Drainage ditch–aquifer interaction with special reference to surface water salinity in the Thurne...

Drainage ditch–aquifer interaction with special reference tosurface water salinity in the Thurne catchment, Norfolk, UK

Trevor Simpson�, Ian P. Holman & Ken Rushton, MCIWEM

Natural Resources Department, Cranfield University, Bedfordshire, UK

Keywords

ditch drains; drain coefficient; Norfolk Broads,

UK; numerical models; saline water.

Correspondence

Ken Rushton, Natural Resources Department,

Cranfield University, Bedfordshire MK43 0AL,

UK. Email: [email protected]

�Present address: Serco Technical Assurance,

Birchwood Park, Risley, Cheshire WA3 6GA,

UK.

doi:10.1111/j.1747-6593.2009.00195.x

Abstract

Open drainage ditches located in low permeability material can interact with an

underlying aquifer, especially if the drains almost or totally penetrate through

to the aquifer. This interaction can be represented by drain coefficients

incorporated in regional groundwater models. The drain coefficients depend

on both the vertical distance from the base of the drain to the aquifer and the

hydraulic conductivities of the low permeability deposits and the underlying

aquifer. In a case study of drained marshes in the Thurne catchment in Norfolk,

UK, drains with a water level below ordnance datum (OD) draw in saline water

from the coast and freshwater from recharge areas. Pathlines, derived from a

regional groundwater model analysis, explain the salinities measured in drains.

In addition a series of vertical section numerical model solutions are used to

develop general guidance on the selection of drain coefficients.

Introduction

Drainage ditches are used to control water levels in

marshes and fens that are often situated on low perme-

ability deposits such as peat or alluvium. If these low

permeability deposits are underlain by an aquifer, inter-

action with the aquifer may have a significant impact on

the flow into the drain. This interaction is especially

important when drains penetrate close to, or through to,

the underlying aquifer. To quantify the impact of the

interaction between these drains and the aquifer, regional

groundwater models are often used. For example, under-

standing the interaction between drains and the under-

lying aquifer proved to be of importance in a study of the

groundwater resources of the Sherwood Sandstone aqui-

fer in the vicinity of Doncaster in north-east England

(Brown & Rushton 1993; Rushton 2003). Modelling

studies of drain–aquifer interaction require a technique

that allows the representation of drains, with width and

depth of no more than a few metres, in regional models

where cell sizes are hundreds of metres. This is normally

achieved using a drain coefficient (drain conductance)

which is conceptually similar to the river coefficient

currently used in regional groundwater modelling (An-

derson & Woessner 1992; Rushton 2003).

When ditch drains are represented in regional ground-

water models such as MODFLOW, the conventional

approach is to estimate drain conductance for a model

cell primarily from the hydraulic conductivity and dimen-

sions of low permeability deposits in the bed of the drain

and the cell length (Anderson & Woessner 1992). This

approach is based on the groundwater modelling river

package of Prickett & Lonnquist (1971) who assumed that

the most important process is vertical flow (leakage)

through low permeability bed deposits. The unsatisfactory

nature of this conventional approach has been demon-

strated by Rushton (2007) who showed that riverbed

deposits only have a minor effect on the river–aquifer

interaction; instead river coefficients depend primarily on

the hydraulic conductivity of the aquifer over which the

river flows. There are, however important differences

between river–aquifer interactions and the interaction

between a drain in a low permeability material underlain

by an aquifer.

A detailed representation of drain–aquifer interaction is

required for the Thurne catchment of the northern Nor-

folk Broads, an area in which there is extensive drainage

of low-lying marsh areas situated on low permeability

peat or clay (Holman & Hiscock 1998). These marshes

have water levels in many of the drainage ditches at

1.0–2.0 m below sea level. Some of the drains contain

water with a substantial chloride content. Freshwater

rainfall recharge occurs to areas surrounding the marshes

with the result that in some locations the aquifer contains

Water and Environment Journal 25 (2011) 116–128 c� 2009 The Authors. Water and Environment Journal c� 2009 CIWEM.116

Water and Environment Journal. Print ISSN 1747-6585

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only freshwater. Freshwater from the aquifer is drawn

into some of the drains, elsewhere the groundwater

contribution to the drains is of brackish or saline water.

This occurs because the marsh deposits are underlain by

an aquifer, which is in contact with the sea; saline water is

drawn into the aquifer due to the groundwater gradient

towards the low water levels in the drains. The salinity

of the drainage water has a serious ecological impact,

especially when it is discharged into the internationally

important system of rivers and lakes which form part

of the Norfolk Broads (Bales et al. 1993; Barker et al.

2008).

Although evidence about the hydrology and hydro-

geology of this area is limited (Holman & Hiscock 1998;

Holman et al. 1999), measurements of the salinity of

water in the drains provide useful information. However,

the presence of saline water in a drain does not necessarily

mean that saline water is entering from the aquifer at that

specific location; the saline water may originate from

upstream. Drain–aquifer interaction is the key to under-

standing the distribution of saline water in the drains, and

is the subject of this paper.

This paper opens with a review of the various compo-

nents which contribute to flows in a drainage ditch. This is

followed by an introduction to the Thurne catchment, in

which the interaction between drained marshes and the

underlying aquifer has a dominant effect on the quality of

water in the drains. The methodology used to represent

this interaction, based on the use of a vertical section

numerical model, is considered in two stages, first by

confirming that the concept of drain coefficients is valid,

and then a methodology for estimating drain coefficients

for the Thurne catchment is described. A time-invariant

multilayer regional groundwater model, which incorpo-

rated the drain coefficients, is outlined and pathlines

derived from the model are used to explain the observed

drain salinities. Finally generic guidance on the estima-

tion of drain coefficients for alternative locations is pro-

vided.

