Hydrographs will be

generated for individual gauging stations and compared with rainfall volume to assess the

contribution of rainfall to peak discharge.

Interpret the results to explain flood wave generation and progressions. Observe flood wave

movement across different spatial scales using hydrographs.

Comparison will be undertaken between the hydrographs at different stations to understand and

explain how the peak discharge varies as it progresses through the catchment.

Contrast the event with the January 2005 flood

The rainfall variability and peak discharge at the different gauging stations for the January 2005

flood will be compared to develop an understanding of the differences in upscaling of peak

discharge between events.

3

3. Literature Review

This section provides a review of literature studied for the purpose of developing knowledge about

the subject. Existing work on the subject has also been researched with the intention of identifying

knowledge gaps that could be addressed during this study.

3.1 Introduction

The human population has been growing at a faster rate than ever before. In 2003, the annual

growth rate of population was 1.22%. It was then predicted that by 2050, the human population

would be at 7.7 billion (Cohen, 2003). However, this prediction has drastically changed, as the

current population is already at 7.3 billion. The United Nations have now predicted that the

population levels are going to increase to 9.7 billion by 2050 (United Nations, 2015). This growth

in population has been accompanied by a growth in the world economy, agriculture, industrial

output, and perhaps most importantly, energy use (Crutzen, 2006). The World Energy Council

(2013) published a report on past, current, and future energy resources. It was predicted that by

2020, energy demand would be 17208Mtoe (million tonnes of oil equivalent). The predicted

sources to meet this demand are displayed in Figure 1.

With fossil fuels accounting for a substantial proportion of energy sources, significant greenhouse

gas emissions can be expected. Greenhouse gas emissions have been widely attributed as the

highly likely driver of global warming (Intergovernmental Panel on Climate Change, 2014;

Crowley, 2000; Houghton, 2004; Yamin and Depledge, 2004).

In his book, Global Warming, Houghton (2004) carefully assesses the widespread impacts of

global warming and the changing climate. A change in temperature affects agriculture,

Figure 4: Predicted Energy Sources for 2020 demand. Reproduced from: (World Energy

Council, 2013)

76%

16%

2%6%

Predicted Energy Sources 2020

Fossil Fuels Renewables Hydro Nuclear

4

ecosystems, sea-level rise, and precipitation. Houghton suggests that global warming leads to

increased evaporation of surface water, which in turn results in higher atmospheric water vapour

content, therefore causing greater amounts of precipitation. This suggestion is further augmented

by the findings of the Intergovernmental Panel on Climate (IPCC). The Fifth Assessment Report

(AR5) published by the IPCC cites that in Europe and North America, the frequency and intensity

of heavy precipitation events has likely increased as a result of climate change (Intergovernmental

Panel on Climate Change, 2014). Heavy, persistent precipitation over large areas can result in

fluvial flooding (Douben and Ratnayake, 2006).

3.1.1 Recent Flood Regime in the UK

Looking at the UK specifically, wetter winters are expected, with heavy events constituting a

large proportion of precipitation (Department for Environment, Food and Rural Affairs, 2012).

This is likely to increase the risk of flooding. Flooding can cause significant damage to

communities because it affects residential properties, business, and infrastructure. The flood

regime in the UK since 2000 is listed in Table 1.

Table 8: Flood Regime in the UK since 2000 (Met Office, 2015a).

Year Month Location

2000 April, May, and Sep-Nov Throughout the UK, Berkshire

2001 February and October Eastern UK

2002 October-December Southern and Eastern England

2003 November South-east England

2004 July and August Throughout England and Boscastle

2005 January and June Carlisle and North Yorkshire

2007 May-July Throughout England

2008 September Morpeth

2009 November Lake District

2010 November Cornwall

2012 April-July, and November Throughout England

2013 December to January 2014 Scotland and Northern England, then South England

2014 January - February Throughout UK

2015 December North West England and Yorkshire

From Table 1 it can be observed that heavy rainfall events have increasingly occurred in the winter

months. The impacts of the events were also severe, with lives being lost in some cases. In the

December 2013 event, the Thames Barrier performed its purpose successfully (Met Office,

2015a). However, if it had been designed inadequately, the consequences would have been

5

substantial. North Western England in general seemed to have faced some of the more severe

storm events.

3.1.2 Notable Flood Events in Cumbria

In January 2005, the worst flooding event to affect Carlisle since 1822 occurred. The impacts of

this event were disastrous, with three lives being lost, along with the closure of businesses,

schools, and widespread disruption to transport due to all of Carlisle’s buses suffering damage.

The event was associated with a return period of 200 years (Met Office, 2012a). Subsequently,

investment of £38 million was spent on flood defences to ensure that the flooding of this

magnitude would not occur again (Freeman, 2015). These flood defences were successful during

the 2009 event (Met Office, 2012b).

During the November 2009 event, the highest rainfall recorded was 316.4 mm at Seathwaite (Met

Office, 2012b). To provide some context, the highest rainfall recorded for the January 2005 event

was 180.4mm at Rydal Hall (Met Office, 2012a), which is not far from Seathwaite. Comparing

the damages caused by both events, it can be argued that if the flood defences had not been

commissioned, the November 2009 event could have been much more disastrous. Investigating

the December 2015 event, a record rainfall of 341.4 mm was observed at Honister Pass. Whilst it

may seem that the rainfall amount was only slightly larger than the November 2009 event,

Cumbria had already experienced more than twice the monthly average rainfall in November.

This rendered the ground saturated, further intensifying the flooding. The flood defences put in

place in Carlisle following the January 2005 floods did not work as intended (Met Office, 2015b).

This could be because events with a larger return period were not expected during the design

stage. Whilst considering events with large return periods may result in overdesign which could

be costly, the damage from such events would result in even greater costs.

The UK government is committing to invest £2.3 billion by 2020 for the construction of over

1400 flood and coastal erosion risk management schemes. (Department for Environment, Food

and Rural Affairs, 2014). To be able to successfully adapt against floods, an understanding of

how floodwaves generate and propagate through a catchment is needed. This can allow the

creation of models which can predict future floods, and thus help design appropriate defences.

However, the upscaling of peak discharge as the catchment scale increases has been identified as

an issue, which is discussed further in Section 2.6.

To better understand flood generation and progression across a range of scales, an opportunity

has presented itself in the form of the unusually well instrumented Upper Eden catchment in

Cumbria. This catchment is one of four large scale catchments, and extensive hydrometric

instrumentation has been implemented within it as part of the CHASM initiative (O’Connell et

al., 2002). The specific event that shall be studied is the November 2009 event.

6

3.1.3 Sequence of Events Leading up to the November 2009 Flood

There was a period of heavy and persistent rain from the 18th to 20th November 2009. The origins

of this storm were supposed to be tropical, with some indications linking it to ex-hurricane Ida.

This event was nor strongly developed, neither did it traverse very far, but it did result in in warm,

moist air being directed towards Britain and Ireland. On the 16th of November, a depression (a

low pressure area), emerged from Newfoundland and engaged with the warm plume of air. Rapid

development of this low pressure system was observed centred around the south of Iceland on the

18th of November. The prolonged period of rainfall was a result of the upper confluent trough

associated with the event (Sibley, 2010).

Prior to the event, Cumbria had already experienced close to the whole-month November average

of rainfall. As a result, the ground was already saturated when the heavy rainfall occurred (Met

Office, 2011). This likely resulted in both infiltration excess and saturation excess overland flow,

discussed further in Section 2.4.2. The effects of the rainfall were devastating, with over 1,300

homes being affected, disruption to transport networks, and sadly, the death of a police officer

due to a bridge collapse (Met Office, 2011). Although these tragic events took place towards

western Cumbria, flooding of the River Eden also occurred.

7

3.2 CHASM Initiative and the Eden Catchment

In the UK, the Catchment Hydrology and Sustainable Management (CHASM) initiative was

launched in 1998 by an association of universities and research institutes. The scale issues

(Section 2.6) are one of the key drivers for the CHASM initiative. The initiative aims to contribute

towards the understanding of these issues through a series of multi-scale monitoring networks

across four mesoscale catchments. The Upper Eden catchment is one of these four catchments,

and is well instrumented for a catchment of its scale. Therefore, detailed data on rainfall,

discharge, and river stage can be obtained (O’Connell et al., 2002; Mayes et al., 2006).

The Eden valley catchment is situated in Cumbria with a total area of 2288 km2 (Mayes et al.,

2006). The valley originates in the south from the village of Brough, and stretches northwards

through Appleby-by-Westmorland, ending around the outskirts of Carlisle. The drainage of the

valley is north-westwards, with the outlet being Solway Firth (Figure 2). It is a primarily rural

area, with agriculture, mineral extraction, and tourism being the chief industries (Younger and

Milne, 1997).

The entire Eden catchment can be split into two parts, the upper and lower. The upper catchment

is situated above the town of Temple Sowerby. It has a steeper gradient terrain and moorland,

whilst the lower catchment is identified by the Eden floodplain and a drumlin field. Flashy runoff

is observed in the upper catchment as a result of the steeper terrain, whilst the limestone and

sandstone aquifers in the lower catchment result in greater contributions from groundwater.

Figure 2: Map of Eden Valley Catchment (MAGIC, 2015)

8

However, there are some interbedded sandstones and mudstones which behave as aquitards.

(Mayes et al., 2006; Younger and Milne, 1997).

The National River Flow Archive set up by the Centre for Ecology and Hydrology (CEH)

provides information on the gauging stations along the rivers in the UK (Centre for Ecology and

Hydrology, 2015). A list of stations belonging to the Environment Agency along the Eden, the

catchment area they cover, and their elevation is tabulated in Table 2.

Table 9: Environment Agency Gauging Stations along the Eden

Station Name (Upper/Lower) Elevation (m,

A.O.D)

Catchment area (km2)

76014 – Kirkby Stephen (U) 158.1 69.4

76806 – Great Musgrave Bridge (U) null 223.1

76005 – Temple Sowerby (U) 92.4 616.4

76017 – Great Corby (L) 19 1373

76002 – Warwick Bridge (L) 17.5 1366.7

76007 – Sheepmount (L) 9.9 2286.5

9

3.3 Instrumentation in the Upper Eden Catchment

To successfully study the Eden catchment, data will be required. Data, or information, can be

obtained through monitoring networks (Viessman and Lewis, 1996).

Mayes et al. (2006) have published a thorough report on the Upper Eden catchment as part of the

CHASM initiative. Heavy instrumentation of the catchment was undertaken between 2002 and

2004, which has augmented the existing instrumentation by the Environment Agency. The

existing instrumentation comprises of discharge gauges at three locations, and raingauges at nine.

To supplement this, eight stage gauges have been added which monitor the river levels in different

areas of land use, ranging across different catchment scales. A network comprising of 11 tipping-

bucket (TB) raingauges along a series of elevations adjuncts the nine Environment Agency

raingauges. Meteorological data to calculate evapo-transpiration is provided by two automatic

weather stations at Gais Gill and Great Musgrave.

The groundwater is also monitored across the catchment, with over 15 boreholes at Great

Musgrave which measure the interactions between the river and the sandstone aquifers. A series

of piezometers at a shallow depth (< 2 m) measure the soil moisture and water table depth. These

piezometers are located at varying locations at Great Musgrave and Gais Gill.

All instruments have limitations and potential for error. These limitations can inevitably have an

effect on the data provided. Therefore, they need to be understood in order to get a more realistic

appraisal of the data.

