On a fractional derivative form of the Green-Ampt infiltration model

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34 Scopus citations

Abstract

The Green-Ampt model for infiltration into homogeneous soils predicts a monotonically decreasing infiltration rate and a wetting front that initially advances as the square root of time. Infiltration in heterogeneous soils, however, can exhibit non-monotonic infiltration rates and wetting front advances that differ from the square root of time (" anomalous diffusion" ).Here it is postulated, that if the length scales of the heterogeneities can be assumed to be power law distributed, it may be appropriate to model infiltration in heterogeneous soils in terms of fractional derivatives. Then, by expressing the hydraulic flux as a Caputo fractional derivative (order 0 < α 1) of the head, a fractional Green-Ampt infiltration model is obtained. It is shown that solutions of this model predict non-monotonic and anomalous diffusion behaviors consistent with observations in field infiltration trials; a finding that indicates that a non-local moisture flux model, based on fractional derivatives, is a plausible model for describing infiltration into heterogeneous soils.

Original languageEnglish (US)
Pages (from-to)257-262
Number of pages6
JournalAdvances in Water Resources
Volume34
Issue number2
DOIs
StatePublished - Feb 2011

Bibliographical note

Funding Information:
This work was supported by the STC program of the National Science Foundation via the National Center for Earth-surface Dynamics under agreement EAR-0120914. The author would also like to thank the editor and reviews of this article for many worthwhile and helpful suggestions.

Keywords

  • Anomalous diffusion
  • Fractional derivative
  • Green-Ampt
  • Heterogeneous soils
  • Infiltration

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