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a Center of Agroforestry, and Dep. of Soil Environ. and Atmospheric Sci., School of Natural Resources, Univ. of Missouri, Columbia, MO 65211
b Dep. of Soil, Environ. and Atmospheric Sci., School of Natural Resources, Univ. of Missouri, Columbia, MO 65211
c Center for Agroforestry, School of Natural Resources, Univ. of Missouri, Columbia, MO 65211
* Corresponding author (UdawattaR{at}Missouri.edu).
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ABSTRACT |
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 TOPNOTES ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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Abbreviations: 3DMA, Three-Dimensional Medial Axis • AG, agroforestry buffer • CN, coordination number • Co, characteristic coordination number constant • CT, computed tomography • GB, grass buffer • MinIP, minimum intensity projection • PL, path length • PLo, characteristic path length constant • RC, row crop • UTCT, University of Texas-Austin High-Resolution X-ray Computed Tomography facility
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INTRODUCTION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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Although the use of buffers has been shown to increase infiltration, soil hydraulic properties, and porosity and to decrease bulk density with time, few studies have examined buffer effects on porosity at an 
100-µm scale. Quantitative information on soil structure is required to improve understanding of infiltration, contaminant movement in aquifers, and model parameters associated with fluid and gas movement (Ioannidis and Chatzis, 2000). Development of relationships between water flow and porosity parameters has been limited by the unavailability of three-dimensional volume data and direct measurements of pore parameters, and the random nature of pore structure (Lindquist et al., 2000; Mooney, 2002).
Tomographic image slices produced with x-ray, 
radiation, or nuclear magnetic resonance energy combined with image analysis software can be used to obtain interior structural features of samples at micrometer-scale resolution (Asseng et al., 2000). By combining adjacent cross-sectional images and using a process called "volume rendering," combined images may be used to analyze volumes rendered in three-dimensional space with computer software, producing porosity information (Mooney, 2002; Carlson et al., 2003) characterizing pore parameters that would be otherwise undetectable (Akin and Kovscek, 2003). Two important hydrologic pore parameters, connectivity and tortuosity, are difficult or impossible to measure without such analysis. Another benefit of x-ray computed tomographic image analysis is that it allows nondestructive study of sample interiors, retaining connectivity and spatial variation in pores (Al-Raoush, 2002; Carlson et al., 2003). This allows the possibility of examining dynamic soil processes and quantifying pore geometry (Pierret et al., 2002; Mooney, 2002). With the development of synchrotron facilities and laser confocal microscopy, images can be acquired at submicrometer resolution (Lindquist et al., 2000). These instruments have greatly improved microstructural investigations, as the size of the smallest pore and neck that can be measured corresponds with a single voxel (Ioannidis and Chatzis, 2000). Collection of high-resolution images requires an extremely small sample size (<1 mm), however, restricting the study of centimeter-scale intact soil cores.
Geometrical porosity properties of interest to flow include pore coordination number, pore size, throat-size distribution, pore body/pore throat size ratio, pore body/pore aspect ratio, pore continuity, and tortuosity (Ioannidis and Chatzis, 1993, 2000; Tollner et al., 1995; Lindquist et al., 2000). Lindquist et al. (2000) compared tortuosity, pore connectivity, pore-channel length, and throat and nodal parameters of Fontainebleau sandstone ranging from 7.5 to 22% porosity. The 5.7-µm resolution images distinguished sandstone materials based on coordination numbers of nodal pores, and channel, pore, and throat parameters. In a geometry and topology evaluation study of a simulated porous medium, coordination number distributions and pore and neck size distributions correlated with porosity (Ioannidis and Chatzis, 2000). Studying different size materials, Al-Raoush (2002) observed that the coordination number was smaller for larger diameter particles and larger for smaller diameter particles.
Udawatta et al. (2006) compared agroforestry buffer and grass buffer effects using medical x-ray CT-measured pore characteristics of a Putnam silt loam. Buffer treatments had a significantly greater number of pores, number of macropores, porosity, and macroporosity than row crop areas and lower pore circularity. These parameters correlated well with measured saturated hydraulic conductivity. The image resolution for that study was 190 by 190 by 500 µm, with five equally spaced scans collected throughout the 76-mm cores. Adjacent scans were not collected, which prevented three-dimensional analysis of pore connectivity, pore tortuosity, and characteristic pore parameters.
