Many water quality and ecosystem functions performed by streams occur in the benthic biolayer, the biologically active upper (~5 cm) layer of the streambed. Solute transport through the benthic biolayer is facilitated by bedform pumping, a physical process in which dynamic and static pressure variations over the surface of stationary bedforms (e.g., ripples and dunes) drive flow across the sediment-water interface. In this paper we derive two predictive modeling frameworks, one advective and the other diffusive, for solute transport through the benthic biolayer by bedform pumping. Both frameworks closely reproduce patterns and rates of bedform pumping previously measured in the laboratory, provided that the diffusion model’s dispersion coefficient declines exponentially with depth. They are also functionally equivalent, such that parameter sets inferred from the advective model can be applied to the diffusive model, and vice versa. The functional equivalence and complementary strengths of these two models expands the range of questions that can be answered, for example by adopting the advective model to study the effects of geomorphic processes (such as bedform adjustments to land use change) on flow-dependent processes, and the diffusive model to study problems where multiple transport mechanisms combine (such as bedform pumping and turbulent diffusion). By unifying advective and diffusive descriptions of bedform pumping, our analytical results provide a straightforward and computationally efficient approach for predicting, and better understanding, solute transport in the benthic biolayer of streams and coastal sediments.

The hyporheic exchange below dune-shaped bedforms has a great impact on the stream environment. One of the most important properties of the hyporheic zone is the residence time distribution (RTD) of flow paths in the sediment domain. Here, we evaluate the influence of dimensionless sediment depths d b * = 2 π d b / λ where λ is the dune wavelength and different values of dimensionless groundwater underflow values u b * (similar to dune migration celerity), on the shape of the hyporheic exchange RTD. Empirical RTDs were generated, over a range of combinations between d b *     and u b *   values, from numerical particle tracking experiments in which 10000 particles were released over a flat domain. These empirical RTDs are represented by different distributions over the range of d b *     and u b *   . A Fréchet RTD is the best fit for deep beds ( d b *   >3.2) and negligible underglow ( u b * <0.1). A LogNormal RTD is often the best representation for u b * ≤ 0 . 8 , while a Gamma RTD performs better for larger values of u b * . In general, a LogNormal RTD provides a good representation of the empirical RTDs in all cases, as it is identified as either the best or the second-best fitting distribution according to the Anderson-Darling test. The parameters of these analytical distributions vary with d b *     and u b * , and this dependence is graphically represented in this work. These results contribute to our understanding of the physical and mixing processes underpinning hyporheic exchange in streams and paves the way for a quick evaluation of its potential impact on nutrient and contaminant processing (e.g., based on the magnitude of the Damköhler number).

The hyporheic exchange below dune-shaped bedforms has a great impact on the stream environment. One of the most important properties of the hyporheic zone is the residence time distribution (RTD) of flow paths in the sediment domain. Here we evaluate the influence of an impervious layer, at a dimensionless sediment depth of \(d_{b}^{*}=\frac{2\pi d_{b}}{\lambda}\) where \(\lambda\) is the dune wavelength, on the form of the hyporheic exchange RTD. Empirical RTDs were generated, over a range of \(d_{b}^{*\ }\ \)values, from numerical particle tracking experiments in which \(10000\) particles sinusoidally distributed over a flatbed domain were released. These empirical RTDs are best represented by the Gamma, Log-Normal and Fréchet distributions over normalized bed depth of \({0\ <=d}_{b}^{*\ }\leq 1.2\),\({1.2<d}_{b}^{*\ }\leq 3.1\), and \(d_{b}^{*\ }>3.1\), respectively. The depth dependence of the analytical distribution parameters is also presented, together with a set of regression formulae to predict these parameters based on \(d_{b}^{*\ }\)with a high degree of accuracy (\(R^{2}>99.8\%\)). These results contribute to our understanding of the physical and mixing processes underpinning hyporheic exchange in streams and allow for a quick evaluation of its likely impact on nutrient and contaminant processing (e.g., based on the magnitude of the Damköhler number).Keywords: Dunes, bedforms, residence times distribution, sediment depth effect, Hyporheic residence times, analytical representation, two parametric distributions, Damköhler Number.