We formulate soil grain transport by rain splash as a stochastic advection‐dispersion process. By taking into account the intermittency of grain motions activated by raindrop impacts, the formulation indicates that gradients in raindrop intensity, and thus grain activity (the volume of grains in motion per unit area) can be as important as gradients in grain concentration and surface slope in effecting transport. This idea is confirmed by rain splash experiments and manifest in topographic roughening via mound growth beneath desert shrubs. The formulation provides a framework for describing transport and dispersal of any soil material moveable by rain splash, including soil grains, soil‐borne pathogens and nutrients, seeds, or debitage. As such it shows how classic models of topographic “diffusion” reflect effects of slope‐dependent grain drift, not diffusion, and it highlights the role of rain splash in the ecological behavior of desert shrubs as “resource islands.” Specifically, the growth of mounds beneath shrub canopies, where differential rain splash initially causes more grains to be splashed inward beneath the protective canopy than outward, involves the “harvesting” of nearby soil material, including nutrients. Mounds thus represent temporary storage of soil derived from areas surrounding the shrubs. As the inward grain flux associated with differential rain splash is sustained over the shrub lifetime, mound material is effectively sequestered from erosional processes that might otherwise move this material downslope. With shrub death and loss of the protective canopy, differential rain splash vanishes and the mound material is dispersed to the surrounding area, again subject to downslope movement.