Imaging and quantification of preferential solute ... - Wiley Online Library

PUBLICATIONS Water Resources Research RESEARCH ARTICLE 10.1002/2014WR015351 Key Points:  We imaged solute transport through undisturbed soil with 3-D resolution  We calculated the evolution of the dilution index directly from 3-D measurements  We quantified solute diffusion from a cylindrical macropore into the soil matrix

Correspondence to: J. Koestel, [email protected]

Citation: Koestel, J., and M. Larsbo (2014), Imaging and quantification of preferential solute transport in soil macropores, Water Resour. Res., 50, 4357–4378, doi:10.1002/ 2014WR015351. Received 23 JAN 2014 Accepted 26 APR 2014 Accepted article online 30 APR 2014 Published online 27 MAY 2014

Imaging and quantification of preferential solute transport in soil macropores John Koestel1 and Mats Larsbo1 1

Department of Soil and Environment, Swedish University of Agricultural Sciences (SLU), Uppsala, Sweden

Abstract Despite significant advances during the last decades, there are still many processes related to nonequilibrium flow and transport in macroporous soil that are far from completely understood. The use of X-rays for imaging time-lapse 3-D solute transport has a large potential to help advance the knowledge in this field. We visualized the transport of potassium iodide (20 g iodide l21 H2O) through a small undisturbed soil column (height 3.8 cm, diameter 6.8 cm) under steady state hydraulic conditions using an industrial Xray scanner. In addition, the electrical conductivity was measured in the effluent solution during the experiment. We attained a series of seventeen 3-D difference images which we related to iodide concentrations using a linear calibration relationship. The solute transport through the soil mainly took place in two cylindrical macropores, by-passing more than 90% of the bulk soil volume during the entire experiment. From these macropores the solute diffused into the surrounding soil matrix. We illustrated the properties of the investigated solute transport by comparing it to a 1-D convective-dispersive transport and by calculating the temporal evolution of the dilution index. We furthermore showed that the tracer diffusion from one of the macropores into the surrounding soil matrix could not be exactly fitted with the cylindrical diffusion equation. We believe that similar studies will help establish links between soil structure and solute transport processes and lead to improvements in models for solute transport through undisturbed soil.

1. Introduction Soil macropores have long been recognized as important pathways for preferential water flow and solute transport [Beven and Germann, 1982; Vogel et al., 2006; Jarvis, 2007]. Despite significant advances during the last decades, there are still many processes related to nonequilibrium flow and transport in macroporous soil that are far from completely understood. For example, the exchange of solutes between the macropores and the surrounding soil matrix and adsorption and degradation of reactive solutes on macropore €hne et al., 2002; Jarvis, 2007, Beven and Germann, walls are processes that need to be investigated further [Ko 2013]. The use of new techniques such as 3-D imaging of macropore geometries in combination with realtime measurements of solute transport has the potential to advance the knowledge of nonequilibrium flow and transport in soil macropores [Jarvis, 2007; Wildenschild and Sheppard, 2013]. In recent years several imaging methods have been tested for measuring the 3-D evolution of water or solute fronts. Most prominently these were electrical resistivity tomography (ERT) [Binley et al., 1996; Koestel et al., 2009], positron emission tomography (PET) [Khalili et al., 1998; Boutchko et al., 2012], single-photon computed tomography (SPECT) [Perret et al., 2000b; Vandehey et al., 2013], magnetic resonance imaging (MRI) [Amin et al., 1993; Bechtold et al., 2011], neutron computed tomography (NCT) [Lopes et al., 1999; Kaestner et al., 2007] and X-ray tomography (XRT) [Heijs et al., 1996; Luo et al., 2008]. PET and SPECT yield rather coarse resolutions of some millimeters or centimeters. The spatial resolution of ERT is in the same range if the method is applied to small soil columns with heights and diameters of centimeters up to a few decimeters. XRT, NCT and, in principle also MRI are better suited to resolve fine structures as they allow resolutions in the micrometer range. Olsen et al. [1999] presented an illustrative example demonstrating the different resolutions of ERT and XRT images of soil columns. The strength of ERT is its applicability to larger scales [e.g., Revil et al., 2004; Nguyen et al., 2009], whereas PET and SPECT may prove useful for tracing specific radio-labeled organic compounds, colloids, viruses or microbes. MRI is a powerful tool for noninvasive 3-D visualizations of organic materials. MRI has also been used to image the time-lapse evolution of tracer plumes in sands [e.g., Bechtold et al., 2011]. Its application to undisturbed soil has, however, been found problematic due to the abundance of elements with undesirable paramagnetic properties [Cislerova and Votrubova, 2002].