In soils with high smectitic clay content and very low conductivity (0.002 mm h–1), the absence of macropores can increase runoff. To better understand the benefit of management to reduce runoff in these soils, soil pore parameters such as connectivity and tortuosity among soils need to be quantified (Pachepsky et al., 1996; Fox et al., 2004). Tollner et al. (1995) stated that additional research is needed to identify promising procedures to estimate connectivity and tortuosity reliably. The literature lacks information on three-dimensional characterization of macroporosity for intact soil cores (Perret et al., 1999) and no study has compared the influence of vegetative buffers on three-dimensional measured structural pore parameters. A need exists to obtain this information to improve our understanding of soil management effects on pore-size distributions. Such knowledge will improve predictions of water and gas transport as influenced by management practices and assist in the development of buffer establishment guidelines.
We hypothesized that grass and agroforestry buffer practices improve soil porosity by changing three-dimensional soil pore characteristics. The objective of this study was to compare soil pore tortuosity, pore connectivity, and characteristic pore parameters among buffers and row-crop treatments using 3DMA software (Lindquist, 1999; Lindquist et al., 2005) for a claypan soil under a corn–soybean rotation watershed in northeastern Missouri.
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MATERIALS AND METHODS |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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About 600 mm of the 920-mm long-term average annual precipitation falls from April through September in the area (Owenby and Ezell, 1992). Mean annual air temperature is approximately 11.7°C, with an average monthly low of –6.6°C in February and an average monthly high of 31.4°C in July (Owenby and Ezell, 1992). Snow can stay on the ground for extended periods and the snowfall averages about 590 mm yr–1.
Sampling Procedures
Three treatments were sampled: row crop (RC), grass buffer (GB), and agroforestry buffer (AG). Intact soil cores of 76.2-mm diameter and 76.2-mm length were taken with two replications in 3.2-mm-thick wall plastic cylinders in June 2003 from 0- to 100-mm depth during a soybean crop year (Seobi et al., 2005; Udawatta et al., 2006). Soil from the third contour buffer strip counting from the southern edge of the watershed was sampled for the GB and AG treatments (Fig. 1). For the AG treatment, soils were sampled 200 mm from the base of pin oak trees. For the GB treatment, samples were taken midway between two trees (1.5 m from trees) in the grass area of the buffer. For the RC treatment, two samples were taken midway between the second and third buffers (18 m from the buffers). Cores were trimmed, sealed with caps, placed in plastic bags, transported to the laboratory, and stored at 4°C before measurements. Details on sampling can be found elsewhere (Seobi et al., 2005; Udawatta et al., 2006).
Sample Preparation
The bottom cover of each soil core was replaced with fine nylon mesh to secure soil in the cylinder. Cores were placed in a 150-mm-deep tray after removing covers. Cores were slowly saturated from the bottom with a CaCl2 (6.24 g L–1) and MgCl2 (1.49 g L–1) solution using a Mariotte bottle to avoid changes in structure while wetting. This concentration is similar to the natural ionic concentration of claypan soils (Palmer, 1979). After 24 h, weights were recorded and samples were then drained and equilibrated to –3.5 kPa for 24 h using a glass-bead tension table, which removed water from pores >86-µm equivalent cylindrical diameter to enhance image contrast between pores and soil solids. Sample preparation procedures were similar to Seobi et al. (2005) and Udawatta et al. (2006).
Samples were weighed and made watertight for transport to the high-resolution x-ray CT scanner. In addition to the soil samples, two standard cores were prepared with fine sand, containing imbedded objects of air-filled and water-filled sealed Al tubes and Cu wire for use as x-ray phantoms and to help ensure uniformity of x-ray CT analysis among samples. The Cu wire was 0.55-mm diameter, and air and water phantoms were 1.6-mm outside diameter and 1.1-mm inside diameter.
