Published online 26 July 2006
Published in Vadose Zone J 5:886-893 (2006)
DOI: 10.2136/vzj2005.0105
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Soil Heterogeneity Effects on Solute Breakthrough Sampled with Suction Cups
Numerical Simulations
Lutz Weihermüller*,
Roy Kasteel and
Harry Vereecken
Agrosphere Inst., ICG IV, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
* Corresponding author (l.weihermueller{at}fz-juelich.de)
Received 29 August 2005.
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ABSTRACT
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Porous cups are widely used to extract soil solution for monitoring solute transport; however, it is not always clear how soil heterogeneity influences solute breakthrough sampled by suction cups. The objective of this study was to evaluate the influence of soil heterogeneity on the breakthrough of solute extracted by suction cups. We conducted numerical simulations using the HYDRUS-2D code. Local-scale heterogeneity in hydraulic properties was generated using Miller–Miller scaling theory. Results of the simulations show that effective transport parameters derived from the measured breakthrough curves in the suction cups depended on the location of the suction cup in the heterogeneous flow field. Mean pore water velocities obtained from suction cup measurements ranged by a factor of 1.6 and dispersivities by a factor of 1.5 for the different heterogeneous structures. As a consequence, the arrival time (first moment) of the tracer plume derived from suction cup measurements was accelerated or delayed compared with the homogeneous case. Mass recoveries and suction cup sampling areas were also influenced by the underlying structure. The applied suction in the cup as well as the suction cup sampling area were found to have important effects on the mean pore water velocity, dispersivity, and mass recovery. The effect of variation in applied suction was analyzed using reference point data taken from 10 locations in the undisturbed flow field. Contrary to the general assumption that solute spreading measured with suction cups depends only on the mean pore water velocity, our results show that solute spreading is also influenced by (i) the suction cup sampling area and the deformation of streamlines to the cup, and (ii) the flow channels that are sampled. The numerical simulations indicate that the number of suction cups required for calculating a mean breakthrough curve in the chosen heterogeneous flow field must to be >20.
Abbreviations: MTV, arithmetic mean of the travel velocity distribution • SCAD, suction cup activity domain • SCSA, suction cup sampling area
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INTRODUCTION
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POROUS CUPS, which provide a simple and direct method for extracting water from the vadose zone, are still widely in use (e.g., Krone et al., 1951; Reeve and Doering, 1965; McGuire and Lowery, 1994; Williams and Lord, 1997; Köhne, 2005). The presumed advantage of porous cups is that disturbances of the surrounding soil are negligible after installation and, as a consequence, only minor changes in natural percolation behavior are induced (Grossmann and Udluft, 1991). This offers the possibility to simultaneously sample soil water at different depths to record a time series of solute breakthrough. In the last decades, various researchers have evaluated the impact of suction cups on the natural flow field using analytical solutions (Warrick and Amoozegar-Fard, 1977; Hart and Lowery, 1997), and numerical approaches (Germann, 1972; van der Ploeg and Beese, 1977; Grossmann, 1988; Weihermüller, 2005; Weihermüller et al., 2005).
Weihermüller (2005) and Weihermüller et al. (2005) showed that the suction cup activity domain (SCAD, the influence of the suction cup on the surrounding matric potential) and the suction cup sampling area (SCSA, the soil surface area from which water will be sampled) are largest for fine-textured soils in homogeneous flow fields. The activity domain and the sampling area were found to decrease with increasing infiltration rates. They also indicated that the breakthrough of solutes in homogeneous soils showed earlier arrival in the suction cup and more pronounced tailing due to deformation of the streamlines than an undisturbed flow field (no applied suction in the cup). Both studies were limited in the number of realizations for the heterogeneous case, and, therefore, no general statements were given in terms of the behavior of the SCSA and the solute breakthrough in heterogeneous flow fields.
