Estimating Head Induced by Moving Bedforms Using Dye Tracer Tests and Modeling

Under moving bedform conditions, the shape of the sediment-water interface (SWI) is known to evolve over time. 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 sediment-water interface (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. We propose a method to quantify the dynamics of hydraulic head at the SWI using timelapse photos of dye tracer tests, without installing any sensors in the flume. 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, which is run until the estimate of head at the SWI converges. Preliminary results show agreement with experimental observations from dye penetration tests. In providing a new way to estimate head under moving-bed conditions, this work is an important advance in realistic modeling of bedform-induced HEF and its effect on flow, transport, and biogeochemical processes in streams.