Long-term slowdown of river tracer pebbles: Generic models and implications for interpreting short-term tracer studies

Abstract

We propose generic approaches to modeling the reduction in mobility that occurs as tracer pebbles seeded on the surface are mixed to less active locations (e.g., beneath the bed or high on bars) or advected downstream to reaches with different shear stress or bed grain size. Advection slowdown, which may be negligible, is quantified using a regression equation relating virtual velocity to tracer and reach properties. Mixing slowdown, which is always present, is simulated using a Markov model of exchanges between three stores and assumptions about relative mean velocities of tracers in each store. The model can be calibrated from a full search on one date and at least a surface search on another date. Calibration to six reaches of Allt Dubhaig, Scotland, in which tracers were mapped after 2 and 8 years, Suggests mixing took 3-5 years to approach equilibrium in five reaches and was still proceeding in one. Simulated slowdown through mixing is far greater than that through advection and goes much of the way to explaining the 50% observed reduction in virtual velocity over 8 years compared to 2 years. Implications for the design and comparison of tracer-pebble experiments are considered.