The influence of soil heterogeneity on solute movement and solute extraction with suction cups was analyzed by Tseng et al. (1995) using just a single realization of a heterogeneous flow field. Tseng et al. (1995) showed that, in contrast to a homogeneous flow field, individual locations in a heterogeneous flow field behave quite differently in terms of solute breakthrough. They also found that the solute extraction device can dramatically influence the flow field. Variations in solute concentration extracted with suction cups at different locations were not investigated in their study, however.
The objective of this study was to examine the influence of soil heterogeneity on solute breakthrough sampled by suction cups, as well as derived effective transport parameters such as mean pore water velocity and dispersivity as well as mass recovery. The numerical simulations also give information about the minimum number of suction cups that need to be installed in a heterogeneous flow field to correctly estimate a mean solute breakthrough curve. Note that preferential flow due to cracks, worm holes, and root channels, which may be important in naturally structured soils, was neglected in our calculations.
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MATERIALS AND METHODS
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For the simulation of water flow, we used the finite element code HYDRUS-2D (Simunek et al., 1999), which numerically solves Richards' equation for saturated–unsaturated water flow:
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where 
is the volumetric water content (cm3 cm–3), 
is the pressure head expressed in head units (cm), x and z are spatial coordinates (cm) in the transverse and longitudinal directions, respectively, and K() is the unsaturated hydraulic conductivity (cm h–1). The parameterization of the hydraulic conductivity of the soils and the suction cup is based on the Mualem–van Genuchten approach (van Genuchten, 1980), in which the effective volumetric water content Se is given by
 | [2] |
where r (m3 m–3), and s (m3 m–3) are the residual and saturated volumetric water contents, respectively, and 
(cm–1), n (unitless), and m (unitless; m = 1 – 1/n) are shape parameters. Assuming that the tortuosity factor equals 0.5, the Mualem–van Genuchten approach leads to
 | [3] |
where Kr (unitless) is the relative hydraulic conductivity and Ks is the saturated hydraulic conductivity (cm h–1).
Solute transport is calculated with the convection–dispersion equation:
 | [4] |
with xi (i = x, z) are the spatial coordinates (cm), Dij is the dispersion coefficient tensor (cm2 h–1), v is the mean pore water velocity (cm h–1), and C is the solute concentration (g m–3).
Water flow was simulated for a two-dimensional vertical region 100 cm wide and 100 cm deep, which was discretized nonequidistantly with smaller nodal distances in the vicinity of the suction cup (total number of nodes = 17 594). The suction cup had an outer radius of 2.4 cm and was located 40 cm below the surface in the horizontal center of the flow domain. A cross section of the flow domain is shown schematically in Fig. 1
. Infiltration was uniform and constant in time through the upper boundary with water flux density Jw = 0.4 cm h–1. The boundary condition of the suction cup was represented as a prescribed constant head. The lower boundary of the flow domain was defined as free drainage, which is typical when the groundwater table is far below the soil surface. No-flow boundary conditions were imposed along the remaining boundaries. A loamy soil was chosen for the simulation. The hydraulic parameters for the soil and suction cup were taken from the HYDRUS-2D soil catalog, while Ks was taken from laboratory experiments (Weihermüller, 2005). Hydraulic parameters for the soil and the suction cup are listed in Table 1. The water retention curve and the unsaturated hydraulic conductivity as a function of the pressure head of both the reference soil and the suction cup are plotted in Fig. 2
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The initial pressure head condition was set at –33 cm for all nodes except for the suction cup. The molecular diffusion coefficient (D) in free water was set at 0.0738 cm2 h–1, and the longitudinal and transversal dispersivities at 5 cm. A Br– pulse of 38 g L–1 was applied for 1 h after 200 h. At this point, stationary conditions for water flow were reached. The simulation period was chosen to be 1000 h, which was sufficiently long for complete tracer breakthrough in the suction cup. The global water and solute mass balance errors were always <1% for all time steps. All outputs for the velocity fields were taken at the final time step. To obtain information about the pressure head distribution in the flow field, 10 observation points were selected at the same depth as the suction cup, at 5, 10, 15, 20, and 25 cm from the left and right borders of the flow domain (see Fig. 1; simulations labeled x-1). The observation points are used below as reference points for calculation of the suction applied to the suction cup. In all simulations, an offset of –30 cm was added to the reference point values for the applied suction in the cup (simulation set x-2). This value was chosen to minimize the spatial influence of the suction cup on the surrounding pressure head as recommended by Grossmann and Udluft (1991).
