evaluation of a dual-porosity model to predict field-scale solute transport in a macroporous soil

Evaluation of a dual-porosity model to predict field-scale solutetransport in a macroporous soil

M.H. Larsson*, N.J. Jarvis

Department of Soil Sciences, SLU, Box 7072, 750 07 Uppsala, Sweden

Received 15 December 1997; accepted 30 June 1998

Abstract

A one-year field-scale leaching experiment was conducted on a structured clay soil for the purpose of evaluating the dual-porosity/dual-permeability model MACRO. The model was first calibrated against measurements of water contents, drainflow,and bromide contents in the soil profile and concentrations in drain discharge. Bentazone transport was then simulated withoutany further model calibration. The model gave acceptable predictions of the water balance, providing the significant waterinflow into the plot from the surrounding areas was accounted for. Simulated bromide contents in the soil were, for the mostpart, within one standard deviation of the measured values. Bromide was measured in tile drainage 26 days after spraying atconcentrations. 3 mg l21 (after 43 mm of precipitation), while groundwater concentrations at 2 m depth were as large as10 mg l21 only 42 days after spraying. This is a strong indication of macropore flow. The agreement between model predictionsand bentazone measurements was on the whole good, especially for the depth profiles and the initial breakthrough in thedrainflow, whereas short-term fluctuations in drainage water concentrations were poorly captured. This was probably caused bythe model description of first-order mass-exchange between micro- and macropores, which neglects lateral concentrationgradients. Judging from statistical criteria, the model accurately predicted bentazone amounts in the soil profile (modelefficiency 0.87), while 66% and 89% of the simulated bentazone concentrations in tile drainage were within a factor of 2and 5 of measured values respectively. Simulations run without macropore flow overestimated bentazone leaching by ca. 20%.In other words, macropore flow reduced leaching in this clay soil, because much of the bentazone was ‘protected’ againstbypass flow in macropores, being stored in micropore water moving at a ‘reduced’ convective transport velocity.q 1999Elsevier Science B.V. All rights reserved.

Keywords:Macropore; Solute transport; Model; Evaluation; Field-scale; MACRO

1. Introduction

Field evidence suggests that surface-applied agri-cultural chemicals such as pesticides can be rapidlytransported through the unsaturated zone of soils bypreferential flow, thereby increasing the risk of pollu-tion of surface waters and groundwater (e.g. Isensee etal., 1990; Kladivko et al., 1991; Steenhuis et al., 1994;Harris et al., 1994; Steenhuis et al., 1994; Johnson et

al., 1995). Widely-tested and validated models areuseful to help improve understanding of the complex-ity of flow and transport processes in the unsaturatedzone. They may also be used as tools to analyse andevaluate alternative agricultural and environmentalmanagement strategies to minimize impacts onwater quality.

A number of models that account for preferentialwater flow and solute transport are available (seereview by Jarvis, 1998). Dual-porosity/dual-perme-ability models, characterised by mobile water in two

Journal of Hydrology 215 (1999) 153–171

0022-1694/99/$ - see front matterq 1999 Elsevier Science B.V. All rights reserved.PII: S0022-1694(98)00267-4

* Corresponding author: e-mail: [email protected]

independent, but interacting, pore systems with differ-ent water pressures and solute concentrations (Gerkeand van Genuchten, 1993; Jarvis, 1994), have shownpromise in describing solute transport in macroporoussoils at the soil column or monolith scale (Saxena etal., 1994; Jarvis et al., 1994). However, the accuracyof these models has not been thoroughly tested andevaluated using measurements at the field-scale. It istherefore still uncertain to what extent they can beused with confidence for predictive use as manage-ment tools. Errors in model output occur as a result ofeither (i) model errors, or (ii) parameter errors, includ-ing errors in driving data (Loague and Green, 1991).Thus, in order to reveal the extent of model errors, it isimportant that parameter errors are minimised.Ideally, parameter estimation should be based as faras possible on direct measurements. However, someparameters can be difficult to measure or may onlyhave a vague physical definition, so that model cali-bration may be necessary. Calibration is an iterativeprocess, intended to minimize parameter errors, inwhich model results are compared to measured datauntil a ‘best fit’ is obtained. As some parameters areinterdependent, non-unique parameter sets may result,particularly if the calibration procedure is not highlyconstrained by measurements. Consequently, properevaluation of pesticide leaching models requiresmeasurements of all major components of the massbalance, including state variables (e.g. solute contentsin soil) and complementary flux measurements suchas water samples from tile drainage or lysimeteroutflows. This is especially critical when preferentialsolute transport occurs, since this may not always bedetected by soil core samples because of the largerdetection limits for soil extracts compared to watersamples (Jarvis et al., 1995). Similarly, to minimizethe uncertainty in calibration of parameters related tothe water balance, both soil water contents and waterdischarges should be measured.

The main objectives of this study were to (i) eval-uate the ability of the dual-porosity model MACRO(Jarvis and Larsson, 1998) to describe solute leachingat the field-scale, (ii) use the model to quantify theimpact of preferential flow on solute leaching in astructured clay soil (iii) identify critical processesand parameters governing macropore flow at thissite. To achieve these objectives, model predictionswere compared with measurements of the leaching of

a non-reactive tracer (Br2) and a pesticide (benta-zone) to tile-drains in a clay soil during a one-yearperiod. To illustrate the consequences of macroporeflow for leaching of bentazone, the results obtained byrunning the model in two domains (i.e. with macro-pore flow) are compared with the model output fromone-domain simulations (i.e. without macroporeflow).

