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Published in Vadose Zone Journal 4:101-111 (2005)
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

ORIGINAL RESEARCH

Characterization of Field Tracer Transport Using High-Resolution Images

R. Kasteela,*, M. Burkhardtb, S. Giesaa and H. Vereeckena

a Agrosphere Institute, ICG IV, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
b Swiss Federal Institute for Environmental Science and Technology (EAWAG), Überlandstrasse 133, 8600 Dübendorf, Switzerland
* Corresponding author (r.kasteel{at}fz-juelich.de)

Received 15 June 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Flow and transport in soils and groundwater are greatly affected by subsurface heterogeneity. We present results from infiltration experiments on four heterogeneous field plots (Orthic Luvisol) for plowed and nonplowed conditions. A 2-mm pulse of Br– was applied, followed by a 40-mm application of a 5 g L–1 solution of the food dye Brilliant Blue FCF (Color Index 42090) in a 6-h period. Horizontal cross sections were photographed at 0.05- and 0.10-m depth intervals, representing the Ap and Bt horizons, respectively, either immediately or 90 d after the tracer application. High-resolution spatial maps of Brilliant Blue concentration were derived from the scanned photographs using one single calibration relationship between Brilliant Blue concentration and the color spectra for all plots and depths. No significant or consistent directional dependence was observed in the spatial correlation structure of the dye concentration for the horizontal cross sections. However, the integral scale showed a distinct depth dependency, partially caused by horizonation, with a larger value in the Ap than in the Bt horizon. Disturbed soil samples were taken at 15 locations for each cross section and analyzed for Br–. Although Brilliant Blue was retarded in the soil matrix with respect to Br–, both tracer concentrations showed an exponential decay with depth because of preferential flow enhanced by plowing. Only a small fraction of the dye was subjected to fast transport. The plot-scale information of the dye distribution revealed that our 15 sampling locations at each depth were sufficient to identify the averaged plot-scale transport behavior in the soil matrix, but failed to represent the conducting preferential flow pathways.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
FLOW AND TRANSPORT in soils and groundwater are greatly affected by the heterogeneous nature of the subsurface. Heterogeneity implies that the physical, chemical, and biological properties of the medium vary in space and time. These variations are often not completely disordered, but may exhibit a structural arrangement. Our knowledge about the spatial structure of heterogeneities and their effect on flow and transport processes is still limited.

Solute transport is subjected to variations in the local water flow velocity, among other factors, which depends on soil structure. While concentration patterns therefore should contain information about the underlying heterogeneity in hydraulic properties, they represent integral measures of the transport distance at increasing depths. Ellsworth and Boast (1996) interpreted the change in the correlation length of concentrations as a change in lateral solute mixing at or above the depth of observation, although a certain correlation length can also be obtained without any lateral mixing if a heterogeneous flow field is present. Van Wesenbeeck and Kachanoski (1991) found the presence of spatial correlation lengths for solute transport in both a forested and a cultivated site, likely because of pedogenesis and/or soil past management practices. Furthermore, the correlation length also provides a measure of the minimum plot size necessary to include the full range of horizontal variability in the local pore-water velocity, which can then be compared with spatial distributions of soil properties affecting solute transport (Van Wesenbeeck and Kachanoski, 1991).

The correlation structure of the concentration field is a function of the correlation structure of the hydraulic conductivity field, local-scale dispersion, and the travel distance. When the conductivity field can be represented as a Gaussian random field, the correlation structure of the concentration field can be predicted in terms of the above-mentioned parameters (Vanderborght, 2001). However, the reverse situation of deriving the correlation structure of the conductivity field from the concentration field is less easily accomplished since conductivity fields with different structures can lead to concentration fields with a similar structure.

A prerequisite for determining the correlation length from concentration correlograms is the need for concentration measurements at high spatial resolution. Dye tracer experiments have recently become increasingly popular to visualize the heterogeneous nature of flow and transport pathways at the field plot scale (Flury and Wai, 2003). Since stained soil profiles can be photographically recorded, the information for the dye patterns can be obtained at a high spatial resolution. The food dye Brilliant Blue FCF (Color Index 42090) was previously used by Forrer et al. (2000) to determine absolute solute concentrations in small-scale field plots with a pixel resolution of 1 mm2 using image analysis procedures. The resident concentration of the dye in their study was estimated using a second-order polynomial regression with depth and the primary colors red, green, and blue as the explanatory variables. This method appears very promising for analyzing high spatial resolution flow and transport processes in the vadose zone.

