Multiple scale analysis of soil hydraulic properties of heterogeneous fields using multifractals

Owing to the heterogeneous nature of the natural environment, aggregation and disaggregation of water flow and transport variables remain one of the most challenging problems. Recently, several investigators documented a scale dependent and nonlinear spatial variation, and attributed this to the nested and hierarchical effect of environmental factors and processes. Hence, understanding and quantifying spatial variability across several spatial scales is crucial in transferring locally measured data to larger scales and vise versa. The objectives of this study were to identify: (i) scaling type (simple scaling, multi-scaling, or nonscaling); (ii) the spatial extent over which a given scaling property apply; and (iii) which soil properties best reflect the variability in a given hydraulic property across several spatial scales. Soil physical and hydraulic property data were collected at two sites---Smeaton and Alvena, in SK, Canada that are located within the Black and Gray Soil Zones, respectively. At the Smeaton site, 128 locations were monitored along a 384-m transect that has a sandy loam soil on a gentle landscape; and at the Alvena site 104 locations were monitored along a 576-m transect on a rolling landscape with clay loam soil. Scaling type, multiple scale variability, and multiple scale relationships were characterized using multifractal and joint multifractal techniques. The results showed a multifractal type scaling for clay content, organic carbon, water storage at higher matric potentials, saturated conductivity, and fitted hydraulic parameters. Monofractal type was observed for bulk density, sand content, and water content at saturation. Substantial cutoff scales were observed in field-measured soil water distribution and fitted retention parameters. It was also observed that the relationships between the variability in soil physical properties and the variability in hydraulic properties vary with the scale of observation. The results indicate that: (i) different soil and hydraulic variables have different scaling properties; (ii) information on scaling property of a given soil and hydraulic variable is essential to avoid either over-sampling (for simple scaling ones) or under-sampling (for multiscaling ones); (iii) predictive models such as pedotransfer functions should not rely on a single scale observation only, but rather need calibrations over several spatial scales.