2. Model description

The MACRO model is a comprehensive physi-cally-based model describing the water balance,solute transport, and solute transformation processesin the soil/crop system. Driving variables used by themodel consist of hourly measured rainfall, daily maxi-mum and minimum air temperatures, wind speed,vapour pressure, and global radiation. As the modelis presented in detail elsewhere (Jarvis and Larsson,1998), we will give a brief description of the mainfeatures of the model here, and only describe in detailthose parts that are especially relevant for this study.

2.1. Soil water flow and temperature

In MACRO, the soil pore system is partitioned intomicropores and macropores, with the divisionbetween the two flow domains defined by a givenwater potentialcb and a corresponding water contentub, and hydraulic conductivityKb. Micropores andmacropores act as separate flow regions, each charac-terized by a degree of saturation, conductivity, andflux. Vertical water movement in the micropores iscalculated with Richards equation:

2u

2t� 2

2

2zK

2c

2z1 1

� �� 2 Sr ^ Sw �1�

whereu is water content,t is time, z is the verticaldistance,K is the hydraulic conductivityc is the soilwater potential, andSr andSw are sink terms for rootwater uptake and lateral water exchange betweenmicro- and macropores respectively. In the micro-pores, the soil water release characteristicc(u ) isgiven by the Brooks and Corey (1964) function, andthe hydraulic conductivityKmi by Mualem’s (1976)model. Water flow in the macropores is treated as anon-capillary, gravity-driven process, with thehydraulic conductivity in the macroporesKma,

M.H. Larsson, N.J. Jarvis / Journal of Hydrology 215 (1999) 153–171154

expressed as a simple power law expression of thedegree of saturation:

Kmi � KbSn1212=lmi ; Kma� Ks 2 Kb

ÿ �Sn*

ma �2�where Smi and Sma are the effective saturations inmicro- and macropores,l and n are the pore sizedistribution index and tortuosity factor in the micro-pores andn* is an empirical exponent accounting forpore size distribution in the macropores.

Lateral water flow from macro- to microporesSw

(see also equation 1) is described as a first orderapproximation to a reduced form of Richard’s equa-tion that ignores the effect of gravity:

Sw � 3Dwgw

d2

� �ub 2 umi

ÿ � �3�

whered is an ‘effective’ diffusion pathlength,Dw is aneffective water diffusivity,gw is a scaling factor tomatch the approximate and exact solutions to thediffusion problem (van Genuchten, 1985), andumi isthe micropore water content. Water exchange canoccur in the reverse direction if the microporesbecome saturated. Here, any excess water is instanta-neously routed into the macropores. Uptake of waterby roots can take place from both regions, with waterpreferentially extracted from the macropores (Jarvis,1989). The bottom boundary condition used in thisapplication considers a water table located in theprofile. The model deals with saturated lateral seepagefluxes to two different kinds of field drainage systems(i) a primary drainage system located in the soilprofile/field, and (ii) a secondary drainage systemsurrounding the profile/field. In both cases, drainageis described as a sink term in the vertical one-dimen-sional flow equation using seepage potential theoryfor layered soils (Youngs, 1980; Leeds-Harrison etal., 1986). Lateral flow to the secondary drainagesystem is calculated assuming a square-shapeddrainage basin of known area.

Precipitation at the soil surface will be routed intothe macropores if the infiltration capacity of themicropores is exceeded. Depending on the measuredair temperatures, precipitation can be treated as rainand immediately infiltrate or be lost as runoff, or assnow which accumulates at the soil surface. Attemperatures below2 28C all precipitation is treatedas snow, while the fraction of snow decreases linearlyup to 1 28C, at which temperature all precipitation is

treated as rain. The rate of snow melt, which isassumed to begin at temperatures above 08C, dependson the air temperature and a degree-day snow meltfactor. Soil temperatures are calculated from airtemperatures and the physical properties of the soilusing the heat conductivity equation. For snow-freeconditions, the top boundary condition is simplyapproximated by the air temperature, while thebottom boundary condition is calculated from ananalytical solution of the heat conduction equationassuming a sinusoidal variation of temperature at thesoil surface on an annual basis. If a snow cover exists,the temperature at the soil surface is calculated fromthe air temperature and the temperature at the mid-point of the surface soil layer, assuming a constantdensity and heat conductivity of the snow.

2.2. Solute transport and transformations

Solute transport is predicted using the convection–dispersion equation with source/sink terms

PU repre-

senting mass exchange between flow domains, soluteuptake by the crop, lateral leaching losses to drainsand/or groundwater seepage and biodegradation:

2 uC 1 gSÿ �

2t� 2

2zDu

2c2z

2 qc� �

^X

U �4�

where c and s are the solute concentrations in theliquid and solid phases,g is the bulk density,q isthe water flow rate andD is the dispersion coefficient.In the macropores, dispersion is neglected since solutetransport is assumed to be dominated by convection.If the solute under consideration is an anion, a part ofthe micropore volume can be excluded from storageand transport. Solute exchange between macro- andmicropores,Ue is given by a combination of diffusionand convection (Jarvis, 1994):

Ue � 3Deumi

d2

� �cma 2 cmi

ÿ �1 Swc0 �5�

whereDe is the effective diffusion coefficient,cma andcmi are the solute concentrations in the macroporesand the micropores respectively, andc’ indicateseither cma or cmi depending on the direction of thewater flow. The solute concentration in water routedinto the macropores at the soil surface is calculatedassuming instantaneous local equilibrium andcomplete mixing of incoming net rainfall with the

M.H. Larsson, N.J. Jarvis / Journal of Hydrology 215 (1999) 153–171 155

water stored in a shallow surface soil layer or ‘mixingdepth’ (Steenhuis and Walter, 1980).