Flow in ditch drained systems withconnections to an underlying aquifer

At a given location in a drainage ditch, there are five main

sources of water, although their relative contributions

vary with time. The schematic diagram of Fig. 1 illustrates

the possible sources of water for a drainage ditch in a low

permeability zone which is underlain by a permeable

aquifer. Above the low permeability zone there is a

cultivated layer with extensive tile (or pipe) drainage,

the elevation of the water table in the cultivated layer is

indicated by a broken line. A drainage ditch drain pene-

trates a significant distance into the low permeability

zone. Because this is a low-lying area, the groundwater

(piezometric) head in the aquifer (indicated by the chain-

dotted line on the right-hand side of the diagram) is

higher than both the water table in the cultivated layer

and the water level in the open drainage ditch.

The following components contribute to flow in the

drain:

(a) flow from the aquifer through the lower permeability

zone to the drain; if the drain penetrates through to the

underlying aquifer the flow is larger,

(b) flows from the underlying aquifer to the cultivated

layer; upward flows only occur when the groundwater

head in the underlying aquifer is higher than the water

table in the cultivated layer,

(c) outflows from tile drains in the cultivated layer which

collect water originating from recharge (including any

irrigation) and upward flows into the cultivated layer,

(d) surface runoff following rainfall,

(e) flows from upstream drains.

Each of these components influences both the quantity

of water flowing and the quality of the water. However,

from measurements of the discharge and quality of the

water in the drain at a sampling point, it is not possible to

quantify the different components. Consequently, the

presence of a contaminant at a sampling point does not

mean that the contaminant is entering at that location.

Recharge

Outflow fromtile drains

Water table incultivated layer

Small upward flowsto cultivated layer

Drain flowfrom upstream

Surfacerunoff

Flow fromaquifer to

drain

Groundwater headin underlying aquifer

Cultivated layer

Low permeability

AquiferFig. 1. Schematic diagram of flow components

associated with a drainage ditch; elevations of

water table and groundwater head in aquifer

indicated on right hand side of diagram.

Water and Environment Journal 25 (2011) 116–128 c� 2009 The Authors. Water and Environment Journal c� 2009 CIWEM. 117

Drainage ditch–aquifer interactionT. Simpson et al.

This is important, for example, when attempting to

identify where saline water enters drains from an under-

lying aquifer.

The focus of this paper is the estimation and represen-

tation, using a regional groundwater model, of flow from

an aquifer to drains, item (a). Reference is also made to

flows between aquifer and cultivated layer, item (b).

Flow in drainage ditches in the Thurnecatchment

The Thurne catchment in Norfolk is selected as an exam-

ple of contributions from an aquifer to flows in drainage

ditches.

Introduction to study area

The Thurne catchment covers an area of approximately

110 km2 of flat and gently undulating land in north-east

Norfolk, centred around 11350E and 521450N. The catch-

ment forms the north-eastern part of The Broads National

Park and contains several internationally important shal-

low lakes or Broads including Hickling Broad, Martham

Broad and Horsey Mere.

A simplified geological map of the catchment is in-

cluded as Fig. 2. The catchment is underlain by the

Pleistocene Crag aquifer, which consists of shelly sands

and micaceous clays. Although considered a single unit,

the Crag represents a very complex and heterogeneous

unconfined aquifer with the presence of clay and silts

Fig. 2. Location map and geology of the Thurne

area.


Drainage ditch–aquifer interaction T. Simpson et al.

layers possibly producing aquitards (Holman et al. 1999).

The higher land above the floodplain is covered by

brown-red silty till of the Happisburgh Glacigenic forma-

tion (previously called the North Sea Drift or Norwich

Brickearth). The highest land in the south of the catch-

ment above about 20 m ordnance datum (OD) is also

covered by the clayey till of the Lowestoft Formation. The

floodplain is covered by the alluvium (peat and estuarine

alluvium) of the Breydon Formation. Finally coastal

deposits forming the beach and dunes complete the

sequence of Quaternary sediments.

The River Thurne is largely separated from the under-

lying Pleistocene Crag aquifer with the river flowing

above the level of the marshes. Most of the natural flow

of the river now comprises tidal movements and dis-

charges from the land drainage pumps. The drainage of

the marshes of the Thurne catchment has been an on-

going operation for centuries, with the oldest wind pump

in the catchment built in 1753. Water from the large

networks of drainage ditches flows into the main drains

where they are pumped into the river system. Drainage

standards have been progressively improved over the

centuries with the transition from wind to steam (early

20th century) to diesel and electric powered pumps (mid

20th century), which have allowed increasingly lower

water levels to be maintained in the main drains (Wil-

liamson 2005).

The Brograve subcatchment is located in the upper part

of the catchment, north of Horsey Mere, Fig. 2. The

drainage system has gone through a sequence of changes

because the Brograve Mill was built in 1771. In the

1850s–1880s, the Waxham Cut (a high-level carrier lead-

ing into Horsey Mere) was constructed, into which water

was pumped from the Lessingham catchment by Randall’s

Drainage Mill and water from the Brograve Level by the

Lambridge and Brograve Mills. All the east coast sub-

catchments drained into the Brograve Level via ‘trunks’

that were constructed under Waxham Cut.