Local-scale heterogeneity in hydraulic properties was generated using the Miller–Miller scaling theory (Miller and Miller, 1956). The spatial correlation structure of the log-normal distributed scaling factor was described using an exponential autocovariance model with a variance 
2f of 0.25 in accordance with Roth (1995), and a correlation length 
f of 10 cm in accordance with findings by Kasteel et al. (2005).
In total, 100 realizations of the heterogeneous flow field were simulated. The procedure of simulating flow fields of only 100 by 100 cm instead of simulating the entire ensemble of all realizations at one time greatly facilitated our study of the influence of a suction cup on solute breakthrough as sampled by the suction cups. In general, 100 realizations will lead to an ensemble being 10 000 cm wide and 100 cm deep, containing a total of 100 suction cups installed at 40-cm depth with a horizontal spacing of 100 cm. The suction cup sampling area (area of the overlying soil surface from which water could be captured by the suction cup on a continuous application of tension [Weihermüller et al., 2005]) was calculated by tracking the streamlines using particles. The suction cup sampling area was calculated following procedures described by Weihermüller et al. (2005). In total, 2000 particles were uniformly applied to the soil surface.
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RESULTS AND DISCUSSION
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To evaluate the influence of soil heterogeneity on Br– breakthrough measured by the suction cups, 100 realizations of random fields of scaling factors were generated and compared with results of the reference homogeneous soil. For the 100 realizations of the heterogeneous flow field, the maximum, minimum, arithmetic mean, and standard deviation of the transport parameters dispersivity (), mean pore water velocity (v), mass recovery, and SCSA are listed in Table 2. The values in Table 2 match more or less the results of the homogeneous case, which had a mean pore water velocity of 0.830 cm h–1, a mass recovery of 32.6%, and a SCSA of 29.3 cm. Only the dispersivity showed some difference between the 100 realizations (mean = 6.04 cm) and the homogeneous flow field (mean = 5.45 cm).
In the next step, six samples were taken from the 100 realizations to visualize the effect of the location of the suction cup within the flow field on the solute breakthrough as measured with the cups. The samples were taken with the highest and lowest dispersivity values (simulation set x-3 for the lowest reference point values and x-4 for the highest reference point values), the mean pore water velocity, and the mass recovery. Specifically, we used Simulation 18 with the highest dispersivity (7.28 cm), Simulation 88 with the lowest dispersivity (4.47 cm), Simulation 56 with the highest mean pore water velocity (0.970 cm h–1), Simulation 40 with the lowest mean pore water velocity (0.637 cm h–1), Simulation 65 with the highest mass recovery (48.8%), and Simulation 34 with the lowest mass recovery (20.1%).
Figure 3
shows the absolute water flux, |Jw| (cm h–1), of the six realizations of the heterogeneous flow fields when no suction was applied to the cup. The underlying heterogeneous structure leads to a typical network of preferred pathways for water flow confined to more conductive regions. Depending on the realization of the hydraulic conductivities, the suction cup was located either in a preferred flow channel or outside one of these structures. We used particle tracking to determine the effect of the location of the suction cup within the heterogeneous flow. For this purpose, particles were uniformly applied at the soil surface and the MTV (arithmetic mean of the travel velocity distribution [cm h–1]) of those particles that reached the suction cup was calculated. Compared with the homogeneous case (Simulation 0-1, not shown, MTV = 0.994) the suction cups of Simulations 40-1 (MTV = 1.554), 65-1 (MTV = 1.145), and 88-1 (MTV = 1.488) were located in regions with higher absolute water fluxes. The suction cup of Simulation 18-1 (MTV = 0.700) is located in a region with low fluxes, whereas Simulations 34-1 (MTV = 0.836) and 56–1 (MTV = 0.879) showed intermediate absolute water fluxes.