3.3.1 Raingauge Errors

The simplest hydrological instrument is the raingauge. It has been suggested that raingauges date

back to almost 2500 years ago, but despite their antiquity, errors still occur when measuring the

amount of precipitation. Some errors are easier to eliminate, and generally require proper spatial

location of raingauges. However, an issue that is quite common and more difficult to deal with is

wind turbulence that can be caused around the gauge (Goodison et al., 1998; Rodda and Dixon,

2012). This problem is created by the rain gauge itself since it poses an obstacle to the airflow

leading to the generation of eddy currents around its opening. These eddies may blow the

precipitation away from the opening resulting in an ‘undercatch’, which is a recorded value lower

than actual precipitation (Herschy and Fairbridge, 1998). The underestimates can be substantial,

with Rodda and Dixon (2012) suggesting that actual rainfall volumes in the UK are regularly

underestimated by 5-20%.

There is a variety of raingauges available. In the Upper Eden catchment, TB gauges have been

used. They operate by funnelling collected water into a balanced two-compartment bucket. A

designed quantity of rain, usually 1mm, will fill a compartment, causing it to tip and move the

second compartment underneath the funnel. Each time a compartment tips, the water is spilled

10

which leaves a trace on a strip chart, or sometimes, produces an electrical impulse which is

transmitted to a recording device. To record snow measurement, the collector can be heated, but

this is not advisable due to the possibility of evaporation, which will blatantly cause an inaccuracy

with the measurement (Linsley, Kohler and Paulhus, 1982; Viessman and Lewis, 1996; Marsalek,

1981). If the rainfall intensity is not too high, TB gauges are able to record rainfall amount and

time variation with great accuracy. Through the use of the electric impulses, they are suitable for

remote recording as well (Marsalek, 1981). However, Bruce and Clark (1966) objected that during

intense storms, water would be lost whilst the bucket was tipping. It was proposed by Smoot

(1971, cited in Marsalek, 1981) that simply calibrating the gauges would eliminate this limitation.

To test this theory, Marsalek (1981) performed an excellent study on the effects of calibration on

different type of raingauges. His study concluded that during extreme events, even calibrated

tipping-bucket raingauges could underestimate the actual intensities by approximately 10%, thus

disproving Smoot’s theory. Without the calibration, more errors could occur.

Sevruk et al. (2009) have highlighted the need to correct point precipitation measurements. A

simple equation has been proposed by Sevruk (1984):

𝑃𝑘 = 𝑘𝑃𝑐

(Eqn. 1)

where Pk is the corrected amount of precipitation, Pc is the precipitation caught by the gauge, and

k is the correction factor. The correction factor can be experimentally estimated by field

comparisons of national and pit gauge measurements. However, within the Eden catchment, there

are no pit gauges available, hence this correction method cannot be applied in this study.

Therefore, data accuracy will have to be treated with caution.

Not all of the rainfall recorded will contribute to runoff. This is because precipitation can be

distributed in several ways.

11

3.4 Distribution of Precipitation

The hydrological cycle is a continuous process where water is transported from the surface, to the

atmosphere, and then back to the surface. Radiant energy from the Sun results in the heating of

surface waters, leading to evaporation. The water vapour is stored in the atmosphere for an

average of ten days. Through condensation, clouds are formed, and if conditions are favourable,

precipitation occurs. Precipitation is the process through which water returns to land from the

atmosphere. It can take the form of rain, hail, or snow. (Shaw et al., 2011). It is accepted that

precipitation can be distributed across land in primarily four different ways: Interception,

depression storage, infiltration, and overland flow (Viessman and Lewis, 1996).

3.4.1 Interception and Depression Storage

Vegetation and other forms of cover are the first encounters precipitation faces. Part of the

precipitation adheres to these surfaces. It can be retained by leaves, or it can flow down the plants

and contribute to streamflow. Interception occurs when precipitation is retained, or intercepted,

by the leaves. The storm characteristic, species and density of dominant vegetation, and the season

are all variables which determine the amount of water intercepted. Precipitation that reaches the

ground can become trapped in small depressions. This phenomenon is knows as depression

storage. Water can exit depressions only by evaporation, or seepage into the ground. The size of

depressions and their origins largely depend on the land-use in practices in the catchment.

Therefore, depression storage can vary significantly between catchments (Viessman and Lewis,

1996). For this study, the effects of depression storage will be considered to be negligible. This is

because the calculation requires field measurements (Viessman and Lewis, 1996), which are not

available.

3.4.2 Infiltration and Overland Flow

Infiltration occurs when water moves downwards through the ground surface, replenishing soil

moisture and recharging aquifers. Infiltration can influence when overland flows occur, making

it an essential part of any hydrologic model. The rate of infiltration depends greatly on surface

condition, groundwater storage, soil profile, and rainfall intensity. Within a single catchment, the

infiltration capacity tends to vary spatially and temporally (Viessman and Lewis, 1996). The

permeability of soils can change over time. Smaller particles can be transported by water, and can

eventually clog the pores within the soil (Heathcote, 1998). If the infiltration capacity is less than

the rainfall rate, infiltration excess overland flow can be observed. This is due to the soils inability

to allow for any further infiltration, thus resulting in excess water flowing overland. Infiltration

excess overland flow is the main response to rainfall in urban locations, due to the large amount

of impermeable areas. It depends on the nature of the catchment, and more importantly, the

intensity of the rainfall rather than the rainfall amount. Another form of overland flow is saturation

12

excess overland flow. This is independent of the rainfall intensity because it results from perched

water tables and rising subsurface flow. It is commonly observed in areas near a river channel

since this is where subsurface flows emerge (Brutsaert, 2005). It is highly likely that these

phenomena occurred during the 2009 event due to the ground being saturated from previous

events. Any water moving naturally across the surface due to gravity is known as surface runoff.

Runoff is the most likely cause of floods (Hamill, 2011).

13

3.5 Flood Generation and Progression

To understand floods, the factors which affect runoff must be understood. Hamill (2011) has

identified these factors, which can either be climatic factors or catchment characteristics. These

factors and their implications are listed below:

1. Type of precipitation and intensity.

Snowmelt can result in large amount of runoff in a short amount of time. However this is not

applicable to the November 2009 event since the type of precipitation was rainfall. If the rainfall

intensity is high, the infiltration capacity will be severely exceeded resulting in surface runoff. If

it is low, more groundwater flow may be observed.

2. Duration of precipitation.

As the duration increases, the catchment becomes increasingly saturated, resulting in surface

runoff. This is irrespective of rainfall intensity.

3. Areal extent of the storm.

Low intensity rain falling uniformly over the catchment may not surpass the infiltration capacity,

therefore resulting in minimal runoff. Conversely, intense rain over a small part of catchment can

lead to localised runoff and flooding.

4. Orientation of storm and catchment.

If the orientation of the storm and the catchment are the same, and the storm travels the full length

of the catchment, then a larger amount of rainfall will be deposited upon the catchment. To

investigate this scenario for the November 2009 event, rainfall maps will be generated.

5. Weather and antecedent catchment conditions.

Long periods of no rainfall can render the ground unsaturated, and therefore absorbent. However,

if rainfall events happen in succession, as was the case for the November 2009 event, severe

flooding can occur.

6. Land use.

Deforestation can reduce interception, and natural storage can be reduced by field drains.

Impermeable areas can also increase surface runoff, but they will not be applicable to the Upper

Eden catchment due to its rural nature.

7. Type of soil or rock.

The type of soil will influence the infiltration capacity and therefore runoff. As mentioned earlier,

in the Upper Eden catchment, sandstone and limestone aquifers are situated in the lower parts,

which act as aquifers. However, flooding can still occur due to intense rainfall.

8. Catchment shape.

14

The catchment shape will affect the time of concentration, which is the time taken for water falling

upon the furthest part of the catchment to reach the outlet. After this time period, the entire

catchment area contributes to the flow. The Upper Eden catchment is relatively long, and

therefore, a longer time of concentration can be expected.

9. Stream frequency.

The likelihood of runoff reaching the main channel is increased with the frequency of streams in

close proximity to each other.

10. Catchment area.

Lastly, runoff can be expected to increase as the area of the catchment increases. However, the

amount peak discharge increases by is not proportional to the area, as upland catchments are

steeper, and larger catchments tend to have more storage.

All these factors will have an effect on the runoff, with some prevailing more than others. A

simple and very useful way to represent the behaviour of water during a time period is a

hydrograph. Without generating hydrographs the aim of this study will be unachievable.

Understanding how a flood hydrograph behaves during the course of a flood event will be

necessary as well. The hydrographs for the 2009 event should demonstrate the effects of

translation and attenuation; an example is shown in Figure 3. Translation quite simply means that

the peak discharge occurs at a later time downstream. This is an obvious expectation since the

flood wave would take time to travel downstream. Attenuation is the ‘flattening’ out of the

hydrograph in the event that there are no large secondary inflows to the river channel (Shaw et

al., 2011).

Fortunately for the Upper Eden catchment, discharge gauges are available both upstream and

downstream. If this was not the case, flood routing would have to be applied. This involves

observing the comportment of the flood wave using models, at different parts of a river reach and

Figure 3: Translation and Attenuation of a Hydrograph (Shaw et al., 2011)

15

through the flood plain. Flood routing can be approached in two ways by using either hydrological

routing or hydraulic routing. Hydrological routing employs the principle of continuity and a

relatively simple relationship between discharge and the temporary storage of excess volumes of

water during the flood. Hydraulic routing utilises the St. Venant equations, which are based on

the conservation of mass (continuity) and conservation of energy equations. These are complex

equations describing the motion of unsteady flow in open channels. Due to the complexity, it is

often necessary to make assumptions and approximations (Shaw et al., 2001; Viessman and

Lewis, 1996).

16

3.6 Spatial Scaling

Hydrological processes can be observed across a range of scales. Scale can be defined as the

‘…characteristic time (or length) of a process, observation or model.’ (Blöschl and Sivapalan,

1995). In hydrology, as the scale of a phenomenon increases, so does the complexity of the inter-

connection between individual processes. Thus, any model describing the system becomes more

complex, and the solution becomes more difficult to obtain (Dooge, 1982). Runoff generation is

non-linear, and varies across catchments of different scales. Yet, most hydrological models are

based on a localised model of catchment response and expected to work at large scale of

catchments. This inevitably requires extrapolation across scales, and therefore the predictive

response may be different than the empirical one (Blöschl and Sivapalan, 1995; Wood, Sivapalan

and Beven, 1990). These problems are known as ‘scale issues’. These issues provide a purpose

for this study: researching the upscaling of peak discharge as the catchment scale increases.

Extensive research has been undertaken to help understand scale issues better. Six of these studies

agree that a power law variation between peak discharge and area exists (Goodrich et al., 1997;

Ogden and Dawdy, 2003; Furey and Gupta, 2005; Furey and Gupta, 2007; Mandapaka et al.,

2009; Ayalew et al., 2014). This equation generally takes the form of:

𝑄𝑝 = 𝑐𝐴𝑑

(Eqn. 2)

where Qp is the peak discharge associated with a specific return period, A is the catchment area,

c is the regression co-efficient, and d is the scaling exponent. This scaling exponent determines

the degree to which the transformation from rainfall to runoff is diminished by the catchment

(Goodrich et al., 1997). It is subject to numerous variables such as rainfall rate, soil moisture,

infiltration capacity, groundwater table elevations, land use, and geomorphology (Ogden and

Dawdy, 2003). Therefore, whilst the equation is simple, an issue arises in the form of obtaining a

universal value of d, due to its variance across different catchments. However, Leopold et al.