Field experiments at scales of a few meters should represent a scale that is manageable for establishing links between laboratory measurements and larger-scale field experiments. Simultaneous application of Brilliant Blue with a conservative tracer that follows the water flow pathways may provide a very detailed description of solute transport, as shown by Zehe and Flühler (2001), Kasteel et al. (2002), and Öhrström et al. (2004), among others. These studies show that images of the dye patterns can identify the transport behavior in much greater detail than is possible with a conservative tracer using current sampling methodologies. However, because of solute retardation effects, dye tracers such as Brilliant Blue may not be suitable compounds for tracing the travel time of water itself.

The experimental work presented here is part of a multitracing study to characterize the effect of bypass flow on the transport of tracers with different chemical affinities to the soil matrix (Burkhardt, 2003). The plots used in that study differed in terms of soil management, date of application, and exposure to rain and evaporation. Our objectives were to (i) deduce high-resolution spatial distributions of Brilliant Blue concentrations using images of the dye patterns following methods used previously by Forrer et al. (2000), (ii) determine if it is possible to derive the spatial correlation structure of Brilliant Blue concentration from these dye patterns, and (iii) compare the transport characteristics of Brilliant Blue with those of the conservative tracer Br– using moment analysis.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Tracer Experiment
The experimental site was located near Merzenhausen, Germany, on arable land used intensively for agricultural production. The mean annual precipitation and temperature for this region are 689 mm and 9.5°C, respectively. The soil is classified as an Orthic Luvisol, with silt being the dominant textural fraction accounting for about 80% by mass. Selected soil properties are given in Table 1. The groundwater table was approximately 15 m below the soil surface. Earthworm burrows (diameter between 5 and 10 mm) were found to be abundant to a depth >1.5 m, although few direct connections to the soil surface existed because of frequent plowing. We found roots mostly in the plow layer only. Root channels were generally <10 mm in diameter and were found up to a depth of 1.2 m. We estimated the number of earthworm burrows and root channels for four horizontal planes in the subsoil to be about 15 and 350 m–2, respectively.


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  		Table 1. Selected physical and chemical properties of the soil at the experimental test site in Merzenhausen.{dagger}

 
The field experiment was conducted between April 2000 and February 2001. The transport of Br– and Brilliant Blue was studied in four 1.4 by 1.4 m field plots. The spatial arrangement of the plots is shown schematically in Fig. 1 . We implemented two soil management treatments before tracer application: plowing (P) and no plowing (NP), each comprising two plots. A plow pan was present in all four plots. Instrumentation trenches were dug next to two of these plots and were equipped with horizontally installed time domain reflectometry probes and tensiometers at five depths with four replications per depth.



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  		Fig. 1. Spatial arrangement of the four plots in the field. The irrigated areas measured 1.4 by 1.4 m, with photographs taken of the inner square meter, represented by dashed lines. Symbols in the P-90 plot show the 15 sampling locations for Br– in the inner square meter of each cross section.

 
Barley (Hordeum vulgare L.) was sown in the autumn of 1999. Preparation of the two NP plots started in March 2000 by manually removing the sprouted barley, including its roots. The soil surface of these two plots remained bare for the duration of the experiment. On 21 March, the soil was excavated to a depth of approximately 0.15 m. The soil surface was subsequently harrowed using a tractor-drawn implement, and the soil surface made even by hand with a rake. The soil was next exposed for 3 wk to rain and evaporation before application of the tracer applications. The average initial water contents, {theta}i, of the NP plots before tracer application were 0.16, 0.31, 0.34, 0.34, and 0.34 at the 0.05, 0.20, 0.40, 0.60, and 0.80 m depths, respectively.

The barley of the P plots was harvested in the beginning of July. On 9 October, the soil was plowed to a depth of approximately 0.35 to 0.38 m, after which the plots were raked. The average initial water contents were 0.21, 0.33, 0.34, 0.33, and 0.34 for the same depths as given above. Thus, the upper part of the plow layer was slightly wetter for the P plots, but no differences were found at larger depths.

To each of the four plots we next applied a 2-mm pulse (20-min duration) of Br– with an input concentration C0 = 66.5 g L–1 using a hand-operated pesticide sprayer. Bromide was applied in the form of a KBr solution. After 1 h, the application of the Br– tracer was followed by 40 mm of a Brilliant Blue solution with an input concentration C0 = 5.0 g L–1. The Brilliant Blue solution was intermittently applied for 6 h using an automated rainfall simulator. The interval between each run of the spray bar was 5 min, resulting in an irrigation rate of 6.7 mm h–1. Bromide and Brilliant Blue were applied with an areal density, M0, of 133 and 200 g m–2, respectively.

