Ammonium (NH4+) is a major constituent of many contaminated groundwaters, but its movement through aquifers is complex and poorly documented. In this study, processes affecting NH4+ movement in a treated wastewater plume were studied by a combination of techniques including large-scale monitoring of NH4+ distribution; isotopic analyses of coexisting aqueous NH4+, NO3−, N2, and sorbed NH4+; and in situ natural gradient 15NH4+ tracer tests with numerical simulations of 15NH4+, 15NO3−, and 15N2 breakthrough data. Combined results indicate that the main mass of NH4+ was moving downgradient at a rate about 0.25 times the groundwater velocity. Retardation factors and groundwater ages indicate that much of the NH4+ in the plume was recharged early in the history of the wastewater disposal. NO3− and excess N2 gas, which were related to each other by denitrification near the plume source, were moving downgradient more rapidly and were largely unrelated to coexisting NH4+. The δ15N data indicate areas of the plume affected by nitrification (substantial isotope fractionation) and sorption (no isotope fractionation). There was no conclusive evidence for NH4+-consuming reactions (nitrification or anammox) in the anoxic core of the plume. Nitrification occurred along the upper boundary of the plume but was limited by a low rate of transverse dispersive mixing of wastewater NH4+ and O2 from overlying uncontaminated groundwater. Without induced vertical mixing or displacement of plume water with oxic groundwater from upgradient sources, the main mass of NH4+ could reach a discharge area without substantial reaction long after the more mobile wastewater constituents are gone. Multiple approaches including in situ isotopic tracers and fractionation studies provided critical information about processes affecting NH4+ movement and N speciation.
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 Ammonium (NH4+) is present in groundwater naturally as a result of anaerobic degradation of organic matter and artificially as a result of organic waste disposal. Anthropogenic NH4+ is one of the major dissolved components in some types of groundwater contaminant plumes. NH4+ concentrations of the order of 1–10 mmol/L have been observed in aquifers contaminated by landfill leachate and concentrated wastewater disposal practices [Baedecker and Back, 1979; LeBlanc, 1984; Cozzarelli et al., 2000; Christensen et al., 2001; Heaton et al., 2005]. Septic systems and agricultural practices also may result in locally elevated recharge rates of NH4+. NH4+ in aquifers can cause degradation of groundwater quality and usability, it can have substantial effects on water-rock interactions, and it can be a substantial source of N in surface waters receiving groundwater discharge. Despite the environmental importance of NH4+, there are few studies documenting NH4+ transport and reaction processes in aquifers.
 Ammonium movement may be retarded by physical-chemical processes such as sorption (including cation exchange), or biological processes such as microbially induced transformations (Figure 1), depending on aquifer geochemistry and the nature of the groundwater flow system. Retardation of NH4+ transport has been observed in contaminated groundwaters [Ceazan et al., 1989; DeSimone and Howes, 1998; van Breukelen et al., 2004], and it may lead to much longer aquifer flushing times for NH4+ than for other more mobile aqueous species, with relative retardation factors potentially ranging over 3 orders of magnitude (100 to 103) [Buss et al., 2003]. Ammonium oxidation occurs commonly in conjunction with O2 reduction (nitrification) and possibly may be associated with Mn-oxide reduction [Luther et al., 1997; Hulth et al., 1999]. Nitrification results in production of NO2− followed by NO3−:
where the NO2− may be derived from NO3− by denitrification. These physical and biogeochemical processes need to be evaluated before the movement and fate of NH4+ in contaminated or uncontaminated aquifers can be rationalized or predicted.
