ANALYTICAL SOLUTIONS FOR WATER-FLOW AND SOLUTE TRANSPORT IN THE UNSATURATED ZONE

Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and Whi te nonlinear mode) to solve the Richards' equation for vertical flow u nder a constant infiltration rate. Then we extend the water flow solut ion and develop an exact parametric solution for the advection-dispers ion equation. The method of characteristics is adopted to determine th e location of a solute front in the unsaturated zone. The dispersion c omponent is incorporated into the final solution using a singular pert urbation method. The formulation of the analytical solutions is simple , and a complete solution is generated without resorting to computatio nally demanding numerical schemes, Indeed, the simple analytical solut ions can be used as tools to verify the accuracy of numerical models o f water flow and solute transport. Comparison with a finite-element nu merical solution indicates that a good match for the predicted water c ontent is achieved when the mesh grid is one-fourth the capillary leng th scale of the porous medium. However, when numerically solving the s olute transport equation at this level of discretization, numerical di spersion and spatial oscillations were significant.