Analytical model for vadose zone solute transport with root water and solute uptake

An efficient method is presented for calculating one-dimensional solute transport through the vadose zone in the presence of vertically distributed root water and solute uptake. The method is based on an analytical solution of the convective transport equation, which is solved by the method of characteristics. The solution requires a time-invariant leaching fraction, and assumes that transport occurs by convection alone; that is, hydrodynamic dispersion and molecular diffusion are neglected. From this solution, two variables of practical importance are calculated, (i) the average solute concentration in the root zone, weighted by the root distribution, and (ii) the cumulative solute flux to the groundwater. Model parameters are related to water management, crop type, and soil type, through the following parameters: leaching fraction, root distribution, and soil hydraulic properties. Simulation results are presented for both downward and upward flow scenarios. Simulations with a nonuniform moisture profile indicate that nearly identical results are obtained by replacing the profile by a uniform moisture content equal to the arithmetic average or the uptake-weighted average moisture content, so that closed-form analytical expressions for travel time and travel depth can be obtained. A sensitivity analysis of the relevant model parameters shows that solute concentrations are largely determined by the magnitude of the effective water application ratio, defined by the fraction of infiltrated water that is removed by evapotranspiration. We present suggestions of how dispersive mixing and temporal changes in leaching fraction are readily incorporated into the current model. Although potentially simplistic, the presented methodology can be extremely useful for longer-term and field-to-regional scale characterization of contaminant movement.