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a Dep. of Water Resources Engineering, Lund Univ., Box 118, SE-221 00 Lund, Sweden
b Swedish Meteorological and Hydrological Institute, SE-601 76 Norrköping, Sweden
* Corresponding author (magnus.persson{at}tvrl.lth.se)
Received 13 September 2004.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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was calculated for nine different artificial column widths, from 0.0014 (local-scale) to 0.72 m (meso-scale). The horizontally averaged proved to be identical for column widths from 0.0014 to 0.045 m. For larger scales, gradually increased. We noticed that the two experiments with higher flow (1 and 2) and the two experiments with lower flow (3 and 4) showed an almost identical variation of meso-scale with depth. We concluded that above a specific critical value of 
(
0.22 m3 m–3), solute mixing is enhanced, leading to a lower , and that solute transport can be described as a convective-dispersive process. When is lower than this critical level, part of the porosity is deactivated and mixing between individual stream tubes decreases, which implies that transport then occurs as a stochastic-convective process.
Abbreviations: Pe, Peclet number • TDR, time domain reflectometry
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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There have been numerous studies of the dispersion coefficient D. This coefficient includes the effects of molecular diffusion and mechanical dispersion. The latter is due to variation in pore-scale velocities, both within and between pores. Thus, the mixing process in a soil depends on the distribution of water flux velocities, mixing due to convergence and divergence of flow paths, and molecular diffusion. The relative contributions of convective mixing and molecular diffusion is often expressed using the Peclet number (Pe). When Pe is larger than unity, convective mixing dominates and molecular diffusion can be neglected (Bear, 1972). The proportionality constant between D and the pore water velocity v is called dispersivity, . In saturated porous media, is often found to be independent of v and can be considered a soil property depending on the pore geometry, including both structural and textural effects. In unsaturated soils, the tortuosity depends not only on the pore geometry but also on the water content, and thus on the water flux (Padilla et al., 1999; Nützmann et al., 2002). Due to the increased tortuosity of the flow paths, is greater for unsaturated soils than for saturated soils. Several studies have also noticed a scale effect on (e.g., Khan and Jury, 1990; Porro et al., 1993).
Depending on the mixing regime, solute transport can be described using different concepts. For example, Vanderborght et al. (2001) defined mixing time t* as "the time interval during which a particle travels with a constant velocity or ‘remembers’ its velocity." If the travel time of a solute is less than t*, the solute travels in the flow direction without mixing in a plane perpendicular to the flow. This makes to increase linearly with depth and the transport concept is called stochastic convective. If, instead, the solute travel time is larger than t*, transverse mixing will occur and smooth out concentration differences in planes perpendicular to the flow. Since t* is related to , the same factors that affect will also affect t*. Indeed, studies have shown that soil texture and structure will determine the mixing regime. Even within a soil profile, mixing regimes can depend on v and , and whether flow is transient or steady state (Persson and Berndtsson, 1999).
Another scale effect of has also been observed. In Nützmann et al. (2002), it was shown that increased from 0.05 cm for a column having a diameter of 0.044 m to a value of 4 cm for a column with the same soil having a diameter of 0.36 m. Javaux and Vanclooster (2003) found to increase by a factor of 2 when comparing values using data from single time domain reflectometry (TDR) probes and the average of three probes. Roth and Hammel (1996) showed the same scale effect in their numerical simulation. This scale effect is caused by increasing heterogeneities as the sample volume is larger. However, for a sufficient large (or small) area, it should be possible to find a constant heterogeneity.
Studies of solute transport require accurate measurements of solute concentration. Several techniques have been developed. Requirements are that they should be accurate, provide measurements for a well-defined measurement volume, have high temporal and spatial resolution, and be nondestructive. Existing methods typically meet a few, but not all of these requirements. For example, promising methods like small-scale TDR probes (Nissen et al., 1998; Persson and Haridy, 2003; Persson and Wraith, 2002) and fiber optic mini-probes (Ghodrati, 1999) will have to be inserted in the soil and may interrupt the flow paths.
