O2 reduction and denitrification rates were determined in shallow aquifers of 12 study areas representing a wide range in sedimentary environments and climatic conditions. Zero- and first-order rates were determined by relating reactant or product concentrations to apparent groundwater age. O2 reduction rates varied widely within and between sites, with zero-order rates ranging from <3 μmol L−1 yr−1 to more than 140 μmol L−1 yr−1 and first-order rates ranging from 0.02 to 0.27 yr−1. Moderate denitrification rates (10–100 μmol N L−1 yr−1; 0.06–0.30 yr−1) were observed in most areas with O2 concentrations below 60 μmol L−1, while higher rates (>100 μmol N L−1 yr−1; >0.36 yr−1) occur when changes in lithology result in a sharp increase in the supply of electron donors. Denitrification lag times (i.e., groundwater travel times prior to the onset of denitrification) ranged from <20 yr to >80 yr. The availability of electron donors is indicated as the primary factor affecting O2 reduction rates. Concentrations of dissolved organic carbon (DOC) and/or sulfate (an indicator of sulfide oxidation) were positively correlated with groundwater age at sites with high O2 reduction rates and negatively correlated at sites with lower rates. Furthermore, electron donors from recharging DOC are not sufficient to account for appreciable O2 and nitrate reduction. These relations suggest that lithologic sources of DOC and sulfides are important sources of electrons at these sites but surface-derived sources of DOC are not. A review of published rates suggests that denitrification tends to occur more quickly when linked with sulfide oxidation than with carbon oxidation.
 Understanding the spatial distribution of redox processes in aquifers is essential when assessing the quality of groundwater [McMahon and Chapelle, 2008]. Specifically, the fate of many contaminants in groundwater depends to a large extent on the redox processes that occur along flow paths [e.g., Tesoriero et al., 2000, 2001; Carlyle and Hill, 2001; Cozzarelli et al., 2001]. As a result, quantifying redox reaction rates is critical to predicting the fate of many contaminants and delineating redox reaction zones in groundwater (e.g., zones of dominant terminal electron acceptors).
 Microbial metabolism depends on the oxidation of organic or inorganic (e.g., FeS2) species to generate energy for growth and maintainance. The metabolic reaction that yields the most energy will typically dominate over competing reactions [e.g., Stumm and Morgan, 1996]. Consequently, microbial processes are expected to change as a function of the redox state of groundwater, progressing to reactions with lower energy yields (Table 1). Organic carbon is the most common electron donor in groundwater. Microbes will first oxidize organic carbon using O2 as an electron acceptor through aerobic respiration because it is the most energetically favorable reaction (Table 1). When O2 is depleted, facultative anaerobes begin to use nitrate ( ) as an electron acceptor during denitrification. Subsequent reactions include the reduction of Mn(IV), Fe(III) and sulfate, and methanogenesis (Table 1).
Table 1. Sequence and Free Energy of Microbial Redox Reactions, Assuming Organic Matter (CH2O) is Electron Donora
 The rate of O2 reduction and the amount of O2 initially present in recharge determine the groundwater travel time in the oxic zone and influence the portion of the aquifer system that is oxic. Consequently, the rate at which O2 is reduced will have a significant influence on the susceptibility of aquifers to many contaminants. Until recently, aerobic respiration rates were determined using O2 gradients along flow paths of varying length (e.g., <1–80 km) coupled with approximations of groundwater travel time derived from estimates of groundwater velocity. A review of these studies concluded that the fate of oxygen in groundwater between aquifers depends largely on O2 consumption rates rather than travel time [Malard and Hervant, 1999]. O2 consumption rates varied widely between aquifers, ranging from <0.02 μmol L−1 yr−1 in deep sedimentary basins of the Southwestern United States and a sandstone aquifer in Namibia [Winograd and Robertson, 1982; Vogel et al., 1981] to ∼25 μmol L−1 yr−1 in a fluvial-sand aquifer in Ontario, Canada [Jackson and Patterson, 1982; Malard and Hervant, 1999]. Push-pull tests have also been used to determine aerobic respiration rates in groundwater [Schroth et al., 1998] and are particularly useful in aquifers contaminated with organic compounds where rates are expected to be high. First-order rates ranging from 700 to 15,000 yr−1 were determined in contaminated aquifers in the United States [Schroth et al., 1998; McGuire et al., 2002]. Environmental tracers (e.g., chlorofluorocarbons and sulfur hexafluoride) have improved groundwater age estimates of recently recharged water [e.g., Busenberg and Plummer, 2000]. The use of these tracers offers an opportunity to refine rates in shallow aquifers. For example, O2 and tracer-based age gradients along flow paths have been used to estimate aerobic respiration rates in shallow aquifers using multiple wells along a flow path [e.g., Böhlke et al., 2002] or individual well data [e.g., McMahon et al., 2008], with zero-order rates ranging from 0.9 to 190 μmol L−1 yr−1 and first-order rates ranging from 0.005 to 1 yr−1.
