Peak and Tail Scaling of Breakthrough Curves in Hydrologic Tracer Tests

Abstract:

Power law tails, a marked signature of anomalous transport, have been observed in solute breakthrough curves time and time again in a variety of hydrologic settings, including in streams. However, due to the low concentrations at which they occur they are notoriously difficult to measure with confidence. This leads us to ask if there are other associated signatures of anomalous transport that can be sought. We develop a general stochastic transport framework and derive an asymptotic relation between the tail scaling of a breakthrough curve for a conservative tracer at a fixed downstream position and the scaling of the peak concentration of breakthrough curves as a function of downstream position, demonstrating that they provide equivalent information. We then quantify the relevant spatiotemporal scales for the emergence of this asymptotic regime, where the relationship holds, in the context of a very simple model that represents transport in an idealized river. We validate our results using random walk simulations. The potential experimental benefits and limitations of these findings are discussed.