Corresponding author: L. Bardini, Department of Environment, Land and Infrastructure Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy. (firstname.lastname@example.org)
 Aquatic sediment hosts coupled pore water flow and biogeochemical reactions that mediate water quality across the fluvial corridor including adjacent alluvial aquifers. However, the effect of small-scale variations in sediment hydraulic properties on nutrient transformation occurring within the sediment is poorly understood. We show through numerical flow and transport simulations, for two realistic heterogeneous permeability cases typical of lowland rivers and two idealized homogeneous ones, that there is little difference in the reactive transport fields, the bulk reaction rates, and nutrient sink/source function despite stark differences in flow fields. This is because the reactions are ultimately controlled by characteristic or bulk residence times that are similar for the heterogeneous and homogeneous cases. This is a promising result for predictive models based solely on relative ratios of residence times and reactive time scales.
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 Water and solute exchange across the riverbed plays a fundamental role in the ecology and quality of fluvial environments [Findlay, 1995; Alexander et al., 2000; Battin et al., 2008; Bottacin-Busolin et al., 2009]. The transport processes occur at different spatial scales in response to variations in discharge, ambient groundwater flow, bed topography, and permeability. The flow exchange zone between surface water and groundwater (hyporheic zone) typically hosts intense biogeochemical activity. Thus, stream-borne chemicals entering the hyporheic zone are subject to biogeochemical transformation before returning to the river, and their fate is controlled by the interplay of both hydrological and biochemical processes [Smith et al., 2008]. For this reason, a good knowledge of hyporheic exchange processes is essential for the assessment of chemical zonation and nutrient transformation in the fluvial environment.
 Some researchers have investigated the interactions between hydrodynamical and biogeochemical processes in the hyporheic zone [e.g. Boano et al., 2010; Bardini et al., 2012; Gomez et al., 2012; Kessler et al., 2012; Zarnetske et al., 2012], assuming homogeneous permeability conditions for the sediments. Only a small number of works have studied the role played by sediment heterogeneity on hyporheic exchange [Cardenas et al.2004; Marion et al.2008; Salehin et al.2004; Sawyer and Cardenas, 2009], but they did not take into account the biogeochemical reactions. Therefore, understanding the impact of sediment heterogeneity on both advective and dispersive fluxes and hyporheic chemical reactions has been elusive.
 The aim of this work is to investigate the effect of sediment heterogeneity on reactive solute spatial distribution in a rippled riverbed, by taking into account both hydraulic and biochemical processes. The cross-bedded sediments examined here are typical of lowland rivers, with no armoring layers. To isolate the effects of heterogeneous permeability fields on reactive transport, we do not consider heterogeneity in solid sediment chemistry such as organic matter content. We considered two different bed form configurations and compared the numerically simulated chemical distributions resulting from the heterogeneous permeability fields with two equivalent anisotropic homogeneous cases. We focused on four compounds: dissolved organic carbon (DOC), oxygen, nitrate, and ammonium, which are among the most important substances for stream ecology.
2 Permeability Data Sets
 We considered two permeability (κ) fields from the Brazos River and the Massillon Sandstone (USA). The first data set was created by Sawyer and Cardenas  from an image of climbing ripple deposits of the Brazos River near Wallis in Texas. These sediments are ripple-laminated and bimodal in composition (Figure 1a). The ln (κ) values range between − 27.5 and − 22.9, typical of sand and organic-rich silt, with a variance of one.
 The Massillon conductivity field resulted from high-resolution direct permeability measurements conducted by Tidwell and Wilson  on a two-dimensional face of a block from the Massillon Sandstone in Ohio. The structure is composed of cross-stratified sets bounded by subhorizontal, undulatory to planar surfaces, and it is moderately well sorted (Figure 1b). To correct for permeability reduction due to diagenetic alterations, we uniformly scaled the permeability values by a factor of 10 [Sawyer and Cardenas, 2009]. The final ln (κ) varies between − 26.4 and − 23.7 values, characteristic of sands, with a variance of 0.15.
