Governing Equations

Soil Matrix Transport

For unsaturated solute transport in the soil matrix the advection-dispersion equation is

(33.17)   

where c is the concentration of the solute, R_c is sum of sources and sinks, D is the dispersion coefficient, and v_z is the vertical velocity.

The advective transport is determined by the water flux calculated during a MIKE SHE WM simulation. As the water flow is assumed strictly vertical, this restriction applies also to the advective transport of the dissolved solutes.

To determine the velocity, v_z, the flux is divided by the moisture content:

(33.18)   

The mathematical formulation of the dispersion of the solutes follows the for­mulation derived for groundwater flow with a linear relation between the dis­persion coefficient and the seepage velocity but limited to one dimension. In this case the dispersion coefficient can be written as:

(33.19)   

where a_L is the longitudinal dispersivity of the porous medium which repre­sents the heterogeneity of the soil hydraulic parameters. a_L is allowed to vary vertically to account for different degrees of inhomogeneity in the soil. For unsaturated flow, the dispersivity is dependent on the water content, how­ever, this relationship is neglected. .