Stream denitrification is thought to be enhanced by hyporheic transport but there is little direct evidence from the field. To investigate at a field site, we injected 15NO3−, Br (conservative tracer), and SF6 (gas exchange tracer) and compared measured whole-stream denitrification with in situ hyporheic denitrification in shallow and deeper flow paths of contrasting geomorphic units. Hyporheic denitrification accounted for between 1 and 200% of whole-stream denitrification. The reaction rate constant was positively related to hyporheic exchange rate (greater substrate delivery), concentrations of substrates DOC and nitrate, microbial denitrifier abundance (nirS), and measures of granular surface area and presence of anoxic microzones. The dimensionless product of the reaction rate constant and hyporheic residence time, λhzτhz define a Damköhler number, Daden-hz that was optimal in the subset of hyporheic flow paths where Daden-hz ≈ 1. Optimal conditions exclude inefficient deep pathways where substrates are used up and also exclude inefficient shallow pathways that require repeated hyporheic entries and exits to complete the reaction. The whole-stream reaction significance, Rs (dimensionless), was quantified by multiplying Daden-hz by the proportion of stream discharge passing through the hyporheic zone. Together these two dimensionless metrics, one flow-path scale and the other reach-scale, quantify the whole-stream significance of hyporheic denitrification. One consequence is that the effective zone of significant denitrification often differs from the full depth of the hyporheic zone, which is one reason why whole-stream denitrification rates have not previously been explained based on total hyporheic-zone metrics such as hyporheic-zone size or residence time.
 Hyporheic flow in streams brings stream water into close contact with the reactive surfaces of sediment grains and periphyton [Boano et al., 2010; Winter et al., 1998] and as a result, small streams tend to be hotspots for denitrification [Duff and Triska, 2000; Alexander et al., 2000] with the reaction occurring wherever nitrate can be delivered to reaction sites where microbial activity and redox conditions and availability of electron donors favor the reaction [Groffman et al., 2005; Hill et al., 1998; Holmes et al., 1994]. Labile organic carbon may be delivered with hyporheic flow in dissolved form [Kaplan and Newbold, 2000] or as fine particulates [Harvey et al., 2012]. Favorable conditions for denitrification tend to occur where algal communities are attached to rocks [Kim et al., 1990; Gooseff et al., 2004), in epiphyton layers on plant stems [Smith et al., 2006], or in streambed sediments [Holmes et al., 1996; Gu et al., 2007; Kaushal et al., 2008; Böhlke et al., 2009; Hubbard et al., 2010; Koch et al., 2010; Zarnetske et al., 2011a]. Field measurements often show a strong correlation between denitrification, labile organic carbon supply, and high sediment oxygen demand [Mulholland et al., 2008; Arango et al., 2007; Smith et al., 2006], with denitrification being strongly linked with DOC concentration in pore water [Kaplan and Newbold, 2000; Zarnetske et al., 2011b], which may have a source in rapid turnover from autotrophic production or in decomposition of particulate organic carbon [e.g., Groffman et al., 2005].
 Additional factors affecting the reaction include presence and persistence of oxic-anoxic interfaces [Kessler et al., 2012] or anoxic microzones in heterogeneous sediments [Strong and Fillery, 2002; Brandes and Devol, 1995]. The hyporheic flux of oxygen into the streambed has been shown to inhibit denitrification in algal canopies [Arnon et al., 2007] and in shallow hyporheic sediments [O'Connor and Hondzo, 2008]. Despite the effects of greater oxygen delivery, greater hyporheic flow tends to stimulate denitrification by combined effects of enhancing ancillary reactions such as nitrification [Jones et al., 1995; Duff and Triska, 2000] and aerobic decomposition that can supply substrates for denitrification [Mulholland et al., 2008; Findlay, 1995]. As a result of these complex interactions, some researchers find that denitrification may be concentrated near the entry point at the sediment-water interface [Hill et al., 1998; present study] whereas others find that denitrification may not begin immediately in hyporheic flow but instead be delayed until oxygen becomes sufficiently depleted [Holmes et al., 1996; Zarnetske et al., 2011a; Kessler et al., 2012] and, in ammonium dominated streams, until sufficient nitrate is produced by nitrification [Jones et al., 1995; Duff and Triska, 2000].
1.1. Challenge of Connecting Flow Path-Scale Processes to Reach-Scale Consequences
 Most stream reach-scale assessments of biogeochemical reactions are based on in-stream tracer injections [Mulholland et al., 2008] or mass balance approaches [Seitzinger et al., 2006], and these generally do not identify the specific mechanisms or reaction sites (e.g., hyporheic, algal canopies, in-channel transient storage) that are involved [Hall et al., 1998; Ensign and Doyle, 2006]. Flow path-scale studies in the hyporheic zone support increased delivery of potentially limiting reactive substrates and increased contact area and contact time with microbially active sediments [Briggs et al.,2013; Lautz and Fanelli, 2008; Hedin et al., 1998; Baker et al., 1999], which potentially enhances whole-stream denitrification [Groffman et al., 2005; Cook et al., 2006; O'Connor et al., 2006]. Fine-scale biogeochemical processes have been linked to reach-scale consequences by field-based experimental comparisons [e.g., Ensign and Doyle, 2005, Argerich et al., 2011], and by matching timescales of hydrologic and chemical responses across spatial scales [e.g., Mulholland et al., 1997, Hall et al., 1998, Thomas et al., 2003, Gooseff et al. 2004]. However, few field studies have made direct linkages between flow path-scale measured biogeochemical reactions and whole-stream significance (except see Harvey and Fuller ).
 A useful way to view interactions between hydraulic and biogeochemical factors in hyporheic zones is from a dual perspective that considers (1) limitations imposed on reaction progress in hyporheic flow and (2) significance of hyporheic reactions to whole-stream chemical budgets. Theoretical studies support the importance of hyporheic flow on denitrification [Bardini et al., 2012; Boano et al., 2010; Gomez et al., 2012; Marzadri et al., 2011; Cardenas, 2008], often using a dimensionless Damköhler number that contrasts timescales of transport and reaction [e.g., Ocampo et al., 2006]. Denitrification is reaction limited if the timescale of hyporheic exchange is faster than the reaction timescale. Denitrification is transport limited if the timescale of transport is slower than the reaction timescale. Intrinsic sedimentological and microbiological factors limit denitrification in the reaction limited case and hydrologic flux limits denitrification in the transport limited case. Both cases may be affected by substrate depletion if the demand for reaction substrates (e.g., NO3− and labile organic carbon) are not met by hydrologic resupply. In those situations, the substrate concentrations decrease with time causing the reaction rate to slow substantially. Slowing of the reaction rate often may begin before the reaction becomes transport limited. In addition to being caused by substrate depletion, a reaction rate that slows with time also could be caused by subsurface transport into a zone with less favorable sedimentary conditions (e.g., low sediment surface area or low activity of microbial denitrifier community). Eventually, the reaction timescale either slows so much that the reaction rate becomes insignificant or a key substrate becomes exhausted after which the reaction ceases altogether. Any further subsurface transport contributes to physical storage but not to reaction progress.
 From a mass balance (N flux) perspective, denitrification tends to be most important where the transport and reaction timescale are relatively well matched (but before the effects of substrate depletion begin to occur). Under those conditions, the reaction rate remains as high as possible throughout the duration of subsurface transport, which maximize reaction flux [McClain et al., 2003]. The significance of hyporheic reactions to the stream as a whole also depends on the flux of stream flow through the hyporheic zone relative to stream discharge [Harvey and Fuller, 1998; Findlay, 1995]. The styles of reaction limitation in hyporheic flow paths and their consequences for reach-scale significance of those reactions are illustrated in Figure 1.
