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Solute Dispersion in Unsaturated Heterogeneous Soil at Field Scale: I. Theory¹

ABSTRACT

In a heterogenous field whose hydraulic properties vary from point to point the transport of solute also differs from profile to profile. In this paper solute concentration on the field scale was treated as a random variable. The field heterogeneity was described in terms of the statistical distribution of the hydraulic parameters, which implies a corresponding distribution of the concentration. Equations for computing this distribution, as well as its average and variance, in a heterogeneous field were derived explicitly for a simple, but representative case, of leaching under random recharge distribution on the surface. The water and solute flow in unsaturated soil was assumed to be vertical and steady. The randomness of the hydraulic properties was reduced to that of the saturated hydraulic conductivity by adopting a scaling hypothesis and a log normal distribution.

¹ Contribution from Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel. 1978 Series, no. 193-E.

² Professor of Fluid Mechanics, School of Engineering, Tel-Aviv Univ. and Hydrologist, The Volcani Center, A.R.O., and Soil Physicist, The Volcani Center, A.R.O., Bet Dagan, Israel, respectively.

Received for publication July 18, 1978. Accepted for publication January 4, 1979.

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