Characterizing scale-dependent spatial relationships between soil properties using multifractal techniques

Measurement of soil hydraulic properties under field conditions is expensive and time consuming. Indirect methods that include estimating soil water properties from readily available soil physical data (known generally as pedotransfer functions) are preferred options. However, since environmental factors and processes operate at multiple spatial scales, the accuracy and reliability of these indirect techniques is often below expectations. The objective of this study was to determine if there is a scale-dependent relationship between soil water storage at three commonly used matric potentials (0, − 30, and − 1500 kPa) and basic soil physical properties (bulk density, sand, silt, clay, and organic carbon content). Soil physical property and water storage measurements were taken from a 384-m transect on a sandy loam soil, located at Smeaton, SK, Canada. The multiple scale relationships between these variables were studied using multifractal and joint multifractal techniques. Results indicate that at the observation scale, the spatial patterns of water storage at 0 and − 30 kPa matric potentials were significantly (r2 = 0.2 to 0.42, P < 0.01) related to clay and organic carbon content. Multifractal analysis, however, showed that the spatial pattern and variability of water storage at 0 and − 30 kPa matric potentials were related largely to sand and silt contents. Residual water (− 1500 kPa) was related only to clay content at all spatial scales studied. This study suggests that single scale analysis may not be sufficient to fully characterize spatial variability in soil and soil water properties.