 Modeling of denitrification in hyporheic flow is hampered by a general lack of field data that directly quantify hyporheic exchange and associated subsurface biogeochemical reactions and determine both their vertical distribution and their overall contribution to whole-stream denitrification. Consequently, there is little understanding of the overall role of hyporheic flow in whole-stream denitrification or the specific types of hyporheic zones (e.g., hyporheic flow beneath the midchannel with coarser sediments or beneath marginal areas with finer sediments) that increase its importance. The present study addresses the need for greater understanding of the role of hyporheic processes through detailed subsurface sampling conducted simultaneously with an in-stream injection of an isotopically labeled nitrate tracer.
 The study goal was to determine contributions of hyporheic flow in different geomorphic subunits and to characterize controls on their overall contributions to whole-stream denitrification. We examined the influence of specific variables such as hydrologic flux, grain size, organic carbon content, microbial denitrifier abundance, and other factors affecting denitrification rate. Field observations provided rates and controlling factors as they varied in shallower versus deeper hyporheic flow in each geomorphic unit. We showed that differing combinations of local hydraulics and biogeochemical characteristics in these geomorphic units each can contribute substantially to whole-stream denitrification. We found that the effective zone of significant denitrification often differs from the full depth of hyporheic flow, illustrating an important reason why generic hyporheic and transient water-storage metrics have not usually been successful as predictors of nutrient transformations. This research provides a strong basis for evaluating controls on denitrification, which has the potential to inform design criteria for stream management and restoration [Hester and Gooseff, 2010].
2.1. Site Description
 The research was conducted in first and second order reaches of Sugar Creek, a headwater stream in northwestern Indiana that is a part of the Iroquois, Illinois, and Mississippi River basins (Figure 2). Sugar Creek is an incised stream that historically was ditched and straightened to increase drainage of the relatively flat and loamy topsoil in western Indiana to support intensive corn and soybean agriculture. The stream's width varied between 1 and 5 m with depths ranging between 0.05 and 0.4 m and stream velocities ranging from near zero to 40 cm s−1. The average depth was 17 cm and the average velocity was 8 cm s−1 Riparian areas were very limited as a result of the stream's confinement at the base of steep “engineered” banks. Shrubs and sapling trees were periodically removed every decade or so over the past century by a combination of dragline and mowing. The stream was fully exposed to light and wind except for early morning or late afternoon shading and wind protection provided by banks.
 The dominant large scale roughness features in Sugar Creek were riffles created by bank collapses that narrowed the stream. Riffles were spaced approximately 100 m apart. Between the riffles were “runs” with more slower and more uniform flow. Along the runs the edges of the stream had undulating side cavities where stream flow was separated from the faster flow. Flow within side cavities was in a slowly rotating gyre pattern [Jackson et al., 2013] that contributed to the energy causing turbulent transfer between side cavities and the main flow [Ensign and Doyle, 2005]. Side cavities also were the focal point for groundwater discharge to the channel as well as locations where longer “parafluvial” hyporheic flow paths beneath the bank undulations occurred [Stonedahl et al., 2012] (Figure 2).
 The important “small” topographic features on the Sugar Creek streambed are small roughness features on the bed associated with current-driven hyporheic flow. Occasional cobbles exposed 3–5 cm above the surrounding bed cause pressure variations on the bed on the upstream and downstream sides that promote hyporheic flow. At a slightly larger scale, submerged sand/gravel bars have a similar height (3–5 cm above the bed) and typically had a wavelength of 20 cm. The streambed itself is composed of a heterogeneous mixture of sand, gravel, and pebbles eroded from exposed banks of loam and glacial sediments. Sugar Creek has a median grain size of 1500 μm, which is representative of coarse sand. On top of the sand, gravel, and cobble bed was usually a thin layer of fine particulate mineral and organic material derived from allochthonous vegetation, streambed periphyton, and filamentous algae that settled to the bed between storm periods. The fine layer on the streambed was thickest in the marginal areas of the channel (0.3–1 cm), especially in side cavities at the channel sides protected from highest flow velocities. Elsewhere, the fine layer was very thin (<0.3 cm) or was intermixed with coarser gravel and pebbles, as in central channel areas with relatively high velocity. The underlying sand, gravel, and pebble layer was 30–50 cm thick but was as thin as 15 cm and as thick as 1 m in some areas. Below these fluvial deposits were relatively thin units of clay, organic-rich sediments, and discontinuous carbonate-cemented hard layers.
 It is important to mention that Sugar Creek is similar to headwater streams in many agricultural areas in the midwestern U.S. Nitrate dominates N load in upper midwestern streams although organic N may be slightly more important in many other streams and rivers [Scott et al., 2007]. Thus in our study, denitrification was poised to occur in streambed sediment without requiring substantial nitrification. Also, riparian trees were thinned in our study area as they are in many agricultural landscapes. Absence of canopy promoted high levels of in-stream primary production that could supply labile organic carbon at the sediment interface [Tobias et al., 2007; Tobias and Böhlke, 2011]. In addition, the heterogeneous grain size distributions of channel beds in the upper midwestern U.S. basins produce streambeds with moderately high hydraulic conductivity (6.3 × 10−2 cm s−1) [Stonedahl et al., 2012]. Thus, they permit vigorous hyporheic flow while also having sufficient fine sediment with high surface area that provides physical substrate that supports high activity of microbial denitrifiers and anoxic microzones. Such characteristics are common among agricultural areas of the midwestern U.S., including removal of riparian canopies, which is also an increasingly common management practice in urbanizing areas.
2.2. Experimental Overview
 We injected conservative and reactive solutes directly into two subreaches of Sugar Creek, Benton County, Indiana, in September 2001 and September 2003. The injections occurred in late summer when nitrate concentrations (70 and 150 μmol L−1, respectively) and stream flows (40 and 50 L s−1, respectively) were near their annual minima and suspended sediment loads were low. Bromide, SF6, and 15N-enriched nitrate (15N[NO3−]) were coinjected into streamflow at steady rates lasting 7 h in the 2001 experiment and 12 h in the 2003 experiment.
 The concentrations of tracers in the stream reached plateau values at the upstream sampling stations of around 59 and 152 μmol L−1 for Br, and 15N mole fractions in NO3− (x15N[NO3−]) of approximately 0.020 and 0.043, respectively, for the 2001 and 2003 tracer experiments. The injections caused relatively little alteration of the total NO3− concentration (approximately 8% in 2001 and 14% in 2003). Details of the reach-scale tracer experiments are described elsewhere, including injection methods, analyses of stream water samples, and modeling of in-stream solute transport and reaction [Böhlke et al., 2004, 2009; Tobias et al., 2007, 2009].
 Here we analyze subsurface tracer data that were collected simultaneously with the in-stream tracer data. Simple reactive transport models are used to determine the denitrification rate and mass flux (section 3). Ancillary measurements were made of streambed water chemistry (Fe2+, NO3−, DOC, and DON), streambed physical properties (porosity, grain size, and particulate organic carbon (POC)), and abundance of the nitrite reductase (nirS) gene bearing denitrifier microbial community, all collected at the same depths in sediment where pore water tracers were measured. We calculated Pearson Product Moment correlation coefficients to determine the sign and strength of collinear relationships among hydraulic and sedimentary factors controlling denitrification. We then evaluated the relative importance of contributions of shallow and deeper hyporheic flow to whole stream denitrification, and used a Damköhler type analysis to classify denitrification either as reaction-rate limited or transport limited.