Dye tracers have been used for many years in vadose zone research for investigating the effects of soil heterogeneity by visualizing spatial flow patterns (see, e.g., Flury and Flühler, 1995). After infiltration of dye-stained water vertical sections are excavated and the dye patterns are photographed. This method has proven very useful for detecting preferential flow paths to identify spatial flow patterns at the millimeter scale. Dyes have revealed preferential flow in terms of vertical plumes (Kung, 1990), flow in fissures and worm channels (Lin and Mcinnes, 1995), and along ped faces and through cracks (Yasuda et al., 2001; Mortensen et al., 2004).
Traditionally, image analysis of dye photos has only involved separation between stained and nonstained soil. However, during the 1990s, image analysis has improved to also include estimation of dye concentrations (Aeby et al., 1997; Ewing and Horton, 1999), but it is not until very recently that it has been used in solute transport studies. Forrer et al. (2002) calculated concentration of the dye Brilliant Blue FCF in field experiments. They applied corrections to the original photographs for geometrical distortion, inhomogeneous illumination, and color tinges. Small soil samples from the photographed sections were analyzed and the dye concentration was determined. A depth-dependent relationship was found between the dye concentration and soil color. Aeby et al. (2001) and Vanderborght et al. (2002a), using fluorescent dyes, applied similar corrections to their photos. The advantage of using fluorescent dyes is that different dyes can be used simultaneously. However, more advanced equipment is needed, including special lamps and optical filters.
Even though dye experiments have been widely used, very few attempts have been made to use dye image data for modeling purposes. Dye data have been used for development of models based on random walk and diffusion limited aggregation (Schwartz et al., 1999; Persson et al., 2001), but in these studies only stained and nonstained soil was differentiated. Forrer et al. (2002) used concentration data using image analysis to quantify mixing processes in a field soil. Vanderborght et al. (2002b) used image analysis to identify transport process in soil cores for modeling purposes. We believe that the use of dye infiltration experiments has tremendous potential for solute transport modeling purposes.
While dye infiltration experiments combined with image analysis can provide very high spatial resolution data, they usually do not give insight into the dynamics of solute transport because of the need for destructive sampling. However, in a controlled laboratory experiment where images can be obtained through a transparent wall, experiments allow for multiple measurements during transport. Measuring techniques that offer both high temporal and spatial resolution data are virtually nonexistent, but would indeed be valuable for detailed transport studies. This paper presents such a method.
The main objective of this study was to develop a laboratory procedure which produces measurements of solute concentration with an unrivaled temporal and spatial resolution using dye infiltration and image analysis. The accuracy of the concentration measurements was analyzed in detail. The method was tested during four solute transport experiments. The dye concentration estimates were compared with both TDR measurements and numerical model simulations to asses the quality of the data. The obtained solute concentration data over time was used to calculate at different scales using time moment analysis. Due to the high spatial resolution of the dye concentration data, the behavior of over different scales and depths could be studied in detail. We also investigated whether local-scale variations in transport velocity could be used for describing meso-scale .
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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) was calculated from the measured Ka using a soil specific Ka– relationship (Persson and Haridy, 2003).
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b) of 1.55 Mg m–3, using the packing procedure of Glass et al. (1989). Their method includes the use of a so-called soil randomizer, which has the same dimensions as the cell and is lowered into the cell while packing. Two wire meshes (0.002 m), separated 0.1-m apart, randomize the sand as the grains drop to the bottom. The soil randomizer was elevated as the sand was packed into the cell, to maintain a 0.1-m distance to the sand surface. During packing, a rubber hammer was used to pack the sand by tapping the front wall of the cell. The irrigation system consisted of a Plexiglas pipe, 1-m long and 0.012-m diam. Holes of 0.0006-m diam. were drilled at 0.02-m intervals along the pipe. Each end of the pipe was connected to a 5-mL syringe, in turn connected to a syringe pump (Soil Measurement System, Tucson, AZ). To further distribute the applied water over the sand surface, a 0.02-m thick layer of coarse sand was placed on top of the fine sand.
