JH_2004_299_136-158

Modelling of macropore flow and transport

processes at catchment scale

Jesper Skovdal Christiansend, Mette Thorsena, Thomas Clausena,Søren Hansenb, Jens Christian Refsgaardc,*

aDHI Water and Environment, Hørsholm, DenmarkbRoyal Veterinary and Agricultural University, Copenhagen, Denmark

cGeological Survey of Denmark and Greenland, Department of Hydrology, Oster Voldgade 10, DK-1350 Copenhagen, DenmarkdAtkins Danmark, Copenhagen, Denmark

Received 15 August 2002; revised 20 April 2004; accepted 26 April 2004

Abstract

Macropores play a significant role as a preferential flow mechanism in connection with pesticide leaching to shallow

groundwater in clayey and loamy soils. A macropore description based on some of the same principles as those of the MACRO

code has been added to the coupled MIKE SHE/Daisy code, enabling a physically based simulation of macropore processes in a

spatially distributed manner throughout an entire catchment. Simulation results from a small catchment in Denmark suggest

that although the point scale macropore processes have no dominating effect on groundwater recharge or discharge at a

catchment scale, they will have significant effects on pesticide leaching to groundwater at a catchment scale. The primary

function of macropores in this area is that they rapidly transport a significant part of the infiltrating water and solutes from the

plough pan at 20 cm depth some distance downwards before most of it flows back into the soil matrix. This has a very significant

effect on the leaching of pesticides from the surface to the groundwater table, because some of the pesticides are transported

rapidly downwards in the soil profile to zones with less sorption and degradation. It is concluded that the spatial variations of

macropore flows caused by the variation in topography and depth to groundwater table within a catchment are so large that this

has to be accounted for in up-scaling process descriptions and results from point scale to catchment scale.

q 2004 Elsevier B.V. All rights reserved.

Keywords: Preferential flow; Leaching; Pesticide; Catchment; Modelling

1. Introduction

The importance of macropores as a preferential

flow mechanism for infiltrating water and transport

of solutes has been generally recognised during

a couple of decades (Beven and Germann, 1982;

Barbash and Resek, 1996). Macropores play signifi-

cant roles in many contexts such as leading to more

infiltration and thus reducing overland flow and is

rapidly transferring pesticides and other pollutants

through the soil toward the groundwater. Pesticides

have been detected in shallow groundwater world-

wide (US Environmental Protection Agency, 1990,

Journal of Hydrology 299 (2004) 136–158

www.elsevier.com/locate/jhydrol

0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.jhydrol.2004.04.029

* Corresponding author. Fax: þ45-3814-2050.

E-mail address: [email protected] (J.C. Refsgaard).

http://www.elsevier.com/locate/jhydrol

1992; EEA, 2000; Stockmarr, 2000) and preferential

flow is recognised as an important mechanism in this

connection (Barbash and Resek, 1996; Thorsen et al.,

1998).

Field scale studies of tracer movements to the

groundwater system in clayey till areas (Sidle et al.,

1998; Nilsson et al., 2001) show that rapid transport of

solutes to shallow groundwater at 4–7 m depth can be

explained by preferential flow mechanisms. Similarly,

field scale studies of preferential flow to the drains in

glacial till agricultural soils (Villholth et al., 1998;

Villholth and Jensen, 1998) have shown that macro-

pore flow is essential in describing the observed flows

and concentrations in tile drains. The results from

these field studies emphasised the importance of

taking the considerable spatial variability of hydraulic

parameters into account.

At the point scale, where only vertical flows are

considered, the classical modelling approach for

preferential flow and transport phenomena is a two-

domain or dual permeability description in one

(vertical) dimension. An example of a model code

of this type is the MACRO (Jarvis, 1994; Jarvis and

Larsson, 1998; Larsson and Jarvis, 1999), where the

vertical flow in the matrix is described by Richards’

equation and the preferential flow is assumed to take

place in a separately defined pore domain. The

interaction between the macropore and the matrix is

described by an approximation to a diffusion equation.

This macropore modelling approach has shown to

provide significantly improved description of the

pesticide breakthrough curves as compared to models

not considering preferential flows (Bergstrom and

Jarvis, 1994; Thorsen et al., 1998; Larsson and Jarvis,

1999; Armstrong et al., 2000). This model type may

be characterised as physically based, because it is

based on the point scale partial differential flow and

transport equations and contains process descriptions

and parameters, which are recognisable in the field.

Thus, it is in principle rather easy to modify this

model type to incorporate new knowledge on process

descriptions as it becomes available (Jarvis, 1998).

Hydrological models at catchment scale may be

classified according to the description of the physical

processes as conceptual or physically based, and

according to the spatial description of catchment

processes as lumped or distributed (Refsgaard, 1996

and many others). In this respect, two typical model

types are the lumped conceptual and the distributed

physically based ones. Examples of the two model

types are the Stanford Watershed Model (Crawford

and Linsley, 1966) and the MIKE SHE (Abbott et al.,

1986; Refsgaard and Storm, 1995), respectively.

In lumped conceptual catchment models preferen-

tial flow and transport are treated in a relatively simple

manner by empirical approaches. Thus, catchment

model codes that include pesticide transport com-

ponents such as HSPF (Donigian et al., 1995),

CREAMS (Knisel and Williams, 1995) and SWRRB

(Arnold and Williams, 1995) do not consider prefer-

ential flow explicitly by a two-domain approach.

Instead, the equations describing e.g. infiltration have

implicitly built in some kind of spatial variability or

preferential flow dynamics. In the CREAMS and

SWRRB, the core of the infiltration equation is the

curve number approach, while the HSPF that is based

on the classical Stanford Watershed Model considers a

combination of catchment average infiltration capacity

with its dependence on the average soil moisture

content and the spatial variability of this average

catchment infiltration capacity. However, the spatial

variability is not considered explicitly and all state

variables represent average catchment conditions, and

hence, the knowledge existing at point scale on

macropore processes and parameter values is incom-

patible with the catchment scale equations built into

these model codes.

While it is thus fundamentally very difficult to

include a physically based macropore description in

lumped conceptual catchment models, it is in

principle easier in the more sophisticated catchment

models of the distributed, physically based type,

where the process equations and parameters at the

individual computational grids are point scale

equations and as such compatible with e.g. macropore

formulations such as the one in MACRO. However,

none of the existing model codes of the distributed

physically based type presently includes a physically

based macropore description. In most of them, such as

Thales (Grayson et al., 1995), preferential flow is not

considered, while in others, such as MIKE SHE (DHI,

2000a), an empirical ‘bypass flow’ formulation is

built in as an optional add-on description. This bypass

flow is required to match observed hydrographs when

a model like MIKE SHE is used for large scale

modelling, in order to compensate for the lack of

J.S. Christiansen et al. / Journal of Hydrology 299 (2004) 136–158 137

spatial variability of soil parameters, topography,

climate input etc that is often a problem when the data

basis is scarce and/or the model grid size is very large

(Overgaard, 2000).

Many factors influence leaching of pesticides to the

phreatic aquifer. The present paper focuses on the

importance of macropore flow and transport and

specifically on the interaction between the depth to

ground water table and macropore flow processes at

the catchment scale. As macropore flow is dependent

on the soil moisture content at the beginning of the

rainfall events, it is as such sensitive to the depth of

the groundwater table that is varying considerably in

time and space throughout a catchment. The assump-

tion usually made in pesticide leaching models is to

use either a lower boundary condition that is constant

in time and space (e.g. constant gradient or constant

dept to groundwater table) or, at best, a time variable

groundwater table. No studies have so far been

reported on the possible differences of the macropore

processes between a point scale and a natural

catchment with a temporally and spatially varying

groundwater table.