(1964, as cited in Goodrich et al., 1997) have suggested 0.65-1.0 as a range of values for d in

natural basins. Benson (1962; 1964, as cited in Goodrich et al., 1997) observed that d = 0.85 for

humid watersheds in the New England region, and decreased to 0.59 for watersheds in primarily

semiarid regions of Texas and New Mexico. He then concluded that the values for d tend to

decrease as the watershed area, aridity, and the return period of the event increase. He also noted

an increase in the value with the amount of watershed and climatic variables applied in a

multivariate regression of peak runoff rate. These discoveries provide some guidance towards

possible values of the scaling exponent across different catchments.

In a more recent and highly extensive study, Ogden and Dawdy (2003) observed that flood flow

quantiles followed simple scaling theory, meaning that there were similarities in distributions of

peak discharge across a range of scales. However, it must be noted that their study was undertaken

17

for a catchment with a maximum area of 21.2 km2, and therefore it would be interesting to

investigate the applicability of the same rules to a larger catchment. This forms the basis of one

of the aims of this study, which is to observe the flood wave behaviour in terms of peak discharge

for a single event across a catchment ranging from micro-scale (1 km2) to above meso-scale (100

km2).

Bell and Moore (2000) highlighted the issue of the impact of spatial variability of rainfall on the

flow response. Mayes et al. (2006), have addressed this issue for the Upper Eden catchment, and

concluded that spatial variability of rainfall was significant in controlling the flow response, with

flashy runoff in the uplands and attenuated runoff in the lowlands. Following their findings, in

this study, rainfall distribution maps will be generated, and the cumulative rainfall will be

compared with the corresponding runoff at each of the gauging stations. This will provide

information on the volume of rainfall transformed to runoff during a specified time period. The

rainfall maps will be generated using the inverse distance weighting method. This is a tool

available within the geographic information system (GIS) package ARCVIEW, which will

generate a surface representing rainfall amount that is influenced more by the nearby raingauges

and less by those that are further away (Mayes et al., 2006).

18

3.7 Conclusion

There has been an increase in energy demand following the recent surge in human population.

This demand is projected to grow along with the population. It has been found that the primary

sources used for fulfilling this demand are fossil fuels. The usage of fossil fuels is linked to the

production of greenhouse gases, which are in turn proposed to be the most likely driver for global

warming. One of the effects of global warming is an increase in the frequency and intensity of

precipitation. This can result in fluvial flooding. This effect has been repeatedly observed in the

UK within the past 15 years. The flood events have had drastic consequences in most cases, such

as disruption to transport, power, businesses, and more importantly, loss of life. Logically, the

UK government has committed to increasing funding for flood defence schemes. However, to

effectively design these schemes, a greater understanding of flood wave behaviour is required.

One of the key design factors is the peak discharge during a flood event. However, it has been

found that ‘scale issues’ are present. Specifically, the upscaling of peak discharge as the

catchment area increases is an issue that has been identified and investigated. It has been found

that a power law variation between peak discharge and area exists (Eqn. 2). However, the

coefficient and exponent in this equation vary between events and catchments, making it difficult

to obtain a universal value. In addition, similarities between peak discharge distributions have

been discovered in an earlier study (Ogden and Dawdy, 2003), but the study has been limited by

the scale of the catchment in question. It is a fact that flood waves are, naturally, a result of surface

runoff, which is largely dependent on various factors. These factors can be climatic or they can

be catchment characteristics. The climatic factors can be understood and analysed through

instrumentation.

The Catchment Hydrology and Sustainable Management (CHASM) initiative that has been

launched within the UK aims to study the scale issues through extensive hydrometric

instrumentation of four meso-scale catchments. The Upper Eden catchment is one of these

catchments, and is unusually well instrumented for a catchment of its size. It varies across several

orders of magnitude of area, which makes it an excellent choice for this study. The specific event

that will be studied will be the November 2009 flood. The data obtained from the instrument

networks will allow the generation of rainfall distribution maps, as well as the generation of

hydrographs at different sub-catchments within the entire catchment. This will undoubtedly help

achieve the aim of this study, which is to improve the understanding of flood generation and

progression across different spatial scales.

Possible errors with instrumentation have also been identified, such as undercatch and improper

calibration. Whilst correction procedures exist, they will not be applied in the study due to the

inability to acquire the necessary information. Nevertheless, an awareness of the errors has been

created, and as a result, all data measurements will be treated with caution.

19

4. Methodology

The purpose of this study is to analyse the November 2009 flood of the River Eden and place it

in the context of other notable floods in the region. This will be achieved by creating and studying

hydrographs, hyetographs, and rainfall maps for the events. This will allow the identification of

the magnitude of peak discharges, the rainfall pattern, and the calculation of lag times and wave

speeds as the floodwave progresses through the catchment. The catchment average rainfall and

the corresponding runoff response for different events will also be studied. Return periods also

need to be calculated to show the severity of floods. Finally, the upscaling of peak discharge with

respect to catchment area will be studied with the hope of increasing the understanding of the

‘scale issues’ identified in the literature review. This section provides details about the origins of

the data, and the processes by which the required graphs, maps, and tables were created.

4.1 Study Site

Figure 4 shows the different sub-catchments within the Upper Eden and Table 3 lists the

corresponding gauging stations. The stations that were not used at all due to a lack of data are

listed in red. The Upper Eden has an important tributary in the form of Scandal Beck, upon which

most of the smaller gauging stations in the CHASM nested instrument network lie. Kirkby

Stephen, whilst being on the main stem of the Eden lies outside the nested system, as do Blind

Beck and Helm Beck.

Table 10 – List of Upper Eden Catchments and

corresponding number on Figure 4.

Name Area (km2) Number on

Figure 4.

Gais Gill 1.1 1

Artlegarth 2.7 2

Ravenstonedale 25.6 3

Scandal Beck at Smardale 36.6 4

Scandal Beck at Soulby 40 5

Eden at Great Musgrave 223.4 6

Eden at Temple Sowerby 322 7

Eden at Great Corby 616.4 8

Blind Beck 9.8 9

Swindale Beck 16 10

Helm Beck 18 11

River Belah 53 12

Kirkby Stephen 69.4 13 Figure 4 – The Upper Eden sub-catchments (Mills

and Bathurst, 2015)

20

4.2 Data Origins

The two main datasets that were used were stage-discharge data and rainfall data. These were

available from the Environment Agency and the CHASM project. However, a key issue with the

data was availability for all three events. This arose from the fact that the CHASM project is no

longer active, and as a result, the data for the December 2015 event from the CHASM gauges was

not available. The data from the CHASM stations for the January 2005 event was also unavailable.

However, an earlier study was used (Wilkinson, 2009), which provided the hourly peak

discharges for the CHASM discharge stations. These values were utilised alongside the data

provided by the EA. Since the EA data was sub-hourly, it was converted to hourly data by taking

the averages. This was to allow a fairer comparison with the hourly CHASM data. Taking the

averages did reduce the actual peaks, albeit by a slight amount. Since the raw data was not

available, hydrographs could not be created for the CHASM stations.

4.3 Data Limitations and Corrections

There were only seven raingauges available for the November 2009 event, and five for the January

2005 event. Naturally, this would not accurately cover the spatial variability of rainfall across the

catchment, but it would show the general pattern of the rainfall. Another issue was that Kirkby

Thore and West Clove Hill were located just outside the catchment boundary. As a result, their

coordinates were adjusted on the rainfall map, and they were assumed to be just within the

catchment boundary.

With the raw data provided for Helm Beck for the November 2009 event, an error was found in

the formula for the rating curve, which resulted in the graph flat topping. This error was rectified

easily in Microsoft Excel. The data available for Ravenstonedale and Artlegarth was available as

stage data, and therefore a rating curve had to be applied to the data. The rating curves were

obtained from an earlier study (Wilkinson, 2009). However, it was found that the rating curves

used within the earlier study were different to the curves used for the other data in this study.

Nevertheless, since they were the only rating curves available, they were used. It was found that

the Artlegarth data had a flat top. This was attributed to the flood levels exceeding the stage

recorder maximum, and as a result, the data was unusable.

There would also be some uncertainties regarding the rainfall data obtained from the Environment

Agency, since the 15-minute data was not validated.

To make the reader aware of the data which was used, Table 4 lists the stations, the events, and

the discharge stations and raingauges. Green cells indicate the data was used, and red cells indicate

that it was not.

21

Table 11 – Data used within the study.

Discharge

Stations

Peak Discharge Raingauges Rainfall

2005 2009 2015 2005 2009 2015

Gais Gill Aisgill

Artlegarth Barras

Ravenstonedale Brackenber

Smardale Scalebeck

Great

Musgrave

Kirkby

Thore

Appleby Sykeside

Temple

Sowerby

West Clove

Hill

Great Corby

Blind Beck

Helm Beck

Kirkby

Stephen

22

4.4 Identification of Storm Periods

Before any results were produced, the storm period had to be identified. The raingauge chosen

for this purpose was Aisgill. This was because it was the most upstream raingauge, and with the

goal of calculating lag times in mind, using it would be most appropriate. Figure 5 shows the

rainfall at Aisgill during the November 2009 event.

It was found that over the course of the entire storm event, the rainfall occurred in three stages,

which were separated from each other by slight dry spells. Initially, the rainfall occurred from the

16/11/2009 08:15 to 17/11/2009 02:45. After this, there was a short dry spell, and the rainfall

picked up again from 17/11/2009 10:45 to 18/11/2009 09:30. This was the main rainfall event.

After this, there was a dry spell until 14:00 on the same day. The remainder of the rainfall fell in

short, less intense bursts from the 18/11/2009 14:00 to 20/11/2009 14:00.

A similar procedure was used to identify the storm period for the 2005. For the January 2005

period, there was a clear storm event which lasted from the 06/01/2005 22:15 to 08/01/2005 13:30

(Figure 6).

After the storm periods were identified, the hydrographs and hyetographs were created using

Microsoft Excel. They are presented in the Results Section.

0

0.5

1

1.5

2

2.5

3

3.5

15

No

v

16

No

v

17

No

v

18

No

v

19

No

v

20

No

v

21

No

v

Rai

nfa

ll (m

m)

Aisgill Rainfall - November 2009

Figure 5- Rainfall at Aisgill used for identifying the storm period for the November 2009 event

23

4.5 Calculation of Runoff

The discharge data was available as cumecs. This had to be converted into millimetres, so that it

could be expressed as runoff and compared with the rainfall. To do this, the discharge data for

each gauging station was divided by the catchment area that encompassed the station. This was

then multiplied by the data time interval in seconds (900 seconds), then it was finally multiplied

by 1000 to give discharge in millimetres. The areas covered by the discharge stations can be found

in Table 3.

4.6 Calculation of Lag Times

To calculate the lag times, the centroid of the rainfall at Aisgill had to be identified. This was

done in two stages. Firstly, the total rainfall during the main stage was calculated, which amounted

to 61.2mm. The next stage was to find when half of this rainfall, 30.6mm, occurred. This was

done by a simple formula in excel which allowed the calculation of cumulative rainfall at each

time step. The example is shown below.

0

0.5

1

1.5

2

2.5

3

05

Jan

06

Jan

07

Jan

08

Jan

09

Jan

10

Jan

11

Jan

Rai

nfa

ll (m

m)

Aisgill Rainfall - January 2005

Figure 6 – Rainfall at Aisgill used for identifying the storm period for the January 2005 event

24

Through the formula, it was found that 30.6mm of rainfall occurred at 01:45 on the 18th of

November.

The final step was then to calculate the difference between this time, and when the peak discharges

occurred at each station. The peak discharges, which were expressed as runoff, were found by

using a MAX formula to identify the highest recorded value, and then applying a data filter to

find the time of occurrence. The lag times are shown in the Results section.

