field and undisturbed-column measurements for predicting transport in unsaturated layered soil

Field and Undisturbed-Column Measurements for Predicting Transportin Unsaturated Layered Soil

A. L. Ward,* R. G. Kachanoski, A. P. von Bertoldi, and D. E. Elrick

ABSTRACTTransport properties vary considerably over small distances in

most soils. The stochastic streamtube model offers one approach toincorporating heterogeneity into transport predictions. This studytested the ability of the streamtube concept to predict transport inheterogeneous fields using measurements from undisturbed columns.Fifty undisturbed columns (0.15-m diam. by 1.5 m deep) were takenevery 0.4 m from a 20-m-long transect in a loamy sand soil withvariable horizon thickness. Each core was instrumented at 0.1-mintervals with time domain refiectometry probes to measure residentfluid concentrations of a conservative (Cl~) tracer under steady flowconditions. Large-scale concentration curves of Cl" from solutionsamplers and coring were obtained from field experiments conductedon the same soil under similar boundary conditions. Differences wereobserved in the solute spread and mass recovery, but not in the centersof mass. Horizontal scale dependence of transport was observed inthe field but not in the columns. This suggests that a higher dimensional-ity of transport, probably along the horizon interfaces, may be respon-sible for the observed scale dependence in the field. Although thestochastic streamtube model gave good predictions of the center ofmass, it does not appear to be a realistic physical analogue for describ-ing solute dispersion in soils with spatially variable layer thickness.

SOIL PROPERTIES may vary by several orders of magni-tude over relatively short distances, even in appar-

ently homogeneous soils (Nielsen et al., 1973). Oneapproach to incorporating heterogeneity into the predic-tion of field-scale solute flux is the stochastic streamtubemodel (Dagan and Bresler, 1979; Jury and Roth, 1991;Destouni, 1992). In this approach, the soil is conceivedas a series of parallel, noninteracting, vertical columns.A.L. Ward, Battelle Pacific Northwest Lab., Battelle Boulevard, P.O.Box 999, Richland, WA 99352; A.P. von Bertoldi and R.G. Kachanoski,Univ. of Guelph and Waterloo Centre for Groundwater Research, Water-loo, ON, Canada N2L 3G1; and D.E. Elrick, Dep. of Land ResourceScience, Univ. of Guelph, Guelph, ON, Canada N1G2W1. Joint contribu-tion from the Dep. of Land Resource Science, Univ. of Guelph, andWaterloo Centre for Groundwater Research, Univ. of Waterloo. Received6 Aug. 1993. *Corresponding author ([email protected]).

Published in Soil Sci. Soc. Am. J. 59:52-59 (1995).

Each column is characterized by local flow and transportproperties, which vary between columns but remain con-stant for any one column. A further assumption is theexistence of steady one-dimensional flow, in which thedistribution of solute depends on the pdf of solute veloc-ity, /(v) (Dagan and Bresler, 1979). Use of the stochasticstreamtube model has been justified for soil profiles thatare vertically homogeneous and in domains in which thevertical variation is small relative to horizontal variations(Dagan and Bresler, 1979). It may also be applicable toshallow depths near the soil solute entry zone, whichmay be relevant to agricultural fields (Russo, 1991).

All soils have at least one horizon that is differentfrom the underlying parent material. Thus, water andsolutes must travel through layers with different transportproperties. Recent field studies (Ellsworth and Jury,1991; Kachanoski et al., 1990) and numerical simulations(Russo, 1991; Destouni, 1992) have shown that verticalheterogeneity may enhance large-scale solute dispersion.Thus, evaluation of the effects of spatial heterogeneityrequires measurement of both the horizontal and verticalvariability in soil properties. In the field, measurementand interpretation may be complicated by the generallyunknown layer-interface boundary conditions and com-plex flow patterns.

Many of these limitations, especially unknown inter-face conditions, may be avoided through the use oflaboratory-column experiments (Jury and Utermann,1992). These experiments also guarantee 100% massrecovery of inert solutes, which is required for applica-tion of the streamtube model. Unfortunately, the extrapo-lation of repacked-column data to the field scale has beenonly partially successful. It has been suggested that theresults from undisturbed columns may be more meaning-ful (White and Hend, 1990). Although the streamtubemodel seems feasible, the ability to predict the large-scaleflow and transport behavior of a field soil from theAbbreviations: ETC, breakthrough curve; TDR, time domain reflectome-try; pdf, probability density function; PVC, polyvinyl chloride.