For reactive solutes, the distribution betweenliquid and solid phases is described as an instan-taneous process and sorption is calculated accord-ing to a Freundlich isotherm. Sorption sites areassumed to be partitioned between macro- andmicropores (van Genuchten and Wierenga, 1976).Solute degradation is predicted in the modelassuming first-order kinetics. Field degradationrate coefficients are predicted from the labora-tory-measured reference values accounting forsoil moisture and temperature effects using simplefunctions (Boesten and van der Linden, 1991).

Solute losses to field drainage systems arecalculated as sink terms to the one-dimensionaltransport equations assuming complete mixing ofsolute in the lateral direction in each soil layer. Toaccount for general groundwater movement, a resi-dence time for the solute in the saturated zone canalso be specified. Depending on the specifiedsolute concentration in the groundwater, this willadd or remove solute from the profile, but notalter the water balance, since water inflow isassumed equal to outflow.

3. Materials and methods

3.1. Site characteristics

The model simulations presented here were basedon a field experiment carried out at the Lanna experi-mental farm, situated in south-west Sweden (lat.588210N, long. 138080E), during a one-year periodfrom October 1994. Lanna is situated on a flat plain,with the slope at the field site less than 1%. The siteconsists of seven experimental plots, each 0.4 ha (95×42 m) in size. In 1935, separate tile drainagesystems were installed at 1 m depth and 13.5 mspacing. A secondary drainage system surroundsthe experimental field with the aim of preventinginflow from the surroundings. The experimentdescribed in this paper was conducted on one ofthese plots, which has been under no-till practicesince 1988, with a crop rotation of spring cerealsand rape. The crop during the 1995 growing seasonwas spring-sown rape.

The soil is classified as a Typic Eutrochrept(U.S.D.A.) Four different layers can be distinguishedwith respect to texture and structure (Table 1). Theclay below 2.2 m depth is normally water saturated,


Fig. 1. Daily maximum and minimum air temperatures (a) and hourly precipitation (b).


Tab

le1

Soi

lphy

sica

lpro

pert

ies

(afte

rB

ergs

tro

¨ met

al.,

1994

)

Dep

thin

terv

al(c

m)

Par

ticle

size

dist

ribut

ion

(%)

Org

anic

carb

onco

nten

tb

(%)

pHS

truc

ture

Cla

y(,

2m

m)

Silt

(2–

60m

m)

San

d(.

60m

m)

0–

3046

.546

.27.

32.

07.

2st

rong

coar

sesu

bang

ular

bloc

ky30

–60

56.1

40.6

3.3

0.8

7.4

stro

ngfin

eto

med

ium

angu

lar

bloc

ky60

–10

060

.637

.42.

00.

37.

4st

rong

coar

sean

gula

rbl

ocky

105

–17

5a66

.630

.52.

90.

2cn.

i.dn.

i.d

aF

rom

(Wik

lert

etal

.,19

83).

bF

rom

(Lin

den

etal

.,19

93).

cE

stim

ated

.d

No

info

rmat

ion.

structureless, with a fluid consistency, while the soil inthe unsaturated zone is characterized by numerouscracks and biotic macropores. At approximately11 m depth, the clay is underlain by a 0.2 m layer ofsandy till on top of the bedrock (Brink and Linde´n,1980).

Meteorological data and soil temperatures atdepths of 5, 10, 20, and 50 cm were recorded atan automatic weather station at the field site. Preci-pitation was measured on an hourly basis, whiledaily mean values of wind speed, air humidity,solar radiation and temperatures were recorded.Precipitation was also measured manually on adaily basis in a sheltered place ca. 50 m from theweather station. As the weather station is placed onan open field, and wind drift has a large influenceon precipitation measurements (Eriksson, 1988) theprecipitation data were corrected according to themanual measurements from the less-exposed raingauge. The daily values of precipitation wereapproximately distributed in proportion to theamounts measured on an hourly basis. For periodsof missing data, precipitation was taken from themanual measurements and distributed assuming arainfall intensity of 3 mm h21. Correction factorsfor precipitation losses owing to wind drift wereset to 1.07 for rain and 1.14 for snow (Jansson,1991).

Fig. 1(a) and (b) shows measured daily airtemperatures and hourly precipitation for the studiedperiod. As can be seen, air temperatures often fluc-tuated around 08C during the winter. The accumu-lated precipitation for the whole period was767 mm.

3.2. Solute application and field measurements

A mixture of ca. 150 l water, 28.1 kg KBr, and1.1 kg of bentazone (3-isopropyl-1H-2,1,3-benzothia-diazin-4[3H]-one-2,2-dioxide) was applied to thebare soil surface of the 0.4 ha plot with a tractor-mounted sprayer on the 18th October 1994. Tomeasure the actual mean amount of Br2 applied andthe spatial variability, 33 aluminium trays, each withan area of 54.7 cm2, were placed on the ground beforespraying. The trays were then rinsed with a fixedvolume of distilled water and the samples were storedat 1 48C until analysis for Br2 concentrations (see

Section 3.3). The measured mean amount of appliedBr2 was 4.44 g m22 with a standard deviation of1.45 g m22 (minimum and maximum values of 1.99and 8.47 g m22 respectively), which should becompared with the nominal applied amount of4.78 g m22. The large variation was probably owingto wind drift, overruns and bare spots. As we wishedto imitate standard agricultural practices in thisexperiment, no extra measures were taken to prevent‘normal’ field variation in applied solute amounts.The applied amount of bentazone (250.8 mg m22)was calculated as the nominal amount sprayed,divided by the ratio between nominally sprayed andrecovered amounts of Br2. It should be noted here thatthis dose of bentazone is much larger than would beapplied in normal agricultural practice.