4.7 Rainfall Map Generation using Inverse Distance Weighting

To generate a rainfall map, the ArcMap software was used. The first step was to obtain a

catchment map. This was provided by Dr. Claire Walsh of Newcastle University, in ASCII

format. This then had to be converted to a raster format. This step can be done within the ArcMap

software. Next, the coordinates, elevation, and total rainfall of each raingauge were tabulated in

Microsoft Excel. An example is shown in Table 5. This table was then imported into ArcMap, so

that the raingauges could be located on the raster map. The coordinates were obtained from

Wilkinson (2009).

Table 12 – Example of a table used for locating the raingauges on the raster map.

Raingauge X Y Elevation (m) Cumulative

Rainfall (mm)

Aisgill 377863 496341 360 61.2

Barras 384468 512126 343 32

Brackenber 372198 519481 176 29.8

Scalebeck 367388 514401 183 42.2

Sykeside 374700 512200 180 41.8

West Clove

Hill

383044 519400 505 41.4

Kirkby Thore 364400 525900 128 24

The raster map then had to be converted to a predictive rainfall map based on the elevations. To

complete this step, a regression equation between cumulative rainfall and elevation had to be

found. This was done using the Minitab software. The total rainfall for each gauge for the storm

period was known, and so were the elevations. The resulting equation for one of the stages of the

2009 event was:

Cumulative Rainfall = 28.2 + 0.0398 Elevation (m)

25

This equation was applied to the raster map using the raster calculator tool in ArcMap, allowing

a new raster map to be generated. However, since this map was based on the regression equation,

and the rainfall data for only six raingauges was available, the regression obtained was not

suitable. Hence, ‘anomalies’ had to be calculated. This was done by using the ‘Identify’ tool in

ArcMap, and selecting the raingauges on the new raster map. This would then provide a ‘pixel’

value, which was the rainfall value that the new map predicted at that raingauge. The anomalies

were then found by subtracting the pixel value from the actual rainfall value, and were tabulated

(Table 6).

Table 13- Example of a table used to create a layer to be used with the Inverse Distance Weighting technique.

Raingauge X Y Elevation

(m)

Cumulative

Rainfall (mm)

Pixel Value Anomaly

Aisgill 377863 496341 360 61.2 129 -67.8

Barras 384468 512126 343 32 117 -85

Brackenber 372198 519481 176 29.8 36 -6.2

Scalebeck 367388 514401 183 42.2 43 -0.8

Sykeside 374700 512200 180 41.8 33 8.8

West Clove

Hill

383044 519400 505 41.4 193 -151.6

Kirkby

Thore

364400 525900 128 24 15 9

The data from this anomaly table was then added to ArcMap as a new XY layer. The Inverse

Distance Weighting tool was then used with the Anomaly layer. When the IDW map was

obtained, the final step was to use the raster calculator to add this map to the calculated rainfall

map, which provided the final output. The rainfall maps are shown in the Results section.

The main limitation to this method was the number of raingauges available, which resulted in an

unsuitable regression equation. Hence, whilst the map succeeded in showing the general pattern

of rainfall, the values that it predicted were not realistic.

4.8 Calculation of Catchment Average Rainfall

To allow the comparison of runoff at different catchment scales, the average rainfall across the

catchment for both events was calculated. To do this, the Thiessen method was used. The Thiessen

method involves diving the catchment area into polygons by equidistant lines between adjacent

raingauges. The individual areas for each raingauge are then measured. The catchment average

rainfall can then be calculated by applying Equation 3:

26

�̅� = 1

𝐴∑ 𝑎𝑖𝑅𝑖

(Eqn. 3)

where A is the total catchment area, ai is the area corresponding to a raingauge, and Ri is the

rainfall at that raingauge.

The Thiessen polygons were generated using the Thiessen polygon tool in ArcMap. Once they

were generated, their individual areas were calculated using the Field Geometry calculator. The

procedure was as follows:

1) Add the raingauges to the catchment raster in the form of XY data.

2) Convert the raingauge layer into a shapefile.

3) Apply the Thiessen Polygon tool to the shapefile, ensuring that the processing extent is

the same as the catchment raster.

4) Clip the new Thiessen Polygon layer generated to the catchment raster.

5) Open the attribute table of the Thiessen Polygon layer.

6) Add a new field called Area, selecting ‘Float’ as the field type.

7) When the new field is added, right-click and select ‘Calculate Geometry’. This should

provide the areas of each polygon.

Once all the areas were calculated, Equation 3 was applied at each time interval to the data in

Microsoft Excel to provide catchment average rainfall during the two storm events. Figures 7.a

and 7.b show the Thiessen polygons generated for the two events, and Table 7 lists the areas of

the polygons.

Figure 7.a – Thiessen Polygons, January 2005. Figure 7.b – Thiessen Polygons, November 2009.

27

Table 14 – Areas of the Thiessen Polygons generated for the two events.

4.9 Return Periods

The return periods for the two flood events at Temple Sowerby were calculated using the

WINFAP-FEH software. The software uses the Flood Estimation Handbook (FEH) statistical

methods, which are based on flood frequency curves. Flood frequency curves simply show a

relationship between the return period of a flood and the peak flow. There are two data sets used

within the software; the Annual Maximum (AM) data and Peaks Over Threshold (POT) data.

There are three steps involved in the FEH approach for estimating peak flow for a given return

period of time T. First an index flood, which is the median annual maximum flood (QMED), is

estimated. The next step is the estimation of a flood growth curve (zt). The final step is to derive

the flood frequency curve which gives the estimate for the peak flow for a specified return interval

(Qt). This is done by using the equation Qt = QMED*zt.

The QMED can be estimated from the flood flow record. The flood growth curve, zt, can be

constructed by fitting a distribution to the observed AM data. The recommended distribution for

UK flood data is the Generalised Logistic distribution (Wallingford Hydrosolutions Ltd, 2009),

and therefore this was used. The growth curve parameters were estimated using the L-Moment

method.

Before estimating the flood frequency curve, the user has a choice of two analysis options. These

are single-site analysis and pooled analysis. Single site analysis is simpler to run, but as the name

suggests, it uses data from one site only. The issue with this is the length of the record since there

are very few gauging stations with a record longer than 100 years. Estimating a flood with a larger

return period would obviously require a longer record. Pooled analysis aims to solve this issue by

‘pooling’ catchments with similar characteristics together. This increases the cumulative length

of the record. It is recommended that a pooling group should have a minimum of 500 years of

AM data to provide a good estimate of a 1 in 100 year event (Wallingford Hydrosolutions Ltd,

2009).

Station January 2005 Area (km2) November 2009 Area (km2)

Aisgill 72.32 58.08

Barras 128.47 73.58

Brackenber 119.15 88.55

Scalebeck 163.07 123.07

Kirkby Thore 129.99 129.96

Sykeside n/a 108.40

West Clove Hill n/a 31.31

28

Pooled analysis does have some additional steps to use. A check for heterogeneity across the

catchments is recommended. There are many factors involved when a pooling group is created,

such as catchment area, Standard Annual Average Rainfall (SAAR), and Flood Attenuation due

to Reservoirs and Lakes (FARL) (Wallingford Hydrosolutions Ltd, 2009).

The pooling group that was created for the Temple Sowerby analysis was set up to use a minimum

of 1000 years of data. The pooling group that the software automatically generated had one station

which was discordant and highlighted in red (Figure 8.a). This station was removed from the

group. The total years of data was 1002 years. The heterogeneity was checked and the pooling

group was deemed acceptably homogenous, meaning a review was not required (Figure 8.b.).

The final step was to create the flood frequency curve and obtain the return periods and the

associated flood peaks. These are shown in Figure 9.

Figure 8.a – Pooling group automatically generated by the software. Figure 8.b- Check for heterogeneity

Figure 9 – Return periods

obtained from pooling

group

29

4.10 Wave Speed Calculation

To calculate the speed of the flood wave at each gauging station, the distance between gauging

stations was used from a previous study (Wilkinson, 2009). The original method involved drawing

a polyline along the river in ArcMap and then calculating the length of the line. This yielded an

approximate distance since the polyline was unable to estimate the bends in the river channel

accurately. For the 2005 event, due to a lack of data, the time of peak for the CHASM stations

were also obtained from this study. The speed was then calculated by dividing the distance

between stations by the difference in the time of peak. The distances were available for stations

along Scandal Beck, therefore, the wave speeds from Kirkby Stephen to Great Musgrave were

not calculated.

The distances between the stations are tabulated below (Table 8). For Artlegarth and

Ravenstonedale, the time of peak and peak discharge was not used due to uncertainties with the

rating curves. The peak discharge at Appleby for the January 2005 event was also unavailable.

Therefore, the wave speeds were calculated from the last station for which the discharge and time

of peak was known. The calculated wave speeds are tabulated in the Results section.

Table 15 – Distances between stations taken from Wilkinson (2009).

Station Distance from Preceding Station

Gais Gill -

Artlegarth 2.0

Ravenstonedale 3.1

Smardale 4.6

Great Musgrave 8.3

Appleby 15.2

Temple Sowerby 17.0

Great Corby 43.2

30

5. Results

The raw rainfall and discharge data has been represented as hydrographs in this chapter.

The rainfall maps generated using the methodology described previously are also

presented. A selection of graphs depicting the variance of lag time and peak discharge

across the different catchment scales are also presented. The wave speeds of the peak

discharge at different stations have been tabulated for both events. Lastly, graphs

depicting the comparison of catchment average rainfall and runoff for the two events are

also shown. The results for each event are shown in different subsections for clarity.

5.1 November 2009

5.1.1 Rainfall

For the 2009 event, sub-hourly rainfall data was available for seven raingauges. The full storm

period was identified to be from 16/11/2009 08:15 to 20/11/2009 14:00, and within the full storm

period the rain fell in three different stages. The seven raingauges that were available were spread

across the catchment, and were at different elevations. Table 9 lists the raingauges, their

elevations, and the total rainfall for each stage.

Table 9- Raingauges, elevation and rainfall totals for November 2009.

Station Elevation

(m)

1st Stage

(mm)

2nd Stage

(mm)

3rd Stage

(mm)

Total

(mm)

Aisgill 360 25.6 62.2 40 127.8

Barras 343 12.2 32.6 12 56.8

Brackenber 176 10.4 30 42.6 83

Scalebeck 183 13.8 43.2 75.2 132.2

Sykeside 180 12.2 42.4 31 85.6

West Clove

Hill

505 13.6 42 39.4a 95

Kirkby Thore 128 10.6 24 32.8 67.4

Figure 10 on the next page shows the rainfall at each raingauge.

31

0

0.5

1

1.5

2

2.5

3

3.5

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Rai

nfa

ll (m

m)

Aisgill

0

0.5

1

1.5

2

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Rai

nfa

ll (m

m)

Barras

0

0.5

1

1.5

2

2.5

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Rai

nfa

ll (m

m)

Brackenber

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Rai

nfa

ll (m

m)

Scalebeck

0

0.5

1

1.5

2

2.5

3

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Rai

nfa

ll (m

m)

Sykeside

0

0.5

1

1.5

2

2.5

3

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Rai

nfa

ll (m

m)

West Clove Hill

0

0.5

1

1.5

2

2.5

3

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Rai

nfa

ll (m

m)

Kirkby Thore

Figure 10 – Rainfall at each raingauge available for the

November 2009 event.

32

From the hyetographs, it can be seen that the intensity and timing of rainfall varied greatly across

the catchment. The two interesting graphs are Scalebeck and Sykeside. The largest rainfall pulse

occurred at Scalebeck, which is a lowland gauge. Meanwhile at Sykeside, a large rainfall pulse

occurred much later during the main storm event. Looking at the total rainfall, the raingauges at

higher elevations seemed to have experienced similar or less rainfall than the lowland raingauges,

with the exception of Aisgill.