 Stable N isotope fractionations and N isotope tracers can provide valuable information about the processes affecting NH4+ transport. Isotope fractionations have been reported for NH4+ sorption/desorption processes and for nitrification in the presence of excess NH4+. Laboratory studies indicate that NH4+ sorbed from solutions by clays and artificial cation exchange resins commonly is enriched in 15N relative to the NH4+ that remains in solution, with apparent equilibrium isotope fractionation factors (α = [15N/14N]solid/[15N/14N]aqueous) of around 1.001 to 1.011 [Delwiche and Steyn, 1970; Karamanos and Rennie, 1978]. In contrast, nitrification of NH4+ yields 15N-depleted products and commonly results in a substantial increase in the δ15N value of the residual NH4+. Kinetic isotope fractionation factors (α = [15N/14N]product/[15N/14N]reactant) ranging from about 0.962 to 0.983 have been reported for laboratory studies of nitrification [Delwiche and Steyn, 1970; Mariotti et al., 1981; Casciotti et al., 2003]. Given these opposing isotope fractionation effects, it should be possible to distinguish between sorption and nitrification as major processes affecting the distribution of NH4+ by evaluating variations in concentration and δ15N in field settings. In addition, artificial 15N-enriched NH4+ tracers can be used to investigate the movement of NH4+ relative to water and the rate of NH4+ oxidation can be determined from the rate of appearance of 15N tracer in NO3− or N2, depending on the process. The precision of stable isotope measurements at low to moderate levels of 15N enrichment (e.g., <10 percent 15N) permits field experiments to be done with minimal disturbance to the chemical composition of the system, and with a higher degree of sensitivity than most chemical methods.
 The objective of the current study was to determine the distribution and importance of various processes affecting the transport and reaction of NH4+ in a wastewater-contaminated aquifer by using a combination of chemical and isotopic measurements including in situ isotope tracers. Two related studies at the same site assessed local nitrification potentials by using single-well tracer tests [Smith et al., 2006] and biomolecular approaches [Miller et al., 1999]. This paper addresses controls of NH4+ movement at larger spatial and temporal scales and provides a comparison of multiple approaches. Tested approaches include injection of 15N-enriched NH4+ with Br− to determine retardation factors for NH4+ transport, isotopic analysis of NO3− and N2 from the tracer tests to determine rates of NH4+ oxidation, sediment extraction experiments to determine sorption behavior of NH4+, long-term monitoring of the shape and position of the NH4+ contaminant mass, and isotopic analyses of NH4+, NO3−, and N2 gas in the absence of tracers to seek evidence for isotopic fractionation associated with sorption, nitrification, denitrification and anammox. Results of these different approaches provide an unusually comprehensive picture of NH4+ behavior in a contaminated aquifer, with guidelines for future studies of complex N-rich systems.
2. Study Site and Methods
2.1. Treated Wastewater Plume and Ammonium “Cloud”
 At the Massachusetts Military Reservation (MMR) on Cape Cod, a linear plume of contaminated groundwater was created as a result of local artificial recharge of treated wastewater from 1936 to 1995 [LeBlanc, 1984; Savoie and LeBlanc, 1998] (Figure 2). The aquifer containing the plume is largely glacial outwash sand consisting of quartz and feldspar, with a few percent or less of phyllosilicates, oxides, and other accessory minerals and <0.1% organic C [Barber et al., 1992]. The overall size and shape of the MMR wastewater plume is indicated by high concentrations of B (Figure 3). Boron is a common constituent of domestic wastewater and it is a mobile and stable component when present in high concentrations in sandy aquifers such as the MMR site [LeBlanc, 1984]. The upper plume boundary also is delineated by steep vertical gradients of specific conductance, dissolved organic and inorganic C, SO42−, Cl−, O2, δ18O, and δ2H, among other constituents [LeBlanc, 1984; Smith et al., 1991; Savoie and LeBlanc, 1998; Böhlke et al., 1999].
 Groundwater velocities in the plume are known from a combination of injected tracer studies and groundwater dating by 3H and 3H-3He methods [LeBlanc et al., 1991; Shapiro et al., 1999] (Figure 3). The distributions of B and groundwater age indicate that the movement of the wastewater through the aquifer was governed by a combination of processes: (1) rapid recharge and downward transport beneath the infiltration beds with a local vertical velocity of around 10–20 m/yr, (2) lateral downgradient transport with regional groundwater flow with an average horizontal velocity of about 120 m/yr in the plume, and (3) gradual sinking below the water table at an average rate of about 0.8 m/yr in the downgradient direction caused by a combination of regional recharge and density differences between the plume and surrounding groundwater. The combined result of these processes after 60 years of wastewater disposal was a flattened plume about 15–20 m thick and more than 6 km long, overlain by a wedge of oxic local recharge water, with minimal lateral (vertical) dispersion (Figures 2 and 3).
