hydrology 4 - report

Catchment Hydrology - Practical 4 Report Cobain Schofield

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Assessing the extent to which phosphorus is impacting the trophic status of Loweswater, Cumbria

Introduction

This report aims to assess the extent to which phosphorus is impacting on the trophic status of Loweswater

Lake in Cumbria, UK as shown in Figure 1.

Figure 1 - Location of Loweswater within the United Kingdom

Loweswater Lake is situated at 54.6 degrees latitude and at approximately 130m altitude, in an area of the

UK which has an annual average temperature of 9 degrees Celsius and receives an average of 1500mm of

rainfall per year. According to Figure 2, this places Loweswater within the range of a dimictic lake.

Figure 2 – The global distribution of thermal lake types in relation to latitude and altitude (Wetzel, 1975) from Chowdrey et al (2014).

The dimictic nature of Loweswater means that it should theoretically stratify twice each year; once in

summer and once in winter, whilst full mixing of the lake will occur in spring and autumn at which point the

lake is isothermal. The implication of this is that particles which are washed into the lake become trapped in

200m

N

Google Maps

Loweswater


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greater quantities during stratification, whilst particles are largely held in suspension during mixing. The

lake can therefore be viewed as a particle trap during stratification, and during mixing the particles in

suspension are able to chemically trap freely available phosphate ions in the water. This effectively

removes the trapped ions from the system once the particles settle into the sediment after the lake

stratifies. In abstract, this means that Loweswater has the potential to remove phosphorus from the water

as it flows through. In the case of most lakes, and in the case of Loweswater, phosphorus is the limiting

nutrient of primary production (Elser et al, 2007). According to Elser et al, phosphorus levels have been

‘massively altered’ by anthropogenic activities and land use. Given the status of phosphorus as a limiting

nutrient, varying levels of phosphorus in the lake could potentially cause primary production to be too low if

phosphorus is present in low concentrations, or it could cause primary production to occur beyond the

lake’s ecological limits if it is present in high enough concentrations (Søndergaard et al, 2003). It is

therefore imperative that phosphorus levels in Loweswater are monitored so as to assess the trophic status

of the lake and to work out potential management strategies to mitigate any negative effects that occur.

Methods Employed

In order to establish the trophic status of Loweswater, data must be obtained or produced. First, water

sampled at each inflow stream into Loweswater was measured using methods outlined in Carlson and

Simpson (1996) in order to obtain values for the total phosphorus content of each sample. Once these

values are obtained, they could be applied to a basic box model to work out how much phosphorus enters

the lake, is trapped as sediment, and leaves the lake in the outflow stream(s). The box model is shown

below in Figure 3. Table 1 shows the parameters used in and produced by the box model.

Figure 3 - A basic phosphorus box model outlined in Imboden (1974)

L A K E

Lin = Lsed + Lout

(inflow loading = sediment loading + outflow loading) Lin = qin * TPin

(qin is the water influx and

TPin is the TP conc. of

inflow water)

Lout = qout * TPout

(qout is the water influx and

TPout is the TP conc. of

outflow water)

Lsed = Psed burial flux * Alake

(where Psed is the sediment

phosphorus burial rate)

Lin

Lout

Lsed

The box model assumes a

closed system, so everything

that enters must either leave

the system or stay within it.


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Table 1 – Parameter dictionary and data origins

Parameter Origin of the data Description Units *

Lin

Box Model

= Lout + Lsed kg/yr

Lout = qout * TPout kg/yr

Lsed = Psed burial flux * Alake kg/yr

Alake Calculated using maps

Area of the lake km2

Acatchment Area of the catchment km2

qin Calculated from climatic data

Water inflow m3/yr

qout Water outflow m3/yr

qs,in Calculated using qin/qout and Alake Normalised water fluxes m/yr

qs,out

TPin

Measured from water samples

Total phosphorus entering lake mg/L (g/m3)

TPsed Total phosphorus in sediment mg/L (g/m3)

TPout Total phosphorus leaving lake mg/L (g/m3)

