Abstract
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.