Fractal dimension of soil aggregates as an index of soil erodibility

SummaryAggregate stability is an influential factor governing soil erodibility. The fractal dimension of soil aggregates has been related to their size distributions and stabilities. Several fractal models have been proposed for estimating fractal dimension of soil aggregates. This study was conducted to investigate how closely the soil interrill erodibility factor in WEPP model can be correlated to and predicted from soil aggregate size distribution or from their fractal dimensions. Samples from 36 soil series with contrasting properties were collected from northwest of Iran. The fractal dimensions of soil aggregates were calculated from Rieu and Sposito (Dn), Tyler and Wheatcraft (DmT), and Young and Crawford (DmY) models using aggregate size distribution (ASD) data. A rainfall simulator with drainable tilting flume (1 × 0.5 m) at slope of 9% was employed and total interrill erosion (TIE), total splashed soil (TS) and interrill erodibility factor (Ki) were calculated for 20, 37, and 47 mm h−1 rainfall intensities. Results showed that both Dn and DmT estimated from aggregate wet-sieving data characterized ASD of the examined soils and significantly (p < 0.01) correlated to TS, TIE and Ki. Values of Dn and DmT estimated from dry-sieving data only correlated to TS but not to TIE and Ki. Using air-dried aggregates of 4.75–8 mm size range, instead of aggregates <4.75 mm, in wet-sieving was better for estimating Dn as an index for the predication of TIE, TS and Ki. Correction of ASD for the particle fraction greater than lower sieve mesh size in each size class decreased the correlation coefficient between TIE, TS or Ki and Dn or DmT. The values of DmY were not correlated to TS, TIE and Ki. The correlation coefficient TIE and Ki with Dn and DmT derived from wet-sieving data, were higher than those with wet-aggregate stability (WAS), mean weight diameter (MWD) and geometric mean diameter (GMD), implying that Dn and DmT may be better alternative variables for empirically predicting soil erodibility factor and hence interrill erosion.

Research highlights
► The interrill erodibility (Ki) values were not correlated to the density-based fractal dimensions.
► The number- and mass-based fractal dimensions (Dn and DmT) were appropriate indices to estimate Ki.
► The total splash values were correlated to Dn and DmT obtained from dry-sieving data.