Tile drain discharge was continuously measuredwith a device in which a float activated a pump-switchand the time and length of each pumping event wasrecorded on a data logger. Comparing all seven plots,significantly larger tile drain discharges weremeasured from the plot used in this study, indicativeof either lateral groundwater inflows from thesurrounding area occurring as a result of failure inthe protective secondary drainage system surroundingthe field, or of local upwardly-directed artesian flows.As this extra inflow of water could not be accountedfor in the model, measured tile-drain discharge fromour plot was divided by 1.43 which was the ratiobetween discharge from our plot and the average ofthe other six plots during the study period.

To measure Br2 and bentazone concentrations intile-drain discharge, flow-proportional samples werecollected using an automatic sampler, and sent to thelaboratory within two weeks, where they were storedfrozen until analysed. Measured solute concentrationsin tile-drain discharge were adjusted to account for theextra inflow of water described above (i.e increasedby a factor 1.43 to account for the presumed dilutioneffect). Groundwater samples for Br2 determinationwere taken at 2 m depth, in a groundwater tubelocated within the plot (described in detail by Berg-strom and Brink, 1986). The tube was pumped dry oneday before sampling.

Randomly distributed undisturbed soil cores weretaken on six occasions (see Table 2) to a depth of90 cm with a motor-driven soil column cylinder (ca.10 cm inner diameter) (Hendrickx et al., 1991). Soil


samples were then taken from within each core at10 cm depth intervals down to 90 cm with small cylin-ders, 203 cm3 in volume (7.2 cm in diameter, 5.0 cmin height). All samples were frozen within 12 h aftersampling and stored frozen until analysed. The risk ofcross-contamination was eliminated, since the outer-most layer of the soil cores was removed beforesampling with the small cylinders.

3.3. Physical and chemical analyses

Soil moisture content and dry bulk density wasmeasured by drying 30–70 g of soil at 1058C for72 h. Measurements of volumetric water content andbulk density were made for all depths, whereas Br2

and bentazone amounts were determined at 0–10 cmdepth and for combined samples at depths of 10–30,30–50, 50–70, and 70–90 cm. To measure back-ground levels of Br2 and bentazone, only one of thereplicate soil cores from the first sampling event (priorto solute application) was analysed. All soil samplesafter application were analysed for Br2, while soilfrom only three sampling events (3,4, and 6) wereanalysed for bentazone.

All soil samples for Br2 analysis were extractedwith 405 g of deionized water for 45 g of field-moistsoil. For practical reasons, two different analyticalmethods were used. For sampling events 1,3,4, and 6,and for all water samples collected from tile drainage,Br2 was analysed using HPLC and an Ag-electrodeaccording to the method described by Lindgren et al.(1995). Bromide in soil extracts from sampling occa-sions 2 and 5, the groundwater samples, and watersamples obtained from aluminium trays following thesolute application, were analysed using a Dionex 2000ion chromatograph. For both methods, the detection

limit for Br 2 in water was 0.1 mg l21, and 1 mg kg21

for Br2 in soil, with recoveries of 73–132%.For bentazone analysis, 50 g of field-moist soil was

extracted with ethanol and 5M NH3 (1701 5 ml), andthereafter hydrolysed and extracted with dichloro-methane (2× 50 ml). Extractive alkylation withpenthafluorobenzyl-bromide was then carried out asdescribed by A˚ kerblom et al. (1990). Apart from theextraction procedures, bentazone in tile-drain watersamples was analysed in the same way. The detectionlimits for bentazone were 0.1mg l21 in water samplesand 2mg kg21 in soil samples.

3.4. Modelling strategy

Simulations were run from 12th October 1994 to30th November 1995. The modelling strategy adoptedwas first to calibrate the model against the fieldmeasurements of water and bromide. Simulationswith bentazone were then made without any furthercalibration. To illustrate the consequences of macro-pore flow for bentazone leaching, simulations werealso performed with the effective diffusion pathlengthd, set to 1 mm to represent one-domain flow. That wehave calibrated for two-domain flow, and not for theone-domain case, effectively implies that we assume atwo-domain pore system to be the best representationof flow processes in this soil. We consider that this is areasonable assumption to make, since one-domainsimulations were not able to reproduce all aspects ofobserved transport behaviour in this soil, althoughthey could be made to fit some.

The fact that the Br2 tracer and bentazone wereapplied simultaneously eliminated potential problemsduring the calibration and validation process whichmay otherwise have arisen owing to temporal varia-tions in macropore properties.


Table 2Dates for solute application, soil sampling events, number of cores and accumulated precipitation after application

Application and sampling events Number of soil cores Date Accumulated precipitation (mm) Days after application

1 9 1994-10-12 2 6application 1994-10-18 0 02 9 1994-11-10 35 233 9 1994-12-15 99 584 11 1995-03-07 240 1405 9 1995-05-18 343 2126 8 1995-09-19 621 336

3.5. Model parameterization

The depth of the soil profile in the model was set to1.75 m, comprising 15 numerical layers. The upper-most numerical layer was set to 1 cm. A thin surfacelayer was found to be necessary in order to match theobserved pattern of Br2 in both soil and tile-drainoutflow. Initial soil temperatures were set accordingto the measurements down to 50 cm depth, and to 98Cin deeper soil layers. Initial water contents were setaccording to measurements to 90 cm depth, and indeeper soil layers calibrated to match the early flowin tile-drains.