WARD ET AL.: FIELD VS. COLUMN MEASUREMENTS FOR PREDICTING TRANSPORT 53

ensemble-averaged behavior of undisturbed soil coreshas not been tested.

This study had two main objectives. The first was totest the ability of the streamtube model to predict theensemble-averaged transport behavior from the resultsof a laboratory experiment. The utility of estimates ofspatial scale dependence of solute transport in identifyingthe scale at which horizontal velocity variations dominatefield-scale dispersion has been recently demonstratedby van Wesenbeeck and Kachanoski (1990). Thus, thesecond objective was to compare the horizontal scaledependence from a laboratory transport experiment withthat measured in field experiments conducted on thesame soil. The required data were obtained using 50undisturbed, layered soil columns instrumented with hor-izontally installed TDR probes that were used to measurewater content, 9, and solute concentration in the residentfluid, cf.

MATERIALS AND METHODSSoil Characteristics

The laboratory experiment was conducted in 50 undisturbedcolumns of a layered sand, from the Fox series (Typic Haplu-dalf), obtained from the Agriculture Canada Research Stationin Delhi, ON. The surface A horizon contains 85 to 90%sand, while the B and C horizons contain 90 to 95% sand.The B horizon is characterized by a spatially periodic tonguinginto the underlying C horizon and varies in thickness from 0.30to 3.0 m. The mean depth to the water table is 4.0 m. Kachanoskiet al. (1990) measured a higher macroscopic capillary length inthe B horizon. This suggests that the tongues may act aslocalized zones of rapid solute transport.

Transport ExperimentsOver the past several years, water-flow and solute-transport

studies have been conducted on this site as part of a mandate toinvestigate the effects of management practices on groundwaterquality. These experiments, including collection of the undis-turbed cores, were all conducted within 20 to 40 m of eachother. Two of these studies were used for comparison withthe undisturbed-column experiment. The first is the work ofvan Wesenbeeck (1993), which focused on the horizontal spa-tial scale dependence of vertical solute transport. The secondis the work of Younie (1993), which focused on the effectof tillage, crop growth stage, and row-interrow position onfield-scale solute transport.

Undisturbed-Column ExperimentA series of PVC tubes (0.15-m i.d., 1.6 m long) were

inserted to a depth of 1.5 m, one every 0.4 m, along a 20-mtransect (i.e., n = 50) using the Meta-Probe system. Thissystem, which uses a combination of downward pressure andhigh-frequency vibration (200 Hz), has been used to obtainundisturbed cores from depths in excess of 4.5 m in various soilsand sediments (Meta-Probe, 1986). A trench was excavatedadjacent to the cores to facilitate horizon demarcation and coreextraction. Comparison of the height of the soil in the coreswith the surrounding soil surface, and bulk density measure-ments taken on trial cores, suggested minimal disturbance.

In the laboratory, the bottom of each core was fitted witha vacuum assembly (1.5-m air-entry pressure head) to permitthe application of a vacuum for unsaturated experiments. Cores

were instrumented at 0.1-m increments from the surface to1.5 m with horizontally installed, two-wire TDR probes (2.0-mm o.d., 148 mm long, 15 mm apart). The theory of Knight(1992) predicts a cylindrical zone of influence with a diameterof =21.0 mm. A porous ceramic tensiometer, constructedfrom acrylic tubing (0.7-cm i.d., 1.0-cm o.d.) and 0.1 MPastandard porous ceramic cups (Soilmoisture Equipment Corp.,Santa Barbara, CA), was installed 25 mm to the right of eachTDR probe. At each depth z, TDR probes, accessed throughrotary switches, were used to obtain the time distribution ofwater content, Q(z,f) and impedance, R(z,t). Tensiometers wereused to obtain the corresponding distributions of soil waterpressure, h(z,t). A detailed schematic of the experimental setupfor the column experiment was presented by Ward et al. (1994).