Two plots (NP-0 and P-0) were covered immediately after the tracer applications to prevent soil evaporation. The other two plots (NP-90 and P-90) were exposed to natural weather conditions for 90 d. Rainfall intensity was measured at the experimental site. We did not have good values for the net cumulative infiltration rates because no accurate estimates of the actual evaporation rates were available. Selected information about the tracer applications is summarized in Table 2. Upon completion of the tracer experiments, horizontal cross sections of the Ap and Bt horizons were prepared parallel to the soil surface, at 0.05- and 0.10-m depth intervals, until no further staining was observed.


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  		Table 2. Overview of the Br– and Brilliant Blue (BB) tracer application and excavation dates for the different plots.

 
Photographic Recording
We used a similar photographic setup as described by Ewing and Horton (1999). The soil profiles were photographed in a single fabric layer white tent, which allowed only for diffuse light. The photographs were taken on Kodak E 100 S color films with a Hasselblad camera using a 60-mm lens. The camera was mounted on a tripod with a fixed position in the center of the plots; the distance between the camera and the soil profile was always 1.4 m. Four flash units were installed in the corners of the plot. The angle between the flash units and the soil surface was 45°. Photographs of the soil were obtained in color, together with Kodak color and gray scales in the image (Forrer et al. 2000). The soil surface was then covered with a gray paperboard and the gray-covered surface was photographed again with the Kodak scales. The paperboard was later used to reduce the effect of inhomogeneous illumination. For each plot we photographed and sampled 12 to 16 horizontal cross sections, at a rate of about four profiles per day. During the photographic recordings we did not observe an increase in the intensity of the blue dye at the soil surface due to evaporation of water; therefore, we concluded that evaporation did not affect concentration estimates. All photographs were taken in either the fall or spring.

Soil Sampling Procedures and Measurements
To estimate Brilliant Blue concentrations in the images from the color spectra, a calibration against measured dye concentrations is needed. We used the crosshairs of the lens to fix a grid with a 0.10-m mesh to obtain the spatial coordinates of the soil sampling positions. A thin layer of approximately 12 to 15 g of soil was scraped from homogeneously stained and unstained areas with different dye intensities. In total, 302 stained and 82 unstained samples were taken from the four plots. The sampling locations were marked and each cross section was recorded on separate photographs.

For the extraction of Brilliant Blue, 3 g of oven-dried soil were equilibrated with 30 mL of a 3:2 (v/v) water and acetone solution by shaking for 3 h. The suspension was centrifuged for 1 h and 10 mL of the supernatant was collected. The extraction procedure was repeated once more to produce another 10 mL supernatant, for a total of 20 mL. These two extraction steps removed most of the Brilliant Blue from the soil. Brilliant Blue concentrations were measured with a photospectrometer.

For the Br– measurements we used the 0.1 by 0.1 m mesh to collect 25 to 30 g of soil from 15 fixed positions, which were identical for all depths and all plots. The sampling positions were randomly distributed across the plot area according to a predetermined pattern (Fig. 1) so they were different from those used for the dye calibration samples. The soil was dried for 24 h at 105°C and homogenized. For the extraction of Br–, 10 g of dry soil were equilibrated with 20 mL of a 0.01 M CaCl2 solution by shaking for 16 h. The suspension was then centrifuged for 1 h, with 10 mL of the supernatant used to determine Br– concentration by ion chromatography. Brilliant Blue and Br– concentrations were both expressed in terms of tracer mass per mass of dry soil.

Image Processing
We followed the image processing steps below, first proposed by Forrer et al. (2000), to quantify Brilliant Blue concentration per mass of soil from the photographs.

Image Corrections
For each profile, an image of the Brilliant Blue pattern and the gray paperboard were scanned with a resolution of 5900 by 5900 pixels. After scanning, the images were manually adjusted for color differences using the KODAK color scale values. For further processing, the image resolution was reduced to 316 by 316 pixels for the inner 1 m2 (pixel area is 10 mm2) using Adobe Photoshop 5.0. Inspection of all gray paperboards revealed that they consisted of nearly equal parts of red, green, and blue and that their ratios were fairly constant with depth. Therefore, no additional color correction was performed. Since the camera was always positioned in the center of the area of interest, with a distance to the imaged surface of 1.4 m, geometric distortions were minimal.