The present study was carried out within the

framework of a research project aiming at modelling

of pesticide leaching, transport and degradation at

catchment scale with particular emphasis on ground-

water aspects. Some aspects of the pesticide modelling

are reported elsewhere (Brun et al., 2000; Thorsen

et al., 2000). The present paper, focusing on macropore

flow, transport and leaching to shallow groundwater at

catchment scale, has the following objectives: (1) to

describe incorporation of a physically based macro-

pore formulation into a physically based spatially

distributed catchment model; (2) to investigate how the

spatial and temporal variations of depth to the ground

water table influence macropore flows and transport at

the catchment scale; and (3) to test the extent to which

the traditional approach of using pesticide leaching

models at the point scale gives different results than

using a spatially distributed model with similar

macropore descriptions at catchment scale.

2. Catchment modelling framework

2.1. The integrated model concept

The integrated modelling concept (Fig. 1), aiming

at simulation of pesticide transport and fate at

catchment scale, is based on a coupling between a

spatially distributed hydrological model code

Fig. 1. A scetch of the integrated modelling system for simulation of pesticide transport and fate at catchment scale.

J.S. Christiansen et al. / Journal of Hydrology 299 (2004) 136–158138

operating at catchment scale (MIKE SHE) and a point

scale agro-ecosystem model code (Daisy).

MIKE SHE (Abbott et al., 1986; Refsgaard and

Storm, 1995) is a modelling system describing the

flow of water and solutes in a catchment in a

distributed physically based way. This implies

numerical solutions of the coupled partial differen-

tial equations for overland (2D) and channel flow

(1D), unsaturated flow (1D) and saturated flow

(3D) together with a description of evapotranspira-

tion and snowmelt processes. In addition an

optional macropore flow module, described below,

has been added. The solute transport processes are

described by the classical advection dispersion

equation.

Daisy (Hansen et al., 1991; Abrahamsen and

Hansen, 2000) is a 1D modelling system describing

crop production as well as water and nutrient

dynamics in the root zone according to various

management strategies, including crop rotations,

fertilisation, irrigation, soil tillage and crop residue

management. The model simulates processes such as:

plant growth and crop production; heat flux and soil

temperature; soil water uptake by plants and evapo-

transpiration; carbon and nitrogen mineralisation;

nitrification and denitrification (nitrogen transform-

ation); and nitrogen uptake by plants.

2.2. The MIKE—SHE DAISY coupling

A full coupling has been developed between

MIKE SHE and Daisy at the code level. The

pesticide application, evapotranspiration, crop

growth, and temperature calculations take place in

Daisy while the flow and solute transport is

described by MIKE SHE. All these sub modules

are being executed simultaneously. The division of

calculational tasks and the data flow between

the MIKE SHE Water Movement, MIKE SHE

Advection-Dispersion and Daisy modules are

shown in Fig. 2.

The sorption and degradation processes of pesti-

cides are simulated by use of the MIKE SHE that

includes simplified descriptions of geochemical and

microbiological processes (DHI, 2000b). The sorption

may be described by linear or non-linear equilibrium

or by kinetic sorption. Pesticide degradation is

described by a first order process.

3. The macropore flow model component

3.1. Physical processes

Macropores are defined as a secondary,

additional continuous pore domain in the unsatu-

rated zone, besides the matrix pore domain repre-

senting the microporous bulk soil. Macropore flow

is initiated when the capillary head in the micropore

domain is higher than a threshold matrix pressure

head ðctÞ; corresponding to the minimum pore size

that is considered as belonging to the macropore

domain. Water flow in the macropores is assumed to

be laminar and not influenced by capillarity,

corresponding to gravitational flow. The vertical

volumetric flux (positive upwards) qmp is then

given by:

qmp ¼ 2KmpðumpÞ ð1Þ

where KmpðumpÞ is the hydraulic conductivity of the

macropores depending on the volumetric soil

moisture content of the macropores, ump: The

continuity equation is expressed as:

›ump

›t¼ 2

›qmp

›z2 Smp ð2Þ

Fig. 2. Sequence of calculation and data exchange between MIKE

SHE AD, MIKE SHE WM and Daisy.


where Smp is a sink term for water exchange with

the surrounding matrix. Combining Eqs. (1) and (2)

yields the governing equation for the macropores:

›ump

›t¼

›ðKmpðumpÞÞ

›z2 Smp ð3Þ

The term Smp becomes a source/sink term in

Richards’ equation used in the matrix domain. This

term is given by

Smp ¼ bmpKðumatrixÞðcmp 2 cmatrixÞ ð4Þ

where cmp and cmatrix are the capillary heads in the

macropores and in the matrix, respectively, and

KðumatrixÞ is the hydraulic conductivity in the matrix

depending on the volumetric soil moisture content of

the matrix, umatrix: The exchange flow from matrix to

macropore is only considered when the capillary head

in the matrix exceeds the threshold pressure ðcmatrix $

ctÞ:bmp is a first-order linear water transfer coefficient,

which is expected to increase with decreasing distance

between macropores and with increasing hydraulic

matrix-macropore contact. It can be expressed as:

bmp ¼Cf

d2ð5Þ

where d (m) is an effective diffusion path length. Cf

(–) is a contact factor to take care of coatings at the

interior walls of the macropores. Such a coating could

be present due to e.g. root remnants, worm slime or

mineral precipitation and can decrease the contact

between matrix and macropore significantly. The

contact factor ranges from 0.0 (no contact) to 1.0 (full

contact).

In the macropores, a simple power law function is

assumed to represent the conductivity relation:

KmpðumpÞ ¼ Ks;mp

ump

us;mp

!np

ð6Þ

where Ks;mp is the saturated hydraulic conductivity of

the macropores, us;mp is the macroporosity, and n* is

an empirical exponent accounting for size distri-

bution, tortuosity, and continuity of the macropores.

n* may vary from two to six, according to Jarvis

(1994). The lower values represent soils of coarse

structure with macropore networks of narrow pore

size distribution and little tortuosity, whereas the

higher values apply to soils with a wider macropore

size distribution and larger tortuosity. If macropores

are included in the simulation the hydraulic

conductivity used to represent the soil matrix should

exclude the effect of macropores.

The actual size, form and number of macropores

are not explicitly considered in the modelling.

Instead the macropore characteristics appear

indirectly from ct; n* and bmp that in the present

formulation are dependent on soil type. The

capillary head in the macropores cmp is supposed

to vary linearly with the macropore moisture

content ump between zero (at ump ¼ us;mpÞ and ct

(at ump ¼ 0Þ: Neither root water uptake nor soil

evaporation are considered to take place from the

macropore domain.

The infiltration process description includes

water entering the macropores as well as the soil

matrix at the soil surface. In this case water is only

ponded on the ground surface when the infiltration

capacities of both pore regions are exceeded. Water

flow into the macropores commences as the matrix

infiltration capacity is surpassed.

The bottom boundary condition for flow in the

macropores is a vertical flux at a unit hydraulic

gradient. This flux is input to the saturated zone. A

coupling of the saturated zone and the unsaturated

zone is necessary when the groundwater level

fluctuates. During groundwater rise, the water

present in the macropores in the bottom unsaturated

zone layer is released instantaneously to the

groundwater and during groundwater decline, the

macropores are exposed as empty.

Internally in the macropores, solute transport is

assumed to be dominated by advection, neglecting

the influence of dispersion and diffusion.