Water was applied (flux density [/„] = 2.26 ± 0.4 cm d~')via an acrylic reservoir fitted with hypodermic needles, usinga precision pump fitted and flow-rated pump tubes. The onsetof steady state was determined from 6 and outflow measure-ments to verify Jw. At steady state (dQ/dt = 0), a pulse ofKC1 equivalent to a specific mass, M0 = 1.318 g m~2 ofCl~, was applied at the surface. Measurements ofR(z.t) wereobtained and used to calculate resident fluid concentration,Cf, of Cl~ using an indirect calibration procedure (Ward etal., 1994):

C\(zk,t) = [1]where pa is a specific calibration constant that is core (k) anddepth (zt) dependent, and R(Zk,td is the initial soil impedancemeasured at time t\. The calibration constant may be obtainedfor each spatial location, Zk (Ward et al., 1994):

[2]

where C0 is the concentration of Cl~ in the applied solutephase, and t0 is the pulse duration (30 s in this case). Theexperiment was conducted in two stages, with five blocks (25columns) in each stage, to produce hydraulic and transportdata at 750 locations (50 cores X 15 depths per core).

Field Experiment: Resident ConcentrationIn this study, a plot (5 m wide, 13.2 m long) was trickle

irrigated (/w = 4.0 cm d"1) until a steady-state water contentof 0.16 m3 m"3, over a depth of 1.0 m, was attained (vanWesenbeeck, 1993). At steady state, a solute pulse of Cl~tracer (M0 = 49.1 g m~2) was applied at the surface. Irrigationwas resumed until the net applied water, / = 13.13 cm, anda trench was excavated along the plot to a depth of 2.0 m. Itwas estimated that this amount of water (13.13 cm) wouldleach the center of mass to a depth of 0.8 m. Horizontalsoil cores (5-cm diam., 5 cm long) were taken every 20cm horizontally along the trench face and at 10-cm verticalincrements to a depth of 1.5 m (van Wesenbeeck, 1993). Thecores were sealed in plastic containers and transported tothe laboratory, where bulk densities and water contents weredetermined. Pore-water extracts were used to estimate Cl~concentration using the TRAACS method of Tel and Hesseltine(1990). These measurements, which provided the horizontaland vertical distributions of Cl~ concentrations for the entiresoil profile, were discussed in detail by van Wesenbeeck (1993).

Field Experiment: Flux ConcentrationForty solution samplers (2.5-cm o.d., 5.0-cm-long ceramic

cups, 0.1 MPa standard) were installed in each of two 14.0-m-long by 4.8-m-wide zero-tillage plots, and another 40 were

54 SOIL SCI. SOC. AM. J., VOL. 59, JANUARY-FEBRUARY 1995

installed in similar conventional-tillage plots of the same dimen-sions. In each plot, samplers were evenly distributed betweenrow and interrow positions with 20 each at depths of 0.4 and0.8 m (Younie, 1993). After harvest, the plots were trickleirrigated at a net Jw = 0.75 cm d~', which was adjusted forrainfall events. In each plot, TDR probes were used to measure0, and at steady state, a pulse of KC1 (M0 = 26 g m~2 ofCl~) was applied. Pore-water samples collected over a periodof 42 d were analyzed for Cl~ using a TRAACS autoanalyzer(Tel and Hesseltine, 1990). These data were used to constructflux-averaged solute BTCs, Cf(Zk,f), for each spatial location,k, for z = 0.4 and 0.8 m in each of the four plots. Sincedifferences due to tillage were minimal (Younie, 1993), allthe BTCs were pooled for comparison with the column mea-surements.

Estimation of Transport ParametersTo remove the variability due to fluctuations in irrigation

rates in the field, and to facilitate comparisons between thedifferent experiments, temporal measurements of concentra-tions were reformulated in terms of cumulative net appliedwater, / [V L~2], according to Jury and Roth (1990):

[3]

For comparison of solute concentrations, laboratory concentra-tion data were also scaled to the field data. The scaling factorwas calculated as the ratio of specific mass, M0, applied inthe column study to that in the field.

