modelling sphagnum propagation in bleaklow, peak district national park

8/14/2019 Modelling Sphagnum Propagation in Bleaklow, Peak District National Park

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Modelling Sphagnum Propagation in Bleaklow,

Peak District National Park

byHaoyang Xu

Dissertation presented for the Degree of MSc in EnvironmentalManagement

University of Nottingham

2006

Approximate number of words

I am aware of the Universitys policy on plagiarism and I confirmthat the work presented in this dissertation is entirely my own.

Signed .................. Date ...............


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Contents

1 Research Aims 9

2 Background 11

2.1 Research area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Ecology ofSphagnum . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Identification ofSphagnum using aerial photographs . . . . . . . . . 122.4 Peatland hydrology . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.1 Hydroperiod . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.2 Peat soil characteristics . . . . . . . . . . . . . . . . . . . . . 132.4.3 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.4 Surface flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.5 Groundwater and Darcys Law . . . . . . . . . . . . . . . . . 142.4.6 Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 Blanket bog forming and erosion . . . . . . . . . . . . . . . . . . . . 162.5.1 Peat formation . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5.2 Blanket bog erosion . . . . . . . . . . . . . . . . . . . . . . . 172.6 Recovery work in Dark Peak . . . . . . . . . . . . . . . . . . . . . . 172.7 Hydrological modelling . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.7.1 MODFLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.8 Population modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.8.1 Trends in development . . . . . . . . . . . . . . . . . . . . . 192.8.2 Cellular Automata models and CAPS . . . . . . . . . . . . . 202.8.3 GAM and GRASP . . . . . . . . . . . . . . . . . . . . . . . 21

3 Methodology 23

3.1 Data source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Classification of remote sensing images . . . . . . . . . . . . . . . . 233.2.1 Preparation of remote sensing images . . . . . . . . . . . . . 233.2.2 Supervised classification . . . . . . . . . . . . . . . . . . . . 243.2.3 Unsupervised classification . . . . . . . . . . . . . . . . . . . 25

3.3 Preliminary field survey . . . . . . . . . . . . . . . . . . . . . . . . 253.3.1 Work area . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.2 Selecting survey points . . . . . . . . . . . . . . . . . . . . . 253.3.3 Field activities . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4 Hydrology modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4.1 Processing digital elevation model data . . . . . . . . . . . . 263.4.2 Model parameterisation . . . . . . . . . . . . . . . . . . . . 273.4.3 Model calibration . . . . . . . . . . . . . . . . . . . . . . . . 30

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3.4.4 Model simplification . . . . . . . . . . . . . . . . . . . . . . 313.5 Field survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.6 Presence prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.6.1 Presence in present day . . . . . . . . . . . . . . . . . . . . . 323.6.2 Model prediction of presence . . . . . . . . . . . . . . . . . . 32

4 Result Analysis 35

4.1 Preliminary fieldwork . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Classification of remote sensing images . . . . . . . . . . . . . . . . 36

4.2.1 Unsupervised classification . . . . . . . . . . . . . . . . . . . 364.2.2 Supervised classification . . . . . . . . . . . . . . . . . . . . 36

4.3 Hydrology simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 384.4 Field survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Presence mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5.1 Actual presence . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5.2 Prediction using GRASP and scoring habitat . . . . . . . . 424.5.3 Prediction using CAPS . . . . . . . . . . . . . . . . . . . . . 44

5 Discussion 49

5.1 Implications of results . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 Assumptions and limitations . . . . . . . . . . . . . . . . . . . . . . 505.3 Comparison of two predictions . . . . . . . . . . . . . . . . . . . . . 515.4 Application of the models . . . . . . . . . . . . . . . . . . . . . . . 51

6 Conclusion 53

A Preliminary Fieldwork Data Record 55

B Verification Data Record 57

C CAPS Input Files 59

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Statement of Originality

This work has not been submitted previously for a degree or diploma in anyuniversity. To the best of my knowledge and belief, the dissertation contains nomaterial previously written or published by others except where due reference ismade in the dissertation itself.

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Preface

The blanket bog in the Peak District National Park is a fascinating and fragilehabitat for grouse, sheep, heath and many other species. Its conservation is ofinternational importance. Sphagnum is a key species in this area. The erosionof peatland and decline of Sphagnum are enhancing each other. Consequently,recovery ofSphagnum can contribute to prevention of further erosion in this area.

Sphagnum used to dominate the Dark Peak area. However, today they can

rarely be found except in areas where watertable is close to or above the landsurface (Ingram, 1983). There may be many complicated interactions behind thischange. But from a management perspective, it is necessary to find an limitingfactor of the phenomenon, and take measures in the light of knowledge of its effects.An attempt of modelling the habitat and looking into the effects of environmentalvariables may help identifying such key factor and improve our understanding ofthe ecosystem.

Thus this project is proposed. It attempts to tell optimised Sphagnum habitatsin the area, as well as to tell possible locations of Sphagnum patches in the future.Though no single model can simulate a complex ecosystem, nor a species within

it, the modelling method described here should establish a scheme of using limiteddata to map niche and habitats.

I would like to thank Professor Roy Haines-Young, Doctor Christopher Lavers,Doctor Jack Rieley for their constant and inspiring advice, support and encour-agement; Dr. Aletta Bonn and Moors for the Future Partnership as well as PeakDistrict National Park Authority for providing all digital data used in this thesisand valuable suggestions. I also want to express my gratitude to the authors ofMODFLOW in the U.S.G.S. (Harbaugh and McDonald, 1996), and the authorof the front end, Processing MODFLOW (Chang and Kinzelbach, 1998), as wellas the authors of GRASP and CAPS model (Lehmann et al., 2002; Plotnick and

Gardner, 2002). Last but not least, I appreciate support from my family andfriends during the project.

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Abstract

The blanket bogs or mires of the Peak District National Park are part of a U.K. resource which is of international importance. The regeneration of peat accu-mulating Sphagnum is a part of peat forming cycle and plays an essential partin bog conservation. Therefore the propagation of Sphagnum in the context ofdisturbances should be studied.

The study combined data from multiple sources, including Digital Elevation

Model (DEM), ESA vegetation map, and field observation. Utilising knowledgeon Sphagnum ecology, this study uses both infrared and visible spectrum imagesto identify Sphagnum presence in the study area, which was verified by field ob-servation. The surface and subsurface waterflows of the study area were simulatedusing MODFLOW-96.

Combining species presence, hydrology and topography data, GRASP-R wasused to find how the factors influence Sphagnum presence and determine the rel-ative importance of the factors. A map of predicted Sphagnum presence can thenbe produced.

The statistical description of variables in GRASP shows that waterhead draw-

down is the most important variable. A Cellular Automata model named CAPSwas then used to predict future Sphagnum distribution. In short-term simulationthat has a time span less than ten years, the distribution of Sphagnum was in goodagreement with remote sensed and field observed patch distribution. However, ifthe simulated time is long, the predicted Sphagnum coverage suddenly falls. Fromthe simulation results it can be concluded that Sphagnum recovery is most likelyto happen in some lower areas, especially near the river and streams. Reducedprecipitation may lead to diminishing Sphagnum presence.

The study provides an approach of using limited environmental data to maphabitat for certain species. The information can be used by the management to

determine optimised and sensitive areas, thus better conservation using limitedresources can be achieved.Keywords: ecosystem modelling; Peak District; Cellular Automata; General

Additive Model; blanket bog.

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Chapter 1

Research Aims

The blanket bogs or mires of the Peak District are part of a U.K. resource whichis of international importance. It supports around 1015% of the global resource

and a variety of rare species such as Labrador tea and bog rosemary, as well as abreeding bird community of international importance (Ecology Service and Farm& Countryside Service, 2001).

The quality of bogs in the Peak District is deteriorated by air pollution, over-grazing, wildfire, peat extraction and drainage. As a result, substantial erosion istaking place. Especially in the Dark Peak Natural Area where up to 33km2 maybe degraded.

Erosion of peat can influence carbon balance (Evans et al., 1999) and hydro-logical balance, eventurally lead to habitat destruction (Mackay, 1997). Thereforeit is necessary to protect peatlands from erosion. The regeneration of peat accu-mulating Sphagnum is a part of peat forming cycle and plays an essential part inbog conservation (Price et al., 1998).

Therefore the propagation of Sphagnum in the context of disturbances shouldbe studied.

