Bioavailable forms of nitrogen (N), such as nitrate (NO3), are necessary for aquatic ecosystem productivity, and the availability of this reactive N often limits ecosystem productivity [Jones and Holmes, 1996]. However, human alterations to the global N budgets have more than doubled the supply of reactive N over the last century which in turn has caused increasingly negative impacts on water quality and aquatic ecosystems (e.g., biodiversity loss [Sala et al., 2000], water quality degradation [Smith, 2003], accelerated global carbon and N cycling rates [Gruber and Galloway, 2008], and increased hypoxic events [Diaz and Rosenberg, 2008]). Streams are particularly important locations in the landscape for the reactive N cycle, because they integrate many N sources and control N export to downgradient systems via internal N source and sink processes (e.g., mineralization of organic forms of N and denitrification of NO3, respectively). Consequently, there is a need to determine the key factors controlling sources and sinks of reactive N in stream ecosystems. Unfortunately, N transformations in aquatic ecosystems are typically complex and couple multiple N species in both space and time. Thus, it is difficult to predict if a particular component of an aquatic system will function as a net source or sink, and over what critical temporal and spatial scales it will function. In this study, we focus on how and why stream–groundwater (hyporheic, HZ) interactions are important for coupled N transformations in stream systems, and how they function as both a source and a sink of NO3 to downgradient aquatic systems.
 HZs are locations in the streambed and adjacent surficial aquifers where stream and groundwater mix. HZs are known to be important locations for N transformations in streams [e.g., Duff and Triska, 1990; Holmes et al., 1994] because they contain strong hydrologic and biogeochemical gradients [Jones and Holmes, 1996; Baker et al., 2000a]. These gradients lead to different redox conditions, which in turn control the conditions under which many biogeochemical reactions can occur [Hedin et al., 1998]. In particular, redox conditions control where and when nitrification and denitrification can occur. Both nitrification and respiratory denitrification are facilitated by microbes. Nitrification represents the chemoautotrophic oxidation of NH4 to NO3 and thus is a source of NO3 to aquatic ecosystems. Denitrification, on the other hand, is the reduction of dissolved NO3 to dinitrogen gas (N2), which can subsequently return to the atmosphere (Table 1). Denitrification is a particularly important N transformation in streams, because it represents the one true sink of NO3 in aquatic ecosystems. Therefore, there is much interest in identifying when and where denitrification will be the dominant fate of NO3 versus when and where NO3 production via nitrification will dominate in a system.
|Reaction Processes||General Stoichiometric Reaction Equation||Free Energy ΔG0b (kJ mol−1)|
|Aerobic Respiration||CH2O + O2 → CO2 +H2O||−501|
|Nitrification||O2 + (½) → (½) + H+ + (½)H2O||−181|
|Denitrification||CH2O + (4/5) + (4/5) H+ → (7/5) H2O + (2/5) N2 + CO2||−476|
|Microbial Uptakec||5CH2O + + → C5H7NO2 + 4H2O + CO2|
 There are both physical and biogeochemical conditions of HZs that regulate N biogeochemistry. The physical factors regulate the supply rate of solutes and include advection, dispersion, hydraulic conductivity, and flow path length. These physical conditions determine the solute flux through the HZ and the characteristic residence time distributions of the water and solutes in the HZ. The biogeochemical factors are oxygen (O2), labile dissolved organic carbon (DOC), dissolved organic nitrogen (DON), inorganic nitrogen (NH4 and NO3), temperature, and pH. Most nitrifying microbes require O2 and NH4, while denitrifiers require anoxic conditions, a DOC source to serve as an electron donor, and a supply of NO3 to serve as an electron acceptor [Hedin et al., 1998; Baker et al., 2000b]. In many systems, nitrification and denitrification are tightly coupled because nitrification consumes O2 while producing NO3, and both anoxic conditions and NO3 availability will stimulate denitrification [e.g., Duff and Triska, 1990, Holmes et al., 1996; Sheibley et al., 2003] as long as there are sources of labile DOC available [e.g., Sobczak et al., 2003; Zarnetske et al., 2011b]. Natural heterogeneity in streams leads to unique combinations of both the physical and biogeochemical conditions which in turn result in unique N source and sink conditions. This heterogeneity makes it hard to identify a priori the function of an HZ, so it is important to identify and account for the key components of the HZ N cycle.