Figure 11 – Cumulative Rainfall at each raingauge over the November 2009 storm period

To map the rainfall pattern, the Inverse Distance Weighting (IDW) technique was used in

ArcMap. Figure 12 shows the rainfall for the entire storm period.

127.8

56.8

83

132.2

85.695

67.4

0

50

100

150

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

Cu

mu

lati

ve R

ain

fall

(mm

)

Cumulative Rainfall over the Storm Period

Aisgill Barras Brackenber Scalebeck

Sykeside West Clove Hill Kirkby Thore

Figure 12 – Rainfall map for the entire storm period created

using the Inverse Distance Weighting technique

33

5.1.2 Discharge

Discharge data was available for nine stations within the Upper Eden catchment, as well as Great

Corby which lies outside the nested catchment. Table 10 summarises the stations, their peak

discharge and runoff, and the lag times as calculated by applying the procedures outlined in the

Methodology section. Figure 13 shows the runoff at the stations along Scandal Beck and the main

stem of the Eden, including Kirkby Stephen. Blind Beck and Helm Beck are not shown to improve

the clarity of the graph. From the graph, it can be observed that Ravenstonedale has an unusually

high runoff compared to the other stations. Whilst it makes sense that the runoff is greater for a

smaller catchment area, the reader is reminded that for the Ravenstonedale data, a rating curve

from an earlier study was applied. The rating curves for the other stations in the earlier study did

not match the rating curves that were applied to the data used in this study. Hence, it is possible

that the use of this rating curve has resulted in an exaggeration of the actual runoff at

Ravenstonedale. Figure 14 shows the variation in peak runoff including the peak runoff at Blind

Beck and Helm Beck, which do not lie on the main stem of the Eden. The peak runoff at Great

Corby is also shown, which is located outside the Upper Eden catchment.

Table 10 – Gauging stations, peak discharges, and lag times calculated from Aisgill for November 2009 event.

Station Area

(km2)

Peak

Discharge

(m3/s)

Peak Runoff

(mm)

Time of Peak Lag

Time

(hours)

Gais Gill 1.1 1.154 0.94378071 18/11/2009 05:00:00 3.25

Blind Beck 9.2 3.128 0.30603227 18/11/2009 07:15:00 5.5

Helm Beck 18 20.365 1.018 18/11/2009 03:15:00 1.5

Ravenstonedale 25.6 88.515 3.11185862 18/11/2009 05:30:00 3.75

Smardale 36.6 62.544 1.53796544 18/11/2009 05:45:00 4

Kirkby

Stephen

69.4 97.000 1.25792507 18/11/2009 06:30:00 4.75

Great

Musgrave

223.4 241.000 0.97090421 18/11/2009 08:15:00 6.5

Appleby 322 248.234 0.69382229 18/11/2009 13:15:00 11.5

Temple

Sowerby

616.4 346.000 0.50519143 18/11/2009 14:45:00 13

Great Corby 1373 817.000 0.535542607 19/11/2009 22:30:00 44.75

34

0

0.5

1

1.5

2

2.5

3

3.5

16

No

v

17

No

v

18

No

v

19

No

v

20

No

v

21

No

v

Ru

no

ff (

mm

)

Runoff Hydrographs - November 2009

Gais Gill (1.1km^2) Ravenstonedale (25.6 km^2)

Smardale (36.6 km^2) Great Musgrave (223.4 km^2)

Appleby (322 km^2) Temple Sowerby (616.4 km^2)

Kirkby Stephen (69.4 km^2)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Ru

no

ff (

mm

)

Stations

Peak Runoff at All Stations - November 2009

Figure 13 – Runoff hydrograph for the stations along Scandal Beck and Eden main stem

Figure 14 – Peak Runoff at all stations for which data was available.

35

The upscaling of peak discharge with catchment area was also studied. Figure 15 shows the peak

discharges at all stations against area on a logarithmic scale with a power law fitted to them. Great

Corby, whilst being outside the Upper Eden catchment is included to allow the investigation of

flood peak scaling for larger catchments. An R2 value of 0.9095 indicates an acceptable fit.

However, the fit can be improved by eliminating some of the stations, as shown in Figure 16. The

stations eliminated include Blind Beck, Helm Beck and Ravenstonedale. Blind Beck and Helm

beck are not shown since they do not lie on the main stem of the Eden, and represent smaller

catchments towards the west. Ravenstonedale, whilst being on the main stem was eliminated

because of the uncertainty of the rating curve. This improved the fit, but also showed a reduction

in the scaling exponent, from 0.9306 to 0.8959. Both these values are within the range of values

suggested by Leopold et al. (1964, as cited in Goodrich et al., 1997) for natural basins.

y = 1.3199x0.9306

R² = 0.9095

1

10

100

1000

1 10 100 1000

Pea

k D

isch

arge

(m

3/s

)

Area (km2)

Peak Discharge vs. Area

y = 1.5458x0.8959

R² = 0.9749

1

10

100

1000

1 10 100 1000

Pea

k D

isch

arge

(m

3/s

)

Area (km2)

Peak Discharge vs. Area - Excluding Blind Beck, Helm Beck and Ravenstonedale

Figure 15- Peak Discharge vs. Area for all stations with a power law fitted.

Figure 16 – Peak Discharge vs. Area excluding Blind Beck, Helm Beck and Ravenstonedale

with a power law fitted.

36

The lag time at different stations was also calculated using the rainfall at Aisgill. As with the peak

discharge, a power law was fitted, but only to the stations in the Upper Eden catchment. As can

be observed from Figure 17, the lag time for the Great Corby peak is much greater than expected.

This is attributed to inflow from tributaries to the Eden below Temple Sowerby. The R2 value is

also very poor, and to improve it, the lag times at Blind Beck and Helm Beck were eliminated

again (Figure 18). This was because due to their location, they are highly likely to not be

influenced by the rainfall at Aisgill.

y = 2.0469x0.2356

R² = 0.4976

1

10

100

1 10 100 1000 10000

Lag

tim

e (h

ou

rs)

Area (km2)

Lag time vs. Catchment Area - All stations

Upper Eden stations Great Corby

y = 2.321x0.2234

R² = 0.7325

1

10

100

1 10 100 1000 10000

Lag

tim

e (h

ou

rs)

Area (km2)

Lag time vs. Catchment Area Excluding Blind Beck and Helm Beck

Upper Eden stations Great Corby

Figure 17 – Lag time vs. Catchment area for all stations, with a power law fitted up to Temple Sowerby.

Figure 18 – Lag time vs. Catchment area excluding Blind Beck and Helm Beck, with a power law fitted up to

Temple Sowerby

37

5.1.3 Wave Speed

Table 11 lists the speeds of the flood peak at the different gauging stations. It was found that the

wave speeds generally decreased as the flood wave moved further downstream. The exception to

this rule was Temple Sowerby, where the flood peak travelled to very quickly from Appleby.

Table 11 – Calculated wave speeds for the November 2009 event.

Station Peak Discharge (m3/s)

Time of Peak Time to travel (mins)

Distance from previous gauging station (km)

Wave speed (m/s)

Gais Gill 1.15 18/11/2009 05:00:00 - - -

Ravenstonedale 88.52 18/11/2009 05:30:00 30 5.1 2.83

Smardale 62.54 18/11/2009 05:45:00 15 4.6 5.11

Great Musgrave 241.00 18/11/2009 08:15:00 150 8.3 0.92

Appleby 248.23 18/11/2009 13:15:00 300 15.2 0.84

Temple Sowerby 346.00 18/11/2009 14:45:00 90 17 3.15

Great Corby 817.00 19/11/2009 22:30:00 1905 43.2 0.38

5.1.4 Catchment Average Rainfall versus Runoff

The catchment average rainfall for the storm event was calculated by applying the procedures in

the Methodology section. This was then compared with the runoff at five different catchment

scales (Figure 19).

0.0

0.5

1.0

1.5

2.0

2.5

3.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

16

No

v

17

No

v

18

No

v

19

No

v

20

No

v

Ru

no

ff (

mm

)

Cat

chm

ent

Ave

rage

Rai

nfa

ll (m

m)

Catchment Average Rainfall vs. Runoff

Catchment Average Rainfall Temple Sowerby (616.4 km^2)

Kirkby Stephen (69.4 km^2) Great Musgrave (223.4 km^2)

Gaisgill (1.1 km^2) Smardale (36.6 km^2)

Figure 19 – Catchment Average Rainfall calculated using Thiessen Polygons vs Runoff at five different

catchments scales.

38

For the first peak, with the exception of Gais Gill, runoff was higher at the smaller catchment

scale, which was as expected. However, for the second, smaller peak in runoff, the runoff at

Temple Sowerby was greater than the runoff at Kirkby Stephen and Great Musgrave. The rainfall

and runoff is further investigated in Figure 20, from which it can be seen that the cumulative

runoff at Kirkby Stephen and Smardale is much greater than the cumulative rainfall. The runoff

at Temple Sowerby and Great Musgrave is lower than the rainfall for the majority of the storm

duration, but then it manages to surpass it towards the end of the storm.

5.2 January 2005

5.2.1 Rainfall

For the January 2005 event, sub-hourly rainfall data was available for only five raingauges. The

storm period identified was from the 06/01/2005 22:15 to 08/01/2005 13:30. There was as a

second, distinct storm event after the initial event as well. Table 12 summarises the raingauges,

elevations, and total rainfall for the initial storm, and Figure 21 shows the rainfall at each

raingauge.

Table 12 – Raingauges and Total Rainfall – January 2005

Raingauge Elevation

(m)

Total Rainfall

(mm)

Aisgill 360 140.6

Barras 343 59.4

Brackenber 176 75.2

Scalebeck 183 128.8

Kirkby Thore 128 53.4

0

20

40

60

80

100

120

140

160

16 Nov 17 Nov 18 Nov 19 Nov 20 Nov 21 Nov

Rai

nfa

ll an

d R

un

off

(m

m)

Cumulative Catchment Average Rainfall and Runoff

Cumulative Rainfall Temple Sowerby Kirkby Stephen

Great Musgrave Gais Gill Smardale

Figure 50 – Cumulative Catchment Average Rainfall against Cumulative Runoff at five different catchment

scales.

39

In comparison to the November 2009 event, it can be observed that for a smaller time period, the

amount of rainfall that fell within the main storm event was significantly greater. The intensity of

the rainfall was greater as well. During the November 2009 event, there were numerous intervals

where the rain stopped. However, for the January 2005 event, it can be seen that rainfall was

generally constant throughout the storm.

The cumulative rainfall at each raingauge is shown in Figure 22, and as with the November 2009

event, a rainfall map was generated using the IDW technique, which is shown in Figure 23.

0

0.5

1

1.5

2

2.5

06 J

an

07 J

an

08 J

an

09 J

an

10 J

an

11 J

an

Rai

nfa

ll (m

m)

Aisgill

0

0.2

0.4

0.6

0.8

1

1.2

1.4

06 J

an

07 J

an

08 J

an

09 J

an

10 J

an

11 J

an

Rai

nfa

ll (m

m)

Barras

0

0.5

1

1.5

2

2.5

06 J

an

07 J

an

08 J

an

09 J

an

10 J

an

11 J

an

Rai

nfa

ll (m

m)

Brackenber

0

0.5

1

1.5

2

2.5

3

06 J

an

07 J

an

08 J

an

09 J

an

10 J

an

11 J

an

Rai

nfa

ll (m

m)

Scalebeck

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

06 J

an

07 J

an

08 J

an

09 J

an

10 J

an

11 J

an

Rai

nfa

ll (m

m)

Kirkby Thore

Figure 21 – Rainfall at all available raingauges for

the January 2005 event

40

Figure 22 – Cumulative Rainfall at each raingauge for the January 2005 event.