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2-D Neutron radiography has often been used for visualizing time-lapse processes like infiltration of water into soil [e.g., Badorreck et al., 2013] or root-water uptake [e.g., Carminati et al., 2010]. 3-D imaging studies using this technique in soil science are, however, still scarce. One example is Schaap et al. [2008], who measured the 3-D resolved water content in a heterogeneously packed sand box during a drainage and imbibition experiment. The main reason is probably the limited availability of adequately equipped neutron sources. A similar limitation exists for XRT if a synchrotron beamline is used for imaging, as for example in Altman et al. [2005] or Wildenschild et al. [2005]. However, synchrotron XRT was introduced earlier than NCT into geosciences [e.g., Coles et al., 1998], and soil science applications are more common. The main advantage of synchrotron XRT compared to industrial or medical XRT is that it provides monochromatic X-ray beams whose wavelengths are adjustable [Wildenschild and Sheppard, 2013]. This leads to fewer image artifacts and offers the possibility of visualizing tracers by capitalizing on their X-ray fluorescence properties [Wildenschild and Sheppard, 2013]. In contrast to NCT, compact XRT scanners are commercially available in the form of medical, industrial and lately even desktop X-ray scanners. These systems operate with a polychromatic X-ray beam and, compared to a synchrotron beamline, with less power. Since the early 1980s, numerous hospitals acquired medical 3-D XRT scanners which were sometimes made available to image soil samples [Wildenschild and Sheppard, 2013]. The first publications using this technique in soil science date to the 1980s. In these early studies, XRT was used to map the 3-D distribution of soil bulk density and water content [Petrovic et al., 1982; Hainsworth and Aylmore, 1983], image the soil macropore system (i.e., all pores larger than two or three times the XRT resolution) and the distribution of air and water therein [e.g., Hanson et al., 1991; Heijs et al., 1996]. With XRT it is possible to detect the location of a tracer plume or front if the tracer exhibits a sufficiently large density contrast to the soil water [Steude et al., 1990; Anderson et al., 1992]. Comprehensive reviews on XRT studies within soil science and hydrology have been published by Helliwell et al. [2013], Taina et al. [2008], and Wildenschild et al. [2002]. Early studies on solute transport that involved XRT were restricted to conventional breakthrough curve (BTC) experiments where the effluent BTC was compared to the 3-D structure of the macropore network [Gupte et al., 1996; Olsen et al., 1999]. Similar later studies involved solute transport models that were parameterized using XRT image data [Kasteel et al., 2000] or compared the soil macropore structure with dye staining patterns [Cislerova and Votrubova, 2002; Vanderborght et al., 2002]. Another notable example is the study by Luo et al. [2010] who used linear regression to investigate relationships between structural characteristics of the macropore network and corresponding BTC features. Finally, significant progress has recently €hne et al. [2011] who successfully predicted inert tracer BTCs under unsaturated flow been achieved by Ko conditions from a pore network model constructed from the statistics of topological features of the X-rayderived pore space. However, none of the above discussed studies contain images of the evolution of a solute plume or front. Studies that include time-lapse XRT image data of the progression of a solute plume in two or three dimensions are still scarce. Already in the early 1990s, Steude et al. [1990] presented vertical cross sections of a tracer plume progression, and Anderson et al. [1992] presented tracer velocity distributions in horizontal cross sections of repacked soil columns. To our knowledge, the first 3-D XRT-derived solute transport data were published by Clausnitzer and Hopmans [2000]. They investigated solute breakthrough in a subcentimeter-scale sample with packed glass beads using an industrial XRT scanner. The temporal resolution was, with approximately 30 min per image, relatively poor but the spatial resolution of the equipment was, however, comparably good and provided voxel sizes with edge lengths below 100 lm. While the article of Clausnitzer and Hopmans [2000] focused on technical aspects of the time-lapse imaging process, Perret et al. [2000a] published a data set including thirteen horizontal time-lapse 2-D sections of an inert tracer front progression in an 85 cm long and 7.7 cm wide saturated, undisturbed soil column. The experiment of Perret et al. [2000a] was conducted with a medical X-ray scanner which provided a spatial resolution of 195 lm in the horizontal plane for each 2 mm thick slice. According to the authors, the acquisition time for one 2-D slice was as short as 2 s. The publication of Perret et al. [2000a] features, among other things, a quantitative comparison of the BTCs in the matrix and macropore domain. They also observed diffusion of the tracer from the macropores into the matrix and that a large fraction of the matrix as well as dead-end or isolated macropores were by-passed. Luo et al. [2008] also conducted experiments with an inert tracer on a saturated undisturbed soil column. The tracer concentration evolution with time was imaged in two horizontal

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2-D breakthrough planes. As a complement to this analysis, two radiographs of the tracer front progression in the whole column were obtained from orthogonal positions. The column was 10 cm in diameter and 30 cm in height and the spatial resolution in the breakthrough plane was 105.5 lm. The acquisition time for one pair of radiographs and the two horizontal cross sections was approximately 27 min. The water flow was stopped during scanning. The findings of Luo et al. [2008] are very similar to the ones of Perret et al. [2000a] except that Luo et al. [2008] observed that 10 to 19% of their soil column contained entrapped air. They, therefore, stressed the importance of entrapped air for understanding solute transport under assumed saturated conditions. Thus, the potential of time-lapse XRT-imaging of solute transport through soil has so far only marginally been exploited. A full 3-D XRT-derived visualization of a tracer plume or front with equally good resolution in all space direction has, as far as we know, not yet been published in peer-reviewed literature. Time-lapse 3-D data sets of solute transport through soil offer new possibilities for quantifying solute transport properties. The objectives of our study were, therefore, (i) to demonstrate that present industrial XRT scanners are able to provide high-quality and high-resolution 4-D data on solute transport through undisturbed macroporous soil, and (ii) to make use of this 4-D data to quantify properties of the transport process which cannot be inferred from traditional breakthrough experiments. To illustrate the potential benefits of such a data set we calculated the evolution of the dilution index [Kitanidis, 1994], a measure of the strength of preferential transport. The dilution index has previously been calculated from 2-D experiments on repacked sands [Ursino et al., 2001] or investigated in numerical experiments [e.g., Kapoor and Kitanidis, 1996; Rolle et al., 2013]. As an additional illustration of the value of such data, we quantified the diffusion of solutes from a cylindrical macropore into the surrounding soil matrix and compared the measurements to a numerical solution of the cylindrical diffusion equation.

2. Methods and Materials 2.1. X-Ray Tomography In this study, we used the GE Phoenix v|tome|x m XRT scanner installed at the Department of Soil and Environment at the Swedish University of Agricultural Sciences (Uppsala), which has a 240 kV X-ray tube, a tungsten target (beryllium window) and a GE 1600 flat panel detector. We imaged the transport of a KI-solution (potassium iodide) through a soil column, collecting 1372 radiographs per 3-D image frame with a discretization of 2024 3 2024 pixels, corresponding to a resolution of 48.93 lm. The acquisition time for all 1372 radiographs was 3 min. The X-ray scans were carried out at a voltage of 170 kV with an electron flow corresponding to 350 lA. The exposure time for each radiograph was 131 ls. The radiographs were subsequently inverted to a 3-D image using the GE image reconstruction software datos|x and exported as TIFFstacks (tagged image file format) with 16-bit grayscale resolution. The resulting spatial resolution of the reconstructed 3-D images was 48.9 lm in all directions. 2.2. Experimental Setup The experiments were carried out on a cylinder sample (approximately 38 mm high, 68.2 mm diameter) with undisturbed soil from Ultuna (59 490 N; 17 390 E), three km south of Uppsala, Sweden. The sample was taken on 20 November 2012 at 10 cm depth from a field under long-term reduced tillage. Shallow cultivation had been carried out on 18 September. At the time of sampling, the soil was bare. The soil is a silty clay (44% clay, 42% silt, 14% sand) developed from postglacial lake sediments and has a large potential for preferential transport [Larsbo et al., 2009]. The organic carbon content (2.6%) and the porosity (55%) have previously been measured for this soil [Larsbo et al., 2009]. A polyamide cloth (mesh size 50 lm) was attached to the bottom of the sample in order to minimize internal erosion. The sample was then placed on a perforated plastic lid. An approximately 3 mm thick layer of fine sand was placed on the sample surface to ensure good contact between the sample and a mini-disk tension infiltrometer (Decagon Devices Inc., Pullman, WA, USA), which was used to supply iodide solutions in subsequent transport experiments. The sample was first slowly saturated from the bottom with tap water. To further reduce entrapped air in the sample, about ten pore volumes of tap water were slowly forced to flow through the column from the bottom upward. Finally, the saturated sample was placed in a sealed container under near-vacuum for one night. The whole process took approximately 20 days and was carried out at approximately 20 C. The tracer experiment was conducted inside the X-ray scanner to minimize disturbance which would occur during the moving and installation of the sample and to enable multiple scans at a high time resolution

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Tension infiltrometer Detector Soil sample X-ray source

Electrical conducvity probe

Staonary drainage collector Rotang scanning stage

[Wildenschild and Sheppard, 2013]. The simple experimental setup is described schematically in Figure 1. The sample was attached firmly to the rotating scanning stage. The drainage from the column was collected in a funnel which directed the drainage into a stationary circular collector. The drainage water was then led through a 3 mm diameter tube to a flow-through vessel (D201, WTW GmbH, Weilheim, Germany) where the electrical conductivity was measured every minute using an electrical conductivity meter (Cond 3310, WTW GmbH, Weilheim, Germany).