 The two data sets are representative, respectively, of moderate and mild variation in permeability. The ln(κ) variances are small compared to others measured or simulated in previous studies of heterogeneous fluvial sediments at larger spatial scales [e.g. Genereux et al., 2008; Kalbus et al., 2009]. Instead, we consider a permeability structure at the smaller scale of fluvial bed forms and corresponding to a single depositional facies.
 From the heterogeneous permeability fields, we obtained the equivalent homogeneous anisotropic permeability tensors κB (for Brazos) and κM (for Massillon) by applying the method of Durlofsky 
These permeability tensors were used to compare solute dynamics in the hyporheic zone in equivalent homogeneous conditions.
3 Biogeochemical and Hydraulic Model
 The sediment-water interface was shaped in order to represent a rippled riverbed, with three two-dimensional repeating bed forms, triangular in shape. Bed form size differed for Massillon and Brazos cases (Table 1), while the length to height ratio was kept constant. A Cartesian reference system was adopted, with x and y as the streamwise and upward coordinates, respectively, and the axis origin was placed at the first ripple trough.
Table 1. Geometrical and Hydraulic Model Parameters
Bed form length L (m)
Bed form height h (m)
Mean stream velocity U (m/s)
Stream depth d (m)
Porosity θ (-)
Longitudinal dispersivity αL (mm)
Transverse dispersivity αT (mm)
Molecular diffusion coefficient Dm ( m2/s)
5 × 10 − 11
5 × 10 − 11
 We considered four chemical compounds, that is, DOC, oxygen, nitrate, and ammonium, and three biochemical reactions: aerobic respiration (CH2O + O2 →CO2 + H2O), denitrification +2N2 + 7H2O), and nitrification + 2H+ + H2O). The overall reaction rates were
where kDOC is the DOC decay constant, kn is the second-order nitrification molar rate coefficient, CDOC, , , and are the molar concentrations of DOC, oxygen, nitrate, and ammonium, respectively, and are the molar limiting concentrations for oxygen and nitrate. The latter ones define the concentration under which aerobic respiration and denitrification rates become linearly proportional to and , respectively. Denitrification can start only when oxygen concentration is lower than the limiting value . The influence of pH variation on reaction kinetics was considered negligible, due to the buffering capacity of other chemical processes occurring in the hyporheic zone.
 The overall reaction rates were coupled with the hyporheic advective flow field q and the hydrodynamic dispersion tensor D in order to define the solute reactive transport equations in steady state conditions
where θ is the sediment porosity, Rs is the consumption/production rate of the compound s, Cs is the molar concentration of the chemical s, and D is the hydrodynamic dispersion tensor with components
where i,j = x,y, αL and αT are the longitudinal and transverse dispersivities, Dm is the molecular diffusion coefficient in the porous medium, and δij is the Kronecker's delta. The steady state advective flow in the sediments q was simulated by solving the groundwater flow equations
where γ is the specific weight of water, μ is the dynamic viscosity of water, κ is the permeability tensor, h is the hydraulic head, and q = (qx,qy) is the Darcian velocity vector. For a more detailed explanation of the model equations (3)-(11), see Bardini et al. .
 Lateral boundaries were periodic in both head and concentration, with a prescribed head drop representing the river slope. The lower boundary was assigned a no-flow condition for fluid and solute. On the upper boundary, we prescribed a constant concentration value (i.e. the in-stream concentration) at inlet zones and a negligible dispersive flux at outlet zones. Head along the top boundary was estimated by Sawyer and Cardenas  through open channel flow simulations, by numerically solving, in steady state conditions, the Reynolds-Averaged Navier-Stokes equations for incompressible and homogeneous fluids, with the k − ω closure scheme (for further details, see Cardenas and Wilson ).