 The meta-analysis bySeitzinger et al.  and recent experimental and modeling studies [e.g., Zarnetske et al., 2011a; Marzadri et al., 2011; Bardini et al., 2012] showed that net nitrification and denitrification are coupled and related to residence time in the HZ, where net nitrification dominates short residence times and net denitrification dominates long residence times. There are also a growing number of numerical modeling studies of groundwater–surface water exchange that have focused on how the physical sediment and hydrodynamic conditions can regulate NO3flux and transformations across two-dimensional (2-D) HZ features (e.g., bed forms and meander bars). For example,Cardenas et al.  and Boano et al.  showed that varying these physical transport conditions can change the biogeochemical zonation of where specific redox conditions occur in the subsurface, including NO3 reduction. Expanding on these modeling studies, Marzadri et al.  and Bardini et al.,  showed that varying only the physical transport can shift a streambed from net nitrification to net denitrification system and that the hydrologic variability may be more important than reaction substrate (DOC and NO3) variability.
 Theoretically, linking NO3dynamics to residence time helps simplify some of the above-stated complexities in the biogeochemical substrate limitations while offering an explanation as to why previous field studies of HZ NO3 dynamics showed inconsistent HZ functioning—as either a source of NO3 via nitrification or a sink of NO3 via denitrification. For example, Holmes et al. showed that short residence time oxic HZ flow paths within a desert N-limited stream function as net nitrification systems, while much longer residence time anoxic HZ flow paths of a more temperate N-rich river function as a net denitrification system [Pinay et al., 2009]. Larger-scale synoptic sampling of spatially diverse stream ecosystems also shows heterogeneity in whether the stream sediment functions as a net source or sink of NO3 given catchment setting and land use type [Inwood et al., 2005; Arango and Tank, 2008]. Accounting for the differences in residence time should collapse some of the variability seen between these systems with respect to HZ N source-sink processes [Seitzinger et al., 2006, Zarnetske et al., 2011a; Marzadri et al., 2011, Bardini et al., 2012].
1.2. Objectives and Conceptual Framework of Study
 Our goal is to construct a general but practical theoretical framework to predict the NO3 source and sink potentials of a given stream HZ. To do this we need to identify the fundamental subset of physical and biogeochemical factors controlling N transformations in HZs (see section 1.1 for factors). The theoretical studies discussed above clearly illustrate that variability in the hydrologic kinetics play an important role in determining the HZ function as a source or sink of NO3. Field and laboratory studies show that N reaction kinetics are controlled by the availability of terminal electron donors (labile DOC) and acceptors (O2 and NO3) and environmental factors such as temperature and pH. Representing all of these hydrologic and reaction kinetics in numerical models is possible; however, it is less feasible and practical to do so when scaling HZ function across a river system or making comparisons between several different HZs. Clearly there is a need to develop a minimally parameterized, scalable model to make robust predictions about the net source or sink function of HZs in streams.
 We hypothesize that the net source or sink function of a HZ will be primarily a function of the characteristic residence time scales of water and solute in the HZ and the characteristic reaction (uptake) rate time scales of O2. In other words, the potential function of an HZ as a source or sink of NO3 will be primarily controlled by the supply and demand rates of O2, because O2 controls the redox conditions which regulate where and when nitrification and denitrification occur [Seitzinger, 1988; Hedin et al., 1998]. Dissolved oxygen is critical to this hypothesis because it is known that O2 availability in saturated sediment strongly inhibits denitrification [e.g., Terry and Nelson, 1975; van Kessel, 1977; Christensen et al., 1990], but when O2 becomes scarce, NO3 is thermodynamically favorable as the terminal electron acceptor (Table 1 [Champ et al., 1979; Hedin et al., 1998]). Furthermore, we focus on the O2 uptake (respiration) rate because it is regulated by the labile DOC availability in the system, where low labile DOC availability will limit O2 respiration rates [Pusch and Schwoerbel, 1994; Baker et al., 2000b]. Oxygen uptake rate is also a function of temperature and pH conditions [Stumm and Morgan, 1981; Hedin et al., 1998]. Therefore, O2 uptake rates subsume some of the complex dynamics of labile DOC and other physiochemical conditions in a system. Additionally, the logistics of directly measuring or modeling water residence times and oxygen dynamics in HZ systems is easier than that of NO3 and DOC (e.g., field and experimental tracer tests, groundwater flow models, and O2 measurement instruments). Consequently, we hypothesize that the Damköhler number for O2, DaO2 (the ratio of O2 reaction rate time scales to water residence time scales) in an HZ system will be a good indicator of the potential for the HZ to function as a net nitrification or denitrification location in the landscape. We define the Damköhler number for O2 as
where is the oxygen reaction rate (T−1), τ is the water residence time (T), and τ = L/v, L is the length of the flow path (L), and v is the mean advected water velocity (LT−1).