Illumination is usually not completely constant over space and time under field conditions. Nevertheless, shading should be a smoothly varying function of location at any point of time. Forrer et al. (2000) showed that background subtraction is an effective procedure to correct the Brilliant Blue images for spatial variations in illumination. These authors interpolated brightness values using fixed points from the gray frame for the entire soil profile, whereas we used the photographs of the gray paperboard to avoid the interpolation step. We additionally scaled the brightness to the average value across all depths and plots. An essential assumption for this correction procedure is that light conditions do not change during the imaging period of the gray paperboard and the Brilliant Blue pattern. This condition is generally met if the time interval between the recordings is small. Still, we do note that local illumination may have differed slightly between the gray paperboard and the prepared soil surface images because of differences in surface roughness.

Statistical Regression Analysis
A single calibration relationship was determined for the four plots between the measured Brilliant Blue concentration and the associated red, green, and blue values used as explanatory variables. First, the spatial coordinates of the Brilliant Blue sampling locations were determined on the corrected images. We computed the 20%-trimmed mean of the red, green, and blue values of 49 pixels, each representing a sampling location with area of 4.9 cm2 of the corrected images. To reduce multicollinearity between the first- and second-order terms, the explanatory variables were standardized to zero means and unit variance (Table 3).


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  		Table 3. Mean and standard deviation (SD) of the explanatory variables (values between 0 and 255) used in the calibration procedure.

 
The background color of a soil is generally not constant with depth because of soil layering. In contrast to Forrer et al. (2000), who treated the depth, Z, of the sampling location as an additional independent variable, we included Z as an indicator variable in the regression analysis. This allowed us to include the horizon effect in a single equation. The indicator for depth, Z, was arbitrarily set to unity in the plow layer and was zero otherwise.

We fitted the logarithm of the dye concentration by means of a second-order polynomial using the standardized mean variables , , and as explanatory variables, and Z as an indicator variable. The stained and nonstained samples were both used for the regression analysis. Since the number of independent variables in the model is large, we selected a subset of the full parabolic model by eliminating nonsignificant terms using a stepwise backward procedure (Forrer et al., 2000).

Postprocessing of the Maps of Dye Concentration
We applied the following corrections to the predicted dye concentrations. First, extrapolation of a second-order polynomial beyond the range of calibration may result in erroneous Brilliant Blue concentration predictions. Estimated concentrations for these situations were set to the highest measured dye concentration of the calibration set. Also, we measured small nonzero (apparent) concentrations of Brilliant Blue in the nonstained calibration samples, probably due to absorption of light by dissolved organic matter. This required the use of a threshold value in the low concentration range to distinguish between the stained and nonstained areas. The highest measured apparent Brilliant Blue concentrations of the nonstained soil samples were used as threshold values for all plots. These values were very close to the lowest measured Brilliant Blue concentrations of the stained calibration samples for both horizons.

Spatial Correlation Structure
The spatial correlation structure of the Brilliant Blue concentration was characterized with the autocorrelation function or correlogram for all horizontal cross sections. We used the GSLIB software package (Deutsch and Journel, 1998) to determine the experimental correlograms. The autocorrelation coefficient, {rho}(h), is defined as

[1]
where C(h) is the spatial covariance function at lag distance h, and {sigma}–h and {sigma}+h are the standard deviations of the tail and the head values, respectively. The covariance does not implicitly assume that the mean of the tail values are the same as the mean of the head values. A nested exponential autocorrelation function was fitted to the experimental correlograms:

[2]
where {omega} is a weighing factor and {alpha}1 and {alpha}2 are characteristic length scales. These parameters were obtained using a least-square fitting procedure.

We calculated the integral scale, I, to determine the spatial correlation length for dye concentration. The integral scale may be interpreted as the average largest distance for which dye concentrations are spatially correlated and is defined by (e.g., Lumley and Panofsky, 1964; Russo and Bresler, 1981)

[3]
Note that I = {surd} for a nested exponential autocorrelation function, obtained by substituting Eq. [2] into [3] and integrating.

Transport Characteristics
The method of moments summarizes the transport behavior in a statistical way without making any assumptions about the governing transport processes. The method provides an effective way of comparing the transport behavior perpendicular to the mean direction of flow for the different treatments. The depth profiles of the mean tracer concentration per volume of soil, t = bs, were calculated by horizontal averaging, where s and b are the mean tracer mass per mass of soil and the mean bulk density at depth, z, respectively. Since no information was available about the distribution of bulk densities within the area of interest, we used mean bulk density values, which were measured with 12 100-mL cylinders at 0.10-m depth intervals. The normalized nth depth moments, Zpn, of the solute mass distribution for a pulse application were estimated from

[4]
Mass recovery, mr, is defined as the ratio between m0 = {int}{infty}0 t dz and the total mass applied per unit area, M0. The first moment, µz = Z1, represents the mean travel depth, whereas the second moment describes solute spreading around the mean travel depth.