Given the uncertainty in identifying the correct processmodel for this soil a priori, BTCs were analyzed using themethod of moments. For each spatial location k, a pdf of netapplied water, to depth z, may be defined as

/(a,/) = [4]

The first moment of /fa,/) represents the mean or expectedvalue of /, and is defined as

rfe,/)/d/ [5]

while the second moment quantifies the spread about M\ andis given by

I/ [6]In the use of time-moment analysis on profiles cf\(z,t), it shouldbe noted that while the first time moment for c\(z,f) correspondsto the mean travel time (z/v), an analogous moment for <?(z,t)depends on the magnitude of dispersion (Kreft and Zuber,1978). This is also true for higher order moments. In ouranalysis no attempt has been made to correct Aft and M2 fordispersion, as this would require assumptions about the processmodel.

The first and second moments of the individual pdfs representthe smallest scale of observation, and the local-scale valuescan be obtained from the spatial average of these moments.By assuming that the measurements were statistically homoge-neous and second-order stationary, the ergodic hypothesis wasinvoked and an ensemble-averaged pdf obtained for each depthby spatially averaging the pdfs. The ensemble-averaged pdf,fn(z,I), represents a single realization of the transport process(Gillham et al., 1984). This was calculated using Eq. [4] aftersubstituting Cfc,/) for Cfc,/).

The spatial moments of the tracer distribution are defined

similarly to those above, but using the depth variable, z. Thedepth-normalized curves were used to obtain pdfs of traveldepth, f(I,Zk), at the local scale (i.e., at each horizontal locationk, k = 1, . . ,n). Substitution off(I.z) into Eq. [5] and [6]provided estimates of the mean travel depth, E(z), and theexpected variance, Var(z), respectively, for the large-scalecurves after a net cumulative infiltration / = 13.13 cm. Thisform of analysis permitted comparison of the laboratory andfield experiments across spatial scales.

Horizontal Scale Dependence of Vertical TransportA procedure for estimating the horizontal spatial scale depen-

dence of vertical transport has been discussed in detail by vanWesenbeeck and Kachanoski (1991). Briefly, the spatial ortemporal moments at different spatial scales may be estimatedby varying the scale of the pdf used in their calculation. Thefirst and second moments at any scale J are given by

[7]

[8]

= E [ \ n f j ( Z k , I ) I d I ]

(M2) = E ] 0 f j (a, /)[/-Mi,

where the variable / represents the number of sampling inter-vals over which the spatial averaging is performed and rangesfrom 0 to N — 1. For example, in the column experiment inwhich the sampling interval between cores was 0.4 m, at the2.0-m scale, 7 = 5 and//(a,/) represents the average of fiveadjacent pdfs. For the column experiment, there are 45 (i.e.,N—J) possible estimates of //&,/) at the 2.0-m scale (J =5). This gives 45 estimates of A/t and M2 at this scale. Theaverage values E5[Mi] and E5[M2] represent the averages ofthe 45 estimates of Af, and M2 for the 2.0-m scale. Generally,a plot of Ej[M2] vs. spatial scale should show the progressionof dispersion from the local scale to a sill equivalent to thelarge-scale variance (van Wesenbeeck and Kachanoski, 1991).The distance to the sill represents the minimum horizontaldistance (on average) needed to obtain an average pdf withthe same characteristics as the large-scale pdf. To compare thespatial dependence in the different experiments, a normalizedvariance was calculated as \Ej(M2) — Eo(M2)]/[EN(M2) —Eo(M2)], where Eo(A/2) represents the local-scale variance andEN(M2) represents the field-scale variance. A normalized vari-ance scales Ey(M2) between 0 and 1.0.

RESULTS AND DISCUSSIONAnalysis of Resident Concentration

The high temporal resolution of the solute distributionat each measurement depth in the columns allowed theeasy generation of the time evolution of the residentconcentration profile for each column. These data wereanalyzed at the local and large scales. Figure 1 comparesthe large-scale resident concentration curves obtainedfrom the columns and the field experiment of van Wesen-beeck (1993), both after / = 13.13 cm of applied water.Considering that the column concentrations were ob-tained by scaling the TDR-measured curves to the specificmass applied in the field, the two curves are remarkablysimilar in their general shape and concentration.