 The many consequences of increased reactive nitrogen in the hydrosphere have led to several studies on denitrification rates in groundwater. In situ denitrification rate calculations have primarily relied on three methods: N2 gradient, gradient, and injected . Denitrification rates from injection experiments tend to have the highest rates [Green et al., 2008 and references therein], with most occurring in aquifers with strongly reducing conditions either occurring naturally (e.g., Tesoriero et al. ; 1.4 × 105 μmol N L−1 yr−1) or from contamination with organic compounds (e.g., Schroth et al. ; 2000 yr−1). Nitrate gradient experiments typically have rates ranging from 370 to 3.7 × 105 μmol N L−1 yr−1 [Green et al., 2008 and references therein], while N2-gradient experiments typically have lower rates, often <370 μmol N L−1 yr−1. Denitrification rates determined from N2 gradients may better represent aquifer conditions than other methods because they rely on the product of denitrification (excess N2) occurring under ambient conditions to obtain rates and are not as susceptible as the nitrate-gradient method to artifacts resulting from historical changes in nitrate loadings at the land surface.
 Improved estimates of O2 reduction in shallow aquifers are critical to assess the vulnerability of aquifers to redox-sensitive contaminants. Similarly, improved estimates of the location and rates of denitrification in watersheds [Boyer et al., 2006] and its ability to remove reactive nitrogen from agroecosystems [Galloway et al., 2003] are needed to improve both local and global assessments of the risk posed by reactive nitrogen and other contaminants to aquatic ecosystems and human health. The availability and reactivity of electron donors likely have a major influence on the delineation of redox zones and reaction rates [e.g., Starr and Gillham, 1993]. In global assessments of the fate of nitrogen, it has been assumed that the supply of electron donors is largely surface-derived dissolved organic carbon [Van Drecht et al., 2003; Seitzinger et al., 2006], resulting in denitrification estimates that are negligible below 5 m of saturated thickness. An assessment of denitrification rates and the availability of electron donors for denitrification can help refine these global nitrogen budgets.
 Age-based tracers and concentration gradients along shallow groundwater flow paths offer the opportunity to expand and improve estimates of O2 reduction and denitrification rates, and to evaluate how these rates change as a function of hydrogeologic setting. In this study, water chemistry and tracer-based groundwater ages (defined as the time of travel from the water table to the point of sampling) were used to determine redox-reaction rates for surficial aquifers from 12 study areas in the United States and Canada. Objectives of this study were to: (1) determine O2 reduction and denitrification rates across a range of hydrogeologic settings, (2) examine the importance of electron donors on reaction rates, and (3) estimate groundwater travel time prior to denitrification (denitrification lag time).
2. Study Site Descriptions
 Twelve study sites were selected to represent a range of sedimentary environments and climatic conditions (Figure 1; Table 2). Sites were selected from existing U.S. Geological Survey (USGS) studies that had transects that were approximately parallel to the primary direction of flow and groundwater samples that were analyzed for dissolved O2 and at least one tracer that could be used to estimate the year of recharge. The 12 study sites selected cover most of the major climatic regions in the contiguous United States and a wide range in recharge rates, from <10 cm yr−1 to >70 cm yr−1. The hydrogeologic settings of these sites also cover a range of sedimentary environments, including sites in glacial outwash environments, coastal plain settings, alluvial deposits, and other unconsolidated deposits. Study sites were typically in agricultural areas; however, at some sites, rural residential or suburban areas were present. Details of each site are provided in the references shown in Table 2.