 The governing equations of the biogeochemical model were numerically solved in Comsol, a generic multiphysics finite element solver, with adaptive meshing and error control. For both Brazos and Massillon cases, we considered two opposite chemical conditions: a polluted one, with higher in-stream solute concentrations (CDOC = 60mg-C/L, = 10 mg/L, mg/L, mg/L), and a pristine one, with lower in-stream solute concentrations (CDOC = 2 mg-C/L, = 10 mg/L, mg/L, mg/L). The physical and hydraulic parameters used in the simulations are listed in Table 1. Since the aim of the work was to investigate the effect of permeability heterogeneity on hyporheic flow and reactions, we compared the results of simulations with heterogeneous and equivalent homogeneous permeabilities for both Brazos and Massillon cases.
 Sediment heterogeneity affects the advective flow field in both Brazos and Massillon cases (Figures 1-3). In general, permeability heterogeneity produces more irregular flow cells within shallow sediments, promotes deeperexchange, and longer path lengths. Details on the flow behavior and implications for conservative solute transport are available in Sawyer and Cardenas .
 Inspection of the streambed chemical zonation shows marginal effects of sediment heterogeneity in both the Brazos and Massillon sediments, as shown in Figures 2 and 3 for the polluted stream case. Results for the pristine case (see Figures 4 and 5 in the Supporting Information) are analogous. Concentration fronts are quite similar in size and shape for heterogeneous and homogeneous permeability conditions. The main reason is that, despite the relevant variations in fluid flow paths, the residence time distributions are fairly similar for these cross-bedded heterogeneous sediments and their equivalent homogeneous media [Sawyer and Cardenas, 2009]. This finding is also confirmed by the net solute removal/production rates in the streambed (Tables 2 and 3). The reaction rate differences between homogeneous and heterogeneous conditions are higher in the Massillon sediments (almost 20 % for nitrate), with the exception of DOC, which varies the same amount (10 %) in all cases. In general, these results indicate that bed form scale heterogeneity typical of lowland rivers does not dramatically alter nutrient reactions in both the Brazos and the Massillon cases.
Table 2. Solute Reaction Rates for Heterogeneous and Homogeneous Brazos River Sediments in the Pristine and Polluted River Cases. Positive and Negative Values are Indicative of Net Solute Production and Removal, Respectively. The Relative Variations of Net Rates in Heterogeneous Conditions Compared to the Equivalent Homogeneous Conditions are Also Reported
Heterogeneous Case Rates mg/(m · s)
Homogeneous Case Rates mg/(m · s)
Rate Difference %
− 1.46 × 10 − 5
− 1.63 × 10 − 5
− 4.22 × 10 − 5
− 4.67 × 10 − 5
+ 3.12 × 10 − 6
+ 3.05 × 10 − 6
− 9.06 × 10 − 7
− 8.85 × 10 − 7
− 4.38 × 10 − 4
− 4.90 × 10 − 4
− 2.67 × 10 − 4
− 2.47 × 10 − 4
− 1.14 × 10 − 4
− 1.05 × 10 − 4
− 2.28 × 10 − 5
− 2.08 × 10 − 5
Table 3. Solute Reaction Rates for Heterogeneous and Homogeneous Massillon Sandstone Sediments in the Pristine and Polluted River Cases. Positive and Negative Values are Indicative of Net Solute Production and Removal, Respectively. The Relative Variations of Net Rates in Heterogeneous Conditions Compared to the Equivalent Homogeneous Conditions are Also Reported
Heterogeneous Case rates mg/(m · s)
Homogeneous Case Rates mg/(m · s)
Rate Difference %
− 4.61 × 10 − 5
− 5.16 × 10 − 5
− 1.30 × 10 − 4
− 1.46 × 10 − 4
+ 6.84 × 10 − 6
+ 8.15 × 10 − 6
− 1.99 × 10 − 6
− 2.37 × 10 − 6
− 1.38 × 10 − 3
− 1.55 × 10 − 3
− 5.27 × 10 − 4
− 6.17 × 10 − 4
− 2.41 × 10 − 4
− 3.00 × 10 − 4
− 4.44 × 10 − 5
− 5.24 × 10 − 5
 The role of the streambed in nutrient transformation appears to be fairly influenced by water fluxes across the sediment-water interface. The heterogeneous Massillon case has slightly lower water fluxes across the sediment-water interface than equivalent homogeneous case [Sawyer and Cardenas, 2009], and all reaction rates are correspondingly slower (Table 3). The influence is less evident for Brazos sediments, where the slight increase of hyporheic flux in heterogeneous conditions [Sawyer and Cardenas, 2009] corresponds, on the one hand, to an increase of nitrate and ammonium reaction rates and, on the other hand, to a decrease of DOC and oxygen rates (Table 2). This behavior indicates an influence, albeit small, of the structure of the flow field.