MAR Calculated using the Turc (1954) equation, requires MAP and MAT

Mean Annual Runoff mm/yr

MAE = (MAP/[0.9 + (MAP/k)2]0.5) Mean Annual Actual Evaporation mm/yr

k = 300 + 25MAT + 0.05MAT3 Empirical coefficient

MAP Values provided; Met Office

Mean Annual Precipitation mm/yr

MAT Mean Annual Temperature degrees Celsius

Rp Calculated using methods outlined by Kirchner and Dillon (1975)

Phosphorus Retention Coefficient

*parameter values may not necessarily be in these units; conversions may be necessary for certain calculations.

When using the box model it is important to remember that this is a simple base model for understanding a

much more complex system. As such, there are some large uncertainties associated with values,

particularly Lin, which has a number of factors affecting it (each with potential for large variation) and

cannot be measured all of the time.

Using parameters from Table 1, it is possible to work out the retention coefficient of phosphorus within

Loweswater using the Kirchner and Dillon (1975) equation:

𝑅𝑝 = 0.426 exp(−0.271𝑞𝑠,𝑜𝑢𝑡) + 0.574 exp (−0.00949𝑞𝑠,𝑜𝑢𝑡)

The numbers calculated or provided for Loweswater (see appendix 1) can be substituted into the above

equation to give an estimated value for phosphorus retention for the lake:

𝑅𝑝 = 0.426 exp(−0.271 ∗ 14.5) + 0.574 exp (−0.00949 ∗ 14.5)

𝑅𝑝 = 0.509

Now that Rp has been established it is possible to check whether the values from the box model are within

the acceptable range considering uncertainties. To do this, the following equation can be used:

𝐿𝑠𝑒𝑑 = 𝐿𝑖𝑛 ∗ 𝑅𝑝

𝐿𝑠𝑒𝑑 = 268 ∗ 0.509

𝑳𝒔𝒆𝒅 = 𝟏𝟑𝟔 𝒌𝒈/𝒚𝒓

(Calculated Lsed = 160kg/yr from Appendix 1)


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𝐿𝑜𝑢𝑡 = (1 − 𝑅𝑝) ∗ 𝐿𝑖𝑛

𝐿𝑜𝑢𝑡 = (1 − 0.509) ∗ 268

𝑳𝒐𝒖𝒕 = 𝟏𝟑𝟐 𝒌𝒈/𝒚𝒓

(Calculated Lout = 120kg/yr from Appendix 1)

For the purpose of this report, the value for Lin will be taken from the mass balance of the lake (Lout+Lsed),

the values of which will be those produced by the box model and included in Appendix 1. Using this data,

the Lin value is calculated to be 280kg/yr (labelled in Appendix 1 as [Lin (mass balance)]), which is very

close to the box model output of 268kg/yr considering the uncertainties involved.

Trophic status of Loweswater

The trophic status of a lake describes its metabolism and is based on the nutrient supply from both the

catchment of the lake and from within the lake itself. In the case of Loweswater, it has already been

established that phosphorus is the limiting nutrient, so the lake’s metabolism is dependent on phosphorus

more so than any other nutrient.

Figure 4 - Phosphorus boundary values for fixed trophic classification system (P in µg/L == mg/m3) based on Ryding and Rast (1992, Chapter 7).

The trophic status of the lake is given by the value of TPlake. A back-of-the-envelope value can be obtained

by simply calculating TPin - TPout to work out what is left behind, and is based on the data in Appendix 1.