Parameters used for soil hydraulic properties in themodel were either measured, taken from the literature,calibrated, or estimated from soil texture, soil struc-ture, bulk density, and organic carbon content usingpedo-transfer functions (Jarvis et al., 1997). Key para-meters are shown in Table 3. Saturated water contentswere estimated from the measured bulk densities,whereas saturated hydraulic conductivity,Ks, wascalibrated against the measured tile-drain discharge.An initial estimate of the boundary conductivity,Kb

(0.1 mm h21 at 2 10 cm pressure head) was obtainedfrom tension infiltrometer measurements made at thesoil surface for the Lanna soil (Jarvis and Messing,1995). To match the observed bromide transport in thesoil profile,Kb at 1–30 cm and 30–60 cm depth wassubsequently increased to 0.3 and 0.2 mm h21 respec-tively (Table 3). This suggests that the hydraulic prop-erties directly measured at the soil surface aresignificantly different to those just underneath. Reduc-tion of hydraulic conductivity at the soil surfaceowing to rainfall impact and surface sealing hasbeen reported by Gimenez et al. (1992), Messing

and Jarvis (1993), and Murphy et al. (1993). Corre-sponding values for the boundary pressure headcb

and water contentub were set according to soilwater retention measurements made with standardsand tables (Wiklert et al., 1983; Jarvis and Messing,1995). The initial values ofd for the different layersbased on visual observations of the soil structure(Table 1) were increased considerably to obtain abetter fit with measured bromide concentrations intile drain discharge. Larged values (i.e. 100 mm)were also required by Saxena et al. (1994) to matchsolute breakthrough curves observed in a lysimeterstudy with Lanna soil. They suggested that organicand clay coatings on the aggregate surfaces mayreduce mass transfer rates between macropores andthe intra-aggregate soil matrix (e.g. Thoma et al.,1992) resulting in large ‘effective’d values.

Parameters affecting water uptake by the springrape crop were tuned to obtain a reasonable agreementwith the soil moisture content profile measured on19th September 1995. Crop emergence and harvesttimes were set according to field observations.

The ‘mixing depth’ was set to 0.1 mm to matchthe bromide concentrations measured in tile drainoutflow during the first month after applicationand the bromide amounts in the uppermost part ofthe soil on the first sampling event after application.Other solute transport parameters were set either toliterature values (e.g. diffusion coefficient) or to thedefault values in the model (e.g. dispersivity�1 cm).

The half-life of bentazone was set to 12.5 days inthe topsoil and effectively infinite in the subsoil basedon measurements made in the Lanna soil reported byBergstrom et al. (1994). The exponent in the


Table 3Soil hydraulic parameters used in the model simulations

Depth interval Ks Kb cb u s ub d l(cm) (mm h21) (mm h21) (cm) (m3 m23) (m3 m23) (mm)

0–30 200 0.1a–0.3 10 0.46–0.48b 0.39–0.41c 150 0.0730–60 50 0.2 10 0.46 0.42 100 0.0560–100 30 0.1 10 0.47 0.45 300 0.05100–175 20 0.1 10 0.47 0.45 300 0.05

a 0.1 mm h21 at 0–1 cm depthb 0.48, 0.47 and 0.46 (m3 m23) at 0–6, 6–12 and 12–30 cm depth respectivelyc 0.41, 0.40 and 0.39 (m3 m23) at 0–6, 6–12 and 12–30 cm depth respectively


Fig. 2. Simulated and measured mean one standard deviation soil water contents.

Freundlich isotherm was set to unity (i.e linear sorp-tion) and the sorption constant in the topsoil (kd value)was set to 0.1 cm3 g21 based on akocvalue of 5cm3 g21(van der Pas, 1994). Sorption in the subsoilwas assumed proportional to soil organic carboncontent (Table 1), resulting in sorption constants of0.04, 0.015, and 0.01 cm3 g21 for layers at 30–60, 60–100, and 100–175 cm depth respectively. On the basisof experience from other studies, the fraction of sorp-tion sites in the macropores was fixed at 0.02. Valuesbetween 0.01 and 0.09 were also examined, but theeffect on bentazone leaching was marginal.

Soil pores draining at soil water pressure heads

smaller or equivalent to2150 mH2O were assumedto be free from Br2 and bentazone owing to anionexclusion. By calibration against the measured soluteconcentrations in tile-drain water and groundwater atlong times, the ‘within-plot’ residence time for solutein groundwater was set to 10 days.

3.6. Model evaluation

In addition to graphical displays of simulated andmeasured results, statistical measures (coefficient ofresidual mass, CRM, and model efficiency, EF) wereused to evaluate the performance of the model, as


Fig. 3. Simulated and measured tile drain discharge rate (a) and accumulated discharge (b).

