Soil Science Society of America Journal 64:62-74 (2000)
© 2000 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
Time Domain Reflectometry Measurements of Solute Transport across a Soil Layer Boundary
H.H. Nissena,
P. Moldrupa and
R.G. Kachanoskib
a Environmental Engineering Lab., Dep. of Civil Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
b Room 50, Murray Building, 3 Campus Drive, Univ. of Saskatchewan, Saskatoon, SK, Canada S7N 5A4
i5hn{at}civil.auc.dk
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ABSTRACT
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The mechanisms governing solute transport through layered soil are not fully understood. Solute transport at, above, and beyond the interface between two soil layers during quasi-steady-state soil water movement was investigated using time domain reflectometry (TDR). A 0.26-m sandy loam layer was packed on top of a 1.35-m fine sand layer in a soil column (0.15-m i.d.). Soil water content (
) and bulk soil electrical conductivity (ECb) were measured by 50 horizontal and 2 vertical TDR probes. A new TDR calibration method that gives a detailed relationship between apparent relative dielectric permittivity (Ka) and was applied. Two replicate solute transport experiments were conducted adding a conservative tracer (KCl) to the surface as a short pulse. The convective lognormal transfer function model (CLT) was fitted to the TDR-measured time integral–normalized resident concentration breakthrough curves (BTCs). The BTCs and the average solute-transport velocities showed preferential flow occurred across the layer boundary. A nonlinear decrease in TDR-measured in the upper soil toward the soil layer boundary suggests the existence of a 0.10-m zone where water is confined towards fingered flow, creating lateral variations in the area-averaged water flux above the layer boundary. A comparison of the time integral–normalized flux concentration measured by vertical and horizontal TDR probes at the layer boundary also indicates a nonuniform solute transport. The solute dispersivity remained constant in the upper soil layer, but increased nonlinearly (and further down, linearly) with depth in the lower layer, implying convective-dispersive solute transport in the upper soil, a transition zone just below the boundary, and stochastic–convective solute transport in the remaining part of the lower soil.
Abbreviations: BTC, breakthrough curve • CD, convective–dispersive • CDE, convective–dispersion equation model • CLT, convective lognormal transfer function model • DC, direct current • ECb, bulk soil electrical conductivity • ECw, electrical conductivity in the soil solution • LSO, least squares optimization • pdf, probability density function • SC, stochastic–convective • TDR, time domain reflectometry
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INTRODUCTION
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THE RAPID INCREASE in the number of groundwater reservoirs, streams, lakes, and coastal areas contaminated with nitrate and organic chemicals has emphasized the need for accurate models to predict the transport of solutes through the vadoze zone. The commonly used solute-transport models are simplified and idealized descriptions of the actual transport processes in the soil based on current knowledge. The quality of predictions made with these models naturally depends on how well they describe the actual solute- transport processes. To improve our understanding of the transport processes in natural, heterogeneous soil systems, and to test new model concepts, detailed measurements of solute transport are needed.
Time domain reflectometry is an accurate and widely used nondestructive technique for measuring soil water content (Topp et al., 1980) and bulk soil electrical conductivity (ECb) (Dalton et al., 1984; Nadler et al., 1991; Dalton, 1992). The TDR principle is based on launching a spectrum of electromagnetic (EM) waves into a waveguide (TDR probe) embedded in the soil under investigation and measuring the reflected signal as a function of time. The travel time of the waves in the waveguide is proportional to the soil water content and the attenuation can be related to ECb. No physical destruction (soil coring) or extraction of solute (solution samplers) is necessary and there are no health hazards involved (radioactive tracers) with the TDR technique. TDR also enables a very high temporal and spatial measurement frequency.
Both flux and resident concentration can be measured with TDR. The attenuation of the EM waves is proportional to the total amount of solute within the volume of influence of the waveguide (the resident concentration). Horizontally inserted TDR probes have been used to measure the temporal development in resident solute concentration, evaluate the transport processes, and estimate parameters in solute-transport models (Vanclooster et al., 1993; Mallants et al., 1994; Ward et al., 1994; Ward et al., 1995; Mallants et al., 1996a; Vanderborght et al., 1996). Kachanoski et al. (1992) showed in a field study how vertically inserted TDR probes can be applied to estimate the solute mass flux at quasi-steady-state water movement during constant flux infiltration. If the solute is added to the soil as a short pulse, the attenuation of the EM waves is constant as long as the solute remains above the end of the TDR probe. As the solute starts leaching beyond the end of the probe, the attenuation of the EM waves decreases, which can be related to the mass of solute passing beyond the end of the probe. Recently, Vanclooster et al. (1995) presented a method to estimate solute mass flux at quasi-steady-state water movement during constant flux infiltration from measurements of resident concentration with horizontally inserted TDR probes. In this case the mass of solute remaining above a given depth (z) is found by integrating the depth profile of resident concentration. The temporal change in mass equals the mass flux beyond z.
One of the unresolved problems in soil physics is the formulation of solute transport through layered soil. Most soils are highly heterogenous in the z-direction and some have distinct horizons with radically different transport properties. In order to extrapolate from one location to another in vertical heterogenous soil it is necessary to incorporate a depth-dependent description of the soil properties into the transport model (Jury and Roth, 1990). If transport of solute through a layered soil is represented as a transfer function, it is possible to predict the solute flow input-response function at a given depth (z) if the solute flow input-response function of the individual soil layers and the correlation between the layers above z are known (Jury and Roth, 1990). In the special cases of perfectly correlated or independent soil layers, the solute flow input-response function at depth z is given in terms of the properties of the individual layers (Jury and Roth, 1990). The convective lognormal transfer function model (CLT) represents a soil with perfectly correlated travel times whereas the convective–dispersion equation model (CDE) represents a soil with uncorrelated travel times (Jury and Roth, 1990). Both models have well-known analytical solutions. For the intermediate correlations, however, there are no analytical solutions. Therefore both fundamental and applied research studies of solute transport across interfaces are necessary to develop a comprehensive theory (Jury and Roth, 1990) and better models for predicting the transport of contaminants in layered soil systems. The objective of this study was to investigate solute transport at, above, and beyond the layer boundary between a fine-textured and coarse-textured soil at quasi-steady-state soil water movement, based on high-resolution TDR measurements.