Results of the moment analysis are shown in Table1. There was less than a 1% different in mean traveldepth, EN(z), of the two large-scale curves. Momentanalysis gave EN(Z) = 0.845 m for the large-scale field


Ch Cone, [g cm"3soil].01 .02 .03 .04 .05 .06

0 -

0.3

0.6

Q.a 0.9

1.2

1.5 -

Fig. 1. Field-averaged resident concentration vs. depth for one-dimensional undisturbed columns compared with three-dimensionalfield results after / = 13.13 cm of applied water.

curve and 0.850 m for the large-scale column curve. Inthe columns, 5 was almost identical at 0.16 ± 0.02 m3

m~3. The piston flow prediction using the field-averagedwater content, 9 = 0.16 m3 m~3, estimated EN(Z) to beat 0.821 m (van Wesenbeeck, 1993). The ability topredict the center of mass in the field with 97% accuracyusing the assumption of one-dimensional piston flow andan accuracy of 99% with the undisturbed columns isencouraging since the variability in hydraulic and trans-port properties and horizon thickness would probablylead to a three-dimensional flow. The accuracy of thepiston-flow prediction suggests that, on average, theeffect of this variability on the location of the center ofmass was minimal.

Horizontal Scale Dependence of TransportDespite the similarity of EN(z) for the field and column

data, the spread about EN(z) was higher in the field-measured curve (Table 1), as shown in Fig. 1. At thelocal scale, the variance of the field curve, Var(z), was67% higher than the column curve, and 58% higher atthe large scale. The increase in Var(z) from the smallestto the largest spatial scale was 27% in the columns and21% in the field. An increase in Var(z) from the localscale to the large scale is not unusual (Schulin et al.,1987; van Wesenbeeck and Kachanoski, 1991), sincethe large-scale variance encompasses all of the local-scalevariability plus the variation between local scales.

Table 1. Moment analysis parameters for undisturbed columnsand resident concentration field experiment.

Experiment

ColumnsField

Local scaleEfe) Varfe)(m) (m2)

0.825 0.0690.844 0.115

Large scaleEN(z) Var,,(z)(m) (m2)

0.850 0.0880.845 0.139

Steady-statewater content

(m3 m-3)0.1610.160

Figure 2 shows the normalized variance for the columnand field data. The plot was truncated at 5.0 m, the lengthof the field transect used for comparison. Normalizedvariance showed a sharp increase between 0 and 0.4 m(the horizontal sampling distance between cores), whichaccounted for 80% of the observed variance. This abruptchange was followed by a more gradual increase asspatial scale increased. Over the length of the transect(20.0 m) this additional variance accounted for. the re-maining 20%. The field data, which were obtained at a0.2-m horizontal increment, showed a more gradualtransition from the local scale to a sill with a range of1.8 to 3.0 m. About 80% of the field-scale varianceoccurred in this range. The remaining 20% occurredover a spatial scale of 3.0 to 5.0 m. An analysis of thescale dependence of solute mass recovery also showeda similar response, and suggested a range of 1.8 to 2.0 mfor consistent recovery of solute mass (van Wesenbeeck,1993). The results of this comparison have some im-portant implications.

The range of the sill represents the minimum horizontaldistance necessary to obtain an average pdf with thesame characteristics as the large-scale pdf. The columndata suggests that a scale of 0.4 m or less would beadequate to encompass all horizontal variability. Com-parison with the field results suggests that the absenceof scale dependence may be due to other factors. In thefield experiment, most of the increase in variance hadoccurred by about 1.8 to 2.0 m. The range of the sillcoincides with the scale necessary to encompass theoccurrence of deep tongues in this soil, which is aboutevery 2.0 m (van Wesenbeeck and Kachanoski, 1991).Most of the large-scale dispersion occurs at scales equalto, or less than, the scale of the minimum size of a singlestreamtube; a minimum spatial scale for a streamtubemay now be defined. These results suggest that it shouldbe at least large enough to ensure equal mass recovery,on average, for streamtubes. This observation raises aquestion about how much of the observed large-scalevariance is due to velocity variations, as opposed tovariation caused by <100% mass recovery, which maybe the result of three-dimensional flow.