Image Acquisition and Reconstruction
Computed tomographic image acquisition was done at the University of Texas-Austin High Resolution X-ray Computed Tomography facility (UTCT). The microfocal system utilizes a dual-spot FeinFocus FXE microfocal x-ray, and an image intensifier combined with a 1024 by 1024 CCD video camera for the detector. The FeinFocus source has a continuously changing spot size dependent on total load (Ketcham and Carlson, 2001).
Computed tomographic images were created by directing x-rays through a slice plane from multiple orientations and measuring the x-ray attenuation. Soil cores were positioned on the scanner stage so that the x-ray beam was perpendicular to the longitudinal axis and were completely scanned through the length of each core. Scans were conducted at 180 kV and 0.222 mA, resulting in a spot size of about 50 µm. Sample rotation was continuous during data collection, with 1600 views and an acquisition time of 133 ms per view (Ketcham and Carlson, 2001; UTCT, 2007; R.A. Ketcham, personal communication, 2007). The CT field of view (cross-sectional dimension) was 79.3 mm (1024- by 1024-mm picture elements [pixels]) or 74 by 74 µm in size. The slice thickness was 84 µm, producing a volume element (voxel) of 4.59 x 105 µm3.
The UTCT has an image intensifier combined with a video camera for the detector. The image intensifier consists of a partial sphere of cesium iodide scintillators attached to a photocathode. The signal from the photocathode is electronically focused onto a phosphor screen, producing a real-time x-ray image. Images are converted to digital data using the video camera. The video signal, consisting of scan lines divided into pixels, creates 1024 virtual detectors by software (Ketcham and Carlson, 2001). Raw data are displayed such that each line contains a single set of detector readings for a view, with time progressing from top to bottom. This image is called a sinogram, as any single point in the scanned object corresponds to a sinusoidal curve.
Images had a field of reconstruction of 75 mm, with an offset of 10,000 and reconstruction scale of 500 acquired from 25 slices per rotation. Adjacent scans were stacked to render three-dimensional images. Reconstruction is a computer process in which sinograms are converted to two-dimensional slice images. The filtered backprojection reconstruction technique first convolves data with a filter, and each view is then successively superimposed over a square grid at an angle corresponding to its acquisition angle. The primary convolution filter used at UTCT is a Laks filter (Ramachandran and Lakshminarayanan, 1970), which is preferred for high-resolution images. During reconstruction, the raw intensity data in the sinogram are converted to CT numbers that have a range determined by the computer system. For geologic materials, reconstruction parameters are selected to maximize the CT-value contrast for each scanned object. The system uses a 16-bit scale, which allows values to range from 0 to 65,535 (216). Reconstructed three-dimensional soil core data were stored on DVDs for image analysis.
Image Analysis
The 3DMA software was used for three-dimensional quantification of pore characteristics (Lindquist and Venkatarangan, 1999). A number of algorithms are imbedded in the image analysis software to accomplish the six main steps: segmentation of the image, extraction and modification of the medial axis of pore paths, throat construction using the medial axis, pore surface construction, assembly of the pore throat network, and geometrical characterization of the pore throat network (Lindquist et al., 2005).
To reduce edge effects, only the middle 800 scans from each core were analyzed. Calibrated CT values obtained from standard cores were: air (21 ± 2.6), water (30 ± 1.0), sand (38 ± 1.0), and Cu (220 ± 9.3; eight-bit scale). These values were used to determine the segmentation (an image-processing term for describing the algorithm that identifies each population type for each voxel in the image) thresholds for separating pores from solids. The simple thresholding separated the voxels to two populations using intensity values, with an intensity <T0 set to Population 1 and voxels having an intensity >T1 set to Population 2. Indicator kriging (Oh and Lindquist, 1999) separated voxels having intermediate intensities between T0 and T1 by using the maximum likelihood estimate of the population set.
The medial axis algorithm of Lee et al. (1994), an erosion-based algorithm, is used in 3DMA to extract and modify the medial axis of the pore space. The medial axis of a digitized object is a 26-connected centrally located skeleton that preserves the original topology and geometry of the object. In an object with no cavities, the medial axis is a network of voxel paths. Due to noise, the medial axis may contain spurious paths that are not significant descriptors of the object. These spurious paths are trimmed. Since irregularities in the void–solid field cause dead-end pore channels that are difficult to distinguish from true dead-end pore channels, all dead-end paths were removed (trimmed) from the volume. A filter was used to avoid misidentification of segmentation artifacts such as small isolated pores or clusters. Trimming and removal of extraneous branches and dead-end pores produced the medial axis "backbone."