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Theory
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Consider the scenario where solute travels through a layered soil in individual stream tubes containing different local water fluxes with small or no mixing in the plane perpendicular to the direction of flow. If the stream tubes are continuous across the layer boundary (i.e., stream tubes containing high water fluxes in Layer 1 are connected to stream tubes containing high water fluxes in Layer 2 and the same applies for stream tubes containing intermediate and low water fluxes), then the solute travel times through the second layer are perfectly correlated with the travel times of the first layer (Jury and Roth, 1990). In the described scenario the solute transport is stochastic–convective (SC) in the individual layers and can be described by a convective lognormal transfer function model (CLT).
Another extreme scenario arises if there is perfect mixing between the stream tubes in the horizontal plane caused by mechanical dispersion and solute diffusion (Vanclooster et al., 1995). Here the solute travel-time distribution in the second layer is unaffected whether the solute continues in a stream tube containing a water flux of the same relative order of magnitude or not and the solute travel times in the second layer are uncorrelated with the travel times of the first layer. This is conceptualized in the CDE model where the travel-time distribution in each layer is described as the sum of the mean drift motion and the random longitudinal dispersion of the solute plume (Vanclooster et al., 1995).
Although the CLT and CDE models represent two radically different solute-transport scenarios, it is impossible to distinguish between the two models if the solute transport is observed in only a single depth (Jury and Roth, 1990). If the model parameters are determined in a nonlinear least squares optimization (LSO) between measured and modeled solute BTCs at a given reference depth, both models will provide practical identical descriptions of the measured BTCs. However, model predictions at depths different from the reference depth will be erroneous if the wrong model is applied. Thus, BTCs measured at several depths are needed to recognize which model is most correct. Due to the identical descriptions of the individual BTCs, either the CDE or CLT model can be fitted to the BTCs. The depth dependency of the model parameters will reveal whether the solute-transport process is stochastic–convective or convective–dispersive (CD), assuming that one of the models applies. In this study the CLT model was chosen following Vanderborght et al. (1996).
Solute flow transfer function models are based on flux-averaged concentrations Cf(z,t). The outflow flux concentration is calculated by convoluting with time the input solute flow with a soil-specific solute flow input response function (ff[z,t]). Traditionally, ff(z,t) is determined by adding the solute at the soil surface as a narrow pulse (Dirac delta function) and subsequently measuring Cf(z,t) at the depth of interest (z = l) as a function of time (t). In the case of steady water flow, ff(z,t) can easily be calculated from the measured Cf(l,t) values
 | (1) |
where Cf*(l,t) is the time integral–normalized flux concentration (Vanderborght et al., 1996). If the solute is conservative, the measured ff(z,t) equals the travel-time probability density function (pdf), which is assumed lognormal in the CLT model (Jury and Roth, 1990)
 | (2) |
where µl and 
2l are the mean and variance of the population ln(t) at reference depth l, and z is distance (positive downwards). The CLT model parameters are determined in a nonlinear LSO of Eq. [2] to the experimentally obtained solute flow pulse input response function (Eq. [1]). Unfortunately there are very few sampling techniques that are able to determine Cf(z,t) and the available techniques such as solution samplers have several drawbacks: only small volumes of water can be withdrawn from unsaturated soil, the removal of water disturbs the flow path, and the concentration in the sampled water may yield anything between resident and flux concentration (Parker and van Genuchten, 1984).
Vanderborght et al. (1996) presented an alternative approach to determine the CLT model parameters at reference depth l using time integral–normalized resident concentrations (Crt*[l,t]) defined as
 | (3) |
Assuming that the solute transport is SC, and the solute is added as a Dirac delta function during steady-state water flow, Vanderborght et al. (1996) derived an expression for the travel-time resident pdf which equals Crt*(z,t) for a conservative tracer
 | (4) |
Thus, the CLT model parameters at reference depth l can be obtained from time series of Cr(l,t) by fitting Eq. [4] to the experimentally determined Crt*(l,t) (Eq. [3]) and applying nonlinear LSO. Since TDR measures Cr(z,t) and the TDR probes are usually positioned in the plane perpendicular to the direction of flow (horizontally inserted), the resulting measurements are time series of Cr(l,t) at the position of the probe (l). Thus, if a large number of TDR probes are horizontally inserted in a soil profile, detailed information on the development in the CLT model parameters can be obtained as a function of depth.
To determine the CLT model parameters from time series of Cr(z,t) measured in a soil monolith by horizontally inserted TDR probes, Vanderborght et al. (1996) compared the time integral–normalized resident concentration approach with (i) the time integral–normalized flux concentration approach and (ii) the depth integral- or mass-normalized resident concentration approach. The time integral–normalized flux concentration (Cf*[z,t]) is calculated at a given depth (l) by integrating Cr(z,t)(z)/M0 (where M0 is the total mass per unit area applied at the surface) with respect to depth, which yields the relative mass of solute above l (MR[l,t]). Subsequently, the first derivative of MR(l,t) with respect to time yields Cf*(l,t). The CLT model parameters are obtained by fitting Eq. [2] to the measured Cf*(l,t) profile using nonlinear LSO. The depth integral- or mass-normalized resident concentrations (Crm*[z,t]) are determined as a function of time by dividing TDR-measured Cr(z,t) by M0 or by the depth integral of Cr(z,t)
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The model parameters are obtained by fitting the travel depth pdf of the CLT model
 | (6) |
to the Crm*(z,t) time series using nonlinear LSO.
When applying either the mass-normalized resident concentration or the time integral–normalized flux concentration approach to determine the CLT model parameters, the a priori assumption is that the mass per unit area passing through the sampled stream tubes (M'0) equals M0. Furthermore, both methods require knowledge of Cr(z,t), which calls for a calibration of the individual TDR probes relating TDR-measured load impedance (ZL) to Cr(z,t). It is inherent in the calibration approach that M'0 equals M0. Thus, errors are introduced in both the mass-normalized resident concentration and the time integral–normalized flux concentration approach if the sampled set of stream tubes do not represent the solute transport at the column scale. In the time integral–normalized resident concentration approach no individual calibration of the TDR probes is necessary since any multiplicative constant relating TDR-measured ZL to Cr(z,t) cancels out in Eq. [3] (Vanderborght et al., 1996). Besides, if the solute transport in the sampled set of stream tubes is SC (i.e., no solute exchange between the tubes), the CLT model parameters only characterize the solute transport in the sampled stream tubes. Since the horizontally inserted TDR probes sample only a fraction of the stream tubes at a certain depth and since heterogeneous solute transport may occur in a soil column where a fine textured soil is layered upon a coarse textured soil, the time integral–normalized resident concentration approach was preferred in this study to determine the CLT model parameters.