Table 2. Site Location, Hydrogeologic Setting, and Climate for the Study Areas Included in This Investigationa
 Monitoring-well transects were installed along hypothesized groundwater flow paths in nests of generally three or four wells at each location. Details of the network locations are provided in the references in Table 2. Well screens were generally 1 m or less in length. The uppermost well was screened near the water table. The remaining wells at each location were screened at various depths to intercept likely flow paths in a transect parallel to the primary direction of flow. Flow paths were determined using measured head values [e.g., Puckett et al., 2002] or hydrologic simulations [e.g., Saad, 2008]. Dissolved O2 and pH were measured while water was being pumped, using electrodes placed in a flow cell chamber to minimize atmospheric interactions. Water samples for nutrients were filtered with a 0.45-μm capsule filter. Samples were age-dated using chlorofluorocarbons (CFC11, CFC12, CFC113), sulfur hexafluoride (SF6), or tritium-helium using published methods [Busenberg and Plummer, 2000; Plummer et al., 2006; Poreda et al., 1988]. Tracer concentrations, coupled with known trends in the atmospheric concentrations of these compounds over time, were used to provide estimates of groundwater age. The tracers were selected based on their suitability for each environment. One potential concern is the degradation of chlorofluorocarbons, which can result in overestimates of groundwater age. Degradation of chlorofluorocarbons does not occur during aerobic conditions but may [e.g., Hinsby et al., 2007] or may not [e.g., Cook et al., 1995] occur under more reducing conditions. Multiple tracers, hydrologic data, and/or modeling were used to identify and exclude age dates derived from tracer concentrations that were appreciably affected by degradation. For example, chlorofluorocarbons degraded under pyrite oxidizing conditions in one of the study sites (Sumas Aquifer, Tesoriero et al. ); the age estimates in this study were based on SF6 analyses of samples collected in 2006 and 2007.
 Samples were also collected and analyzed for N2 and Ar gas to estimate the amount of N2 derived from denitrification. N2 and Ar are incorporated into groundwater during recharge by air-water equilibration processes and by entrainment of air bubbles (“excess air”) [Heaton and Vogel, 1981]. Estimates of excess N2 from denitrification were calculated by subtracting the estimated concentration of atmospheric nitrogen, derived from both air-water equilibration and excess air, from that of the total amount of nitrogen gas measured in the groundwater sample [Dunkle et al., 1993]. Samples from the Sumas Aquifer site were collected and analyzed for δ34S of sulfate using methods described by Révész and Qi [2006a, 2006b].
3.2. O2 and Denitrification Rate Calculations
 The rate of O2 reduction in each aquifer was evaluated by relating dissolved O2 concentrations to groundwater age using the approach described by Böhlke et al. . This technique has the advantage of relying on in situ field conditions, rather than batch or column experiments that may not replicate aquifer conditions. For comparison, apparent zero-order (rate independent of concentration) and first-order (rate dependent on concentration) rate constants were determined. These estimates rates are considered apparent rate constants because of their dependence on tracer-based apparent recharge ages. Zero-order rate coefficients were determined using the following expression:
where C is the concentration of the reactant (i.e., dissolved O2) at the time of interest, C0 is the initial concentration of the reactant, k0 is the apparent zero-order rate constant, and t is time.
 Zero-order rate constants were determined by fitting a linear regression curve to a plot of C versus t. Samples with apparent ages exceeding a threshold value, where older samples typically have very low concentrations of O2 (typically <25 μmol L−1), were excluded from the zero-order analysis because concentration-dependent kinetics were indicated. Large errors in zero-order rates are more likely to occur when reactant concentrations become limiting [Bekins et al., 1997].
 Apparent first-order rate constants were determined using the following expression [Wright, 2004]:
where C, C0, and t are as described above and k1 is the apparent first-order rate constant. First-order rate constants (and C0 values) were determined by fitting a linear regression curve to plots of ln C versus groundwater age.
 Denitrification rates were determined using methods similar to those used for O2 reduction rates. Zero-order denitrification rates were determined by relating concentrations of N2 from denitrification, hereafter referred to as excess N2, with apparent groundwater age. First-order rate expressions were calculated by first determining the initial concentration at the time of recharge, C0. C0 was calculated by summing the (C) and excess N2 concentrations in the sample. Nitrous oxide (N2O) is also an end product of denitrification but was not included in the calculation of C0. Excluding N2O has a minimal impact on C0 estimates because N2O is typically very small relative to excess N2 [e.g., Weymann et al., 2008]. Because C0 can be estimated, first-order rate constants for denitrification were determined by fitting a linear regression curve to plots of ln C/C0 versus apparent groundwater age.
 Denitrification rates were determined only using samples that were in or near an active denitrification zone, which is defined as having <60 μmol L−1 of O2 and detectable concentrations of . In selected study areas, denitrification rates were so high that no samples were present in the denitrification zone. In these cases, samples on either end of the denitrification zone were used to provide a minimum rate. It should be noted that denitrification rates were not determined in the watersheds with low O2 reduction rates, resulting in oxic conditions in all samples, even in decades old water. Because of inhibition by the presence of O2, little or no excess N2 was detected in any of these groundwater samples resulting in negligible denitrification rates in these systems.
 Parameter estimates and fit statistics for first- and zero-order regressions for both O2 reduction and denitrification rate estimates were calculated using statistical analysis software [SAS Institute, 2009]. In cases where rates for these sites have been published previously, rates were recalculated using the methods described above to facilitate comparisons.
