Quantifying Head and Hyporheic Fluxes in Moving Bedforms with variable size and shape

Moving bedforms in streams have variable shape and size and thus the shape of the sediment-water interface (SWI) is dynamic. However, existing mathematical models of bedform-induced hyporheic exchange flux (HEF) assume a fixed bedform shape in determining the pressure boundary condition at the SWI. This simplifying assumption is adopted because there is no established method for prescribing head along an arbitrary, changing SWI. This gap has prevented most flow modeling efforts from accounting for the dynamics of bedform sizes and shapes, and it is currently not well understood how such dynamics are expected to affect transport and biogeochemical processes in streams. Previously, measurements of head along the SWI have been taken under stationary bed conditions using pressure sensors installed within bedforms, but installing sensors to take the same measurements under moving-bedform conditions is impractical. Therefore, we propose a method to quantify the dynamics of hydraulic head at the SWI using timelapse photos of dye tracer tests in flume experiments. For every photo, an initial guess of head along the SWI is generated using established methods from the literature. Flow paths in the bed are calculated using the steady-state groundwater flow equation and Darcy's Law. The predicted evolution of the dye plumes in the photo is compared against the dye plumes from the subsequent photo. This comparison is used as the objective criterion in an optimization procedure. The optimization results in a head function that accounts for spatiotemporal changes in the shape of the SWI. The procedure was first tested on a synthetic data set generated using a model of HEF under moving bedforms, and the recovered head function was found to be in very close agreement with the original imposed head. The procedure was then applied to experimental observations of dye penetration tests. The propagation of the dye plume resulting from the recovered head function shows agreement with observations. In providing a new way to estimate head under moving-bed conditions, this work is an important advance in realistic measurements and modeling of bedform-induced HEF and its effect on flow, transport, and biogeochemical processes in streams.