Plot-Scale Solute Transport in a Semiarid Agricultural SoilHiroshi Yasuda,* Ronny Beradtsson, Akissa Bahri, and Kenji Jinno

ABSTRACTIn semiarid areas, agricultural production is determined by limited

water and nutrient supply. To develop efficient management practices,it is of importance to predict solute transport. In line with this,we present observed and calculated plot-scale solute transport in anagricultural experimental field in northern Tunisia. A pulse of Br~-tagged water was applied on the surface of two small field plots andleached under steady-state soil water conditions. Solute samples werewithdrawn through ceramic samplers at five different depths withineach plot. The experimental data indicated a high degree of bypass orpreferential flow within the small plots and nonsigmoid breakthroughcurves, suggesting tailing phenomena and immobile fractions of soilwater. The data were evaluated using the classical two-parameterconvection-dispersion equation (CDE) and the four-parameter non-equilibrium convection-dispersion equation (NECDE). Pore watervelocities, v, and dispersion coefficients, D, were calculated by fittingthe analytical solution of these two models to the breakthrough curvesbased on individual sample locations as well as using all samples inthe plot simultaneously. None of the models could be fitted whendata from all solute sampling depths were used in the optimizationsimultaneously. When using data at individual sample locations, thefit was somewhat better for the NECDE than for the CDE. Theestimated values of D and v could be described by a power lawrelationship.

SMALL-SCALE VARIABILITY in the hydraulic conductiv-ity and related bypass or preferential flow phenomena

play an important role in the transport of solutes at thefield scale (Beven and Germann, 1982; Bowman andRice, 1986; Zhang and Berndtsson, 1991). Preferentialflow is especially important for solute transport withrespect to managing farm lands for control of nutrients,herbicides, and pesticides. Small-scale variability hasbeen shown to be important for the hydrology of mostundisturbed soils and forest soils (Luxmoore et al., 1981;Beven and Germann, 1982; Jardine et al., 1989). Dueto farming practices, the upper soil layer of agriculturalsoils is expected to be less heterogeneous than untilled soil(e.g., Zhang and Berndtsson, 1988). However, severalstudies during the past few years have shown that variabil-ity in soil hydraulic properties also has a significant effecton solute transport for soils that exhibit little or no visiblestructure (Bowman and Rice, 1986; Jaynes et al., 1988).

There have been numerous investigations of soil heter-ogeneity. For example, Ghodrati and Jury (1990) per-formed field experiments to directly observe bypass flowof water and solutes by adding soluble dye to stain flowpathways. The dye trace patterns were used to investigate

H. Yasuda and R. Berndtsson, Dep. of Water Resources Engineering,Lund Univ., Box 118, S-221 00 Lund, Sweden; A. Bahri, Rural Engi-neering Research Center, B.P. no. 10, Ariana 2080, Tunis, Tunisia; andK. Jinno, Dep. of Civil Engineering, Kyushu Univ., Hakozaki 6-10-1,Higashi-ku, Fukuoka 812, Japan. Received 5 Mar. 1993. "Correspondingauthor (tvrls@gemini.ldc.lu.se).

Published in Soil Sci. Soc. Am. J. 58:1052-1060 (1994).

the effect of the soil structure and the irrigation methodson the preferential flow patterns. The observed verticaland horizontal distribution of the soluble dye clearlyindicated different bypass flow patterns, depending on theexperimental conditions. These patterns included 0.05- to0.20-m-wide vertical fingering of dye traces that extendedto more than twice the mean displacement of the dye.They also observed isolated, horizontal paths indicatinglateral flow. Starr et al. (1986) conducted tracer testsfor a layered field soil and showed that water and solutemovement were influenced by fingering caused by thethree-dimensional soil structure.

Solute transport in an unsaturated horizontally hetero-geneous field soil was investigated by Bresler and Dagan(1981). They introduced the concepts of field-scale andaverage dispersivities to show that laboratory-scale pa-rameters are generally smaller than those of field soils.Silliman and Simpson (1987) conducted laboratory teststo investigate the changes hi dispersivity caused by thepresence of -macroscale heterogeneities. Their resultsindicated a continuous increase in the dispersion withdistance from the surface.