The research aims to answer the question that how changed groundwater tableand topography reduce population of Sphagnum and whether management aim-ing at raising watertable help recovery of Sphagnum and peat bog. It is knownthat drainage in Peak District and change of climate lead to lower groundwatertable and decline of Sphagnum. However, the interaction between Sphagnum andthe environment in the area has not been spatial-explicitly modelled. While gullyblocking is being carried out in the area, it is important to understand the im-

plication of changed hydrological conditions in Sphagnum regeneration and peaterosion prevention.

The objectives of the research include:

Model groundwater condition in the area, taking in consideration of gullyblocking;

Model Sphagnum propagation in this area.

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Chapter 2

Background

2.1 Research area

The research area is in the Dark Peak area of Peak District National Park. Itcovers Bleaklow Head and vicinity areas, the reference grids in British NationalGrid System are from SK0791 to SK1499. The map for this area is OrdnanceSurvey Explorer Map OL1.

The ancient upland plateau of Bleaklow is dissected by a series of valleys,which have been cut by the westerly flowing tributaries of the River Etherow(Byne, 1971). The major rock group, the Kinder Grit group, consists of fourlenses of grit separated by thick shale beds and it outcrops over the bulk of theupland. It is a coarse-grained conglomeratic sandstone, with quartz and feldsparpebbles which are often only poorly cemented together. Prolonged weathering

often lead to a tough cemented surface skin which overlies a bleached interior.The ancestral drainage system began to develop in early Tertiary time. Al-

though the rivers have progressively cut deeper into the original upland, a seriesof partial erosion surfaces were developed from time to time during periods whenthe rate of uplift of land slowed down or temporarily ceased. The surface bestdeveloped in this area is the Bleaklow summit plateau, which is probably of earlyTertiary age (Byne, 1971).

The moorland on Bleaklow today is an upland area with an altitude of about600 metres where the soil cover is bog grasses, heather and bilberry cloaking thicklayers of peat (Porter, 1989). The vegetation was formed after human clearing of

forest about 5,000 years ago (Peak District National Park Authority, 2004a).The pressures on plants of this area include heather burning, improved drainage

of the marginal lands, air pollution, and acid rains (Porter, 1989). Due to lowergrazing intensity in recent years, the steep valley sides tend to be invaded bywoody and scrubby plants.

2.2 Ecology ofSphagnum

Sphagnum is a kind of tall turfs bryophyte. The shoots grow on after gametangia

formation or production of acrotonous regenerative shoots is continued. They areable not only to hold water by capillary action but also to conduct it (Smith, 1982).

What makes Sphagnum special is the unusually slow rate of decay which makes

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the dead plants accumulation as peat possible (Smith, 1982). There are severalreasons. One is the very low concentration of nitrogen in the plants. The secondreason may be the acidic conditions produced by Sphagnum itself. The thirdreason is linked to the wet environment required by Sphagnum. The extensivecarpet-like growth and slow rate of decay make Sphagnum an important bryophyte

genus which is the major component of peatlands.

The distribution and rate of growth of Sphagnum plants and the performanceof one species relative to another are determined primarily by the supply of waterand by the concentration of solutes, particularly of Ca2+ and H+. The generalrequirements are an assured water supply with a relatively low concentration ofCa2+.

The general conditions for Sphagnum to recolonise a bare cutover peat includea high and stable water table, high soil moisture and high pore-water pressure(Price and Whitehead, 2004). The shading also plays a part determining growthof Sphagnum. It has been suggested that Eriophorum vaginatum cottongrass isa keystone species for the re-establishment of Sphagnum as it provides shade andprevents desiccation (Sundberg and Rydin, 2002).

Sphagnum reproduce easily from detached branch and stem fragments, al-though not from leaves (Sundberg and Rydin, 2002). However, there is evidencethat Sphagnum spores are important for long-distance dispersal and colonisationof disturbed habitats. Natural regeneration of Sphagnum spores requires onlythe presence of more or less constant, rather acid, wet conditions and of litterproducing plants that provide nutrients and shade.

The productivity of Sphagnum is affected by the availability of water supplied

to their growing apices or capitula (Harris et al., 2006). Because Sphagnums arenon-vascular, water is supplied to the capitula either by rainfall or via capillary risefrom the water table through the pore space between Sphagnum stems, branchesand leaves. During dry conditions, the water table falls and deprives capitulawater supply. The rates of Sphagnum production may thus decrease.

Under desiccation conditions Sphagnum can survive for different periods untilthe water stores are exhausted. Generally, larger species can survive longer, thismay be because they can store more water.

2.3 Identification ofSphagnumusing aerial pho-

tographs

All vegetation has higher reflectance of infrared radiation (Alexander and Milling-ton, 2000) than other land cover types. Sphagnum are reported to have evenhigher reflectance in near infrared (NIR) spectral bands (Burnett et al., 2003).However, infrared images alone are not enough to classify Sphagnum in a scenebecause other vegetation may have similar tones due to conditions when images

are taken. On the other hand, Sphagnum patches on visible spectrum images of-ten appear as bright green pixels. Combining these two features it is possible toclassify Sphagnum patches from the images.

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2.4 Peatland hydrology

2.4.1 Hydroperiod

The hydroperiod is the seasonal pattern of the water level of a wetland and is

like a hydrologic signature of each wetland type (Mitsch and Gosselink, 2000).It characterise each wetland type, and the stability of wetland depends on itsconstancy from year to year.

Peatlands in cooler climate have very little seasonal watertable fluctuation.However, in areas with warm summers, seasonal watertable change can be signif-icant.

Watel levels in wetlands are generally not stable. But many wetland man-agement practice, whose objective is to counter act the effects of seasonal andlongterm draughts, tend to restrict water flows through the managed area, thusreducing both the range of fluctuation and the water renewal rate (Mitsch and

Gosselink, 2000).

2.4.2 Peat soil characteristics

The conductivity of peat soil can vary with many factors, including depth, sub-strate and local climate (Ingram, 1983). Thus the measurement or estimation ofhydraulic conductivity for peat soil is difficult. Holden and Burt (2002) gave somesuggested values of hydrological conductivity, which was used to define layers inMODFLOW. Among which he cited Rycroft et al. (1975), who suggested thatCarex-Sphagnum peats horizontal conductivity is 8.0 103 cm sec1, and thatof Dry peat is 4.6 1056 horizontal and 1.0 105 vertical. Using rigid soil

theory, Rycroft et al. (1975) suggested conductivity k ranging from 1.1 105 cms1 at 30 cm depth to 6 108 cm s1 at 1m. In his field experiment in the sameyear, Rycroft et al. (1975) found that k during falling head is about 104 to 106.Reeve et al. (2000) assigned k values of 102, 104, 105, 105, 105, 106 m s1

for the acrotelm layer and catotelm layer 15 respectively.Ingram (1983) cited Rycroft et al. (1975) stating that the conductivity in the

acrotelm is 3.1 103m s1. But Romanov (Romanov, 1968) reported muchhigher values in the acrotelms of bogs in the Soviet Union.

For mineral soil underneath peat, most soil conductivity is between 104 and107 m s1. Thus here 106 m s1 is used for all mineral soil layers. The porosity

of peat may influence this value (Baird, 1998) but to determine it precisely needsfield sampling and measuring which exceeds the time frame allowed in this study.

2.4.3 Precipitation

Precipitation is the only source of water and major source of nutrient in blanketbogs (Gore, 1983). This is because the surface vegetation in bogs is largely isolatedfrom telluric recharge (Ingram, 1983).

Meteoric water may be precipitated in a variety of forms in addition to rain.Snow and hail are also important sources. Fog or dew may be involved, too. The

latter two are distinguished as occult precipitation. Many attempts were madeto explain the distribution of mires in terms of patterns of precipitation. It wasfound that in Wales, ombrotrophic mires were in an area delimited by the 1270

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millimetres average annual isohyet, or by the 305 metres contour or both. But inScotland 1000 millimetre annual precipitation is enough to sustain ombrotrophicmires (Ingram, 1983).

2.4.4 Surface flowThe percentage of precipitation converted to surface flow is determined by anumber of variables, with climate being the most important (Mitsch and Gos-selink, 2000). It was observed that in warmer parts of the world higher tempera-ture leads to higher evapotranspiration rate, greater soil moisture deficits, highersoil infiltration rates, and less surface flow.

Wetlands can be receiving systems for surface water flows, as well as sourcesof downstream systems.

Channelised streamflow

Channelised streamflow into and out of wetlands can be described simply as theproduct of the cross-sectional area of the stream (A) and the average velocity (v):

Si or So = Axv (2.1)

where

Si,So = surface channelised flow into or out of wetland (m3/s)

Ax = cross-sectional area of stream (m2)

v = average velocity (m/s)

The velocity can be determined both from field measurement and calculation.