Table 4Measured mass balance of Br2 with ^ one standard deviation for Br2 in soil in parenthesis

Sampling event and date Accumulated loss todrains (g m22)

Remains in soil (g m22) Unaccounted for (%)

Application 941018 4.44 (3.0–5.9)2 941110 0.001 4.00 (3.4–4.6) 103 941215 0.09 3.19 (2.9–3.5) 264 950307 0.52 1.85 (1.3–2.4) 455 950518 0.84 2.81 (0.7–4.9) 186 950919 1.12 0.97 (0.8–1.1) 53


Fig. 4. Simulated and measured mean one standard deviation Br2 concentrations in soil.

suggested by Loague and Green (1991) :

CRM�PNi�1�Pi 2 Oi�PNi�1

Oi

�6�

EF�PNi�1�Oi 2 O�2 2

PNi�1�Pi 2 Oi�2

PNi�1�Oi 2 O�2

�7�

where Pi and Oi represent predicted and observedpesticide amounts for theith layer respectively, and�O is the mean of the observed amounts. If the totalsolute amount in the soil profile equals that measured,CRM is zero, while negative and positive valuesdemonstrate that the model underpredicts or overpre-dicts solute amounts respectively. The maximum andideal value for EF is 1.0, while a negative value of EFindicates a poor fit, such that model predictions areworse than using the observed mean as an estimate ofthe data points. EF is not a good criteria for judgingthe success of time-series model predictions. Instead,the percentage of simulated values that lay within afactor of 2 and 5 of measured values is used as ameasure of the goodness-of-fit between measuredand simulated bentazone concentrations in tiledrainage.

4. Results and discussion

4.1. Soil water contents and drain discharge

Fig. 2(a)–(e) shows a comparison of simulated andmeasured soil water depth profiles. The model is over-all in good agreement with measured values, withmost estimates within one standard deviation of themeasured mean. During the winter period, themeasured soil water contents changed very little, indi-cating that the soil was effectively at ‘field capacity’for much of the time. On 19th September, 11 daysafter harvest, the standard deviations of the measuredwater contents are considerably larger than on theother sampling occasions, especially below 50 cmdepth (Fig. 2(e)). This is presumably due to significant

spatial variability in root water uptake during thegrowing season.

Drain discharge rates, and accumulated waterdischarges are shown in Fig. 3(a) and (b). Withsome exceptions, the model captures the main featuresof the drainage pattern both with respect to magnitudeand timing of flow events. The simple descriptions ofprecipitation partitioning between snow and rain, andsnowmelt appear to work satisfactorily, consideringthe frequent temperature fluctuations around freezing.However, the model fails to predict one large flowpeak in the middle of January, and another in thebeginning of February. From February to May,discharge is also clearly underpredicted, while themodel overestimates discharge in June (see Fig.3(b)). One reason for these discrepancies may beerrors in the precipitation measurements. TheSwedish Meteorological and Hydrological Institute(SMHI) reports that as a result of wind drift,losses might be underestimated by 2%–17% forrain and 5%–50% for snow (Eriksson, 1988). Anotherlikely reason for some differences is that the correc-tion factor for groundwater inflow, which wasassumed constant for the whole period, should varywith time. Even though soil water contents are some-what underestimated on 19th September (see Fig.2(e)), the simulated tile drain flow in autumn 1995starts too early. It is possible that the crop extractedmore water from the deeper soil layers than the modelpredicted, lowering the groundwater table, and leav-ing the upper part of the soil somewhat wetter.However, somedischarge was recorded from the adja-cent plot in the middle of September, and from yetanother plot in late September (not shown), whichindicates that the simulated timing of the start ofdrainflow in autumn 1995 may be quite reasonable.

4.2. Bromide leaching

Depth profiles of simulated and measured Br2 inthe soil are shown in Fig. 4(a)–(e). For the most part,the model predictions lie within one standard devia-tion of the measured amounts, with a particularlyexcellent fit found for all soil depths on the 15thDecember. However, from the 15th December to 7thMarch, the model slightly overestimates downwardtransport resulting in a somewhat skewed simulatedpulse (Fig. 4(c)). Measured Br2 at depths between 50


and 90 cm on the 18th May showed very large meanconcentrations and high variation. The measured massbalance (see Table 4) also shows that the mean recov-ery rate on this date is much higher than on theprevious sampling occasion. The reason for thisanomaly is not clear. On some occasions, for exampleon 10th November (see Fig. 4(a) at 30–90 cm depth),the model apparently overestimates Br2 contentswhen the measured amounts are close to zero.However, this is probably an artefact and the actualmeasured amount may be significantly larger thanshown, since the detection limit for Br2 in soil wasestimated at 2 g m23.

The simulated profile on 10th November suggeststhat considerable amounts of Br2 had already beenrapidly transported to deeper layers in the soil,completely bypassing the tile drains at 1 m depth.This was confirmed by the measurements of Br2 inthe groundwater at 2 m depth (Fig. 5) which showedpeak values of 10.5 mg 121on 29th November 1994,42 days after spraying. Simulated peak Br2 concen-trations in the macropores at 155–175 cm depth

occurred on 17th November 1994, and were of thesame order of magnitude (3.3 mg l21).

On the 19th September 1995, 336 days after spray-ing, some Br2 was detected in the upper 30 cm of thesoil (Fig. 4(e)) even though no Br2 was found at thisdepth on the previous sampling occasion on 18thMay. This is probably due to uptake of Br2 fromdeeper soil layers during the crop growing season(Owens et al., 1985; Kung, 1990). The crop washarvested on 8th September, 11 days before theSeptember sampling, so that the extracted soilsamples most likely contained decaying roots. Thiscould not be simulated by the model, becausealthough crop uptake of solute is included as a sinkterm, re-mineralization of solute contained in cropresidues is not considered

Fig. 6(a) shows simulated and measured Br2

concentrations in tile-drain discharge. The timing ofthe initial breakthrough and subsequent recession, andthe following slow increase until March is wellpredicted, even if the maximum concentration of theinitial breakthrough is somewhat underestimated. The


Fig. 5. Measured Br2 concentrations in groundwater and simulated macro- and micropore concentrations in the deepest soil layer (155–175 cm).