A mini-disk tension infiltrometer filled with 80 ml of tap water was gently placed on the sand surface. The tension at the bottom of the infiltrometer stainless-steel pressure plate was set to 0.5 cm. To minimize artifacts due to X-ray scattering from the stainless steel pressure plate, the sand surface and, hence, the bottom of the pressure plate was positioned in the same horizontal plane as the X-ray source. When the infiltration rate and the electrical conductivity of the effluent water had reached steady state, the column was scanned for the first time. The minidisk tension infiltrometer was then replaced (at time t50) by an identical infiltrometer with the same tension setting filled with 80 ml of KI solution (20 g iodide per liter H2O), corresponding to an electrical conductivity of 207 mS mm21. The exchange of the infiltrometers took about 10 s. The column was subsequently scanned every 5 min during the first hour, every 10 min during the second hour and at half-hourly and hourly time intervals for the remainder of the experiment, which was stopped after 6 h. Because the solution storage volume of the minidisk tension infiltrometer is limited to 80 ml the infiltrometer was replaced a second time with an identical infiltrometer with the same tension settings filled with the same KI-solution 250 min after the first KI-solution filled infiltrometer had been installed. Figure 1. Experimental setup.

After the end of the breakthrough experiment, we scanned an empty PVC column in which one plastic vessel filled with tap water and one filled with KI-solution were placed. The composition of tap water and KIsolution was identical to the ones used during the tracer experiment. High-quality X-ray radiographs were collected (2000 radiographs in 21 min). The corresponding 3-D image was later used to relate the timelapse image gray values to iodide concentrations. The two vessels were placed at the same radial distance from the center of rotation to minimize beam hardening artifacts. The effluent breakthrough curve recorded in the flow-through vessel was affected by a time-lag relative to the bottom of the soil column because of the travel time required for the effluent to reach the flow-through vessel (Figure 1). Furthermore, mixing of solutes took place in the circular collector, in the connecting tubes and in the flow-through vessel. We, therefore, measured the breakthrough curve corresponding to the ‘‘dead-volume’’ of the outflow system by applying a pulse of tracer solution directly to the funnel below the soil sample (see Figure 1) and slowly flushing it through the flow-through vessel. The dead-volume breakthrough curve was used to estimate the breakthrough curve at the bottom of the soil column by deconvolution. 2.3. Image Processing In total, 25 frames (3-D images) were obtained during the transport experiment. The four frames between t 5 2 and t 5 26 min could not be evaluated because of a malfunction during the X-ray image acquisition which had been triggered by an operating error. We lost an additional three frames (at t 5 46, 81 and 181

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min) due to failed data transfers to external hard disks. As a result, 18 frames were evaluated according to the procedure described below. 2.4. Image Registration Image processing was carried out using the FIJI distribution [Schindelin et al., 2012] of ImageJ [Abramoff et al., 2004] and MATLAB. First, the image resolution of each frame was reduced by a factor of two in all dimensions to limit the computation time during the following image processing steps. As a result, each image-voxel had an edge-length of 97.85 lm. In the next step, the 3-D images were registered (i.e., spatially aligned) using the ‘‘descriptor-based series registration (2d/3d 1 t)’’ ImageJ-plugin which is based on the registration approach published in Preibisch et al. [2010]. After this, we removed the horizontal voxel layers on the top and bottom from the 3-D images. The voxel-layers removed at the top corresponded to the sand layer that had been added to ensure good hydraulic contact between the infiltrometer and soil. The discarded voxel layers at the bottom contained parts of the plastic cap at the outlet. The number of horizontal voxel layers retained in each frame was 381, corresponding to a column height of 37.3 mm. 2.5. Illumination Correction A quantitative interpretation of the brightness of X-ray images requires a homogeneous illumination, so that objects of the same density are depicted with identical gray values over the entire 3-D image. This is, however, only approximately the case for images acquired with beams from X-ray tubes where electrons are shot onto a metal anode to generate the X-rays. The electron beam causes abrasions on the anode material, which lead to shifting brightness distributions with time in the beam cone emitted from the X-ray tube. This in turn causes artificial illumination fluctuations in the X-ray images, which need to be corrected for. Beam-hardening artifacts which are inevitable in images acquired with polychromatic X-rays are expected to cancel out with the subtraction of two images. Since we are only investigating difference images, beam hardening artifacts are probably of minor importance. In our case, illumination heterogeneities will result in incorrect estimates of solute concentration. We assumed that the air bubbles and the PVC column wall had a spatially and temporally constant density from which it follows that also the corresponding gray values, g, in the X-ray images should be spatially and temporally constant. We furthermore assumed that the density of individual stones also remained constant during the experiment. We sampled 291 voxels from the PVC column wall in each of the 381 horizontal layers resulting in a total of 110,871 voxels for one 3-D image (Figure 2a). In addition, we sampled voxels from randomly selected air bubbles in 14 individual horizontal layers (in total 1110 voxels per image), water-filled macropores in 35 horizontal layers (in total 3499 voxels per image), and stones in 18 horizontal layers (in total 11,107 voxels per image). The gray values for PVC column wall, air bubbles, water-filled macropores and stones are denoted gp, ga, gw, and gs, respectively. Air bubbles, water-filled macropores and stones were identified by visual inspection. Examples for voxels sampled from the different categories are illustrated in Figure 2a. The gray values of PVC wall, air bubbles, water-filled macropores and stones were samples from each of the 18 evaluated frames. Vertical profiles of the corresponding gray values are shown for frame 1 and frame 18 in Figure 3. As a first correction step, we normalized the gray values for each 3-D image to a vertically constant median gray value (12,000) for the PVC column wall. This was done for each horizontal layer, i, according to: Gi;norm 5Gi;orig 112; 0002median ðgp;i Þ;

(1)

where Gi,orig and Gi,norm are the gray values of all voxels in the horizontal layer i before and after the normalization and gp,i are the 291 gray values sampled from the PVC column wall in layer i. In a second step, we scaled the 3-D images to a unique gray-scale gradient between the median gray values corresponding to air and stones. We derived the respective correction functions from the matrices Ma and Ms consisting of the median sampled gray values of air and stones, respectively:

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Figure 2. (a) Horizontal cross section through one inverted image at a depth of approximately 17 mm (image resolution of 97.85 lm). The outer diameter of the soil column is 75.2 mm, the inner diameter 68.2 mm with a thickness of the PVC wall of 3.5 mm. Bright and dark pixels indicate large and small bulk densities, respectively. The objects marked are air-filled macropores (green), water-filled macropores (blue) and stones (red). (b) Horizontal cross section of the 3-D image used to relate gray scale to iodide mass.