The only difference between van Wesenbeeck's fieldstudy of resident concentration and this column studywas the absence of lateral flow between the columns.The columns included all of the vertical variability in

ufO.8

$0.6

^-0.4—

Hi. 02 3

Spatial scale [m]

Fig. 2. Mean variance, Ey[M2], as a function of spatial scale forresident concentrations in the column and field experiments.


hydraulic and transport properties, and all of the variabil-ity due to variations in horizon thickness. Thus, it appearsthat the spatial scale dependence observed in the fieldwas due to lateral solute fluxes caused by three-dimensional flow induced by variable horizon thickness,rather than a spatial autocorrelation in hydraulic andtransport properties. An increase in variance at spatialscales greater than that at which 100% mass recoveryoccurs, i.e., the streamtube scale, can be attributed tothe pdf of streamtube velocities, f(v). In both studies,the increase was =20%.

Analysis of Flux ConcentrationFigure 3 shows Cr concentration vs. net applied

water, /, for all horizontal sampling coordinates of theundisturbed columns at depths of 0.4 and 0.8 m. Giventhe relatively high degree of uniformity of water and

solute application (Jw = 2.26 ± 0.4 cm d '). any variabil-ity in solute breakthrough can be attributed to variabilityin average vertical transport properties between thecores. The interpretation of measured C(z,t) or C(z,7)to represent the residence-time distribution of a traceris only possible if both injection and detection are per-formed in the flux mode (Kreft and Zuber, 1978). Inthe column study, solute was injected in the flux mode,but the TDR measures the concentration in the residentfluid, Cf. Thus, comparison of cf with flux concentra-tions, Cf, obtained from solution samplers is done onlyto observe the general trends of the solute behavior.

Figures 4a and 4b show the large-scale BTCs, asfunctions of /, at a depth of 0.4 and 0.8 m for both thecolumn and the solution sampler data from the flux-averaged field experiment. Generally, the shapes of theBTCs at both depths were quite similar. At both depths,the solute concentration increased from background lev-

20Distance [m]

Fig. 3. Variability in time domain reflectometry measured solute concentration vs. net applied water across all columns: (a) z = 0.4 m,(b) z = 0.8 m.


els to a peak in « 5 cm of net applied water, althoughthe TDR-measured curves showed a more gradual returnto background levels. Although the TDR-measured con-centrations were scaled to the specific mass, M0, usedin the field, there was still some difference in the concen-tration of Cl~.

The differences in concentration between the columnand field curves could be due to a number of factors.One explanation may lie in the assumption of verticalsolute transport. Calculation of the large-scale ETC fromthe solution sampler data is based on the assumption thatone-dimensional flow occurs in the soil and that the massflux of solute satisfies the following relationship:

= 7W E[Q] [12]where E[ ] is the expectation operator, and Jm is thewater flux density at a location k. This assumption isvalid in the columns. However, in the field where spatialvariability leads to variability in the direction and magni-tude of hydraulic gradients and in the direction of flowand transport, Eq. [12] is probably invalid. This assump-tion does not account for any correlation between thelocal values of Jw and measured Ck. In field studies,where flow would most likely be multidimensional, pointestimates of Jw would be lower than those expectedduring one-dimensional flow. The result would be anapparent decrease in solute mass recovered. In the litera-ture, low mass recoveries have often been reported, even

for conservative tracers. Based on the assumption ofone-dimensional flow, the mass recovery of Cl~ fromthe solution samplers was only 61.2% at the 0.4-m depthand 68.8 % at 0.8 m. In the field, solute could also escapethe solution samplers due to lateral movement and rapidtransport, which would reduce the mass recovery.

The mean water contents, 0, at 0.4 and 0.8 m (Table2) were almost identical for the column and field experi-ments. There was a 1.4% difference in 0 between the0.4- and 0.8-m depths in the field, compared with a2.1% difference in the columns. The magnitude of thedifferences lies within the limit of error expected for theTDK. At z = 0.8 m, the solution-sampler curve reachedits peak concentration more rapidly than the TDR-measured curve. In the field experiment, the irrigationsystem was calibrated to supply 1.25 cm3 cm~2 d"1,although there was some variation (Younie, 1993). Thecalculated / could be a source of error, since it dependedon the estimation of evaporation and rainfall. This errorwould be further compounded for measurements takenover a longer period of time, as was the case at 0.8 m.