The source/sink term ðRcÞ describing solute

exchange between matrix and macropores is given

by a combination of a diffusion component and a mass

flow component:

Rc ¼ bcumatrix

ump

emp

!ðcmp 2 cmatrixÞ þ Smpc0 ð7Þ

where bc is a mass transfer coefficient, cmp and cmatrix

are the solute concentrations in the macropores

and matrix, respectively, and c0 indicates the

concentration in either matrix or macropores depend-

ing on the direction of the exchange flow ðSmpÞ:


The mass transfer coefficient, bc; can be derived as:

bc ¼ Ck

3D0f p

d2ð8Þ

where Ck (–) is the contact factor to take care of an

eventual coating at the interior walls of the macro-

pores. The contact factor ranges from 0.0 (no

contact) to 1.0 (full contact). D0 (m2s21) is the

diffusion coefficient in free water of the solute

species. f * (–) is an impedance factor that represents

and decreases with the tortuosity of the macropores.

f * ranges from 0.0 (zero diffusivity) to 1.0 (full

diffusivity). Thereby, bc depends on both solute

species and soil type.

Even though the applied macropore description

can be regarded as mechanistic with parameters

having physical meaning, some of the parameters

required to characterise the macropore system are

either difficult or impossible to measure. This is

particularly the case for the parameters regulating

exchange between matrix and macropores.

Field observations of soil structure and the

occurrence of biotic macropores can give indications

of the mass exchange parameters (Jarvis et al., 1997;

Jarvis, 1998), though recent experiences reveal that

parameters obtained from such macroscopic obser-

vations often need adjustments towards longer diffu-

sion lengths when applied to field measurements

(Saxena et al., 1994; Larsson and Jarvis, 1999). The

main reason for this is expected to be organic and clay

coatings on the aggregate surfaces which reduce mass

exchange rates between the two domains (Thoma

et al., 1992; Vinther et al., 1999)

3.2. Numerical formulation

The numerical formulation has to take into account

the fact that flows in the macropore and in the matrix

domains occur with significantly different velocities

Priority in development of the numerical scheme has

been put on preserving the water balance and ensuring

numerical stability at time steps that are not much

lower than the time steps used in solving the matrix

flow equation (Richards) alone. The solution method

is mass conserving. The time step length is controlled

by specifying certain limits for flow and exchange

flow (depths) per time step, partly for ensuring correct

dynamics of the macropore flow description and

partly to avoid instability of the Richards solution due

to high source/sink terms. The time step is controlled

by performing an extra (a priori) macropore compu-

tation at the start of each matrix flow time step—with

the matrix conditions from the previous time step. In

case the resulting maximum (a priori) macropore

flows, infiltrations, and exchange flows exceed the

specified limits, a reduced time step is estimated,

assuming linear relationship between time step length

and flow volumes (unchanged flow rates). The

procedure is repeated until the estimated maximum

flows are within limits.

After the time step check a normal time step

simulation is performed, solving the Richards’

equation for the matrix flow—with reduced source/-

sink terms from macropore-matrix exchange flows of

the previous time step. After this the corresponding

macropore time step is performed.

The calculation procedure consists of a double

sweep algorithm with the following characteristics:

3.2.1. Downwards sweep (sweep 1):

† First, a downwards sweep is performed, i.e.

downwards flow from each cell to the cell below

(or ground water table) in the macropore and in

the matrix domains, and exchange flows, are

calculated. Mass conservation is ensured by

reducing the outflow from a cell if it exceeds

the storage volume of that particular cell. The

flow is not influenced by the water content of

the receiving cell below, but the flow is set to 0 if

the cell below has no macropores.

† In the downwards sweep the downwards flow

from a cell is calculated as the average of two

estimates, and exchange flow as average of four

estimates:

– First, flow and exchange flow estimates are

calculated as function of the macropore water

content at the start of the time step. The

estimates are reduced, if they exceed the start

volume plus the inflow from the cell above.

– Second estimate is flow and exchange flow as

function of the resulting macropore water

content from first estimate, including the

inflow from the cell above (or the macropore

infiltration if upper cell). Again a reduction is

made if the resulting volume would become

negative.


– The final flow and exchange flow are

calculated as the average of the two esti-

mates. The flow is used as inflow to the cell

below (or macropore recharge to ground

water if lower cell).

† As mentioned above, each of the two macro-

pore-matrix exchange flow estimates are calcu-

lated as two sub-estimates: The first estimate is

calculated as function of the matrix water

content at the start of the time step, and the

second as function of the matrix water content as

result of estimate one. The same macropore

water content (pressure) is used for both

exchange estimates. Each sub-estimate is limited

by two conditions: Flow from macropore to

matrix is reduced if the resulting matrix water

content would exceed saturation. Flow from

matrix to macropore is reduced if the resulting

matrix pressure would be below the macropore

pressure. The macropore pressure used for

exchange calculation is calculated as the macro-

pore saturation (i.e. actual water content divided

by porosity) multiplied by the cell height, and

then reduced by the entry pressure. If the

macropores of the cell are fully saturated, the

macropore pressure of the cell above is added

(hydrostatic conditions).

3.2.2. Upwards sweep (sweep 2):

† In the second, upwards, sweep the macropore flows

and the matrix-macropore exchange flows are

reduced for situations where the macropores

would otherwise become over-saturated. The

resulting macropore water contents from sweep

no. 1 are checked, and when they exceed the

macropore porosity the flow from the cell above

and the exchange inflow from the matrix are

reduced accordingly. If the cell receives exchange

inflow from the matrix, the exchange flow and the

flow from the cell above are reduced by the same

proportion, otherwise only the flow from the cell

above is reduced. Mass conservation is ensured by

adding the flow reduction volume to the volume of

the cell above (converted to water content).

† The calculational time step is automatically

adjusted in situations with high macropore and

exchange flows so that these flows do not exceed

certain limits, which from experience is known

to generate numerical instability. In case of

an increase of the ground water table, the water

content in macropores now located below the

groundwater table will be added to the ground-

water recharge.

Due to the complex flow description it was not

possible to verify the code through tests against

analytical solutions. Instead, several tests with

different boundary conditions have indicated that the

code is able to simulate the different aspects of the

macropore flow events dynamically in accordance

with the above theoretical basis. In addition, rigorous

water balance tests have demonstrated that the

continuity equation is simulated very well.

3.3. Test of numerical formulation

The numerical algorithm for the macropore

component was previously tested by Thorsen et al.

(1998). The only modification that has been made to

the process descriptions since then is that the

macroporosity that was described as a function of

depth in the version used by Thorsen et al. (1998) now

is described as a function of soil type.

4. Model construction at catchment scale

4.1. Study area

To evaluate the importance of macropore flow at

the catchment scale a 1.5 km2 area near the village

Frankerup in the western part of Zealand, Denmark

was selected (Fig. 3). Because such a small area, in a

groundwater context, is very much influenced by its

transient boundary conditions a three-step procedure

was used. Firstly, a large area consisting of the

62.3 km2 Bjerge A catchment was modelled with a

250 m computational grid. Secondly, using a tele-

scoping approach a more detailed model was

constructed for the 13.7 km2 Øllemose Rende sub-

catchment with a 125 m computational grid. Finally,

in many of the analyses, results from the 1.5 km2

Frankerup area were extracted from the Øllemose

Rende model.

The boundaries of the larger Bjerge catchment

and the smaller Øllemose catchment as well as


the Frankerup area are shown in Fig. 3. The data

required for the construction of the models have been

obtained from existing data sources as outlined

below.

4.2. Topography and river network

The topography and the location of the Bjerge and

Øllemose streams were digitised from geodetic maps

provided by Kort og Matrikelstyrelsen The river

geometry was digitised from municipal stream

regulations. Ten sub-branches with numerous detailed

cross-sections and level points were used in the

construction of the model. A constant Manning

number of 20 m1/3s21 and a leakage coefficient

between the streams and the adjacent aquifer of

1028 s21 have been applied to the entire stream

system.

In addition to the river network, sub-surface tile

drains exist over the main part of the area. The exact

location of these drains is not known. The effect of the

drains is simulated by assuming drains located 1 m

below the ground surface and all over the area. Runoff

through the drains in a particular grid is simulated as

being linearly proportional to the height of the

simulated ground water table above the drain in the

grid. The proportionality factor is a reciprocal time

constant, which on the basis of experience from

modelling of similar regimes was chosen equivalent

to 30 days.