    ð1Þ ð1Þ median ga;1 median ga;2 6 6     6 ð2Þ 6 median gð2Þ median ga;2 a;1 6 Ma 6 6 6 ⯗ ⯗ 6 4     ð14Þ ð18Þ median ga;1 median ga;2 2

  ..

  ð1Þ median ga;18   ð2Þ median ga;18 ⯗

.



 ð1418Þ median ga;18

3 7 7 7 7 7 7 7 7 7 5

(2)

and     ð1Þ ð1Þ median gs;1 median gs;2 6 6     6 ð2Þ 6 median gð2Þ median gs;2 s;1 6 Ms 6 6 6 ⯗ ⯗ 6 4     ð18Þ ð14Þ median gs;1 median gs;2 2

ðhÞ

  ..

.



 3 ð1Þ median gs;18 7  7 7 ð2Þ median gs;18 7 7 7 7 7 ⯗ 7  5 ð18Þ median gs;18

(3)

ðhÞ

where the superscripts and subscripts h and f in ga;f and gs;f correspond to the hth sampled air bubble or stone in the f th frame. From the two matrices we calculated the arithmetic mean of the column vectors ma and ms as well as the arithmetic mean of the row vectors na and ns. Then, matrices of the illumination precision, Ea and Es, were calculated from the following element-wise subtractions: Ea 5½ma

ma

...

ma 2Ma

(4)

Es 5½ms

ms

...

ms 2Ms

(5)

and

where entries of zero denote accurate illumination, while entries smaller and larger than zero denote overly dark and overly bright illuminations, respectively. Boxplots for the values in the 18 columns in Ea and Es are shown in Figures 4a and 4b, where each boxplot corresponds to the illumination accuracies of one of the 18 evaluated 3-D frames.

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Figure 3. Gray values of images 1 and 18 before the illumination correction. It is noted that the gray values corresponding to the soil water are increased for frame 18 due to the presence of potassium iodide.

Figure 4. Illumination precision (i.e., deviations from the mean illumination) for air bubbles, Ea (left side, see equation (4)), and stones, Es (right side, see equation (5)), before (top) and after (bottom) illumination correction step 2.

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Figure 5. Gray values of images 1 and 18 after the second illumination correction step.

For each frame, a correction function, cf(g), was calculated from the matrices N and H with h N5 nTa

nTp

nTs

i

(6)

where np is a row vector with eighteen entries which correspond to the median gray values of the column wall which were set to 12,000 in the first illumination correction step described above. The vectors ea and es are row vectors of the column averages of Ea and Es, respectively, and were used to define h H5 eTa

eTp

eTs

i

(7)

where eTp is a row vector containing 18 zeros, corresponding to the perfect illumination of the column wall attained in the first correction step. The dimensionless correction function cf(gj,norm) for the fth frame was attained by fitting a second-order polynomial to the fth row of matrices N and H. The illumination corrected 3-D frame f was then obtained by applying gj;corr 5gj;norm 2cf ðgj;norm Þ

(8)

to all voxels j in frame f, where gj,norm is the gray value of the jth voxel in frame f after the first illumination correction step and gj,corr is the illumination corrected gray value of the same voxel after the second illumination correction step. The gray values after the second correction step are shown in Figure 5. 2.6. Creating the Time-Lapse Image Series We created 17 time-lapse difference images by subtracting the gray values of frame 1 from all other frames. Assuming no image artifacts, the gray value of a difference image is proportional to the increase in iodide mass with respect to frame 1. Negative gray values in a difference image may be due to noise in the image data or caused by e.g., swelling of the soil matrix or displacement of air bubbles during the experiment. We reduced the amount of image noise by applying a 3-D median filter to the 17 difference images. We chose the footprint-radius of the 3-D median filter such that negative and positive voxels in the stone located at the center of the soil column (see Figure 2a) largely disappeared. This was the case for a radius of four voxel lengths (391.4 lm). Finally, we once again reduced the image resolution by half to shorten the time required to compute and evaluate the 3-D difference images. It follows that each voxel in the time-lapse difference image had an edge length of 195.7 lm. Hereafter, the gray value of voxel j of the time-lapse difference image d is denoted as cj,d.

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3. Evaluating the Image Data 3.1. Segmenting the Soil Column Into Air, Macropore, and Stone Domains We used the maximal gray values sampled for the air-filled voxels (9201) and water-filled macropore voxels (11,120) of frame 1 as a threshold to determine the location of air-bubbles and water-filled macropores at the start of the experiment (see Figure 5a). Likewise, we used the minimum gray value sampled from frame 1 for stones (13,988) to determine the location of stones in the soil column.

3.2. Establishing a Relationship Between Gray Value and Iodide Mass We selected one representative horizontal layer from the 3-D image of the PVC column with the tap water and KI solution samples (Figure 2b) to establish a linear relationship between gray values in the time-lapse difference images and the iodide mass. We sampled 291 gray values from the PVC wall, 61,110 gray values corresponding to tap water and 61,857 gray values corresponding to the tracer solution (Figure 2b). We scaled the tap water and KI solution image linearly, such that the voxels located in the water-filled vessel and in the PVC wall had identical median gray values as the ones of the water-filled macropores and the PVC wall in frame 1 of the illumination-corrected time-lapse images. In a final step, we subtracted the illumination corrected median values corresponding to tracer solution and tap water, which yielded the gray value, csat 5 791, corresponding to the maximum possible increase of tracer concentration, Cmax (i.e., 0.02 g iodide cm23 H2O). The tracer mass mj,d (g) in voxel j in the time-lapse difference image d could then be calculated from the corresponding gray value, cj,d, according to:

mj;d 5

Vvox Cmax cj;d csat

(9)

where Vvox is the volume of one voxel (5 7.495  1026 cm3). It is noted that the gray values g of the timelapse difference images are not only influenced by the iodide mass but also by the abundance of potassium. The latter is known to adsorb to cation-exchange sites in the soil, replacing initially adsorbed ions. Since these will differ in mass, it follows that equation (9) is not an exact calculation of the iodide mass but rather an approximation. We expressed the noise-level inherent in the time-lapse images, eillu, as the standard deviation of the sampled gray values of air, stone and wall after the second correction step in relation to the maximal possible tracer contrast, csat. We assumed that the air bubbles remained stationary during the experiments and that no tracer was able to enter stones or the PVC wall such that the variance of the gray values of these regions should be stationary. The noise-level ratio for the sampled air bubbles was hence defined as

ea;illu 5

stdðca;corr Þ csat

(10)

The noise levels for stones, es,illu, and the PCV wall, ep,illu, were calculated in the same way.