In addition to the 50 horizontally inserted TDR probes, the soil column was monitored by 2 vertically inserted probes along the entire length of the upper soil layer. The vertical probes made it possible to measure the travel-time flux pdf at the layer boundary following Kachanoski et al. (1992). Theoretical expressions relating Cf(z,t) and Cr(z,t) have been derived for both CD (Parker and van Genuchten, 1984) and SC solute transport. In the case where the solute transport can be described by the CLT model, Vanderborght et al. (1996) showed the following theoretical relationship between Cf*(z,t) and Crt*(z,t)
 | (7) |
Measurements of Crt*(z,t) (horizontal probes) and Cf*(z,t) (vertical probes) at the soil layer boundary enable an experimental evaluation of Eq. [7] under the condition that the CLT model is able to describe the solute transport across the layer boundary.
As in the case of the horizontally inserted probes, vertically inserted TDR probes have a finite sample volume. Consequently, the measured solute transport represents only the solute transport in a subsample of the total amount of stream tubes in the upper soil layer. In the CLT model, both Cf(z,t) and Cr(z,t) may vary between different subsamples of stream tubes as long as the solute transport in the sampled stream tubes is SC. Since Cf(z,t) and Cr(z,t) were measured at different lateral positions using vertically and horizontally inserted TDR probes, respectively, we have to make the a priori assumption that the subsamples of stream tubes have identical solute transport properties for Eq. [7] to be valid.
The CLT and CDE models represent extremes regarding solute dispersion as discussed above. In the CDE model the variance of the solute travel-time distribution increases linearly with depth whereas it increases quadratically in the CLT model. Usually the spreading of the solute is expressed by the dispersivity (
), defined as
 | (8) |
for the CLT model. For the CDE model (z) is defined as D/v, where D is the dispersion coefficient and v is the pore water velocity. If the model parameters are constant, then (z) increases linearly with depth for SC solute transport and (z) is a constant for CD solute transport. Thus, a determination of (z) at several depths above and below a layer boundary will provide information on the solute-transport processes in the individual soil layers and across the boundary.
Elrick et al. (1992) denoted the average travel time, µp, to reach a given depth, l, as the estimated population mean of the solute particle travel times (i.e., the mean of the population t). For SC solute transport µp is defined as
 | (9) |
It follows that the average velocity of the solute particles traveling between the soil surface and depth l is
 | (10) |
To eliminate the depth dependency of the average solute transport velocity (v[z]) on , Ellsworth et al. (1991) introduced a coordinate transformed depth (z*)
 | (11) |
where z equals the original depth coordinate and z' is a dummy variable of integration.
Determination of Cr(z,t) and Cf*(z,t) from TDR Measurements
In this study the lumped circuit approach was used to measure ECb with TDR since it provides the most accurate estimate of the direct current (DC) conductivity in the soil (Topp et al., 1988; Nadler et al., 1991). The TDR rods embedded in soil are regarded as a lumped circuit element with impedance ZL at the end of a low-loss waveguide with impedance Z0 and is calculated by
 | (12) |
where 
(the reflection coefficient) is the ratio of the reflected voltage at steady state to the voltage originally transmitted into the waveguide (voltage level of the square wave). Equation [12] is valid only if the voltage level, and hence , at all positions along the waveguide has settled at the same steady-state level, such as when all multiple reflections arising between differences in impedances along the waveguide have ceased (Nadler et al., 1991; Lancaster, 1992; Heimovaara et al., 1995). For a given TDR probe geometry the load impedance is inversely proportional to the conductivity of the soil surrounding the probe
 | (13) |
where Kp is the cell constant of the TDR probe and ft is a temperature correcting factor. Heimovaara et al. (1995) found that ft in soil equals ft in KCl solutions. In addition, Heimovaara et al. (1995) showed that TDR-measured ZL includes a constant contribution from cables, connectors, and the cable tester (Zcable) which must be corrected for to obtain ZL of the soil (Zsample), such that Zsample = ZL - Zcable.
According to Rhoades et al. (1976), Kachanoski et al. (1992), and Vogeler et al. (1996), a linear relationship exists between ECb and the electrical conductivity in the soil solution (ECw) at constant . At low solute concentrations linearity also applies between ECw and resident solute concentration Cr(z,t). Combining the linear expressions with Eq. [13] and solving for Cr(z,t) yields
 | (14) |
where ZL(z,t)-1 is the DC conductance in depth z at time t, ZL(z,ti)-1 is the DC conductance in depth z prior to application of solute, and ß(z) is a calibration constant depending on soil type, temperature, , type of solute, and TDR probe geometry (Kachanoski et al., 1992). Ward et al. (1994) examined the linearity of the relationship shown in Eq. [14] and found that it becomes nonlinear if (i) the combination of and concentration leads to excessive attenuation of the TDR signal, and (ii) at low solute concentrations where the nonlinearity is probably related to an effect of exchangeable ions on the solid phase (Rhoades et al., 1989; Ward et al., 1994).
Due to the nonrigid probe design used in this study ß(z) had to be determined in an indirect calibration. Two approaches are applicable for horizontally inserted TDR probes: (i) application of solute as a pulse of limited duration and then the mass of tracer is related to the measured pulse response following the principles of convolution, or (ii) continuous leaching of solute until the concentration of the soil solution equals the input concentration (Ward et al., 1994; Mallants et al., 1996b). Regarding (ii), the time required to reach a uniform solute distribution is often long, making this method tedious to apply. Method (i) also provides more information on the transport processes in the soil (Ward et al., 1994). Therefore method (i) was used in this study. Following the method of convolution presented by Ward et al. (1994), ß(z) was determined as
 | (15) |
where Jw is the area-averaged water flux. Note that if the area-averaged mass passing the sampled set of stream tubes deviates from M0, ß(z) will be wrongly estimated. This will introduce errors in Cr(z,t) and the CLT model parameters determined by the mass-normalized resident concentration or the time integral–normalized flux concentration approach. The problem does not exist in the time integral–normalized resident concentration approach since ß(z) cancels out in Eq. [3] when calculating Crt*(z,t).