Discharge data from the two river gauging stations,

5614 and 5610 (Fig. 3), were available for the period

from May 1978 to December 1996.

4.3. Hydrogeology

The Bjerge A catchment is a moraine landscape

characterised by a relatively flat surface and river

valleys (Klint and Gravesen, 1999) The upper layer

consists of a clayey and sandy till with a large number

of fractures and biopores. Below this layer that acts as

an aquitard, various layers and lenses of alluvial and

glacial clay and sand are located. The local geology

has been interpreted on the basis of borehole

information from 509 boreholes obtained from the

database of the Geological Survey of Denmark and

Greenland. Six geological layers functioning as

alternating aquifers and aquitards have been identified

and incorporated in the model. In Fig. 4 a west–east

cross-section of the 3D interpretation of the geology is

shown including some of the borehole information.

The adopted six-layer model is not able to describe all

details of the geology. However, in general, there

seems to be a good accordance between the borehole

information and the geological interpretation.

The hydraulic parameters have been assumed

spatially constant within each of the six geological

layers. The only exception to this is the lower

limestone aquifer that has a distributed hydraulic

conductivity according to the different types of

limestone in the area (the Danien limestone to the

south has lower conductivity than the Selandien

limestone to the north). The parameter values have

been assessed through calibration (see below). The

boundaries for the Bjerge A catchment model are

assumed to be no-flow except for the region very close

to the river outlet, where fixed heads have been

assumed for the two lower aquifer layers.

Thirty one groundwater abstraction wells are

present in the area for drinking water supplies Many

of them are small, with abstractions less than

50,000 m3/year. The main part of the abstraction

originates from two urban waterworks with pumping

in the order of 1 million m3/year. Time series of

groundwater abstractions with monthly data from the

two urban and annual data from the small rural water

works have been collected from the different sources

(Geological Survey of Denmark and Greenland, the

county of Vestsjælland and the respective water

works). For the model calibration and validation,

time series of piezometric heads have been obtained

for 19 observation wells, some of which are equipped

with multilevel screens from different geological

layers. These data were collected from the same

sources as the abstraction data.

4.4. Soil characteristics for matrix and macropore

Four soil types were found to represent the Bjerge

A catchment, comprising three mineral soils and one

organic soil Soil 1 (Loamy sand) covers 16% of the

model area, Soil 2 (Sandy loam) covers 74%, Soil 3

(Loam) covers 5%, and Soil 4 (Organic) covers 5% of

the area.

The hydraulic parameters used for characterisation

of the dominating soil type (Soil 2) originate from


intact soil samples collected just north of the Bjerge A

catchment and measured at the Danish Institute of

Agricultural Sciences, Research Station Flakkebjerg.

Parameters for Soil 1 and Soil 3 were obtained from

similar Danish soil types reported in Jacobsen (1989)

and parameters for the organic soil were obtained

from a European database (Wosten et al., 1998).

Matrix characteristics in terms of retention

curves were fitted to a modified Campbell function

(Campbell, 1974; Smith, 1992). The hydraulic

Fig. 4. Cross-section of the 3-dimentional interpreted geology of the area including some boreholes. The location of the cross-section is shown

as A–A in Fig. 3.

Fig. 3. The Bjerge A and Øllemose Rende catchment areas as defined by their topographical divides, the Frankerup area and the location of the

key hydrological stations and well sites.


conductivity function was calculated according to

Burdine (1952). Table 1 shows the parameter values.

Simulations were made both with and without

macropore flow included to test the importance of this

process. As no data were available describing the

macropore systems in the soils, parameters for the

macropore model were estimated from experiences

obtained in other studies. The macropore system was

assumed to consist of biopores (worm and root

channels) beginning just below the plough layer and

ending at 1.5 m depth. The macroporosity was

assumed to decrease with depth with a porosity of

2 volumetric percent in the upper layers. The water

transfer coefficient ðbmpÞ governing water exchange

flow between matrix and macropores was selected in

order to represent a soil with approximately 11 cm

between macropores (half aggregate length ¼ 5.5

cm). The threshold value for initiation of macropore

flow ðctÞ was selected to 215 cm. These parameter

values are within the ranges recommended for the

corresponding MACRO parameters ASCALE (half

aggregate length) and CTEN ðctÞ in other studies

(Dubus and Brown, 2002; Beulke et al., 2002; Boesten

et al., 2000) as well as with parameterisation

experience in similar Danish soils (Styczen, 2002).

The saturated hydraulic conductivities were only

measured for the bulk soil samples. In order to

seperate the conductivities in matrix and macropore

values and ensure that the total saturated hydraulic

conductivity was similar in simulations with and

without macropores the saturated conductivities

shown in Table 1 were calculated as follows:

Ks;matrix ¼ Ks;bulk

us;bulk 2 us;mp

us;bulk

! 21=b

þ3

� �ð9Þ

Table 1

Hydraulic parameters for the four soil types

Soil characteristics Bulk characteristics Macropore characteristics Matrix characteristics

Soil name Depth below

ground surface

(m)

us;bulk

(–)

Ks;bulk

(m/s)

us;mp

(–)

Ks;mp

(m/s)

ct

(m)

bmp

(m22)

us;matrix

(–)

Ks;matrix

(m/s)

Campbel–

Burdine

parameters

b Hb (m)

