How does reach-scale stream-hyporheic transport vary with discharge? Insights from rSAS analysis of sequential tracer injections in a headwater mountain stream

The models of stream reach hyporheic exchange that are typically used to interpret tracer data
assume steady-flow conditions and impose further assumptions about transport processes on the interpretation
of the data. Here we show how rank Storage Selection (rSAS) functions can be used to extract
‘‘process-agnostic’’ information from tracer breakthrough curves about the time-varying turnover of reach
storage. A sequence of seven slug injections was introduced to a small stream at base flow over the course
of a diel fluctuation in stream discharge, providing breakthrough curves at discharges ranging from 0.7 to
1.2 L/s. Shifted gamma distributions, each with three parameters varying stepwise in time, were used to
model the rSAS function and calibrated to reproduce each breakthrough curve with Nash-Sutcliffe efficiencies
in excess of 0.99. Variations in the fitted parameters over time suggested that storage within the reach
does not uniformly increase its turnover rate when discharge increases. Rather, changes in transit time are
driven by both changes in the average rate of turnover (external variability) and changes in the relative rate
that younger and older water contribute to discharge (internal variability). Specifically, at higher discharge,
the turnover rate increased for the youngest part of the storage (corresponding to approximately 5 times the
volume of the channel), while discharge from the older part of the storage remained steady, or declined
slightly. The method is shown to be extensible as a new approach to modeling reach-scale solute transport
that accounts for the time-varying, discharge-dependent turnover of reach storage.