Monte‐Carlo Simulation of Noninteracting Solute Transport in a Spatially Heterogeneous Soil

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 Δ L /Δ 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 – t 0 was investigated. The lognormal and gamma distributions were fitted to the calculated distributions of t max – t 0 . Good fits were obtained with both theoretical distributions to the values of t max – t 0 . The lognormal distribution was better in describing the values of Δ L /Δ 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 .