The most significant change to the operation and

management of the Brograve system occurred in the

1950s, with a large scale improvement scheme involving

the widening and deepening of existing drains, the

installation of twin electrical pumps with a combined

capacity of around 2.5 m3/s at the new Brograve pump

house and the decommissioning of Randall’s and Lam-

bridge Mill pumps (Williamson 2005). Drainage Board

documents indicate that the main drains were cut to a

bottom width of 2.7–3.0 m and a depth of more than

2.0 m, although feeder drains are smaller. This scheme

resulted in lower water levels in the main drains to allow

arable production, and water levels have been maintained

at around � 2 m OD. Poor quality brackish or saline

groundwater from the underlying Crag aquifer, which is

in hydraulic continuity with the North Sea, is drawn into

many of the drains given their low water levels, especially

where they have been overdeepened such that the peat

has been penetrated (Holman & Hiscock 1998; Simpson

2007).

Conditions in the Lessingham and HempsteadMarshes subcatchments

This paper focuses on the upper part of the Brograve

catchment, Fig. 3, where there is a contrast between

freshwater in the drains of the Lessingham valley and

saline water in many of the drains in the Hempstead

Marshes. Ten monitoring locations are identified in Fig.

3, at each location the drain water level relative to OD and

the salinity of the ditch water levels in g/L chloride ion are

quoted (the salinity of seawater is about 19.5 g/L Cl� );

more detailed information about each location is pre-

sented in Appendix A.

For the whole of the Lessingham subcatchment (loca-

tions A–D), the water levels in the drains are below sea

level, yet the salinity is always o0.5 g/L Cl� indicating

that little or no saline water enters the drains. For

the Hempstead Marshes (locations E–I), some locations

towards the edge of the marshes have salinities below

0.5 g/L Cl� but for most of the drains the salinities are

higher, exceeding 5 g/L Cl� at locations H and I. At the

outlet of each subcatchment the flows are of similar

magnitude; after the two main drainage channels merge,

location J, the salinity is 2.5–3.0 g/L Cl� .

Conceptual model of flow processes in theaquifer system

Figure 4 is a representative schematic cross-section of the

aquifer system. The section extends from the coast

through a region of higher land covered by the permeable

Happisburgh Glacigenic formation, across an area of

drained peat marsh to higher ground inland; the under-

lying Crag aquifer has a depth in excess of 50 m. On this

cross-section the component flows associated with the

aquifer system and the deep drains are illustrated sche-

matically. For clarity the diagram is simplified, for exam-

ple only two deep drains are shown. When considering

this diagram it is important to recognise that there are also

component flows perpendicular to this section.

Flows of saline water into the aquifer occur from the

sea in the direction of the low water levels in the drains.

Over the recharge area adjacent to the coast, inflows of

freshwater occur due to rainfall recharge. Rainfall

recharge also enters the aquifer at the inland recharge

area.



Outflows from the aquifer occur from springs at the

margins of the low permeability peat and in the vicinity of

the coast. In addition there are small flows between the

aquifer and the cultivated layer through the peat;

whether they are upward or downward flows depends

on the relative elevations of the groundwater head in the

underlying aquifer and the elevation of the water table in

the cultivated layer. In addition there are flows to the

deep drains. Because the right hand drain in Fig. 4 is fully

penetrating, the inflow is likely to be substantial; for the

left hand drain, which only partially penetrates the peat,

the inflow is smaller.

An important issue is the quality of the water entering

the left hand drain. It could be freshwater from the

recharge area or saline water from the coast. Saline water

can flow beneath the freshwater from the coastal

Fig. 3. Details of drains in the Lessingham and Hempstead sub-catchments including water level elevations and salinities at ten monitoring locations.

Fig. 4. Representative cross-section illustrating flows associated with the aquifer.



recharge area, but without the development of a three-

dimensional regional groundwater model, the actual

movement of water within the aquifer system cannot be

established. Beneath the peat two arrows are drawn with

a question mark to indicate the uncertainty about flow

directions.

Estimation of flows to cultivated layerand ditches

Basic approach

This section considers the representation of flows between

the aquifer and cultivated layer and flows between the

aquifer and drainage ditches. Figure 5(a) illustrates the flow

processes when the groundwater head in the underlying

aquifer is higher than both the water level in the drain and

the water table in the cultivated layer (see Fig. 1); flows to

the cultivated layer and to the drain are represented in-

dividually in the conceptual model, Fig. 5(b).

Firstly, flows from the underlying aquifer through the

peat to the cultivated layer are considered. Because the

hydraulic conductivity of the peat is substantially less

than the aquifer; the flow per unit plan area qp is

predominately vertical (Neuman & Witherspoon 1969),

Fig. 5(b), and can be calculated from Darcy’s Law as

qp ¼ Kvpðhaq � HcÞ=tp; ð1Þ

where Hc is the effective groundwater head in the culti-

vated layer (which is strongly influenced by the presence

and elevation of tile drains); the unknown head in the

Crag aquifer is haq and the thickness and vertical hydrau-

lic conductivity of the peat are tp and Kvp, respectively.

Flows to a drainage ditch follow complex patterns as

illustrated by the sketches in Figs 1, 4 and 5(a). These

complex flow patterns to a drain, which has dimensions

of only a few metres, cannot be represented precisely in a

regional groundwater model for which the horizontal

mesh spacing is typically 200 m. The conventional

approach (Anderson & Woessner 1992) is to represent

the interaction between a drainage ditch and an under-

lying aquifer using a drain coefficient. The flow into the

drain QD per unit length (units m3/day/m length of drain)

is then estimated as the difference between the ground-

water head in the underlying aquifer haq and the water

level in the drain Hd multiplied by the drain coefficient DC

QD ¼ �DCðhaq � HdÞ: ð2Þ

This flow into a drain is represented in the schematic

computational model of Fig. 5(b) as a vertical flow arrow

from the aquifer.