5.2.2 Discharge

For the 2005 event, raw discharge data was available only for the four EA stations; Kirkby

Stephen, Great Musgrave, Temple Sowerby, and Great Corby. However, in an earlier study,

hourly peak discharges were listed for some of the CHASM stations which had smaller catchment

areas, including Gais Gill, Artlegarth, Ravenstonedale, and Smardale. Hence, the data from the

earlier study (Wilkinson, 2009) was used in conjunction with the data available from the EA to

produce graphs of Peak Runoff as catchment scale increases (Figure 24), Peak Discharge vs. Area

140.6

59.4

75.2

128.8

53.4

0

20

40

60

80

100

120

140

160

06

Jan

07

Jan

08

Jan

09

Jan

Cu

mu

lati

ve R

ain

fall

(mm

)

Cumulative Rainfall over the Storm Period

Aisgill Barras Brackenber Scalebeck Kirkby Thore

Figure 23 – Rainfall map for the January 2005 event generated using the IDW

technique.

41

(Figure 27), and Lag times vs. Area (Figure 26). Hydrographs were produced only for the data

that was available from the EA (Figure 25). To allow some consistency with the hourly data for

the CHASM stations, the EA sub-hourly data was also converted to hourly data. The peak

discharges and lag times for the stations available are listed in Table 13.

Table 13 – Peak Discharges and Lag Times for the January 2005 event.

Station Area

(km2)

Peak

Discharge

(m3/s)

Peak

Runoff

(mm)

Time of Peak Lag Time

(hours)

Gais Gill 1.1 2.175 1.78 07/01/2005 20:00 5.5

Artlegarth 2.7 7.59 2.53 - -

Ravenstonedale 25.6 54.2 1.91 - -

Smardale 36.6 81.1 1.99 07/01/2005 22:15 7.75

Great Musgrave 223.4 275.75 1.11 07/01/2005 23:30 9

Temple Sowerby 616.4 908.75 1.33 08/01/2005 04:00 13.5

Great Corby 1373 1365 0.89 08/01/2005 10:15 19.75

Kirkby Stephen 69.4 128.75 1.67 07/01/2005 21:15 6.75

0

0.5

1

1.5

2

2.5

3

Peak Runoff

Figure 24 – Peak Runoff at all stations in order of catchment area.

42

y = 2.711x0.8877

R² = 0.9924

1

10

100

1000

10000

1 10 100 1000 10000

Pea

k D

isch

arge

(m

3 /s)

Area (km2)

Peak Discharge vs Area

y = 4.9793x0.1232

R² = 0.7742

1

10

100

1 10 100 1000 10000

Lag

tim

e (h

ou

rs)

Area (km2)

Lag Time vs Area

Upper Eden Stations Great Corby

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

06

Jan

07

Jan

08

Jan

09

Jan

10

Jan

11

Jan

Ru

no

ff (

mm

)

Runoff Hydrographs - January 2005

Kirkby Stephen Great Musgrave Temple Sowerby Great Corby

Figure 25 – Runoff Hydrographs for the EA stations for the January 2005 event.

Figure 26 – Lag time vs. Catchment Area for January 2005 event, with a power law fitted up to Temple

Sowerby

Figure 27 – Peak Discharge vs. Catchment Area for the January 2005 event, with a power law fitted to all

stations.

43

From Figure 23 it can be seen that peak runoff seems to increase slightly up to Smardale, after

which it starts to decrease. From Figure 24, the effects of translation are apparent as the flood

peak moves further downstream. However, the peak runoff at Temple Sowerby is greater than

Great Musgrave for the first peak. It would have been expected that the runoff would actually

decrease for the larger catchments. Figure 25 clearly shows that the lag times were reduced, with

the power law exponent of 0.1232, which is almost half of the exponent obtained for the

November 2009 event. Lastly, Figure 26 shows a very strong correlation with an R2 value of

0.9924. The scaling exponent for the power law is still within range of literature values, which is

unsurprising since it is the same catchment. The regression co-efficient however has increased,

which is due to a larger magnitude flood.

5.2.3 Wave Speed

In contrast with the November 2009 event, the data available was more limited, with the

peak discharge and time of peak at Ravenstonedale and Appleby not being available. It

seemed that the wave speed behaviour was much different than the 2009 event, with the

wave speed increasing gradually as the flood wave progressed downstream.

Table 14 – Wave speeds at the available stations for the January 2005 event.

5.2.4 Catchment Average Rainfall versus Runoff

As with the November 2009 event, the catchment average rainfall was calculated for the

January 2005 event. However, due to the limited discharge data, only the runoff

hydrographs at Kirkby Stephen, Great Musgrave and Temple Sowerby could be

compared. Nevertheless, Figure 28 still shows some interesting behaviour. It seems that

the cumulative runoff, as with the November 2009 event, is greater than the cumulative

catchment average rainfall, which is confirmed in Figure 29. This highlights the need for

more comprehensive data collection, since only five raingauges were used, which

inherently do not represent the rainfall accurately across the catchment.

Station Peak Discharge (m3/s)

Time of Peak Time to travel (mins)

Distance from previous gauging station (km)

Wave speed (m/s)

Gais Gill 2.18 07/01/2005 20:00 - - -

Smardale 81.10 07/01/2005 22:15 135 9.7 1.20

Great Musgrave 275.75 07/01/2005 23:30 75 8.3 1.84

Temple Sowerby 908.75 08/01/2005 04:00 270 32.2 1.99

Great Corby 1365.00 08/01/2005 10:15 375 43.2 1.92

44

0

0.5

1

1.5

2

2.5

30

0.5

1

1.5

2

2.5

3

06

Jan

07

Jan

08

Jan

09

Jan

10

Jan

10

Jan

Ru

no

ff (

mm

)

Rai

nfa

ll (m

m)

Time

Catchment Average Rainfall vs. Runoff

Catchment Average Rainfall Kirkby Stephen

Great Musgrave Temple Sowerby

89.2

152.9

98.1

85.4

0

20

40

60

80

100

120

140

160

180

06 Jan 07 Jan 08 Jan 09 Jan

Rai

nfa

ll an

d R

un

off

(m

m)

Cumulative Catchment Average Rainfall and Runoff

Cumulative Rainfall Kirkby Stephen Great Musgrave Temple Sowerby

Figure 28 – Catchment Average Rainfall vs. Runoff at the three available stations in the Upper Eden for the

January 2005 event

Figure 29 – Cumulative Catchment Average Rainfall vs. Cumulative Runoff at the available stations for the

January 2005 event.

45

6. Discussion

This section aims to bring the results obtained together to help achieve the objectives of the study.

To recall, the first objective was to carry out a comprehensive review of literature on the subject

matter. This chapter will draw on key information from the literature review to help compare and

discuss the findings of this study, and highlight any similarities or differences. The second

objective was to assemble data in order to exhibit the rainfall distribution and the river flow

response during the event. The discussion for this objective will rely on the analysis of the

hyetographs, the rainfall maps that were created, and the runoff hydrograph compared to the

catchment average rainfall. The third objective of this study was to interpret the results to explain

flood wave generation and progression across different spatial scales. To help achieve this

objective, the results that will be most useful will be the graphs obtained for peak discharge and

lag times against the corresponding catchment areas. The fourth and final objective of this study

was to contrast the event with the January 2005 flood. This objective was set with the intent to

help develop an understanding of differences in upscaling of peak discharge between events.

Thus, throughout this chapter, comparisons will be made between the two events. Another major

event that occurred in the Eden Catchment was the December 2015 flood. Not all of the data was

available for this event, but peak discharge data for the Environment Agency gauges was

available. This data will be used to provide some additional insight about upscaling of peak

discharge.

6.1 Discussion of Rainfall

From the results, it appeared that for both events, the cumulative runoff at some stations exceeded

the cumulative catchment average rainfall. Theoretically, this does not make sense, since it would

be expected that runoff would not exceed rainfall, unless there was another source located outside

the catchment (Wilkinson, 2009).

Section 2.5 of the literature review lists ten factors which can affect runoff. The first of these is

type of precipitation and intensity. A higher rainfall intensity can cause the infiltration capacity

to exceed greatly and thus result in a high surface runoff. Whilst it can be difficult to decide what

qualifies as high or low intensity, it was clear from the hyetographs that there were periods of

constant rainfall where the volume of rainfall was much greater than the average. Furthermore,

preceding storm events can cause the ground to be saturated, meaning that saturation excess

overland flow can occur regardless of the intensity of rainfall. Since the storm occurred during

the winter, it is likely that the evaporation rates would be lower, meaning the ground would be

saturated and the infiltration capacity would be reduced. The other factors that can affect runoff

include the areal extent of the storm and the orientation of the storm and the catchment. During

the November 2009 event, it seemed that the rainfall largely occurred on the southern and western

46

side of the catchment (Figure 12). However, breaking down the storm into separate stages

demonstrates how the rainfall actually progressed (Figures 30.a – 30.c). From the figures, it can

be observed that initially, rainfall volume was greater towards the southern and north eastern parts

of the catchment. The storm then seemed to move towards the centre of the catchment, before

traversing north-westwards. During the last stage, there was a surge in rainfall over Scalebeck,

which can also be observed from the hyetographs and the cumulative rainfall graph in the results

section.

It is possible that the actual rainfall was greater than the rainfall recorded, as a result of wind

induced losses, and water losses within the raingauge itself during intense storms. This may also

explain why the cumulative runoff at Smardale, Kirkby Stephen, Great Musgrave, and Temple

Sowerby appeared to have exceeded the cumulative rainfall (Figure 20). Whilst a precipitation

correction procedure has been identified in the literature review (Sevruk, 1984), this method was

Figures 30.a-c – Rainfall during the three stages of the storm event, Stage 1-Stage 3 going

clockwise from the top left.

47

not applicable since there were no pit gauges available in the Upper Eden to aid the derivation of

the correction factor required for the procedure.

To compare the total rainfall recorded for both events, the total rainfall at the five EA raingauges

was calculated. This was because these were the common raingauges between the two events. It

was found that for the November 2009 event, this amounted to 467.2mm over 102 hours.

Conversely, for the January 2005 event, the total rainfall was 457.4mm over 39 hours. This shows

that the rainfall intensity for the January 2005 event was much greater.

The key limitation of this study was poor data availability. Having only seven raingauges for the

2009 event, and five for the 2005 event, greatly affected the calculation of catchment average

rainfall. Figure 31 shows the Thiessen polygons for the November 2009 event and the catchment

area influenced by each raingauge as a percentage. It can be deduced that the lowland raingauges

had a greater influence. With the exception of Scalebeck, the rainfall at the lowland gauges was

lower than the rainfall at Aisgill and West Clove Hill (both high elevation gauges). This would

have reduced the catchment average rainfall, once again, helping explain the exceedance of

cumulative runoff when compared to cumulative rainfall. Simply having less raingauges at higher

elevations may have also reduced the catchment average rainfall. This is supported by the findings

that the cumulative runoff at Kirkby Stephen and Smardale, both higher elevation stations, greatly

exceeded the catchment average rainfall.

9.48%

12.00%

14.45%

20.08%

%

17.68 %

5.11%

21.20%

Figure 61 – Thiessen Polygons for the raingauges available for the November

2009 event. The area of the polygon is represented as a percentage of the

total catchment area.

