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Soil Water Relations During Rain Infiltration: I. Theory^{1, 2,}

ABSTRACT

Soil moisture content changes and rates of water entry during rain infiltration into a semi-infinite soil column are analyzed mathematically. The model considered involves, principally, the following assumptions: Darcy's and continuity equations are applicable; the soil's hydraulic conductivity and diffusivity are unique, positive, and monotonically increasing functions of soil moisture contents; rainfall entering the soil can be considered as a continuous body of water.

It is shown analytically that an incessant rain eventually results in ponding if and only if rain intensity, R, exceeds the saturated soil's hydraulic conductivity, K(w_sat). For R K(w_sat) it is proven that as infiltration proceeds soil moisture contents at increasing depths tend to approach a constant level. At this level the soil's hydraulic conductivity equals the rain intensity. For R > K(w_sat) it is indicated how to estimate the water uptake at incipient ponding.

A difference method for solving approximately the differential equation of the model in question is described. An illustrative numerical example of this method's results is presented.

¹ Contribution from the Department of Soils and Water, National and University Institute of Agriculture, Rehovot, Israel.

² The senior author thanks the Computer Center, University of California, Berkeley, for allowing him to use its facilities in connection with this study.

³ Soil Physicist and Assistant Soil Physicist, respectively. The senior author is now Research Soil Physicist, U. S. Geological Survey, Menlo Park, Calif.

Received for publication June 15, 1962. Accepted for publication November 13, 1962.