Peak and tail scaling of breakthrough curves in hydrologic tracer tests

• We obtain a relationship between peak and tail scaling of breakthrough curves.
• We show that at large scales peaks and tails provide equivalent information.
• We present particle tracking results for a conceptual model of river transport.
• We identify the relevant asymptotic scales in the context of this conceptual model.

Power law tails, commonly observed in solute breakthrough curves, are notoriously difficult to measure with confidence as they typically occur at low concentrations. This leads us to ask if other signatures of anomalous transport 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, and validate our results in the context of a very simple model that represents transport in an idealized river.