As mentioned, TDR measures the resident solute concentration (Cr[z,t]) within the volume of influence by the probe. At steady-state and for a conservative tracer it is possible to calculate the relative solute mass flux at a fixed depth as a function of time (ff[l,t]) from measurements of Cr(z,t) as shown by Kachanoski et al. (1992) and Vanclooster et al. (1995) for vertically and horizontally inserted TDR probes, respectively. In the case of vertically inserted TDR probes, three requirements must be fulfilled: (i) solute application must be terminated before any of the applied solute passes the end of the probe rods, (ii) perfect lateral mixing of the solute is assumed, and (iii) the distribution of solute along the probe has no influence on ZL as long as all the applied solute is above the end of the TDR probe. Based on these assumptions, Kachanoski et al. (1992) derived an expression for the temporal development in the relative specific mass of solute remaining above the end of the TDR probe rods positioned at depth l. The mass of solute per unit area above the end of the TDR rods is given by
 | (16) |
where Cr(l,t) (Eq. [14]) is the average resident concentration and l is the average soil water content along the probe (Kachanoski et al., 1992). As long as all the solute is above the end of the probe rods, Eq. [16] yields the total mass of solute applied (M0). As the solute starts leaching beyond the end of the probe rods, Eq. [16] yields the mass remaining above the probe rods (M[l,t]) as a function of time. Inserting Eq. [14] into Eq. [16] and calculating the relative mass of solute (MR[l,t]) = M[l,t]/M0) gives
 | (17) |
where ZL(l,t)-1, ZL(l,ti)-1, and ZL(l,t0)-1 are the load impedance measured as a function of time, prior to application of solute, and before the solute starts leaching beyond depth l, respectively. The relative solute mass flux at the end of the probe rods as a function of time (ff[l,t]) is obtained by taking the first derivative of MR(l,t) (Eq. [17]) with respect to time
 | (18) |
A calibration of the probe is unnecessary since MR(l,t) and ff(l,t) are determined solely from TDR-measured load impedance. If a conservative solute is applied uniformly to the soil surface as a narrow pulse (Dirac delta function), Eq. [18] equals the travel-time flux pdf of the sampled stream tubes and, hence, equals Cf*(l,t) of the sampled stream tubes at depth l (Jury and Roth, 1990).
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Materials and methods
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Soil Characteristics
Two soils, Borden fine sand and Cambridge sandy loam, were used in this study. The Borden sand was collected at the Delhi Research Station, Agriculture and Agri-Food Canada, Ontario, Canada; the Cambridge loam was collected from the top 0.2 m of an agricultural field at the Cambridge Research Station, Ontario, Canada. The soils were air-dried, passed through a 0.002-m sieve, and mixed thoroughly to obtain a homogenous mixture. Some characteristics of the soils are listed in Table 1
. The main drying water retention curve was determined for both soils in the soil water potential range from 0- to 2-m H2O (Fig. 1)
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Time Domain Reflectometry Equipment and Measurement Method
Two different systems for automatic TDR data acquisition were used in this study. Both systems includes the Tektronix 1502B cable tester equipped with an RS 232 interface (Tektronix Inc., Beaverton, OR). Multiplexing was carried out with either (i) a 25-probe system based on the principles described by Heimovaara and Bouten (1990) and developed by Thomsen (1994) and Thomsen and Thomsen (1994), or (ii) a 61-probe system from Dynamax including four TR200 multiplexers and a beta version of the TACQ software (Dynamax Inc., Houston, TX).
A personal computer (PC) controlled cable tester and multiplexing systems. The PC collected data (TDR traces) for data processing later. The apparent relative dielectric permittivity (Ka) was obtained from the TDR traces following the principles presented by Heimovaara and Bouten (1990). The load impedance (ZL) of the TDR probe was determined from values of the reflection coefficient (0, i, and 
) following the ratio metric approach by Wraith et al. (1993). Determination of ZL was only carried out with the Dynamax system. Steve Evett at USDA-ARS, Bushland, TX, furnished a beta version of his TACQ software, enabling us to measure ZL with the Dynamax system.
Simple two-rod TDR probes without a balun were constructed from stainless steel welding rod (0.0016-m diameter). The probe rods were attached to the shield and conductor of a 50-
coaxial cable by cable shoes and the stripped part of the cable, including the cable shoes, were sealed with liquid plastic coating. Due to the lack of a probe housing, the flexible probes made it impossible to determine the geometry factor of the probe (Kp) in a direct calibration experiment. The required rigidity was obtained from the wall of the containers in which the probes were installed or from the soil itself.
Calibration of the Ka– Relationship
To obtain precise measurements of with TDR, a calibration experiment determining the soil-specific relationship between Ka and in both soils was carried out. Usually this relationship is determined by measuring Ka in a large number of soil samples pre-wetted to different values of covering the range from air-dry to saturation. This is a tedious and time-consuming task. Recently, Young et al. (1997) presented a much faster approach where paired values of Ka and were determined during upward infiltration in a soil column with a vertically installed TDR probe. Depending on soil type Young et al. (1997) obtained the Ka– relationship from air-dry to saturation with 140–260 paired values of Ka– over periods ranging between 7 h and 13 h. Due to the continuous infiltration an automated scale is needed to determine .
In this study, the calibration experiments were conducted in two 1-L glass beakers. A water application system made up by a piece of 0.005-m hard plastic tubing, bended and connected at each end to a T-piece, was placed at the bottom of the beakers. Holes were made at the upper surface of the plastic tube with a hypodermic needle. A piece of thin tubing was connected to the vacant position on the T-piece and glued along the wall of the beaker. Subsequently air-dry Borden sand and Cambridge loam were packed in the beakers to bulk densities of 1.65 and 1.55 Mg m-3, respectively. Two TDR probes (two-rod probe without a balun) were installed vertically in each soil covering the whole soil sample (0.12-m length). The soils were wetted from below by adding water to the pierced plastic tubing at the bottom of the beakers from a Boyle-Mariotte bottle until a state of near-saturation was reached. The soils were then left to evaporate. Thus, varied along (and not in) the plane perpendicular (transverse) to the rods. This is important because the Ka of the soil constituents (including the water) positioned in the transverse plane is subject to a complex averaging, where Ka of each infinitesimal area (dA) within the plane is weighted by the relative gradient in electric potential at dA and the resulting TDR-measured Ka is the sum of the weighted Ka distribution, which does not equal an arithmetic average of the Ka distribution (Baker and Lascano, 1989; Knight, 1992; Knight et al., 1994; Petersen et al., 1995; Ferré et al., 1996). However, the travel time of the EM waves in the probe, and hence, TDR-measured Ka, is unaffected by the distribution of Ka along the rods, the latter shown experimentally by Topp et al. (1982) and theoretically by Ferré et al. (1996). The probes could be detached from the multiplexing system, making it possible to move and weigh the beakers. The beakers were weighted twice per day and Ka was determined automatically every hour. In the data analysis it was assumed that evaporation progressed linearly between weighing events. The multiplexing system developed by Thomsen (1994) and Thomsen and Thomsen (1994) was used in this experiment.