48

6.2 Discussion of Flood Response and Lag Times

The river response was studied in terms of runoff to allow for comparison with rainfall to take

place. Figure 32 shows the flood response at two small catchments which are at different

elevations. Gais Gill, is a highland catchment, with an area of 1.1 km2. On the other hand, Blind

Beck is a lowland catchment with an area of 9.2 km2. The rainfall that was used for comparison

was at the raingauge nearest to the catchment. For Gais Gill, this was the Aisgill raingauge, whilst

the raingauge at Sykeside was used for Blind Beck.

The flood response is as expected, and agrees with the findings of a Mayes et al. (2006). The

runoff at Gais Gill is flashy, which is to be expected as the result of the steep gradient. The runoff

also returns to base flow levels rapidly after the first double peaks, which possibly indicates a

faster flood wave. At Blind Beck, the runoff is much shallower and slower moving, which is to

be expected from a lowland catchment. This is attributed to the increased storage within the

floodplain and the gentle gradient. The return to base flow levels is also much more gradual,

indicating a slower wave speed. The amount of runoff generated is also lower, which is to be

expected with the lower rainfall. The type of soils within the catchment also dictate how much

runoff is generated. For example, the limestone aquifers in the lowlands would have resulted in

greater infiltration, thus decreasing runoff. A similar plot could not be carried out for the January

2005 event due to the lack of data for the smaller catchments. However, the peak discharges,

distances between stations, and times of peak were available. This allowed the calculation of lag

times and wave speeds, which are discussed below.

It is worth noting that the uncertainty levels associated with the wave speed are high. This is due

to the original method of estimating the length of the river, which used polylines in ArcGIS

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Ru

no

ff (

mm

)

Gais Gill

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

15 N

ov

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

22 N

ov

23 N

ov

Rai

nfa

ll (m

m)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Ru

no

ff (

mm

)

Blind Beck

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

15 N

ov

16 N

ov

17 N

ov

18 N

ov

19 N

ov

20 N

ov

21 N

ov

22 N

ov

23 N

ov

Rai

nfa

ll (m

m)

Figure 32 – Flood Response at Gais Gill with the rainfall at Aisgill, and Blind Beck with the rainfall at

Sykeside.

49

(Wilkinson, 2009). Figure 33 shows the variation in lag times, and the corresponding wave speeds

at different stations throughout the catchment.

As expected, the lag times increase as the flood wave progresses through the catchment. At the

same time, the speed of the flood wave generally decreases. The exception to this is the wave

speed at Temple Sowerby. The graph is useful in highlighting three key points. Firstly, the wave

speed at Smardale is much greater than the other speeds. This is as expected since Smardale is

located closer to the highlands in the catchment, and therefore, due to the steep gradients leading

to it, faster moving runoff is expected. This also supports the findings discussed earlier regarding

the flashy runoff response at Gais Gill. The second key point is the increase in wave speed

between Appleby and Temple Sowerby, as a result of which the lag time difference between the

two stations is less when compared to the difference between Great Musgrave and Appleby. This

is unusual, since it would be expected that the storage effects in the lowlands would cause a

decrease in the wave speed. However, it is possible that the runoff being drained from the western

side of the Pennines above Temple Sowerby added to the runoff from the main stem of the Eden.

Furthermore, effluent discharge at Appleby increases the runoff at Temple Sowerby (Centre for

Ecology and Hydrology, 2015). This may have also increased the speed of the runoff. The final

key point is the significant increase in lag time between Temple Sowerby and Great Corby. From

Figure 35, it is evident that Great Corby did not follow the same power law variation as the

discharge stations in the Upper Eden.

0

1

2

3

4

5

6

0

5

10

15

20

25

30

35

40

45

50

Smardale (36.6km^2)

Great Musgrave(223.4 km^2)

Appleby (322km^2)

Temple Sowerby(616.4 km^2)

Great Corby (1371km^2)

Wav

e Sp

eed

(m

/s)

Lag

tim

e (h

ou

rs)

Stations (Area)

Lag Times and Wave Speeds - November 2009

Lag Time Wave Speed

Figure 33 – Lag times and calculated wave speeds at different stations for the November 2009 event.

50

The lag times and wave speeds were quite different for the January 2005 event. The wave speed

seemed to increase as the catchment area increased. There were no significant fluctuations with

the wave speeds between stations as with the November 2009 event. Most surprisingly, the

floodwave at Smardale was slower. Nevertheless, due to the wave speed increasing as it

progressed through the catchment, the lag times were reduced significantly. The wave speed was

at its greatest between Great Musgrave and Temple Sowerby. It would have been interesting to

see what the wave speed at Appleby was, but the data was not available. Contrary to the November

2009 event, the wave speed between Temple Sowerby and Great Corby did not diminish greatly.

The flow between Temple Sowerby and Great Corby is affected by inflows from the Lake District,

particularly the Eamont. The Eamont originates from Ullswater, which is the second largest lake

in the Lake District. The runoff is therefore attenuated and slowed greatly by it. During the

November 2009 event, more rainfall occurred within the Lake District. On the other hand, the

Eden catchment experienced greater rainfall during the January 2005 event. This could be a likely

reason as to why the lag times and wave speeds between Temple Sowerby and Great Corby were

so different for the two events. From Figure 35, it can be postulated that the lag time at Great

Corby may be slightly out of line with the lag times at other stations. This slight indifference is

again attributed to the inflows from the Lake District. Another interesting point is that for both

events, the lag times to Temple Sowerby were very similar. This could be a coincidence, attributed

to the sudden increase in wave speed between Appleby and Temple Sowerby during the

November 2009 event.

0

0.5

1

1.5

2

2.5

0

5

10

15

20

25

Smardale (36.6 km^2) Great Musgrave(223.4 km^2)

Temple Sowerby(616.4 km^2)

Great Corby (1373km^2)

Wav

e Sp

eed

(m

/s)

Lag

tim

e (h

ou

rs)

Stations (Area)

Lag times and Wave Speeds - January 2005

Lag Times Wave Speed

Figure 34 – Lag times and calculated wave speeds at different stations for the January 2005 event.

51

The next point of discussion is the runoff hydrograph of all the stations along the main stem of

the Eden. For the November 2009 event, it was seen from Figure 14 that the peak runoff generally

decreased as catchment area increased and the flood wave progressed from highlands to lowlands.

However, from Figure 19 it was found that that towards the end of the storm, the runoff at Temple

Sowerby was greater than the runoff at Kirkby Stephen and Great Musgrave. A possible reason

for this is the rainfall distribution. From the rainfall maps (Figures 30.a-c) it was found that rainfall

increased towards the north western parts of the catchment as the storm progressed. This meant

that there was more rainfall downstream of Great Musgrave, which was drained towards Temple

Sowerby. This highlights the effect of spatial variability of rainfall on flood response. For the

January 2005 event, during the first peak, the runoff at Temple Sowerby was greater than the

runoff at Great Musgrave. Once again, this is attributed to the rainfall at Scalebeck, which was

much greater than the rainfall at Barras. The discharge data from the River Belah (Figure 4) may

have perhaps been insightful, but unfortunately, it was not available.

Figure 35 – Lag times for both events with Power laws fitted to stations up to Temple Sowerby. Great Corby is

marked differently for the 2009 event to highlight the differences due to inflows from neighbouring catchments.

y = 2.321x0.2234

R² = 0.7325y = 4.4862x0.1645

R² = 0.7794

1

10

100

1 10 100 1000 10000

Lag

tim

e (h

ou

rs)

Area (km2)

Lag Times with Power Laws Fitted to Both Events

November 2009 Great Corby 2009 January 2005

52

6.3 Discussion of Peak Discharge and Runoff

From the literature review, it was found that a power law variation between peak discharge and

catchment area exists. Hence, the peak discharges were plotted against catchment area on a log-

log scale. The instantaneous peak discharge for the December 2015 event was available for the

EA gauging stations, which is also shown on the graph (Figure 36).

The scaling exponent is said to determine the degree to which the transformation from rainfall to

runoff is diminished by the catchment. It is suggested that values for the scaling exponent tend to

decrease as the aridity, return period of the event, and watershed area increase (Benson, 1962;

1964, as cited in Goodrich et al., 1997). The suggested range for values for scaling exponent in

natural basins is 0.65-1.0 (Leopold et al., 1964, as cited in Goodrich et al., 1997). Hence, the

values obtained for the scaling exponent are reasonable, since the Upper Eden is far from being

an arid watershed.

The return periods of the events at Temple Sowerby were calculated using the WINFAP-FEH

software (Figure 9). Pooled analysis was used, where data from other catchments of similar

characteristics was ‘pooled’ together to create a growth curve. From this, it was found that the

predicted peak discharge for an event with a return period of 800 years was 926.388 m3/s. The

observed instantaneous peak discharge for the January 2005 event was 925 m3/s, which certainly

shows the seriousness of the event. The December 2015 event had a peak discharge of 1150m3/s,

which was even greater. In turn, the November 2009 event was less disastrous, with a peak

discharge of 346 m3/s. The estimated 5-year return period flood had a peak of 320.486 m3/s whilst

y = 1.5458x0.8959

R² = 0.9749y = 2.711x0.8877

R² = 0.9924

y = 4.0283x0.842

R² = 0.9747

1

10

100

1000

10000

1 10 100 1000 10000

Pea

k D

isch

arge

(m

3 /s)

Area (km2)

Peak Discharge vs Area for the three events

November 2009 January 2005 December 2015

Figure 36 – Peak Discharge vs. Catchment Area with power laws fitted to the three events.

53

a 10-year return period flood had a peak of 372.858 m3/s. This would place the November 2009

flood in the middle, perhaps with a return period of 7 years.

Whilst the data for the December 2015 event is limited, it appears to be consistent with the other

two events. The scaling exponent is also similar across the events, which does not agree with the

findings of Benson (1962; 1964, as cited in Goodrich e al., 1997) when considering the return

periods. The regression coefficient does change, but this is dependent on the magnitude of the

flood, and is therefore expected to increase as the return period and magnitude of the flood

increases.

To investigate the effect of increasing catchment area has on the scaling exponent for the power

law relating peak discharge to catchment area, Figure 37 was created. This was done by taking

discharges at stations up to different catchment scales. The result was five different power laws,

one for all stations up to Kirkby Stephen, one for all stations up to Great Musgrave and so on.

From Figure 36, it was found that the scaling exponent indeed does decrease as the watershed

area is increased, which agrees with the findings of Benson (1962; 1964, as cited in Goodrich et

al., 1997). This suggests that for different sub-catchments within a catchment, the peak discharge

scales differently. For example, if the power law obtained for all stations up to Appleby was used

to predict the peak discharge at Great Corby, it would not be very accurate. This is because of

y = 1.0623x1.0929

R² = 0.9971y = 1.1657x1.0285

R² = 0.9912y = 1.2824x0.9733

R² = 0.9821y = 1.4495x0.9189

R² = 0.9721y = 1.5458x0.8959

R² = 0.9749

1.000

10.000

100.000

1000.000

10000.000

1 10 100 1000 10000

Pea

k D

isch

arge

(m

3 /s)

Catchment Area (km2)

Peak Discharge vs. Catchment Area at different catchment scales

Kirkby Stephen Great Musgrave Appleby Temple Sowerby Great Corby

Figure 37 – Peak Discharge vs. Catchment area for November 2009, with power laws fitted to discharges at

different catchment scales to investigate effect of increasing catchment area.

54

interference from tributaries between Appleby and Great Corby, which would influence the peak

discharge at Appleby.

The power laws fitted to the January 2005 and November 2009 events include gauging stations

that lie on Scandal Beck (Gais Gill, Ravenstonedale, and Smardale). Kirkby Stephen is also

included, which whilst not on Scandal Beck, appears to be in line with the fitted power law.