 The Damköhler number is a useful concept for hydrochemical processes that are a function of both transport and reaction rates, because it is a dimensionless number that compares the role of reaction and transport processes within and across systems [Boucher and Alves, 1959; Domenico and Scwhartz, 1998; Ocampo et al., 2006; Gu et al., 2007; Boano et al., 2010]. In particular, Ocampo et al.  and Gu et al.  showed that this approach is useful in relating dynamic denitrification rates to transport rates in groundwater environments. Similarly, the recent use of a Lagrangian framework for modeling reactive transport and redox conditions in river meander HZs showed that predictions of NO3 reduction rates (as well as SO4, CO2, and CH4 reduction) can be made by relating HZ transport time scales to reduction rate time scales [Boano et al., 2010]. However, no previous study has attempted to use this scaling approach to identify the net NO3 source and sink function, via net nitrification and denitrification, of HZs across variable transport and reaction conditions. Therefore, we expand on our hypothesis to explore different conceptual HZ conditions, including more complex biogeochemical reaction kinetics, and the resulting HZ functioning as a net nitrification or denitrification system. First we define the HZ function as a net source or sink by calculating the fraction change in NO3 mass FN, between the initial NO3 concentrations at the beginning Nin, and end of the HZ flow path Nout:
Thus, FN (0 < FN < ∞), where a net denitrifying system is (0 < FN < 1) and a net nitrifying system is (FN > 1). Next we can relate the FN to the of a system or flow path (Figure 1), such that we see the characteristic of an HZ will control the aerobic and anaerobic domains in the system, and therefore the domains over which net nitrification and denitrification occur. For example, net denitrification will be inhibited at values of < 1, because this region of a system is where the physical supply rate time scale of O2 (i.e., τ = L/v) is smaller than the demand rate time scale of O2 (i.e., and therefore will be oxic. This < 1 domain will promote nitrification if NH4 is present in addition to inhibiting denitrification. A value of = 1 represents a critical point in the system when the physical supply time scale is equal to the biological demand time scale, and therefore represents the point in a system where O2 is exhausted and anaerobic conditions will begin to influence the biogeochemical processes. Lastly, all values of > 1 represent points in a system where demand exceeds the supply of O2, and therefore will be anaerobic and have the potential to experience net denitrification if NO3 and labile DOC are present.
1.3. Approach of Study
 We used a numerical one-dimensional, multispecies, reactive N transport model to test the hypothesis and conceptual model (section 1.2 and Figure 1). The model was used to evaluate the coupling of physical transport conditions (advection, dispersion, and residence time) and biogeochemical redox conditions with modified Monod kinetics for O2, NH4, NO3, and DOC. We used a dimensionless form of the model to simulate O2, NH4, NO3, and DOC concentrations profiles for different hyporheic physical and biogeochemical conditions. Using this model we are able to evaluate the broad biogeochemical parameter space associated with substrate limitations on hyporheic N transformations not included in previous studies, while including the key physical transport parameters of advection and dispersion that govern solute transport in an HZs [Cardenas et al., 2008; Boano et al., 2010; Zarnetske et al., 2011a; Marzadri et al., 2011; Bardini et al., 2011].
 We used this model to conduct an extensive global Monte Carlo sensitivity analysis of possible model parameter combinations seen in the literature to evaluate the general NO3source-sink hypothesis and conceptual model shown inFigure 1. These Monte Carlo simulations explore a broad range of literature values and isolate the fundamental parameters governing the likelihood of simulating a net source or sink system as defined by the resulting values of FN.