2.3. Subsurface Water Sampling Procedures
 During the in-stream tracer injections the tracers were sampled simultaneously at multiple depths in hyporheic flow paths by pumping small-volume water samples (5–10 mL) at low rates (1.5 mL/min) to determine hyporheic-zone water residence times and to quantify depth-dependent denitrification rates. The USGS MINIPOINT sampler collects shallow subsurface samples without disturbing the natural solute gradients in the subsurface [Harvey and Fuller, 1998]. For this study, we present subsurface data collected at two sites during the 2001 injection and four sites during the 2003 injection. Four of the samplers were emplaced in channel thalweg environments with coarser sediments and relatively fast-flowing surface water such as gravel bars, riffles, or runs. The other two samplers were emplaced within channel side cavities where flow was relatively slow moving and sediments were finer. One of the side cavity samplers was positioned to detect both the relatively immediate effects of shallow subsurface exchange and also the slower effects of longer hyporheic transport beneath the stream bank. At a gravel bar site, the sampler was positioned with one point in a thick canopy of filamentous algae growing on the gravel surface.
 At each MINIPOINT, we collected samples simultaneously at seven depths in the subsurface (typically −2.5, 1.5, 3, 5, 7.5, 11, and 15 cm). Pumping rates of 1.5 mL/min were below levels shown previously to maintain integrity of sampling without disturbing natural levels of hyporheic flow. Samples from all depths were collected in a time series throughout the experiment, beginning with four samples collected the day before the injection to represent background conditions. During the injections, the conservative tracer samples were collected every 5 min during transitions following the start and end of the injection, and at 10–30 min intervals at other times. Samples were also collected from 3/8″ (nominal o.d.) stainless steel piezometers inserted to depths of approximately 30, 60, and 90 cm below the streambed. Sampling for reactive tracers and ancillary water chemistry occurred approximately once per hour during the tracer experiment and approximately once per 4 or 6 h for several days afterward.
 Subsurface water samples for analysis of the conservative (Br−) and reactive tracer (15N[NO3−]) and ancillary chemical parameters were coincident with in-stream samples described by Böhlke et al. [2004, 2009] and Tobias et al. [2007, 2009] but were collected differently as noted below. At every time point, one bottle (6 mL) was collected from each depth for Br− analysis by MINIPOINT pumping. At selected time points, more samples were collected: one for anions and nitrogen species (Br−, Cl−, SO42−, NO3−, NO2−, NH4+, and TDN), one for dissolved gases and isotopes ([N2], [O2], [NO3−], 15N[NO3−], and 15N[N2], and one each for DOC and ferrous iron ([Fe2+]). The anion/nutrient samples were collected by filtering in line through 0.2 μM polyethersulfone filters into 20 mL HDPE scintillation vials that were immediately placed on ice and then moved to a freezer within 6 h. DOC samples were filtered through the same 0.2 μM filters into precombusted amber glass vials, acidified, and stored at 4°C until analysis. Dissolved Fe samples were filtered through 0.05 μM Nucleopore filters into 20 mL HDPE scintillation vials, acidified to pH 2 with 100 μL of H2SO4 and stored in the dark until analysis.
 Unlike the rest, the samples for dissolved gases and isotopes were collected unfiltered. The filters were temporarily removed from the tubing and replaced with syringe needles, which were inserted into He-flushed, 30 mL glass serum bottles fitted with 12 mm thick Bellco butyl rubber stoppers and aluminum crimp seals until the bottle was approximately half full, yielding a sample with He headspace at about 2 atm total pressure and about 15 mL of sample water. These bottles had been prepared in the laboratory before sampling by degassing the stoppers under vacuum overnight, injecting approximately 100 μL of 12 mol/L NaOH into the bottles (for preservation), inserting and crimping the stoppers, and then flushing the bottles with ultrapure He through inlet and outlet syringe needles for approximately 300 bottle volumes [Smith et al., 2006].
2.4. Water Chemical Analyses
 Frozen subsurface water samples were thawed and analyzed for Br−, Cl−, SO42−, and NO3− using standard ion chromatographic techniques (Dionex 100). Aliquots from the anion samples were also analyzed for NO2−, NOx (NO2 + NO3−), and NH4+ on a segmented flow autoanalyzer (Astoria SFA 3000) following standard colorimetric techniques. TDN was measured by first performing a persulfate digestion, followed by measuring the digested N (which is converted to NOx) on the nutrient analyzer. DON was calculated by subtracting the dissolved inorganic nitrogen from TDN. DOC was measured using a high-temperature combustion Shimadzu carbon analyzer. Ferrous iron was measured in the lab by the ferrozine method with absorbance measured on a spectrophotometer at 562 nm.
 For isotopic analysis, NO3− (+ NO2−) was converted to N2O by the denitrifier method (using Pseudomonas aureofaciens) and analyzed by continuous-flow isotope-ratio mass spectrometry (CFIRMS) [Sigman et al., 2001; Casciotti et al., 2002; Coplen et al., 2004]. Dissolved N2 was extracted from headspace samples, trapped in a closed loop, and then released in a He carrier stream through a mole sieve capillary gas chromatograph for isotopic analysis of the N2 peak by CFIRMS [Smith et al., 2006]. Argon (Ar) and oxygen (O2) peaks were also monitored to determine O2/Ar ratios and to detect problems with samples or analyses (e.g., leaks). O2/Ar ratios were compared to values in air-saturated water and Sugar Creek surface water as an indication of O2 depletion in the subsurface.
2.5. Streambed Sediment Characteristics
 After tracer sampling was completed the streambed sediments were cored to estimate the grain size distribution, porosity and organic carbon content in approximately the top 10–15 cm of the streambed. Replicate cores were collected from areas directly adjacent to the MINIPOINT set-ups. Coring was accomplished by pushing 20 cm long clear polycarbonate cylinders (nominally 0.048 m internal diameter by 0.00159 m wall) that had been sharpened at one end into the streambed. Stream water was added to fill any remaining headspace and cores were capped with butyl rubber stoppers and removed from the streambed. After removal, the cores were immediately extruded, sectioned into 1-cm increments, bagged, and placed on ice. If a layer of fine sediment was present at the top of the core it was removed to a separate bag, typically the top 0.3 to 1.0 cm of the core. Core samples were immediately returned to the field laboratory for weighing and subsampling for microbiological analysis (section 2.5.2). The remainder of the sample was shipped on ice to the laboratory, where samples were freeze dried and weighed again. Porosity was determined using dry weight and bulk volume of each core increment assuming a grain density of 2.65 g cm−3. The grain size distribution was determined by dry sieving samples through 1000, 500, 250, 125, and 60 μm diameter sieves on a Gilson Model SS-3 shaker and weighing each size fraction. Characteristic grain sizes were determined as indicators of the median grain size (D50) and the diameter of the 10th percentile weight fraction (D10). The latter grain size characterizes the finer sediment that fills in between the larger grains of pebbles and gravel, increasing granular surface area and decreasing the hydraulic conductivity of the bulk streambed sediment.
2.5.1. Particulate Organic Matter
 Organic carbon concentration was determined in streambed sediments using core samples after sieving. Sieved core samples were recombined into < 1000 μm fractions from which three replicates of each fraction were subsampled for elemental CHN analysis. Duplicate samples were acidified with concentrated HCl to extract inorganic carbon prior to analysis. All samples were analyzed on a Thermo Scientific/CE Elantech CHN analyzer and with use of a 6-point calibration curve based on readings of an atropine standard. All samples were run in triplicate and reported in units of percent carbon in dried sample by weight.
2.5.2. Microbial Denitrifier Abundance
 The nirS gene codes for an enzyme that is involved in the first committed step in denitrification (which produces a gaseous end product, NO). To measure nirS, we extracted DNA and purified it from subsamples of bagged core sections the evening of collection. Aliquots of the subsamples (0.5–1 gm) were extracted using the UltraClean Soil DNA Kit (MoBio Laboratories, Carlsbad, CA). To assess nirS bearing denitrifier abundance, quantitative PCR was performed on the purified DNA using the primers described in Hallin and Lindgren, 1999 (Flacd and R4cd) and the SYBR green Quantitect Kit according to the manufacturer's instructions (Qiagen, Inc., Solana, CA). PCR reactions were run on a MX3000P instrument (Stratagene, La Jolla, CA) with an annealing temperature of 55°C and a primer concentration of 0.6 μM. Standard curves were generated using a serial dilution of a plasmid containing the full length amplicon. A melting curve was performed to eliminate any nonspecific fluorescence from the calculation. The nirK gene also codes for the same enzyme as nirS in some bacteria but we determined that nirS was the dominant enzyme in this system and only the nirS data are discussed.