3.3. Mass-Balance Calculations Using equation (9) the total X-ray-derived iodide mass in the column, Md,Xray (g), was calculated for each time-lapse difference image d by summing overall mj,d in each difference image,

Md;Xray 5

jmax X

mj;d

(11)

j51

where jmax (5 18,279,900) is the number of voxels located within the soil column. The value of Md,Xray at the time when frame d was scanned, td (min), should equal M d,I/O, defined as the difference between cumulative iodide mass inflow and outflow from time t50 to td.

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ð td Md;I=O 5q Cmax 2Cout ðtÞdt

(12)

t50

where q is the constant water flow rate (l h21) and Cout(t) (g l21) the iodide concentration in the effluent at time t. The iodide concentration in the effluent at the bottom of the soil column, Cout(t), was obtained from the breakthrough curve measured during the experiment, Uex(t’) (mS mm21), and the dead volume breakthrough curve, Udv(t’) (mS mm21) by deconvolution, where t’ (min) denotes time discretized into 1 min steps (i.e., the resolution of the electrical conductivity data). Uex(t’) and Udv(t’) designate the electrical conductivity breakthrough curves after the background electrical conductivity of tap water (U0 5 5.2 mS mm21) was subtracted. We constrained the deconvolution problem by first fitting a log-normal transfer function to Udv(t’) by minimizing the sum of squared differences according to:

0

udv ðt Þ5 arg min l;r

tend X 0

0

U ðt Þ 0 Xdv 0 2udv ðt ; l; rÞ Udv ðt Þ

!2 (13)

where tend (min) is the last time for which electrical conductivity was measured and m (min) and r are the parameters of the log-normal transfer function ( ) 1 ½lnðtÞ2l2 uðtÞ5 pffiffiffiffiffiffi exp 2 : 2r2 2prt

(14)

Next we fitted a double log-normal transfer function to Uex(t)

0

uex ðt Þ5 arg min l1 ;r1 ;l2 ;r2 ;bex

0 tend  X Uex ðt Þ

0

Umax

0

2

0

2aðt Þ  uex ðt ; l1 ; r1 ; l2 ; r2 ; bex Þ

(15)

where the asterisk denotes a convolution, a(t’) is the Heaviside step function which is one for all t’  0 and zero otherwise, Umax (5 201.8 mS mm21) is the electrical conductivity of the tracer solution minus the electrical conductivity of the background (tap water), and 0

0

0

uex ðt ; l1 ; r1 ; l2 ; r2 ; bex Þ5bex u1 ðt ; l1 ; r1 Þ1ð12bex Þu2 ðt ; l2 ; r2 Þ;

(16)

where m1 and r1 as well as m2 and r2 are the dimensionless parameters of the first and second log-normal transfer functions u1 and u2 and bex is a weighting factor. The transfer function corresponding to the breakthrough curve at the bottom of the soil column, uso(t’), was obtained by fitting another double log-normal function such that

0

uso ðt Þ5 arg min l3 ;r3 ;l4 ;r4 ;bso

tend  2 X 0 0 0 Uex ðt Þ2udv ðt Þ  uso ðt ; l3 ; r3 ; l4 ; r4 ; bso Þ

(17)

0

where m3 (min), r3, m4 (min), r4, and bso are the parameters defining the shape of uso(t’). Finally, Cout(t) was obtained by assuming a linear relationship between electrical conductivity and iodide concentration according to: Cout ðtÞ5Cmax ½aðtÞ  uso ðtÞ

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3.4. Characterizing the Solute Transport Process The degree of physical nonequilibrium is an important property of a solute transport process through porous media, which reflects the extent to which solute transport is channeled within so-called preferential transport paths, thereby by-passing large fractions of the soil matrix [Jarvis et al., 1991; Fl€ uhler et al. 1996; Hendrickx and Flury, 2001]. The dilution index, E (mm3), which characterizes the degree of dilution of a solute plume [Kitanidis, 1994] is an explicit measure of the degree of preferential transport. It can also be interpreted as a measure of the entropy inherent in a solute transport process. The dilution index Ed (mm3) of the solute distribution calculated for the whole column in image d is defined by " Emeas;d 5Vvox exp

jmax X mj;d j51

Md

ln

 # mj;d : Md

(19)

At least a two-dimensional tracer mass distribution is required to calculate the dilution index. To our knowledge, calculations of the dilution index for three-dimensional tracer transport through undisturbed soil have not yet been published.

3.5. Comparison With Equivalent One-Dimensional Convective-Dispersive Transport One-dimensional solute transport models are often used to predict solute transport for engineering and environmental management purposes. The most widely used model is the convection-dispersion equation (CDE), which is implemented in popular off-the-shelf software such as CXTFit [Toride et al., 1999] and HYDRUS [Simunek et al., 2008]. The CDE describes solute transport assuming perfect (maximal) dilution or mixing given a specific transport velocity, vCDE (mm min21), and dispersivity, k (mm). The CDE, therefore, corresponds to a solute transport process which is macroscopically devoid of preferential transport characteristics. In our study, the scale of discretization corresponds to the resolution of the X-ray time-lapse difference images. It is illustrative to compare Ed to the dilution index of an equivalent one-dimensional convectivedispersive solute transport process. This provides an opportunity to quantify the difference between the measured transport process and transport assuming absence of preferential transport characteristics. We fitted the one-dimensional CDE to the breakthrough curve at the bottom of the soil column:

0

ff ;CDE ðt Þ5 arg min T;

P

tend  X

h 0 0 i2 0 Cout ðt Þ2Cmax aðt Þff ;CDE t ; T; P

(20)

0

where ff,CDE(t’) is the solution of the CDE for a first-type boundary condition and a Dirac-input tracer application [Toride et al., 1999] with the retardation coefficient and the dimensionless transport distance set to one and   0  rffiffiffiffiffiffiffiffiffiffi P P 2 ff ;CDE t ; T; P 5 ½ 12T  exp 2 4pT 3 4T

