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a Department of Environmental Sciences and Land Use Planning, Université Catholique de Louvain, Croix du Sud, 2 Bte. 2, B-1348 Louvain-la-Neuve, Belgium
b Currently, Agrosphere Inst., ICG-IV, Forschungszentrum GmbH, D-52425 Juelich, Germany
* Corresponding author (m.javaux{at}fz-juelich.de)
Received 30 September 2003.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: BC, boundary condition • BTC, breakthrough curve • CD, convective–dispersive • CDE, convection–dispersion equation • PCS, porous cup samplers • WRC, water retention curve
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Also, structural discontinuities between layers may interrupt pore-scale transport processes. Therefore, preferential flow may be disrupted at such boundaries. Layering may additionally generate a local saturated zone above the interfaces due to textural or capillary barriers. It is well known that the water content may have an effect on the dispersion by changing the tortuosity and continuity of the flow paths. The effect of moisture content on dispersivity, however, is not unique. Some authors observed an increase in the dispersivity with moisture content and flow rate (e.g., Vanderborght et al., 2001) and explained this by the fact that macropores are activated when moisture content at higher flow rates. Other studies showed that water content decreases the apparent dispersivity (Maraqa et al., 1997; Nützmann et al., 2002) and explained this by the flow paths becoming less tortuous when the moisture content increases. Finally, wetting front instability may be induced just below a structural interface. It has been observed for many years that vertical flow from a fine to a coarse-textured layer is a condition that promotes fingering and wetting front instability. Observations in laboratories under various conditions have been reported by several authors (Hill and Parlange, 1972; Glass et al., 1989a; Baker and Hillel, 1990; Wang et al., 1998b; Sililo and Tellam, 2000). Using a simple descriptive approach, Hillel and Baker (1988) introduced the concept of water entry suction 
e as the maximum suction (in absolute value) that will allow water to enter an initially dry porous matrix. If the potential flow rate at e in the lower layer exceeds the actual discharge through the upper layer, then the flow paths tend to constrict and concentrate into individual streams (Hillel and Baker, 1988). This was further confirmed experimentally by Wang et al. (1998b) and Miller and Gardner (1962). Furthermore, Glass et al. (1989b) showed that hysteresis in the water retention curve (WRC) promotes stability of the nonuniform moisture content distribution. This finding was experimentally confirmed by Dicarlo et al. (1999).
The effect of fingering on solute transport is multiple. Glass et al. (1989a) compared observed breakthrough curves (BTC) of a blue dye solution in a two-layered disturbed soil with simulations of the convection–dispersion equation (CDE), assuming homogeneous flow. The authors performed a series of infiltration experiments with different initial water content profiles and application times. Three different cases were reported: (i) a uniform, homogeneous flow case; (ii) a very structured flow field with well-defined fingers; and (iii) an intermediate case with fewer differences between fingers and matrix flow. They found that the apparent dispersivity obtained from CDE optimization for the first two cases was roughly the same, whereas for the third case, this factor was 2 to 10 times higher. Conversely, the apparent velocity was higher for Case ii than for Case iii and lower for Case i. This suggests that, for fingered flow only, transport takes place through a much smaller volume at a higher velocity, but that the dispersion process is not affected. However, when a supplementary mixing process due to interactions between matrix and finger flow is added, the apparent heterogeneity could be increased by means of a fluid-induced term, and the apparent dispersivity could increase. However, divergence phenomena in the wetting part of soils have been observed by several authors (Wang et al., 1998a; Sililo and Tellam, 2000). For example, Bauters et al. (2000) showed that wetting front stability was dependent of the initial volumetric soil water content in a sand.