3. Transport and Reaction Equations
3.1. Equations for Hyporheic Flow and Reaction
 Subsurface transport and reaction were characterized using a two-end member mixing analysis similar to Fuller and Harvey , Harvey and Fuller , and Triska et al., . The hyporheic zone is defined as the subsurface volume that actively exchanges water and solutes with the stream, and that also may exchange water and solutes with deeper groundwater. At steady state, the hyporheic-zone water and solute balance for a conservatively transported solute is:
where Chz [M L−3] is the solute concentration in the hyporheic zone and Cs and Cg are end-member solute concentrations representing contributions from stream and ground waters, respectively. On the left side of equation (1) is the mass flux of solute exiting from the hyporheic zone [M t−1], which is balanced on the right side by mass fluxes entering the hyporheic zone from the stream above, Csqs, and from deeper groundwater below, Cgqg. Dividing each side of equation (1) by the hyporheic-zone flux, qhz [L3 L−2 t−1], defines the spatially averaged hyporheic-zone concentration and the mixing fractions that contribute:
where fs and fg are mixing fractions from surface water and groundwater, respectively, defined by: fs = qs/qhz and fg = qg/qhz and fs + fg = 1. For a potentially reactive solute in the hyporheic zone, equation (2) can be expanded:
where is the average hyporheic-zone concentration, and are the surface water and groundwater end-member concentrations of the potentially reactive solute, and is the mass concentration of the solute lost or gained by reaction in the hyporheic zone [M L−3]. Dividing by the hyporheic water residence time expresses the reaction rate (per unit volume of water; M L−3 t−1):
where τhz is the residence time of hyporheic water based on measurements described in section 3.3.
 To quantify the contribution of hyporheic zone reactions to whole-stream solute gains and losses, it is typical to express the reactions in terms of Uhz, a vertical mass flux of a constituent that is reacted after entering the hyporheic zone [M L−2 t−1]. The vertical reactant flux is computed as the hyporheic-zone flux, qhz, multiplied by mass concentration of solute that has reacted, , which is identical to the depth-integrated reaction rate multiplied by the depth-integrated volume of water stored in the hyporheic zone:
where dhz [L] is average depth of the hyporheic zone based on measurements described in section 3.3 and θ  is average porosity.
 A useful expression of the strength of a reaction that can be compared between different studies is a first-order reaction rate coefficient where the coefficient, λhz (1/h), is related to as follows:
where is defined as the expected concentration for nonreactive transport in the hyporheic zone. is calculated using equation (3), which accounts for the dilution effect of mixing between surface water and groundwater in the hyporheic zone (i.e., is set to zero). The reaction rate coefficient is solved for by rearrangement of equation (6):
 Insight about the factors limiting reaction progress is provided by a Damköhler number, i.e., the ratio between transport and reaction timescales (Tt/Tr), which was calculated for hyporheic flow as the ratio between hyporheic residence time (τhz) and reaction timescale (λhz−1):
 Values of the Damköhler number near one indicate that transport and reaction timescales are in balance, which theoretically supports maximal reaction flux. Values away from one suggest the following limitations on reaction: Dahz > 1 indicates transport limitation where substrates become limiting and Dahz < 1 indicates reaction rate limitation where intrinsic sedimentologic conditions are limiting.
 Reaction limitation may create subzones within hyporheic flow where reactions are active or inactive. Here we derive a relation between reaction limitation and an effective depth of reaction, dEff-hz [L], which may differ from the hyporheic zone's full depth. Effective depth of reaction can be estimated from the hyporheic-zone water flux, qhz [L3L−2t−1] by scaling for sediment by dividing by porosity and multiplying by the reaction timescale (λhz−1):
 The effective depth can be expressed as an “active” fraction of the hyporheic zone, fA-hz, by dividing both sides of equation (9) by hyporheic zone depth, dhz:
 Equation (10) demonstrates an inverse relationship between active fraction and reaction limitation. It is apparent that the active fraction is smaller than the full depth of the hyporheic zone if the reaction is transport limited, i.e., if the Damköhler number is <1. In that case, the inactive portion of the hyporheic zone contributes to additional storage time but not to additional reaction. When reaction-limited conditions prevail (i.e., Damköhler >1) the reaction occurs throughout the full volume of the hyporheic zone but the reaction does not progress substantially toward completion in one exchange between stream and hyporheic zone. fA-hz estimates the average number of times a water parcel needs to be exchanged with the hyporheic zone to remove the reactant from a water parcel (note therefore that fA-hz is not bounded between zero and one).
 The whole-stream significance of hyporheic-zone reactions is quantified by Rs [Harvey and Fuller, 1998], which combines dimensionless terms that quantify reaction progress in hyporheic flow, λhz τhz, with the proportion of stream discharge passing through the hyporheic zone in a stream reach of characteristic length, Lc:
where qhz and Qs are hyporheic-zone flux [L t−1] and stream discharge [L3 t−1], respectively, and u [L t−1], d [L], and w [L] are stream velocity, depth, and width, respectively, and Lc (L) is a characteristic stream reach length reflecting in-stream mixing characteristics [Rutherford, 1994]:
where β is a constant on the order of 1 to 10 for rough channels, and kz is the transverse dispersion coefficient. The transverse dispersion coefficient often is estimated as 0.23du* where u* is shear velocity estimated for steady uniform flow as where g is gravity and S is the energy slope (usually estimated as water surface slope or bed slope).
 The significance of hyporheic reactions in equation (11) follows a previous formulation of Harvey and Fuller  who expressed it as
where Ls is the turnover length of stream flow through storage flow paths such as hyporheic flow which is estimated as u/α where α is the rate constant for stream water flux through storage zones [Harvey and Wagner, 2000]. That formulation is identical to the one we used in the present manuscript when α is parameterized to represent hyporheic flow as .
 We used an estimate of in-stream mixing distance for the characteristic reach length in the equation for whole-stream significance of hyporheic reactions equation (11). The reason we used an estimate of in-stream mixing distance was because it scales comparisons using equation (11) between streams of vastly different sizes, which is a common purpose of dimensionless analysis. The in-stream mixing distance increases positively with increasing width, depth, and velocity of streams (see Rutherford  or see equation (12) in Harvey and Wagner ). Using it as a scaling term in equation (11) accounts for the fact that larger rivers require much greater transport distances than smaller streams to achieve well mixed conditions. Note however that other choices for characteristic reach length could be made. For example, to assess basin-scale significance of metal removal by hyporheic reactions, Harvey and Fuller  used a measured distance to the outlet of a watershed for Lc. Furthermore, in a comparison of nutrient spiraling across rivers of various sizes, Ensign and Doyle  used average river lengths for the various stream orders being compared. Those choices and others could easily be substituted for Lc in equation (11) to achieve desired comparisons.
3.3. Field Application of Analysis Equations to Isotopic Tracing of Denitrification
 The previous sections present general equations for characterizing transport and reaction of biologically or geochemically reactive solute in the hyporheic zone. The present section uses those equations to quantify hyporheic denitrification based on a 15NO3− isotopic injection into stream water with subsurface sampling at various depths below the streambed. At each measurement port of the MINIPOINT sampler in the streambed the fractions of surface water and groundwater were estimated from measurements of the conservatively transported solute tracer (bromide):
where Br denotes the concentration of bromide measured after tracer concentrations had plateaued. Subscripts denote either the measured concentration in the hyporheic zone (hz), or the end member concentrations of source waters such as surface water (s) entering the hyporheic zone from above or deeper groundwater (g) entering with a groundwater flux from below.