Pores are asymmetrical; therefore, some medial axis paths lie completely within a pore and other paths connect different pores. A distance measure algorithm was used to determine the length of a path (the distance between the centers of any two adjacent nodal pores along the midline of the connecting path) with the distance to the nearest grain surface as a first pass to eliminate pore-internal paths (Lindquist, 2002). Subsequently, a throat (minimal area cross-sectional surfaces of pore space or pore neck; Kwiecien et al., 1990) finding algorithm was used to locate pore throats (Venkatarangan, 2000). Throat surface areas are determined as triangulated interfaces. The throat region is defined by the voxel sets through which each triangulated throat surface passes.
The marching cube algorithm of Bloomenthal (1988) and Lorensen and Cline (1987) was used to determine pore surfaces. The surface is the triangulated interface separating the pore from the set of grain- and throat-region voxels surrounding it. Void space within the soil (pore body and nodal pore) is connected by pore channels or path lengths. Nodal pores are separated by throat surfaces. Nodal pore volumes are estimated by counting nodal pore voxels with the exception of those cut by throat surfaces. Half of the throat-volume voxels are assigned to each of the two nodal pores.
Once pore throats are identified, pore space can be divided into a network of pores separated by throat surfaces. Then pores are cross-indexed with their connecting throats, and adjoining pores and throats are cross-indexed with the connecting pores. This procedure determined the network of pore paths (a connected curve of voxels) and vertices (a cluster of one or more voxels where three or more paths intersect). The algorithm computes a center of mass and principal directions for each pore. A diameter, passing through the center of mass in each principal direction, is also computed. An effective pore radius can be computed using the sphere of equivalent volume in a similar manner. Distributions of the principal diameters and the effective radii are produced for the pores and throats.
Three-dimensional soil core data were analyzed using 3DMA with a 1.7-GHz Linux computer with 2 GB of memory. Analysis followed information outlined in Lindquist et al. (2005). Analysis generated information for the number of branch clusters and associated number of paths, as well as corresponding probabilities for coordination numbers, path lengths, path tortuosity, pore volume, effective radii, throat area, and throat radii. As explained below, these statistical parameters were graphed to examine differences among treatments.
After segmentation, a general comparison of porosity among treatments was conducted using minimum intensity projections (MinIPs). A MinIP evaluates each voxel along each line of voxels through a target volume to determine the minimum voxel value and creates an image from these values.
The number of branch clusters vs. the number of paths was plotted to show differences among treatments. The coordination number (CN) was measured by directly counting the distribution of medial axis vertex sets. The characteristic coordination number constants (Co) for the samples were determined by fitting an exponential distribution of coordination number and probability-density values. Coordination numbers between 3 and 10 were used in this analysis. Higher CNs (>10) occur in regions of the sample where pore size approaches the limit of voxel resolution and blur the region into a larger scale nodal pore of high CN. Coordination numbers between 3 and 10 consistently display an exponential (log-linear) distribution (Lindquist et al., 2000).
Path length (PL) and probability density were used to develop exponential relationships to examine differences due to treatments. Path lengths increased from RC to GB to AG. The characteristic path length constant (PLo) was determined using path length 0 to 6 mm for the RC and 0 to 10 mm for the buffer treatments. The smaller range for the RC treatment was used because of the absence of pore path lengths >6 mm.
Path tortuosity was determined by running Dijkstra's algorithm (Cormen et al., 1990) embedded as part of the 3DMA software. The algorithm uses a gamma distribution for tortuosity probability distribution (Lindquist et al., 1996). The ratio of actual path length to the shortest distance along the direction of the pore was used. It is a dimensionless factor expressing the degree of winding or twisting of a pore. Tortuosity of each pore and average and cumulative tortuosities were compared to examine differences among the treatments.