model estimates the largest Br2 concentrations inFebruary–April (maximum 8.2 mg l21), with decreas-ing concentrations for the rest of the simulated period,while the largest measured concentrations occurred inJune–July (maximum 5.7 mg 121, excluding onesingle value of 14.3 mg l21), and with relativelyhigh concentrations also found in October andNovember 1995 (maximum 5.0 mg l21). Apart fromthe first two months of the simulated period, themeasured short-term variations in concentrationwere poorly described by the model. This was alsothe case in a lysimeter study using the same soil,comparing measured36Cl concentrations with thosesimulated by the MACRO model (Saxena et al.,1994). These discrepancies may be related to themodel description of first-order mass-exchangebetween micro- and macropores, which neglectslateral concentration gradients. The assumption ofinstantaneously-attained uniform concentrations inthe micropore region will certainly underestimate or‘smooth out’ short-term fluctuations in drainage waterconcentrations since vertical transport in the macro-pores is relatively fast compared to lateral diffusion inthe micropores, and because Br2 concentrations intile-drainage water respond primarily to the macro-pores sinceKs is much larger thanKb andd is large.

The large Br2 concentration of 14.3 mg l21

measured in the drainage water on 4th June (Fig.6(a)) occurred after two weeks of dry weather

followed by 26 mm of rain on 31st May. This singlelarge value may be a measurement error. However, ifit is not, one possible explanation is that Br2 becomesconcentrated at aggregate surfaces owing to drying,and is then easily available for leaching by macroporeflow. During soil drying, water will evaporate, leavingBr2 behind in the liquid phase in small pores. If theconvective transport occurring as a result of evapora-tion is faster than the counteracting diffusion flux inthe soil liquid, Br2 will be concentrated at the aggre-gate surfaces.

Another reason for the discrepancies may be thedivision of the pore system into only two domains.Gwo et al. (1995) divided the soil pore space intothree domains and successfully interpreted the resultsof a soil column experiment using the model MURF/MURT. Even though a three-domain model allowsgreater flexibility in matching simulated results tomeasured data, the increase in the number of para-meters also makes parameter estimation more difficult(Gwo et al., 1995).

Spatial variability in the amount of Br2 applied,and within-field heterogeneity of hydraulic propertiesalso cause discrepancies between observed andpredicted flow and transport dynamics. For example,during soil coring, it was noticed that the groundwaterlevel was about 0.3 m below the soil surface at onelocation while no groundwater was observed at 0.8 mdepth at all other locations. Another reason for some


Fig. 6. Simulated and measured Br2 concentrations in tile drain discharge (a) and simulated mass balance of Br2 including measuredaccumulated loss to tile drains (b).

of the discrepancies between measured and simulatedtile-drain discharge, and solute leaching might betemporal variations in hydraulic properties leadingto variations in the partitioning of water flow betweenmacropores and micropores. For example, Singh et al.(1996) found that infiltration rates were considerablysmaller after the winter period than in November,which they attributed to reduced soil aggregate sizes(Benoit, 1973) owing to freeze-thaw cycles. Messingand Jarvis (1993) reported that near-saturated hydrau-lic conductivity decreased significantly during the

growing season, while Leeds-Harrison et al. (1986)showed a decrease ofKs with time in continuously-saturated clay cores. Even though non-swelling clayminerals (e.g. illite) predominate in Swedish soils,some shrinking and swelling occurs, and this mayhave affected patterns of water flow and solute trans-port during the experiment.

Fig. 6(b) shows that the simulated Br2 loss inlateral groundwater flow for the experimental periodamounts to 46% of the applied dose, which is consid-erably larger than the amount lost to the tile drains


Fig. 7. Simulated and measured mean one standard deviation bentazone concentrations in soil.

(21%), while 31% remains in the soil profile. Eventhough the accumulated losses to tile drains are some-what underpredicted (measured losses amount to31%), this clearly demonstrates that measurementsin tile-drains alone may significantly underestimatetotal leaching to the environment. According to thesimulations, less than 2% of the applied amount waslost to the secondary drainage system and as verticalseepage to deep groundwater (not shown).

4.3. Bentazone leaching

Fig. 7(a)–(c) show comparisons of depth profiles of

measured bentazone in the soil with those simulated inone domain (OD) and two domains (TD) without anyfurther model calibration. The agreement betweensimulated TD results and the measured values is onthe whole good, whereas the rate of bentazone trans-port in the profile is overestimated in the OD simula-tion. However, on the final sampling occasion (19thSeptember) the model (TD) clearly overestimatesbentazone contents measured at 30–50 cm depth. Itis possible that some degradation occurred during thesummer at this depth in the soil, even though none wasmeasured in the laboratory incubation experiments(Bergstrom et al., 1994. The statistical indices confirmthe visual impression of Fig. 7(a)–(c) concerning theresults of the TD simulation (Table 5), with a goodmodel efficiency (. 0.5) for 15th December and 7thMarch, and a poor model efficiency (, 0) for 19thSeptember.