The scaling of the apparent dispersivity along the transport pathway is a good indicator of the mixing regime and a key to understanding the impact of layering on effective transport. In their solute pulse experiment at the plot scale, Butters et al. (1989) observed that the apparent dispersivity increased linearly in the top three meters of soil, and decreased nearly 30% after passing through a relatively thin fine-textured soil layer. Roth et al. (1991) related the observed constant apparent dispersivity in their field-scale transport experiment to the influence of interfaces that homogenized the transport characteristics. Conducting plot tracer experiments, Van Weesenbeeck and Kachanoski (1991) suggested a relationship between the solute transport process, pedogenesis, and soil management (tillage). They found that the recovery and movement of solutes in their soil was largely controlled by the spatial pattern of the thickness of the B horizon. Porro et al. (1993) performed a series of leaching experiments through disturbed uniform and multilayered soil columns. They noticed that the dispersivity was smaller for the layered soil and attributed this to the lateral mixing in these soils.
Snow et al. (1994) performed inert solute transport experiments in a layered soil at the lysimeter scale. They calibrated the CDE model below the surface layer independently of the layering. The surface layer, however, could not be used in the calibration procedure since the transport process differed substantially. In their study, transport through independent soil layers, from the top layer to the rest of the monolith, was modeled using transfer function theory (Jury and Roth, 1990). Huang et al. (1995) calibrated the CDE to BTCs measured at each meter in a 12.5-m-long column filled with heterogeneous materials. They observed that the presence of layers perpendicular to the flow direction had a decreasing effect on the apparent dispersivity. Vanderborght et al. (2001) studied the scaling of the apparent dispersivity for a series of Belgian soil types and linked spatial aspects of the apparent dispersivity to morphological features in the soil profile. They also showed that cemented or clay layers with relatively high bulk densities and lower conductivities promoted lateral mixing.
The impact of layering on transport can be studied by analyzing the lateral mixing regime and hence the spatial scaling of the apparent dispersivity. In a companion paper (Javaux and Vanclooster, 2004), we presented a methodology to assess the spatial scaling of the apparent longitudinal velocity and apparent longitudinal dispersivity in a large-scale unsaturated natural sedimentary formation situated between an infiltration lake and an unconfined aquifer.
Our objective here is to characterize the soil hydrodynamic behavior by analyzing in detail the velocity and dispersivity profiles. Discrepancies between the observations and predictions with the classical CD transport model through layered soil are investigated, and several hypotheses are proposed to explain the discrepancies. Particular attention is devoted to the representativity of the porous cup solution samplers that were used to characterize effective flow.
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THEORY |
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i, may be defined as functions of 
Li (L T–1) and 
Li (L), the local-scale longitudinal velocity and dispersivity respectively for layer i, as
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The apparent (also called effective) longitudinal dispersivity L at depth z of a n-layered medium is defined as (Simmons, 1982):
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 | [3] |
 | [4] |
ij is the correlation coefficient of the local scale travel time between two adjacent layers i, j. Two asymptotic situations can be investigated: perfectly correlated local travel times (ij = ji = 1) or independent local travel times (ij = ji = 0 if i 
j). Here we focus on independent local travel times for which, if steady-state flow conditions 
are valid, the apparent dispersivity at depth z can be derived from Eq. [1], [3], and [4]:
 | [5] |
A general assumption inherent in Eq. [5] is that all layers are considered to be semi-infinite. Barry and Parker (1987) gave the solution for a two-layered medium for which the first layer is finite, and the second infinite, and with a zero correlation between the travel time of both layers:
 | [6] |
A comparison of Eq. [5] for two layers and Eq. [6] shows that only the last term is different. Note also from Eq. [5] that the apparent dispersivity explicitly depends on the soil water content profile. This was also shown for homogeneous soils (Vanderborght et al., 2000).
