Fractal dimension to describe soil macropore structure using X ray computed tomography

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Abstract
The size, shape, and arrangement of structured voids 1–10 mm in size play an important role in the transport of water and solutes through soil. However, these characteristics are complex and difficult to quantify. Improved methods are needed to quantify the characteristics of these voids to better understand and predict the behavior of water and solutes passing through them. This study applied fractal analysis to soil bulk density data measured by X ray computed tomography (CT), a relatively new tool for nondestructively measuring macropore‐scale density in soil cores. Studies were conducted using undisturbed soil cores (7.6 cm ID) from forested and cultivated sites in the A horizon of a Menfro silt loam soil containing macropores and using two groups of soil cores which were uniformly packed with Menfro aggregates from 1–2 mm in diameter for one group and <1 mm in diameter for the other group. Samples were probed using CT to produce a 512 by 512 digital matrix of CT pixel values corresponding to bulk density. Pixels above a specified CT “cutoff” value were designated as occupied. A box‐counting method was used to find the fractal dimension of the perimeters between occupied and unoccupied pixels and of the areas formed by the unoccupied pixels. For length scales from 1 to 10 mm, perimeters and areas of these regions appeared to be fractal systems. Single degree of freedom orthogonal contrast tests determined from analysis of variance showed significant differences between the fractal dimension for (1) forest and cultivated cores versus uniformly packed cores, (2) two groups of uniformly packed cores made of different aggregate sizes, and (3) forest versus cultivated cores.