 The wastewater plume was largely anoxic and contained locally elevated NO3− concentrations. Nitrate concentrations were highest near the wastewater infiltration beds, decreased rapidly as a result of denitrification coupled with C oxidation [Smith et al., 1991, 2004], and persisted at low to moderate levels throughout the plume. In contrast, there was a fairly distinct region of high NH4+ concentrations within the plume with a center of mass about 2 km downgradient from the plume source, referred to subsequently as the NH4+ “cloud” (Figure 3). The shape and position of the NH4+ cloud within the larger wastewater plume presumably reflects some combination of processes whose relative importance is the subject of this study: (1) past changes in the wastewater treatment process resulting in changes in the N speciation of the artificial recharge, (2) retardation of NH4+ transport in comparison to the water with which it was recharged, or (3) reactions such as nitrification, anammox, or NO3− reduction to NH4+.
2.2. Field Sampling and Chemical Analyses
 The distribution and long-term movement of NH4+ in the MMR wastewater plume were investigated by repeated synoptic sampling of multilevel sampling devices in a longitudinal transect beneath Ashumet Valley (sites F262 to F350; see Figure 2) from 1990 to 1998. Additional samples for natural abundance isotope gradient measurements were collected in June 1997 (prior to the isotope tracer tests) at sites F168, F593, F471, and F472 (Figure 2) approximately 2600 m downgradient from the wastewater infiltration beds. The multilevel sampling device (multiport) is a 3.2-cm diameter PVC pipe containing a bundle of 6-mm diameter polyethylene tubes that exit the pipe at 15 discreet elevations in the saturated zone [LeBlanc et al., 1991]. The tubes exit the pipe at intervals ranging from 0.2 to 1.5 m and have Nylon screens over the ends. Samples were pumped from the polyethylene tubes through Norprene tubing by a peristaltic pump at the land surface.
 The distributions of major and minor chemical constituents were used to evaluate isotope mass transfers for the N species and to map the distribution of the NH4+ cloud within the context of the larger wastewater plume. Dissolved O2 and pH were measured in the field by electronic probes (O2 > 30 μmol/L); O2 concentrations <30 μmol/L were measured by colorimetry (CHEMetrics, Inc., 1994) with a detection limit of approximately 5 μmol/L. Samples for analysis of NO3−, NO2−, NH4+, and major cations and anions were filtered in the field (0.45 μm). The NO3− and NO2− samples were frozen, NH4+ samples were acidified to pH < 2 with concentrated H2SO4, and cation samples were acidified to pH 1 with HNO3. Additional filtered samples were collected for analysis of NH4+ isotopes (preserved with H2SO4 at pH < 2) and NO3− isotopes (preserved with KOH at pH > 11). Samples (15 mL) for analysis of N2O were injected with a syringe into 30-mL serum bottles containing He headspace with 0.2 mL of 12.5 N NaOH as preservative. Samples for analysis of N2, O2, Ar, CH4, and isotopes of N2 were collected in 160-mL serum bottles without headspace with KOH as preservative. Water was pumped into each bottle until it overflowed, a single pellet of KOH (∼100 mg) was dropped into the full bottle, then a 12-mm thick butyl rubber stopper was inserted with a syringe needle in place to allow excess water to escape.
 Samples collected in 1990–1994 were analyzed in the laboratory for NO3−, NO2−, and NH4+ using a flow injection autoanalyzer (FIA) [Antweiler et al., 1996]. For subsequent samples, NO2− was analyzed by FIA and NO3− and NH4+ were analyzed by ion chromatography (IC) [Smith et al., 2006]. Other major cations and anions were analyzed by IC. N2O samples were analyzed by gas chromatography on the He headspace in the half-filled 30 mL serum bottles [Brooks et al., 1992]. For the major gases, low-pressure headspace was created in the 160 mL serum bottles in the laboratory by extracting approximately 10 mL of water and the concentrations of Ar, N2, O2, and CH4 in the headspace were measured by gas chromatography, with corrections for the lab solubilities (URL http://water.usgs.gov/lab/dissolved-gas).