Alternatively, it could be suggested that the discharge along Scandal Beck appears to be in line

with the main stem of the Eden.

Figure 38 shows the peak runoff against catchment area for this study. Figure 39 is from an earlier

study, and includes data for six flood events (January and February 2004 are shown as separate

components of a multiday event).

y = 1.3912x-0.104

R² = 0.3442y = 2.4399x-0.112

R² = 0.6768

y = 3.6096x-0.157

R² = 0.5736

0.1

1

10

1 10 100 1000 10000

Pea

k R

un

off

(m

m)

Area (km2)

Peak Runoff vs. Catchment area

November 2009 January 2005 December 2015

Figure 38 – Peak Runoff vs. Catchment Area with power laws fitted to the three events.

55

As expected, the runoff generally decreases as the area increases. However, looking closely at

Figure 38, an increase in runoff up to a certain area before decreasing is detected. Observing the

January 2004, February 2004, and July 2007 events in Figure 39, it can be seen that the peak

runoff also increases up to a certain catchment area before decreasing. It is possible to exclude

the July 2007 event from this analysis since it was a convective storm localised above Kirkby

Stephen. However, the other events do suggest an increase in runoff before a decrease. A possible

reason for this is that at smaller catchment areas, a dedicated river channel is not formed, and

therefore the runoff is pooled instead of being discharged. Alternatively, it is possible that the

rating curve at Gais Gill is incorrect, and is underestimating the discharge.

The data in this study consisted winter events only. This provided a scaling exponent for peak

discharge ranging from 0.842-0.896. These values seem reasonable since the discharge would be

expected to be greater for winter events due to lower infiltration rates. The scaling exponent for

peak runoff ranged from 0.104-0.157. From Wilkinson’s (2009) study, the discharge scaling

exponents for winter events ranged from 0.717-0.793. The most likely reason for this discrepancy

is a difference in data used. For example, the January 2005 data used in this study showed much

greater peak discharges than the ones used in Wilkinson (2009). It is assumed that the

Environment Agency revised the data since then, hence there was a difference.

Figure 39 – Peak Runoff vs Catchment area with power laws fitted to six different events taken from an earlier

study on the Upper Eden Catchment (Wilkinson, 2009).

56

7. Conclusions

The aim of the project was to investigate and analyse the November 2009 flood in the Eden valley

whilst placing it in context of other notable floods within the region, which included the January

2005 and December 2015 floods. To achieve this, four objectives were set out. The first was to

undertake a literature review to develop expertise in the area. This objective was successfully

achieved. The literature review helped with the identification of the limitations of this study,

especially regarding correction procedures for precipitation. The literature review also provided

insight into the different ways runoff is distributed. Lastly, the review brought to light the scale

issues regarding the upscaling of peak discharge with respect to catchment area. Naturally, this

led to another objective of this study which was to provide some more knowledge on the scale

issues.

Whilst the data was obtained from numerous sources, there was still a shortage of data which

affected the results. One of the more intriguing results of this study was that runoff appeared to

exceed rainfall for both events. This was attributed to several factors. Firstly, the actual rainfall

was probably more than the recorded rainfall due to undercatch and losses within the raingauges.

Next, the calculation of catchment average rainfall was performed using Thiessen polygons.

However, due to a limited number of raingauges, the areas of the Thiessen polygons were greatly

influenced by lowland raingauges, which experienced a lower amount of rainfall, thus reducing

the catchment average rainfall. The data available did help show the general pattern of rainfall,

which was done by creating rainfall maps using the Inverse Distance Weighting technique in

ArcMap. This showed the spatial variability of rainfall as the storm progressed. This was

fundamental in helping explain the other results, including the runoff hydrographs.

Another objective of this study was to exhibit the flood response at different catchment stations

to understand the progression of peak discharge. This was done in two stages. The first was to

compare the runoff at Gais Gill, a highland catchment, with the runoff at Blind Beck, a lowland

catchment. The comparison clearly showed flashier, faster moving runoff at Gais Gill, which was

attributed to the steeper gradients. It also showed slower and attenuated runoff at Blind Beck,

which was a result of the lowland nature. These findings agreed with the previous findings of

Mayes et al. (2006). The second stage to achieving the objective involved studying the wave

speeds and lag times of the two events. It was found that the lag times for November 2009 were

much greater than the lag times for January 2005. This was attributed to the spatial pattern of

rainfall. For November 2009, much more rainfall fell over the Lake District, which lies west of

the Upper Eden. This resulted in runoff being slowed by Ullswater which feeds into the River

Eamont, which is a tributary to the Eden below Temple Sowerby. Hence, the time to peak between

Temple Sowerby and Great Corby was significantly increased.

57

To study the scale issues, the peak discharges were plotted against catchment area on a

logarithmic scale with power laws fitted to them. This was because the literature review had

shown that a power law variation between peak discharge and area exists. The exponents obtained

for the power laws were within the range suggested in literature, which is 0.65-1.0 for natural

basins like the Eden. However, in literature it was suggested that the exponent decreased as return

periods increased. This study did not find such behaviour, as the return periods for the events

varied greatly but the exponents did not. It had also been previously suggested that the exponent

would decrease as the watershed area was increased. To test this, power laws were fitted to the

peak discharges for the November 2009 event at different stations, each time including a station

with a greater catchment area. This did show that the scaling exponent decreased. But it also

showed that for a catchment, a single power law would not be suitable for predicting peak

discharge due to inflows from tributaries causing a difference as the catchment scale increased.

The events analysed in this study were winter events. The power laws obtained were compared

with laws obtained in an earlier study, and it was found that the exponents calculated in this study

were greater. This was credited to the Environment Agency revising the data between now and

the earlier study.

The peak runoff for the different events was also plotted against catchment area. This showed

some interesting behaviour, as the peak runoff seemed to increase up to a certain catchment area

(Smardale, 36.6 km2), prior to decreasing. This was attributed to the non-existence of a proper

river channel in smaller areas, resulting in ponding. On the contrary, it is possible that the rating

curves at Gais Gill were wrong, which led to a lower runoff than was actually observed. Therefore,

more research is needed to observe the behaviour of runoff at the smaller catchment scales.

58

8. Recommendations

The results in this study could have been more conclusive if the data quality and quantity was

greater. A prime example of this would be the discharge data for the November 2009 event at

Artlegarth having a ‘flat top’, rendering it unusable. Along with this, the rating curve at

Ravenstonedale seemed to be exaggerating the runoff. If the data for these two stations was more

reasonable, it would have perhaps helped improved the understanding of runoff behaviour at

smaller catchment scales.

Correction procedures were not applied to the rainfall data to account for the effects of wind-

induced undercatch since they require pit gauges to dictate a correction factor. A better

representation of rainfall could therefore be obtained by the installation of pit gauges within a

catchment in order to correct the rainfall measurements.

Having piezometer records could have also improved the analysis of flood response variation at

different parts of the catchment. The groundwater level could have been studied for the November

2009 event to show the effects of infiltration and rising water tables on runoff.

The flood events chosen were all winter events, hence seasonal variation was not accounted for.

If the study was to be repeated, it would be prudent to compare events from the summer months.

This has been done in Wilkinson (2009), and therefore the peak discharge data is readily available.

This study was also limited to flooding of the River Eden. But as the results showed, the runoff

and lag times at Great Corby were also influenced by inflows from neighbouring catchments,

particularly from the Lake District during the November 2009 event. It would be interesting to

expand the scope of the study to analyse these inflows, and it could perhaps shed some light on

lag time variation due to spatial variability of rainfall.

The final recommendation would be to study the runoff at the smaller scale catchments in the

Upper Eden to help explain why it seemed to increase up to a certain catchment area before

decreasing. This study has proposed either a ponding effect at smaller scales, or an inaccuracy

with the rating curve at Gais Gill. Therefore, it would perhaps be best to first check the accuracy

of the rating curve at Gais Gill before carrying out a comprehensive study on the smaller scale

catchments.

59

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62

10. Appendices

A. Project Management Statement

To manage the project, a Gantt chart was created in Microsoft Excel. This was used

throughout the project, including the literature review phase. For the literature review, a list

of topic areas for review was discussed with my supervisor, Dr. James Bathurst. The Gantt

chart was then designed to follow this list. Since there were block modules and other

commitments present this year, the Gantt chart blocked out certain weeks completely to allow

the work for other modules to be carried out. Through the Gantt chart, it was ensured that

enough time was left at the end of both main phases to allow for proofreading, formatting,

and binding. Time was also spared for unforeseen circumstances, such as delays with

obtaining data. This was a wise decision, since there were some technical issues with the

creation of rainfall maps. With the extra time allowed, the project was able to be completed

by a week before the submission deadline. An example of the Gantt chart is appended below

(Appendix A1). The days highlighted in light blue for example, indicate days where I had to

attend a placement as part of the other module. Hence, no work could be done on the project

and nothing was scheduled for then. The pink blocks indicate a block module, where once

again, the project could not be focussed on. Having a Gantt chart helped balance the workload

of this project and other modules, ensuring a successful year.

Appendix A.2 shows that a deadline for the 13th of May was set. This was a fortunate accident,

since the actual deadline turned out to be the 20th of May. As a result, more than enough time

was left to finish the project. The second figure also shows how the creation of rainfall maps

was pushed back by over a month, and yet, allowed the completion of the project. This was

because other major tasks, which were not influenced by the rainfall maps were completed

instead.

Over the course of the project, there were 12 formal meetings with Dr. James Bathurst. A few

informal meetings with Dr. Claire Walsh were also scheduled with the aim to understand how

to create the rainfall maps. In between meetings, any significant progress or findings were

reported to both Dr. Bathurst and Dr. Walsh via e-mail. Appendix A.3 lists the dates of all

meetings, and briefly describes the general topics discussed.

63

Appendix A.1 – Gantt chart during February

Appendix A.2 – Gantt chart after adjustments in April

64

Appendix A.3 – List of meetings and topics discussed with Dr. Bathurst.

Meeting Date Topic Discussed Meeting Date Topic Discussed

15/10/2015 Contents of literature review, Aims and

Objectives

23/02/2016 The storm event was identified. Needed to

gather more data for the January 2005 event.

26/10/2015 Aims and objectives finalised. Further

reading provided.

10/03/2016 The different sections of the dissertation

were explained by Dr. Bathurst, and the

information to be written in those sections

was given.

9/11/2015 Literature review, and climate change

impact on flooding. This formed the

introduction of the literature review.

18/03/2016 The rainfall maps were discussed. At this

point they werent accurate and therefore the

problem had to be fixed. Meeting with Dr.

Walsh arranged.

23/11/2015 Literature review so far was discussed.

This included details about CHASM

initiative and the general rainfall pattern

during the event. Reading material on

raingauge error correction procedures

was given by Michael Pollock.

11/04/2016 The plot of Peak Discharge vs. Area were

discussed, as well as lag time vs. area. It

was recommended by Dr. Bathurst to depict

flood response contrast between Gais Gill

and Blind Beck.

7/12/2015 This was a meeting scheduled before the

holiday to see the general progress.

Literature on spatial scaling had been

reviewed by this point, and most of the

general topics in the literature review had

been covered.

26/04/2016 Remaining data that was needed was

discussed. This included Great Corby data

for the 2005 event. Email was sent to EA

requesting the data.

10/02/2016 This meeting was to discuss the results of

the PIR. The areas where marks were

missed were highlighted. These included

previous findings. Discussion on how to

calculate lag times.

10/05/2016 Final meeting before submission. All data

had been gathered and results presented.

The different points to mention in the

discussion were finalised.