We assumed that dye application occurred by means of a step function in the NP-0 and P-0 plots. To obtain the spatial moments Zsn for a step application, we used the property that a pulse can be regarded as the first derivative of a step. In analogy to Yu et al. (1999), Eq. [4] can therefore be rewritten as

[5]
Equation [5] can only be used if the concentration decreases monotonically with depth. Equations [4] and [5] were numerically evaluated using the trapezoidal rule.

Comparing the mean travel distance of Brilliant Blue and Br– at the time of excavation allows us to make an estimate of the retardation of the dye, assuming that Br– was not subject to either adsorption or anion exclusion. The effective retardation factor, Reff, is then defined as the ratio between the mean travel depth, µz, of Br– and Brilliant Blue, respectively (Perillo et al., 1998).


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
SUMMARY AND CONCLUSIONS
 REFERENCES
 
Concentration Maps
Using the entire dataset, the best-fit second-order polynomial for the base 10 logarithm of dye concentrations contained nine significant terms. Our analysis led to the following equation for the dye concentration:

[6]
The approximate standard errors of the fitted coefficients are listed in Table 4. The mean-square error (MSE) was 0.054 and the coefficient of determination (R2) was 0.918. The impact of the correction for inhomogeneous illumination was found to be relatively small, although the approximate standard errors of the fitted parameters increased. This small effect was likely due to the optimal light conditions.


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  		Table 4. Fitted parameters, their approximate standard errors (SE), and partial coefficients of determination (partial R2) for the second-order polynomial with , , , and Z as independent variables and the logarithm of the dye concentrations, log10, as the dependent variable. Note that Z is unity in the plow layer and zero in the subsoil.

 
The choice of the regression model was based on our pragmatic consideration to obtain estimates of the dye concentration from information that be readily derived from the images. It is feasible to use depth, Z, as an indicator variable if the change in background color is sharp, as was the case between the plow layer and the subsoil. Taking depth as an independent variable (Forrer et al., 2000) gave comparable estimates of MSE and R2 (0.059 and 0.910, respectively) for the base 10 logarithm of dye concentrations. A simple linear regression with and Z reduced the MSE and R2 values to 0.188 and 0.709, respectively. Adding and to this linear model, increased MSE to 0.075 and R2 to 0.885. In general, explained most of the measured Brilliant Blue concentration variations (Table 4). It had a negative coefficient since a blue dye contrasts against a reddish soil.

We performed a single multiple regression for the entire dataset, rather than by treatment. The resulting bias and MSE values for predicting logarithms of dye concentrations for the various treatments are listed in Table 5. A bias was introduced, in contrast to having separate regressions for each plot, whereas the MSE increased by a factor 1.2 to 2.4 for the P-0 and the NP-90 plots, respectively (data not shown). The single multiple regression model estimated concentrations better for the P than for the NP profiles.


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  		Table 5. Bias and mean-square error for predicting logarithms of the dye concentrations for the various plots.

 
The single regression model was used to estimate the Brilliant Blue concentration at each pixel using the corrected images. An example of a corrected image and the corresponding map of Brilliant Blue concentrations is shown in Fig. 2 . The distribution of the calculated dye concentrations generally compared well with the visually observed dye patterns.



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  		Fig. 2. Example of a corrected image (left) with the corresponding calculated concentration distribution of Brilliant Blue (right) for the 0.15-m depth of the P-0 plot.

 
Dye coverage is generally determined by discriminating between stained and nonstained pixels using threshold values. We define dye coverage here as the fraction of a 1-m2 profile face that has a Brilliant Blue concentration larger than zero. A one-dimensional depth profile of dye coverage provides then a qualitative summary of relevant solute transport features, such as the percentage of soil that takes part in conducting water at the time of excavation. Figure 3 shows results for all of our plots. The soil surface was only partially stained in the NP-90 and P-90 plots because of some transport into the profile due to rainfall during the experiment. A larger part of the surface area remained stained in the NP-90 treatment because of some upward flow due to evaporation. Notice also that the dye stained the soil to larger depths in the P than in the NP profiles.



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  		Fig. 3. Depth profiles of dye coverages for the four plots.

 
Figure 4 shows three characteristic shapes of histograms for the dye concentration distribution at a particular sampling depth. For dye coverages of almost 100%, a nearly Gaussian distribution of the dye concentration was observed (Fig. 4a). An exponential decrease in frequency with concentration was found for lower dye coverages (Fig. 4b). The latter has the typical shape of a bounded variable, since concentrations cannot become negative. The sampling depths below the 0.15-m depth all showed exponential forms. A transition between the Gaussian and exponential form was found for both P distributions (Fig. 4c). Although the highest concentrations in the subsoil were found for a few stained macropores, the shape of the histograms indicated that transport was more of a diffuse process, with most of the dye being present in the soil matrix.