Infiltration Experiments in a Two-Layer Soil Column
To investigate the transport of solute within and across the boundary between a fine-textured and a coarse-textured soil at constant and Jw, two replicate experiments referred to as 1 and 2 were carried out in a large PVC pipe (0.163-m o.d., 0.152-m i.d., 1.69-m height ). A long pipe was needed to reduce the influence of the elevated at the lower boundary (drained by gravity) on the flow of water and solute in the upper part of the column. The pipe was cut into nine sections and assembled with PVC pipe connectors during packing of soil into the column. The bottom of the column was encapsulated by a PVC housing. At the interphase between the column and the PVC housing a horizontal porous plastic plate supported the soil and allow the soil water to drain by gravity. Air-dry Borden sand was packed in the lower 1.354 m and air-dry Cambridge loam was packed in the upper 0.258 m of the column to bulk densities of 1.65 and 1.55 Mg m-3 respectively.
Fifty TDR probes (numbering starting at the bottom) were inserted horizontally in the column (0.140-m length of rods inside the pipe) through holes in the pipe wall with a slightly larger diameter than the probe rods (0.0016-m o.d.). The pipe wall provided the necessary rigidity and a fixed inter-rod spacing of 0.016 m. In the vertical direction, Probes 1 to 6 were spaced by 0.180 m, Probes 6 and 7 were spaced by 0.096 m, and Probes 7 to 50 were spaced by 0.012 m. Probes 30 to 50 were inserted in the Cambridge loam, while Probes 1 to 29 were inserted in the Borden sand. Following the approach by Knight et al. (1994) and Petersen et al. (1995), the relative accumulated energy (P[h]) below a surface at height h above the probe axis was calculated for the lowest interprobe spacing (i.e., h = 0.006 m). The resulting P(h) equaled 0.91; thus only 18% of the energy was overlapped by adjacent probes at a probe spacing of 0.012 m. In addition, two TDR probes were inserted vertically covering the whole length of the upper soil (Borden sand) (0.258-m length of rods, 
0.016-m inter-rod spacing, 0.0016-m rod diameter).
The water application system consisted of nine hypodermic needles evenly distributed above the soil surface and attached to stainless steel tips welded to a closed stainless steel chamber. A peristaltic pump supplied the chamber with de-ionized water at an area-averaged rate (Jw) of 0.0214 m d-1 (SD = 0.0003 m d-1) and 0.0205 m d-1 (SD = 0.0006 m d-1) in Exp. 1 and 2 respectively. In- and out-flow rates were monitored daily. Since the soils were air-dry when packed into the column it took approximately 60 d to reach quasi-steady-state water flow in the column, evaluated from TDR estimates of and measurements of in- and out flow rates. During the initial 40 d of wetting only was measured with TDR since the beta version of the TACQ software was developed and tested in this period. After 60 d of wetting a narrow pulse of KCl was added at the surface (Exp. 1: volume = 0.003 L, concentration = 280.4 g KCl L-1) followed by 22 d of wetting. Then a second pulse of KCl was added at the surface (Exp. 2: volume = 0.005 L, concentration = 285.0 g KCl L-1) followed by 31 d of wetting. Simultaneous measurements of ZL and Ka were carried out with 30- and 20-min intervals over periods of 22 d (Exp. 1) and 31 d (Exp. 2) respectively. The experimental setup is shown on Fig. 2
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Fig. 2 The experimental setup used in the infiltration experiments. Only one TR200 multiplexer is shown, but four were used in the experiments. All measures are in millimeters
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Results and discussion
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Calibration of the Ka– Relationship
The results from the calibration between Ka and in Borden sand and Cambridge loam are presented in Fig. 3
, and clearly illustrate the potential of the new calibration approach. Measurement at many values of was possible, and created a detailed description of the relationship between Ka and .
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Fig. 3 The measured relationships between apparent relative dielectric permittivity (Ka) and volumetric soil water content () for (a) Borden sand and (b) Cambridge loam. The solid line represents the best-fit third-order regression line
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The uniformity between the TDR probes in the Borden sand is high except for values between 0.33 and 0.36 m3 m-3, where a minor deviation occurs (<0.025 m3 m-3) likely due to small variations in the pore-size distribution of large pores around the probes. In the Cambridge loam measurements both probes were in perfect accordance, proving the reliability of the new calibration method.
A third-order polynomial was fitted to the measured data of Ka and obtained in both Borden sand (Eq. [19]) and Cambridge loam (Eq. [20]). The relationships were used in the column experiments to calculate the soil water content from TDR measurements of Ka.
 | (19) |
 | (20) |
Infiltration Experiments in a Two-Layer Soil Column
Before application of the solute pulse in Exp. 1 the column was wetted until measured with TDR reached a constant level within each soil layer and the water flux out of the column equaled the flux applied at the surface. Figure 4
shows the distribution of as a function of depth in both experiments. Data is presented as the mean and standard deviation of all estimates measured with TDR during leaching of KCl through the column (Exp. 1: 1004 measurements; Exp. 2: 1804 measurements). The values of in the Borden sand (lower soil) is unfortunately determined with a higher degree of uncertainty because the level of in the soil was too low to enable an individual determination of the probe offset. In dry soil it is usually impossible to locate the actual beginning of the probe on the TDR trace. To overcome this problem, the beginning of the probe is determined as the distance from a well-defined fix point prior to the beginning of the probe, which is independent of , plus the distance between the fix point and the beginning of the probe, i.e., the offset (Heimovaara and Bouten, 1990; Dynamax, 1994). An average offset was calculated from the offsets determined in the Cambridge loam (upper soil). It introduces a systematic error that mainly influences the mean value of with < ±0.01 m3 m-3. Water was applied continuously during the experimental period (4 mo). However, small variations in Jw were unavoidable because of variability in the water transport capacity between the different set of hoses used on the peristaltic pump. Short breaks in water application during change of hoses and during determination of Jw, in and out of the column, explains the higher standard deviation of in the upper soil layer. Surprisingly there are some variations in TDR-measured in the Cambridge loam (upper soil). Variations of this order of magnitude are not to be expected for a homogeneously packed soil column. The variations may be due to non-uniform water redistribution below the soil surface induced by the water application system. Towards the bottom of the column increases with depth, since the column is drained by gravity. An influence on from the lower boundary can only be detected at depths below -1.20 m in both experiments, although the influence shows an upward expansion with time. A close comparison between the two experiments in Fig. 4 reveals a slightly increasing in the Cambridge loam (upper soil), while in the Borden sand (lower soil) remains constant. Taking into account a lower Jw in Exp. 2 it can be concluded that the Cambridge loam had not finished wetting at the end of Exp. 1 after 82 d of continuous infiltration.