The Manning equation can often be used if the slope of the stream and a descrip-tion of the surface roughness is known:

Si or So =AxR

2/3s0.5

n(2.2)

where

n = roughness coefficient (Manning coefficient, for peat gullies, n is between 0.065 to 0.112 (Mitsch aR = hydraulic radiuss = channel slope

The relationship is particularly useful for estimating streamflow where veloci-ties are too slow to measure directly, which are common in wetland studies (Mitschand Gosselink, 2000).

2.4.5 Groundwater and Darcys Law

The flow of groundwater into, through and out of a wetland is often described byDarcys Law (Mitsch and Gosselink, 2000). It states that the flow of groundwateris proportional to (1) the slope of the hydraulic gradient and (2) the hydraulicconductivity, or permeability. For isotropic soil, Darcys Law is often given as(Mitsch and Gosselink, 2000):

G = kAxs (2.3)

where

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G = flow rate of groundwater (volume per unit time)k = hydraulic conductivity or permeabilityAx =groundwater cross-sectional area perpendicular to the direction of flows = hydraulic gradient (slope of water table or piezometric surface)

For anisotropic soil, considering groundwater movement in both horizontal andvertical directions, and differing k values in different directions, the flow rate ofgroundwater in x,y,z directions can be given as (Verruijt, 1970):

Gx = kxxAxsx + kxyAxsy + kxzAxsz

Gy = kyxAysx + kyyAysy + kyzAysz (2.4)

Gz = kzxAzsz + kzyAzsy + kzzAzsz

It can be proved that only when kxx = kyy = kzz = k, the cross-coefficients

kxy, kxz etc. are zero, Equation (2.4) thus can be written as:

Gx = kAxSx

Gy = kAySy (2.5)

Gz = kAzSz

The conductivity is a material constant. Its value depend on both the type ofsoil and the fluid percolating through it (Verruijt, 1970). For peat, the value of kin vertical direction is often between 109107. In general, the conductivity ofpeat decreases as the fiber content decreases through the process of decomposition.

2.4.6 Evapotranspiration

Evapotranspiration include water vaporises from water or soil in a wetland (evapo-ration) and moisture that passes through vascular plants to the atmosphere (tran-spiration) (Mitsch and Gosselink, 2000). The rate of evapotranspiration is pro-portional to the difference between the vapor pressure at the water surface (or atthe leaf surface) and the vapor pressure in the overlying air. This is described ina version of Daltons Law:

E = cf(u)(ew ea) (2.6)

whereE = rate of evaporationc = mass transfer coefficientf(u) =function of wind speed, uew = vapor pressure at surface, or saturation vapor pressure at wet surfaceea = vapor pressure in surrounding air

A large proportion of the water recharge which mires receive is subsequentlydischarged by evaporation (Ingram, 1983). The magnitude of evapotranspiration iscontrolled mainly by three factors, namely the energy available, the sink strength

and the water supply. The energy is represented as the net radiation, or radiationplus; the sink strength is the ability of the atmosphere to take up the evaporatedmoisture.

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Evapotranspiration rate may have relationship with weather conditions. Ingrowth seasons evapotranspiration rate increases significantly. But the evapotran-spiration in non-growth seasons may also contribute a part of evapotranspirationof the year if the non-growth season is long (Lafleur et al., 2005).

Evaporation from a moss surface is primarily derived from a dense crown oflive material called the capitulum, where photosynthesis is also occurring. Onthe order of 12 cm thick, the capitulum is composed of small groups of branchessupporting arrays of tightly packed single-cell leaves and water-holding structurestermed hyaline cells. Although some vapour may diffuse from the dead and de-caying moss below, the tight packing and complete coverage determined that themajority of water must come from the capitulum (Lafleur et al., 2005). The Sphag-num-peat structure is able to conduct water upwards and support capitulum.

When the water supply is limited, the rate of transpiration can also be limited;transpiration can also be physiologically limited in plants through the closing ofleaf stomata during periods of stress (Mitsch and Gosselink, 2000).

The relationship between evapotranspiration, potential evapotranspiration andwater table will vary with vegetation type and density. Evapotranspiration at thebog is usually half of the potential evapotranspiration.

2.5 Blanket bog forming and erosion

2.5.1 Peat formation

Bogs are acid peat deposits with no significant inflow or outflow of surface wateror groundwater, and support acidophilic vegetation, particularly mosses (Mitschand Gosselink, 2000).

Two primary processes necessary for peatland development are a positive waterbalance and peat accumulation (Mitsch and Gosselink, 2000). For peat to accu-mulate, the precipitation must exceed evapotranspiration. The even distributionof precipitation across seasons and excess water is important because peatlandsrequire a constantly humid environment. Besides, the slope should not be exces-sive. The limit most intensively quoted is 15, but it is possible for thin peat toform, despite solifluction, on slopes up to 45 (Ingram, 1967).

Peat growth is initiated within the retention volume of water (Moore andBellamy, 1974). Peat grows to a point at which the surface of the peat reachesthe level at which water drains from the reservoir. Beyond this point the peat nolonger acts as an inert mass but as an active reservoir which holds a volume ofwater against drainage, which is the case of blanket bog.

Early peat development in Britain began after the retreat of glaciers, whichleft a number of small concave areas. Some of these basins became lakes. Peatdevelopment is initiated around the edges of the basin, the mire gradually growinwards filling the basin (Moore and Bellamy, 1974). Peat-forming vegetation mayovergrowth and form blanket bogs or raised bogs.

Given suitable water surplus and peat accumulation, bogs can develop throughpaludification, which means the blanketing of terrestrial ecosystems by overgrowthof peatland vegetation.

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2.5.2 Blanket bog erosion

Blanket mire erosion is widespread in the U.K. (Mackay and Tallis, 1996). Erosionposes a direct threat to blanket bog habitats. It may also have indirect butimportant implications for global climate change through the general lowering of

watertables. But the cause of peat erosion is still controversial. Some studiessuggest that erosion is a long-standing feature of many blanket peat systems.

Bradshaw and McGee (1988) argues that recent human activities may acceler-ated peat erosion, but the removal of peat may have begun when a critical depth orcombination of peat types become unstable on sloping ground. Drainage by sub-peat pipe systems may have created the de-vegetated peat surfaces that becamefoci for subsequent erosion.

Erosion deprive peat soil of organic ingredients, thus hinder establishment ofvegetation (Holden, Bosanko and Gascoign, 2005). This leads to further drainageand erosion.

2.6 Recovery work in Dark Peak

All blanket bogs in the Peak District area are now protected in four SSSIs. Bleak-low area is contained in Dark Peak SSSI. All the areas of blanket bogs in the fourSSSIs are included within the Southern Pennine Moorland candidate Special Areaof Conservation (SAC) (Peak District National Park Authority, 2000).

The SAC status is given when the site is considered as of international im-portance for its habitats and species in meeting with European Unions HabitatDirective (Peak District National Park Authority, 2004b).

Over recent years land managers in this area have proposed various recoveryinitiatives. These projects have began to show the way to landscape scale recoveryof heather moorland and may be used in future to inform recovery of blanket bogs(Peak District National Park Authority, 2000).

A partnership of conservation and land-owning organisations, Moors for theFuture, has set up a project aiming to restore 3km2 of worst eroded moorlandand blanket bog, and 19km2 of badly eroded paths (Peak District National ParkAuthority, 2000). The restoration of peatlands mainly focus on fire-disturbedsites around Bleaklow Head. This is carried out by planting nurse crop such asgrasses and heather which will stabilise peat and give natural vegetation time

to regenerate. In order to support nurse grasses in acidic condition, lime andfertiliser are used to improve suitability for grass seeds (Moors for the FuturePartnership, n.d.).

Gully blocking technique was also used to raise watertable and reduce peat dis-charge. The Partnership has worked with National Trust and NERC to determinethe proper location and design of the gully blocks.

2.7 Hydrological modelling

The basic principles governing fluid flow are derived from principles of conservationof mass and momentum. But the equations utilising these principles in numericalmodels are complicated by Reynold-average, which introduce additional terms

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but no corresponding equations. These terms must be determined by empiricalor semi-empirical formulas and they determine whether the model is a turbulentmodel or a steady flow model (Lane, 1998).

Among the models, some are based on empirical equations and some other arebased on physical theories. The simple models are sometimes unable to give de-tailed results, while the computation-extensive models based on physical theoriesare not able to give results for a larger scale due to limitation of computing capa-bilities. Therefore it is necessary to find a suitable model for a specified applicationand scale (Borah and Bera, 2003).