Another explanation for the discrepancy may lie inthe nature of the comparison, i.e., a comparison ofresident and flux concentrations. The differences betweenthe column and field data are qualitatively similar tothose observed by Parker and van Genuchten (1984)for flux and resident concentrations. If both were fluxconcentration curves, we would have expected a smaller

500

400

,300

200

100

0500

400

,300

100

(a) ColumnsField

(b) ColumnsField

0.20

0.16

— 0.12

QS0.08

0.04

0

0.20

0.16

0.04

0

(d)

ColumnsField

ColumnsField

5 10 15 20 25 30Net applied water [cm]

35 350 5 10 15 20 25 30Net applied water [cm]

Fig. 4. Comparison of large-scale curves for undisturbed column and flux-averaged field data, measured concentrations at: (a) z = 0.4 m, (b)Z = 0.8 m; probability density functions f(I) at (c) z = 0.4 m, (d) /(/) z = 0.8 m.


Table 2. Measured water content (0) and transport parametersdetermined by the method of moments for undisturbed columnsand flux-averaged field experiment.

Local scaleDepth

m0.4

0.8

Experiment /pa* E(/k)—— cm ——

ColumnFieldColumnField

S.867.33

11.0010.30

8.928.22

14.0911.83

Vary*)

cm2

23.476.94

23.4010.49

Large scale

W EN(/)—— cm ——6.006.74

11.009.40

8.908.00

14.0711.68

VarN(J)

cm2

27.138.35

26.7818.12

0

m3m-3

0.1820.1830.1610.169

amount of water to leach the pulse to 0.8 m in thecolumns. Although both experiments would have encoun-tered layers of variable thickness, the effects would begreater in the field where lateral flow can occur. Withthe possibility for lateral flow, the disparity between fluxand resident concentrations would increase. Since theproportion of the profile occupied by soil tongues in-creased to a maximum in the 0.8- to 1.0-m range, thedisparity would probably reach a maximum in this range,after which it should decrease with increasing distancefrom the solute injection point at the surface.

The differences due to mass recovery can be removedby scaling the measured concentration to the specificmass recovered to obtain pdfs of travel volume (Eq. [3]and [4]). Figures 4c and 4d show that the pdfs,/(7), forthe solution-sampler and TDR data are generally quitesimilar. The field data lag slightly behind the columndata at 0.4 m, with the opposite occurring at 0.8 m.The net applied water to the peak concentration, /peak,was 12% lower in the columns than in the field at 0.4m and 14% higher at 0.8 m (Table 2). There wererelatively small differences in the first moments of bothcurves. In the columns, E[/] was 11% higher at the0.4-m depth, and 20% higher at the 0.8-m depth. Thiscould be due to the effects of dispersion on the temporalmoments of concentrations injected in the flux mode anddetected in the resident mode (Kreft and Zuber, 1978).This can be verified by fitting transport models, but asmentioned before, would require the assumption of aprocess model. These differences could also be relatedto the higher dimension of flow in the field. Given thepossibility of lateral movement in the field, it should berecognized that /(/) calculated for the field would atbest be an apparent one-dimensional pdf, which wouldintroduce some error in the interpretation of transportparameters.

Horizontal Scale Dependence of TransportAt the local scale, Var(7) in the columns was about

three times higher than in the field at 0.4 m and abouttwo times higher at 0.8 m (Table 2). Given the effectof dispersion on temporal moments, higher vales ofVar(7) for the TDR-measured curves are not unexpected.However, the observed decrease in Var(7) from 0.4 to0.8 m in the column data violates current assumptionsabout the relationship between solute spreading and dis-tance traveled. In a one-dimensional field study, Br~,Butters and Jury (1989) observed a compression-expan-sion of the solute plume beyond a 3.0-m depth. This

9"^0.8

- 0.6

Cfl.4LU

J-0.2

a.' o

~

: I ............̂ —— ' ]

- /

: / "•'"

0 1 2 3 4 5 6 7Spatial scale [m]

Fig. 5. Mean variance, E/[A/2], as a function of spatial scale for columnmeasurements of resident fluid concentration at / net applied waterC[(7) and field measurements of flux-averaged concentration at /net applied water C'(7).

mechanism, which appears to be operative in verticalheterogeneous soils, may well be operating in this soil.