The apparent longitudinal velocity is not influenced by the correlation of the local travel times, and thus is the same for any mixing regime assumption:
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The objective function for inversely estimating the local scale dispersivity and velocity values was defined as:
 | [8] |
L or ) at depth i, 
i is the modeled parameter with Eq. [5] and [7], and n is the number of data (n = 7 if all depths are used in the inversion). We did not inversely obtain the complete distribution of apparent parameters at each depth, such as characterized in Javaux and Vanclooster (2004), but rather obtained a single realization of possible apparent parameters. For the present inversion, we chose this set of apparent parameters, which resulted in terms of a minimum error in describing PCS observed solute transport. |
RESULTS AND DISCUSSION |
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L. Mean arrival time histograms are given in Fig. 4
. These histograms allow a comparison between depths and detection of possible preferential flows. In our case, the histograms in Fig. 4 reveal some deviations from a uniform transport process. Travel times to the 4.86-m depth are less than those to the 2.83-, 3.89-, and 4.4-m depth, which means that, if strictly convective transport occurred, solute particles would first pass through the deepest layer and then move upward.
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) also help to characterize the transport-active part of the wetted pore space (Jury and Flühler, 1992). Assuming that Jw = 0.2 cm d–1 (chosen to fit the optimized mean velocity at depth 1), that all water in the unsaturated zone is mobile, and that the water content profile is known (Fig. 2 in Javaux and Vanclooster, 2004), the piston flow velocity profile can be calculated using Eq. [7]. Results are shown in Fig. 5
. Notice that the Jw value does not influence the shape of the velocity profile but only the magnitude of the velocities. Also, the apparent flow velocities at the 4.4- and 4.86-m depths (PCS 5 and 6, respectively) again do not match the piston-flow profile. Moreover, if we focus on the sand layer between depths of 1.2 and 4 m (PCS 2, 3, and 4), we observe that the piston-flow steady-state velocity profile tends to increase up to a depth of 3.5 m. On the other hand, apparent velocity profile decreases between the 1.2- and 3.5-m depths.
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Alternatively, the discrepancies between piston flow and our data can also be attributed to a lack of representativity of the PCS time series. Basic assumptions for the inverse modeling are that the PCS samples, at least, the same stream tube, so that continuity exists between the observations at different depths. This is not necessarily the case in our study. The results suggest that the ratio between the PCS sampling window and the representative transport process volume is less than unity. They also suggest that another PCS placed at the same depth could sample another stream tube, resulting in different hydrodynamic parameterization.
The sampling window of the PCS is known to be relatively small, and varies in terms of the boundary conditions that have been imposed on the flow process and the operational mode of the PCS (e.g., Hart and Lowery, 1997). Since the operational mode and the imposed boundary conditions were the same for all PCS in the experiment, other processes are needed to explain the observed variation of the flow processes. We hypothesize that such a variable flow regime could be generated by a combination of lateral variability in the hydrodynamic parameters, thereby promoting three-dimensional heterogeneous flow, together with convergence and divergence of flow paths.
Three-dimensional flow patterns could result from discontinuities in the horizontal fine-textured layers, thus forcing solute mass to circumvent the PCS sampling window. Fingering flow additionally could have occurred in the upper part of the sandy layers, which are confined by a clay layer. In that case, PCS locations could have been bypassed if preferential flow occurred locally (Shaffer et al., 1979). Lateral divergence of the solute plume, enhanced by wetter water conditions and finger aggregation, could be expected in the lower part of the profile, leading to a lower apparent vertical velocity. This could explain the decreasing apparent velocity profile between 1.2 and 4 m.
In our case, none of the above hypotheses can be rejected a priori since the structure of our medium and our actual flow field is not completely known. Still, the probes located just below the clay layers are most prone to sampling problems because of the lower water content and the potential for unstable flow. An analysis below of the dispersivity profile would help to confirm this last hypothesis.
Dispersion Process
Dispersivity Profile
A typical apparent dispersivity profile is given in Fig. 1 (right). Transport across the first and second clay layers produces an increase in the value of the apparent dispersivity. A similar effect is less clear below the third clay layer. Also, the apparent dispersivity declines significantly through the homogeneous second sand layer (between 1.2 and 4 m). This is inconsistent with numerous field- and column-scale transport experiments, which illustrate an increase in the apparent dispersivity with depth in heterogeneous media (Butters and Jury, 1989; Vanderborght et al., 2001).