Pore volume (in cubic millimeters), pore radii (in millimeters), throat area (in square millimeters), and throat radii (in millimeters) were plotted against probability density to examine differences among treatments and to compare buffer effects on these parameters.
Statistical Analysis
Analysis of variance was conducted with SAS using the GLM procedure to test differences between treatments (SAS Institute, 1999). Least square means were calculated to find significant differences between treatments for each measured parameter and differences were declared significant at the 
= 0.05 level.
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RESULTS AND DISCUSSION |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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ová et al., 2006; Gryze et al., 2006; Jiang et al., 2007). In the same study watershed, Seobi et al. (2005) and Udawatta et al. (2006) observed lower bulk densities but higher saturated hydraulic conductivities and porosities in buffer treatments compared with the RC treatment.
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Coordination Numbers
The coordination number refers to the number of paths meeting at one node and it is the simplest concept for characterizing pore topology. The range of coordination numbers used in this analysis was between 3 and 10, since there are no CN 1 pores, and CN 2 pores are part of a pore channel, while pore coordination numbers >10 occur where pore size or channel length approach the voxel resolution (Lindquist et al., 2000). Although the coordination number increases with pore size, the image analysis capability is determined by the voxel resolution and thereby restricts the coordination number range for a particular analysis (Seright et al., 2001). Figure 4
shows that buffer samples had a high probability of low-CN pores, suggesting that these treatments had a simple pore structure with few pore paths joining. In support of this observation, Udawatta et al. (2006) showed significantly different number of pores, number of macropores, porosity, and pore circularity using soil cores from the same treatments.
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10–CN/Co; Fig. 4]. The Co of the relationships was significantly larger for the RC treatment (P < 0.005; Fig. 4). The RC treatment had the largest average Co (4.704), while the AG (3.338) and GB (3.646) treatments had smaller values. No difference was found between the AG and GB treatments. For small coordination numbers, AG and GB treatments had greater probabilities than the RC treatment. For example, the probabilities were 0.57, 0.63, and 0.64 for RC, GB, and AG treatments, respectively, for CN 3 pores. The higher probability of CN 3 pores for GB and AG indicates more direct macropores and a less complex macropore network. Figure 4 also shows that CN 3 dominates other coordination numbers for all treatments. The probability of occurrence of CN 3 pores was 3.4 times greater than the CN 4 pores for both buffer treatments, whereas it was only 3.3 for the RC treatment.
Large pores were located in nodes of higher coordination numbers while small pores correlated with nodes of low connectivity (Ioannidis and Chatzis, 2000). The buffer treatments indicated a greater number of higher coordination number pores than the RC treatment. The average number of pores with a CN >10 for RC, GB, and AG treatments was 5, 7, and 10, respectively. Grass and agroforestry buffers, on average, had a 0.005 probability for CN 10 pores, compared with 0.019 for the RC treatment.
Path Length
Path length, the distance between the centers of two adjacent connected nodal pores, represents the distance along the middle of the pore channel connecting adjacent nodal pores. Path lengths ranged from 0.07 to 6, 0.07 to 16, and 0.07 to 20 mm for RC, GB, and AG treatments, respectively (Fig. 5
). Studying frequency distributions of path lengths for four soil cores of Chicot sandy loam at 195- by 195-µm resolution with 2-mm-thick slices, Perret et al. (1999) stated that path lengths peaked at 40 mm for all four soil columns. In this study, the highest path length was observed in the AG treatment and it was only 19.7 mm. The differences observed between the two studies could be due to soil type and image resolution as well as different analysis procedures.
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Path length probability relationships exhibited an exponential distribution [P(PL) 10–PL/PLo; Fig. 5]. Probability distribution was significantly different among the treatments. The RC treatment had the smallest average PLo (1.558), indicating a more rapid decrease in density with PL. The smaller number of paths in the RC treatment must have influenced the PLo compared with the buffer treatments. The average PLo values were 3.283 and 3.518 for the GB and AG treatments, respectively. The average path lengths for RC, GB, and AG treatments were 1.73, 4.13, and 4.99 mm, respectively. Among the treatments, the RC treatment had the largest probability (0.01) for the smallest path length (0.073 mm) compared with the buffer treatments (0.005).