 The surface water end member that contributed to hyporheic flow was sampled by pumping stream water through the top port of the MINIPOINT which was situated 2.5 cm above the streambed. The “groundwater” end member was measured in the deepest sampling port of the MINIPOINT device unless bromide tracer was detected at that depth. When necessary we used samples that had been collected from one of three conventional 3/8″ stainless steel drive points emplaced approximately 30, 60, and 90 cm below the streambed. In such cases, the shallowest drivepoint that had no detectable bromide was selected as the groundwater end member.
 The hyporheic water residence time, τhz (t), was approximated as the median travel time of a conservative solute tracer from surface water to the subsurface sampling point. For a tracer injected at an upstream point in the stream, τhz was computed as the difference between the median arrival time of the bromide tracer at the intake of the subsurface MINIPOINT sample port and the median arrival time of tracer in the stream above the sampler. Median arrival times were estimated as times when concentration reached the 50th percentile relative to the eventual plateau concentration in the subsurface.
 To quantify denitrification we measured the production rate of 15N-labeled N2 from 15N-labeled NO3− in the hyporheic zone. During plateau conditions in these experiments, the labeled NO3− in stream water had δ15N values around 4600‰ (2001) and 11,000‰ (2003), providing good sensitivity for detection of the tracer in the reaction product N2 with relatively little change in NO3−. Following the form of equation (3), the concentration of labeled N2 tracer measured in the hyporheic zone is equal to:
where the previously undefined variables are: [N2] is measured nitrogen gas concentration at tracer plateau in μmol L−1; is mole fraction of 15N in N2 (= n[15N]/([n[15N]+n[14N]) where n is moles); is mole fraction of 15N in NO3−; and is [N2] produced by denitrification of labeled NO3− during subsurface transport.
 In equation (15), the term on the left side is the measured concentration of 15N[N2] in the hyporheic zone sample, the first two terms on the right side account for conservative mixing between the hyporheic component derived from surface water and the groundwater component and their effect on 15N[N2] in the hyporheic zone, and the third term accounts for 15N[N2] production in the hyporheic zone by denitrification. The target of equation (15) is the total [N2] produced by hyporheic denitrification, [ ]hz, which is solved for by rearrangement. The isotopic composition of NO3− did not vary substantially with depth in the hyporheic zone, as the groundwater mixing fraction had little or no NO3− and nitrification caused little or no dilution of 15NO3− in the subsurface.
 Equation (15) assumes that concentrations of isotopic tracers are steady or varying only slowly. Steady-state conditions are most easily achieved where subsurface residence time is short relative to the duration of injection. For our experiments, the subsurface residence times were generally much shorter (tens of minutes to a few hours) compared with the in-stream injection times (7 h in 2001 and 12 h in 2003), and the tracer concentrations generally had achieved steady plateau concentrations at all sampling points well before the end of the injection, which is favorable for the assumptions of the steady state analysis. The surface water concentration of 15N[N2] varied slightly over time, however. A simple procedure was used to account for temporal variation in the surface water end member concentration, i.e., we lagged the concentration of 15N[N2]s used in equation (15) for the subsurface reaction by one hyporheic residence time, i.e., the calculation for the current time t used a value of 15N[N2]s measured at time t − τhz. Fortunately, the timescale of temporally varying surface water concentration was relatively slow (approximately 12 h timescale) compared to a typical hyporheic residence time of minutes to hours. Thus, incorporating the time lag had almost no effect on calculations, which further supports the use of a simple steady state analysis.
3.4. Denitrification Rate and Mass Flux Estimation
 The rate of denitrification in the hyporheic zone, rh-den (μmol N L−1 h−1), was computed by rearranging equation (15) to solve for [N2*]hz, dividing by the subsurface residence time, τhz, and multiplying by 2 to account for the reaction stoichiometry in producing N2 from reduction of NO3−:
 Typically, there is interest in expressing the reaction as a vertical mass flux to the streambed, i.e., the denitrification flux per streambed area, Uhz-den (μmol NO3− − N m−2 h−1). Following equation (5), Uhz-den is computed as:
 The Damköhler number for hyporheic denitrification, Dahz-den, effective size of reaction zone, dEff-den, active fraction of the hyporheic zone, fA-den, and stream reach-scale reaction significance of the hyporheic zone, Rs-den, were calculated using equations (8)-(11), respectively. The in-stream mixing length, LC, for the 2001 experimental reach in Sugar Creek was somewhat longer (131 m) compared to the 2003 experimental reach (89 m) mainly due to differences in stream width (3.6 and 1.34 m wide in 2001 and 2003, respectively).
3.5. Denitrification Contributions From Shallow Versus Deeper Hyporheic Flow Paths
 We combined data from the multiple depths sampled at each setup of the USGS MINIPOINT sampler to specify contributions of shallow versus deep hyporheic flow paths. Transport pathways to each layer were assumed independent for this analysis, with water flux, tracer dilutions, and reactions computed separately for each layer. Our approach is consistent with an overall conceptualization of complex hyporheic flow pathways as being well characterized by vertical approximation of the exchange process [Elliott et al., 1997aa, 1997bb]. Other calculations are possible, although we believe this approach is efficient because it uses the tracer data directly to specify how transport and reaction vary with depth with minimal assumptions about flow path or residence time distribution. To compute the total denitrification flux to the streambed, we summed the individual mass fluxes detected at each depth (layer):
where Uhz-den(tot) is the total denitrification flux to the streambed, and is the flux-weighted reaction contribution from the ith layer where subscript i denotes the ith layer of n total layers. Layer position and thickness is determined by the number and spacing of subsurface sampling points. The flux weight, Wi, is the fraction of the hyporheic-zone flux reaching layer i:
where qhz(i) is the flux to layer i. Flux is calculated as the product of the sediment thickness in the ith layer (dhz(i)) multiplied by sediment porosity in that layer (θi) and divided by the total subsurface residence time of water in the layer, τhz(i), measured from tracer arrival at the sampling point in that layer (section 3.3).
4.1. Subsurface Tracer Measurements
 Sugar Creek had distinctive hyporheic zone conditions in different geomorphic environments. Hyporheic flow and mixing between surface water and groundwater are indicated by the arrival of the conservative tracer Br- at subsurface sampling points (Figures 3a and 3b). The concentration of isotopically labeled N2 built up over time due to conversion of 15NO3− to 15N2-N by denitrification, especially at mid and greater depths of the channel thalweg site (5–15 cm) and shallow depths of the channel margin site (1.5–3 cm; Figures 3c and 3d). Higher pore water plateau values of δ15N[N2] indicate higher reaction progress in Figure 3 but not necessarily higher reaction rates. Our reaction rate calculations account as needed for the effects of residence time and mixing between surface water and groundwater, showing, for example, that deeper hyporheic flow paths typically had the lowest reaction rates (section 4.7). Also, groundwater that discharged into the hyporheic zone from beneath had little or no measureable O2 or nitrate, but it had substantial excess N2 indicating that NO3− recharged in agricultural fields had been denitrified before entering the hyporheic zone. This groundwater component had no effect on δ15N[NO3−]; however, the effect of introducing N2 with δ15N[N2] = + 2 to +4%, slightly higher than background surface water values [Böhlke et al., 2004, 2009], was accounted for in equation (15).