In the conventional approach, the magnitude of the

drain coefficient is based on the situation when the drain

loses water to the aquifer by vertical flow (leakage)

through the deposits in the bed of the drain. Conse-

quently the drain coefficient equals the product of the

width of the drain and the hydraulic conductivity of the

deposits divided by the thickness of the bed deposits.

However, in practical situations, some drains lose water

to the aquifer but most drains gain water from the aquifer.

Therefore there is a need to re-examine the representa-

tion of drains to include both gaining and losing condi-

tions.

Drainage coefficients have similarities with river coeffi-

cients. In a recent detailed study of river coefficients,

Rushton (2007) examined the validity of the river coeffi-

cient concept for both gaining and losing rivers. In con-

trast to the conventional approach, the river coefficients

derived by Rushton (2007) do not depend primarily on

the river geometry and the hydraulic conductivity and

thickness of the riverbed deposits. Instead, the hydraulic

conductivity of the aquifer and hydraulic conditions on

the boundaries of the aquifer are more important.

The approach of Rushton (2007) for rivers is adapted

for the study of drains in low permeability material which

overlie an aquifer. There are two issues which need to be

addressed.

Validity of the concept of drain coefficients

The first issue is whether the linear relationship of Eq. (2)

is valid. The physical situation and equivalent computa-

tional model are presented in Fig. 6. Because flows to

the cultivated layer are represented independently, the

drained cultivated layer in Fig. 6(b) acts as a zero-flow

upper boundary. The differential equation describing flow

in the system is quoted in Fig. 6(b). Drains are assumed to

Fig. 5. Estimating flows from underlying aquifer to cultivated layer and

partially penetrating drain.



be about 200 m apart; this is represented by lateral no-

flow boundaries at 100 m from the drain as indicated in

Fig. 6(b). In numerical solutions, differing hydraulic con-

ductivities within the vertical section are represented by

modifying the numerical values at appropriate nodes

(cells). At the base of the low permeability zone the

groundwater head is specified; beneath the cultivated

layer the vertical head gradient is zero. The water in the

channel is equivalent to a specified groundwater head.

For the seepage face on the sloping channel sides above

the water surface, the pressure is atmospheric; conse-

quently the groundwater head increases with elevation z

above the water surface.

To explore the validity of the conventional linear

relationship in Eq. (2), a series of numerical solutions

have been obtained using a vertical section x–z finite

difference model of 30� 20-mesh intervals (Rushton &

Redshaw 1979) with a range of different values of

groundwater head in the underlying aquifer. In Fig. 7(a),

which defines the geometry of the problem, the left-hand

side of the diagram represents flows from aquifer to drain

with a high groundwater head in the underlying aquifer

haq(i). However, for the right-hand side of the diagram the

groundwater head haq(ii) is at the bottom of the low

permeability zone so that the drain loses water to the

aquifer. Hydraulic conductivities for the material in which

the drain is constructed and for the underlying aquifer

are, respectively, 0.01 and 5.0 m/day. Calculations are

performed with dp, the distance from the base of the drain

to the top of the aquifer, equal to 1.3 and 0.2 m.

The elevation of the water level in the drain is set at

� 2.0 m OD; results from the numerical model for flows

into the drain are plotted in Fig. 7(b) for groundwater

head in the underlying aquifer within the range � 2.8

to � 1.2 m OD with the vertical axis corresponding to the

groundwater head. For groundwater heads higher than

the drain water level (the upper half of the graph), flows

from the aquifer to the drain take the form sketched in

Fig. 7(a)(i). Results for both values of dp approximate to

straight lines; the slight curvatures occur when the under-

lying groundwater (piezometric) head is lower than the

base of the cultivated layer and the full length of

the seepage face ceases to operate. The inverse slopes of

the upper parts of the lines indicate drain coefficients for a

unit length of drain of 0.026 and 0.074 m2/day/m for

dp=1.3 and 0.2 m, respectively.

When the underlying groundwater head is lower than

the drain water level with water flowing from the drain to

the underlying aquifer, the flow lines follow a signifi-

cantly different pattern, Fig. 7(a)(ii). In this sketch the

underlying water table coincides with the top of the

aquifer; the flow lines are predominantly vertical. How-

ever, when the groundwater head is above than the top of

the aquifer but below the drain water level, there are

horizontal components as water lost from the drain

spreads out laterally. This is reflected in Fig. 7(b) by the

lines deviating from the linear relationship of Eq. (2)

when groundwater heads are below � 2.0 m OD. When

there is only a small distance from the base of the drain to

the underlying aquifer (e.g. the full line with dp=0.2 m),

there is a marked curvature of the line. For greater

distance to the underlying aquifer (e.g. the broken line

with dp=1.3 m) the deviation from the straight line is

smaller with a maximum loss of 0.0178 m3/day/m when

the groundwater head is at the top of the aquifer. Conse-

quently, if the groundwater head is below the drain water

level, the linear Eq. (2) should not be used. If it is used in

these circumstances, losses from the drain are overesti-

mated. Rushton (2007) provides further insights into

losses to an underlying aquifer from channels containing

water.