Convective–Dispersive vs. Observed Apparent Dispersivity Profile
Comparisons between observed and modeled dispersivity profiles may help to detect nonrepresentative sampling depths or model assumption problems. Equation [5] clearly shows that if we assume that each layer has a constant local dispersivity, the apparent dispersivity in a layered soil will be a function of the thickness of the individual layers, the water content profile in the layer, and the local dispersivity of each layer. To elucidate the impact of all these factors on the apparent dispersivity profile, we performed inverse modeling to compare the modeled dispersivity profile to our experimental data. Results of the inverse optimization are shown in Fig. 6
, while the optimized local dispersivity values are given in Table 1. A local dispersivity close to zero for the sand and a value of more than 100 cm for the clay were needed to explain the substantial decrease in the apparent dispersivity through the sand layer between 1.2 and 4 m. Those values are completely out of range of usual local dispersivity values (e.g., Beven et al.. 1993) for coarse or fine-textured media, which suggests that the absolute dispersivity values do not have much physical meaning.
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Discussion
Our comparison of a layered CD model with the observed data showed that the dispersivity profile could not be completely explained by the model (Eq. [5]), leading to unrealistic local dispersivity values. However, we note that at least some agreement existed between the shapes of the simulated and observed dispersivity profiles if the clay has a large dispersivity value. This is especially true if a uniform effective water content profile is considered between 1.2 and 4 m, which allows one to calculate a decreasing dispersivity profile.
The discrepancy between the model and the observations can be attributed to nonrepresentative sampling of the PCS at certain depths. However, other physical processes could also explain this apparent anomalous behavior. Unstable flow could develop below the clay–sand interface, thereby promoting a low transport velocity in the matrix and a high velocity within the fingers, which initially will increase the dispersivity values. Toward the lower part of the profile, however, fingers can aggregate, and thus decrease the apparent dispersivity. Another physical process that may explain the results is the enhancement of lateral mixing when water content increases (e.g., Nützmann et al., 2002). The abnormally high local dispersivity value for the clay layers could be an indicator of unstable flow taking place at the clay–sand interface. The zero value of dispersivity for the sand could reveal the finger convergence process and lateral mixing in the wetter part of the profile. It is worth noting that such CD phenomena do not lead to a constant dispersivity value (Glass et al., 1989a). We could expect that a water content–dependent dispersivity could improve the simulations of the apparent dispersivity profile and decrease local dispersivity estimates.
The data also suggest that the clay layers may not be continuous. This could explain the concentration peaks observed at the 4.86-m depth (Fig. 2), which are much sharper than peaks just above the clay layer (at the 3.89-m depth) and almost as sharp as peaks observed at the 1.9-m depth. This hypothesis is confirmed by the large velocity observed at the 4.86-m depth (Fig. 1). We note here that Javaux and coworkers (unpublished data, 2004) also observed a discontinuous clay layer in a monolith extracted from the same formation.
Effective Transport Processes and Nonrepresentative Sampling Issue
We proposed nonrepresentative sampling as a possible reason to at least partly explain the observations through PCS. Different flow paths with different leaching velocities are sampled by different PCS. The results in Fig. 3 show that higher transport velocities occur immediately below the clay layers (at depths of 1.9, 4.46, and 4.86 m) and lower velocities above those layers (at the 1- and 3.89-m depth). At the same time, peaks observed in the PCS Cl– time series (Fig. 2) seem to be less sharp at these depths, whereas higher velocities correspond to sharper peaks (see peaks after Days 2500 at the 1.9-, 4.86-, and 5.86-m depth). Because of more lateral mixing and converging flow generated by higher water contents and lower velocities, one may expect that PCS located just above clay layers are more representative of the leaching velocities. However, the mixing above the fine-textured layers is not complete since earlier arrival times are observed just below those layers. This can partly be explained by discontinuities in the clay layers, which may locally induce large transport velocities. Moreover, the PCS located below the clay layers are more likely to provide nonrepresentative samples of the process because of the possible presence of unstable flow. If the sampling window does not encompass several fingers and matrix flow areas at the same time, then apparent dispersivity values should be affected (Glass et al., 1989a). Therefore, higher dispersivity values observed at these depths are probably a result of nonrepresentative sampling. By comparison, the lower dispersivity values obtained for the bottom of the sand layers are probably more reliable.