Two 500 W halogen lamps were used to illuminate the cell. The lamps were placed on each side of the cell at approximately 2 m distance and 45° angles. The placement of the lamps was adjusted to make sure that no reflections would be visible to the camera that was placed in front of the cell. As tracer we used the food-grade dye pigment Vitasyn-Blau AE 85 (Swedish Hoechst, Gothenburg, Sweden), which is chemically almost identical to the frequently used dye Brilliant Blue FCF. The dye was used in several field experiments because of its good visibility, low toxicity, and weak adsorption on soils (e.g., Flury and Flühler, 1994; Aeby et al., 1997).
Camera Settings
In this study we recorded the dye infiltration using a digital camera. The camera used was an Olympus Camedia E-20p (Olympus Optical Co. Ltd., Tokyo, Japan). To fix its position, the camera was placed on a tripod and left in that position throughout the duration of the experiments.
In RGB color space, all colors are represented by three values; red (R), green (G), and blue (B). These values can be in the range between 0 and 255. Black is represented by R = B = G = 0 and white by R = B = G = 255. All perfectly gray shades with no color cast will have equal R, G, and B values. To determine the correct exposure and white balance settings, we used a 1 by 1 m gray card. A gray card is commonly used in photography to calculate the correct exposure settings. If correctly exposed, the values for all colors should be 128.
A white balance is needed to make color corrections under differing lighting conditions. Normally our eyes compensate for different lighting conditions; however, the image from a digital photo must include a so-called white point (the requirement that a white object must appear white), to correct other colors cast by the same light. In our study the white balance was preset using the gray card. Each type of light is represented by a numerical color temperature. The color temperature of the halogen lamps in our study was about 3300 K.
Correction of Inhomogeneous Illumination
The two halogen lamps gave a fairly homogeneous illumination. However, small variations in RGB values were detected using the gray card (around ± 10%). We used the method presented by Aeby et al. (2001) to correct for the inhomogeneous illumination. The photo of the gray card provides a map of the spatial distribution of the incident light and is called a flat field image (F(x,y)). Any image I(x,y) can be corrected for inhomogeneous lightning by dividing it with F(x,y), relative to the mean value 
of the flat field image:
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Calibration
To determine the relationship between the RGB values of the images and the dye concentration, a calibration experiment was conducted. Known amounts of water, dye, and sand were mixed and packed into small boxes, which were placed just in front of the cell and photographed. These photographs were taken under exactly the same conditions as for the solute transport experiments, and were corrected using Eq. [1]. The small boxes were 0.10 m wide, 0.05 m high, and 0.025 m deep, and made of the same 0.01-m thick Plexiglas as the cell. In total, 74 calibration samples were prepared and photographed. The dye concentration, Cw (g L–1 of water), of these samples varied between 0 and 6 g L–1 whereas varied between 0.05 and 0.3 m3 m–3. From the corrected images IF(x,y) of the calibration boxes, the mean and standard deviation of the RGB values were calculated. When calculating these values, an area of at least 2000 pixels was selected.
We chose to use the procedure presented by Forrer et al. (2002) to calculate dye concentrations. They used a second-order polynomial equation to model the logarithm of the dye concentration of the soil (Cs = Cw [g dm–3 of soil]), as represented by the RGB values. Since their relationship was developed for a natural soil profile, they also included the depth as an explanatory variable in their model, but this was not necessary for our study.
Two-Dimensional Solute Transport Experiments
Four solute transport experiments were conducted in the cell. The water fluxes for these experiments were 1.47, 0.61, 0.43, and 0.31 mm min–1 for experiments 1, 2, 3, and 4, respectively. The order in which the experiments were conducted was at random to avoid systematic errors. Steady-state conditions (d/dt = 0) were achieved by applying tap water through the irrigation system at the indicated water flux. When as measured by TDR was constant for all probe locations, the tap water was replaced by a dye solution containing 5 g L–1 of Vitasyn-Blau AE 85. The time t for each experiment was set to 0 when the first dye reached the surface of the fine sand layer. The experiments were continued until the entire cell was completely filled with dye stained water. During the experiments photos were taken at preset constant intervals, ranging between 2.5 and 5.5 min, depending on the water flux. In total, between 110 and 204 photos were taken during each experiment.
