Modelling solute transport in soil columns using advective–dispersive equations with fractional spatial derivatives

Solute transport in soils is commonly simulated with the advective–dispersive equation, or ADE. It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solute transport experiments in soil columns to test the new model. The FADE appears to be a useful generalization of the ADE. The order of the fractional differentiation reflects differences in physical conditions of the solute transport in soil.