When applying hydrological models it is important to realise that it is impossi-ble to collect enough detailed data for the whole study area. The non-linearity andthe heterogeneity of the system hamper the validation of the model in traditionalsense (Cooley, 2004). It was argued that validation of such models is impossible,and hydrological models should only serve as a decision-making tool instead of anend result (Hassan, 2006).

2.7.1 MODFLOW

MODFLOW is a finite differential hydrology model developed by U. S. GeologicalSurvey. The model use cells as the basic computation unit to simulate soil, flowchannels, and reservoirs. The model support not only simulation of horizontalwater flow but also that of vertical flows. The model provides a comprehensiveapproach to groundwater modelling and is widely used by researchers around theworld.

MODFLOW is designed to simulate aquifer systems in which (1) saturated-flow conditions exist, (2) Darcys Law applies, (3) the density of groundwater isconstant, and (4) the principal directions of horizontal hydraulic conductivity ortransmissivity do not vary within the system (U. S. Geological Survey, 2005).

The model can simulate groundwater flows in a variety of temporal and spatialscales. Besides, it supports simulation of both steady-state and transient processes.The design of the model is based on a modular approach, thus the model can beextended and simulate hydraulic processes in different water bodies and soil types.

A number of peripheral programs have been developed for MODFLOW tosimplify the input of data and extraction of simulation results. Many of suchprograms are based on graphical user interface thus make parameterisation easier.

One of such front-end software is Processing MODFLOW, developed by Changand Kinzelbach (1998).

MODFLOW uses partial-differential equation to solve flow within and betweencells in x, y and z directions:

x(Kxx

h

x) +

y(Kyy

h

y) +

z(Kzz

h

z) + W = Ss

h

t(2.7)

where

Kxx, Kyy and Kzz are values of hydraulic conductivity along the x, y, and z

coordinate axes, which are assumed to be parallel to the major axes of hydraulicconductivity;

h is the potentiometric head;

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W is a volumetric flux per unit volume representing sources and/or sinks ofwater. Negative values denote flow out of the system;

Ss is the specific storage of the porous material; and

t is the time.On the other hand, the sum of inflow and outflow of cells must be equal,

thus meeting the law of conservation of mass. For every iteration, MODFLOWcalculates the inflow and outflow, then determine whether the error is smaller thanpredetermined criteria and whether the inflow and outflow are equal. However, ina short-term transient simulation the inflow and outflow are often not equal thusnot examined.

2.8 Population modelling

Ecological models are considered as an effective approach to simplify and describe

complicated ecological system processes. By using ecological models people cansimulate dynamics in ecological systems and explore relationships between com-ponents of the system.

Ecological models fall into two broad domains: analytical models and simu-lation models (Wainwright and Mulligan, 2004a). Analytical models tend to beabstract and not concerned with the dynamics of a particular ecosystem. Simu-lation models tend to incorporate more biological detail, including nonlinearities,are usually more system-specific, and are also more constrained to the real regionof parameter space.

2.8.1 Trends in development

Three trends can be identified in the development of ecological modelling. Theyare stochastic modelling, spatial integration and individual-based modelling.

Traditional ecological models are deterministic. They use mathematical equa-tions to describe ecological processes. However, no ecological system is purelydeterministic. Apparently random dynamics, know as chaos, can be produced un-der strictly deterministic conditions (Gillman and Hails, 1997). Stochastic events,which may have strong effects on the dynamics are dominating in every kind ofsystems. Thus simulation of stochastic events is more and more incorporated in

ecosystem modelling.However, a completely stochastic model is not practical. This is because of

the complexity brought along by stochastic processes. Besides, some stochasticevents cannot be predict in short time period or small areas, but demonstratetrends that can be predicted in long-term or large scale observations (Gillman andHails, 1997).

Ecological models are transforming from simple numerical simulation of sys-tems towards simulation of spatial processes. The development of spatial explicitmodel has two main drivers. The first is the development of computer softwaresuch as GIS and increasing capacity of data handling; the second is that incorpo-

ration of spatial processes has revealed and continues to reveal results on stabilityand dynamics that were unpredicted from local population models (Gillman andHails, 1997). Spatial explicit models give ecologists a technique for studying eco-

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logical processes that operate over various scales and for estimating the possibleresponses of organisms to these processes (Dunning, Jr. et al., 1995).

Spatial explicit models can also provide land managers with a method of ex-amining possible responses of species of management interest to changes of man-agement strategies and measures. Comparison of model results with the results of

field implementation of management actions can be an important part of adaptivemanagement (Dunning, Jr. et al., 1995).

The third trend, from simulation of population as a whole to simulation of indi-viduals, is tightly linked with integration of spatial factors in models. Individual-based models are a reductionist approach to ecological problems. Compared toholistic approaches, individual-based models has two supporting arguments: a.individuals are better defined than population or community; b. individualshave unique characters which cannot be reflected in generic population models(DeAngelis and Gross, 1992).

Individual-based models also faces difficulties: they estimate resource parti-

tioning for a certain level of group, which may not always produce satisfactoryresults; such models often lack mathematical tools to give analytical solutions.

Besides, individual-based models are considered as hard to develop, hard tocommunicate and hard to understand (Grimm et al., 1999). Complex modelsare prone to bugs due to modellers and ecologists limited expertise in softwareengineering. The description of the model is often the program itself. Documentsof models are often limited to a list of mathematical functions and rules used inthe model, in addition to verbal meta-descriptions in journals. Thus test of themodels can only be done by re-implementing the model, which is not feasible inmost cases. The understanding of the model also faces problem brought by limited

and vague documentation. The analysis of simulation results, which is influencedby the parameters and may reveal ecological mechanisms under the model, is oftennot carefully carried out. Instead, most work is devoted to development of models.Thus, to remove unnecessary complexity from individual-based models would beextremely beneficial.

2.8.2 Cellular Automata models and CAPS

Self-organisation is considered as universally existing in biological systems, suchas population dynamics and ecology (Wainwright and Mulligan, 2004b).

Cellular automaton (CA) model is the main tool for modelling self-organizationin spatial systems. The basic idea behind such models is that responses which areboth complex and highly structured may result from relatively simple actions(but very many of them) between components of a system. Interactions betweensuch components are governed by local rules, but the whole-system response isto manifest some higher-level emergent organisation, following the formation ofordered structures within the system. The system thus moves from a more uniformstate to a less uniform but more structured state: this is so called symmetry-breaking (Wainwright and Mulligan, 2004b).

CA models discretise continuous space into a series of cells. This is necessary

for the model to be computationally tractable. The rules and relations are thenapplied to these cells at the individual scale. These rules and relationships maybe viewed as feedbacks. Interactions are usually between adjacent or nearby cells,

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thus the models interactions are usually local. The rules for interactions in simpleCA models are often deterministic, but not necessarily so in more complicatedmodels as stochastic factors can be introduced using random numbers.

The reductionist approach of CA models may impede full understanding of thesystem studied. Even if more holistic approaches are employed, the imposition

of an artificial boundary between components of the system will constrain theinteractions between components in the region of the boundary, with potentiallystrong effects on responses of the system. Thus we must accept that even the bestpossible model of a self-organising system remains incomplete (Wainwright andMulligan, 2004b).

CAPS is a spatial-explicit, individual-based and stochastic model based onCellular Automata model. CAPS includes habitat patchiness but does not explorethe role of different ecological factors, both biotic and abiotic, such as spatialheterogeneity in habitat, connectivity among patches regulating dispersal, anddemographic variability among populations (Singh et al., 2004). It can model

large-scale spatial changes and the structure is especially suitable for modellingsessile organisms (Plotnick and Gardner, 2002).

CAPS uses a number of rules to simulate physical and biological interactionsbetween species and the environment. These rules include those of traditionalCA models, percolation and kinetic growth models, and the effects of speciescompetition simulated by a seed lottery (Plotnick and Gardner, 2002). The modelis very flexible in that it can simulate on both random maps or actual landscapemaps, and simulate a variety of species and disturbance.

2.8.3 GAM and GRASP

A series of statistical models are also widely used in ecological modelling. Thesestatistical models need three components to work properly and produce reliableresults: an ecological model concerning the ecological theory to be used or tested,a data model concerning the collection and measurement of the data, and a statis-tical model concerning the theory and methods to be used (Austin, 2002). How-ever, compared to mechanistic models, statistical models require less variables anddata (Lehmann et al., 2002). A number of statistical models are based on pres-ence/absence data, thus gives information about realised niche but can say verylittle about fundamental niche.