2.3. Ammonium Desorption Experiments
 Ammonium exchange between the solid and aqueous phases in the contaminated aquifer was investigated by comparing aqueous NH4+ concentrations with concentrations of exchangeable NH4+ extracted from core samples near F168, F262, and F472 (Figure 2). The NH4+ exchange data were used to estimate retardation factors for NH4+ transport within the contaminated plume. Core samples were collected using a wire line piston core barrel through a hollow stem auger [Zapico et al., 1987] on 13–14 January 1998, and divided into sections approximately 0.5 m long. Each core section was homogenized, then 50 g aliquots were added to flasks containing 150 mL of 2 M KCl solution, which was agitated for 2 hours, then centrifuged for 8 min at 10,000 rpm, filtered, and preserved with H2SO4 for subsequent NH4+ analysis. Corresponding groundwater samples were collected on 13 January 1998, from the multilevel samplers near the core locations and preserved with H2SO4. The average partition coefficient (K′d) for NH4+ sorption in the contaminated aquifer was derived from a linear fit to the NH4+ concentrations of paired core extracts and groundwater samples over a range of concentrations. The concentrations of extractable NH4+ in the cores were expressed as μmol/g of dry sediment; concentrations of aqueous NH4+ in the groundwaters were expressed as μmol/g of water; yielding K′d in units of gH2O/gsolid [Appelo and Postma, 1996].
2.4. Isotope Tracer Experiments
 Rates of NH4+ transport and reaction in the contaminated aquifer were investigated in situ by using natural gradient NH4+ isotope tracer tests similar to the NO3− isotope tracer tests described by Smith et al. . In 1997 and 1998, parcels of groundwater were enriched in Br− and 15NH4+ and then monitored as they moved downgradient with the normal groundwater flow (Figure 4). Effects of advection, dispersion, exchange, and reaction on the transport of NH4+ were determined from variations in Br− concentrations and the 15N contents of NH4+, NO3−, and N2 at the downgradient collection sites.
 The isotope tracer tests were conducted behind the leading edge of the NH4+ cloud approximately 2.4 km downgradient from the wastewater plume source (Figure 2), with injections at 2 depths [Smith et al., 2006]: (1) at an elevation of −8.2 m within the core of the NH4+ cloud where NH4+ concentrations were high and O2 concentrations were at or below the limit of detection (referred to as the “deep” tracer) and (2) at an elevation of −6.3 m in the transition zone along the upper boundary of the NH4+ cloud, where low but measurable concentrations of both O2 and NH4+ were present (referred to as the “shallow” tracer). Isotope tracer solutions were prepared in a gas-tight bladder that had been flushed with pure Ar gas, then deflated. For each test, a concentrated solution of NaBr and (15NH4)2SO4 (98 atom% 15N) was made by adding salts to 3 L of pure degassed (anaerobic) water, with concentrations sufficient to yield a Br− concentration of approximately 100 mg/kg (1200–1300 μmol/L) and a mole fraction of 15N in NH4+ of around 0.2–0.5 when mixed with groundwater to make 200 L of injectate. The tracer solution was injected into the bladder, followed by 200 L of groundwater pumped from multiports at the approximate location and elevation of the tracer injection. The bladder was agitated while submerged in a pool of water held at 12°–16°C to mix the ingredients with minimal alteration of the groundwater temperature, then the injectate solution was reinjected into the aquifer through a single multiport.
 On the day of the tracer injection in 1997, samples were collected from the injection multiport profile before the injection, from the tracer solution in the bladder as it was being injected into the aquifer, and from the injection multiport immediately after the tracer injection was finished. Injection port samples were taken over a period of 10 days as part of a nitrification potential study [Smith et al., 2006]. Samples from downgradient multiports were collected for the current study at intervals of 1–10 days for periods of 3–6 months.
2.5. Isotope Tracer Simulation
 A simple one-dimensional numerical model of advection, dispersion, and isotope exchange was constructed to simulate movement of Br− and 15NH4+ during the tracer experiments. For Br−, at each time step, the contents of all cells were moved downgradient according to the advection velocity (v = Δx/Δt) and then permitted to mix with the contents of adjacent cells according to [Press et al., 1989; Appelo and Postma, 1996]
where C (μmol/L) is concentration and D (m2/d) is the longitudinal dispersion coefficient. Advection and dispersion parameters were adjusted in this model to match the Br− breakthrough curves.
