Analytical Advection–Dispersion Model for Transport and Plant Uptake of Contaminants in the Root Zone

In regulatory and risk management analyses of environmental contaminants, the vadose zone may be treated as a subcomponent within a larger environmental modeling framework. For the complexity of the larger system model to remain at manageable levels, it is desirable that subcomponent models be relatively simple and require few input parameters. In this work, we develop an advective–dispersive solute transport equation that includes plant uptake of water and solute and present an analytical solution. Assumptions underlying the transport model include linear solute sorption, first‐order uptake, and a uniform soil water content. We examine the latter assumption in detail and demonstrate the effects of rooting depth, soil texture, and leaching fraction on the uniformity of the root‐zone water content. The new analytical advection–dispersion model should be useful for estimating the transport and uptake of strongly sorbing and persistent contaminants, where the timescale relevant for assessing environmental impacts is long (decades) and short‐term fluctuations caused by, for example, precipitation can be averaged. As an illustration, model predictions are made for the uptake of cadmium (Cd) by wheat ( Triticum aestivum L.) grown in sludge‐amended soil. The predictions are compared with those of a “one‐compartment” model that has been proposed previously for risk analysis and regulatory studies. The comparison shows that the one‐compartment model overestimates the long‐term, steady‐state Cd concentration in harvested wheat grain. The analytical advection–dispersion model is recommended as a tool for environmental risk assessment of strongly sorbing, persistent contaminants.