GRASP is an implementation of statistical model using R environment (RDevelopment Core Team, 2006). GRASP is based on regression analysis. It stan-dardises the modeling process and makes it more reproducible and less subjec-tive, while preserving analytical flexibility. The current version uses generalisedadditive models (GAMs), a modern non-parametric regression technique (Fivazet al., 2004).

GAMs are non-parametric extension of GLMs, which are themselves a general-isation of classical least square regression (Lehmann et al., 2002). GAMs estimateresponse curves with a non-parametric smoothing function instead of paramet-ric terms. The only assumption in GAM is that the functions are additive and

that the components are smooth. The strength of GAMs is that they can dealwith non-linear and non-monotonic relationships between the response and the setof explanatory variables. GAMs are sometimes referred to as data- rather than

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model-driven, because the data determine the nature of the relationship betweenthe response and the set of explanatory variables rather than assuming from theparametric relationship (Guisan et al., 2002).

GAMs model realised niche rather than fundamental model due to its empiricalnature (Guisan et al., 2002). Thus they implicitly incorporate biotic interactions

and negative stochastic effects that can change from one area to another, andmake predictions across many locations difficult.

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Chapter 3

Methodology

3.1 Data source

In order to model the hydrology conditions, local climate data, especially precip-itation data, and digital elevation model with two-metre resolution are obtainedfrom Peak District National Park Authority and Moors for the Future Partnership,respectively.

In order to find Sphagnum patch locations and make field survey plan, Envi-ronmentally Sensitive Area vegetation map in MapInfo vector format are obtainedfrom Defra Rural Development Service through Moors for the Future Partnership.In order to validate the model, vegetation map drawn by Moss (1913) has alreadybeen copied with the permission from Peak District National Park Authority.

UK Perspective aerial photographs using both normal film and color infrared

(CIR) film are obtained from Moors for the Future Partnership. These pho-tographs can help identify small patches of Sphagnums. The coverage is fromGrid SK0591 to SK1499. The images are stored in compressed ECW format andcan be imported in ERDAS Imagine. The spatial resolution of the image is 0.25metre and each scene is one square kilometre. Thus the size of each file is 4000 4000 pixels. The true color images are all named as SKxxxx.ecw under a workdirectory called 2005-RGB where xxxx denotes the coordinate of the scene inNational Grid system. The CIR images are stored in another directory called2005-CIR.

Holden, Hobson, Irvine, Maxfield, James and Brookes (2005) have identified

gullies on the Bleaklow plateau. The results are provided together with DEM andLidar image by the Moors for the Future Partnership.

Fire disturbance data are also available from Moors for the Future Partner-ship. The data is given as ArcGIS shape file with a database containing timeinformation.

3.2 Classification of remote sensing images

3.2.1 Preparation of remote sensing images

The aerial photographs include true color images taken in visible spectrum andcolour infrared spectrum. Each image contains three bands. For true color images

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Figure 3.1: Supervised classification of SK0796 scene with Sphagnum patchesshown as orange

Band 1, 2 and 3 are blue, green and red channel, respectively. For infrared imagesBand 1 is near infrared, while Band 2 and 3 are green and blue channel.

The images have already been geometrically corrected, rectified and registeredto National Grid Coordinate system.

Both infrared and visible spectrum images are used to classify Sphagnumpatches. In order to combine information from both images, the infrared layer(Band 1) of the colour infrared images and all three layers of the true colour im-ages are composed into a new image using Layer Stack function of ERDAS Imagine8.7, with Layer 4 being the infrared channel. The images generated are all namedas skxxxx_ir_vis.img and stored in another directory named 2005_ir+vis.

In order to increase the contrast between different landcover and vegetationtypes, decorrelation stretch was done to the images being classified. This operationstretches the principle components of the image and equalise the variances, andproduce bands which are linear combination of the original bands (Campbell,1996). The new bands are uncorrelated and have unit variances. The tassel captransformation produces similar results.

3.2.2 Supervised classification

Using Sphagnum patches location information collected in March, it was foundthat Sphagnum patches in grid SK0796 has significantly higher reflectance in in-frared band than heather but lower reflectance in green and blue channel thanCottongrasses.

Thus the possible spectral signature of Sphagnums can be developed usingthe values of the known pixels. The ESA vegetation map was also used to helpidentifying land cover types including cottongrass-dominant heatherland, eroding

peatland and bare peat.The classified image is shown in Figure 3.1. The orange pixels denotes Sphag-num patches.

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In the preliminary field survey more Sphagnum patches were recorded. Com-paring the locations of the patches and the corresponding pixel on the aerial pho-tographs, the spectral signature of Sphagnum is improved. This is done by usingSignature Editor of ERDAS Imagine. The Sphagnum patches were located on theimage. An area of interest can be created around the pixel denoting Sphagnum

patches. The values of these pixels can then be imported into the signature editor.For each patch identified a signature was created. However, due to the error ofpositioning device, the pixels located do not always present typical reflectance ofSphagnums. Signatures derived from these pixels were removed. Twenty-threeeffective signatures were identified and saved in a file. Their reflectance values ininfrared, green and blue channels were then imported into SPSS 12 for a hierar-chical clustering operation. Signatures belonging to the same cluster were mergedin signature editor. By this method five typical spectral signatures were identifiedand used in supervised classification of Sphagnum patches.

3.2.3 Unsupervised classification

Unsupervised classification was attempted using the combined image of sceneSK0796, whose file name is sk0796_ir_vis.img. The number of classes was set as 5and clustering options was to initialize from statistics. The convergence thresholdis using default value 0.950.

The images after decorrelation stretch were also classified into 5 classes afterthe field survey.

3.3 Preliminary field survey

Using Sphagnum patch locations collected in March and UK Perspective aerialphotographs provided by Moors for the Future Partnership, a possible spectralsignature of Sphagnum patches was derived and used in classification of aerialphotographs over the Bleaklow area.

Some ground truth must be obtained to verify the consistency between classi-fication results and actual distribution of Sphagnum. It is also possible to recordmore Sphagnum patch locations which can be used in interpretation of aerial pho-tographs and improve the quality of the spectral signature.

3.3.1 Work area

The work area in this field survey is the area in Peak District National Parkto the north of A50 Snake Road and south of B6105 near Crowden. Due toaccessibility consideration, work was carried out near the Pennine Way in gridsSK0697, SK0796, SK0896, SK09930996, covering an area of 7 square kilometres.

3.3.2 Selecting survey points

The classification results of aerial photographs of the work area serve as the base

of survey points selection. Using subset function of ERDAS Imagine software,possible locations of Sphagnum patches can be extracted and projected on thearea map.

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The number of survey points in each grid cell was determined by the propor-tion of predicted Sphagnum patch area in the 1 square kilometre cell followingprobabilities proportional to the sizes (pps) sampling rule (Barnett, 1991).

To make true random sampling, the XY coordinate pair of each point on theimage should be stored in a table and given numbers so sampling using random

number is possible. However, pixels classified as Sphagnum patches may reach 105

or 106 in each scene, and it may take a few days for ArcGIS to assign coordinateinformation to each point and generate the table. Thus a quota sampling techniquewas employed instead. Ten thousand random XY coordinate pairs were generatedusing GNU Octave software and stored in a 2 10000 matrix. Another randomnumber denoting the column number was used to pick a coordinate pair fromthe matrix. The corresponding point will be located on the image. If the point ison predicted Sphagnum patch, then it is recorded. Then another coordinate paircan be picked. This process was repeated until survey points required in a sceneare all selected. In order to ensure the coordinate pairs are random, for each scene

a new coordinate pair matrix is generated.The coordinates of all survey points were inputed into a GPS handset using

UK National Grid system. Each point was labelled as P-xyy, where x from 1 to 7stands for the scene, and yy stands for the identification number of points.

3.3.3 Field activities

The area of survey are all near Pennine Way thus allowing quick moving by foot.The survey was done one scene by another. After reaching the southern boundaryof a scene, the most southern point is sought using GPS navigation function, then

the next point to its north is sought, until all points in the scene are surveyed andrecorded.On each survey point the vegetation type was recorded on a form and digital

photographs were taken. Whether Sphagnum presents was also recorded. The in-formation can be used to compare with remote sensing images and ESA vegetationmap.

When moving from one point to the next some Sphagnum patches may beencountered and were also recorded using GPS.

3.4 Hydrology modelling

The surface and subsurface water flows of the study area were simulated usingMODFLOW-96 (Harbaugh and McDonald, 1996), with Processing MODFLOWV5.3 (Chang and Kinzelbach, 1998) being its graphical frontend and data in-put/output interface.