Path Tortuosity
Tortuosity is a dimensionless factor, is always >1, and explains the complexity of the pore path. Path tortuosity probability decreased with increasing path tortuosity (Fig. 6
). A dominant characteristic among treatments was the difference in resolved porosity: 0.1% for RC, 1.8% for GB, and 3.9% for AG. The small CT porosity values for the RC treatment limit the accuracy of the probability density vs. path tortuosity for higher tortuosities because there were few pores with higher tortuosities. Given this caveat, the highest probability for any given path tortuosity was observed for the RC treatment. The buffer treatments had some tortuous paths at lower probabilities. Distribution of data was more scattered for higher tortuosity values, except for the RC1 replication.
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The cumulative probability distributions of path tortuosity showed distinct differences among the treatments. The number of paths also varied among treatments, with values being 28 for RC, 94 for GB, and 120 for AG. The average for tortuosity varied among the three treatments. The RC treatment (1.73) had the highest value and the buffer treatments had the lowest (1.55). Path tortuosity values between the RC and the other two treatments were significantly different at P < 0.036. This implies that, on average, pore paths of the RC treatment were 12% more tortuous than the pore paths of the buffer treatments. Paths that are more tortuous could provide more resistance to fluid movement.
Although the average tortuosity was larger for the RC treatment than the two buffer treatments, path lengths were shorter for the RC treatment. Longer path lengths, as found in these buffer treatments, might have a significant impact on the movement of gases and liquids through the soil medium, but their tortuosity was smaller than the RC treatment. Although the RC treatment had shorter path lengths that might have less impact on liquid movement, its higher tortuosity might slow movement of liquids. Saturated hydraulic conductivity and porosity data from the same study area supports this, as liquid movement was significantly slower in the RC treatment than the two buffer treatments (Seobi et al., 2005; Udawatta et al., 2006). Perret et al. (1999) found no relationship between macroporosity and tortuosity. At this time, results are inconclusive as to whether path length can be used as an indicator of path tortuosity.
Nodal Pore Volume and Effective Pore Radius
Average pore volume was 1.56, 4.70, and 4.50 mm3 for RC, GB, and AG treatments, respectively (Fig. 7
). Differences were not significant; however, qualitative differences were found in the distributions. The RC treatment had a sparse distribution of pore volumes compared with the buffer treatments. The pore volume distributions of the buffers appeared to be lognormally distributed, with the exception of a large probability of pores >100 mm3 for the GB5 sample. Lindquist et al. (2000) used a lognormal distribution to explain the distribution patterns, and distributions for their samples were similar to our buffer treatments. The sparseness of volumes for the RC treatment indicates fewer detectable pores, and would be expected to correlate with increased tortuosity and reduced infiltration. The distributions of effective pore radii were calculated directly from the pore volumes. Average diameters were 0.76 ± 0.47, 1.73 ± 1.11, and 1.97 ± 1.39 mm for the RC, GB, and AG treatments, respectively.
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CONCLUSIONS |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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APPENDIX |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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ACKNOWLEDGMENTS |
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NOTES |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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Received for publication February 9, 2007.
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REFERENCES |
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TOPNOTESABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSAPPENDIXREFERENCES |
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ová, R., V. Kode, A. 
igová, and J. 
im
nek. 2006. Impact of plant roots and soil organisms on soil micromorphology and hydraulic properties. Biologia 61:S339–S343.[CrossRef][Web of Science]lindquis/3dma/3dma_rock/3dma_rock.html (accessed 16 Aug 2007; verified 29 Nov. 2007). Dep. of Applied Mathematics and Statistics, State Univ. of New York, Stony Brook.This article has been cited by other articles:
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  S. S. Lee, C. J. Gantzer, A. L. Thompson, S. H. Anderson, and R. A. Ketcham Using High-Resolution Computed Tomography Analysis To Characterize Soil-Surface Seals Soil Sci. Soc. Am. J., August 20, 2008; 72(5): 1478 - 1485. [Abstract] [Full Text] [PDF]
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is the relative attenuation.