Quantifying drain coefficients

The second issue is concerned with the magnitude of

drain coefficients and how they vary with the dimensions

Fig. 6. Details of conditions associated with an

individual drain.



of the drain and properties of the low permeability

deposits and the underlying aquifer. This is illustrated

by quantifying the drain coefficient for the Thurne study

area; guidance on the selection of the drain coefficient in

other situations is considered in a later section.

Rushton (2007) developed a method of estimating river

coefficients using vertical section numerical models of the

river, any riverbed deposits, the aquifer on which the

river is located and any deep aquifer conditions. Modifi-

cations to this approach are required to represent drains,

which partially penetrate the low permeability deposits,

in this case peat, Fig. 8. In fact four different types of

material need to be included in the model, the Crag

aquifer, an intermediate lower permeability layer at the

top of the Crag, the peat and any low permeability

channel deposits. Two possible drain penetrations are

illustrated in Fig. 8; in diagram (a) the drainage channel

partially penetrates the peat but in diagram (b) the

channel penetrates through to the underlying aquifer. In

the study of river coefficients (Rushton 2007), the coeffi-

cients were found to be largely insensitive to the width of

the channel, the channel geometry or the depth of water.

For the current study of drain coefficients, using sensitiv-

ity analyses, similar conclusions have been drawn.

Values of the hydraulic conductivity for each of the

layers and deposits are required; the subscripts h and v

refer to horizontal and vertical components. Estimates are

based on published data and field information.

Hydraulic conductivities of the Crag aquifer have been

estimated from pumping tests (Jones et al. 2000); for the

upper few metres of the Crag, hydraulic conductivities are

lower than the average values of 5–10 m/day. Values

selected are Kh=3.0 m/day, Kv=1.5 m/day.

For the peat, values are based on a detailed study of

horizontal and vertical hydraulic conductivities of a bog

peat (Beckwith et al. 2003) and falling head permeameter

estimates (Simpson 2007); values of Kh=0.01 m/day,

Kv=0.005 m/day are chosen.

The intermediate layer parameters are set an order of

magnitude less than the Crag aquifer with Kh=0.3 m/day,

Kv=0.15 m/day; records from auger holes by Burton &

Fig. 7. Examples of flow between a drain and an underlying aquifer for

differing groundwater heads in the aquifer; the drain coefficient per unit

length of drain equals the inverse slope of the line.

Fig. 8. Examples of drains in peat with different

elevations of the intermediate layer and Crag

aquifer in the Brograve catchment.



Hodgson (1987) suggest that these sandy silt loam-tex-

tured deposits are about 0.3 m thick.

Channel deposits are assumed to extend 0.15 m from the

bed of the channel with Kh=0.02 m/day, Kv=0.01 m/day;

sensitivity analyses show that channel deposits have little

effect on the drainage coefficients (Rushton 2007).

Using the vertical section formulation of Fig. 6, drain

coefficients for a unit length of drain have been calculated

using a numerical model for 16 values of the vertical

distance dp from the base of the drain to the top of the Crag

aquifer; the depth of water in the channel is 0.2 m with the

low permeability channel deposits 0.15 m thick. The max-

imum value of dp is 3.3 m; the minimum is – 0.6 m, which

corresponds to the top of the aquifer 0.6 m above the base

of the drain. Values for the drainage coefficient are plotted

in Fig. 9; the vertical axis corresponds to the vertical

distance dp, a logarithmic horizontal scale represents the

drain coefficients that vary between 0.011 m2/day/m for

the maximum depth to the aquifer and 2.67 m2/day/m

when the top of the aquifer is 0.6 m above the base of the

drain. In Fig. 9 a continuous broken line is drawn through

the numerical results; the slope is uneven for 0.1 m4dp4 � 0.3 m due to the influence of the intermediate

layer. The selection of drain coefficients used in the

regional model is discussed in the following section.

Description and results fromgroundwater model

Outline of regional groundwater model

The groundwater model must include both inflows to and

outflows from the aquifer system. Inflows include rainfall

recharge and flows from the sea, as indicated in the cross-

section of Fig. 4. Outflows include flows to drains, upward

flows through the peat to the cultivated layer, springs on

the margins of the peat and outflows to the sea. Move-

ment of groundwater is slow with lateral velocities typi-

cally 10 m/year or less. Mixing occurs between the

freshwater from recharge areas and saline water from the

coast, this mixing has been occurring for hundreds of years.

Consequently salinities vary laterally and with depth.

Although there are computer codes which permit the

simulation of solute transport advection–dispersion pro-

blems or variable density problems, they are not suitable

for the study area because of unknown variations of

salinity within the aquifer and the complex interaction

between drains and the aquifer. An alternative approach

(Anderson & Woessner 1992) is to opt for a regional

groundwater flow model, with particle tracking used to

trace the movement of water including the progress of

saline water from the coast. Movement through the

aquifer to the drains and the cultivated layer is repre-

sented by a regional groundwater model (Simpson 2007)

using the MODFLOW code, which is based on a quasi-

three-dimensional formulation with multiple layers. The

model includes the whole catchment area shown in

Fig. 2; it is based on a square grid inclined at 451 to the

national grid with a mesh spacing of 250=ffiffiffi

2p

m; which

means that there are eight mesh divisions on diagonals of

the 1 km national grid squares.

