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

English Abstract:

Multifractal analysis describes the variability and 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, the joint multifractal analysis was carried out for three variables coexisting in the same geometric support in order to describe the influence of topography (relative elevation) and soil texture (sand content) on water storage within the soil profile. Soil water storage was measured down to 1.4 m depth along a transect of 576 m long from the hummocky landscape of central Saskatchewan, Canada along with sand content and relative elevation. Joint multifractal analysis was conducted considering both the strange attractor formalism and the method of moments. The variability in soil water storage, sand content and relative elevation were scale dependent. The spatial variability in relative elevation was strongly reflected on water storage across 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 both relative elevation and texture varied highly. This clearly demonstrated the capability of joint multifractal analysis to completely characterize the scaling behavior among three variables.