Multiscaling analysis and random cascade modeling of dye infiltration

Abstract

[1] We aimed at investigating whether the spatial variability of infiltration in field soils, as visualized through dye infiltration experiments, is characterized by a multiscaling behavior. Digitized high-resolution dye images from three sites in an experimental catchment in Tunisia were analyzed using three indicators of scaling: empirical probability distribution functions, power spectra, and raw statistical moments. The two former indicators suggested a general scaling behavior of the data, which through the moments' analysis was found to be of multiscaling type. Random cascade processes are frequently used to model multiscaling processes, and we fitted the ''universal multifractal'' (UM) model of Schertzer and Lovejoy [1987] to our data. The UM model closely reproduced the empirical K(q) functions, and simulated fields reproduced key features in the observed ones. The results indicate that multiscaling random cascade modeling is useful for statistically describing flow processes and solute transport under field conditions.

A review of model applications for structured soils: a) Water flow and tracer transport

“…The Universal Multifractal Model was based on the random cascade process with a multifractal spatial distribution of hydraulic conductivity. The model reproduced hydraulic conductivity functions and key features in the observed dye distribution, and was suitable for describing PF pathways (Olsson et al, 2002).…”

“…There is increasing evidence that PF patterns in soil can be characterized by fractal or multi-fractal geometries (Rieu and Sposito, 1991;Hatano and Booltink, 1992;Baveye et al, 1998;Boufadel et al, 2000;Olsson et al, 2002Olsson et al, , 2007. Liu et al (2005) incorporated fractal PF patterns into a MIM.…”

Application of Multifractal and Joint Multifractal Analysis in Examining Soil Spatial Variation: A Review

“…Use of dye is a common approach to study the preferential flow paths of water in soil. The distribution of dye along with the infiltration water helped illustrate multifractal behaviour [104][105][106]. The multifractal nature of infiltration helped in identifying the input parameters for various rainfall-runoff models [107][108][109].…”

Spatio-temporal patterns in land use and management affecting surface runoff response of agricultural catchments—A review

“…We will not consider within-field variability, which has been treated in several other studies (Govindaraju et al, 2001, Olsson et al, 2002, Meng et al, 2006 because the contrasts within a field are usually much smaller than the contrasts between patches.…”