(21)

where T is the dimensionless time defined as: 0

T5

t vCDE L

(22)

and P is the macroscopic Peclet number: L P5 : k

(23)

The CDE-equivalent flux concentration breakthrough curve, Cf,CDE(t) (g l21) is then directly obtained from the results of equation (20) by:

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  Cf ;CDE ðtÞ5Cmax aðtÞ  ff ;CDE ðtÞ

(24)

We also calculated resident concentration profiles for an equivalent one-dimensional CDE transport according to: h   i   0 0 Cr;CDE z; t 5Cmax a tÞ  fr;CDE z; t ; T; P

(25)

where

fr;CDE



0 1 ffi    rffiffiffiffiffi P P P Z1T B C z; t ; T; P 5 exp 2 ½Z2T 2 2 expðPZ Þ erfc@ qffiffiffiffi A pT 4T 2 4T 0

(26)

P

is the analytical solution of the CDE for a third-type boundary condition [Toride et al., 1999]. The subscript r denotes resident concentration and Z is the dimensionless transport distance given by:

Z5

z L

(27)

where z (mm) is the transport depth. The values of the CDE parameters vCDE and k were obtained from equation (20). The resident concentrations, CDEr (z, t), were used to derive resident mass profiles at times corresponding to the time-lapse difference images d, scaling the zeroth spatial moment of CDEr to Md,Xray. The resident concentration profiles were also used to calculate equivalent dilution indices ECDE,d (mm3) for time-lapse difference images d,

ECDE;d 5

(

1 imax



) imax X Cr;CDE ðzi ; td Þ Cr;CDE ðzi ; td Þ exp ln M0;CDE ðtd Þ M0;CDE ðtd Þ i51

(28)

where imax (5 190) is the number of horizontal voxel layers i. M0,CDE is the zeroth spatial moment of CDEr at time td. 3.6. Investigating Radial Diffusion of Iodide From a Cylindrical Macropore As another example of the usefulness of high quality X-ray tomography data for analysis of small-scale (i.e., macropore scale) solute transport processes, we calculated the radial diffusion from a macropore into the surrounding soil matrix. Solute transport in cylindrical macropores has been studied both theoretically and experimentally [van Genuchten et al., 1984; Rahman et al., 2004]. Cihan and Tyner [2011] recently showed that an analytical solution for advective flow in a cylindrical macropore coupled to diffusion into the surrounding soil matrix could accurately reproduce measured data on solute breakthrough. The use of detailed data on solute concentrations in the macropore and in the matrix surrounding the macropore allows for a direct evaluation of the solute diffusion from the macropore to the matrix. We identified one approximately cylindrical macropore with a radius of 1 mm (Figures 6a–6c) located at 15 mm depth from the soil surface. Average masses per volume of bulk soil in the radial direction were calculated for three times (26, 71, and 301 min) for 0.2 mm radial increments from the macropore wall to a radius of 6 mm (Figures 6d–6f). Measurements were compared to a numerical solution of the cylindrical diffusion equation:   @Cmatrix Dmatrix @ @Cmatrix 5 r @t r @r @r

(29)

where Cmatrix (mg ml21) is the concentration in the soil matrix, Dmatrix (mm2 s21) is the effective matrix diffusion coefficient and r (mm) is the radius. The inner boundary condition (r51 mm) was given by linear

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a

12 mm

b

12 mm

d

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t=26 min

12 mm

c

12 mm

e

t=71 min

12 mm

f

t=301 min

Figure 6. Diffusion from a cylindrical macropore (a) horizontal position of the macropore, (b) zoom-in on the macropore, and (c) illustration of the analyzed area, and d) to f) difference images showing the iodide distribution at three times.

interpolation of measured average concentrations in the macropore at 15 mm depth. Zero diffusion was assumed at the outer boundary of the simulation domain (r550 mm). Equation (29) was solved numerically using the Euler method in the Powersim software (Powersim v. 2.54). The volumetric water content of the soil matrix which is needed to convert concentrations in solution to masses per volume of bulk soil was set to 55% based on previous measurements of volumetric water content at a pressure potential of 210 cm made on the same soil [Larsbo et al., 2009]. The value of the diffusion coefficient, assumed to be spatially uniform, was calibrated by minimizing the root mean square error between measured and simulated data assuming equal weights for all data points.

4. Results and discussion 4.1. Suitability of Experimental Setup The elaborate and time-consuming illumination correction approach clearly facilitated quantification of the image data (compare Figure 3 and Figure 5). However, there was still considerable bias and noise in the illumination corrected images (Figure 5). The presence of a bias is clear from the gray values of the air bubbles for which no trend with soil depth should be visible if only noise was present. Yet the air bubbles closer to the soil surface were imaged somewhat darker than the ones closer to the bottom. Moderate correlations between gray values of the 18 randomly selected air bubbles and distance from the column walls were found (average Spearman correlation coefficients of 0.45 with an average p value of 0.07). This suggests that ring-shaped beam hardening artefacts were present. For future studies, an improved illumination correction may be achieved by using column walls that are made of two materials of contrasting density and also include air pockets at regular intervals, which could be used to harmonize the brightness of time-lapse X-ray images. Beam hardening artifacts were more pronounced in the lower 4 mm of the soil column (Figures 3 and 5). The reason causing the pronounced beam hardening artifacts at the bottom was the fact that we had positioned the top of the soil column into the same horizontal plane as the X-ray source, which led

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Figure 7. Location of (a) air bubbles, (b) macropores, and (c) stones.

to a larger variability in length of X-ray trajectories through the bottom of the soil column. Here the underestimation of gray values corresponding to the PVC column was successfully corrected, whereas the ones for the water-filled macropores were not (Figures 3a and 5a). At these depths, circular dark regions symmetrical to the rotation axis of the column were visible in the horizontal cross sections (not shown). Since we applied a global thresholding segmentation approach, it follows that the extent of air bubbles and water filled macropores (Figures 7a and 7b) was slightly overestimated in the central parts of the column close to the base. Correspondingly, the extent of stones (Figure 7c) was probably underestimated in this region. For the time-lapse difference images, the beam hardening problems were less important because similar artifacts were present in each of the 18 recorded images. Figure 8 demonstrated that respective ringshaped patterns were not prominent in horizontal cross sections of the iodide concentrations in the soil. As already stated, the bottom of the soil column was an exception. Here the subtraction of two images did not completely cancel out beam hardening artifacts in the time-lapse images as the gray values for macropores obviously saturated with tracer solution were systematically smaller close to the rotational axis at the base of the column. This led to an underestimation of the tracer mass in the bottommost voxels of the timelapse images. More problematic than beam hardening were fluctuations in the image illumination asymmetric to the soil column’s outline, which occurred between individual time-lapse images. We believe that these fluctuations were caused by temporal intensity variations in brightness of the X-ray beam cone due to abrasion of the anode material (tungsten) in the X-ray tube. In future experiments, such fluctuations may be reduced by recalibrating the flat panel detector to the X-ray beam in between consecutive image frames.