4. Results and Discussion
4.1. O2 Reduction Rates in Groundwater
 The relations between dissolved O2 concentrations and apparent groundwater ages varied widely between sites (Figure 2) resulting in a wide range in O2 reduction rates (zero-order: <3–140 μmol L−1 yr−1; first-order: 0.02–0.27 yr−1, Table 3). Low O2 reduction rates (i.e., ≤0.03 yr−1) were observed at the Polonia, Wisconsin, Chesterville, Maryland, and York, Nebraska sites (without riparian wells), high rates were observed at sites where lithologic boundaries were crossed (e.g., Sumas Aquifer, Kennedyville, Maryland), with intermediate rates observed at the remaining sites (Table 3).
Table 3. Zero-Order (k0) and First-Order (k1) Apparent Reaction Rate Constants for O2 Reduction and Denitrificationa
O2 Reduction Rates
k0 (μmol L−1 yr−1)
k0 (μmol N L−1 yr−1)
Bold type indicates rate constants are statistically significant (p ≤ 0.05).
Based on sample pair across or in zone of interest. Fit statistics are not meaningful. See text for details.
ND, not determined. Insufficient number of samples in the denitrification zone due to oxic conditions.
Excess N2 data not available. Denitrification rates not determined.
Insufficient number of samples in denitrification zone due to high denitrification rate, minimum values reported.
 O2 reduction rates varied sharply within and between flow paths in some aquifers. For example, O2 reduction rates were among the lowest measured along most flow paths at the York, Nebraska site (High Plains Aquifer, i.e., 0.02 yr−1, Table 3), but rates were much higher along shallow riparian flow paths near Beaver Creek (i.e., 0.27 yr−1, Table 3). Similarly, in the Sumas Aquifer, O2 concentrations remained essentially constant in samples that were less than 15-yr old but then sharply declined in samples that were a few years older (Figure 2). These older, more reduced samples coincide with the riparian zone of Fishtrap Creek and a hypothesized relict channel [Tesoriero et al., 2000]. A similar pattern was also observed at the Kennedyville, Maryland site near the riparian zone of Morgan Creek (Figure 2). In contrast, O2 reduction rates remained low as groundwater entered the riparian sediments adjacent to the Tomorrow River and Chesterville Branch at the Polonia, Wisconsin and Chesterville, Maryland sites, respectively.
 The data at the Sumas Aquifer and Kennedyville, Maryland sites suggest that the rate of reduction of O2 is very low in the upland areas of these sites but increases dramatically once water enters the riparian zone. To better characterize these rates, we estimated zero-order rate constants for the upland, using only samples from this zone in the Sumas Aquifer and Kennedyville, Maryland sites (Table 3). The sharp increase in O2 reduction rates that occurs as water enters the riparian zones of these watersheds was estimated using the zero-order expression (equation (1)). To describe rates across the upland–riparian boundary, C0 was assumed to be the median O2 concentrations in the upland, C was assumed to be the O2 concentration of the youngest suboxic sample found in the riparian zone, and t was the time period over which O2 reduction occurs across this interface. Values for k0 of 140 and 130 μmol L−1 yr−1 were determined across the upland-riparian boundary for the Kennedyville, Maryland and Sumas Aquifer, respectively. These calculations likely underestimate the rate of O2 reduction at the upland–riparian zone interface since the period over which O2 reduction occurs is likely shorter than we could measure with our well network grid. The rates of O2 reduction at the upland–riparian zone interface are approximately two orders of magnitude higher than in the upland areas of these sites and an order of magnitude greater than the highest rates observed in upland portions of other watersheds. While chemical reaction rates typically vary due to changes in temperature [e.g., Wright, 2004], this sharp change in O2 reduction rates within a study area suggests that temperature may not be a significant factor affecting rates in these study areas. In fact, little of the variance (r2 = 0.04, p = 0.53) in O2 reduction rates can be explained by estimated groundwater temperature (based on mean annual air temperature). It is hypothesized that the availability of electron donors both within and between sites is responsible for the observed range in rates. This hypothesis is explored in section 4.4.
4.2. Denitrification Lag Times
 Facultative anaerobes begin to use as an electron acceptor during denitrification (e.g., Table 1) only when O2 becomes limited. The groundwater travel time that occurs before denitrification occurs is referred to as the denitrification lag time. The rate of O2 reduction and the initial O2 concentration influence the denitrification lag time of an aquifer. The O2 concentration at which denitrification begins to occur was evaluated by examining denitrification reaction progress as a function of O2 concentration (Figure 3). The LOESS smooth to this relation illustrates the influence of O2 on denitrification reaction progress. When O2 concentrations exceed 125 μmol L−1, most samples show little or no denitrification. While denitrification is observed in samples having O2 concentrations between 60 and 125 μmol L−1, in this study and elsewhere [e.g., McMahon et al., 2004], the large number of samples showing little or no denitrification reaction progress over this interval suggests that 125 μmol L−1 may not represent a threshold concentration for denitrification, but rather may be an artifact of mixing of water from both oxic and suboxic zones [Green et al., 2010]. Denitrification occurs in nearly all samples with O2 concentrations <60 μmol L−1. We suggest that while denitrification may or may not occur at higher O2 concentrations, denitrification will occur once O2 concentrations are <60 μmol L−1.