3.4.1 Processing digital elevation model data

The Digital Elevation Model (DEM) of the study area was derived from Lidarimage of the area collected on December 2002 and May 2004 and provided by

Environmental Agency. The DEM has been rectified and some missing data pointshave been interpolated (Holden, Hobson, Irvine, Maxfield, James and Brookes,2005).

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The DEM was used to obtain elevation information for each cell in the modeland to identify gullies in the area, as well as determining water heads in and aroundthe study area. Because the grain of the DEM data is relatively small compared tothe proposed cell size, some generalisation is required before applying the data. Inorder to obtain the mean elevation for each 100 100 m2 cell, the generalization

function of ArcGIS was used.The generalised DEM and the gully order and distribution data were then

exported to ASCII text file. Necessary editing was carried out to ensure the filecan be imported to Processing MODFLOW.

3.4.2 Model parameterisation

Spatial and temporal discretization

The study area was divided into cells of 100 100 metres dimension. The cells

out of the study area were defined as having constant head. Using a layer schemesimilar to (Reeve et al., 2000), the area was vertically divided into 11 layers.The first layer was 0.5 metre thick and represented the acrotelm (Ingram, 1983);the following 5 layers, each also has a thickness of 0.5 metre, represented thecatotelm; the rest 5 layers each has a thickness of 0.5, 0.875, 1.53, 2.68, 4.69metres, representing the mineral soil.

All layers were defined as convertible between unconfined/confined conditions.The transmissivity was allowed to vary with the saturated thickness of the layerduring simulation. This is denoted by Type 3 in Processing MODFLOW (Changand Kinzelbach, 1998). All transmissivity values and leakances were calculated by

the model.The fundamental component of time discretization was the time step (Harbaugh

et al., 2000). Time steps were grouped into stress periods. The transient stresswas constant within a stress period and can be changed at the beginning of eachstress period. The time unit in this simulation is day. Each stress period is 1 dayand contain 24 time steps. 15 periods were set active.

The initial hydraulic heads is defined as of equal height to the surface of thearea.

The boundary condition of the model was set as follows: all cells within thesimulated area were defined as active cells. Cells out of the modelled area boundary

were defined as inactive cells, with no flow occurring in them. The eleventh layerof the model was defined as constant-head cells, thus the layer became a sink ofwater from above layers.

The initial head in steady-state simulation was set as equal to the top elevationof the corresponding layer. In order to meet the demand of data correctness checkof PMWIN, a small value was given to inactive cells outside the modelled area.

Soil parameterisation

Combining the results of past measurement and estimation of hydraulic conduc-

tivity in the peatlands (Reeve et al., 2000; Romanov, 1968; Ingram, 1983) the k inthis simulation was set as 104 for the acrotelm, 106 for the catotelm and 107

for the rest layers.

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Similarly, the vertical hydraulic conductivity was set as 104 for the acrotelm,107 for the catotelm and 109 for the mineral soil.

The porosity was set following Ingram (1983). Layer 1 was set as 50%, otherlayers 10%.

The specific yield was reported as 0.048 for cutover peat by Schlotzhauer and

Price (1999). However, Letts et al. (2000) reported that the specific yield for peatin upper, middle and lower layers were 0.66, 0.26 and 0.13, respectively. On theother hand, it was reported that removal of acrotelm reduced specific yield from0.6 to 0.2. Thus in this simulation the specific yield is set as 0.6 for layer 1, 0.2for layer 26 and 0.1 for other layers.

Drain package

The drain package is used to simulate water loss through drainage channels. Thusit can be used to simulate drainage through gullies and surface runoff.

When the hydraulic head h in a drain-cell is greater than the drain elevation,water flows into the drain and is removed from the groundwater model. Dis-charge is zero when the hydraulic head is lower than or equal to the median drainelevation. Recharge from the drain is always zero.

The package is defined by three values:

Drain hydraulic conductance (Cd) [L2/T], which is often given by Cd =K L. Where L is the length of the drain within a cell, i.e. the distancefrom the head to the lower bound of drain elevation.

Elevation of the Drain (d) [L] and

Parameter Number [-]

Cd is calculated byCd = K L (3.1)

The mean drain hydraulic conductance in this area is set to 0.1 m2 day1.This is done by calculation using Equation 3.1 and taking streams and gullies inthis area into account.

Evapotranspiration package

The package simulates evaporation and transpiration of plants and surfaces insaturated groundwater scheme. It simulates water removal when meeting theseassumptions:

The water table is above or equal to the elevation of the evapotranspiration(ET) surface hs. ET loss from the water table is at the maximum ET rateRETM.

No ET occurs when the water table below the ET surface exceeds the ETextinction depth d. and

In between these two extremes ET varies linearly with the water table ele-vation.

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These assumptions can be expressed as:

RET = RET M h > hs (3.2)

RET = 0 h < hs d (3.3)

RET = RETM[h (hs d)]/d (hs d) h hs (3.4)

where RET is the rate of ET.In Processing MODFLOW, the user need to input for every active cell these

values: the maximum ET rate RETM, the evaluation of ET surface hs and theET extinction depth d. This is done by using Processing MODFLOWs matrixeditor and importing data files. The hs value is set equal to the elevation of thelayer top. The maximum ET rate is set as 0.0025 m day1. The d is set to 0.5metres. The ET elevation is set equal to the land surface. ET is set as onlyoccurring on the surface layer.

Recharge package

The recharge package is designed to simulate areally distributed recharge. Here itis used to simulate precipitation recharge to the groundwater.

Ingram (1983) pointed out that recharge to mires can have two sources: themeteoric supply P derived from the atmosphere and the telluric supply N derivedfrom surrounding rocks and soils. But most bogs are recharged mainly by mete-oric water and their surface vegetation is largely isolated from telluric influence(Ingram, 1983). The website (Peak District National Park Authority, n.d.) in-dicates that the average rainfall in the study area is about 1000 mm per year.The observation in Peakshole Water gives total rainfall in 2005 of about 970 cm(Peak District Caving, n.d.). Thus 1000 mm per year was used as the rechargeflux across the whole area. This value was assigned to all the layers and all activecells in the model.

In MODFLOW the user can choose whether the recharge is applied to the toplayer only or applied to the highest active cell. In this simulation the latter optionwas chosen because it is more close to the reality and the simulation can convergewith less iterations.

General head boundary package

The General Head Boundary is used to simulate a boundary of the modelledarea where the inflow or outflow occurs. The water head in these areas is oftendetermined using data of neighbouring cells.

The in- or outflow of the element is determined by the difference between thehead in the element and an external fixed head (Don et al., 2005). The conductanceof the boundary is determined using the following equation (Wishart, 2000):

Cb =KbMW

L(3.5)

where

Kb is the conductivity of the general-head boundary cells; M is thethickness of each layer; W is the width of each general-head boundary sourcecells; L is the length of each general-head boundary source cells.

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the values of Kb, M, W and L are directly available from the discretizationand hydraulic conductivity data.

The general head boundary in this simulation was set at the outermost part ofthe simulated area to model in- and outflow between modelled area and outsideareas. The boundary has a thickness of one cell in the plan view of the model andis placed in all layers except layer 11.

Specific storage

Specific storage and specific yield is required by MODFLOW in transient simu-lations to calculate storage terms. Specific storage is used to calculate confinedstorage coefficient in a confined layer, which is a function of compressibility of thewater and the elastic property of the soil matrix. Following Kellner and Halldins(2002) observation the specific storage in this simulation was set as 5 102 m1

for layer 16 and 1 104

m1

for layer 711.

Specific yields

Specific yields is defined as the volume of water that an unconfined aquifer releasesfrom storage per unit surface area of aquifer per unit decline in the water table.It is a function of porosity.

The specific yield is reported as 0.048 for cutover peat by Schlotzhauer andPrice (1999). However, Letts et al. (2000) reported that the specific yield for peatin upper, middle and lower layers are 0.66, 0.26 and 0.13, respectively. On the

other hand, it was reported that removal of acrotelm reduced specific yield from0.6 to 0.2. Thus in this simulation the specific yield is set as 0.6 for layer 1, 0.2for layer 26 and 0.1 for other layers.

3.4.3 Model calibration

The calibration of the model was done by using inverse models to find a parameterset for which the sum of squared deviations between model-calculated and mea-surement values at the observation boreholes is reduced to a minimum (Chang

and Kinzelbach, 1998).Eight observation boreholes were set in the model. The observations take placethroughout the whole simulated time span. The observed values were then usedin UCODE inverse model to determine optimised parameter.