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Figure 8. Horizontal cross sections of the iodide mass at four different depths (5, 15, 25, and 35 mm) and four different times after the start of the tracer application (26, 61, 151, and 301 min).

Despite these problems, the iodide mass inside the soil column was reasonably well recovered from the X-ray images during the entire experiment (Figure 9a). Figure 9a shows that the X-ray derived iodide mass, MXray, was slightly smaller than the one derived from the difference between iodide inflow and outflow, MI/O, during the first half of the experiment. This is partly explained by the underestimation of tracer mass in the bottom of the column. However, during the second half of the experiment, MXray was larger than MI/O for two out of three time-lapse difference images. The rather small differences between MXray and MI/O may also be partly explained by the removal of voxels at the top and bottom of the column as well as the occurrence of cation exchange processes within the column. An increase in the noise level during the tracer breakthrough experiment was noted (Figure 9b). The noise levels for the sampled air-bubbles and stones, ea,illu and es,illu, increased from between 3% to 5% of the gray value corresponding to a tracer-saturated macropore at the beginning of the experiment to values between 6% and 8% at the end (Figure 9b). In contrast, the noise level for the gray values sampled from the PVC wall was smaller and did not show any clear trend with time (Figure 9b). This suggests that illumination errors present in time-lapse 3-D X-ray images depend nonlinearly on the spatial location as well as on the point in time. This limits the precision with which time-lapse 3-D processes can be quantitatively interpreted. Nevertheless, the root mean squared difference between MXray and MI/O was 15% of the average Md,I/O, which is small enough to allow for a quantitative analysis of the solute transport process (also see Figure 9a).

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Figure 9. (a) Iodide mass inside the soil column. The gray line corresponds to Md,I/O, the black line with circles to the mass derived from the X-ray difference images, Md,Xray. (b) Noise level for the 17 time-lapse difference-images.

Shifting locations of air bubbles, pores and stones during the experiment (e.g., due to swelling or shrinking of clay minerals in reaction to the potassium and iodide ions applied as a tracer) may offer one explanation for the increasing imaging error with time. However, if this was the case, it was at least not visible in the images of tracer concentrations in the soil column. Shifting locations of objects should cause dark and bright ‘‘shadows’’ around individual features in the time-lapse X-ray images, which were not observed (Figure 8). However, this may become more critical when time-lapse images with higher spatial resolution and lower noise levels become available. It should also be noted that we conducted our experiment after we had saturated the soil column for several days with water. For other initial conditions, e.g., when imaging water infiltration into dry soil, we expect that clay swelling will make a quantitative analysis of 3-D timelapse image data even more challenging. Figure 10 shows the iodide breakthrough curve measured in the flow-through vessel, Uex, as well as the breakthrough directly at the bottom of the soil column, Cout, which was obtained by deconvoluting Uex and the dead-volume breakthrough curve, Udv (the latter is not shown). The large coefficients of determination (R2 > 0.998; Table 1) achieved for the fits of Uex and Udv to measured data demonstrate the validity of the deconvolution approach. Figure 10a also shows that the travel time of the tracer in the circular collector, funnel, tubing and flow-through vessel was similar to the travel time through the soil. Figure 10a also shows that additional dispersion was added to the solute plume after leaving the soil column. Although the dead volume between the soil and measurement location could Figure 10. Original (Uex) and deconvoluted breakthrough curves (Cout). For clarity, only be successfully corrected for, the every second data point is plotted. In addition, the equivalent breakthrough curve of a one-dimensional CDE transport is shown (Cf,CDE). The coefficient of determination, R2, for design of the effluent collector fitting Uex is 0.9985. For further information on the effluent breakthrough curves see was not completely optimal Table 1.

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Table 1. Goodness of Fit for Log-Normal and CDE Transfer Functions Used to Model Measured Data Property

Value 2

Coefficient of determination (R ) corresponding to udv (equation (13)) Coefficient of determination (R2) corresponding to uex (equation (15)) Coefficient of determination (R2) corresponding to ff,CDE (equation (20))

Unit

0.9996 0.9985 0.9516

(Figure 1). The circular collector was necessary to collect the outflow water during X-ray image acquisitions when the column rotated around its vertical axis. Occasionally, droplets of effluent solution remained immobile for some time on the surface of the circular collector. These droplets were remobilized during the acquisition of the next X-ray image. This led to the fluctuations in the electrical conductivity measurements observed at late tracer arrival times (Figure 10). Each increase in concentration corresponds to the point of time of one image acquisition. A larger slope of the circular collector and the use of water-repellent material should eliminate these problems. Figure 10 also illustrates that the iodide travel velocity (5 mm per min) was large compared to the time it took to record one 3-D image (in our case 3 min). This means that the tracer front traveled through almost half of the soil column during the time needed for one image acquisition, which would lead to a considerable smearing of the tracer front in the X-ray images. However, the X-ray images that were taken between 2 and 26 min after the tracer application were lost due to technical problems. The difference image at 2 min only shows gray values below the noise level. In the difference image at 26 min, the tracer had already reached the outflow about 20 min earlier (Figure 10). During the remaining 270 min of the experiment the tracer slowly diffused into the soil matrix surrounding the main transport paths (Figure 9). This process was probably slow enough to render any artificial smearing in the images due to long exposure times negligible.