This gives a value of 0.018mg/L, or 155kg/year of phosphorus at lake scale. This value has been included

on Figure 4 and marked ‘A’ (18µg/L). However, this value represents only a single-framed snapshot of the

phosphorus entering the lake and is based upon assumptions and calculations from a variety of academic

texts. To give a more representative value of TPlake multiple measurements of water influx should be used

where possible. Data was provided for Dub Beck (Inflow stream 10 on Appendix 2) at Loweswater. The

average TPlake value was calculated across the year 2012 - 2013 as 12.6mg/m3 and is included on the

Figure 4 as line ‘B’ (12.6µg/L). The data is available in its raw form in Appendix 3. While this reflects a truer

value for the lake, the data point resolution is still low (Figure 5). This means that large storm events, or

times of low flow could see positive and negative spikes away the mean amount of phosphorus entering the

lake, affecting the overall mean and therefore the interpretation of the lake’s trophic state. This is a

limitation which is only rectifiable by increasing the amount of measuring points around the lake and the

frequency at which they are measured at.

Ultra-oligotrophic Oligotrophic Mesotrophic Eutrophic Hypertrophic

<4.0

<10

.00

10 -

35

35 -

10

0

>10

0

A B


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Figure 5 - A graph showing the individual data points set out in Appendix 3, showing TPlake values across the year 2012 – 2013 with the trend line y=0.0024x-86.352 centered on 12.6mg/m3 (point B on Figure 4)

The approximated TPlake value of 12.6mg/m3 still supports the box model TPlake value of 18mg/m3 in that

they both fall comfortably within the range of mesotrophic on the diagram in Figure 4 (Ryding and Rast,

1974 [Chapter 7]).

Managing Eutrophication in Loweswater

Given the limited scope of the data available to produce the graphs in Figures 4 and 5, and to eventually

deduce that Loweswater is a mesotrophic lake, it is important to take larger datasets into account when

considering the wider picture. Boyle et al (2000) took measurements of phosphorus and phytoplankton

during their study which gives a more complete picture of lake quality based on findings by Riding and Rast

(1992). Their report found - based on their own data and other published data - that Loweswater is a

mesotrophic to mildly eutrophic lake, and that it has experienced “slight nutrient enrichment over the last

century”. It is reasonable to assume that this nutrient enrichment is the result of anthropogenic activity as

described by Elser et al (2007). Therefore, management strategies might be considered in order to prevent

the lake exceeding the natural productivity allowed by its catchment.

One approach could be to create a pre-reservoir which would have the sole purpose of capturing as much

phosphorus as possible from inflow streams prior to draining into Loweswater. The box model outlined in

Figure 3 can be re-run for the new reservoir after its boundaries and catchment have been established and

areas calculated using OS maps. It is then possible to reassess the trophic conditions within Loweswater

after the pre-reservoir has been built.

Firstly it is necessary to establish possible locations for pre-reservoirs. These must be able to cover a

sizable portion of the overall catchment in order to intercept as much phosphorus as possible (Figure 6).

y = 0.0024x - 86.352R² = 0.0108

10

12

14

16

18

20

29/0

8/2

01

2

18/1

0/2

01

2

07/1

2/2

01

2

26/0

1/2

01

3

17/0

3/2

01

3

06/0

5/2

01

3

25/0

6/2

01

3

14/0

8/2

01

3

03/1

0/2

01

3

22/1

1/2

01

3

11/0

1/2

01

4

TP

lake

(mg

/m3)

Date of water sample


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Figure 6 - Potential locations for pre-reservoirs within the Loweswater Catchment

(all maps in Figure 6 © Crown Copyright and Database Right 2014. Ordnance Survey (Digimap Licence))

Figure 6.a – Pre-reservoir 1 (North)

Figure 6.b – Pre-reservoir 2 (East)

Figure 6.b – Pre-reservoir 2 (East)

Table i – Pre reservoir 1 parameter values

Catchment Area (km2) 4.32

Reservoir Area (km2) 0.10

MAR (m/yr) 0.97

TP (mg/m3) 30.4

Lsed (kg/yr) 49.3

Loweswater Lin Change (%)

-17.6

Table ii – Pre reservoir 2 parameter values



MAR (m/yr) 0.97

TP (mg/m3) 30.4

Lsed (kg/yr) 10.0


-3.6

1000m

N

N

1000m


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Figure 6.c – Pre-reservoir 3 (West)

Now that the potential sites have been established, the current land uses of the Loweswater catchment

must be considered in order to properly assess the advantages and disadvantages associated with the

proposed pre-reservoirs. Figure 7 shows a generalised land use summary of the catchment.