The movement of solutes in porous media is commonlymodeled by means of the CDE. Van Genuchten andWierenga (1976) used the word "tailing" to describe theappearance of highly asymmetrical or nonsigmoid soluteconcentration profiles, and introduced a four-parametertwo-region NECDE. This model more accurately simu-lates the tailing phenomena. The model assumes that asoil is composed of pore sequences where the water istransported alternately slowly and rapidly. Soil aggre-gates contain micropores in which the transport is mainlydependent on dispersion. Convection in these smallerpores is often negligible. Dispersion results in slow andincomplete mixing and hence tailing hi the breakthroughcurves. Both laboratory experiments and field tests indi-cate the existence of this kind of immobile water. Smet-tem (1984) and de Smedt et al. (1986) reported differentfractions of immobile water for different soils.

In arid and semiarid areas where water, salinity, andnutrients are limiting factors for crop production, knowl-edge of the spatial variability in the solute transportbecomes especially important (e.g., Russo and Bresler,1981). The objective of this study was to investigate thesolute transport in an experimental agricultural field soilin northern Tunisia. Specifically, the study was focusedon estimating the values of selected solute transportparameters and their variation in an agricultural soil.For this purpose a Br-tagged 0.05-m pulse was infiltratedunder steady-state conditions at two field plots. The ex-perimental results were compared with calculated Brbreakthrough curves obtained with the CDE and NECDEmodels. The values of v and D were estimated by usingthese two models. The results are discussed in relationto current concepts regarding solute transport in fieldsoils.

1052

YASUDA ET AL.: PLOT-SCALE SOLUTE TRANSPORT 1053

THEORYThe experimental data were analyzed using the classical

two-parameter CDE and the four-parameter two-regionNECDE (van Genuchten and Wierenga, 1976). Results of thisanalysis are described below.

Convection-Dispersion EquationTransport of solutes is often modeled with the classic CDE

(e.g., Bear, 1979). Assuming no sink or source terms for aconservative tracer, the CDE can be expressed as:

dC—dt

d2C——dx2

dC—dx [1]

where C is the concentration, v is the mean pore water velocity(m/h), D is the apparent dispersion coefficient (m2/h), t is time(h), and x is depth (m). Equation [1] was solved analyticallyby adopting the following initial and boundary conditions fora pulse-type injection:

,_Ddd\ Iv dx) l = 0

0 < t<tit > ti

f C(co,r)=odxC(x,0) = 0

[2]

[3]

[4]where C\ is the injected solute concentration and tt is the timeit takes for the Br-tagged pulse to infiltrate. Because of theexperimental conditions, the concentration is assumed to bea volume-averaged concentration (Bowman and Rice, 1986;Jaynes et al., 1988). The analytical solution of Eq. [1] subjectto Eq. [2] through [4] for a volume-averaged concentration is(Parker and van Genuchten, 1984a):

CiA(x,t) - dA(x,t - t,)[5]

where

1., . ,A(x,t) = -erfc2 (4Dr)1

expF

'—nDj

1/2

(x - vtf\ \- . , vx , v't- - 1 + — + —2 \ D D [6]

Two-Region Nonequilibrium Convection-DispersionEquation

If a porous medium is assumed to contain mobile and immo-bile water with diffusion and exchange of solute between thesetwo liquid regions, the following equations may be used todescribe the solute transport (van Genuchten and Wierenga,1976; Jacobsenetal., 1992):

dt4. flT Di

dtdCgn

' dt

dCm 3Cm~ — ~ VmWm ~ ~~ L / Jdx dx

= Ct (Cm — [8]

where Cm is the concentration of the solute in the mobile zone,Cm is the concentration of the solute in the immobile zone,0m is the water content in the mobile zone (m'/m3), 0jm is thewater content in the immobile zone (m3/m3), Dm is the dispersioncoefficient of the immobile zone (m2/h), and a is a masstransfer coefficient (1/h) between the mobile and the immobilezones.

The general analytical solution to Eq. [7] and [8] subjectto similar boundary and initial conditions of the experiments,which are equivalent for the CDE is (Parker and van Genuchten,1984a)

car> = fc>B(x'T}' \CiB(X,T) - QB(X,T-Ti)

0<T <T>Ti

[9]where

B(X, T) = \TQF(X, T) /(a* - , a* f^) dt0 \ (p 1 - q>/

[10]

exp -

and J(a,b) is Goldstein's J function:

J(a, b) = 1 - exp( -b) 0 exp( - [12]where /o is the modified Bessel function of zero order. Thedimensionless variables are:

Dm vm6m[13]

where L is the depth of the field plot, (p is the fraction of themobile part in the pores, P is the Peclet number, and a* isthe dimensionless mass transfer coefficient.