4.2. Characterization of the Solute Transport The average infiltration rate during the experiment was approximately 0.018 l h21 (4.77 mm h21) with slight, nonsystematic variation (coefficient of variation 5 0.14) and no observed trends toward increased or decreased infiltration rates. Figure 7a illustrates that only a few air bubbles remained in the soil after the 20 day long effort to remove them. In our experiment, air bubbles represented less than 0.5% of the bulk soil volume which is much less than that reported by Luo et al. [2008]. A complete removal of entrapped air may, however, only be achieved using a more elaborate approach, such as the one described in Perret et al. [2000a]. Figure 11 shows the isosurfaces of spreading iodide obtained from the time-lapse difference images using a threshold of 0.04 mg iodide per voxel. This threshold corresponds to an average tracer saturation of 50% assuming an average saturated water content of 55% [Larsbo et al., 2009]. Horizontal layers of the same time-lapse difference images showing iodide masses are shown in Figure 8 for depths of 5, 15, 25 and 35 mm in the soil. Figure 12a shows the percentage of by-passed bulk soil volume using the same threshold of 0.04 mg iodide per voxel. All these figures illustrate that the iodide was transported relatively uniformly close to the surface of the soil column. It was then directed into two large macropores with diameters varying between approximately 0.5 and 3 mm that extended to the bottom of the soil sample. At approximately 18 to 28 mm depth, much of the soil matrix was bypassed by the iodide tracer (Figures 8, 11, and 12a), clearly illustrating preferential transport in a soil macropore [Beven and Germann, 1982; Jarvis, 2007]. Note that the macropores into which the iodide is channeled are not continuous at this image resolution (Figure 7b). However, the hydraulic conductivities of the below resolution bottlenecks were high enough to sustain preferential transport. A comparison between Figures 7b and 11 also reveals that most of the macropore system was nonconducting (i.e., by-passed by the tracer). This is consistent with the fact that the majority of the macropores were isolated from the tracer-conducting soil volume (Figure 7b). During the course of the experiment, iodide slowly diffused from the conducting macropores into the surrounding soil matrix (Figures 8 and 11). Nevertheless, more than 90% of the bulk soil volume between 18 and 28 mm depth still had iodide saturations below 50% 5 h after the start of the experiment (Figure 12a) when the iodide concentration in the effluent had reached 90% of the maximum concentration. Between approximately 28 mm depth and the bottom of the soil column the iodide was partly diverted from one of the two macropores (Figure 11) leading to a spreading of the iodide plume. This delta-like spreading was probably connected to the seepage face at the bottom boundary, which lead to the activation of larger pores that extended only short distances from the

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Figure 11. Iso-surfaces of iodide concentrations exceeding 0.04 mg per voxel at times (a) 26, (b) 61, (c) 151, and (d) 301 min.

Figure 12. (a) Fraction of bulk soil volume with less than 0.04 mg iodide per voxel at different times after the start of the tracer application. (b) The resident iodide concentration profiles at the same times. The resident iodide concentration profiles of the equivalent CDE transport are also shown.

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columns bottom into the soil. Likewise, the solute front in the matrix in the topsoil progressed downward with a speed of approximately 1 mm h21 (Figures 11 and 12a). 4.3. Comparison to an Equivalent One-Dimensional Convective-Dispersive Transport Figure 10 illustrates that the CDE cannot properly fit both the early tracer arrival and extreme tailing observed in our experiment (also see Table 1). The differences between the observed transport Figure 13. The temporal evolution of the dilution index derived from X-ray images and process and the transport modfrom the equivalent one-dimensional CDE transport. eled by the CDE become even more evident when the resident concentration profiles are considered. Figure 12b shows that the 1-D resident tracer concentration profile with depth had maxima both at the top and bottom of the soil column. In contrast, the CDE predicts a monotonically decreasing tracer concentration from top to bottom. The differences between observed and modeled CDE transport are also demonstrated by the comparison of dilution indices (Figure 13). The dilution index corresponding to the CDE, ECDE, quickly converged to one, exceeding a value of 0.98 after approximately 56 min. A value of one is the upper bound of the dilution index and indicates a complete absence of concentration gradients. The small concentration gradients for Cr,CDE compared to the X-ray measured data are illustrated in Figure 12b. In contrast, the dilution index calculated from the X-ray measurements, Emeas, was relatively constant at values smaller than 0.4 during the first hour of the experiment (Figure 13). Due to diffusion from the tracer-conducting macropores into the surrounding soil matrix, Emeas slowly increased to a value of approximately 0.65 toward the end of the experiment (Figure 13; also compare with Figures 9 and 11).

Mass (μg ml-1 bulk soil)

4.4. Radial Diffusion The cylindrical diffusion equation, as applied here, which assumes a spatially uniform effective diffusion coefficient and matrix water content could not exactly reproduce the measured data (Figure 14). There are a number of reasons why a perfect match should not be expected. For example, the properties of the soil matrix at the macropore wall may be different from the interior soil matrix due to enrichment of clay or organic carbon in aggregate 14 Measured t=26 min coatings and biopore linings Measured t=71 min [Worrall et al., 1997; Mori et al., 12 Measured t=301 min 1999], which can lead to differenSimulated t=26 min 10 ces in water content and effecSimulated t=71 min €hne et al., 2002]. tive diffusion [Ko 8 Simulated t=301 min Moreover, the exact boundary 6 between the macropore and the soil matrix was difficult to define. 4 We assumed that this boundary 2 could be approximated by a cylinder both for the measurements 0 and in the modeling. The maxi0 2 4 6 mum possible simulated mass, Radial distance from centre of macropore which would be approached (mm) close to the macropore for large effective diffusion coefficients, is Figure 14. Comparison between measured data using X-ray tomography and modeled equal to the water content times diffusion from a cylindrical macropore.

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the boundary mass per volume bulk soil. Measured values close to the assumed macropore wall were larger than these values, indicating that the shape, size and position of the inner boundary were incorrect. A numerical model of radial diffusion could account for spatial differences in water contents and effective diffusion coefficients. However, such an analysis was beyond the scope of this study.

5. Conclusions We have shown that modern industrial X-ray tomography equipment in combination with an experimental setup which allows for experiments to be carried out inside the X-ray chamber can provide high-resolution 3-D data on the time-evolution of nonreactive solute transport in soil. Limitations in the image precision due to noise and nonlinear bias (depending on both the time of image acquisition and location) made it necessary to apply an elaborate illumination correction procedure, as well as a significant reduction in the effective image resolution by using a median filter with a radius of 4 voxels. The resulting time-lapse image series exhibited average noise-levels between 3% and 8% with respect to the maximum possible contrast in gray values. The value of the generated data was illustrated by a time series of images and comparison of these observations with calculations for a one-dimensional convective-dispersive transport process, the time evolution of the dilution index and modeled diffusion rates from a cylindrical macropore. However, the usefulness of the data is far from limited to these cases. On the contrary, we believe that there is great potential for this kind of 3-D time evolution data to improve understanding of solute transport processes. For example, the assumptions of the many different solute transport model approaches that have been €hne et al., 2009] or porous media in general developed for predicting transport through soil [see e.g., Ko [e.g., Neuman and Tartakovsky, 2009] could be rigorously tested. Furthermore, time-lapse 3-D solute transport imaging will likely be of great use for quantifying relationships between soil or porous media structure and solute transport properties such as transport velocity, spreading and mixing, a topic frequently studied during recent years using numerically generated data [e.g., Willmann et al., 2008; Le Goc et al., 2010].

Acknowledgment We are grateful to Nicholas Jarvis for helpful discussions and language advice.

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