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.

In this paper, we explore the use of unsteady transit time distribution (TTD) theory to model pollutant removal in biofilters, a popular form of nature-based or “green” stormwater infrastructure (GSI). TTD theory elegantly addresses many unresolved challenges associated with predicting pollutant fate and transport in these systems, including unsteadiness in the water balance (time-varying inflows, outflows, and storage), unsteadiness in pollutant loading, time-dependent reactions and scale-up to GSI networks and urban catchments. From a solution to the unsteady age conservation equation under uniform sampling, we derive an explicit expression for solute breakthrough with or without first-order decay. The solution is calibrated and validated with breakthrough data from 17 simulated storm events (+/- bromide as a conservative tracer) at a field-scale biofilter test facility in Southern California. TTD theory closely reproduces bromide breakthrough concentrations, provided that lateral exchange with the surrounding soil is accounted for. At any given time, according to theory, more than half of water in storage is from the most recent storm, while the rest is a mixture of penultimate and earlier storms. Thus, key management endpoints, such as the treatment credit attributable to GSI, are inexorably linked to the age distribution of water stored and released by these systems.