Soil 1 loamy

sand

0–0.15 0.41 1.7 £ 1025 0 – – – 0.41 1.7 £ 1025 7.9 0.046

0.15–0.2 0.41 1.7 £ 1025 0.02 1.0 £ 1025 20.15 300 0.39 6.7 £ 10206 7.9 0.046

0.2–0.3 0.41 5.5 £ 1026 0.02 2.8 £ 1026 20.15 300 0.39 2.7 £ 1026 5.5 0.027

0.3–0.7 0.41 5.5 £ 1025 0.02 2.8 £ 1025 20.15 300 0.39 2.7 £ 1025 5.5 0.027

0.7–1.4 0.33 7.1 £ 1026 0.01 3.2 £ 1026 20.15 300 0.32 3.8 £ 1026 8.3 0.044

1.4–1.8 0.33 7.1 £ 1026 0 – – – 0.33 7.1 £ 1026 8.3 0.044

Soil 2 Sandy

Loam

0–0.15 0.47 6.0 £ 1026 0 – – – 0.47 6.0 £ 1026 8.7 0.026

0.15–0.2 0.47 6.0 £ 1026 0.02 3.5 £ 1026 20.15 300 0.45 2.5 £ 1026 8.7 0.026

0.2–0.3 0.36 1.0 £ 1027 0.02 7.2 £ 1028 20.15 300 0.34 2.8 £ 1028 9.5 0.064

0.3–0.7 0.38 1.0 £ 1026 0.02 7.4 £ 1027 20.15 300 0.36 2.6 £ 1027 11.0 0.079

0.7–1.4 0.35 5.0 £ 1027 0.01 2.6 £ 1027 20.15 300 0.34 2.4 £ 1027 11.3 0.094

1.4–1.8 0.32 1.0 £ 1027 0 – – – 0.32 1.0 £ 1027 12.6 0.149

Soil 3 Loam 0–0.15 0.36 6.2 £ 1026 0 – – – 0.36 6.2 £ 1026 12.0 0.050

0.15–0.2 0.36 6.2 £ 1026 0.02 4.9 £ 1026 20.15 300 0.34 1.3 £ 1026 12.0 0.050

0.2–0.3 0.40 1.9 £ 1026 0.02 1.3 £ 1026 20.15 300 0.38 5.8 £ 1027 10.0 0.070

0.3–0.7 0.40 1.9 £ 1025 0.02 1.3 £ 1025 20.15 300 0.38 5.8 £ 1026 10.0 0.070

0.7–1.4 0.40 1.5 £ 1026 0.01 7.9 £ 1027 20.15 300 0.39 6.8 £ 1027 13.6 0.140

1.4–1.8 0.40 1.5 £ 1026 0 – – – 0.40 1.5 £ 1026 13.6 0.140

Organic soil 0–1.8 0.77 9.3 £ 1027 0 – – – 0.77 9.3 £ 1027 5.7 0.300


Ks;mp ¼ Ks;bulk 2 Ks;matrix ð10Þ

where

Ks;matrix saturated hydraulic conductivity for the

matrix

Ks;mp saturated hydraulic conductivity for the

macropores

Ks;bulk bulk saturated hydraulic conductivity,

measured

us;bulk soil porosity

us;mp macroporosity

This approach can be questioned. A more

commonly accepted approach for catchment and

regional scale applications, where the availability of

measured hydraulic conductivity inevitably is

limited, is to use pedotransfer functions such as

Jarvis et al. (2002) where matrix conductivity is

estimated from soil texture. A comparison of results

from our approach (Eq. (9)) and the two pedotransfer

functions recommended by Jarvis et al. (2002) is

given in Table 2 for the dominant soil type in our

catchment. The two pedotransfer functions, which are

not recommended for arable topsoils, estimate the

hydraulic conductivity at a pressure head of—10 cm,

K10: Table 2 reveals that the pedotransfer functions

and our approach give conductivities of the same

order of magnitude. The main difference is that the

conductivities estimated by the pedotransfer func-

tions show a smaller variation through the profile

than the values from our approach, where the value in

the plough layer (20–30 cm) is significantly smaller

than the values for the other horizons. As the lower

value for the plough layer is believed to be a

consequence of soil structure (compaction) it is not

reflected in the soil texture and can hence not be

explained by the pedotransfer functions. Field studies

from a Danish site with similar soil and climate

conditions and with similar tillage practise showed

that the macropore flow is generated at the interface

to the plough layer (Petersen et al., 1997). We find it

essential to describe the macropore flow generation

mechanism as correctly as possible in the model, and

we therefore think that our approach (Eq. (9)) is

justifiable in the present case. On the other hand it

must be emphasised that Eq. (9), due to its empirical

basis, should not be used in other cases without

adequate support from field data

4.5. Land use

Information on land use was retrieved from the

Corine database 95% of the area is covered by

farmland, 3% by permanent grass, while forest and

urban (paved) areas each cover 1%. The dominating

agricultural crop was winter wheat that in average

covers 32% of the area (Landbrugsstatistik, 1995).

For the modelling of the Bjerge A catchment, the

entire agricultural area was assumed to be covered by

a standard winter cereal. For the more detailed

modelling of the Øllemose Rende catchment, the

crop rotations actually used in the Frankerup areas

have explicitly been simulated. The data on the crop

rotations were obtained from the farmers and the

agricultural extension service.

4.6. Climate data

Time series of daily measurements of global

radiation, mean air temperature, precipitation, and

potential evapotranspiration were provided by the

Danish Institute of Agricultural Sciences, Research

Station Flakkebjerg The daily values were distributed

uniformly within the day. The precipitation data were

corrected for wind effect and wetting according to

guidelines from the Danish Meteorological Institute

(Allerup et al., 1998). The potential evapotranspira-

tion was calculated from a modified Penman formula

(Mikkelsen and Olesen, 1991).

5. Calibration and validation of catchment model

The model calibration was carried out for the

period 1990–1996. A manual trial-and-error method

Table 2

Comparison of matrix conductivity estimated from pedotransfer

functions (Jarvis et al., 2002) and from Eq. (9) for Soil 2

Depth

horizon (m)

K10 (mm/h)

(Jarvis et al.,

2002; Eq. (4))

K10 (mm/h)

(Jarvis et al.,

2002; Eq. (6))

Ks;matrix (mm/h)

(This study,

Table 1)

0.2–0.3 0.30 0.73 0.10

0.3–0.7 0.23 0.49 0.94

0.7–1.4 0.29 0.70 0.86

1.4–1.8 0.37 1.02 0.36


was used and the goodness of the simulations was

assessed from visual inspections of the simulated

versus observed discharge hydrographs at the two

gauging stations and of groundwater level heads at the

observation wells. The parameters assessed through

calibration were the hydraulic conductivities and

storage coefficients of the six geological layers

(Table 3).

Examples of calibration results are shown for a two

year period with respect to catchment discharge at

Bjerge A and three selected observations wells with

filters in the three aquifers (Fig. 5). From the figure it

appears that the average level both with regard to

runoff and groundwater heads are reasonably well

simulated, while the model only partially describes

the dynamics of the annual fluctuations of the

groundwater system.

Subsequently, a split-sample validation test was

carried out on the basis of data from the period 1986–

89, where only discharge data (no groundwater head

data) were available. Two key numerical performance

statistics are shown in Table 4 both for the calibration

and the validation periods. It is seen that the average

discharge is simulated quite well during the cali-

bration period and even slightly better during the

validation period. The hydrograph dynamics, as

reflected by the Nash-Sutcliffe criteria for model

efficiency (Nash and Shutcliff, 1970) on the other

hand shows less accurate simulation during the

validation period as compared to the calibration.

In order to obtain an indication of the capability of

the model to simulate the stream-aquifer interaction, a

few field measurements of discharge were made in the

Øllemose Rende system during the low flow season of

1998. The field data showed low flows in the order of

2–4 l/s in the Frankerup area, where the northern

tributary joins Øllemose Rende (Fig. 3). The model

was not run for the same period, but the low flows

simulated throughout the simulation period at this

location were in the order of 1 l/s. Hence this

independent test suggests that the low flow simu-

lations, and thus the baseflow contributions originat-

ing from the deeper aquifers, are simulated at the right

order of magnitude.

On the basis of the validation tests, the model can

be claimed valid for simulation of discharge with the

given accuracy level. Although groundwater head

observations were not available for the validation

period it is likely that the accuracies are similar, or

slightly poorer, than those obtained during the

calibration period. Due to lack of data it has not

been possible to validate the model with respect to the

internal flow variables such as simulations of macro-

pore flows or the individual flow components that

constitute the water balance. Hence, except from

noting that nothing in the limited validation tests

actually conducted suggests completely wrong

interpretations of these internal variables, it must be

emphasised that it is not possible to prove any model

validity for them.

6. Simulation results from catchment scale

6.1. Water balance and groundwater depths

and recharges

The flow regime simulated by the model is

illustrated for the Bjerge A catchment in Fig. 6 as

average figures for the period May 1987 to May 1995.

The period was selected so that the storage changes in

the unsaturated zones as well as in the two aquifers

Table 3

Hydraulic parameter values for the six geological layers assessed through calibration

Geological

layer

Material Horisontal hydraulic

conductivity (m/s)

Vertical hydraulic

conductivity (m/s)

Specific storage

coefficient (1/m)

Specific yield

(–)

Groundwater

abstraction

1 Till 1 £ 1027 1 £ 1028 0.0001 0.005

2 Sand 5 £ 1025 5 £ 1026 0.0001 0.005

3 Till 1 £ 1026 2 £ 1028 0.0001 0.02

4 Sand 1 £ 1024 1 £ 1025 0.0001 0.02 Yes

5 Till 2 £ 1027 2 £ 1028 0.0001 0.02

6 Limestone 2 £ 1025 2 2 £ 1024 2 £ 1026 2 2 £ 1025 0.0001 0.02 Yes


were negligible. The net percolation out of the root

zone ( ¼ upper till unit in Fig. 4) is seen to be

244 mm/year of which 196 mm/year runs through the

drains to the river system, while 48 mm/year

recharges the upper sandy aquifer. The upper aquifer

is seen to interact considerably with the lower two

aquifers, which in Fig. 6 are aggregated into one unit.