The fit between simulated (TD) and measuredbentazone concentrations in the tile drain discharge(Fig. 8(a)) is also fairly good. In particular, the initialpeak and the maximum concentrations in March arewell matched. However, the recession of the initialpeak and the timing of the response in the tile-drains


Table 5Values of goodness-of-fit (coefficient of residual mass, CRM andmodel efficiency, EF) for two-domain simulations of bentazone insoil

Sampling date CRM EF

15 December 1994 0.04 0.927 March 1995 2 0.22 0.6519 September 1995 0.59 2 0.20Total 2 0.01 0.87

Fig. 8. Simulated (one and two domains) and measured bentazone concentrations in tile drain discharge (a) and simulated (one and twodomains) and measured accumulated loss to tile drains (b).

after the summer period is not so well simulated. Thiscan also be seen in Fig. 8(b),which shows accumu-lated bentazone losses to tile drains. The reason forthese discrepancies can be found in the failure to accu-rately match water discharges from tile drains at thesetimes (see Fig. 3(a)). In the OD simulation, themeasured initial breakthrough is not captured at all,while the bentazone concentrations in tile-drainoutflows are subsequently overestimated for the restof the period. In the TD case, 66% of the simulatedbentazone concentrations in tile drainage were withina factor of 2 of the measured values, and 89% within afactor of 5. Most of the failures were related to discre-pancies in the simulated timing of tile-drain outflow.

Interestingly, the estimated amount of bentazoneleached to tile drains in the OD case is much higherthan in the TD case for the simulated period (see Fig.8(b)). The combined losses to groundwater andthrough tile drains (see Table 6) are 53% and 34%of the applied amount for OD and TD simulationsrespectively. Macropore flow is normally consideredto increase the risk of contamination of surface watersand groundwater, but in this study, with a weaklysorbed pesticide applied in the autumn with low soiltemperatures and thus relatively low degradationrates, the total load to surface water via tile drainsand to groundwater was considerably reduced accord-ing to the model. In the TD case, a significant propor-tion of precipitation flows into the macropores atthe soil surface and has only limited contact with the soilmatrix, both because the mixing depth at the soil surfaceis small and lateral exchange within the soil duringvertical transport is weak owing to large effectivediffusion pathlengths. The rate of convective transportin the matrix is therefore slower, reducing the amount

of bentazone leached compared to the OD case (seealso Fig. 7(a)–(c)). As more bentazone remains in thesoil in the TD case (see Table 6), and because nodegradation is assumed to occur below 30 cm depthwhere most of the bentazone is stored, the differ-ences between the total amount leached from ODand TD simulations would certainly be reduced hadthe experiment continued. However, the results alsoindicate that some degradation may occur in thesubsoil, at least to 50 cm depth (see Fig. 7(c)), sothat significant differences between OD and TDsimulations would presumably be maintained inreality even if a longer period had been considered.

5. Conclusions

The results from this study show that under theexperimental conditions encountered (i.e. soil typeand scale of measurements), ‘effective’ parametervalues in a deterministic dual-porosity model gavelargely satisfactory predictions of solute transportand leaching at the field-scale (0.4 ha). Followingcalibration against measurements of water dischargeand bromide transport, the model was shown tosuccessfully predict bentazone amounts in soil (over-all model efficiency 0.87) and a fairly good agreementbetween measured and simulated concentrations intile-drainage was also obtained. However, the modelcould not capture all the dynamics of the system,especially short-term variations in flux concentrationsmeasured in tile drainage outflow. We believe that onesource of model error is the simplified description offirst-order mass-exchange between micro- and macro-pores, which neglects lateral concentration gradients.


Table 6Simulated (one and two domains) mass balance of bentazone at the end of the simulated period, 30 November 1995

Bentazone Simulated (g m22) % of applied amount Simulated (g m22) % of applied amount(one domain) (two domains)

Remains in profile 20.3 8 65.5 26Degraded 96.8 39 100.8 40Leached to tile drains 47.2 19 22.8 9Leached to secondary drains 1.2 , 1 0.4 , 1Lateral losses in groundwater 85.3 34 61.3 24Total 250.7 250.9

We also believe that significant errors occurred as aresult of uncertainty in the boundary conditions, inparticular errors in precipitation measurements andthe influence of local groundwater inflow/outflow.

Bromide was measured in tile-drainage outflow atconcentrations. 3 mg l21 only 26 days after spraying(after 43 mm of precipitation), while groundwaterconcentrations at 2 m depth were as large as10 mg l21 only 42 days after spraying. This is a strongindication of macropore flow. Nevertheless, benta-zone leaching in this clay soil was significantlyreduced as a result of macropore flow, with the one-domain simulation overestimating leaching by ca.20% during the one-year experimental period. In thetwo domain case, a small value of the mixing-depth atthe soil surface combined with relatively largedvalues (i.e. a weak coupling between the flowdomains, presumably owing to aggregate coatings),resulted in a limited bentazone transport frommicro- to macropores. Thus, the bulk of the applica-tion was effectively ‘protected’ against bypass flow ofwater in macropores, being stored in micropore watermoving at a ‘reduced’ convective transport velocity.

Acknowledgements

We would like to thank the staff at the Lannaexperimental farm, especially Rolf Tunared for helpin the field, and Malin A˚ kerblom, Gunborg Alex,Bodil Ottosson, and A˚ sa Ramberg (Department ofEnvironmental Assessment, SLU), and Gunilla Hall-berg and Amanuel Tesfamikael (Department of SoilSciences, SLU) for carrying out the bentazone andbromide analyses. We would also like to thankAllan Walker (HRI,UK) for a copy of the STATINDprogram for calculating statistical indices of good-ness-of-fit. The research reported in this paper wasfunded by the European Commission – EnvironmentResearch Program (Contract EV5V-CT94-0467),within the project ‘Analysis and improvement ofexisting models of field-scale solute transport throughthe vadose zone of differently textured soils, withspecial reference to preferential flow.’

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evaluation of a dual-porosity model to predict field-scale solute transport in a macroporous soil

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