A Dual Domain stochastic lagrangian model for predicting transport in open channels with hyporheic exchange

The exchange of surface and subsurface waters plays an important role in understanding and predicting large scale transport processes in streams and rivers. Accurately capturing the influence of small-scale features associated with turbulent dispersion on exchange in an upscaled framework is necessary for developing reliable predictive models at the reach scale. In this work, we use high-fidelity direct numerical simulations (DNS) to fully resolve turbulent flow and hyporheic exchange in an open channel. We parameterize a 2D particle tracking model with the average DNS velocity and scalar diffusivity profiles. Breakthrough curves and rate of surface mass loss to the subsurface in both models agree after a sufficient distance downstream from particle injection. Finally we find that the travel time/distance joint pdf contains enough information to parameterize a 1D dual domain coupled Continuous Time Random Walk (ddc-CTRW) model that successfully reproduces the behavior of both the DNS and the 2D particle tracking model, allowing accurate prediction of breakthrough curves. Predicting breakthrough curves with a fully parameterized ddc-CTRW reduces cpu time by orders of magnitude when compared with DNS.