Statistics of the reference point values for the six realizations simulated at the depth of the suction cup are provided in Table 3 for all realizations without suction applied to the cup. For the homogeneous case, the mean reference point value was –28.3 cm. The highest mean reference point value was found for Simulation 34-1 (–10.0 cm) and the lowest for Simulation 88-1 (–37.0 cm).
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Table 3. Arithmetic mean and minimum and maximum values of soil water potential estimated from selected data at the observation nodes.
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In a second set of simulations, we applied a constant suction of 60 cm (ambient pressure head of –30 cm with an offset of –30 cm) to the cup for the same six realizations, and analyzed the flux concentration as measured with the suction cup. The Br– breakthrough curves for the six realizations are plotted in Fig. 4
. The fitted transport parameters, as obtained with CXTFIT (Toride et al., 1999) are listed in Table 4. The mean pore water velocity, v, and dispersivity, , varied between 0.636 and 0.969 cm h–1, and 4.47 and 7.51 cm, respectively. This shows that the arrival time (first moment) of the tracer plume as detected with the suction cups was accelerated or delayed compared with the homogeneous case (Simulation 0-2). The variability in the dispersivity may be attributed to the range in pore water velocity, and therefore to the different location of the solute plume in the sampled flow channels. If the tracer plume in the flow channels reaches the suction cup at different times, the measured solute spreading will increase. Weihermüller et al. (2005) showed that the pronounced tailing of the breakthrough can also be a result of deformation of the streamlines, which leads to a longer travel path of the solute as sampled with the cup.
Mass recovery (see Table 4) also depended on the location in the flow domain and changes in pressure head when a suction was applied to the cup. Weihermüller et al. (2005) previously showed that the SCSA, and as a result the mass recovery, is a function of ambient pressure head producing smaller SCSAs in wetter soils (higher infiltration rates) if molecular diffusion is negligible. For the simulated cases, the water flux, |Jw|, and the soil water content at different locations was directly linked to the underlying heterogeneous structure. Therefore, the local soil water content changes were not only caused by variable infiltration rates compared with the homogeneous soil. The same effect occurs for the SCAD, which also depends on the ambient pressure head and hence on the soil water content. Nevertheless, for the simulations, mass recovery did not depend only on the SCSA due to differences in the location of the solute plume and resulting dilution effects. The absolute concentration peak varied between the different sets due to spatial variability in |Jw|, which is a component of the dispersion tensor, as well as mixing between the sampled flow channels.
Considering that suction cups are often controlled by reference point values installed in the field for offset calculation references (Weihermüller, 2005), the influence of the reference point values was analyzed for the six realizations discussed above. To do so, a constant offset of –32 cm was added to the reference point values measured in the suction cup plane. The variation in the reference point values at the observation points (Table 3) led to differences in applied suction. For these reference point values, simulations were conducted with (i) the highest reference point value (Simulations 18-3, 34-3, 40-3, 56-3, 65-3, and 88-3), and (ii) the lowest value (Simulations 18-4, 34-4, 40-4, 56-4, 65-4, and 88-4).
Results for the various simulations, in terms of the dispersivity, , the mean pore water velocity, v, the mass recovery, and the SCSA for the different applied suctions as calculated from the reference point values and an offset of –32 cm are listed in Table 4. At first sight, some inconsistencies in v occurred within the dataset. The highest pore water velocities due to the higher pressure gradients were not observed as expected for the lowest applied suctions in the cup (Simulations 18-4, 34-4, 56-4, 65-4 and 88-4). Likewise, the calculated MTVs for the suction cups were not correlated with the mean pore water velocity as determined for applied suction in the cups. We attribute these results to the fact that the region from which water is extracted by the cup is not only related to the applied suction but also to the local hydraulic properties. Differences in the applied suction may lead to sampling from flow channels having higher or lower fluxes. For this reason, it is difficult, if not impossible, to estimate the pore water velocity from the location of the cup in the flow channel network and the value of applied suction. Moreover, the correlation length and, as a result, the size of single flow channels will influence the pore water velocity.