Figure 7 - Generalised land use summary for Loweswater catchment, based on OS Mastermap data displayed in Table 2.

Table iii – Pre reservoir 3 parameter values



MAR (m/yr) 0.97

TP (mg/m3) 30.4

Lsed (kg/yr) 23.7


-8.4 1000m

N


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Table 2 - Generalised land use summary for Loweswater from OS Mastermap data, used to make Figure 7 in ArcGIS

Total Area (km2)

P Loadings (kg/P/yr/m2)

TP (kg/P/yr) (area * loading)

Percentage of Catchment

Improved Pasture 2.04 30 61.2 44

Unimproved Pasture 1.04 5 5.2 4

Forest 0.63 35 22.0 16

Idle land 5.16 10 51.6 37

Atmospheric (Forested) 0.63 20 12.6 11

Atmospheric (Rural) 8.27 12 99.24 89

Catchment Sum 8.9 112 140.05 100

Loadings used in Table 2 (and pre-reservoir summaries included in Appendix 4) have been estimated using

chapter 7 of Ryding and Rast (1992), shown in Figure 8 below.

Figure 8 – Total phosphorus unit area loads (kg P / km2 / yr) *Note: table corrected for error in book* (Ryding and Rast 1992, Chapter 7)

Figure 6.a represents the pre-reservoir with the largest phosphorus capture capacity of the 3 proposed, and

the land which would be flooded is largely unimproved pasture with little agricultural value. The catchment

for this reservoir is 52% improved pasture, which has the second largest phosphorus loading behind

forested land.

Pre-reservoir 2 in Figure 6.b would have a smaller upland catchment, consisting mostly of idle land (90%

coverage), and therefore yields very little phosphorus; less than 6.5kg per year.

Pre-reservoir 3 in Figure 6.c has a small catchment for the size of the reservoir, but this reservoir exploits

its position on what is currently forested land to eliminate the largest phosphorus source in the catchment.


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However, given the status of the forested land, this makes building a pre-reservoir here ecologically

unsustainable.

Conclusion

Based on the results of the box model and the subsequent analysis of the Loweswater catchment, the

optimal solution given the restrictive nature of the data would be to build a pre-reservoir at site 1 (Figure

6.a) to reduce the phosphorus loading of Loweswater by 17.6%. This site is best suited over the alternative

sites because it encompasses the largest collection of high-phosphorus producing land within its catchment

and therefore will have the highest phosphorus:catchment-area ratio of the 3 reservoirs. The trophic status

of the lake would not change, but the fixed-trophic classification number (Figure 4) would reduce from 12.6

to 11.3, making the lake border-line oligotrophic-mesotrophic. However, the flooding of this land would

impact at least 5 collections of buildings (Appendix 5) which would incur economic and social issues

associated with relocation agreements, and the pre-reservoir might have a negative ecological impact on

the environment since the problem of eutrophication is not being dealt with per se, but rather is being

moved elsewhere on a smaller scale. This new pre-reservoir would require dredging to remove phosphorus

to ensure that it did not end up becoming a eutrophic lake (or higher up the scale in Figure 4) or that the

excess phosphorus in solution during mixing did not simply wash out into Loweswater, rendering the pre-

reservoir pointless. Providing this pre-reservoir was well-managed, the effects that it has on Loweswater

would be seen very quickly, whereas land use management changes within the catchment could take much

longer to establish, and longer again before quantifiable results are available. Therefore, considering the

limitations of the data made available in this report, it is recommended that pre-reservoir 1 (north) should be

built to the specification detailed in Figure 6.a Table i as the principle management solution for Loweswater.


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References

Boyle. J, Bennion. H, Appleby. P, Carvalho. L, Luckes. S, Henderson, A (2000). “Water Quality Investigation of Loweswater, Cumbria”. Final report to the Environment Agency; May 2000. Environmental Change Research Centre, London.

