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Monte-Carlo Simulation of Noninteracting Solute Transport in a Spatially Heterogeneous Soil¹

ABSTRACT

Monte-Carlo data generation techniques were used to obtain 200 pairs multivariate lognormal values of the physical parameters D (dispersion coefficient) and v (pore-fluid velocity) which appear in the differential equation describing downward leaching of a noninteracting solute in the soil profile under steady-state percolation. The time (t_max), at which the maximum concentration is attained at given soil depth L after a pulse input of solute has been applied at the soil surface for a time t_o, was obtained for each pair of generated D and v values. Values of the ratio L/t_max representing the average rate of movement of the maximum concentration between two depths were also calculated. The effect of changes in the variance of v and the levels of correlation between D and v on the frequency distributions of t_max–t₀ was investigated. The lognormal and gamma distributions were fitted to the calculated distributions of t_max–t₀. Good fits were obtained with both theoretical distributions to the values of t_max–t₀. The lognormal distribution was better in describing the values of L/t_max. The parameters and properties of these calculated distributions were sensitive to changes in the variance of v but were less sensitive to changes in the correlation between D and v. The ensemble average of 200 concentration versus time curves was computed by substituting the generated parameters D and v in the solution to the differential equation. This curve was compared to that obtained using the sample mean values of D and v. The dissimilarity between these curves was sensitive to changes in the variance of v.

¹ Contribution from Dep. of Soil & Environmental Sciences, Univ. of California, Riverside, 92521.

² Respectively, Associate Research Scientist, Texas A&M Univ., College Station; Soil Scientist, Dep. Nacional de Plantas Oleaginosas, I.N.I.A. Spain; Professor, Univ. of California, Riverside.

Received for publication October 5, 1983. Accepted for publication December 6, 1984.