Parameter EstimationThe above analytical solutions to the CDE and the NECDE

were used to analyze the observed solute sample data. Toestimate the parameters (D and v for the CDE, and Dm, vm, (p,and a* for the NECDE), the nonlinear least-squares inversionprogram CXTFIT (Parker and van Genuchten, 1984b) wasused. Data from each individual sampler and from each plotwere treated as independent observations of the solute leachingprocess (Jaynes et al., 1988). In the future, a more sophisticatedheterogeneous model should be used, provided the parameterdistribution is given. A parameter estimation based on inde-pendent observation points is an intermediate step to using amore sophisticated heterogeneous model. The parameter valuesestimated from data for individual samplers were comparedwith parameter values optimized for data from all five depthssimultaneously.

The parameters D and v of the CDE, and Dm, vm, a*, and(p of the NECDE were estimated by error minimizing. Tocompare and evaluate the fit at various observation points, theestimation error for Br concentration was calculated as themodeling efficiency (Loague and Green, 1991):

1054 SOIL SCI. SOC. AM. J., VOL. 58, JULY-AUGUST 1994

Z (Oh. - cmea)2 -

- cmea)2[14]

where Cobs is the observed Br concentration, Ccai is the calculatedBr concentration, Cmea is the mean of the observed Br concentra-tion, j is the time step for the observations, and M is thenumber of measurement points used in the estimation.

The relationship between D and v has been investigated innumerous studies (Biggar and Nielsen, 1976; Bowman andRice, 1986; Jaynes et al., 1988). In most cases, moleculardiffusion is much smaller than field dispersion and usuallyignored when modeling field data. The dispersion coefficientis related to the pore water velocity (e.g., Jaynes et al., 1988):

D = P VY [15]where P is the dispersivity and y is an empirical parameter.

MATERIALS AND METHODSSoil Conditions

The experiments were carried out at the Cherfech experimen-tal field research station in northern Tunisia. The experimentalstation is located at Sidi Thabet, 30 km north of Tunis in theLower Medjerda Valley. The soils at this site are representativeof the region (Research Center for the Utilization of SalineWater in Irrigation, 1970) and is classified as silty clay loam.The vertical soil texture is alternately fine and coarse, formedfrom alluvial sediments of the Medjerda River; the soil profilecan be divided into three layers: (i) an upper layer (0-0.4 m)with a high content of clay and silt (70-80%), (ii) an intermedi-ate layer (0.4-1.0 m) of silty clay loam, and (iii) a lower layer(1.0-1.3 m) of loam and sand (Bahri, 1992). There is ageneral tendency of increasing grain size with depth. The U.S.classification of the soil is a Vertic Xerofluvent. The watertable is located at about 1.5-m depth.

This study is part of a comprehensive investigation of solutetransport and spatial soil chemical properties at the field scale(Bahri et al., 1993; Yasuda et al., 1994). Infiltration experi-ments were performed at two plots separated by 80 m. Thetwo plots were managed identically during several years until1988 when one of the plots (Plot 2) received 47 000 kgdry matter/ha, mainly as domestic sewage sludge. The maininfluence of the sludge (except from its fertilization value) wasthe addition of several trace elements (Cu, Zn, and Pb) tothe original soil (for further details, see Bahri et al., 1993;Berndtsson et al., 1993).

A semiquantitative x-ray diffraction analysis based on CuKaradiation in the interval 3 to 35° 29) of fractions <2 urn (see,e.g., Klute, 1986) showed that the majority of minerals at thetwo investigated plots consisted of mixed-layer clay minerals(smectite group and hydromica, 20-60 % depending on depth),

Table 1. Saturated hydraulic conductivity and bulk density ofdifferent soil layers at Cherfech (Research Center for the Utiliza-tion of Saline Water in Irrigation, 1970).

Depthm

0.2-0.60.6-0.80.8-1.21.2-1.4

Hydraulicconductivity

10-2 m/h1.442.884.321.44

Bulk density

Mg/m3

1.5171.4551.4531.592

kaolinite (20-40 %), smectite (5-35 %), calcite (5-25 %), andhydromica (1-10 %) (Berndtsson and Bahri, 1990). Previousstudies in the area have shown that the major clay mineralwithin the smectite group is montmorillonite (Gallali, 1980).A major difference between the two investigated plots regardingclay mineralogy appears to be that Plot 2 (the sludge-amendedplot) had almost double the content of smectite of Plot 1. Thismay imply swelling and shrinking during wetting and dryingfor Plot 2, and possibly a greater potential for bypass flow.At the experimental plots, cracks were not visible at the soilsurface; however, microscale formations at deeper layers mayhave contained cracks and thus caused enhanced bypass flow.