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  		Fig. 4. Histograms of the dye concentration distribution at three different depths for the P-0 plot. Pixels with zero concentration were not considered. The concentration intervals were 100 and 50 mg kg–1 for z = 0 m, and z = 0.10 and 0.40 m, respectively.

 
Figure 5 shows three-dimensional isoconcentration surfaces of the dye to a depth of 0.70 m. The small isolated surfaces in the subsoil are artifacts caused by the incorrect assignment of concentrations to nonstained pixels having a dark color. These structures can be identified as nonstained earthworm burrows. The spectral signature of these burrows was not part of the set of calibration samples, thus causing a bias in the concentration prediction in the lower concentration range, a feature also observed by Forrer et al. (2000). The introduction of a threshold value in the calibration equation below which concentrations are assumed zero could possibly avoid such incorrect concentration assignments due to dark color features.



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  		Fig. 5. Observed isoconcentration plots of Brilliant Blue. The isosurfaces were drawn for a Brilliant Blue concentration of 75 mg L–1 of soil and are all plotted to a depth of 0.7 m. Note that the plots have a surface area of 1 m2.

 
Figure 5a shows that most of the dye resided in the plow layer of the NP-0 profile. This profile also clearly showed a single conducting preferential flow pathway (earthworm burrow) through the subsoil, probably initialized by lateral spreading of dye above the plow pan. The apparent disconnection of this preferential flow pathway with dye in the plow layer is likely due to the relatively coarse vertical sampling distance. The dye penetrated the subsoil of the NP-90 profile in small, finger-like flow structures (Fig. 5b), presumably induced by the plow pan. Brilliant Blue was found in a few earthworm burrows, down to the 1.6-m depth in this profile. Plowing caused enhanced downward transport as compared with the NP plots, with dye patterns converging toward a few larger flow pathways (Fig. 5c and 5d) that were continuous across the horizon boundary. This phenomenon was also observed in a numerical study of flow in unsaturated fracture networks (Zhang et al., 2004). A few earthworm burrows were stained to a depth of 1.6 m in the P-90 profile. Although root channels were abundant in the subsoil, only a few earthworm burrows were stained throughout all profiles, suggesting that not all burrows contributed to preferential flow. This shows that the occurrence of macropores alone does not always lead to preferential flow of reactive compounds, but that the water-conducting flow pathways must also be connected vertically.

Spatial Correlation Structure
Experimental correlograms were determined for all depths where the percentage of dye coverage was larger than 0.015. The choice for a nested exponential model to describe the experimental correlograms was based on visual inspection of the data, as well as having a significantly better fit. In other cases, a simple exponential model was used, with {omega} = 1 in Eq. [2]. Figure 6 shows typical examples of dye concentration maps and the corresponding experimental omnidirectional correlograms. The concentration maps were selected for three profiles that had approximately the same coverage of dye between low to high. The examples are illustrative of the variations in correlation length scale that we observed for our plots. We note again that the small black dots on concentration maps in the subsoil are due to earthworm burrows rather than to stained areas (see also Fig. 5).



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  		Fig. 6. Concentration patterns of Brilliant Blue (1 by 1 m) and omnidirectional experimental correlograms (symbols) for selected depths. The dashed lines represent the fitted correlograms. Values for the integral scale, I, and the dye coverage, dc, are given in the legend for each depth, z. Notice that the concentration scale differs for the various plots and depths.

 
The NP-90 and P-90 plots at the 0.05-m depth produced experimental correlograms that could be fitted well with the nested exponential autocorrelation function. This particular shape was mostly present in the first 0.10 m of the Ap horizon where the soil was loose. The other examples were fitted with the simpler exponential model. The (nested) exponential autocorrelation model adequately described the experimental data. The correlograms did not show significant or consistent directional dependencies, which indicates that the isotropy assumption was applicable to the horizontal cross sections.

Values of the integral scales for all treatments are summarized in Fig. 7 . The results clearly show that the correlation structure of the dye concentration is not constant with depth. As suggested above, the observed dye patterns at increasing depths should be integral measures of the transport distance in that they are the result of flow through the entire soil profile, and in some cases even of transport at deeper depths. For example, under local ponding conditions the layer above a plow pan may retain dye for an extended time, thereby allowing it to diffuse into aggregates and increasing the apparent correlation length. Sampling smaller vertical units by removing the topsoil could alleviate the fact that the integral scale strongly depends on the flow history. We note that two transition zones exist in the soil profile: one near the bottom of the harrowed layer at about the 0.15-m depth and one near the bottom of the plow layer between 0.3 and 0.4 m, the latter zone corresponding with a plow pan but partially mixed with the Ap and Bt soil horizons.



