Simple models for subsurface solute transport that combine unsaturated and saturated zone pathways

A series of semi-analytical and analytical solutions are presented for transport of a surface released contaminant vertically through the unsaturated zone to the watertable and then within groundwater. Vertical migration through the unsaturated zone is represented by a one-dimensional solution to the advection–dispersion equation, which is used to calculate the solute flux at the watertable. This is coupled to a solution to the three dimensional advection–dispersion equation in Laplace space to represent the subsequent lateral groundwater transport. The slender plume approximation is used to derive a concise equation for this three-dimensional transport in the saturated zone and forms of this equation are derived for point, line and rectangular area sources. Three different approaches to describing unsaturated zone transport are presented that differ in how the plant root zone is represented. The resultant coupled transport relations are in Laplace space and are numerically inverted using the de Hoog algorithm for transient calculations. Analytical expressions are developed for steady state solute transport. In a series of hypothetical simulations transient results are compared with equivalent numerical analyses using SUTRA. The developed approach is shown to work well and offers an efficient alternative to numerical analyses, particularly where the steady state is of interest.