A previous study investigated the hydraulic conductivity ofthe experimental field. The results are presented in Table 1(Research Center for the Utilization of Saline Water in Irriga-tion, 1970). The table shows that the hydraulic conductivityat the 0.8- to 1.2-m depth is greater than at other depths,which is probably caused by the coarser soil material at thisdepth.

Infiltration ExperimentsThe experiments were conducted in February and March

1990 (Jonsson et al., 1991). Previous to the experiments, thearea experienced the most intense rainfall observed for severaldecades (150 mm during January). At the time of the experi-ments, wheat (Triticum durum L.) was growing on the plots.The plots were subsequently cleared of plants and leveled byhand in order to obtain a smooth soil surface.

The edge of the plot was dug to 0.1-m depth to insert0.2-m-high plastic sheets, after which it was refilled to a bulkdensity of 1.5 Mg/m3. Plot 1 had an area of 3.6 m2 and Plot2 an area of 3.5 m2. Each of these plots had previously (1985)been instrumented with a neutron access tube (aluminum tubeswith a diameter of 41-45 mm; neutron probe type was Solo25, 40 mCi, Nardeux Humisol1, Tours, France; to 1.5-mdepth), seven tensiometers (Nardeux Humisol; 0.1, 0.2, 0.3,0.5, 0.8, 1.2, and 1.5 m), and five ceramic soil water samplers(soil water sampler type 1900L, Soil Moisture EquipmentCorp., Santa Barbara, CA; 0.3, 0.5, 0.8, 1.2, and 1.5-mdepth). Solute samplers were installed with a horizontal spacingof 0.3 m for the different depths (Fig. 1).

A calibration of the neutron probe was previously carriedout for different depths at each plot. Before each tracer addition,the plots were ponded to a depth of 0.05 m. After * 2 to 3h, steady-state soil water conditions were indicated by neutronprobe measurements (Fig. 2) and tensiometer readings (datanot shown). No gravimetrical samples were taken during theinfiltration experiments. A constant water depth of 0.05 mwas maintained on the surface during the tracer test. Thesteady-state soil water distribution with depth was similar forthe two plots. The tracer (KBr) was diluted in irrigation waterand then put on the plot surface to keep the 0.05-m pondingdepth. The volume of the tracer liquid was 0.180 m3 for Plot1 and 0.175 m3 for Plot 2. The Br concentration was 1917mg/L for Plot 1 and 2007 mg/L for Plot 2. The tracer pulsewas allowed to infiltrate, after which the depth of water onthe surface was rapidly restored and maintained for >10 huntil the tracer experiment was completed. During leaching,solute samples were withdrawn at approximately 15-min inter-vals from the five depths within each plot. The Br concentra-tions were analyzed immediately after sampling by use of anion-selective electrode (Selectrode F1022Br, Radiometer Co.,Copenhagen). The ion-selective electrode was connected to a

1 Mention of product or trade name does not constitute endorsementby Lund University to the exclusion of other products.

YASUDA ET AL.: PLOT-SCALE SOLUTE TRANSPORT 1055

Plotl O Soil water samplera Tensiometer

A Neutron access tube

Plot 2

Fig. 1. The experimental setup at the two infiltration plots.

precision pH meter (PHM85, Radiometer Co.) with a referenceelectrode (calomel electrode K701, Radiometer Co.).

RESULTS AND DISCUSSIONTracer Experiments

Figure 3 shows breakthrough curves for Br at differentdepths in the two plots. The relative concentration inthe figure refers to the concentration in the sample dividedby the initial input concentration. The figure displays

0.5 (m)i i i

typical properties of solute transport in soils influencedby bypass or preferential flow, e.g., a rapid transportdownward of the Br pulse and tailing phenomena. TheBr peak in both plots reached the 0.8-m depth before,and with a higher concentration than the 0.5-m depth.This phenomenon has been observed in the field andlaboratory (Starr et al., 1986). The relative concentrationat the 0.8- and 1.2-m depths for Plot 2 indicated moretailing than at the 1.5-m depth.

