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 (Formula presented.) 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.