The dispersivity for the simulations also varied between the highest and lowest applied suction for the same heterogeneous field, with the dispersivity increasing with higher applied suctions (Table 4). The dispersivity between the lowest and highest applied suctions was found to vary from 0.18 to 0.26 cm, respectively.
In general, for homogeneous soils, solute spreading should be larger for smaller mean pore water velocities as a result of longer residence times. As shown in Table 4, the dispersivity is not only linked to the mean pore water velocity in heterogeneous soils, but also to the size of the SCSA. Weihermüller et al. (2005) showed that a larger SCSA leads to a larger dispersivity due to deformation of streamlines, and thus to longer travel paths for the solute. As a consequence, the dispersivity is not only related to the material properties of the surrounding soil but also to the applied suction and the associated streamlines to the suction cup.
In contrast to the homogeneous case, the mass recovery is negatively correlated with the SCSA (y = 881.1x–0.977, with R2 = 0.99). The data indicate that solute transport is partly decoupled from pure water flow (as calculated by particle tracking) due to diffusion of the solute between different flow channels having different solute concentrations. In general, a smaller SCSA will exhibit less heterogeneity in the direct vicinity of a suction cup, thus implying a more homogeneous flow field and less diffusion between the various flow channels, and hence better mass recovery. Therefore, the SCSA calculated by particle tracking is not applicable to heterogeneous flow fields without taking into account diffusion processes. This is in contrast to findings by Weihermüller et al. (2005) and Warrick and Amoozegar-Fard (1977) for homogeneous soils.
In general, the variability in the mean breakthrough curve derived from single measurements, and the variance in the transport parameters, will be reduced with a larger number of realizations. But this general behavior does not give any information about the total number of suction cups required to adequately measure tracer breakthrough in a heterogeneous flow field. To study this, we analyzed 100 realizations having the same statistics of the heterogeneous flow field (2f = 0.25, f = 10 cm). The calculated arithmetic mean and the standard deviation, , of the mean pore water velocity, the dispersivity, and the mass recovery are plotted in Fig. 5
. The calculated arithmetic mean of the mean pore water velocity, the dispersivity, and the mass recovery reached an asymptotic value at infinity, with the standard deviation decreasing for larger numbers of realizations. The mean pore water velocity varied within in a relatively narrow range of <0.04 cm h–1. By comparison, the mean dispersivity was in a range of <0.35 cm, and the mean mass recovery in a range of <7.5%. To obtain information about the minimum number of suction cups required for estimating a mean breakthrough curve, we calculated the standard error of the mean (SEM = n/
, where n is the number of realizations) for the transport parameters and the mass recovery for each fifth realization. The results are plotted in Fig. 5. In general, the SEM will decrease with more realizations but will not reach zero at 100 realizations. This indicates that 100 realizations are, in general, not sufficient to represent all possible hydraulic conductivity fields.
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Fig. 5. Arithmetic mean, standard deviation, and standard error of the mean for the transport parameters: (a) mean pore water velocity, (b) dispersivity, and (c) mass recovery as calculated from 100 simulations.
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Even if small variabilities are detectable in the arithmetic mean and standard deviation of the transport parameters and the SEM is not zero after 100 realizations, however, the simulation setup seems to represent the chosen statistics of the flow field sufficiently well enough for our purpose. From our simulations, the minimum number of realizations for calculating a mean breakthrough curve is estimated to be 
20. More realizations do not significantly improve the result and the SEM is acceptable for suction cup measurements with a variability in the mean pore water velocity of <0.03 cm, dispersivity of <0.35, and mass recovery of <3%. In contrast, fewer realizations still show a relatively large variability (see also Fig. 5) in the transport parameters. This value of 20 is only valid for the selected statistics of our heterogeneous flow field. Larger or smaller 2f values and f may require more or fewer suction cups. In general, a smaller 2f will show less variability in the transport parameters (results not shown), whereas larger 2f values will lead to more variability.