 For 15NH4+ breakthrough, equation (3) was modified to include isotope exchange by assuming the total NH4+ concentrations in the solid and aqueous phases were constant and the isotopes were exchanged rapidly between the phases in each time step with no fractionation:
where X15N is the mole fraction of 15N in aqueous NH4+ (X15N = 15N/(15N + 14N)) and F[NH4+]solid is the fraction of the total NH4+ in a representative volume of the aquifer that is in the solid phase (F[NH4+]solid = [NH4+]solid/([NH4+]solid + [NH4+]aq) = (1 + 1/Kd)−1, where Kd is a dimensionless distribution coefficient). The lack of isotope fractionation in the model is consistent with the δ15N profiles and the desorption experiments (see section 3). The assumption that total NH4+ concentrations were constant is based on (1) the tracer experiment had a short timescale and small spatial scale in comparison to the movement of the NH4+ cloud through the aquifer, which means the longitudinal concentration gradients were small and the partitioning between solid and aqueous NH4+ was near steady state, and (2) the NH4+ concentrations during the 15N breakthrough curves did not change systematically in response to the tracer cloud. This model would not be appropriate for larger-scale simulations in which concentrations of NH4+ and other chemical species were changing.
 Isotope effects of tracer NH4+ oxidation to produce 15N-enriched NO3− (nitrification; Figure 1, equations (1a) and (1b)) were simulated by assuming that the NO3− in a cell at a given time was a mixture of new NO3− formed from coexisting NH4+ (equation (4)) during the previous time step plus NO3− that moved downgradient during the previous time step. The nitrification rate in the model is expressed as the fraction of total NO3− derived from tracer NH4+ per day. Movement of NO3− was simulated in the same way as Br− (equation (3)). Production of 15N-enriched N2 by anaerobic oxidation of tracer NH4+ (anammox; see Figure 1 and equation (2)) was simulated in the same way as the NO3− production. Mineralization and assimilation were assumed to be negligible as net sources and sinks of NH4+ in the vicinity of the tracer test because of the low abundance of organic matter in the aquifer [Barber et al., 1992]. Gas losses during transport were considered to be negligible because the tracer tests were done under sufficient hydrostatic pressure to prevent formation of a gas phase.
2.6. Isotope Analyses
 Stable N isotope measurements were used in a variety of ways that imposed different requirements on the methods of preparation and analysis: (1) artificially enriched 15NH4+ was tracked during the isotope tracer experiment to monitor NH4+ transport through the tracer array; (2) minor amounts of tracer 15N were sought in potential NH4+ reaction products (NO3− and N2) to determine reaction rates at short timescales (weeks to months); (3) ambient isotopic variations in NO3−, NH4+, and N2 were evaluated with respect to constituent sources and the cumulative long-term (years to decades) effects of reactions involving isotope fractionations; and (4) isotopic differences between aqueous NH4+ and NH4+ extracted from sediment cores were compared to determine isotope effects of NH4+ sorption. For the relatively small ambient isotope variations, the stable isotope ratios are reported as delta (δ) values in parts per thousand (‰), as defined for each element by
where Ri and Rs are the mole ratios of 15N/14N or 18O/16O of the sample and standard, respectively, and the standards are atmospheric N2 and VSMOW, respectively. For the large variations encountered in the tracer experiments, the N isotope ratios also are reported as mole fractions (X15N), which were used in the mass balance calculations. Atmospheric N2 has a 15N/14N mole ratio of 0.0036765, a 15N mole fraction of 0.003663, and a δ15N value of 0‰ [Junk and Svec, 1958; Coplen et al., 1992].