Between the experiments the cell was washed with several pore volumes of tap water. This proved to be an efficient way of completely removing all dye from the sand. Thus, all four experiments were done for the same sand.
All digital photos taken were corrected for inhomogeneous illumination using Eq. [1]. For each pixel, Cs was calculated using the second-order polynomial equation derived during the calibration. The size of each pixel was about 0.0006 by 0.0006 m. To minimize boundary effects, pixels closer than 0.09 m from the sides of the box were discarded. In the end, a 1441 by 1287 matrix of Cs(x,y) values was determined from each photograph.
To facilitate comparison between the experiments, relative concentrations Csrel (0 < Csrel < 1) were calculated. For each experiment, this was done by first calculating the final maximum concentration in the cell for each pixel, Cmax(x,y), by taking the average of the pixel value in the three last photos of the experiment. This averaging was done to reduce image noise. The matrix of relative concentrations Csrel(x,y) was calculated as
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The water content can also be estimated using Cmax. Since the dye concentration in the soil solution was 5 g L–1 and Cmax = 5, the water content can be calculated for every pixel. The horizontally averaged Cmax/5 was used as a estimate. This relationship only holds if the sorbed amount of dye is negligible compared to the amount present in the water phase. This was likely the case in our experiments, since the sorption capacity will be low for this rather coarse material. A profile was also calculated using the HYDRUS model (
imunek et al., 1996). The modeled profile was compared to the TDR measurements and the dye concentration estimates of , that is, Cmax/5. The hydraulic parameters (van Genuchten, 1980) of the soil were known from earlier experiments for the same sand (r = 0.05 m3 m–3, s = 0.40 m3 m–3, Ksat = 0.000145 m s–1, 
= 3.44 m–1 = and n = 3). Using a constant water flux at the surface, a profile was calculated with depth increments of 0.01 m.
Time Moments
To study solute dispersion, we conducted a time moment analysis. In the present study, we divided each image into 512 vertical ‘columns’. This was achieved by first rescaling the images to a size of 1536 pixels wide, and averaging the rescaled images over 3 by 3 pixel areas to produce a 573 by 512 pixel image with an pixel size of 0.001406 by 0.001406 m. Subsequently, a 3 by 3 median filter was applied to each image. While this reduced the noise in general, some noise remained for the highest concentration values. To further reduce image noise, a tanh function, Cfit, was fitted to the breakthrough curves (BTC; concentration over time). Since we did not want to constrain the BTCs to be symmetrical, two different tanh functions were fitted, one on each side of the inflexion point of the BTC.
Time moments provide the most versatile approach to study solute transport since no assumption about the underlying physical process is needed. The time moments were calculated using the procedures described by Yu et al. (1999):
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was calculated as D/v.
The time moments were calculated for every pixel in the 573 by 512 pixel images. For each of the 512 columns, the was plotted over the depth. The horizontal mean and standard deviation of the was also calculated. To study possible scale effects on , the concentration values within column widths of 2, 4, 8, 16, 32, 64, 128, 256, and 512 times the pixel size was horizontally averaged. Using the BTCs produced, the time moments and was calculated for all column widths.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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The Cs could be successfully modeled with the second order polynomial calibration equation. Some basic statistics of the variables used in the calibration equation are presented in Table 1. The R and G colors were both highly correlated to Cs, whereas B was more or less independent of Cs. Thus, B was not included in the final calibration equation, which is in agreement with Forrer et al. (2002) who also found that B did not improve the calibration. It is interesting to note, however, that B was correlated with (r = –0.708). The R and G values were also correlated with (r = –0.341 and –0.520, respectively); however, this was indirectly due to the correlation of with Cs (r = 0.469). Apart from the samples with no dye, the lowest Cs of our calibration samples was 0.015 g dm–3 (Cw = 0.1 g L–1 and = 0.15 m3 m–3). Thus, the minimum value of log Cs for the dye-stained areas was –1.82. In this sample, the blue color was barely visible. When fitting the calibration equation to the data, the log Cs of the samples containing no dye was set to –2. Our final calibration equation was
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Since the standard deviation was almost constant with R and G, the relative variation was higher for low values of R and G. Thus, when Cs was high, R and G values were low, but the relative variation was higher than for low Cs. This was also reflected in the Cs estimates obtained using Eq. [4] (see Fig. 2). The overall RMSE of Eq. [4] was 0.057 g dm–3; however, for Cs below 0.75 g dm–3, the RMSE was only 0.032 g dm–3. Thus, the errors in Cs can be reduced by lowering the concentration. Alternatively, one might overexpose the photos to increase the RGB values. This idea was tested in another study (Persson, 2005).