The total abstraction directly from the area is 16 mm/

year, while the groundwater flow across the catchment

boundaries totals 25 mm/year. The significant bound-

ary flows take place over the fixed head boundary near

the river outlet and is directed towards the ground-

water abstraction wells located just outside

the boundary (Fig. 3). Such large boundary flow

may be critical for simulating reliable flow conditions

Table 4

Model performance statistics for simulation of catchment discharge

during the calibration and validation periods

Average discharge

% deviation

Model efficiency on

15-days basis Nash–

Sutcliffe criteria ðR2Þ

Calibration period

(1990–96)

25 0.80

Validation period

(1986–89)

1 0.71

Fig. 5. Discharge hydrograph from station 56.10 and selected

hydraulic heads for the three aquifer layers from two years of the

calibration period. The location of the observation wells and the

discharge station are shown in Fig. 3. Fig. 6. The total water balance for the Bjerge A catchment as

simulated during the period May 1987 to May 1995. All figures are

averages over the eight years period (mm/year). The two upper

layers shown on the figure correspond to the upper till unit and

the upper sandy aquifer of Fig. 4, while the lower layer shows the

aggregated water balance for the lower sandy aquifer and the

limestone.


for areas close to the boundary. However, as the

focus of the present study is primarily the small

Frankerup area and secondarily the Øllemose Rende

catchment, both located at significant distances from

the boundary, the importance of the uncertainties

generated by the critical boundary conditions are not

believed to be very significant. This is particularly the

case, because the macropore flow does not depend

on groundwater flows, but only on the groundwater

heads.

Macropore flow is, according to the above process

description, mainly governed by soil moisture con-

ditions in the root zone, which in case of shallow

groundwater table with upwards capillary flux is

influenced by the depth to the groundwater table.

(Fig. 7) shows average figures for the period 1990–

1996 for the depth to the ground water table in

the Frankerup area together with the split of

groundwater recharge into flows directly through

macropores and flows reaching the groundwater table

through the soil matrix. According to the model, the

average depth to groundwater table varies between

1 m and 3 m over the area. This is mainly governed by

the variation in topography and the location of the

river. The minimum depth of 1 m is due to the

existence of artificial tile drains at that depth. The total

recharge varies between 200 mm/year and 300 mm/

year. This spatial variation is caused partly by

differences in actual evapotranspiration between the

different crops and partly by differences in the depth

to the groundwater table causing differences in the

rate of upwards capillary flux from the shallow

groundwater table to the root zone. The recharge

that enters the groundwater storage directly through

the macropores are seen to be small, but with a

relatively large variation, between 0.1 mm/year and

1.3 mm/year.

6.2. Macropore flows at plot scales within catchment

To illustrate the flow processes and the macro-

pore dynamics, results for a two years period from

two selected calculational grid points (soil columns)

are shown in Fig. 8. The precipitation and recharge

values are aggregated to monthly values in the

figure while the water content in the macropores are

shown as average weekly values. The two grid

points are located within the Frankerup area on a hill

and in the valley close to the river, respectively. As

can be seen from the figure, the conditions at the

two grid points differ significantly with respect to

depth to groundwater table and as a result of this

also with respect to groundwater recharge and soil

moisture conditions. At the hill site, the groundwater

table varies between 1 m and 4.5 m depth. At the

valley site, the groundwater table is at the depth of

the tile drains (1 m) most of the years with a

decrease of only 0.5 2 1 m during the dry periods.

Fig. 7. The spatial variability of groundwater recharge and the depth

to the upper groundwater table for the Frankerup area as simulated

during the period 1990–96.


Fig. 8. Simulation results for two soil columns at the Frankerup area during 1993–94. The two columns are located on a hill site (results to the

left) and in the valley close to the stream (results to the right), respectively.


Thus, the shallow groundwater table at the valley

site is seen to cause significantly higher rate of

upwards capillary flow during the summer season as

compared to the site on the hill.

The macropores are seen to contain water fre-

quently during the two years period. All the macro-

pore events are generated by high water content at

20–30 cm depth. Both locations have soil type 2

(Table 1), which is characterised by a decrease of

saturated hydraulic conductivity by two orders of

magnitude due to a plough pan at this depth. It is

furthermore noticed that for both sites, all the

macropore flux generated at this depth returns to the

soil matrix before it reaches the groundwater table.

In Fig. 9, the distribution over the Frankerup area of

macropore flows at different depths are shown as

average values for the period 1990–96. In accordance

with the results shown in Fig. 8, Fig. 9 substantiates

that macropore flow is predominantly generated in the

upper part of the profile and that almost all the

macropore flow is diverted back to the soil matrix

through diffusion before the water reaches the ground

water table. While the macropore flow that directly

recharges the groundwater is less than 0.5% of the total

groundwater recharge (Fig. 7), the amount of macro-

pore flow at 30 cm depth is more than two orders of

magnitude larger. Thus, of the macropore flow of about

170 mm/year at 30 cm depth, there is a net ‘loss’ of

about 80% before the water reaches 50 cm depth and of

about 98% before 100 cm depth. This clearly shows

that macropore flow has a very significant effect in

terms of rapidly transporting some water downwards in

the soil profile. According to the parameterisation

chosen here the transport distance in the macropores is

typically between 20 and 80 cm.

6.3. Effects of macropore flows on catchment response

An assessment of the effect of macropore flow on

the catchment response in terms of river discharge and

groundwater heads have been made by comparing

results from two model simulations with and without

macropores, respectively The results (not shown here)

showed that the effect of macropores on both

discharge and groundwater heads were negligible

with differences generally much less than one percent

of the natural variation.

6.4. Effects of macropore transport on

catchment scale

In order to assess the importance of the macropore

flow processes on the transport of solutes at catchment

scale, model simulations were conducted as follows

for the Frankerup area In order to focus on macropore

effects and eliminate the effects of rotating crops and

associated varying pesticide applications, the entire

area was assumed to be covered by the same crop,

namely winter wheat. A tracer was applied uniformly

over the area at a time in the autumn when pesticide is

typically applied and with application rates corre-

sponding to a typical autumn applied herbicide. The

tracer was applied once and the effects over the

subsequent years were simulated by the model. In

order to investigate the effects of different climate

conditions around the time of tracer application

simulations were conducted for tracer applications

in three different years, 1990, 1991 and 1992. The

simulation period was in all cases 1990–1996.

The tracer simulations were carried out for two

alternative tracers, namely a conservative non-reac-

tive tracer, and a reactive tracer (hypothetical

pesticide) with sorption and degradation parameters

as given in Table 5. The simulations were carried out

for two alternative conditions with respect to macro-

pores, namely one simulation with macropores and

another simulation without macropores (i.e. only

matrix flow).

Summary results from the simulations with respect

to fate of the tracers by the end of the simulation

period are shown in Table 6 in terms of accumulatedFig. 9. The distribution of macropore flow at different depths over

the Frankerup area as simulated during the period 1990–96.


mass fluxes and total mass balances. The tracer is

applied as a pesticide, i.e. it is assumed to be sprayed

on the leaves of the crop. The fate of the tracer in the

canopy in terms of storage, degradation and through-

fall to the soil surface is calculated by the model and

results in different throughfall rates for the three years.

Therefore, in spite of the same application rate of

500 g/ha over the entire catchment (97 grids £ 125

m £ 125 m) ¼ .75.8 kg for all three years, the fluxes

into the soil varied and were approximately 75.8, 61.9

and 64.8 kg for the three respective years.

For the conservative tracer, the differences

between the macropore and the no-macropore simu-

lations are small. The amounts of tracer that reached

the groundwater by the end of the simulation period

are approximately 67, 65 and 63% of the total tracer

inputs for the three respective application years. The

remaining amount of tracer is still retained in the

unsaturated zone at the end of the period.