 Determining denitrification lag times have important implications for assessing aquifer vulnerability to contamination and other redox-active constituents that are transformed under suboxic conditions. Denitrification lag times were determined using the first-order rate expressions determined from O2-groundwater age relations (Table 3) and assuming denitrification conditions commence when O2 concentrations are <60 μmol L−1. While denitrification may occur at higher O2 concentrations, using an O2 concentration of 60 μmol L−1 for the onset of denitrification results in a conservative (i.e., higher) estimate of the denitrification lag time. Denitrification lag times varied widely between sites, ranging from <20 yr at sites with high O2 reduction rates to >60 yr at sites with low O2 reduction rates (Figure 4). Furthermore, lag times may also vary markedly within a site when O2 reduction rates vary. Lag times of <10 yr and >50 yr observed at the York, Nebraska site illustrate this effect (Figure 4).
 Nitrogen applications to the land surface have increased markedly in the last 60 yr, increasing fourfold since 1960 [Ruddy et al., 2006] resulting in sharp increases in concentrations in recharging groundwater [Tesoriero et al., 2007; Puckett et al., 2011]. The extent to which the accumulation of in shallow aquifers affects deeper aquifers and streams depends on the presence of suboxic conditions. Watersheds having long denitrification lag times are more susceptible to the migration of into deeper portions of the aquifer and into streams.
4.3. Denitrification Rates
 Most suboxic systems had zero-order rates ranging from 15 to 70 μmol L−1 yr−1 (Table 3). One notable exception was the much higher rate (>280 μmol L−1 yr−1) that was observed as groundwater entered a hypothesized relict channel in the Sumas Aquifer. The increasing supply of electron donors in the form of iron sulfides and organic carbon (Figure 5) is likely responsible for the quick loss of both O2 and as groundwater enters these deposits. A similarly high rate may also occur as groundwater enters the riparian zone at Morgan Creek at the Kennedyville, Maryland site; however, only one sample was located in the denitrification zone. These findings suggest that zero-order dentrification rates can be broadly generalized into three categories: low rates (e.g., <3 μmol N L−1 yr−1) found in areas having elevated O2 concentrations, moderate rates (10–100 μmol N L−1 yr−1) in most areas with low O2 concentrations, and high rates (>100 μmol N L−1 yr−1) that occur when crosses a lithologic contact and enters a more reduced zone. The range in denitrification rates observed (10–100 μmol N L−1 yr−1) is consistent with rates calculated at other sites using the N2 gradient method [Green et al., 2008]. First-order rate constant values show a similar pattern, with nondetectable rates in oxic groundwater, rates ranging from 0.08 to 0.30 yr−1 in most suboxic systems, and higher rates (>0.36 yr−1) in systems where sharp redox gradients were observed (Table 3).
 The heterogeneity of redox conditions between flow paths within an aquifer is exhibited at the York, Nebraska site, where some flow paths remain oxic for 50 yr while others become suboxic in <20 yr (Figure 2). These suboxic wells are shallow and near a stream. It is hypothesized that organic-rich floodplain deposits may lead to suboxic conditions in these areas [McMahon et al., 2008]. A first-order denitrification rate of 0.08 yr−1 was observed along suboxic flow paths at the York, Nebraska site, resulting in the loss of most of the initial within 20 yr (Figure 6). This is in contrast to the observation that little or no denitrification occurred along other flow paths in this aquifer that remained oxic even after 50 yr of groundwater travel time (Figure 2).
4.4. Electron Donors
 As necessary reactants in the reduction of O2, the concentration and reactivity of electron donors are hypothesized to be the major factors causing O2 reduction rates to vary. Organic carbon and iron sulfide minerals have been identified as sources of electrons in groundwater systems [e.g., Postma et al., 1991; Tesoriero et al., 2000; Visser et al., 2009]. It has been suggested that dissolved organic carbon in recharge may be an important source of electrons for reduction reactions [e.g., Starr and Gilham, 1993]. Recent global estimates of denitrification assume that DOC from recharge is the primary source of electrons for denitrification [Seitzinger et al., 2006]. Conversely, recharging electron donors have been found to be insufficient to account for losses of O2 and in groundwater in agricultural areas [Green et al., 2008].