To reduce the uncertainty of the concentration estimates due to image noise and small-scale variations, an averaging procedure was adapted. Previously published studies also used some kind of averaging. For example, Vanderborght et al. (2002a) used a 9 by 9 pixel median filter. They reported that this "considerably" reduced the noise, although no details were given. We analyzed the (macroscopically homogeneous) calibration samples to study the effect of pixel averaging on noise. An area of 64 by 64 pixels was selected from five different calibration samples having concentrations between 0.07 to 1.33 g dm–3. The concentration was calculated for each pixel using Eq. [4]. Next, an average filter was applied and the coefficient of variation (CV) was calculated for each size of the average filter. We analyzed CV for 1 by 1 (i.e., no averaging), 2 by 2, 4 by 4, 8 by 8, 16 by 16, and 32 by 32 pixel filters. The results are shown in Fig. 3 . In this figure the average CV for each filter is plotted against the averaging area. The uncertainty of the concentration estimate was reduced by a factor of almost 2 when a 4 by 4 pixel averaging filter is applied. Increasing the averaging area would reduce the uncertainty even more.
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profile was found to be very similar to the one estimated using the Cmax images by taking Cmax/5. Furthermore, measured with the TDR probes were also found to be close to the estimated using the HYDRUS model and image analysis. This confirms the accuracy of the concentration estimates in the cell. The results are presented in Fig. 5
. In all experiments, was constant down to the 0.5-m depth, whereas at deeper levels increased up to saturation. There was a clear dependency of in the 0 to 0.5-m interval on the water flux.
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All experiments produced dye patterns that were relatively homogeneous. The homogeneity seemed to increase with increasing water flux. In Exp. 1, the solute front was sharp and uniform. However, a closer look revealed some horizontal variations including vertical fingers of higher concentration. In the two low flow experiments (3 and 4), this fingering was more pronounced in the 0.1- to 0.5-m zone. The fingers were separated by 0.04 to 0.06 m. The location of areas with higher transport velocities was consistent between the experiments. We believe that the variation in transport velocity is mainly linked to small changes in bulk density and by micro-layers formed during packing of the cell. Some layering was visible, for example, at the 0.13-m depth. However, these layers did not have any noticeable effect on the dye front.
Time Moment Analysis
In Fig. 6
horizontally averaged distributions of are plotted vs. depth for all experiments for different averaging areas. For convenience, the <> values are indexed with their column width in centimeters, for example, 72 represents the value for average transport in the entire cell (column width = 72 cm), whereas 0.14 represents the value for a single pixel width. First we consider meso-scale transport (i.e., average transport in the cell). The 72 values were low in all experiments, around 0.05 to 0.8 cm. A lower means more solute mixing between individual flow paths such as may be encountered in homogeneous material like repacked sand (e.g., Khan and Jury, 1990; Padilla et al., 1999; Toride et al., 2003). In undisturbed structured soils, can be several orders of magnitude higher (e.g., Beven et al., 1993). The value of depends on several factors, for example, pore geometry, water content, solute transport velocity variability and water flux. A higher leads to a lower tortuosity of the flow paths and thus, a lower . This is the major reason why generally is higher for unsaturated than for saturated flow (Toride et al., 2003). On the other hand, a higher might activate macropore flow, thus leading to less mixing. It is apparent that is a very difficult parameter to estimate and much effort has been made on describing it for different soils under different conditions (Roth and Hammel, 1996; Nützmann et al., 2002). We observed a larger 72 for Exp. 3 and 4 (around 0.5 cm), compared to experiments 1 and 2 (around 0.1 cm). This is in line with other results for homogeneous soils without significant macropore flow. For example, Toride et al. (2003) observed to increase by a factor of three when decreasing the water content from 0.3 to 0.2 m3 m–3, which corresponded to the change in for the uppermost 0.5-m depth between the high and low flow experiments.