The general properties of the breakthrough curves

£"a.01O

0.4 0.5 0

Volumetric soil water contentFig. 2. Development of steady-state soil water content profiles at the two infiltration plots during ponding.

1056 SOIL SCI. SOC. AM. J. , VOL. 58, JULY-AUGUST 1994

Plot 1 Plot 20.20

0.15

0.10-

0.05

3 4 5 6 Q 1

Time (hr)Fig. 3. Experimental Br breakthrough curves depending on depth at the two experimental plots.

display a strong influence of bypass or preferential flow.Without detailed soil sampling, however, it is not possibleto explain if this behavior is a result of macropores inthe soil, small-scale variation in hydraulic conductivityof the soil, or the experimental arrangement, since eachsampler is at a different horizontal location. The dataindicate that at least two types of flow occur within theplot. The first type of flow is linked to the rapidlyconducting pores or soil media causing a rapid responseto surface-applied solutes and a concentration peak atrelatively large depths. The second type of flow is relatedto the more slowly conducting pores or soil media causinga comparatively slow downward movement with theconcentration peak lagging the peak of the previouslydescribed flow type. In an earlier study, drainage dis-charge and related Cl concentration in drainage wateralso suggested two flow types: an initial rapid dischargejust after irrigation characterized by short peak flowlasting a few hours, and a second discharge that couldlast 5 to 10 d (Bahri, 1992). Consequently, this indicatesthat the effect of bypass flow can be observed at boththe field scale in the earlier study and the plot scale inthe present study.

The experimental procedure used assumes one-dimen-sional vertical flow. However, this is not the case whenbypass-flow phenomena are present. The degree of hori-zontal flow, however, cannot be estimated without de-tailed soil information. In previous experiments at a

larger field scale, horizontal water movement was moni-tored (Bahri, 1992). In the present study, the tune scaleis rather short and the measurement scale is smallercompared with the earlier study, so horizontal flow canbe neglected. The breakthrough curves and mass conser-vation of Br are further analyzed below.

Modeling ResultsThe parameter estimation procedure described above

was applied to estimate the optimum parameter valuesof the two models used. The minimum value of theobjective function in CXTFIT (squared error of the devia-tion between observed and calculated values; Parker andvan Genuchten, 1984b) was used to determine optimumparameter values. The outcome of these calculations forthe two models is shown in Tables 2 and 3 and Fig. 4and 5. The modeling errors (the modeling efficiency ofEq. [14]) are given in Table 4. The table shows that theNECDE gives a consistently better fit to the observeddata than the CDE, although the difference between themodels is small.

As mentioned above, the CDE and the NECDE werefitted to the observed data by using data from eachindividual solute sampler as well as using all samplersin one plot. Thus, in the first case, the observations fromeach sampler were treated as independent observationsand used in the models to evaluate the heterogeneity. In

Table 2. Parameter values for Plot 1 using the convection-dispersion equation (CDE) and the nonequilibrium convection-dispersionequation (NECDE).

CDE NECDEDepth

m0.30.50.81.21.5MeanAll five depths

Dnf/h

0.77750.13580.39450.84271.87020.80420.4123

V

m/h0.22040.22320.47000.41910.44030.35460.4662

Dm

mj/h0.21080.13890.03350.79680.90810.41760.0683

Vn,

m/h0.76480.22940.23240.42750.34090.39900.2460

a*

1/h112.3

4.1651.155

22.290.7527

28.132.202

<P

0.6690.9550.2670.9640.6120.6930.351

YASUDA ET AL.: PLOT-SCALE SOLUTE TRANSPORT 1057

Table 3. Parameter values for Plot 2 using the convection-dispersion equation (CDE) and the nonequilibrium convection-dispersionequation (NECDE).

DepthCDE

DNECDE

m0.30.50.81.21.5MeanAll five depths

m2/h0.03170.07740.10040.17880.28780.13520.2843

m/h0.21750.13300.44350.34950.17140.26300.1569

m2/h0.03250.01380.05130.03270.01200.02850.1467

m/h0.21970.08900.37570.27880.12370.21740.2918

1/h103.9

1.5450.0211.8222.819

22.027.807

0.8770.3690.3760.4160.1760.4430.738

the second case, it was assumed that the soil texture ishomogeneous with depth, and all five solute observationsin one plot were included in the model fitting.