 Trends in DOC concentrations were examined as a function of groundwater age to evaluate the importance of surface-derived DOC as a source of electrons in reduction reactions. While concentrations of reactants or products of redox reactions can provide clues that help determine the dominant reactions occurring, more direct evidence may be obtained by examining the changes in concentrations along flow paths. This approach assumes that changes in the composition of recharge are negligible over the time period examined. If surface-derived DOC is a source of electrons for O2 reduction (e.g., Table 1), a negative correlation between groundwater age and DOC would result as DOC and O2 are consumed.
 Significant (p < 0.05) correlations between DOC and groundwater age were observed at five sites (Figure 5). Negative correlations between groundwater age and DOC were observed at the Polonia, Wisconsin and York, Nebraska (without riparian flow path) sites (Figure 5), both sites having very low O2 reduction rates. The fact that O2 reduction rates are low in systems where surface-derived DOC is indicated (i.e., a negative correlation between DOC and age) suggests that surface-derived DOC is not sufficient to cause significant amounts of O2 reduction to occur. In contrast, systems with high O2 reduction rates (e.g., York, Nebraska riparian, Perham, Minnesota, Sumas Aquifer) have DOC concentrations that increase with groundwater age (Figure 5), suggesting that a lithologic source is needed if carbon oxidation is to supply electron donors for significant O2 and reduction to occur. Lithologic sources may also be significant even when DOC concentrations do not increase with groundwater age. This may occur if DOC is oxidized rapidly as it enters the aquifer from a confining layer, resulting in no measurable increase in DOC concentrations but still providing a source of electrons to the aquifer [McMahon and Chapelle, 1991].
 To further evaluate the influence of surface-derived DOC, the amount of O2 reduction coupled with DOC oxidation was estimated using best fit relations between O2 and age and DOC and age at the Polonia, Wisconsin site (Figure 7). Assuming the stoichiometry shown in Table 1, 1 mole of DOC oxidized will result in 1 mole O2 reduced. The number of μmoles of DO lost during the time period examined is more than three times greater than the loss of DOC, indicating that the percentage of O2 reduction that could be linked to surface-derived DOC oxidation was only 30% for the Polonia, Wisconsin site. This is consistent with the finding that DOC is not a significant source of electrons for O2 and reduction in agricultural areas [Green et al., 2008].
 Additional evidence that DOC at the Perham, Minnesota site is derived from lithologic rather than surface-derived sources is indicated by the increase in ammonium concentrations observed at this site (Figure 8). An increase in ammonium concentrations as apparent groundwater age increases could result from either a dissimilatory reduction of nitrate to ammonium or from the mineralization of organic matter. However, previous nitrogen isotope studies [e.g., Hinkle et al., 2007] and the fact that nitrate is not detected in groundwater where ammonium concentrations are increasing indicate that mineralization of organic matter is the source of ammonium. While ammonium is likely being generated throughout the flow path, it only begins to accumulate in the aquifer after O2 is depleted; in the oxic portion of aquifers, ammonium is nitrified to or is sorbed to oxide mineral surfaces [e.g., Hill, 1990]. DOC does not increase with groundwater age in the oxic portion of the aquifer (Figure 8), suggesting that DOC liberated by the mineralization of organic matter quickly reacts with O2; however, once the aquifer becomes suboxic, the oxidation of DOC slows and DOC begins to accumulate (Figure 8). Increases in DOC and ammonium concentrations at the oxic/suboxic boundary may also be due to an increase in organic carbon in aquifer sediments; however, soil core data did not indicate a major change in lithology [Puckett and Cowdery, 2002]. Other sites examined in this study did not show systematic increases in ammonium concentrations with apparent groundwater age, either because organic matter sources were not as abundant and/or redox conditions were not sufficiently reducing. The Perham, Minnesota site had the highest median DOC concentrations and was one of the more reduced sites, with sulfate-reducing conditions prevalent in older groundwater.
Suggested reactions where reduced forms of sulfur are electron donors in denitrification reactions include [Kölle et al., 1985]:
This is often termed autotrophic denitrification since bacteria derive energy from an inorganic source, whereas the denitrification reaction in Table 1 is referred to as heterotrophic denitrification because bacteria use an organic source for growth and maintainance [Korom, 1992]. Pyrite occurs in freshwater wetlands and sediments of marine origin [Marnette et al., 1993]. As oxic groundwater moves into portions of aquifers containing iron sulfide deposits, oxidative dissolution of these deposits occurs [e.g., Poulton, 2003]. Increases in sulfate concentrations with groundwater age at the Sumas Aquifer, Princeton, Minnesota, and Brighton, Michigan sites (Figure 5) suggest that sulfide oxidation supplies electrons for O2 reduction and denitrification at these sites.
