A fractional dispersion model for overland solute transport

Using the kinematic-wave overland flow equation and a fractional dispersion-advection equation, a process-oriented, physically-based model is developed for overland solute transport. Two scenarios, one consisting of downslope and the other of upslope rainstorm movements, are considered for numerical computations. Under these conditions, the hydrograph displays a long-tailed distribution due to the variation in flow velocity in both time and distance. The solute transport exhibits a complex behavior. Pollutographs are characterized by a steep rising limb, with a peak, and a long, stretched receding limb; whereas the solute concentration distributions feature a rapid receding limb followed by a long stretched rising limb. Downslope moving storms cause much higher peak in both hydrographs and pollutographs than do upslope moving storms. Both hydrographs and the pollutographs predicted by the fractional dispersion model are in good agreement with the data measured experimentally using a soil flume and a moving rainfall simulator.