Fingering
Soil layering often promotes the development of unstable wetting fronts. Javaux et al. (unpublished data 2004) derived a set of criteria from the Chuoke equation (Chuoke et al., 1959) for unstable flow in porous media. To check the susceptibility of our soil to fingering, the following inequality must be used. Unstability is predicted when
 | [9] |
50 cm d–1, Javaux and Vanclooster, 2003), we conclude that our soil profile is prone to fingering. Moreover, in addition to layering, increased air pressure in the unsaturated pores may be another factor promoting unstable wetting fronts (Peck, 1964; Wang et al., 1998c). Unfortunately, the air pressure in the pores was not measured in our study but is expected to be positive given the boundary conditions of our system (i.e., an unsaturated layer between an aquifer and a lake). Furthermore, many studies have shown that preferential flow paths created by a fingering process may be persistent (Glass et al., 1989b; Dicarlo et al., 1999). For these reasons we hypothesize that the upper part of the sand layer interbedded between the two clay layers exhibited a series of fingers separated by drier, less conductive regions. Continuous increase in water content with depth would subsequently enhance divergence of streamlines, resulting in more mixing between stream tubes, homogenization of the vertical flow field, and a decrease in the apparent dispersivity. Sandy layers between two fine-textured layers would then behave similarly. We note that transport in the bottom layer of the profile was influenced by the capillary fringe of the aquifer. Similarly as for the upper layer, transport toward the bottom of the profile must have been affected also by the unsteady-state boundary conditions (i.e., influence of the long term regional groundwater flow; see Fig. 4 in Javaux and Vanclooster, 2004). These changes in flow and/or water content change may stabilize the front or mask the actual mixing mechanisms using a steady-state analysis.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Apparent dispersivity values were found to decrease with depth in the thick layer between 1.2 and 4 m. Theoretical dispersivity values assuming a constant local dispersivity were compared with observed apparent dispersivity profiles. The theoretical apparent dispersivity profile was found not to match the observed profile. This suggests that the local dispersivity may not be a constant for a given soil layer, but must be a function of the decreasing with water content. This dispersivity profile is consistent with an increase in transverse mixing with travel depth, a finding that is also needed to explain the observed velocity profile.
We partly attributed the unrealistic dispersivity values and deviations between simulated and observed dispersivity profiles to a lack of representativity of the PCS time series. This is because the PCS sample only local flow domains, while their sampling windows are a function of the velocity field induced jointly by the variable boundary conditions and the heterogeneity of the porous medium. The PCS located immediately above the clay layers likely sample a larger flow domain. Larger water content may induce convergence of streamlines and increase lateral mixing. The lower dispersivity values observed at lower parts of the thick sand layer between 1.2 and 4 m depth confirm this assumption. Conversely, the larger dispersivity values just below the clay layers more likely reflect the nonrepresentativity of the PCS samples due to the large flow variability and unstable flow. The relatively small spatial sampling scale of the PCS and their low spatial resolution limited reliable assessment of the mixing regime.
Considering criteria derived from Chuoke et al. (1959) and the fact that a positive air pressure may have developed in the air phase of the vadose zone for the specified boundary conditions, we hypothesize that the increase in dispersivity directly below the clay–sand interface could be due to unstable flow processes, and that finger aggregation and lateral mixing lead to a reduction in the apparent dispersivity when the subsoil becomes wetter. It is important to note that this process probably remained stable for the 17 yr of observations, especially since the fine-textured layer regulated the flow rate through time, thereby creating a quasi-steady-state flow condition.
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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