Experimental Evaluation of Three Backward Transit Time Distributions (bTTD) for Solute Storage and Release During Hyporheic Exchange

Hyporheic exchange in streams supports many important ecosystem services but can also contribute to legacy pollution, by trapping less reactive contaminants in streambed sediments that are then slowly released back to the stream over time. In this study we evaluated three different analytical representations of the backward transit time distribution (bTTD) of water leaving the hyporheic zone, corresponding to different mechanisms for how water and solutes in hyporheic zone storage are sampled for outflow: (1) uniform sampling (exponential bTTD), plug-flow sampling (Dirac delta bTTD), and preferential sampling of either young or old water (Gamma bTTD). Using the Method of Moments, these three bTTDs were tested against data from 47 previously published hyporheic exchange experiments conducted in laboratory flumes over a range of flow conditions, sediment grain sizes, and bedform sizes and types. Based on measures of model fit and parsimony (AICc), in all 47 experiments hyporheic exchange was best represented by either the Gamma or exponential distributions. Further, values for key process variables, including hyporheic exchange flux and the Gamma distribution's shape parameter are correlated with readily measured field variables, including mean grain diameter of the streambed, streambed roughness, and mean stream discharge and velocity. This work advances understanding of hyporheic exchange processes and their representation in models of pollutant fate and transport in streams.