UCODE uses non-linear regression to perform inverse modelling which is posedas a parameter-estimation problem. The non-linear regression is solved by min-imising a weighted least-squares objective function with respect to the parametervalues using a modified Gauss-Newton method (Poeter and Hill, 1998). The laststep of each parameter-estimation involves comparing two values against iterationcriteria: the variation of the parameter values and change in the sum-of-square-weighted residuals.

When parameter estimation converges or the maximum number of iterationshas been reached, sensitivities are calculated using central-difference method.

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3.4.4 Model simplification

After the simulation result is examined, it was found that water flow in the thirdlayer and below have no effect on the watertable, which is not in agreement withpeatland hydrology theories. Thus the model was simplified by reducing the num-ber of layers. The first five layers in the original model, which denote acrotelmand catotelm, are combined into one layer representing peat soil. Layers 6 to 10 inthe original model were combined into the second layer representing mineral soil.The third layer was defined as with constant head, which can receive water flowfrom above layers.

The first layer was set as unconfined, the second and third layers as uncon-fined/unconfined convertible. The transmissivity and specific storage were auto-matically calculated by the model.

The other parameters were copied from the original model.

3.5 Field survey

Two field surveys were conducted during 29th June to 1st July and 17th July to18th July respectively in Peak District. The purpose of the first survey was tofind whether classification of aerial photographs correctly reveals the location ofSphagnum patches. If the result is not satisfying, Sphagnum patches identified inthis survey can still be used in modelling and prediction. The second survey was

carried out to verify the relationship between groundwater depth and presence ofSphagnum.

In the first survey, the classification results for grid SK0796, SK0894, SK0895,SK0896, SK0993, SK0994, SK0995, SK0996, SK1094, and SK1095 were used to-gether with ESA vegetation map to choose verification points. Points with twotypes of signatures were chosen because these two signatures have better agree-ment with actual Sphagnum patches recorded. The verification points were chosenfor each vegetation type with pixels classified as Sphagnum in a scene of aerial pho-tograph. The route of survey was planned after the points are determined in orderto make the distance of walking shorter.

In the second survey, six grids were chosen: SK0796, SK0896, SK0996, SK0894,SK0994 and SK1094. For each grid, five verification points were chosen accordingto remote sensing results and groundwater model. All five points were classifiedas possible Sphagnum patches by unsupervised classification. Three of them havewaterhead drawdowns less than 2 metres in the hydrology simulation and areconsidered as having favourable condition; the other two have drawdowns morethan 2 metres.

The activities in the field is similar to preliminary field survey. A GPS handsetis used for navigation to the verification points. After arriving at the point, in

order to reduce the influence of positioning error, a round area with the point asthe center and 10-metre radius was searched. If Sphagnum patches were found inthis area, the point is recorded as having Sphagnum presence.

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3.6 Presence prediction

3.6.1 Presence in present day

After the relationship between spectral signatures, waterhead drawdown and Sphag-

num presence is proved by field verification, the present-day Sphagnum locationscan be derived from unsupervised classification of aerial photographs and hydrol-ogy model simulation by aggregating them in GIS software. Three maps with dif-ferent levels of spatial coverage were made: Level 1 contains grid SK0894, SK0994and SK1094, where Sphagnum locations have best conformity with waterheaddrawdown simulation; Level 2 contains grid SK0796, SK0894, SK0895, SK0896,SK0993, SK0994, SK0995, SK0996, SK1094, SK1095, and SK1096, which are vis-ited during the field verification; Level 3 contains all grids in the dataset provided,covering area from grid SK0791 to grid SK1499.

Sphagnum patches located in areas with favourable hydrology conditions are

identified using PICK function in ArcGIS software. The pixels identified by PICKfunction were then examined by comparing them with remote sensing images, onwhich vegetation types can be identified.

3.6.2 Model prediction of presence

Prediction using GRASP and scoring habitat

To model propagation ofSphagnum, the habitat suitability needs to be scored andspatial-explicitly described. Factors used to describe habitat suitability for Sphag-num include groundwater drawdown, elevation, slope, aspect and vegetations in

the vicinity, because of Sphagnum ecology mentioned in Section 2.2. These datawere imported into ArcGIS and processed to produce a single data file containinglocations and variables. The data file is purely ASCII file thus can be read bymany statistical and GIS software packages with only minimum editing.

In the field survey a number of data points with Sphagnum presence were ob-tained. However, the absence data were not reliable due to limited survey coverageand effort restrained by time allowed. Thus the prediction used only presence data.The absence data points needed by the GRASP model were randomly generated.The presence and pseudo-absence data together can generate prediction resultsbetter than the combination of presence and biased absence data does (Zaniewski

et al., 2002).The data is first imported into R statistical environment (R Development Core

Team, 2006). A package developed for R called GRASP-R was used to find how thefactors influence Sphagnum presence. This involves creating a matrix describingthe location of Sphagnum presence and absence, and another matrix describingenvironmental conditions at the corresponding location. Then GRASP-R usesGeneralised Additive Model (GAM) method to determine the relationship betweenenvironment and species (Hastie and Tibshirani, 1990; Wood and Augustin, 2002).The degree of freedom for the smoother was chosen automatically by the model.The choice of degree of freedom can provide good regression results, while was not

leading to overfit. The model is then examined using ANOVA and Wald method(Wood, 2004). They test if each parametric or smooth term is significant. A mapof predicted Sphagnum presence based on statistical characters of the significant

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variables can then be produced. The prediction can be based on different sets ofparameter values, and scenario simulation is possible.

Then the variables considered as significant in this step are imported intoSPSS 14 for cluster analysis. Because the dataset is very large, hierarchical clusteranalysis cannot produce any result within acceptable time. Thus Two Step cluster

method is employed. This method can handle both continuous and categoricalvariables. In the first step, the data are pre-clustered into many sub-clusters.Then these sub-clusters are clustered into the desired number of clusters (SPSSInc, 2006). SPSS gives mean values with error bar of variables for each cluster, thusa rank can be determined for each cluster using known knowledge of Sphagnumecology. Then all ranks of variables for a cluster were aggregated using weightedmean value to obtain an overall rank for this cluster. The weight of variables wasdetermined by its contribution to explanation of GAM model deviances.

Preparation of habitat map

The result of cluster analysis was edited and imported into ArcGIS to obtain thespatial distribution of each cluster. Then by editing the values of each cell in theraster map, the habitat suitability score can be attached to the map. This becamethe base of habitat map required by CAPS model.

Parameterisation of CAPS

CAPS can run interactively through a command window, but in most instances itreads a few files which contains the parameter and data needed. In this study thelatter approach is used. The files include one giving overall parameters, one mapfile which is an ArcGIS ASCII grid file without file head, and one file describingthe dispersal pattern of the species. The parameter file and the dispersal file arein Appendix C. The meaning of the flags in these files are explained in (Plotnickand Gardner, 2002).

The disturbance type can be chosen from five types, denoted by letters f, s, r, w,and b respectively. In this simulation type w is chosen, which means disturbancerandom in time and extent (Plotnick and Gardner, 2002), to simulate bog fires.The maximum disturbance length is 0.1 year and the fraction of disturbance in ayear is 0.15. The spatial distribution of disturbance was set to random.

The initial condition was set as placing patches close to the boundary first to

simulate immigrants from outside. The boundary of the simulated area was set asabsorbing, i.e. propagation towards outside the boundary was not counted. Theinverse abundant exponent was set to 0.5, which determines the off-site abundancewhen generating initial species distribution. The distance immigration parameterwas set to 0.8, which determine the longest range that off-site immigrants cantravel. The mortality adjust and extinction check was enabled.

One important aspect in simulation of Sphagnum propagation is the dispersalpattern. In this simulation the distribution of Sphagnum was considered as fol-lowing an inverse distance function, which describes the probability of presence asa function of the square root of the distance from the parental site:

d(r)sqd,j =r2i

i = 1Sr2i

(3.6)

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where d(r)sqd,j is the probability for species j; i is the index of the site; S is thetotal number of sites that the species can reach; r is the distance of the site fromthe parental site. When ri = 0, d(r)sqd,j is arbitrarily set to 1 to allow self-seeding(Plotnick and Gardner, 2002). The assumption of dispersal pattern is supportedby research conducted by Sundberg (2005).

It was reported that spores ofSphagnumcan travel over 60 kilometres (Sundberg,2005). However, considering the inverse distance function, most spores will fallto the ground within 1 kilometre from the parental site. Thus the maximum dis-persal range in CAPS was set as 10 cells. The fecundity parameter describes howmany propagules are produced by an individual. For Sphagnum species this valueis difficult to measure. It was set to 2 as a conservative estimation. The seed rainparameter was set to 0.001. This parameter is the ratio between the proportion ofarea receiving long distance propagules and the proportion of area occupied by thespecies. The disturbance threshold was set to 1.0, which means the disturbancewill lead to reduced propagule.

