Estimating and Predicting Bedform-Induced Head Gradients Using Dye Tracer Tests

Head induced by bedforms at the sediment-water interface (SWI) is typically represented in one of two ways: either by solving the RANS equations for the water column, or by a sinusoidal boundary condition defined by Elliott and Brooks (1997). Both of these methods have been used to model bedform-induced hyporheic exchange flux (HEF) on domains of constant shape. Under sufficiently fast flow conditions, however, bedform shape is irregular and evolves over time. For these conditions, neither method is fully appropriate: RANS is too computationally intensive, while the Elliott and Brooks boundary condition is based on measurements taken using rigid bedforms of an idealized triangular shape (Fehlman, 1985). We present a procedure for estimating head induced by arbitrarily-shaped bedforms using timelapse photos of dye tracer tests. At a given time t, an initial guess of head along the SWI is generated. The predicted evolution of the dye plume observed in the photo at time t is calculated using the model of Teitelbaum et al. (2022). The predicted dye plume location is compared against the observed plume location from the next 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. Results show agreement with experimental observations from dye tracer tests. The estimated head is used as input data to predict head distribution based solely on SWI shape. This work provides a new way to estimate head under arbitrary SWI shape. Thus, it constitutes an important advance in realistic modeling of bedform-induced hyporheic exchange flux.