2.6.1. Ammonium Isotopes
 NH4+ was separated from groundwater samples for isotopic analysis by a previously undocumented method involving direct sorption on NH4+-selective zeolite. The separation was done by adding 200 mg of IONSIEV W-85 zeolite (Union Carbide) to 100 or 200 mL of sample, stirring for 40 min, then collecting the zeolite on a glass fiber filter by vacuum filtration. The solution pH was monitored and held between 5.0 and 5.5 by titration throughout the equilibration of NH4+ with the zeolite. Samples that were preserved by acidification with H2SO4 were titrated to pH 3.5 with LiOH before adding zeolite. Experiments indicated that Li+ interfered substantially less than did Na+ or K+ with the uptake of NH4+ by the zeolite. The zeolite plus filter was dried for 2 hours in a vacuum oven at 30°C, then loaded into a quartz glass tube with Cu2O and CaO, evacuated overnight, sealed, baked at 650°C for 4 hours, and cooled slowly to produce pure N2 gas. Isotopic analyses of samples were calibrated by analyses of solutions containing laboratory NH4+ isotope reference materials prepared the same way as the samples (including acidification and LiOH titration). The NH4+ isotope data were normalized with respect to IAEA-N1 (δ15N = +0.4‰; X15N = 0.3664), USGS-26 (δ15N = +53.7‰; X15N = 0.3859), and IAEA-311 (δ15N = +4730‰; X15N = 2.0632). Typical reproducibilities (1σ) after normalization were less than ±0.2‰ (δ15N) or ±0.00007 (X15N) for δ15N near 0‰ (nontracer samples) and less than ±100‰ (δ15N) or ±0.035 (X15N) for δ15N near 5000‰ (tracer peak samples).
 The direct zeolite extraction procedure cannot be used for high-salinity samples like the sediment KCl extracts from the sorption experiments because the NH4+ selectivity of the zeolite is not strong enough to exclude large amounts of competing cations. For those experiments, NH4+ was separated from both the sediment KCl extracts and the corresponding groundwaters by steam distillation with MgO [modified from Velinsky et al., 1989]. The distilled NH3 was collected in a trapping solution containing 3.6 mmol/L H2SO4, then the NH4+ was recovered from the trapping solution with zeolite as described above. This procedure yielded δ15N values with reproducibilities of around ±0.3‰ (1σ) when calibrated by analyzing with freshwater and saltwater solutions containing isotope reference materials. For groundwaters analyzed by both extraction methods, the average difference δ15N[distillation] − δ15N[direct zeolite] was 0.1 ± 0.2‰.
2.6.2. Nitrate Isotopes
 Samples for NO3− isotope analysis were filtered in the field (0.45 μm) and preserved with KOH (pH ≈ 11–12). In the laboratory, aliquots containing 10–20 μmol of NO3− were freeze-dried, sealed into quartz-glass tubes under vacuum with combustion reagents (0.2 g of CaO plus 2.0 g of a Cu-Cu2O mixture), baked at 850°C and cooled slowly to produce purified N2 gas, which was admitted to a Finnigan MAT 251 isotope ratio mass spectrometer and analyzed in dual-inlet mode [Böhlke and Denver, 1995; Smith et al., 2004]. Concentrations of NO2− in samples from the NH4+ cloud were less than 1 μmol/L and were negligible in comparison to the NO3− concentrations. The NO3− N isotope analyses were calibrated by interspersed analyses of laboratory standard NO3− salts and solutions whose δ15N values are known with respect to the normalized scale defined by IAEA-N3 (+4.7‰) and USGS32 (+180‰) [Böhlke and Coplen, 1995].
 Because high-precision ambient δ15N[NO3−] measurements were needed in samples containing tracer-level 15NH4+, experiments were done to ensure that isotopic cross contamination and transformation of N species within samples were minimized during sample storage and analysis. Cross-contamination effects of tracer 15NH4+ were eliminated by freeze-drying NO3− isotope samples 2–3 times after adjusting to pH > 11. However, irregularities in δ15N[NO3−] values indicated that small amounts of tracer NH4+ oxidation may have occurred in some of the 1997 samples during storage. No detectable NH4+ oxidation occurred in samples stored at room temperature at pH > 11 for periods of 1–3 years, but NH4+ oxidation did occur commonly in samples stored at pH < 11. Analyses of NO3− coexisting with tracer NH4+ in serum bottles collected for dissolved gas analyses (with pH ≥ 12) indicated no measurable change in δ15N[NO3−] after 6 years of storage. Therefore δ15N[NO3−] data for 15NH4+ tracer samples preserved at pH < 11 were not used for interpreting the tracer test results. In nontracer samples, the rate of NH4+ oxidation in the stored samples was too low to have a measurable effect on the concentrations or isotopic compositions of NO3− or NH4+.
