Fractal analysis of the infiltration curve and soil particle size in a semi-humid watershed

Although fractal mathematics has been commonly used to quantify particle size distribution (PSD), limited attention has been paid to the fractal dimension of the infiltration curve (D-I). Therefore, it is necessary to determine whether theD(I)and fractal dimensions of PSD (D-m,D-clay,D(silt)andD(sand)) can reflect the infiltration process, and soil erodibility and degradation. Accordingly, this study aimed to provide new information on the quantification of infiltration processes, and soil erodibility and degradation, usingD(I)andD(m)in the Soorak basin in the northern part of Iran. The soil and infiltration properties were calculated by field and laboratory practices on 46 topsoil samples and 34 infiltrometer double-ring tests. Correlation, regression and redundancy analysis (RDA) were used to identify relationships between the infiltration curve and PSD coordinates with soil and infiltration properties. Results indicated that theD(I)was significantly linearly correlated with other infiltration curve characteristics, with the correlation coefficient ranging from -0.737 to -0.403 (sig. = 0.000-0.037). However, there was no significant correlation betweenD(I)andD(m),D-clay,D(silt)andD(sand). Different erodibility factors, especiallyK(USLE), had significant relations withD(m),D-clay,D-silt,D(sand)andD(I)(p < .01), suggesting that these fractal dimensions are indicators of soil degradation. Other findings indicated that the land use had no significant effect onD(I)and infiltration properties, whereasK(USLE),D-m,D-clay,D(Silt)andD(Sand)were significantly affected by land-use patterns (p < .01). These findings demonstrate that fractal dimensions of PSD and infiltration can be practicable indices to analyse soil degradation under different land-use types. Highlights How fractal geometry adds to understanding of the infiltration process and soil degradation. Fractal dimensions of infiltration (D-I) can describe the infiltration process. Fractal dimensions of soil (D-m) andD(I)can be used as indicators of the soil erodibility. Erodibility and fractal properties of soil were significantly affected by land use.