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 2D advective model can be applied to the 1D diffusive model, and vice versa. The functional equivalence and complementary strengths of these two models expand the range of questions that can be answered, for example, by adopting the 2D advective model to study the effects of geomorphic processes (such as bedform adjustments to land use change) on flow-dependent processes and the 1D diffusive model to study problems where multiple transport mechanisms combine (such as bedform pumping and turbulent diffusion). By unifying 2D advective and 1D 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. Plain Language Summary How far and fast pollutants travel downstream is often conditioned on what happens in a thin veneer of biologically active bottom sediments called the benthic biolayer. However, before a pollutant can be removed in the benthic biolayer, it must first be transported across the sediment-water interface and through the interstitial fluids of these surficial sediments. In this paper we demonstrate that one important mechanism for transporting solutes to, and through, the benthic biolayerbedform pumping-can be interchangeably represented as either a two-dimensional advective process or a one-dimensional dispersion process. The complementary nature of these models expands the range of benthic biolayer processes that can be studied and predicted with the end goal of improving coastal and stream water quality.

The hyporheic zone (HZ) is the area where surface water and groundwater interact in sediments immediately beneath and adjacent to streams, rivers, and riverine estuaries. It possesses unique chemical and biological properties stemming from the mixing between groundwater and surface water (Hester & Gooseff, 2010), and its high potential for nutrients removal and pollutant attenuation has attracted the attention of many researchers (Galloway et al., 2019). The hyporheic flow (Q h) is hydrologically defined as the volume of stream water per unit of time, which flows through the subsurface domain, and it starts and terminates at the stream after a certain period of time (Gooseff, 2010). The hyporheic flux (q h) is the corresponding flow per unit area through the streambed. It differs from groundwater flux by its exchanging back and forth across the sediment-water interface (SWI) at a relatively small scale, typically centimeters to tens of meters; however, groundwater flow travels unidirectionally over much longer distances (Boano et al., 2014). Geomorphic features, including alternate bars, ripples, and meanders, can play a significant role in hyporheic flow characteristics (Herzog et al., 2016). A distinctive feature of alternate bars emerges from the induced 3-D patterns of hyporheic flow due to the hydraulic head variation on its morphology (Tonina & Buffington, 2007, 2009; Trauth et al., 2013). Many studies have been carried out on the HZ characteristics in the 3-D gravel bars morphology. Laboratory experiments and 3-D dimensional modeling were conducted to investigate the effect of streamflow and bar's amplitude variations on hyporheic exchange (Tonina & Buffington, 2007). Besides, the alluvium depth can constrain the HZ extent (Tonina & Buffington, 2011). A predictive model was proposed to estimate the hyporheic residence times (T) dependence on bar submergence, hydraulic conductivity, and the slope of a stream reach (Marzadri et al., 2010). Moreover, the undermining effect of ambient groundwater on HZ was analyzed by Trauth et al. (2013) for fully submerged bars. Despite these many studies, the HZ characteristics in partially submerged bars are not fully understood. The importance of bars with low submergence lies in their common occurrence during low stream flow periods,

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 2D advective model can be applied to the 1D diffusive model, and vice versa. The functional equivalence and complementary strengths of these two models expand the range of questions that can be answered, for example, by adopting the 2D advective model to study the effects of geomorphic processes (such as bedform adjustments to land use change) on flow-dependent processes and the 1D diffusive model to study problems where multiple transport mechanisms combine (such as bedform pumping and turbulent diffusion). By unifying 2D advective and 1D 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. Plain Language Summary How far and fast pollutants travel downstream is often conditioned on what happens in a thin veneer of biologically active bottom sediments called the benthic biolayer. However, before a pollutant can be removed in the benthic biolayer, it must first be transported across the sediment-water interface and through the interstitial fluids of these surficial sediments. In this paper we demonstrate that one important mechanism for transporting solutes to, and through, the benthic biolayerbedform pumping-can be interchangeably represented as either a two-dimensional advective process or a one-dimensional dispersion process. The complementary nature of these models expands the range of benthic biolayer processes that can be studied and predicted with the end goal of improving coastal and stream water quality.

<p>The importance of the benthic biolayer (the first few centimeters in the shallow part of the streambed) comes from the active biogeochemical reactions that happen within this thin layer. Currently, many studies use the simplified approach of using the constant profile to represent the diffusivity in the sedimented; however, other studies claim that the exponential profile is a better representation due to the turbulence penetration into the sediment bed. In this work, we are using an analytical model to simulate the temporal variation of solute concentration in water column in bedform morphology type by adopting two diffusivity profile; constant diffusivity profile, and exponential diffusivity profile. This rigorous analytical framework was built by Grant et al. 2019 (not published yet),  and is based on Duhamel’s Theorem. The model is used to fit a set of laboratory data that were performed on streams with dunes type bedforms, where temporal concentration variation is measured in the water column. Based on Root Mean Square Error (RMSE), coefficient of determination (R<sup>2</sup>), and modified Akaike Information Criterion (AICc), the exponential profile is superior over the whole range of Permeability Reynolds Number, and it can be considered as the best fit for the laboratory data compared to the constant diffusivity.  Additionally, the influence of sediment bed depth on the effective diffusivity, and therefore, on the benthic biolayer characteristics is investigated here by running the model with constant diffusivity profile in Infinite and finite sediment bed cases. An indicator () to determine whether the sediment bed depth influences the diffusivity within the sediment domain or not, is introduced here. when this indicator is larger than 1, the sediment bed depth will likely influence the diffusivity within the sediment. Based on our results, our analytical framework can be a predictive tool for the solute transfer into the benthic layer in bedform morphology type.</p><p><img 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" alt=""></p><p> </p>

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^*=(2πd_b)⁄λ where λ 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^(* )≤1.2, 〖1.23.1, 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).