 Another important consideration is the effect of river water quality on the role of the streambed in nitrogen cycling. For example, the pristine river configurations lead to a net nitrate production, as confirmed by the positive values of the nitrate reaction rates in the sediments for both the heterogeneous and homogeneous conditions (Tables 2 and 3). In fact, the low DOC concentrations limit the aerobic respiration rate and maintain higher oxygen concentrations than the limiting value for denitrification. Thus, nitrate is not removed by denitrification and is produced by nitrification, and its concentrations increase with depth (see Figures 4 and 5 in the Supporting Information). Therefore, in this case where nutrients are relatively scarce, the sediments represent a nitrate source.
 In contrast, the polluted river configurations lead to a net nitrate removal, as shown by the negative nitrate reaction rates. Nitrate concentration increases with depth in the shallower layers of the sediments, where nitrification prevails, and it decreases below a specific depth, where denitrification prevails, until being completely consumed (Figures 2 and 3). The interaction between nitrification and denitrification rates in the whole domain eventually results in a nitrate sink behavior of the riverbed. This last result differs from the one presented by Bardini et al. , who found a nitrate source behavior for the same in-stream concentrations as in the polluted river configuration but with bed forms of larger size. The explanation of this difference is that the larger bed forms enhanced water exchange through the streambed, with higher oxygen influxes to the sediments, preventing denitrification. This comparison further confirms that nutrient fate in streambeds is controlled by nontrivial and nonlinear interactions among water chemistry, transport processes, and microbial reactions.
 Though flow fields in both Brazos and Massillon sediments are altered by moderate permeability heterogeneity, solute reaction rates and concentrations in riverbed sediment are similar. Thus, sediment hetereogeneity at the bed form scale does not strongly influence streambed nutrient dynamics.
 These results are coherent with those of Sawyer and Cardenas , who found that permeability heterogeneity induced moderate differences in the distributions of residence times despite relevant variations in water flow paths. Thus, residence times are a better indicator and predictor of subsurface reactions than pore water flow patterns, at least in the case of homogeneous solid sediment biochemistry. This supports the proposed approach by Zarnetske et al.  and Gomez et al.  of using primarily the ratio of characteristic residence and reaction times to predict the biogeochemical role and regime of aquatic sediment.
 The pristine river case, with low in-stream nitrate and DOC concentrations, proved to induce a net nitrate production in the sediments, while the polluted one led to a net nitrate removal. The same nitrate sink/source behavior was found for heterogeneous and homogeneous conditions, suggesting that variations of permeability at the bed form scale do not measurably alter the role of streambeds in nutrient cycling. This is fortunate because adequate representation of nitrogen cycling in shallow streambed sediment is possible without detailed information about the small-scale permeability structure.
 The PhD project of L. B. was funded by the Italian Ministry of University and Research (MIUR). M. B. C. was supported by a National Science Foundation CAREER Grant (EAR-0955750). We thank the Editor, Paolo D'Odorico, Andrea Marion, and an anonymous Reviewer for their accurate and constructive comments.