During steady-state water flow through the column, the matric potential (
) should be constant from the soil surface to z = -1.20 m if Darcy's law is valid. Due to the different soil water characteristics of the two soils (Fig. 1), was expected to settle at two different levels in each soil layer resulting in a steep gradient in at the layer boundary. In the upper part of the Cambridge loam (upper soil) and the Borden sand (lower soil), settled at average values of C 0.33 m3 m-3 and B 0.17 m3 m-3, respectively, during Exp. 2 (Fig. 4b). In Fig. 1 the matric potentials corresponding to C and B are indicated on the main drying water retention characteristic curves and the values are almost identical as expected. Note that the column has been under wetting conditions and the use of main drying water retention characteristic curves ignores the effect of hysteresis. This likely explains the small difference between the estimated (C) and (B) values in Fig. 1.
Water Flow Confinement Region
The TDR measurements on Fig. 4 imply that decreases approximately 0.1 m3 m-3 over the lower 0.10 m of the Cambridge loam (upper soil). Only 9 and 2% of the electrostatic energy surrounding the probes situated 0.006 m (Probes 30 and 29) and 0.018 m (Probes 31 and 28) above and below the boundary, respectively, are expected to cross the layer boundary according to the theory by Knight et al. (1994). Since dielectrics within the sample volume of a TDR probe are weighted by the electrostatic energy density distribution, contributions from dielectrics beyond the layer boundary do not explain the observed decreasing tendency of towards the layer boundary in the Cambridge loam (upper soil). This is supported by the fact that measured right below the boundary is insensitive to the higher level above the boundary. Thus, the steep decrease in over the lower 0.10 m of the upper soil layer cannot be explained by TDR measurement sensitivity but must be explained by an irregular flow pattern above and at the layer boundary.
It is well known that a special type of preferential flow-denoted fingered flow often arises at the boundary during water movement from a fine-textured soil to an underlying coarse-textured soil (Hill and Parlange, 1972; Glass et al., 1989; Liu et al., 1994). Water infiltrates uniformly in the fine-textured soil until the water eventually reaches the layer boundary. Due to a high matric potential in the underlying coarse-textured soil the water does not readily penetrate beyond the layer boundary. This results in a pileup of water until (z) above the boundary exceeds (z) below the boundary. Subsequently, the water penetrates into the underlying soil in a fingerlike pattern, saturated at the tips and traveling fast downwards (Glass et al., 1989; Nissen et al., 1999).
At the early stages of fingered flow, water is only transported through the lower soil in fingerlike channels. Later the surrounding soil wets, but because of hysteretic effects, and the hydraulic conductivity (K) in the fingers remains elevated compared to the surrounding soil (Glass et al., 1989). Fingers have been shown to persist for a substantial period in soil during continuous infiltration (Glass et al., 1989) and it is likely that lateral differences in K, created by fingered flow during the initial wetting of the column, were present in the Borden sand (lower soil) while conducting the solute transport experiments.
Consider the case where water is transported in a fully wetted fine-textured upper soil and in a few well-defined fingers in a lower coarse-textured soil. The water flux at the layer boundary equals the constant flux applied at the surface. In order to reach the fingers, water molecules in the upper soil must move both vertically and laterally except for the molecules positioned directly above the fingers. Thus, a three-dimensional confinement of the initially vertical flow lines towards the fingers must occur. Miyazaki (1993)(p. 108, Fig. 4.12a) visualized this phenomenon experimentally in a Hele-Shaw cell packed with sand over glass beads. Dye was added at various vertical positions along transects next to the fingers. This visualized how the flow lines in the sand (upper soil) confined towards the fingers in the glass beads in a confinement region above the boundary. As the lower soil matrix wets, the relative contribution from the fingers to the total transport of water decreases, but there is still a higher K in the fingers compared to the surrounding soil resulting in a confinement of flow above the boundary.
Now, assume that water traveling through the Cambridge loam (upper soil) can be divided into: (i) confined water that crosses the boundary at a finger(s) and (ii) nonconfined water that crosses the boundary between the fingers (interfinger regions). As the water enters the confinement region, the confined Jw will increase continuously with depth, since the water is transported through a decreasing cross-sectional area, reaching a maximum value as it enters the finger(s). The opposite scenario arises in the interfinger regions where the nonconfined Jw decreases with depth, since the water is transported through an increasing cross- sectional area, reaching a minimum value at the boundary. It follows that will be three-dimensionally distributed in the confinement region due to the proportionality between and Jw. In addition, the confinement of the flow must be associated with an acceleration of the water (from the lower velocity above the confinement region in the Cambridge loam [upper soil] to the higher velocity in the finger), thereby creating a three-dimensional velocity field in the confinement region.
We suspect that a major part of the sample volumes of the TDR probes inserted in the Cambridge loam (upper soil) have been situated in an interfinger region, which explains the decreasing tendency in TDR measured in the lower 0.10 m of the Cambridge loam (upper soil). However, more research, both theoretically and experimentally, is needed to validate the confinement theory.
Solute Breakthrough Curves
For simplicity, mainly results from Exp. 2 will be presented hereafter. A comparison of Crt*(z,t) measured by horizontally inserted TDR probes right above (Probe 30) and below the layer boundary (Probes 29, 27, and 25) as a function of time is shown on Fig. 5
. This reveals that the solute (KCl) is transported across the layer boundary at uneven velocities in the horizontal plane. The solute clearly reached Probe 27 (z = -0.288 m) before it reached Probe 29 (z = -0.264 m), the time difference being approximately 0.3 d. A similar situation occurred in Exp. 1, where the effect of preferential flow on the BTCs was even more distinctive since the solute reached probes below the boundary before it reached probes right above the boundary (not shown). Apparently a preferential flow path bypassed Probe 29 (z = -0.264 m) in Exp. 2 (Fig. 5) and Probes 29 and 30 (z = -0.252 m) in Exp. 1, before entering the sample volume of Probe 27 (z = -0.288 m). The fact that solute reached probes below the boundary before it reached probes above the boundary in Exp. 1 strengthens the hypothesis that a confinement region with spatial variations in solute transport velocities was present in a 0.10-m zone above the boundary. Variations in K between the fingers and the surrounding soil is known to reduce over time (Glass et al., 1989) which could explain the decreasing influence of the confinement in Exp. 2 compared to Exp. 1. In conclusion, the sampled set of stream tubes right above and below the boundary is not representative for the entire set of stream tubes.