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at several different scales. The lowest dispersivity values were found in Exp. 2, with 0.14 as low as 0.015 cm and <0.14> = 0.034 cm. These values are in the range of the theoretical for an ideal saturated porous media, which is defined as dp/2, where dp is the particle diameter (Bear, 1972). As expected, the meso-scale dispersivity was always larger than <0.14> with a factor of 2 to 5. The minimum local-scale 0.14 was between 4 to 11 times smaller compared to the meso-scale . Remarkably, the dispersion values were virtually identical for scales from 0.0014 to 0.045 m. This implies that the solute transport variability was similar in this range of scales. For larger scales, <> gradually increased up to 72. Several previous examples have also shown this increasing with scale both numerically and experimentally (Roth and Hammel, 1996; Nützmann et al., 2002; Javaux and Vanclooster, 2003). In our study, it seems that this scale dependency is only valid over a certain range of scales. It is interesting to note that the upper scale limit for equal <> was the observed mean distance between the fingers discussed in the previous section.
As mentioned above, the variability in v affects dispersion. In fact, can be defined according to the coefficient of variation (CV) of the solute transport velocity (Bear, 1972; Javaux and Vanclooster, 2003). To evaluate the effect of the CV of the local-scale v (CVv) on the meso-scale (72), CVv was calculated and plotted as a function of depth. Figure 7
shows that all CVv's decrease with depth. The high CVv values at shallow depths could be caused by incomplete solute mixing due to the spatially variable water application. When considering Fig. 7 one should realize that the stream tube velocity at a certain depth calculated with time moments is a measure of the average velocity of a particle from the injection to the observation point. Therefore, v integrates information of local scale velocities from the injection surface to the observation point. Due to mixing the CVv decreases with depth. But, this does not necessarily mean that the heterogeneity or CV of the local-scale pore water velocity decreases with depth. Therefore the relationship between CVv and 72 will be strictly depth dependent. For depths >0.3 m, there is a clear dependency of CVv on water flux. At depths above 0.3 m, the CVv from Exp. 2 was higher than expected. It was somewhat surprising that in Exp. 3 and 4, the CVv decreased with depth between 0.1 and 0.5 m, whereas 72 increased. This would imply that dispersion within the stream tubes is increasing at the same time as meso-scale mixing due to differences in convective transport velocity between stream tubes decreases. While the exact mechanisms are not known, they could be related to the increased tortuosity of the flow paths due to the lower . For every depth, we found a significant correlation between CVv and 72, similarly as was found previously by Javaux and Vanclooster (2003). If we instead consider each experiment separately, the correlation between CVv and 72 was very high for Exp. 1 and 2, but much lower or even negative in Exp. 3 and 4. This again implies more dispersion within the stream tubes. We also noted that the CVv was independent on the scale for column widths from 0.0014 to 0.045 m.
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72, it is remarkable that the variation is almost identical for Exp. 1 and 2 and Exp. 3 and 4, respectively. Apparently a shift occurs in the flow regime and the transport processes between the flow rates. The only experimental condition that differs between the experiments is the flow rate, leading to differences in for the 0 to 0.5-m depth. Thus, the change in is likely causing the shift in the dispersion process. Apparently, some larger pores are activated in Exp. 1 and 2, which enhanced mixing due to decreasing tortuosity of the flow paths. Since the difference in between Exp. 2 and 3 was very small, (about 0.02 m3 m–3), this shift occurs suddenly at a specific . Toride et al. (2003) performed a series of experiments in saturated and unsaturated dune sand and found a similar sudden shift in the dispersion process at 0.15 m3 m–3. This shift in the dispersion process is likely linked to pore geometry. Both the sand used in the present study and the one by Toride et al. (2003) were fairly uniform. Since most pores hence were of a specific size and around a critical point, a small change in could then have caused a significant change in tortuosity of the flow paths.