As seen in Tables 2 and 3, D values (CDE) tend toincrease with distance from the surface (observationsfrom each sampler treated individually). This characteris-tic has been shown in many studies previously (e.g.,Kinzelbach, 1986; Silliman and Simpson, 1987; Butterset al., 1989). It is widely recognized that the dispersioncoefficient increases with scale and this is also the casefor the investigated plots except at the 0.3-m depth. Thetop layer does not follow this tendency. This may bedue to higher bulk density for the upper soil layers (Table1). The An values (NECDE) do not show the same clearincreasing tendency with depth.

Plot 1

From Fig. 5 and Table 4, it is seen that the solutetransport cannot be well described by either the CDEor the NECDE if the solute observations at all five depthsare considered simultaneously. The model efficiency us-ing data from all five depths concurrently is low (Table4), e.g., at a scale of 0.2 to 0.3 m there is alreadyconsiderable variability that significantly influences sol-ute transport. For accurate modeling of solute transport,the heterogeneity has to be considered.

When comparing the optimum parameters of the CDEfor the two plots, it can be seen that they differ approxi-mately one order of magnitude (Tables 2-3). This isalso the case for the NECDE when comparing Dm andvm values. There are also similar tendencies for a* valuesat the two plots. Both plots, however, have high a*

0.20

0.15

0.10

0.05

0.20

0.15-

0.10 -

0.05

Plot 2

Time (hr)Fig. 4. Observed breakthrough curves compared with model results using the convection-dispersion equation (CDE) and the nonequilibrium

convection-dispersion equation (NECDE) using an independent optimization for each solute sampler.

1058 SOIL SCI. SOC. AM. J., VOL. 58, JULY-AUGUST 1994

Plot 10.20

0.15

0.10

0.05

0.20

0.15-

0.10

0.05

Plot 2

CDE

Time (hr)Fig. 5. Observed breakthrough curves compared with model results using the convection-dispersion equation (CDE) and the nonequilibrium

convection-dispersion equation (NECDE) using simultaneous optimization for all five solute samplers.

values at 0- to 0.3-m depth, suggesting a high rate ofexchange between the mobile and immobile soil waterphases. This is probably an effect of higher bulk densitynear the soil surface (Table 1). If data from the 0.5-msolute sampler are separately fitted by the NECDE, thea* drops two orders of magnitude. Results drop furtherwhen data from the 0.8-m solute sampler is separatelyfitted (two orders of magnitude for Plot 2). This isprobably an effect of the much coarser material at the0.8-m depth. The <p parameter does not show any similarvariation with depth for the two plots.

The dispersion coefficients and pore velocities of theCDE and the NECDE are similar when the mobile frac-tion (p is large, but differ greatly when cp is small. Thetwo models are consistent and display similar tendencies

Table 4. The modeling efficiency of the convection-dispersionequation (CDE) and the nonequilibrium convection-dispersionequation (NECDE) as quantified by Eq. [14].

Depthm

0.30.50.81.21.5All five depths

CDE

0.9880.9480.8730.9720.9450.633

Plot 1NECDE

0.9900.9500.9550.9730.9630.699

CDE

0.8380.8990.8700.7300.6780.540

Plot 2NECDE

0.8440.9730.9960.8670.9980.572

for the various depths at the two plots. The NECDEshowed a better fit in Table 4 (e.g., 0.8-m depth of Plot1, 0.8- and 1.5-m depths of Plot 2). The fit of thecalculated breakthrough curve to the observed curve forthe 1.5-m depth is excellent, as shown in Fig. 4.

Values of D estimated in field experiments are oftenlarge compared with values reported for laboratory ex-periments (e.g., Jaynes et al., 1988), which was alsoobserved in this study. The reason for this increase inthe field is due not only to the increased heterogeneitiesof natural soil material itself, but also to the influenceof small-scale heterogeneities in the hydraulic conductiv-ity at the field scale. This may be described as macro-dispersion (Kinzelbach, 1986).

Figures 4 and 5 show that the parameter estimationfor each independent sampler gave good results and thatCXTFIT gave a better fit. In this study, the parameteroptimization was carried out for independent observa-tions of the solute transport and this methodology is anintermediate step to a more elaborate model that considersheterogeneity.

Figure 6 shows the Br concentration distribution withsoil depth at different times for the two plots. The curveswere interpolated by use of the fitted NECDE model.It can be seen that two concentration peaks are movingdownward through the soil profile for both plots.

