Fractal dimensions of mass estimated from intact and eroded soil aggregates

Scaling of mass within soil aggregates is characterized with a power-law model relating mass, M, and radius, r, of aggregates. When distribution of mass is fractal, the constants of the power-law model are the fractal dimension of mass, Dm, with a value <3, and a linear constant km. Tillage may alter mass scaling in soil by changing the internal arrangement of matter inside aggregates. Estimates of Dm and km have been made from measurements of mass contained in aggregates covering a range of sizes, but they could also be obtained by eroding aggregates of a single size class. Studies on eroded aggregates have shown that matter may be concentrically arranged in soil aggregates as a result of wetting and drying processes. The objective of this study was to estimate and compare Dm and km values from intact and eroded aggregates from wooded and cultivated sites of the same soil. Soil aggregates were sampled from the surface horizon of wooded and cultivated sites of a Typic Hapludults (Gladstone series), an Aquic Hapludults (Holmdel series), and an Ultic Hapludalfs (Ryder series) soil. A group of initially large air-dried aggregates was subjected to cycles of erosion that removed concentric layers of soil leaving increasingly smaller aggregates. Volumes of intact and eroded aggregates were measured by submerging kerosene-saturated aggregates in a 1:1 mix of water and glycerin and estimating the volume displaced by solving a balance of forces. An equivalent aggregate radius, r, was calculated as the cubic root of aggregate volume. Parameters Dm and km, and the variance of km (lacunarity), were estimated separately from the air-dried mass and r of intact and eroded aggregates with r>1 cm and r<1 cm. Scaling of mass was influenced by the soil type and soil management. In general, fractal scaling of mass was consistently found only in intact and eroded aggregates (r>1) of the Gladstone and Holmdel soils. For the wooded Gladstone and Holmdel soils, mass scaling of intact and eroded aggregates was statistically characterized by the same values of Dm and km, suggesting a concentric arrangement of mass, but only within aggregates that are not subjected to tillage. The km values of intact and eroded aggregates were correlated (R=0.97) to aggregate bulk density of intact aggregates. Typically, small aggregates (r<1 cm), aggregates from wooded sites, and intact aggregates had larger values of lacunarity than their corresponding counterparts. This study indicates that fractal scaling of mass cannot be assumed for all soils, but it can be maintained in cultivated soils despite changes in mass scaling introduced by tillage.