Fractal topography and subsurface water flows from fluvial bedforms to the continental shield

Surface-subsurface flow interactions are critical to a wide range of geochemical and ecological processes and to the fate of contaminants in freshwater environments. Fractal scaling relationships have been found in distributions of both land surface topography and solute efflux from watersheds, but the linkage between those observations has not been realized. We show that the fractal nature of the land surface in fluvial and glacial systems produces fractal distributions of recharge, discharge, and associated subsurface flow patterns. Interfacial flux tends to be dominated by small-scale features while the flux through deeper subsurface flow paths tends to be controlled by larger-scale features. This scaling behavior holds at all scales, from small fluvial bedforms ( tens of centimeters) to the continental landscape ( hundreds of kilometers). The fractal nature of surface-subsurface water fluxes yields a single scale-independent distribution of subsurface water residence times for both near-surface fluvial systems and deeper hydrogeological flows.