Carlson, R.E. and J. Simpson. (1996). “A Coordinator’s Guide to Volunteer Lake Monitoring Methods”. North American Lake Management Society. 96 pp.

Chowdrey S, Hasan K, Alam K. (2014). “The Use of an Aeration to Prevent Thermal Stratification of Water Bodies: Pond, Lake and Water Supply Reservior”. Applied Ecology and Enivornmental Sciences Journal. 2014 Volume 2, No. 1. Page 3. DOI: 10.12691/AEES-2-1-1

Elser J, Matthew E, S. Bracken, Elsa E. Cleland, Daniel S. Gruner, W. Stanley Harpole, Helmut Hillebrand, Jacqueline T. Ngai, Eric W. Seabloom, Jonathan B. Shurin and Jennifer E. Smith. (2007). “Global analysis of nitrogen and phosphorus limitation of primary producers in freshwater, marine and terrestrial ecosystems”. Ecology Letters. Vol 10, issue 12, p1135-1142. DOI: 10.1111/j.1461-0248.2007.01113.x

Imboden, D. M. (1974). “Phosphorus model of Lake Eutrophication”. Swiss Federal Institute for Water Resrouces and Water Pollution Control (EAWAG), Dübendorf.

Met Office. (2014). “What are seasons?”. UK Met Office. Available online at: http://www.metoffice.gov.uk/learning/learn-about-the-weather/how-weather-works/seasons. Last Accessed: 12th December 2014.

Ryding S and Rast W. (1992). “The control of eutrophication of lakes and reservoirs”. Paris. Unesco and the Parthenon Publishing group.

Søndergaard, M., Jensen, J., Jeppesen, E. (2003). “Role of sediment and internal loading of phosphorus in shallow lakes”. Hydrobiologia 506. p135-145. Kluwer Academic Publishing, Netherlands.

Turc, L. 1954: “Calcul du bilan de l’eau evaluation en fonction des precipitations et des temperatures”. IASH Symposium, Rome 188-202.

Wetzel, R. G. (1975). “Limnology”. 743 pp. WB Saunders Co., Philadelphia

http://www.metoffice.gov.uk/learning/learn-about-the-weather/how-weather-works/seasons


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Appendices

Appendix 1 :: Parameter values for parameters listed in Table 1

Appendix 2 :: Inflow stream locations for Loweswater

Appendix 3 :: Temporal Variation of Phosphorus Influx

Appendix 4 :: Land use summaries for proposed pre-reservoirs for Loweswater

Appendix 5 :: Buildings impacted by building Pre-reservoir 1


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Appendix 1 :: Parameter values for parameters listed in Table 1

This table contains the initial dataset after running the box model for Loweswater

Parameter Value Units *

Lin 268 kg/yr

Lout 120 kg/yr

Lsed 160 kg/yr

Lin (mass balance) 280 kg/yr

Alake 0.6 km2

Acatchment 8.9 km2

qin 8641154 m3/yr

qout 9262541 m3/yr

qs,in 13.5 m/yr

qs,out 14.5

TPin 0.031 mg/L (g/m3)

TPout 0.013 mg/L (g/m3)

TPsed 0.018 mg/L (g/m3)

MAR 970 mm/yr

MAE 529 mm/yr

k 561

MAP 1500 mm/yr

MAT 9 degrees Celsius

Rp 0.509

*parameter values may not necessarily be in these units; conversions may be necessary for certain calculations.