Gerke and van Genuchten (1993) introduced a dualporosity model that contains two pore systems, a mac-

YASUDA ET AL.: PLOT-SCALE SOLUTE TRANSPORT 1059

Plot 1 Plot 2

0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1

Relative concentration (C/Co)

ig. 6. Bromide concentration distribution with depth at different times for the two plots (curves were interpolated by use of the fitted nonequilibriumconvection-dispersion equation model).

ropore system and a less permeable matrix-pore system.Although the limited observations cannot give supportfor a dual porosity model, the first peak seems to becaused by the macropore system and the second oneby the less permeable matrix-pore system. The deepestconcentration peak is a result of solute transport in rapidlyconducting soil media, whereas the upper concentrationpeak is a result of solute transport in more slowly conduct-ing soil media.

The optimum dispersion coefficients and pore veloci-ties for both the CDE and the NECDE are plotted in Fig.7 together with the results of two other field experiments,those of Bowman and Rice (1986) and Jardine et al.(1989). Bowman and Rice (1986) performed the tracertest in a field plot and measured the distribution of Brconcentration to 3-m depth (0.3, 0.6, 1.0, 1.4, 1.8, 2.4,and 3.0 m). Jardine et al. (1989) conducted a similarBr tracer test in a field plot. Figure 7 shows that the Dand v values from our study fell between the results ofBowman and Rice (1986) and Jardine et al. (1989).The plotted parameter values indicate that a relationshipbetween D and v according to Eq. [15] may be used.Using all the data, the parameters (3 and 7 were obtainedthrough linear regression, after a log transformation ofD and v, as P = 0.55 and 7 = 1.08 (the correlationcoefficient/?2 = 0.736). The main range of dispersitivitiesis located between 0.1 and 1.5 m, which coincides withthe scale of the experiments. This is consistent with manyprevious investigations regarding the close relationshipbetween the scale of measurement and the magnitude ofthe dispersivity |3 (Beims, 1983). There is no significantdifference between the CDE and the NECDE in Fig. 7.Instead, the dispersion and pore velocity values shouldbe considered together with the other field experimentsin the figure.

CONCLUSIONSThis study has displayed some of the variability in

the hydraulic and solute transport properties of an agricul-tural field soil in northern Tunisia. Tracer experimentsusing Br showed that bypass flow or small-scale varia-tions in hydraulic conductivity can have a large impacton the transport of nonreactive solutes in the soil.

The estimated dispersion coefficients (D and Dm) andthe pore velocities (v and vm) as well as mass transfercoefficients a* and mobile pore fractions (p varied consid-erably across small horizontal and vertical distances (0.2-0.3 m). Because of this variability, solute transport data

100

<M

E

10-

1

0.1

0.01

0.001

0.0001

° CDE

* NECDE* Bowman and RicG (1986)

x Jardine et al. (1989)

0.001 0.01 0.1v (m/hr)

10

Fig. 7. Relationship between optimum values of the convection-disper-sion equation (CDE) and the nonequilibrium convection-dispersionequation (NECDE) for dispersion coefficients D and pore velocitiesv compared with other field studies. The correlation coefficient (R2)is 0.736.

1060 SOIL SCI. SOC. AM. }., VOL. 58, JULY-AUGUST 1994

could not be well fitted by either the CDE or the NECDEif data from all observation points were used simultane-ously. However, by using data from each sampler asindependent observations, the solute leaching processcould be described by an analytical solution to theNECDE. Using the NECDE improved the fit (modelingefficiency). The NECDE consistently gave a better fitto the observed data than did the CDE. If errors anduncertainties in the data are considered (not quantifiedhere) the difference between the two models appearssmall. However, the parameter estimation for indepen-dent observation points is an intermediate step to a moresophisticated heterogeneous model in the future.

Observed dispersion coefficients and pore velocitieswere large compared with values measured hi the labora-tory, but of similar magnitude to other field measure-ments. The optimum parameter values together withother field measured parameters indicated a power lawrelationship, D = PVY.

ACKNOWLEDGMENTSThis research was supported by the Swedish Natural Science

Research Council, the C. F. Lundstrom Foundation, the Lis-shed Foundation, and the Futura Foundation. H. Yasuda grate-fully acknowledges the international technical cooperation pol-icy of Sweden. The study was partly supported also by theJapan Society for the Promotion of Science and the JapanMinistry of Education by giving R. Berndtsson the opportunityto spend a sabbatical year at Kyushu University. The SwedishInstitute gave support to A. Bahri for guest research periodsat Lund University.