Page Banner

United States Department of Agriculture

Agricultural Research Service

Title: Fractional Advective-Dispersive Equation to Simulate Solute Transport in Soils

Authors
item Pachepsky, Yakov
item Rawls, Walter

Submitted to: International Symposium on Preferential Flow
Publication Type: Proceedings
Publication Acceptance Date: December 9, 2000
Publication Date: December 20, 2000

Interpretive Summary: Understanding solute transport in soils is a key to managing the fate of agricultural chemicals in environment, crop productivity, and agricultural sustainability. Models of solute transport package the knowledge that has been accumulated and quantified. Existing models fail to describe several important features of solute transport in soils, in particular the enhanced dspreading of solutes in soils as the solute transport progresses. Some developments in simulating scale dependencies have led to theory of fractional dispersion. This theory assumes that the solute particles can stay trapped for a long time and then travel a large distance with a relatively large speed. This assumption is well applicable to field soils, in which large stagnant zones border with small pathways of preferential flow. The theory leads to the fractional convective-dispersive equation that we have tested in this work. This equation simulates solute transport in field soil better than the classical convective-dispersive equation and is a promising enhancement in the hydrologists toolbox.

Technical Abstract: Solute dispersivity in the conventional advective-dispersive equation (ADE) was found to increase with a distance from the source. This can be explained assuming the movement of solute particles belongs to the family of Levy motions. A one-dimensional solute transport equation was derived for Levy motions using fractional derivatives to describe the dispersion. Our objective was to test applicability of this fractional ADE, or FADE, t soils. The FADE has two parameters - the fractional dispersion coefficient and the order of fractional differentiation alpha, 0 < alpha 2. Scale effects are reflected by the value of alpha, and the fractional dispersion coefficient is independent on scale. The ADE is a special case of the FADE. Analytical solutions of the FADE and the ADE were successfully fitted to the data from field experiments on chloride transport in sandy loam and clay loam soils. The FADE simulates scale effects on solute transport and is a promising model.

Last Modified: 10/25/2014
Footer Content Back to Top of Page