Jury and Roth (1990) showed that to precisely describe the solute transport process, breakthrough curves should be measured at different depths. They also showed that if solute transport is accurately described by the convection-dispersion equation, should remain constant with depth. If solute transport is described with a stochastic-convective process, should be increasing with depth (see also Javaux and Vanclooster, 2003). When studying 72 between 0.1- and 0.5-m depth we see that in Exp. 1 and 2, 72 was fairly constant with depth, but increased linearly in Exp. 3 and 4. Below 0.4 m increased to saturated conditions at the bottom of the cell in all experiments, while 72 decreased slightly for Exp. 3 and 4, but increased for Exp. 1 and 2. When the solute front reaches the part of the cell where is increasing, a compression of the front occurs, which in turn increases horizontal mixing. Obviously, the solute transport process is different for relatively high and low flow rates. At low flow rates transport in the fully developed unsaturated flow part of the cell (0.1–0.5-m depth) is stochastic-convective and at the high flow rate it is convective-dispersive. Again, we believe that these qualitative differences in the transport between high and low flow are a result of differences in . When is lower than a critical value (0.22 m3 m–3), solute mixing decreases, which was also observed visually (in Exp. 3 and 4 some fingers developed between the 0.2- to 0.4-m depth). The same depth dependency as for 72 exist also for 0.14. Thus, local and meso-scale transport could be described with the same concepts. An example of the opposite was observed by Javaux and Vanclooster (2003).
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SUMMARY AND CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Using the first and second-order time moments, was calculated for nine different column sizes, from 0.0014 (local-scale) to 0.72 m (meso-scale). We noticed that the two experiments with the higher flow rates (1 and 2) and the two experiments with the lower flow rates (3 and 4) showed almost identical variations in the meso-scale (72) with depth. The local-scale <> showed a similar dependency vs. depth as the meso-scale in all experiments, albeit by a factor two to five times smaller. The <> values proved to be identical for column widths from 0.0014 to 0.0045 m. When considering the CV of the local-scale velocities derived using the first-order time moment, we noticed a significant depth dependent relationship between CVv and 72. However, when considering CVv vs. 72 relationships for each experiment individually, we found a significant correlation between CVv and 72 only for Exp. 1 and 2. This means that could not be determined using only knowledge of the solute transport velocity variability.
We conclude that above a specific critical (0.22 m3 m–3), solute mixing is enhanced, leading to lower values. This caused the high flow experiments to have a lower compared with the low flow experiments. Furthermore, the solute transport processes involved changed with . At relatively high water contents, the solute transport could be described by a convective-dispersive process. When was lower than some critical value, part of the porosity was deactivated leading to reduced mixing between individual stream tubes, which in turn implies that transport could be described with a stochastic-convective process. Thus, a small change in can lead to fundamental differences in the solute transport process. This suggests that results from one experiment at a specific water flux may be difficult to translate to a different flux.
Dye infiltration and image analysis of the type described in this paper may produce high quality data. The temporal scale can be very fine, in our case down to one image every 2.5 min; however, images could be taken much more frequently if desired. The spatial scale was also very fine. Our results clearly show that the method presented can give unrivalled spatial and temporal resolution. High-resolution data like those achieved in this study may be particularly attractive in future small-scale variability studies of solute transport.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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imunek, J., M. ejna, and M.Th. van Genuchten. 1996. HYDRUS-2D-Simulating water flow and solute transport in two-dimensional variably saturated media. U.S. Salinity Lab., USDA/ARS, Riverside, CA.This article has been cited by other articles:
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  M. Van Praagh and K.M. Persson Metal releases from a municipal solid waste incineration air pollution control residue mixed with compost Waste Management Research, August 1, 2008; 26(4): 377 - 388. [Abstract] [PDF]
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