 Electron and mass balance calculations indicate that sulfide oxidation provides most of the electrons needed for O2 and nitrate reduction at the Sumas Aquifer site [Tesoriero et al., 2000]. Sulfate δS34 gradients along flow paths can provide additional evidence into the sources of added sulfate and electron donors. The sulfate δS34 values at the Sumas Aquifer site decrease dramatically across the redoxcline, while sulfate concentrations increase markedly (Figure 9). This pattern is consistent with pyrite oxidation as a source of the added sulfate. While these reversals are not always observed during sulfide oxidation [Strebel et al., 1990], a decrease in sulfate S34 content during pyrite oxidation is expected in agricultural areas due to the lower S34 content of sulfides than fertilizers [Moncaster et al., 2000; Böhlke et al., 2002] and the potential for fractionation during pyrite oxidation with sulfate-sulfur isotopes lighter than sulfide [Toran and Harris, 1989]. Sulfur isotope results from the Princeton, Minnesota site suggest that pyrite oxidation also occurs at this site [Böhlke et al., 2002]. Evidence of sulfide oxidation is not conclusive at the Brighton, Michigan site (e.g., no sulfur isotope data and a weaker correlation between age and sulfate concentrations).
 The importance of sulfide oxidation as a source of electrons at the Sumas Aquifer and Princeton, Minnesota sites was examined by estimating the number of electrons donated by this reaction and comparing it to the number of electrons accepted during O2 and reduction [Postma et al., 1991]. Electrons released during sulfide oxidation at each of these sites were estimated using the increase in sulfate concentrations across the redoxcline and the stoichiometry shown in equations (3) and (4). Similarly, the loss of O2 and gain in excess N2 across the redoxcline were used with the stoichiometry shown in equations (3) and (4) to estimate the amount of electrons accepted during O2 and reduction. Sulfide oxidation could be responsible for most, if not all, of the O2 and reduction at the Sumas Aquifer site (Figure 10). At the Princeton, Minnesota site, sulfide oxidation may initially supply most of the electrons for O2 and reduction; however, after ∼10 yr, electrons from sulfide oxidation are no longer sufficient to account for the reduction of O2 and , indicating that another source of electrons must be present (Figure 10). While mass balance calculations suggest that organic carbon is the additional source of electrons at the Sumas Aquifer site [Tesoriero et al., 2000], this was not the case at the Princeton, Minnesota site; however, dissolution of carbonates may have masked the contribution of organic carbon as an electron donor at this site [Böhlke et al., 2002]. Sulfide oxidation may also be an important supply of electrons for O2 and reduction at other sites where sulfide mineral deposition may occur (e.g., wetlands), but may be masked by other sources or sinks of sulfate.
4.5. Rate Comparisons
 O2 reduction and denitrification rates determined in this study were compared to rates from other studies to further elucidate the factors responsible for the spatial variation in rates. Rates were obtained directly from previous studies or were determined using concentration gradient and travel time estimates provided in these publications (Table 4). Studies examining point source contamination or using injected solutes were not included in this compilation to focus on ambient conditions and to allow a more direct comparison with our results. It should be noted that the rates from this study and those presented in Table 4 represent average rates over the time periods examined. Higher rates have been observed when more discrete zones have been examined using core samples [e.g., Jakobsen and Postma, 1994].
Table 4. Compilation of Selected O2 Reduction, Denitrification, and Sulfate Reduction Rates
 While most O2 reduction rates in this study and previous investigations varied over a similarly wide range (Tables 3 and 4), two previous studies had much lower rates. The presence of O2 concentrations between 60 and 250 μmol L−1 in groundwater >1000-yr old illustrates that very low O2 reduction rates (e.g., <0.01 μmol L−1 yr−1) occur in some systems [e.g., Winograd and Robertson, 1982; Vogel et al., 1981]. Low O2 reduction rates were found in two of our study areas (the uplands of the Sumas Aquifer and the Kennedyville, Maryland sites, Table 3); however, the age range was not sufficient to quantify very low rates.
