Toward a Universal Model of Hyporheic Exchange and Nutrient Cycling in Streams

In this paper we demonstrate that several ubiquitous hyporheic exchange mechanisms can be represented simply as a one-dimensional diffusion process, where the diffusivity decays exponentially with depth into the streambed. Based on a meta-analysis of 106 previously published laboratory measurements of hyporheic exchange (capturing a range of bed morphologies, hydraulic conditions, streambed 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 streambed 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: (a) 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; (b) under steady-state conditions nitrate uptake in the streambed is primarily biologically controlled; and (c) median reaction timescales for nitrate removal in the hyporheic zone are $\approx$0.5 and 20 hr for uptake by assimilation and denitrification, respectively. 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 their scale-up to watersheds and beyond.