Shape‐free inference of hyporheic traveltime distributions from synthetic conservative and “smart” tracer tests in streams

Abstract

The hyporheic zone has been identified as important for river ecology, natural biogeochemical turnover, filtration of particles, degradation of dissolved pollutants—and thus for the self‐cleaning capacity of streams, and for groundwater quality. Good estimation of the traveltime distribution in the hyporheic zone is required to achieve a better understanding of transport in the river system. The transient‐storage model has been accepted as an appropriate tool for reach‐scale transport in rivers undergoing hyporheic exchange, but the choice of the best parametric function for the hyporheic traveltime distribution has remained unclear. We present an approach to obtaining hyporheic traveltime distributions from synchronous conservative and “smart” tracer experiments that does not rely on a particular functional form of the hyporheic traveltime distribution, but treats the latter as a continuous function. Nonnegativity of the hyporheic traveltime distribution is enforced by the application of Lagrange multipliers. A smoothness parameter, needed for regularization, and uncertainty bounds are obtained by the expectation‐maximization method relying on conditional realizations. The shape‐free inference provides the opportunity for capturing unconventional shapes, e.g., multiple peaks, in the estimation. We test the approach by applying it to a virtual test case with a bimodal hyporheic traveltime distribution, which is recaptured in the inversion of noisy data.