A time-invariant analysis is adopted. Although there

are some seasonal fluctuations in water table elevations in

the recharge areas, the water levels in the drains remain

almost constant, relative to sea level. Consequently the

groundwater flows from the coast and from recharge

areas to the drains change little with time. This is con-

firmed by estimates of the salt load at the drain dis-

charge pumps, which do not vary significantly between

summer and winter (Holman 1994). The effective

recharge is estimated from a daily water balance (Rushton

et al. 2006); an annual average value is used in the

simulation.

To the north-east the sea is simulated as a specified

head at locations where the sea bed intersects individual

layers, the model extends a distance of at least 700 m

beyond the coastline. On other boundaries no-flow con-

ditions apply.

Selection of drain coefficients

The drain coefficients, which were discussed earlier, are

plotted in Fig. 9 as a broken line. For the regional ground-

water model, this line is approximated by five constant

values as indicated by the vertical lines in Fig. 9. These

values are summarised in Table 1; column 3 lists the

Fig. 9. Variation of drain coefficient with dp; vertical solid lines indicate

values used in groundwater model.



coefficients for a unit length of drain. Because the regional

model uses square cells of sides 250=ffiffiffi

2p

m, drainage

coefficients for individual cells take the values listed in

column 4 of Table 1.

Field information is used to estimate the magnitude of

dp for each cell within the marshes. From a survey of the

drainage ditches (Harding & Holman 2005) the elevation

of the base of drain and the marsh level are available at

locations 100–200 m apart. However, within a single cell

there may be two or more drains at different elevations;

usually data for the deeper drain are used. Information

about the vertical depth from marsh level to the base of

the peat is available over most of the area at 0.5 km

spacing (Burton & Hodgson 1987); in addition there are

further auger hole results along most of the main drains

(Harding & Holman 2005). From this information values

of dp are calculated. The higher drain coefficients occur

when the drain penetrates at least 0.1 m into the aquifer

(dpo� 0.1 m); these areas are shaded and bounded by a

continuous line in Fig. 10. There are extensive areas

where this condition applies in the Lessingham and

Hempstead Marshes catchments. A lighter shading with

broken boundary lines indicates locations where the

drains just penetrate or nearly penetrate the aquifer

(0.24 dp4 � 0.1 m).

Particle tracking

Particle tracking provides a method of identifying the

route of water (pathline) from specified sources (Ander-

son & Woessner 1992). In Fig. 10 the start of a pathline is

Table 1 Drainage coefficients used in model

dp (m) Penetration (m) DC (m2/day/m) DC for cell (m2/day)

o� 0.3 4 0.3 2.4 424

� 0.3 to–0.1 0.1 to 0.3 1.4 247

� 0.1 to 0.2 � 0.2 to 0.1 0.3 53

0.2 to 1.0 � 1.0 to � 0.2 0.03 5.3

4 1.0 o� 1.0 0.013 2.3

Fig. 10. Locations of areas where drains penetrate to the aquifer (shown shaded) and saline and fresh pathlines for the Lessingham and Hempstead

sub-catchments.



shown by the symbol � , arrows show the direction of

flow. Pathlines are produced by the MODPATH postpro-

cessor of the MODFLOW package (Pollock 1994). Path-

lines, which originate from the coast are shown as broken

lines; they represent routes of saline water. Pathlines,

which are drawn as full lines, originate from locations

where recharge occurs; consequently they indicate the

flow of freshwater. A number of pathlines are drawn on

Fig. 10 to illustrate the main flow directions.

Considering first the Lessingham catchment, even

though the water levels in the drains are below sea level,

all flows into the drains are freshwater as indicated by the

full lines in Fig. 10. These flows originate from recharge

areas. Inflows to the drainage ditches feeding into the

Commissioners Drain are also of freshwater. These

inflows of freshwater are consistent with the low salinities

at locations A–D of o0.5 g/L Cl� , see Fig. 10 and Appen-

dix A, which considers each of the monitoring locations in

detail.

Flows into the Hempstead Marshes consist of both

saline and freshwater. Substantial flows occur from the

sea into the marshes; most of the saline pathlines, indi-

cated by broken lines, terminate in areas where the drains

penetrate more than 0.1 m. This explains the higher

salinity at location F of Fig. 10. However, there are also

inflows of freshwater from recharge areas into the Hemp-

stead Marshes. For example, in the north-west of Hemp-

stead Marshes, the label freshwater path indicates a

pathline from a recharge area into drains towards the

edge of the marsh. This pathline ends close to location G,

Fig. 10, and accounts for the low salinity water in this

location of o0.5 g/L Cl� . There is also a saline pathline

passing close to location G which continues a further

600 m to the south-east. This saline pathline follows a

deeper route than the shorter freshwater pathline. For

location E, most of the water is collected from sand dunes

and surrounding fields, hence the low salinity.

Guidance on estimating draincoefficients

This section presents general guidance for the estimation

of drain coefficients. For rivers in unconfined aquifers,

Rushton (2007) found that river coefficients for a unit

length of river usually lie within the range RC=0.9 K to

1.2 K m2/day/m, where K is the hydraulic conductivity of

the stratum in which the river is located. However, this

paper is concerned with a different physical situation of

ditch drains in lower permeability material with an

underlying more permeable aquifer. Vertical section mod-

els are used to deduce values of the drain coefficient for a

unit length of drain. The upper diagram in Fig. 11 refers to

a drain, with a water surface width of 1.2 m and water

depth of 0.4 m located in a low permeability zone with a

more permeable underlying aquifer. Although not shown

in that diagram, the drain can penetrate through to the

underlying aquifer.