There was also an increase in Var(7) from the localscale to the large scale for both the column and solutionsampler data. There was a 20% increase in Var(/) acrossspatial scales at 0.4 m and a 73% increase at the 0.8-mdepth in the field experiment. The smaller difference at0.4 m is probably related to the combined effects ofcropping and cultivation, which would tend to smooth outlateral variations. These mechanisms are mainly effectivenear the surface and would have less of an effect at 0.8m. Transport processes at 0.4 m would probably showmore of an effect of surface management than at 0.8m, hence the smaller increase in Var(/) across scales.Kachanoski et al. (1990) found a 44% increase in Var(7)across scales at 0.2 m and an increase of only 33% at4.0 m in the same soil.

Figure 5 compares the scale dependence of transportvariance in a plot of the normalized variance for thecolumn and field experiments. Since Younie's (1993)experimental design did not permit this type of analysis,the solution-sampler data discussed by van Wesenbeeckand Kachanoski (1991) are used. These data (z = 0.4m and /w = 83.8 cm d"1) were obtained at 0.2 mincrements along a 9.6 m cultivated transect at the samesite. Again, the column data showed an abrupt increasein the normalized variance within 0.4 m. This reiteratesthe suggestion of spatial independence of the transportprocess in the columns. Although this is consistent withthe requirement of noninteracting streamtubes, it is in-consistent with field observations on the same soil, whichshowed a gradual increase in scale-dependent transportvariance to a sill with a range of 3.5 to 4.0 m. Theobserved increase in the range of the sill to a value abovethe 2.0-m period of tonguing of the B horizon is probablydue to tillage-induced smoothing in the Ap horizon (vanWesenbeeck and Kachanoski, 1991).

SUMMARY AND CONCLUSIONSIn this study, we tested the ability to predict the large-

scale transport behavior of a vertically heterogeneous soilfrom the ensemble average behavior of 50 undisturbedcolumns sampled along a horizontal transect. Althoughthe column and field data describe the extremes of possi-


ble behavior, i.e., one-dimensional vs. three-dimensionaltransport, the results show either approach to be equallyaccurate for estimating the center of mass. In the compari-son of the resident concentrations, the increased varianceobserved in the field is probably due to lateral movementin response to the variable B horizon thickness. Compari-son of TDR-measured data with solution-sampler datashowed a higher Var(7) in the TDR data. IncreasedVar(7) could be due to the spatial averaging of solution-sampler concentration data without considering varia-tions in 7W caused by three-dimensional flow or by thedifferent modes of detection of the TDR and solutionsamplers.

Although the column measurements showed no spatialscale dependence of transport, it was demonstrated inboth the flux and resident measurements in the field.Given the similarity in the large-scale column- andfield-measured transport properties for this soil, it ispossible that the absence of spatial scale dependence inthe column measurements may be due to the forcedone-dimensional flow regime. In the field where flowappears to be three dimensional, there is a greater proba-bility that the transport at one spatial location will beinfluenced by an adjacent location, especially given thenature of the B horizon. The observed spatial scaledependence in the field is probably caused by the distribu-tion of horizon thickness and its effect on lateral transportrather than spatially autocorrelated transport propertieswithin a horizon.

Overall, the stochastic streamtube concept was usefulfor predicting the center of mass under the specifiedboundary conditions in a soil with variable horizon thick-ness. However, neglect of the higher dimensionality ofsolute transport, which appears to be caused by variationsin horizon thickness, may limit its application as a realis-tic physical model in this type of soil. In many soils,especially when layering may be due to tillage or crusting,thickness variations occur at relatively shallow depthsin the soil profile. Under such conditions, predictionsof the stochastic streamtube model will require carefulinterpretation.

ACKNOWLEDGMENTSFinancial support for this work was provided by the Natural

Sciences and Engineering Research Council of Canada, theOntario Ministry of Agriculture and Food, and AgricultureCanada.

field and undisturbed-column measurements for predicting transport in unsaturated layered soil

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