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  		Fig. 7. Plots of integral scale vs. depth.

 
Except for the 0.05- and 0.10-m soil depths of the NP-90 treatment, we did not observe an effect of the transient water fluxes at the soil surface on the integral scale for the NP profiles in the plow layer. Also, the integral scale of the Ap horizon for P-0 does not differ from both NP treatments, except for the 0.35-m soil depth. The larger integral scale length of the plow layer of the P-90 treatment suggests that lateral solute mixing was less pronounced in that plot than for the other treatments. Ellsworth and Boast (1996) conjectured that a change in texture may have initiated differences in the lateral solute mixing regime at or above textural discontinuities at their field site, which eventually resulted in a change in integral scale length. However, since our textural analysis did not show pronounced differences between the plots (data not shown), we have no definite explanation for the observed correlation structure for the P-90 treatment.

Transport Characteristics
Using image analysis, we were able to calculate Brilliant Blue concentrations at the 15 Br– sampling locations. The horizontally averaged concentration profiles for Br– and Brilliant Blue are shown in Fig. 8 , while the corresponding results of the moment analysis are listed in Table 6. We found a linear decline with depth of the base 10 logtransformed Br– and Brilliant Blue concentrations. The concentration profiles cannot be described with a simple convection–dispersion equation because the sorbing dye tracer was detected at about the same depths as the Br–, notwithstanding their different chemical properties. These results must have been caused by preferential transport by the Brilliant Blue. However, the absolute quantities that reach the larger depths are small relative to the total mass applied. Nevertheless, these small quantities may affect groundwater quality by allowing the rapid transport of organic compounds such as pesticides or antibiotics (Flury, 1996).



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  		Fig. 8. Concentration distributions of the tracers vs. depth. The total tracer concentration per volume of soil, t, was horizontally averaged and normalized by the total mass of tracer recovered per unit area, m0. Concentration distributions for sampling directly after application are shown for (a) Br– and (b) Brilliant Blue (BB), as well as for sampling after 90 d for (c) Br– and (d) Brilliant Blue. The data for Brilliant Blue represent averaged concentrations of 15 sampling locations corresponding to those where Br– was sampled (local scale).

 

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  		Table 6. Mass recovery, mr, mean travel depth, µz, and variance, {sigma}2z, of the tracer distributions. Local scale refers to the mean concentration of the 15 sampling locations, whereas plot scale refers to the average concentrations for the 1-m2 cross-sectional area of the plot.

 
Mass recoveries for Br– varied between 86 and 134% for the different plots. Mass recoveries were generally smaller than 70% for Brilliant Blue, except for the P-0 treatment. Several factors may have contributed to these relatively poor mass recoveries, including biodegradation, effects of the image analysis procedure, and inadequate sampling. Biodegradation of the dye has been reported in laboratory studies (Flury and Flühler, 1994). However, Forrer et al. (1999) found excellent mass recovery after 40 d of irrigation in a field study where the dye was applied continuously. Although we do not have direct evidence of biodegradation in our study, we do not exclude this possibility since it explains part of the differences between the 0- and 90-d treatments.

Another possible explanation for the poor dye mass recovery may be our use of an inaccurate color–concentration calibration procedure, particularly at the higher concentrations. Inspection of the residuals of the calibration samples for the NP-0 treatment showed that the single regression model systematically underpredicted all measured Brilliant Blue concentrations at the soil surface by a factor of about two. This partly explains the relatively low mass recovery for this treatment. Furthermore, a potential bias could have been introduced by decreasing the spatial image resolution early in the analysis by averaging pixel values arithmetically. This may have introduced some errors since the relationship between pixel values and dye concentration is exponential. The total dye recovery for low resolution images may have been much less than for the original, higher resolutions.

Much of the Brilliant Blue in our 90-d field plots was transported as a result of rainfall (see dye coverage at the soil surface in Fig. 3). A relatively large fraction of the dye mass for the 90-d treatments resided between the soil surface and the second sampling depth at 0.05 m, which was inadequately sampled. In a separate study at this site using polymeric microspheres, Burkhardt (2003) could increase mass recovery from 66 to 82% of the P-90 treatment by including the 0.02-m depth. We conclude that sampling intervals smaller than 0.05 m are needed near the soil surface to characterize transport behavior for reactive compounds, at least for the conditions of our field experiment. Hence, our poor mass recoveries were not necessarily caused by an inaccurate regression model. Excellent mass balances were obtained for Br–, with mass recoveries sensitive to neither the selected sampling intervals nor to biodegradation.