4.2. Physical Setting for Hyporheic Flow Beneath Contrasting Stream Geomorphic Units
 Stream water velocity was relatively high in the channel thalweg sites (0.13–0.4 m s−1) with relatively coarse sediment (D50's averaging 1800 μm and the D10's averaging 409 μm) that were likely to have lesser grain surface area and greater hydraulic conductivity. Side cavities, in contrast, had slower stream water velocities (<0.01–0.06 m s−1) that created lesser driving force for hyporheic flow through the finer than average sediments (D50's averaging 895 μm and D10's averaging 263 μm) that were likely to have grater surface areas but lower hydraulic conductivity. Tracer data indicated greater hyporheic fluxes in sediments beneath channel thalwegs, 17 cm h−1, compared with 7 cm h−1 beneath side cavities.
4.3. Surface Water and Groundwater Mixing in the Hyporheic Zone
 The surface water mixing fractions at each depth, fs, which were estimated after the tracer concentrations had plateaued, indicated that stream water typically contributed 60% or more of hyporheic flow beneath channel thalweg sites to depths of up to 15 cm (Figure 4a). In contrast, at a typical side cavity more than two thirds of the water in the deepest sampling port was from a combination of groundwater discharge and longer flow-path hyporheic flow beneath the bank margin (note second tracer peak long after in-stream tracer was shut off in Figure 3b).
4.4. Physical and Biogeochemical Conditions in the Hyporheic Zone
 Channel thalweg sediments had pore water chemistry more similar to the stream because of more rapid hyporheic exchange. Sediment grain size, dissolved nitrogen species, dissolved oxygen, dissolved iron, microbial denitrifier abundance, and penetration depth of the bromide tracer are compared for representative channel thalweg and side cavities in Figure 4. Nitrate was the dominant form (other than N2) of dissolved nitrogen in channel thalweg sediments (150 μM), being only slightly lower than surface water concentrations. Dissolved organic nitrogen (8 μM), ammonium (2 μM), and nitrite (1 μM) also were at concentrations similar to surface water in channel thalweg sediment pore waters.
 A nearby side cavity site, in contrast, had lower dissolved oxygen in the hyporheic zone compared with channel thalweg sediments and lower nitrate that decreased to the detection limit at a relatively shallow depth (<4 cm). Also, ammonium (15–30 μM) and DON (10–20 μM) were higher in side cavity sediments compared with channel thalweg sediments and nitrite (0.2 μM) was lower. These differences are consistent with lower redox states and more reduced forms of nitrogen in sediments of the side cavity.
 Also suggesting more reducing conditions in sediment pore waters beneath side cavities was dissolved iron (Fe2+). Concentrations were up to 400 μM in side cavity sediments compared with channel thalweg sites where Fe2+ concentrations in pore water were mostly 10 μM. Particulate organic carbon in sediments varied only modestly, between 0.2 and 0.4%, with slightly higher values associated with side cavities. Particulate organic carbon was highest in a surface layer of very fine sediments that where present, had POC values ranging between 1 and 3% by weight.
 At all sites DOC in pore water ranged between 3 and 5 mg/L and tended to be higher in the shallow hyporheic zone and to decrease slightly with depth in sediment. In side cavities, DOC was higher in shallow pore water compared to beneath channel thalwegs. DOC also decreased more steeply with depth in sediment beneath side cavities (Figure 4). The nirS marker of microbial denitrifier abundance was approximately a factor of three higher in shallow sediment of side cavities compared to channel thalwegs. Also, nirS decreased more steeply (two order of magnitude decline) with depth in side cavity sediment compared to channel thalwegs where there was a comparatively smaller (factor of 4) decline in nirS.
4.5. Hyporheic Exchange Fluxes and Residence Times in Shallower and Deeper Subsurface
 The hyporheic water residence time increased approximately exponentially with depth from a minimum of several minutes at 2 cm below the sediment interface to a maximum of 88 h at 15 cm deep. The inverse of hyporheic water residence time, τ−1 [h−1] is a time constant referred to as hyporheic exchange rate that was at a maximum of 16 h−1 just beneath the sediment interface and declined to a minimum of 0.01 h−1 at 15 cm (Figure 5c). The short residence times and fast exchange of hyporheic water just beneath the sediment surface reflects the dominance of the shallow hyporheic flux, expressed here as the proportion of hyporheic flow at a given depth. The dominant proportion of hyporheic flow generally occurred in the top 4−6 cm of the streambed and declined very steeply to 10% below that (Figure 5b). An exception occurred at one of the channel thalweg sites where a gravel bar that had pooled water upstream caused relatively deep hyporheic flow with flow deeper than 5 cm accounting for approximately 30% of the total at that site (Figure 5b).
4.6. Correlations Among Physical and Biogeochemical Variables Controlling Denitrification
 Correlations among the physical and chemical variables measured in the hyporheic zone revealed favorable conditions for high rates of denitrification in hyporheic flow (Table 1). The denitrification rate (rhz-den) (equation (15)) was correlated positively with the concentrations of DOC and NO3−, which are substrates for the reaction (Table 1). Denitrification rate was also negatively correlated with residence time, indicating the importance of shorter residence times (i.e., greater hyporheic fluxes) in transporting substrate from surface water to reaction sites in the sediment. Sedimentary conditions were also important as indicated, for example, by the positive correlation between denitrification rate and nirS, a marker of microbial denitrifier abundance. Denitrification rate was positively correlated with sediment porosity (Table 1), which tends to be higher in finer sediments with greater surface area. Denitrification rate also was negatively correlated with Fe2+, an indicator of anoxic conditions in sediment pore water (Table 1).
Table 1. Pearson Product Moment Correlation Coefficients for Physical and Chemical Variables Related to Denitrification in Hyporheic Flow Paths of Sugar Creek, INa
Abbreviations for variables are in parentheses and ln indicates log transformation of the variable. Subscript a indicates that the p value is less than or equal to 0.001, b indicates a p value less than or equal to 0.01, and c indicates a p value less than or equal to 0.15.
4.7. Relative Importance of Shallower Versus Deeper Denitrification in the Hyporheic Zone
 Denitrification reaction rate constants, λhz-den, were highest near the streambed surface of side cavity geomorphic units and declined with depth from a maximum of 3 to a minimum of 0.003 h−1 (Figure 5c). Denitrification rate constants were 2–10 times lower in shallow sediments of channel thalwegs compared with side cavities. Rate constants declined less with depth beneath channel thalwegs and were more similar to side cavities at depths below 5 cm (Figure 5c). Rates of reaction and hyporheic exchange were relatively similar in side cavity sediments. In contrast, reaction rates were 5–50 times slower than hyporheic exchange rates beneath channel thalwegs (Figure 5c).
 Denitrification vertical fluxes, Uhz-den, were highest near the sediment surface and decreased from a maximum of approximately 600 μmol N m−2 h−1 at 1.5 cm deep to the minimum detection value of approximately 1 μmol N m−2 h−1 at 15 cm below the streambed (Figure 5d). Denitrification vertical fluxes were undetectable beneath side cavities deeper than 4 cm and, although detectable in deeper hyporheic flow beneath channel thalwegs, were insignificant to whole-stream denitrification below 4 cm (Figure 5d).
4.8. Relative Importance of Denitrification in Contrasting Stream Geomorphic Units
 Depth-integrated hyporheic denitrification at the six sites ranged between 0 and 780 μmol N m−2 h−1, which explained between a few percent and as much as 240% of simultaneously measured whole-stream denitrification (120 μmol N m−2 h−1, Böhlke et al.,  and 320 μmol N m−2 h−1Böhlke et al., ). Both channel thalweg and side cavity hyporheic environments were effective contributors to whole-stream denitrification, with channel thalweg flow paths tending to have lower reaction rates (Figure 6a) but a higher exchange timescale (Figure 6b) compared with side cavities. The highest measured denitrification flux (approximately three times greater than whole-stream denitrification) occurred in an algal canopy (1303 μmol N m−2 h−1).