The hydraulic conductivity of the underlying aquifer is

Kaq. Three types of low permeability material are consid-

ered with hydraulic conductivities, Klow1=0.02 Kaq,

Klow2=0.002 Kaq and Klow3=0.0002 Kaq. The greatest

distance of the underlying aquifer beneath the base of

the drain is dp=3.6 m. In the other limiting case, the top of

the aquifer is 0.6 m above the base of the drain

(dp=� 0.6 m). Values of the drain coefficient, per unit

length of drain, divided by the aquifer hydraulic conduc-

tivity are plotted, to a logarithmic scale, against dp in

Fig. 11; these curves are similar in shape to Fig. 9. The

maximum value of DC/Kaq and the three minimum values

of DC/Klow are quoted (to one decimal place) in the boxes.

When the top of the aquifer is above the base of the

drain, the drain coefficient depends primarily on the

hydraulic conductivity of the aquifer. The maximum

value of 1.3 Kaq is slightly higher than the maximum of

1.2 Kaq quoted for the river coefficient; this larger value is

mainly due to the effect of the seepage face. Minimum

values of the drain coefficient occur when the top of the

aquifer is 3.6 m below the base of the drain; for each of the

low permeability materials DC/Klow=1.6.

Suggested values for the drain coefficient for a unit

length of drain with different elevations of the interface

Fig. 11. Variation of drain coefficients per unit length of drain with the

depth of low permeability material beneath the base of the drain.



between low and high permeability material are listed

below. Because uncertainties about the magnitude of

both dp and the hydraulic conductivities of the layers

always arise, the following values should be used as initial

estimates:

For dpo� 0.1 m, DC/Kaq � 1.2,

� 0.1 mo dpo0.1 m, DC/Kaq reduces rapidly by up to

three orders of magnitude,

dp=0.5 m, DC/Klow � 5.0,

dp=1.0 m, DC/Klow � 2.5,

dp4 3.0 m, DC/Klow � 1.5,

with interpolated or extrapolated values for other

values of dp.

The above estimates should only be used for drains

with a water surface width of no more than 3 m and a

water depth of o1 m. If the horizontal and vertical

hydraulic conductivities are different, an average should

be used in the above calculations.

Conclusions

(1) The representation of individual ditch drains in

regional groundwater models has been achieved by mod-

ifying the river coefficient approach to represent drains

which are located in low permeability strata and under-

lain by an aquifer. In this methodology, the flow between

the aquifer and drain equals the drain coefficient multi-

plied by the difference between the water surface level in

the drain and the groundwater head in the underlying

aquifer, Eq. (2). This approach is valid when the ground-

water head in the underlying aquifer is higher than the

drain water level. When the underlying groundwater

heads is lower than the drain water level, the linear

relationship of Eq. (2) no longer holds. If Eq. (2) is used,

the calculated flow is larger than the correct value.

(2) Values of drain coefficients are determined from

vertical section numerical models which represent the

geometry and depth of water in the drain, different

distances to the underlying aquifer and alternative

hydraulic conductivities of deposits in the bed of the

drain. Although drain geometries, water depths and low

permeability bed deposits have a minor influence on the

drain coefficient, the most important parameters are the

hydraulic conductivities of the low permeability deposits

and the vertical distance to the underlying aquifer. The

coefficient for a drain that penetrates through to the

underlying aquifer may be two or more orders of magni-

tude greater than when the underlying aquifer is several

metres below the drain.

(3) A satisfactory representation of drains in a regional

groundwater model of the Thurne catchment allows the

identification of flows from the coast or from the recharge

areas, through the underlying Crag aquifer and into the

drainage ditches. Drain coefficients are estimated for

individual drains in the catchment. They are based on

field information of drain water levels, elevations of the

base of the drains, locations of interfaces between the low

permeability material and the underlying aquifer and

hydraulic conductivity values for each stratum. Pathlines

of saline or freshwater, which are deduced from the

regional groundwater model, indicate why saline water

enters certain drains while freshwater enters other drains.

(4) In addition to the estimation of drain coefficients for

the specific location of the Thurne catchment, guidance is

given on the selection of drain coefficients for other

situations. These drainage coefficients are estimated from

a series of vertical section numerical model simulations.

Acknowledgements

This work was funded by the Water Management Alliance

(WMA) and the Engineering and Physical Sciences Re-

search Council (EPSRC). The assistance of John Worfolk,

Lou Mayer and Tony Goodwin at WMA is gratefully

acknowledged.

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References

Anderson, M.P. and Woessner, W.W. (1992) Applied Ground-

water Modeling: Simulation of Flow and Advective Transport.

Academic Press, San Diego.

Bales, M., Moss, B., Phillips, G., Irvine, K. and Stansfield, J.

(1993) The Changing Ecosystem of a Shallow, Brackish

Lake, Hickling Broad, Norfolk UK: II Long Terms Trends

in Water Chemistry and Ecology and their Implications

for Restoration of the Lake. Freshw. Biol., 29 (1),

141–165.

Barker, T., Hatton, K., O’Connor, M., Connor, L., Bagnell, L.

and Moss, B. (2008) Control of Ecosystem State in a

Shallow, Brackish Lake: Implications for the Conservation

of Stonewort Communities. Aquat. Conserv., 18 (3),

221–240.

Beckwith, C.W., Baird, A.J. and Heathwaite, A.L. (2003)

Anisotropy and Depth-Related Heterogeneity of Hydraulic

Conductivity in a Bog Peat. I: Laboratory Measurements.

Hydrol. Process., 17, 89–101.