The pesticide is seen to behave significantly

different in several respects. First of all, almost all

the applied amount is sorbed and degraded in the

unsaturated zone with the result that the fractions of

tracer reaching the groundwater are in the order of

1026–1023. Secondly, the differences between the

macropore and the no-macropore simulations are

significant. Thirdly, the differences among the years

are very significant. For one of the application years

(1990) the effects of the macropores are approxi-

mately a doubling of the leaching to the groundwater,

while the leaching for the two other years are

increased by factors 4 and 8, respectively. This

difference can be explained with differences in

climatic conditions and hence in macropore activities

in the weeks following the tracer application for the

three respective years.

In Table 6, a mass balance measure is calculated as

an indicator of the numerical accuracy of the

calculations. The mass balance error is simply

calculated as the input at the soil surface minus the

outgoing flux to streams minus the degradation and

sorption in the unsaturated and saturated zones minus

the storages in the unsaturated and saturated zones.

For the conservative tracer, the mass balance errors

are between 0.6 and 1.1 g, which is negligible

compared to the flux values. For the pesticide, the

mass balance errors are between 0.0 and 0.5 g, which

is negligible relative to the input at the soil surface,

but in some cases of the same order of magnitude as

the calculated flux to the saturated zone. This implies

that absolute figures of the calculated mass in the

saturated zone must be taken with reservation due to

uncertainty in the basic numerical calculations. In this

context it may be noted, however, that the uncertainty

resulting from uncertainty of the assessed sorption and

degradation parameters is significantly larger than the

errors in the numerical calculations.

The variations within the Frankerup area of the

pesticide flux at 100 cm depth are illustrated in Fig. 10

for the three application years and for the situations

with and without macropores. It should be noticed that

the y-axis is logarithmic. The significant differences

among the three years clearly appear from this figure,

with 1992 being the year generating the largest

amount of leaching to the saturated zone and 1991

being the year with the lowest leaching and without

effects of macropores. The variation across the

catchment is significant. Thus, for the 1992 appli-

cation, the variation over the catchment for the

macropore simulation is between 2 and 61 mg/ha.

And even for the 90% of the area generating leaching

closest to the average conditions, the range is from 8

to 60 mg/ha, i.e. a factor of 7.5. It is noted that the

variation over the catchment is the same for

simulations with and without macropores.

7. Discussion and conclusions

A spatially distributed model code capable of

describing macropore flow and transport processes at

Table 5

Parameter values for description of degradation and sorption for the

simulation with hypothetical pesticide

Parameter Value

Degradation rate, T 1

2

0–1 m depth 29 days (at 10 8C)

Below 1 m depth No degradation (cm3/g)

Sorption distribution coefficient, Kd (linear equilibrium) (cm)

Unsaturated zone, 0–20 1.174

Unsaturated zone, 20–70 0.294

Unsaturated zone, 70–150

Unsaturated zone, below 150 0.059

Saturated zone 0.029


Table 6

Mass balance elements for numerical simulations with three different years of tracer application, two macropore conditions and two different tracers. The fluxes are accumulated

over the entire catchment (151.5625 ha) and the seven years simulation period (1990–96) and the mass storages are status by the end of 1996

Conservative tracer Reactive tracer (hypothetical pesticide)

No macropores Macropores No macropores Macropores

1990 1991 1992 1990 1991 1992 1990 1991 1992 1990 1991 1992

Mass fluxes accumulated

over period (g)

Input to soil surface 75781 61876 64804 75781 61931 64458 75781 61878 64808 75781 61932 64462

Flux from soil matrix

to macropores

0 0 0 116 110 108 0.00 0.00 0.00 0.00 0.00 0.03

Flux from soil matrix

to saturated zone

53892 42069 42452 55256 43335 43661 0.47 0.23 4.15 1.02 0.91 33.88

Flux from macropores

to saturated zone

0 0 0 116 110 108 0.00 0.00 0.00 0.00 0.00 0.04

Flux from saturated

zones to stream

47497 36080 35510 48386 36848 36089 0.41 0.19 3.27 0.87 0.76 27.26

Uptake by vegetation 319 265 280 179 149 157 0.00 0.00 0.03 0.00 0.00 0.05

Degradation in

unsaturated zone

0 0 0 0 0 0 10394 8071 9369 10543 8323 9397

Sorption in unsaturated

zone

0 0 0 0 0 0 65388 53808 55439 65239 53610 55073

Degradation in

saturated zone

0 0 0 0 0 0 0.01 0.00 0.06 0.02 0.02 0.56

Sorption in saturated

zone

0 0 0 0 0 0 0.79 0.32 5.21 1.67 1.50 50.53

Mass storage by end

of period (g)

Storage in unsaturated

zone

21570 19542 22072 20230 18336 20532 0.09 0.05 1.42 0.19 0.19 9.00

Storage in saturated

zone

6396 5990 6943 6987 6599 7681 0.06 0.03 0.82 0.12 0.14 6.10

Mass balance errors

in calculations

Mass balance error (g) 20.76 20.59 20.85 21.11 20.69 20.84 0.12 20.34 20.22 20.54 0.27 20.03

Error relative to input

to soil surface

20.00001 20.00001 20.00001 20.00001 20.00001 20.00001 0.00000 20.00001 0.00000 20.00001 0.00000 0.00000

Error relative to net

flux to saturated zone

0.00 0.00 0.00 0.00 0.00 0.00 0.26 21.50 20.05 20.53 0.30 0.00

J.S.

Ch

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53

a catchment scale has been developed within the

framework of the coupled MIKE SHE/Daisy code.

The adopted macropore formulation has many

conceptual similarities to the principles behind the

well tested MACRO code, but it differs in some

important aspects. Most importantly, the water

exchange between the two pore regions (Eq. (4)) is

driven by the product of the matrix conductivity and

the pressure head difference between the pore regions,

while the approach in MACRO is based on an

approximation to the water diffusion equation. In the

existing dual-permeability model codes a variety of

approaches exist for describing the water exchange

between the two domains, and an accurate description

is recognised as a great challenge (Simunek et al.,

2003). As we have had no detailed field data to check

our formulation we cannot document that our

approach is better than other existing ones. Further-

more, the numerical formulation in our code is

different from that in the MACRO by being based

on an explicit algorithm. Our algorithm is quite fast

and mass conserving, but we have not made direct

comparison tests with MACRO or other codes.

The MIKE SHE/Daisy model was then set up for a

small catchment. The model was subject to calibration

and validation tests against discharge and ground-

water levels corresponding to standard procedures in

catchment modelling. As no field data exists for

internal variables such as macropore flow, the model’s

capability to correctly simulate macropore processes

at the catchment scale could not be documented.

The simulation results designed to investigate the

importance of macropore processes at catchment scale

can therefore not be claimed as valid, but should

rather be seen as outputs from a numerical exper-

iment. Hence, in order to confirm the findings from

the present study it will be required to have support

from dedicated field data.

There are several important sources of uncertainty

related to using a model with macropore formulations

at a catchment scale as in the present study. The most

important source is related to assessment of macropore

parameters, in particular the exchange coefficient,b; or

the related diffusion length governing the exchange of

water and solutes between macropores and matrix. In

addition, soil characteristics are known to exhibit large

spatial variations at catchment scale, but soil data in

terms of soil texture, soil structure and hydraulic

parameters will only be available for representative

soils. Simple extrapolation of such data to similar soils

in the area may not be valid with regard to

representation of macropores, because other factors

such as the management history of a particular soil

(cropping and tillage practice) has major impact on

frequency and extent of macropores (Edwards et al.,

1990; Caron et al., 1996). Another critical assumption

is the estimation of matrix hydraulic conductivity. As

field data are seldom (or never) available at catchment

scale pedotransfer functions such as the ones rec-

ommended by Jarvis et al. (2002) are often used. In

order to preserve the vertical variation in conductivity

with a low value in the plough pan we have instead used

an empirical approach based on an estimation of matrix

hydraulic conductivity from measured bulk hydraulic

conductivity. Based on past Danish field studies

(Petersen et al., 1997) we have argued that this is

likely to provide a more realistic description of the

macropore generation process in our particular case.