4.9. Reaction Versus Transport Limited Denitrification in Hyporheic Flow Paths
 Rate limitation is revealed by examining the denitrification timescale plotted versus hyporheic residence time (Figure 6). From that plot, it is evident that the reaction timescale in shallow sediments was initially 10 times faster beneath side cavities compared with channel thalweg sediments, possibly resulting from side cavities having finer sediment with greater surface area and higher populations of microbial denitrifiers (Figure 4). However, after less than an hour of transport, the timescale of denitrification beneath side cavities slowed considerably due to substrate depletion (note break in slope in green dashed line in Figure 6) and in some cases denitrification became transport limited (fhz values as low as 0.6).
 Denitrification in coarser channel thalweg sediments occurred in fast exchanging hyporheic flow and had intermediate values of the denitrification rate constant. In the first two hours, denitrification in the shallowest flow paths was reaction limited as a result of a more vigorous hyporheic flux that replenished substrates but less favorable sediment and microbiological conditions compared with finer sediments of side cavities. However, the benefit of greater hyporheic delivery of substrates beneath channel thalwegs eventually gave way to effects of substrate depletion or movement into a deeper sediment layer with less favorable sediment and microbiological conditions (Figures 4 and 6). Values of fA-hz ranged between 2 and 100 in channel thalwegs. These values indicate that repeated exchange with channel thalweg hyporheic flow paths would be necessary to remove all nitrate from a parcel of stream water.
 In general, the deeper and longer hyporheic flow paths beneath channel thalwegs and side cavities had much slower reaction timescales that resulted from unfavorable sediment conditions (e.g., lower denitrifier abundance), lower rates of replenishment of reaction substrates (nitrate and DOC) by hyporheic flow, or dilution of substrate concentrations by mixing with groundwater (Figure 6).
4.10. Reach-Scale Significance of Hyporheic Denitrification
 Hyporheic denitrification at Sugar Creek accounted for a potential removal of nitrate of between 0.01 and 10% of the total stream load of nitrate in a characteristic mixing reach length on the order of 100 m in Sugar Creek. Reaction within individual hyporheic flow paths removed between 1 and 100% of the nitrate that entered (y axis, Figure 7), although reach-scale removal was tempered by hyporheic fluxes that ranged between 0.1 and 50% of the stream discharge in one mixing reach. The result for channel thalwegs was removal at a rate that could account for between 0.07 and 4% of the nitrate load in a characteristic in-stream mixing reach. In contrast, hyporheic flow beneath side cavities removed a higher fraction of nitrate in one mixing reach that could account for between 4 and 10%. The higher removal was due to the order of magnitude higher rate constants for denitrification in side cavities (Figure 5c). All of that removal was accounted for in flow paths ≤ 4 cm in depth, with deeper flow paths being part of the inactive volume resulting from transport limitation (Figures 6 and 7). The lower denitrification rate constant beneath channel thalwegs (Figure 5c) was the primary reason for lower overall significance of hyporheic denitrification compared with side cavities. However, denitrification in channel thalwegs extended deeper than side cavities and did contribute significantly to whole-stream denitrification (Figure 5d). Denitrification in channel thalwegs is especially important in streams where aerial fraction of stream bottom composed of side cavities is small.
 Hyporheic flow paths often have favorable conditions for denitrification [e.g., Holmes et al., 1996; Böhlke et al., 2009; Hubbard et al., 2010; Zarnetske et al., 2011a]; however, few studies have directly quantified the contribution of hyporheic-zone denitrification to whole-stream denitrification. Smaller streams generally have been thought to be hotspots for denitrification due to higher concentrations of nitrate and due to the larger surface area to volume ratio that promotes contact time with sediments [Alexander et al., 2000]. In part due to a lack of published measurements at the actual sites of reaction in streams and rivers, denitrification generally only correlates with total transport time [Green et al., 2009; Seitzinger et al., 2006] rather than with measurements of storage time or storage zone size [Mulholland et al., 2008; Webster et al., 2003]. Thus, even though denitrification has been investigated across the nation and around the world [Seitzinger, 1988; Mulholland et al., 2008; Seitzinger et al., 2006] it remains difficult to predict why one stream may have greater denitrification than another [Ensign and Doyle, 2006].
5.1. Hydrologic and Sedimentary Controls on Hyporheic-Zone Denitrification
 Hyporheic flow is strongly influenced by stream velocity, streambed slope and topographic variability, sediment permeability, and groundwater hydraulic head, all of which affect the hydraulic-head and gravity-driven forces that control hyporheic exchange [Bhaskar et al.,2012; Boano et al., 2010; O'Connor and Harvey, 2008; Winter et al., 1998]. Hyporheic flow paths may have exponential [Boano et al., 2007] or broader residence time distributions such as lognormal [Jonsson et al., 2003; Worman et al., 2002; Tonina and Buffington, 2011]. Our measurements were consistent with those expectations, showing approximately exponential declines below side cavities and broader (approximately lognormal) distributions below channel thalwegs (Figure 5).
 Finding greater denitrification with faster hyporheic exchange (i.e., shorter residence time, Table 1) is consistent with laboratory studies showing denitrification was positively related to velocity of overlying surface water that increases hyporheic flux [Cook et al., 2006; O'Connor and Hondzo, 2008; Arnon et al., 2007]. When the hyporheic flux was low the resupply of substrates limited denitrification and when it increased both the size of the hyporheic zone and rate increased until reaction sites were saturated [Cook et al., 2006] by availability of nitrate and labile dissolved organic carbon substrates. With further increases in flow velocity denitrification in sediment and periphyton canopies, respectively, became limited by oxygen inhibition [O'Connor and Hondzo, 2008; Arnon et al., 2007]. Related studies by others have observed that hyporheic delivery of O2 stimulates organic matter decomposition and nitrification, which, after a lag, stimulates denitrification [Holmes et al., 1996; Zarnestke et al., 2011a; Koch et al., 2010; Smith et al., 2006].
 Our results indicated that denitrification rate was greatest just beneath the streambed interface and was supported by presence of anoxic microzones. These findings are difficult to reconcile with recent modeling suggesting that hyporheic denitrification mainly occurs deeper in anoxic layers that form below an oxic layer in sediment [e.g., Cardenas, 2008, Boano et al., 2010; Bardini et al., 2012; Marzadri et al., 2011 and Marzadri et al., 2012]. The importance of anoxic microzones is indicated by measureable Fe++ in shallow (centimeter-scale) hyporheic flow paths, which is an indicator of locally anoxic conditions in the otherwise oxic flow paths (Figure 4). Deeper zones with full anoxic conditions had lower denitrification rate (Figure 5). Findings were further supported by strong positive correlations of denitrification with nirS and porosity and a negative correlation with Fe++, together suggesting the importance of high granular surface area for microbial attachment in developing anoxic microzones. Marzadri et al.  and Zarnetske et al.  implicitly accounted for anoxic microzones using a Damköhler number for O2 transport and reactive uptake to predict conditions for net nitrification and denitrification. Our results suggest a next step of refining these approaches to explicitly account for development of anoxic microzones in hyporheic flow paths.
5.2. Counterbalancing Factors Produced Similar Denitrification Rates in Different Stream Geomorphic Units
 Hyporheic flow beneath channel thalwegs and side cavities had similarly high rates of denitrification, but for different reasons. The hyporheic exchange flux rate was greater, by approximately an order of magnitude, in channel thalweg sediments with greater flow velocities, coarser grained sediments, and higher hydraulic conductivity. Also, the depth of hyporheic exchange was deeper by approximately a factor of three beneath channel thalwegs compared to side cavities. However, side cavity sediments had denitrification timescales that were an order of magnitude faster (Figure 5), probably due in part to finer sediments with greater microbial denitrifier populations and higher concentrations of DOC. A remaining uncertainty is the source of labile carbon for denitrification, i.e., whether it was locally produced by autotrophs on or within the streambed of side cavities, or whether DOC of well mixed surface water was most important.
