In this paper we demonstrate that hyporheic exchange can be represented simply as a one-dimensional diffusion process, where the diffusivity decays exponentially with depth into the sediment bed. Based on a meta-analysis of 106 previously published laboratory measurements of hyporheic exchange (capturing a range of bed morphologies, hydraulic conditions, sediment properties, and experimental approaches) we find that the reference diffusivity and mixing length-scale are functions of the permeability Reynolds Number and Schmidt Number. These dimensionless numbers, in turn, can be estimated for a particular stream from the median grain size of the sediment bed and the stream’s depth, slope, and temperature. Application of these results to a seminal study of nitrate removal in 72 headwater streams across the United States, reveals: (1) streams draining urban and agricultural landscapes have a diminished capacity for in-stream and in-bed mixing along with smaller subsurface storage zones compared to streams draining reference landscapes; (2) under steady-state conditions nitrate uptake in the sediment bed is primarily biologically controlled; and (3) under transient conditions (e.g., spills or storms) physical transport processes are likely to influence nitrate removal rates as well. While further research is needed, the simplicity and extensibility of the framework described here should facilitate cross-disciplinary discussions and inform reach-scale studies of pollutant fate and transport and facilitate their scale-up to watersheds and beyond.

The Lattice-Boltzmann (LB) method is applied here for the first time to simulate bedform-induced hyporheic exchange flow in a reduced complexity model. The flexibility of the LB allows surface and hyporheic flows to be resolved together, in contrast to other approaches for similar model domains, in which surface flow is usually solved independently, and then the solution of the surface flow provides the boundary conditions to model the hyporheic exchange flow. At the same time, the superior computational efficiency of LB allows the use of Large Eddy Simulations within transient simulations. Numerical results show a faithful reproduction of pressure along the bedform surface—especially, the pressure drop leeward to the dune. Results also show short-time-dependent phenomena which were previously described only in the context of DNS studies over reduced-size computational domains. Short-time-dependent phenomena include pressure oscillations and time-dependence of hyporheic zone morphology, with the latter eventually extending beyond the limits of a single bedform element.