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SUMMARY AND CONCLUSION
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The results of our numerical experiments showed that the breakthrough of solutes in a suction cup depends on the location of the cup in the heterogeneous flow field. As a consequence, the effective transport parameters (i.e., the mean pore water velocity, v, and dispersivity, ) will vary, even when the same suction is applied in the cup. The mean pore water velocity varied by a factor of 1.5 and dispersivity by a factor of 1.6 for the various realizations of the heterogeneous flow field. As a result, the breakthrough of the solute plume is accelerated or delayed compared with the homogeneous case. Mass recovery and SCSA also depend on the material properties of the surrounding soil; they varied in our study by factors of 2.3 and 2.2, respectively. The height of the peak concentration depends on the spreading within the flow channels, and on the fact that different flow channels with differences in solute concentration can be sampled at the same time. The latter can lead to dilution of the solute concentration in the sampled probe. Variations in the pressure head of the flow field, as measured by reference points, cause changes in the applied suction in the cup depending on the location of the reference points. The reference point values and applied offset in the cups will again lead to changes in the mean pore water velocity, dispersivity, mass recovery, and SCSA compared with the heterogeneous case with an applied suction of 60 cm. In general, the dispersivity should be larger for smaller mean pore water velocities due to a longer residence time during the drainage period. This was not confirmed by our simulations.
The discrepancy between velocity and dispersivity dependencies was caused by (i) deformation of the streamlines and a longer travel path to the cup, and (ii) the fact that more than one flow channel can be sampled at the same time. If one of the sampled flow channels shows a delay in solute movement due to a smaller pore water velocity, the solute concentration in the suction cup will still be high after main breakthrough occurred in the other flow channels. Therefore, dispersivities calculated from suction cup experiments in heterogeneous soils should be interpreted carefully. A comparison of the mean pore water velocity and dispersivity from suction cup experiments and other soil solution sampling devices may therefore be inappropriate. To obtain reliable information of the mean breakthrough curve, the minimum number of suction cups was determined to be 20; however, this value is only valid for the selected statistics of the heterogeneous flow field. Also, variations in the installation depth of the suction cup will influence the results and therefore the total number of suction cups needed. The horizontal spatial distribution of the suction cups themselves in the flow field is independent of the number of suction cups as long as the spatial variability (soil hydraulic heterogeneity) is constant within the plot. Nevertheless, the suction cups should not be installed too close to each other to avoid interferences and to allow sampling of different flow channels. In general, the maximum distance between suction cups depends on the hydraulic properties of the surrounding soil (hydraulic conductivity and soil heterogeneity), the infiltration rate, and the applied suction in the cup. The maximum distance between the suction cups can be drawn from Weihermüller (2005) and Weihermüller et al. (2005).
The reliability of reference point values for feed forward control (pressure head plus offset calculation) of the suction cup unit also depends on the heterogeneous structure of the surrounding soil. Single reference point values may influence the results of the solute breakthrough in the cup. In general, the number of reference points should be the same as the number of suction cups to provide reliable information on the ambient pressure head. In general, reference points (e.g., tensiometers) should not be installed in a region where the suction cup influences the surrounding pressure head.
Summarizing our findings, suction cup data should be carefully interpreted; the calculated mean pore water velocity and dispersivity especially can differ from expected values in the undisturbed flow field. The use of reference points for calculation of an offset for the applied suction in the cup should be carefully considered. Preferential flow through macropores, which was not considered in our simulations, may further increase overall variability in the transport parameters, mass recovery, and the SCSA of natural systems. At the same time, occasional breakdowns of the system, circumvention of the sampling devices due to macropore flow, and insufficient hydraulic contact between cup and the surrounding soil probably also contribute to variability under field conditions.
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L. Weihermuller, J. Siemens, M. Deurer, S. Knoblauch, H. Rupp, A. Gottlein, and T. Putz
In Situ Soil Water Extraction: A Review
J. Environ. Qual.,
October 24, 2007;
36(6):
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TOP
ABSTRACT
INTRODUCTION
for the soil and suction cup.