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Fig. 5 Time integral–normalized resident concentrations (Crt*[z,t]) as a function of time measured by horizontally inserted time domain reflectometry (TDR) probes right above (Probe 30, z = -0.252 m) and below (Probe 29, z = -0.264 m; Probe 27, z = -0.288 m; Probe 25, z = -0.312 m) the layer boundary in Experiment 2
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Usually it is difficult to recognize the effect of a soil layer boundary on the solute transport if the temporal change in solute concentration is only evaluated in a single depth (Jury and Roth, 1990). A better approach is to evaluate the spatial development in solute concentration as a function of time. Figure 6
shows the depth integral–normalized resident concentration (Crm*) as a function of depth at three selected times after application of solute where the peak concentration was positioned (i) above the boundary (t = 3.40 d), (ii) approximately at the boundary (t = 4.03 d), and (iii) below the boundary (t = 5.14 d). From a visual evaluation of the BTCs the boundary had no effect on the concentration measured by the probes situated right above the boundary and the first probe below. However, at the three successive probes below the boundary an influence was easily recognized, caused by differences in solute travel-time distribution in the sampled stream tubes (i.e., preferential flow as discussed above). Further down in the column some minor scatter could be recognized, but the shape of the BTCs suggests a fairly uniform transport within the sampled soil volume. The relative influence of preferential flow across the boundary on the shape of the BTCs was most pronounced at the front of the BTCs and diminished as the peak concentration passed the layer boundary (Fig. 6). Also, the increased solute particle velocity (v) below the boundary, caused by the lower level in the Borden sand (Fig. 4), influences the shape of the BTCs.
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Fig. 6 Depth integral–normalized resident concentration (Crm*[z,t]) as a function of depth measured by the horizontally inserted time domain reflectometry (TDR) probes at different times (t = 3.40, 4.03, and 5.14 d) after application of the solute pulse at the soil surface in Experiment 2. Position of the soil layer boundary is marked by a broken horizontal line
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Depth Dependency of Model Parameters
A quantitative method to evaluate the variability in the solute transport between the sampled sets of stream tubes is to calculate the average solute particle velocity (v) (Eq. [9] and [10]) from the TDR-measured BTCs. If (i) the solute transport in the sampled stream tubes is representative for the entire set of stream tubes at a given depth, (ii) the TDR-measured equals the effective soil water volume through which solute transport takes place, and (iii) the tracer is nonreactive, then v equals Jw when v is plotted as a function of the transformed depth coordinate (z*). Figure 7
shows the position of the estimated population mean of the solute particle travel times (µp) calculated by Eq. [9] in the transformed depth coordinate (z*). The first derivative with respect to µp(z*) equals v(z*). A segmented linear regression analysis was performed on µp(z*) measured above and below the layer boundary and the lines and equations are shown in Fig. 7 along with the 95% confidence intervals of the predicted lines. The presence of an immobile phase or an underestimation of will lead to v(z*) > Jw, whereas an overestimation of results in v(z*) < Jw. At the measurement scale of the TDR probes, substantial local variations in the distribution of immobile water is not expected in repacked soil at almost constant (z). Therefore, immobile water is expected to increase v(z*) in the entire layer rather than in a few selected depths. From Fig. 7 it is evident that v(z*) is almost constant in the Cambridge loam (upper soil) except for small deviations at z* -0.05 m and right above the boundary, likely caused by confined flow. In the Borden sand (lower soil), small deviations from linearity can be recognized right below the boundary, likely due to preferential flow, and at z* -0.12 m where a decrease in v(z*) is observed at three successive probes followed by an increase in v(z*). As expected, the solute transport is not totally uniform in the Borden sand (lower soil), a tendency that increases with depth (see the 95% confidence intervals). The average v(z*) in each soil layer is defined as the slopes of the regression lines in Fig. 7 and equaled 0.022 m d-1 and 0.025 m d-1 in Cambridge loam (upper soil) and Borden sand (lower soil), respectively. The velocities are significantly different since the regression line of the Cambridge loam (upper soil) is not contained within the 95% confidence interval of the regression line of the Borden sand (lower soil). In both soils, v(z*) is slightly higher than the applied Jw of 0.0205 m d-1. Since the immobile fraction of is expected to be lower in Borden sand (lower soil) than in Cambridge loam (upper soil) because of textural differences, immobile water is not the sole explanation to the observed variations in v(z*). It seems more likely that preferential flow paths have been a part of the sample volume in the Borden sand, resulting in an increased average v(z*). This could also explain the variations with depth of v(z*) in the lower soil (Fig. 7).
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Fig. 7 Temporal development in the position of the estimated population mean (µp[z*]) as a function of the transformed depth coordinate (z*) (Experiment 2). Segmented linear regression was carried out on the data for each soil layer (solid lines) and the 95% confidence intervals of the regression lines were calculated (broken lines). Position of the soil layer boundary is marked by a broken horizontal line
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To further evaluate the solute-transport processes in each layer and across the layer boundary, the dispersivity ([z]) was calculated (Eq. [8]) from the solute BTCs measured by TDR. This is shown in Fig. 8
where is plotted as a function of the transformed depth coordinate (z*). In the upper soil (Cambridge loam), (z*) is practically constant with z*, although some minor deviations can be recognized towards the upper boundary. Hence, in the Cambridge loam (upper soil) the CDE model provides a good description of the solute transport in the sampled stream tubes (Jury et al., 1991). As the solute passes the boundary, (z*) increases slightly until the solute reaches the depth of -0.12 m, at which point an almost linear increase in (z*) can be recognized to the depth of -0.25 m (see Fig. 8). Apparently the sudden increase in (z*) at z* = -0.12 m is coupled to a local decrease in v(z*) (compare Fig. 7 and 8). A likely explanation is that a part of the solute has been trapped in an area with limited water flux leading to extensive tailing on the BTCs measured at depths < -0.12 m. This is supported by the shape of the BTCs since they show a very sharp increase in solute concentration at the front followed by a long tail. Also it appears from Fig. 8 that a transition zone existed right below the boundary where the preferential flow paths were generated and the transport switched from CD above the boundary to SC at depths < -0.12 m. As a consequence of the nonlinear behavior of (z*), neither the CDE or CLT model can describe the solute transport in the transition zone. In addition the model fits to the measured BTCs become increasingly poorer with depth.