However, because this approach is empirical without a

sound theoretical basis, one should generally be

cautious about its use and it should not be applied in

other areas without support from field data.

We have used daily rainfall data and distributed the

rainfall evenly over the day. This approach is

definitely not applicable in many hydrological

regimes where overland flow is common and macro-

pore flow is generated due to saturation of the top soil.

However, in our case the principal macropore

Fig. 10. The spatial variability of the accumulated flux of pesticide

at 100 cm depth as simulated for the Frankerup area during the

period 1990–1996 with three alternative years of pesticide

application and with, respectively without, macropores included

in the model simulations.


generation mechanism is related to saturation above

the low permeable plough pan at 20–30 cm depth.

Due to the soil moisture storage in the upper 20 cm, it

is rather the volume than the intensity of rainfall that

is important. A sensitivity analysis, where we

distributed the daily rainfall over two hours instead

of 24 hours, showed that the effect of the rainfall

intensity was small for the total amount of macropore

flow and had no impacts for the spatial variation of

macropore flow over the catchment. This is supported

by the field tracer experiments reported by Gjetter-

mann et al. (1997) who found that application of

25 mm Brilliant Blue dye tracer with intensities

varying from 3.1 to 25 mm/h resulted in macropore

flow generated above the plough pan in all cases.

The simulation results show that the macropore

processes, as they are formulated in the model for the

particular catchment, has the primary function of

rapidly transporting a significant part of the water (and

solute) from the plough pan at 20 cm depth to a depth

of 40–100 cm, where most of it flows back into the

soil matrix. Only a minor part of the macropore flow

reaches the groundwater table directly through the

macropores. It must be emphasised that we have no

specific field data to support these findings. Therefore,

we do not claim that the depths and amounts of flow in

the macropores are correct, but rather that the process

equations of the MACRO and similar codes using

typical parameter values generate such results for our

conditions. Other field studies (Villholth et al., 1998;

Nilsson et al., 2001) in similar soils and climate

suggest that the biopores in the upper soil layers are

connected with geologically generated fractures in the

deeper layers so that the combined macropore-

fracture system is able to transport tracers signifi-

cantly deeper than found in the present study.

This indicates that either the macropore parameter

values used in the present case or the process

equations may not be fully adequate for catchment

scale application.

The present study suggests that the macropore

processes appear to have only negligible effects on the

discharge and groundwater levels. This is interesting

when comparing with other catchment modelling

studies using similar distributed physically based

models (Refsgaard and Hansen, 1982; Overgaard,

2000). They report that, in order to simulate the

discharge hydrographs properly and in particular

the early peaks in the autumn after the dry summer

period, a significant part of the infiltration through the

root zone has to be routed through a fast track

bypassing the lower part of the root zone. These

hydrograph peaks are simulated quite well in our case

(Fig. 5). The reason for the necessity of introducing

the so-called bypass flow in catchment modelling is

the need to account for the spatial variability of soil

hydraulic properties, root zone depth, vegetation

types, climate input, etc. within large computational

grids (Refsgaard and Hansen, 1982; Overgaard,

2000). This is apparently not required in our case

study, where the grid size is relatively small. In any

case, our results indicate that the small scale

macropore flow processes, included in our case,

can not provide the same effects on simulated

hydrographs as the bypass flows that can be

considered a large scale phenomena.

In spite of the fact that macropore flow thus is not a

dominating process for simulation of discharge at

catchment scale, the simulation results suggest that it

has a very significant effect on the leaching of

pesticides from the surface to the groundwater table,

because some of the pesticides are transported rapidly

downwards in the soil profile to zones with less

sorption and degradation. This is in agreement with

the conclusions of Simunek et al. (2003).

An important finding from the study is the apparent

erratic nature of the macropore processes. The

generation of macropore flows depends in a very

complex manner on both the soil characteristics and

the hydrological regime. Investigation of the simu-

lation results suggests that it is not possible before-

hand to identify which rainfall events generate the

highest macropore flows and as such posses the

largest potential for pesticide leaching. The large

variations of macropore transport among the three

years of simulated tracer application show that three

different years of tracer applications are not sufficient

to estimate neither the average importance of the

macropore transport nor the average pesticide leach-

ing to groundwater.

Furthermore, the simulation results show a con-

siderable spatial variation of macropore flows and

transport throughout a catchment. Thus, the variation

of pesticide leaching to the groundwater varies in the

simulations with a factor of 30 over the catchment and

a factor of 7.5 within the 90% of the catchment, where


the leaching is closest to the median value. This

spatial variation is not caused or increased by the

macropore processes. It is simulated alone as a

consequence of variations in topography, depth to

groundwater table and distance to streams. In the

actual field situation the variation in pesticide

leaching will be significantly larger, because spatial

variations in soil physical and chemical properties and

vegetation parameters will also play a significant role.

The key finding of the present study that macro-

pore flow is highly depending on depth to ground-

water table is supported by Haria et al. (2003), who

from two field experiments on sites with deep and

shallow water tables, respectively, found that prefer-

ential flow only occurred at the site with shallow

water table. Haria et al. (2003) explained this finding

by the importance of the capillary fringe in sustaining

a higher moisture content in the unsaturated zone at

the shallow groundwater site.

The absolute figures on amount of leaching and

quantities of flow in macropores should be taken with

reservation. In order to assess this, the analysis should

be supplemented by thorough sensitivity analyses and

preferably also by additional field data to confine the

uncertainty range. However, this need for further

studies, does not disqualify the more general con-

clusions that we are making here on the spatial

variation within a catchment.

An interesting question is how large an error one

would experience by conducting pesticide leaching

simulations on a soil column basis instead of carrying

out catchment simulations. The present study with its

lack of field data and with only one field site cannot

provide the general answer to this question. However,

the simulation results indicate that the variation of

pesticide leaching within a catchment is very signifi-

cant and should be taken into account. Thus, the present

study suggests that results from column simulations

often may not provide pesticide leaching results that

are representative at a catchment scale.

The methodology applied in the present study is

basically an up-scaling methodology, where the

equations and parameter values, previously used

only at point and field scales, through a spatially

distributed approach have been applied for catchment

modelling. In this way it is possible to combine

the knowledge and experience existing at point/field

scale with the other factors, such as topography

and groundwater depth, that is known to be of

importance at catchment scale. Two general con-

clusions emerge from the simulation results: (1) The

point scale macropore processes are not important for

groundwater recharge and discharge at catchment

scale, but are nevertheless dominating processes for

pesticide leaching also at the catchment scale. (2) The

presently adopted up-scaling methodology is signifi-

cantly better than just assuming that the point scale

column simulations are representative for an entire

catchment with respect to simulation of leaching of

pesticides at catchment scale. This methodology can

be implemented by using a comprehensive 3D

catchment model as we have done, but it may be

sufficient to carry out several single column simu-

lations, if the range of columns adequately represents

the spatial and temporal variations of depth to

groundwater throughout the catchment.

Acknowledgements

This work was partly funded through the project

‘Large scale modelling of pesticide transport’ under

the Danish Environmental Research Programme.

Karen Villholth is thanked for giving valuable

comments to the manuscript.

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JH_2004_299_136-158

Documents

small catchment

entire catchment

groundwater table

acatchment scale

groundwater recharge

leaching of pesticides

preferential flow mechanism

modelling of macropore