Joint multifractal analysis for three variables: Characterizing the effect of topography and soil texture on soil water storage

Multifractal analysis describes heterogeneity in the distribution of a variable by characterizing and summarizing the variability across scales. Joint multifractal analysis has been widely employed to characterize scale relationships between two variables co-existing along a single geometric support. In this study, joint multifractal analysis was used for three variables coexisting in the same geometric support to describe the influence of topography (relative elevation) and soil texture (sand content) on water storage within a soil profile. Soil water storage, as well as sand content and relative elevation, were measured down to 1.4 m depth along a 576 m long transect in the hummocky landscape of central Saskatchewan, Canada. Joint multifractal analysis was conducted to consider both the strange attractor formalism and the method of moments. The variability in soil water storage, sand content and relative elevation was scale dependent and showed multifractal behavior. The spatial variability in relative elevation was strongly reflected on water storage across the analyzed spatial scales but the joint multifractal spectrum for sand content and water storage suggested a lower degree of correlation. The change in multifractality was also observed when there was high variability in relative elevation and texture. This clearly demonstrated the capability of joint multifractal analysis to completely characterize the scaling behavior among three variables.