Brown, I.T. and Rushton, K.R. (1993) Modelling of the Doncaster

aquifer. Final Report, School of Civil Engineering, University

of Birmingham, Birmingham, UK.

Burton, R.G.O. and Hodgson, J.M. (1987) Lowland peat in

England and Wales. Soil Survey of England & Wales Special

Survey No. 15, Harpenden, 146 pp.



http://mc.manuscriptcentral.com/wej

http://mc.manuscriptcentral.com/wej

www.wileyonlinelibrary.com

Harding, M. and Holman, I.P. (2005) Feasibility Study for Solu-

tions to the Salinity and Ochre Issues in the Brograve Catchment.

ELP and Cranfield University, Ipswich.

Holman, I.P. (1994) Controls of saline intrusion in the Crag aquifer

of north-east Norfolk. Unpublished PhD Thesis, University of

East Anglia, Norwich.

Holman, I.P. and Hiscock, K.M. (1998) Land Drainage and

Saline Intrusion in the Coastal Marshes in Northeast

Norfolk. Q. J. Eng. Geol., 31, 47–62.

Holman, I.P., Hiscock, K.M. and Chroston, P.N. (1999) Crag

Aquifer Characteristics and Water Balance for the

Thurne Catchment, Northeast Norfolk. Q. J. Eng. Geol., 32,

365–380.

Jones, H.K., Morris, B.L., Cheney, C.S., Brewerton, L.J.,

Merrin, P.D., Lewis, M.A., MacDonald, A.M., Coleby, L.M.,

Talbot, J.C., McKenzie, A.A., Bird, M.J., Cunningham, J.

and Robinson, V.K. (2000) The Physical Proprieties of Minor

Aquifers in England and Wales. British Geological Survey Techni-

cal Report WD/00/4, Environment Agency R&D Publication 68.

Environment Agency, Bristol.

Neuman, S.P. and Witherspoon, P.A. (1969) Theory of Flow in

a Confined Two Aquifer System. Water Resour. Res., 5,

803–816.

Pollock, D.W. (1994) User’s guide for MODPATH/MODPATH-

PLOT, version 3: a particle tracking post-processing package for

MODFLOW, the US Geological Survey finite-difference ground-

water flow model. US Geological Survey Open-File Report

94-464, 6 ch.

Prickett, T.A. and Lonnquist, C.G. (1971) Selected digital compu-

ter techniques for groundwater resources evaluation. Illinois State

Water Survey, Urbana, Bull. No. 55.

Rushton, K.R. (2003) Groundwater Hydrology: Conceptual and

Computational Models. Wiley, Chichester.

Rushton, K.R. (2007) Representation in Regional Models of

Saturated River–Aquifer Interaction for Gaining/Losing

Rivers. J. Hydrol., 334, 262–281.

Rushton, K.R. and Redshaw, S.C. (1979) Seepage and Ground-

water Flow. Wiley, Chichester.

Rushton, K.R., Eilers, V.H.M. and Carter, R.C. (2006) Improved

Soil Moisture Balance Methodology for Recharge Estima-

tion. J. Hydrol., 318, 379–399.

Simpson, T.B. (2007) Understanding the groundwater system of a

heavily drained coastal catchment and the implications for salinity

management. PhD Thesis, Cranfield University, Cranfield.

//hdl.handle.net/1826/2460.

Williamson, B. (2005) Historical Review of Changes to Drains in the

Brograve Catchment. ELP, Ipswich.

Appendix A: description of contributionsof fresh and saline water at monitoringlocations

Table A1

A Water level 0.4 m below OD, drain penetrates 0.4 m into the aquifer,

freshwater inflow from aquifer hence low salinity drain water of o0.5 g/

L Cl� .

B Water level 1.2 m below OD, drain penetrates 0.1 m into the aquifer,

low salinity drain water of o0.5 g/L Cl� because inflow from the

aquifer and flow from upstream are both of low salinity.

C Water level 1.3 m below OD, base of drain located 0.5 m above the

aquifer, very small inflow from aquifer, low salinity drain water of

o0.5 g/L Cl� because inflow from upstream is of low salinity.

D Water level 1.4 m below OD, base of drain located 0.6 m above the

aquifer, negligible inflow from the aquifer but all flows from upstream

are of low salinity, hence salinity of drain water o0.5 g/L Cl� .

E Water level 0.8 m below OD, base of drain 0.3 m above aquifer, low

salinity drain water of o0.5 g/L Cl� because it is mainly supplied by

seepage from sand dunes, etc.

F Water level 1.4 m below OD, drain penetrates 0.7 m into the aquifer,

salinity of drain water 1.5–2.0 g/L Cl� due to saline water flow from

aquifer combined with both fresh and saline inflows from upstream

drains which penetrate into the aquifer.

G Water level 0.7 m below OD, drain penetrates 0.1 m into the aquifer,

freshwater inflow from recharge area to the west, hence salinity

o0.5 g/L Cl� .

H Water level 1.5 m below OD, about 0.3 m of peat beneath base of drain,

high salinity of 4 5 g/L Cl� primarily due to saline flows from

upstream.

I Water level 1.5 m below OD, drain penetrates 0.3 m into the aquifer,

possibly freshwater inflow from aquifer but high salinity drain water

from upstream results in saline water in drain 4 5 g/L Cl� .

J Water level 1.5 m below OD, drain penetrates 0.4 m into the aquifer,

freshwater inflow from aquifer and much larger contribution of

freshwater from Lessingham (location D) and saline water from

Hempstead Marshes (location I) leads to salinity of 2.5–3.0 g/L Cl� .



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