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Appendix 2 :: Inflow Stream locations for Loweswater

Stream ID Latitude Longitude Flow litre/s

Catchment area km2

1 54.57715 -3.340821 90 8.2237

2 54.5782 -3.352949 0.5 0.118

3 54.58044 -3.357977 0.6 0.118

4 54.58325 -3.359232 1.5 0.975

5a 54.58445 -3.36425 0.4 0.047

5 54.58425 -3.36496 0.6 0.047

6 54.58487 -3.365802 2 0.463

7 54.58556 -3.366054 0.3 0.008

8 54.58618 -3.367279 0.05 0.024

9 54.5879 -3.366591 0.01 0.01

10 54.58949 -3.368307 2.5 3.243

11 54.58865 -3.363671 0.1 0.0215

12a 54.58849 -3.361044 0.025 0.037

12 54.58834 -3.360375 0.05 0.0103

15a 54.58261 -3.349123 0.1 0.044

15 54.58177 -3.347776 3 0.892

N


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Appendix 3 :: Temporal Variation of Phosphorus Influx at Dub Beck

** NOTE: Dub Beck is listed in Appendix 2 as stream 10 ** - Seasonal definitions obtained from Met Office (Met Office, 2014).

Inflow # Inflow # Lake Lake Outflow Outflow

TP SRP TP SRP TP SRP

mg/m3 mg/m3 mg/m3 mg/m3 mg/m3 mg/m3

DATE

Avg season mg/m3

(P measured in mg/m3)

Winter 22/01/2013 7.6 2.6 13.8 1.4 11.4 1.1 In 6.95 0.0070

Winter Inflow 0.007

26/02/2013 6.3 2.8 12.5 1.8 10.6 1 Out 11.00 0.0110 Outflow 0.011

Spring 18/03/2013 20.1 6.3 10.2 1.4 11 1 In 14.40 0.0144

Spring Inflow 0.014

23/04/2013 11.8 3.7 10.3 1.7 11.7 3 Out 13.30 0.0133 Outflow 0.013

29/04/2013 10.7 1.1

Summer Inflow 0.011

20/05/2013 11.3 3.7 10.5 1.1 17.2 3.2 Outflow 0.014

Summer 25/06/2013 12.3 3.1 11.8 1.8 12.7 2 In 11.37 0.0114

Autumn Inflow 0.063

17/07/2013 9.5 5.4 19.2 3.3 19.8 5.4 Out 13.90 0.0139 Outflow 0.013

19/07/2013 17.2 6.2

29/08/2013 12.3 4.5 14.7 2.3 9.2 1

Autumn 26/09/2013 56.4 19.1 10.3 1.7 10.6 1 In 63.64 0.0636

22/10/2013 163 23.3 10.4 1.2 14.7 2 Out 13.43 0.0134

18/11/2013 44.6 6.9 11.4 1 12.5 1

10/12/2013 9.6 3.2 13.7 1.2 15.9 1.3

16/10/2012 44.6 12 1.8

Average (mg/m3) 30.4 7.05 12.6 1.942857 13.10833 1.916667

Average (g/m3) 0.0304 0.00705 0.012 0.001943 0.013108 0.001917


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Appendix 4 :: Land use summaries for proposed pre-reservoirs for Loweswater

Pre reservoir 1 – Figure 6.a (plus Table i)

Total Area (km2)


TP (kg/P/yr/m2) (area * loading)


Improved Pasture 1.44 30 43.2 52

Unimproved Pasture 0.9 5 4.5 5

Forest 0.63 35 22.0 26

Idle land 1.35 10 13.5 16

Atmospheric (Forested) 0 0 0 0


Catchment Sum 4.32 92 140.05 100

Pre reservoir 2 – Figure 6.b (plus Table ii)

Total Area (km2)




Improved Pasture 0 0 0 0

Unimproved Pasture 0 0 0 0

Forest 0.018 35 0.63 10

Idle land 0.582 10 5.82 90



Catchment Sum 0.6 77 6.45 100

Pre reservoir 3 – Figure 6.c (plus Table iii)

Total Area (km2)




Improved Pasture 0 0 0 0

Unimproved Pasture 0 0 0 0

Forest 0.354 35 12.39 83

Idle land 0.846 10 2.49 17



Catchment Sum 1.3 77 14.85 100


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Appendix 5 :: Buildings affected by building pre-reservoir 1

N

300m

Pre-reservoir 1 outline

Buildings impacted by the reservoir

hydrology 4 - report

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