 The influence of electron donors on O2 reduction and denitrification rates was examined by identifying those sites where sulfides were a significant source of electrons. When sulfide oxidation was indicated, zero-order O2 reduction rates tend toward the upper range of rates observed at other sites (Figure 11; Tables 3 and 4). Similarly, denitrification coupled with sulfide oxidation often occurs at higher rates than at sites where carbon was the dominant electron source for denitrification (Figure 11). High-denitrification rates coupled with sulfide oxidation (e.g., >250 μmol L−1 yr−1; Figure 11) were observed at the Führberg Aquifer in Germany [Böttcher et al., 1989], the Oostrum Aquifer in Netherlands [Zhang et al., 2009], the Sumas Aquifer in Canada [this study; Tesoriero et al., 2000], and in a sand aquifer in Denmark [Postma et al., 1991]. These results are consistent with the suggestion by Postma et al.  that nitrate reduction by pyrite oxidation occurs quickly and can, to a first approximation, be modeled using an equilibrium approach. These findings also suggest that when organic carbon and pyrite are both present, denitrification coupled with pyrite oxidation may be the dominant process even though it is not as favorable thermodynamically [e.g., Kölle et al., 1985]. A possible exception is the high-denitrification rate observed in the Lincolnshire Limestone in the United Kingdom [Hiscock et al., 2011]. While pyrite oxidation occurs in this system [Lawrence and Foster, 1986; Bottrell et al., 2000], organic carbon is suggested as the dominant electron source for denitrification [Hiscock et al., 2011].
 Sulfate reduction rates also vary widely between studies (Table 4; Figure 11) and over a similar range as O2 reduction and denitrification rates when sulfide is not an electron donor. However, sulfate reduction rates are typically lower than denitrification rates coupled with sulfide oxidation. This finding is consistent with the electron donor effect on rates stated above since sulfate reduction relies on a carbon source of electrons. An important exception is the rate obtained in a river recharged portion of an aquifer providing young reactive carbon to groundwater [Massmann et al., 2003]. It has been suggested that younger sediments are more likely to contain reactive carbon, resulting in faster redox reaction rates [e.g., Jakobsen and Postma, 1994].
5. Summary and Conclusions
 O2 reduction and denitrification rates from 12 study sites were determined using concentration gradients and tracer-based groundwater ages. O2 reduction rates varied markedly both within and between sites, with first-order rates ranging from 0.02 to 0.27 yr−1. While rates at most sites were generally consistent over decades of groundwater travel time, abrupt increases in reaction rates were often (but not always) observed when riparian sediments were encountered. Identifying these localized areas with high O2 reduction and denitrification rates is critical to understanding the transport of redox-sensitive contaminants.
 The groundwater travel time that occurs before denitrification commences is referred to as the denitrification lag time. Denitrification lag time is an important metric for assessing the susceptibility of aquifers to nitrate and other redox-sensitive contaminants (e.g., arsenic, atrazine, and volatile organic compounds). Measured denitrification lag times varied from <10 yr to >80 yr when low O2 reduction rates were extrapolated beyond the age range of sampled groundwater.
 Denitrification rates were determined assuming zero- and first-order kinetics. Zero-order denitrification rates can be broadly generalized into three categories: low rates (e.g., <3 μmol L−1 yr−1) found in areas having elevated O2 concentrations, moderate rates (10–100 μmol N−1 yr−1) in areas with low O2 concentrations, and high rates (>100 μmol L−1 yr−1) when changes in lithology result in a sharp increase in the supply of electron donors. First-order rates show a similar pattern, with nondetectable rates in oxic groundwater, rates ranging from 0.06 to 0.30 yr−1 in most suboxic systems, and higher rates (>0.36 yr−1) in systems where a sharp redox gradient was observed.
 The availability of electron donors is indicated as the major factor influencing O2 reduction rates. Likely electron donors at these sites include organic carbon and sulfide deposits. The relations between DOC concentrations and apparent groundwater age suggest that lithologic sources of carbon are a major source of electron donors for O2 reduction in these aquifers, while surface-derived sources of DOC are not. Sulfide oxidation was indicated as a major source of electrons for O2 reduction and denitrification at two of the 12 sites studied. A review of published rates suggests that denitrification tends to occur more quickly when linked with sulfide oxidation rather than carbon oxidation.
 This research was funded by the U.S. Geological Survey's (USGS) National Water Quality Assessment Program (NAWQA). L.N. Plummer, E. Busenberg, and their colleagues at the USGS CFC laboratory are gratefully acknowledged for the interpretation and analysis of samples for CFCs, SF6, and other dissolved gases. The authors thank the many USGS scientists that conducted research on these sites and laid the foundation upon which this work could build, including: J.K. Böhlke, Stephen Hinkle, Peter McMahon, Steven Phillips, David Saad, Gary Speiran, and Mary Ann Thomas. Private landowners are gratefully acknowledged for permitting us to access their land to install and sample monitoring wells. We thank Peter McMahon and Christopher Green (both of USGS) for many helpful suggestions. Three anonymous reviewers and the associate editor of this journal are gratefully acknowledged for their insightful comments on a previous version of this manuscript.