Breakthrough curve moments scaling in hyporheic exchange

The interaction between stream flow and bed forms creates an uneven distribution of near-bed energy heads, which is the driving force of hyporheic exchange. Owing to the large disparity of advection characteristic times in the stream and within the hyporheic zone, solute mass exchange is often modeled by considering the latter as an immobile region. In a recent contribution Gonzalez-Pinzon et al. (2013) showed that existing models employing this hypothesis are structurally inconsistent with the scaling revealed by the analysis of 384 breakthrough curves collected in 44 streams across five continents. Motivated by this result, we analyze the scaling characteristics of a model that we recently developed by combining the analytical solution of the advective flow within the hyporheic zone with a Lagrangian solute transport model. Results show that similarly to the experimental data our model predicts breakthrough curves with a constant skewness, irrespective of the stream size, and that the scaling of the first three moments observed by Gonzalez-Pinzon et al. (2013) is also respected. Moreover, we propose regression curves that relate the first three moments of the residence time distribution with the alternate bar dimensionless depth (Y-BM(*)), a quantity that is easily measurable in the field. The connection between BTC moments and Y-BM(*) opens new possibilities for modeling transport processes at the catchment scale.