Two other species were simulated as competitors. Species As character waslike that of grasses or heaths. It can establish in all five habitat types defined inthe model; the maximum distance of dispersal was 3 and seed rain of long-rangedispersal was suppressed. Species B was used to simulate species that can befound in wet environments, such as fern. It has a maximum distance of dispersalof 3 and seed rain similar to that of Sphagnums; it can only establish in habitattype 2 and 5, which have the most favourable hydrology condition.

Prediction using CAPS

After the parameterisation file and habitat optima file are ready, CAPS can readthese files and do the simulation. The output is stored in a file whose name isspecified in the input files. A script was written to generate an ArcGIS ASCIIGRID file with file headers from the output of CAPS. The GRID file then canbe imported into GIS software packages to make a visual presentation of thesimulation result.

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Chapter 4

Result Analysis

4.1 Preliminary fieldwork

In total sixty-five points were scheduled to visit in the field survey. However, dueto access rights and topology problems, 10 points could not be approached thusno data were recorded at these points. The other points all have vegetation typesrecorded and most have corresponding photographs. A list of points visited canbe seen in Appendix A.

The record also includes locations of Sphagnum patches encountered duringfieldwork. The locations of Sphagnum presence are labelled on the aerial pho-tographs and stored as ERDAS Imagine Areas of Interest (.aoi) file. These loca-tions can help identifying spectral signatures.

It was found that in gullies where water supply is abundant, the Sphagnumis still dominating. Well-developed patches of Sphagnum can be found in gulliesmade by erosion in grid SK0993. In grid SK0697 and 0796, scattering Sphagnumpatches can also be found beneath grass layer on slopes which are close to the riverTorside Clough and not very steep. However, during the visit in early June, muchof the patches on the slopes appeared stressed, especially those on the south-facingslopes. A book by Institute of Terrestrial Ecology (1990) suggest that the patchesfound on slopes may be S. teres, and those in gullies in SK0993 may be in sectionCuspidata.

It was also noticed that in areas where no apparent surface water can be found,

the presence of Sphagnum patches is related to other vegetation patches. Usingdata collected from the 89 points, it was found that areas defined as occupiedby vegetation, include continuous bracken, Molinia dominated grass, dry dwarfshrub heath, cottongrass moorland, and dry bogs have 35 records of Sphagnumpresence and 29 absence; while areas defined as not occupied by other vegetation,including bare peat and eroding moorland, have 0 records of presence and 23absence. A 2 test gives 2 = 18.83, p = 0.000. However, due to the bias inselecting points, i.e. points not scheduled and has no Sphagnum presence arenot recorded, it is too hasty to assert that presence of other vegetation has anyrelationship with Sphagnum distribution. On the other hand, Sundberg and Rydin

(2002) suggest that Eriophorum vaginatum cottongrass is a keystone species forthe re-establishment of Sphagnum as it provides shade and prevents desiccation.Besides, it provides the necessary nutrients for establishment from spores.

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4.2 Classification of remote sensing images

4.2.1 Unsupervised classification

The classification of the combined image of SK0796_ir_vis.img is shown in Figure

4.1. The result shows relatively clear difference of land cover types. However,Sphagnum patches cannot be separated from other vegetation types. The classifiedimage shows that a large area is covered by Sphagnum, which is not in agree withfield observation. This is because both Sphagnum and Cottongrass Moorlandpatches reflect more infrared radiation and are classified as the same type.

Figure 4.1: The result of unsupervised classification of an aerial photographycovering grid SK0796, light pixels may denote Sphagnum

After decorrelation stretch, the classification result was improved. However,

many areas has virtually no Sphagnum cover are still classified as Sphagnumpatches. The result can be improved by cross examination with waterhead draw-down simulation from the MODFLOW model. Figure 4.2 shows Sphagnum pres-ence in areas surveyed. It can be seen that red points denoting Sphagnum presenceare mostly located in areas with drawdowns less than 2 metres. The agreementbetween ground truth and classification in low-drawdown areas can reach 61%, insome areas 100%.

4.2.2 Supervised classification

The first attempt to conduct supervised classification proved that it is difficultto find a uniform signature for Sphagnum patches across different scenes of aerialphotographs. However, in most scenes the class 3 (IR:G:B = 0.744:0.577:0.463)

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Figure 4.2: Distribution of waterhead drawdown and Sphagnum. The green cellsdenote drawdown < 2m; the pink cells denote drawdown > 2m; black pointsdenotes possible Sphagnum distribution according to unsupervised classification;red dots denotes Sphagnum patches identified in field survey.

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and class 4 (IR:G:B = 0.729:0.461:0.352) signatures apparently correspond wellwith known possible locations of Sphagnum patches.

On the other hand, all patches recorded in preliminary field survey are closeto class 3 and 4 pixels. The distance between recorded patches and pixels withclass 3 or 4 usually do not exceed 10 metres. However, many of the recordeddata points do not fall on pixels classified as Sphagnum, but many are classified asgrassland. The error of positioning device may lead to such result, but it is alsopossible that some Sphagnum patches in grassland cannot be identified and moreprecise signature sets are desirable.

The differences between scenes of aerial photographs made it difficult to gener-ate one signature set that can be applied to all photographs. Therefore the benefitof supervised classification, which is better agreement between ground truth andimages, is limited.

4.3 Hydrology simulation

Both steady-state and transient simulations were attempted. The steady-statesimulation shows an equilibrium condition of water storage across the area inconditions of normal evapotranspiration, drainage and recharge. The result is notinfluenced by the length of stress period or time step. It provides comparison oflong term water availability in undisturbed condition among cells with differenttopography and elevation. As Figure 4.3 shows, the highest part of the area is likelyto lose water to lower ground, thus become dry and inhabitable for Sphagnums.The lower areas have negative drawdown in steady-state simulation, which implies

that they can contribute to runoff and channel flow in long-term and are sources ofwater. However, it is worthy noticing that the model does not include interceptionof surface vegetation, nor tremendous water storage capacity of live Sphagnumpatches.

The transient simulation can help uncover water table changes and flux in ashort time and unequilibrium conditions such as in a precipitation process. Figure4.4 shows the watertable drawdown when the simulated time is 1, 5, 10, and 15days, respectively. It shows that watertables in steep slopes tend to drop muchrapidly than that in flat areas does. The elevation has influence on the extent ofdrawdown, but not as significant and obvious in the transient simulation. The

transient simulation reveals the influence of topography and neighbourhood cellsin acrotelm hydrology, which is of most importance in the ecology of Sphagnums.

In the transient simulation eight observation boreholes were set, which is de-noted by crosses (see Figure 4.4). The watertable drawdown in these boreholes areshown in Figure 4.5. It can be seen that the watertable in borehole 1 rises at first.The negative drawdown indicates a rise of water level. However, from the eleventhday the water table falls if the precipitation is maintained at the initial level. Atlast borehole 1 will become dry, as steady-state simulation shows in Figure 4.3.

The simplified model converges better than the original model. The discrep-ancy for short-term simulation is about 2 percent. But in long-term simulations

the discrepancy reduces significantly to about 0.2 percent. This may be due tothe imbalance caused by storage of water in the soil in short terms and transientconditions. In long-term simulation such imbalance is reduced (Ingram, 1983). Be-

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Figure 4.3: Simulated steady-state watertable drawdown distribution in bleaklow

(a) Day 1 (b) Day 5

(c) Day 10 (d) Day 15

Figure 4.4: Simulated transient watertable drawdown distribution in Bleaklow

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Figure 4.5: Drawdown curve in eight boreholes

cause the hydrology processes in peatlands are transient, the long-term transientsimulation can better simulate the actual conditions.

A simulation of 900 days with constant recharge and potential evapotranspi-ration is done using the simplified model. The result waterhead drawdown mapis shown in Figure 4.6. The waterhead drawdowns in 8 observation boreholes areshown in Figure 4.7.

Figure 4.6: Waterhead drawdown at the end of simulation

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Figure 4.7: Waterhead drawdown observed in 8 boreholes

4.4 Field survey

Eighty points were chosen for verification. One of them (V-0505) was not included

in the designed route thus data were not collected from this point. The other 79points all have photograph taken and vegetation type recorded. The data recordform is in Appendix B.

It is shown in the result that the two signatures have similar correctness whenpredicting Sphagnum presence. The first signature (Spha