A direct comparison of the moments of the different treatments is not possible because of differences in timing of the tracer applications, the initial water content, and net cumulative infiltration. It is therefore difficult to quantify the effect of different management practices on tracer transport. Nevertheless, we can derive some general statements from the moment analysis. Because the initial water content differed only in the upper part of the plow layer for the 40-mm applications, we concluded that plowing enhanced not only the transport of the bulk mass of Br–, but also the transport of small amounts to larger depths of both Br– and the dye tracer.

Since the mean travel depth, µz, can be biased in case of poor mass recovery, we computed an effective retardation factor, Reff, of about 2.2 only for the NP-0 treatment. Note that this effective retardation factor holds only for transport up to the time of excavation. Hence, Brilliant Blue is not an optimal water tracer, even when continuously applied at relatively high input concentrations. Nevertheless, we believe that this dye is a valuable tracer that visualizes flow pathways and provides quantitative information about concentration patterns at a much finer resolution than other techniques.

The spatial moments based on plot-scale information are also listed in Table 6. Averaged concentration profiles were very similar in the plow layer (data not further shown), where matrix flow dominated. The 15 sampling locations were sufficient to represent the averaged transport of bulk mass through the soil matrix. However, some deviations were observed for the lower concentrations in the subsoil where only a few conducting flow paths contributed to transport. Since only a few high concentration zones were present, 15 locations were not enough for accurate sampling in that part of the profile. Inadequate sampling was the main reason for differences in the spatial moments for Brilliant Blue determined at the local and plot scales. The largest deviations between the local and plot-scale moments were found for the P-90 treatment. Since the concentrations are correlated to a greater lateral distance in the plow layer, it is necessary to average more samples to include the full range of horizontal variability. Therefore, more sampling locations are needed, both to capture preferential flow events in macropore regions and for application to areas with larger integral scales. Assuming that Brilliant Blue and Br– follow the same flow pathways, it is reasonable to assume that Br– concentration profiles reflect the averaged transport behavior for flow through the soil matrix at the plot scale.


   SUMMARY AND CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
REFERENCES
 
We successfully used the image analysis method of Forrer et al. (2000) in a silty soil and obtained high-resolution spatial maps of Brilliant Blue concentrations using a single regression model for all four plots. Improvements were made by including soil samples from nonstained areas in the calibration relationship and by photographing a gray paperboard, which enabled us to make corrections for illumination. Still, relatively poor mass recoveries were obtained for the dye, except for one treatment. Since volumetric concentrations are needed to characterize transport behavior using moments, measurements of the soil bulk density are required. For this reason, our analysis was limited, since we used depth-averaged bulk density measurements.

The concentration correlograms were adequately described with a (nested) exponential autocorrelation function, while no significant or consistent directional dependence in correlation structure was observed for the horizontal cross sections. The larger integral scale length of the plow layer of the P-90 treatment suggests that lateral solute mixing was less pronounced at or above the depth of observation than in the other cases. Since the correlation lengths for both the Ap and Bt horizons were generally small compared with the plot size, an area of 1 m2 represented most of the small-scale variability in solute transport at the experimental site. Thus, Brilliant Blue concentration maps obtained from images are a useful alternative for characterizing small-scale soil heterogeneities.

The plot-scale information about the dye distribution revealed that sampling from 15 locations was sufficient to represent the averaged plot-scale transport behavior in the soil matrix, but failed to represent the few conducting flow pathways that contributed to transport in the subsoil. Profiles of dye coverage and its concentration both showed that plowing caused more deep transport. Although Brilliant Blue was retarded in the soil matrix with respect to Br–, both tracers were found to a depth of 1.6 m, indicating that a small part of the dye was transported by preferential flow, notwithstanding its chemical adsorption properties.


   ACKNOWLEDGMENTS
 
The authors thank Wilhelm-Peter Schneider and Ralf-Uwe Limbach for their support by taking the images at the field site, and for digitization. We are also grateful to Jan Vanderborght for discussions and helpful comments on an early draft of this paper. We want to express our appreciation to the anonymous reviewers of an earlier version of this paper for their helpful comments. Michael Burkhardt wishes to acknowledge the Federal Environmental Agency in Berlin, Germany, who funded this study as part of the project Pollution of Groundwater by Pesticides under Silty Soils (no. 12605E204).


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 




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