 Previous studies point to the need for distinguishing “hot spots” for particular reactions in streams (e.g., McClain et al., 2003), however most of those lack a means to compare results for whole-streams with various geomorphic units. We found that side cavities had the greater reaction rate constants; however, those rate constants declined sharply with depth in sediment and the reaction became either substrate or transport limited. In contrast, channel thalwegs had lower intrinsic reaction rate constants but greater hyporheic flux, which replenished substrates for reaction, which resisted substrate and transport limitation for as much as 10 h of transport (Figure 6). Thus, counterbalancing factors produced a net result that two highly contrasting stream geomorphic units both contributed about equally to whole-stream denitrification (Figure 5d). These results are supportive of using simple physically based models of hyporheic flow and biogeochemical modeling to predict, as was recently undertaken by Marzadri et al. [2011, 2012] to predict the emissions of N2O from streambeds of seven natural streams.
5.3. Hyporheic Active Volume for Denitrification Differs From Full Volume
 In our study, the full volume of the hyporheic zone is estimated based on solute tracer penetration depth in the bed. Others have based their estimates on modeling [e.g., Argerich et al., 2011; Stonedahl et al., 2012]. We found that the active volume fraction for denitrification in the hyporheic zone, fA-hz, generally differed from the full hyporheic-zone volume. Argerich et al.  made related observations that aerobic decomposition of organic matter occurs in a volume less than the full hyporheic volume. At Sugar Creek, we observed that side cavities were efficient in their shallow exchange (e.g., Damköhler numbers, Daden-hz, and values of active fractions, fA-hz, near one) but also had a deeper component of transport-limited flow paths with active fractions as low as approximately 0.6. In contrast, shallow fast-exchanging hyporheic flow paths in channel thalwegs were generally reaction-limited and had active fractions ranging between 2 and 100, indicating that multiple passages through the hyporheic were required for reaction completion.
 Our study indicates how reaction limitation influences physical zonation of reaction zones in streambeds that would be unpredictable based only on knowledge of physical hydrology of hyporheic zones. This result explains, at least in part, why standard metrics of hyporheic or storage zone characteristics (e.g., storage zone residence time and cross sectional area, fraction of time spent in storage) are poor predictors of whole-stream reactions [e.g., Mulholland et al., 2008]; even when there is strong circumstantial evidence that hyporheic zones are involved [Webster et al., 2003].
 The active volume fraction for denitrification in the hyporheic zone, fA-hz, provides insight about reaction efficiency. For example, consider how time that water spends in the inactive volume of deeper hyporheic flow is inefficient because, although there is storage, there is no contribution to reaction progress. In contrast, fast exchanging hyporheic flow remains efficient in that substrate depletion is avoided; however, each exchange returns unreacted nitrate to the stream and only nominally contributes to reaction progress, which may be inefficient if the active fraction is very large (e.g., fA-hz >> 1) or if stream discharge is high such that the time elapsed and distance traveled before stream water reenters the hyporheic are large. Both types of inefficiencies are accounted for and contrasted in our metric of reach scale significance (Figure 7).
5.4. Significance of Hyporheic Reactions to Whole-Stream Denitrification
 Both reaction rates and hyporheic-zone fluxes decreased with depth in streambed sediment, and we observed that the steepness of the decline in hyporheic-zone fluxes was greater than the decline in reactivity (Figure 5c), which is what controlled the effective depth for significant denitrification. At Sugar Creek, the effective depth limit of denitrification was ≤ 4 cm because that was the depth where hyporheic exchange fluxes began to decline faster with depth than did reactivity (Figure 5c). This meant that denitrification occurring at depths >4 cm deep generally was insignificant at the reach scale due to the small hydrologic flux involved (Figures 5d and 7). Because sediments of side cavities had order of magnitude higher reaction rate constants compared to channel thalwegs, and because corresponding hyporheic exchange rates were only a factor of two less, the side cavities had the greater potential reach-scale removal of nitrate, between 4 and 10% compared to between 0.7 and 4% for channel thalwegs (Figure 7).
 Recent modeling of hyporheic denitrification uses various versions of the experimental Damköhler number to characterize controls at the bank meander [Marzadri et al., 2011; Gomez et al., 2012] and small bed form scales [Boano et al., 2010; Bardini et al., 2012]. Those models tend to emphasize variability in hyporheic residence time as the factor controlling whether net nitrification or denitrification occurs. Most of the models assume rate constants for denitrification that depend on substrate concentrations that are affected by aerobic respiration, nitrification, and microbial uptake of N in addition to denitrification. They found that hydrologic variability was as important, or more important, than reaction substrate variability in controlling denitrification. The behaviors are captured in various forms of the experimental Damköhler number [Boano et al., 2010; Marzadri et al., 2011; Gomez et al., 2012; and Bardini et al., 2012]. Our field characterization of hyporheic denitrification in terms of vertical denitrification flux, hyporheic active fraction, and reach-scale significance metrics should inform and improve modeling studies.
 In this productive, nitrate-rich stream we found that denitrification began almost immediately upon stream water entry into shallow and faster exchanging hyporheic flow paths. The shallow sediments therefore dominated in their contribution to whole-stream denitrification because those sediments had the highest intrinsic reaction rate constants as well as highest exchange fluxes. Reaction rate constants decreased with depth, but hyporheic-zone fluxes decreased more rapidly, such that the effective depth of hyporheic denitrification contributed insignificantly to reach-scale nitrate loss.
 We presented scaling metrics that quantify the active fraction of the hyporheic zone involved in reactions and the reach-scale significance of hyporheic reactions. These analyses provide insight into why previous meta-analyses have not found measures of total hyporheic zone size or hyporheic residence time to be useful predictors of whole-stream denitrification [e.g., Mulholland et al., 2008]. Depending on local hydraulics and physical and chemical characteristics of the sediment, hyporheic-zone denitrification accounted for between a few percent and roughly twice the rate of whole stream denitrification. Further evidence of the hyporheic contribution is the reach-scale reaction significance index, which demonstrated the potential to remove up to 10% of the stream's nitrate in one surface water mixing reach (approximately 100 m) in Sugar Creek. The improvement over other metrics is greater specificity in processes and reaction limitations in specific reaction zones that are left unspecified by metrics such as spiraling length or vertical mass flux [e.g., Ensign and Doyle, 2006]. The new metrics that we developed in the present study are potentially useful as predictive tools for anticipating outcomes of flow and geomorphic changes or management practices such as stream restoration.
 There are few available tools for predicting importance of various types of natural geomorphic features or built features for enhancing stream functions for improving water quality. We found that the hyporheic contribution to stream denitrification was not dominated by a single geomorphic subunit. Instead, both channel thalweg and side cavity geomorphic units were important contributors, although for different reasons, side cavities had greater rate constants for the reaction in hyporheic flow compared to channel thalwegs, which had lower rates but higher fluxes that processed the stream nitrate load efficiently.
 Our study indicates that wider use of metrics such as active volume and reach-scale significance of hyporheic reactions could improve understanding of hydrologic contributions to enhancing biogeochemical reactions in streams. Increased understanding of interactions between biogeochemical, sedimentary, and hydraulic factors could aid in design of stream restorations that optimize reaction rate constants and stream-water processing, which come closer to optimizing the timescales involved.
 This project was funded by USGS HR&D and NAWQA Programs and by NSF Grants EAR-0810140 and EAR-0814990 and a grant from the U.S. Department of Agriculture Cooperative State Research, Education and Extension Service (National Research Initiative Competitive Grants Program in Watershed Processes and Water Resources). We thank Joel Detty, Mike Doughten, Janet Hannon, Julie Kirstein, Stan Mroczkowski, Jessica Newlin, and Eric Nemeth for assistance in the field and laboratory. Helpful comments on the manuscript were provided by Rich Alexander, Josh Koch, and two anonymous reviewers at WRR. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.