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Fig. 8 Dispersivity () as a function of the transformed depth coordinate (z*) (Experiment 2). Position of the soil layer boundary is marked by a broken horizontal line
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Comparison of Vertical and Horizontal TDR Probe Measurements
The previous discussion has focused on the influence of the soil layer boundary on Crt*(z,t) as measured by horizontally inserted TDR probes. In addition Cf*(z,t) was measured at two vertically inserted TDR probes enabling a comparison between Crt*(z,t) and Cf*(z,t) at the soil layer boundary. Unfortunately, a defect relay on the scanner resulted in useful results from only one vertical probe as shown in Fig. 9
. A numerical integrated lognormal travel-time flux pdf (Eq. [2]) was fitted to the data in Fig. 9 using nonlinear LSO. Vanderborght et al. (1996) derived an expression relating Crt*(z,t) and Cf*(z,t) for an SC solute-transport process (Eq. [7]). By using the model parameters determined at the horizontally-inserted TDR probe right above the boundary (Probe 30, l = 0.252 m), model parameters and Crt*(z,t) were predicted at the boundary (z = 0.258 m) using Eq. [4] and subsequently inserted in Eq. [7] to yield Cf*(z,t), which is shown as the broken line in Fig. 9. Subsequently, Cf*(z,t) determined by the vertically and horizontally inserted probes will be denoted Cfv*(z,t) and Cfh**(z,t), respectively. Although the TDR-measured data are scattered it is evident that Cfv*(z,t) deviates from Cfh*(z,t) at the boundary. Two major differences can be recognized: (i) Cfh*(z,t) is more dispersed than Cfv*(z,t) and (ii) the center of mass of Cfh*(z,t) arrives later at the boundary compared to Cfv*(z,t). These observations indicate lateral variations in both v(z*) and (z*) at the boundary and most likely also in the upper soil profile. Thus, the solute-transport properties in any of the two sampled set of stream tubes are not representative for the entire set of stream tubes, in agreement with the confined flow theory.
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Fig. 9 Comparison between the relative mass of solute remaining in the upper soil layer (0–0.258 m) measured by a vertically inserted time domain reflectometry (TDR) probe (circles) and predicted (Eq. [7]) from measurements of time integral–normalized resident concentrations obtained by a horizontally inserted TDR probe (Probe 30; broken line) (Experiment 2). The best-fit parameters in the CLT model (Eq. [4]) were found by least squares optimization (solid line)
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In perspective, given the above knowledge of the solute-transport processes in the column, the used TDR probe array was not optimal. Additional probes inserted horizontally at equal distances but different lateral positions above and below the layer boundary could have improved the level of information. Since the fingers and the effects of confined flow apparently induce a three-dimensional flow pattern, it is desirable to measure the solute transport in all stream tubes, either as an average or as spatially distributed subsamples. The latter could possibly be obtained with a large number of small-scale TDR probes, such as the coil probe presented by Nissen et al. (1998). This requires that the probe be downsized and modified to measure both and ZL.
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Conclusions
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A modified TDR calibration method to obtain the relationship between the soil water content () and the apparent relative dielectric permittivity (Ka) was presented and tested. The very detailed measurements and low degree of labor associated with the method makes it superior to conventional calibration principles. Furthermore, the method seems ideal for determination of the –Ka relationship in packed as well as undisturbed soil columns.
To examine the solute-transport processes at, above, and beyond a soil layer boundary where a coarse textured soil is overlain by a fine textured and less conductive soil, two replicate infiltration experiments were carried out in a large soil column at quasi-steady-state water movement. The solute was applied as a short pulse at the surface. Soil water contents and time integral–normalized resident concentrations were measured by 50 horizontally inserted TDR probes and time integral–normalized flux concentrations were measured at the layer boundary by a vertically inserted TDR probe.
The measured BTCs at different depths showed preferential flow in the form of early breakthrough at probes below, but close to, the soil layer boundary. This was likely due to horizontal variations in hydraulic conductivity created by fingered flow during the initial wetting. Because of an elevated hydraulic conductivity in the fingers, the water and solute movement would narrow from a zone with uniform vertical transport toward a number of fingers. The measured profiles, representing the stream tubes contained within the relatively small TDR measurement volume, suggested this took place within a 0.10-m confinement region above the soil layer boundary where decreased approximately 0.1 m3 m-3. The area-averaged water flux (Jw) into the fingers would exceed Jw at the soil surface, while the area-averaged water flux at the remaining parts of the layer boundary would consequently be lower than Jw at the soil surface, explaining the observed decrease in TDR measured towards the boundary.
Parameters in the convective lognormal transfer function model (CLT) were determined by fitting the CLT model to time integral–normalized resident concentration BTCs measured at 50 depths as a function of time using nonlinear least squares optimization. The mean residence time in each soil showed a linear increase as a function of the transformed depth coordinate. A linear regression analysis showed that the slopes and hence the average solute particle velocities were significantly different in the two layers and higher than the area-averaged water flux applied at the surface, likely a result of immobile water in the upper soil and the presence of preferential flow paths within the sample volume of the TDR probes in the lower soil.
The dispersivity was independent of the transformed depth coordinate in the Cambridge loam (upper soil), suggesting that a CDE model would provide a sufficient description of the solute transport in the upper soil layer within the sampled stream tubes. In the Borden sand (lower soil) the dispersivity increased nonlinearly with the transformed depth coordinate in a transition zone right below the layer boundary before entering a region with an apparently linear increase. This suggests that preferential flow paths were generated in the transition zone and transport gradually switched from convective-dispersive to stochastic–convective.
A comparison of the time integral–normalized flux concentration at different lateral positions at the layer boundary confirmed that lateral variations in the solute transport across the layer boundary took place. The observed transport phenomena, including preferential flow and lateral variations in solute transport at the layer boundary, a flow confinement region above the layer boundary, and a transition zone from convective–dispersive to stochastic–convective solute-transport behavior below the boundary, appear to be interrelated. These transport phenomena need to be further investigated, possibly by using improved and downsized TDR probes and a more comprehensive probe array. The governing mechanisms need to be identified and possibly included in wa
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ABSTRACT
INTRODUCTION