 Because the background values of δ15N[NO3−] at the tracer test location exhibited variations caused by denitrification in upgradient areas of the wastewater plume [Smith et al., 1991, 2004], some of the tracer breakthrough samples were analyzed for δ18O[NO3−] by the bacterial N2O method [Casciotti et al., 2002] to resolve the effects of tracer 15N[NH4+] nitrification from preexisting variations in the effects of denitrification. For these analyses, aliquots containing 20 nmol of NO3− were incubated with Pseudomonas aureofaciens to produce N2O, which was admitted to a Finnigan Delta Plus mass spectrometer in continuous flow mode for peak integration at m/z = 44, 45, and 46, from which δ15N and δ18O were calculated by assuming mass-dependent covariation of 16O:17O:18O. The δ18O[NO3−] data were normalized to values of −27.9‰ for USGS34 and +25.6‰ for IAEA-N3 [Böhlke et al., 2003].
2.6.3. Nitrogen Gas Isotopes
 For δ15N analysis of dissolved N2, the low-pressure headspace remaining in each 160 mL serum bottle after GC analysis was expanded in a high-vacuum extraction line into quartz glass tubes containing combustion reagents (0.2 g of CaO plus 1.2 g of Cu + Cu2O). The tubes were baked at 850°C and analyzed by dual-inlet mass spectrometry, as described for the NO3− isotope samples. The dissolved N2 results were calibrated by analyzing aliquots of air N2 (δ15N = 0‰) and air-saturated water that were prepared the same way as the groundwater samples. The average δ15N[N2] value of lab-equilibrated water samples was +0.7 ± 0.1‰, similar to published experimental results [Knox et al., 1992]. Overall uncertainties of the δ15N[N2] values are estimated to be approximately ±0.1–0.2‰.
 Because the dissolved-gas samples were stored at pH > 11, where almost all the NH4+ should have been neutralized to NH3, it is important to know if small amounts of tracer NH3 could have affected the δ15N values of the total headspace N that was analyzed as N2. Samples with relatively high-NH4+ concentrations (≥600 μmol/L), when preserved with KOH, could have bulk NH3/N2 mole ratios approaching 1. Nevertheless, given a ratio of Henry's law solubility constants KH[NH3]/KH[N2] of about 9 × 104 at room temperature [Stumm and Morgan, 1996], the headspace in the samples would be expected to have NH3/N2 mole ratios of the order of 10−5 or less. To test this prediction, lab solutions containing NH4+ with varying δ15N values and concentrations bracketing those of the samples were equilibrated with air, treated with KOH, and analyzed as samples. No isotope effect on the headspace N2 was detected (±0.1‰) for aqueous δ15N[NH4+] values as high as +54‰, indicating that naturally fractionated NH4+ was not a problem. A more sensitive test was provided by field tracer samples that had NH4+ concentrations as high as 380 μmol/L and δ15N[NH4+] values ranging from +12 to +3100‰. Measured δ15N[N2] values were indistinguishable (within ±0.2‰), indicating that the mole ratio of NH3/N2 in the analyzed headspace from the serum bottles was <10−4 and that NH3 cross contamination did not have a measurable effect on the N2 isotope results.
3.1. Distribution and Migration of the Ammonium Cloud
 In contrast to B and other mobile wastewater indicators, the distribution of NH4+ is dominated by a relatively small “cloud” of high concentrations with a peak that was about 2000 m downgradient from the infiltration beds in 1994 (Figure 3). The NH4+ cloud was elongated in the direction of groundwater flow but confined to a relatively narrow vertical interval near the upper boundary of the wastewater plume. The NH4+ concentrations decreased in all directions around the NH4+ cloud, but the steepest gradient was near the upper boundary between the anoxic plume and overlying oxic groundwater. The lower boundary of the NH4+ cloud was within the wastewater plume where B concentrations were high and O2 concentrations were <5 μmol/L. The peak concentration and center of mass of the NH4+ cloud were relatively close to the upper leading edge of the cloud. Concentrations of NH4+ upgradient from the NH4+ cloud were variable (0 to 108 μmol/L), but not as high as in the NH4+ cloud. Concentrations of NH4+ downgradient from the cloud generally were lower (<10 μmol/L). Qualitatively, these patterns resemble what might be produced by partial chromatographic separation of NH4+ from other wastewater constituents. The distance traveled by the NH4+ peak from the wastewater infiltration beds (∼2000 m) is approximately 0.28 times the total hypothetical length of the wastewater plume after 60 years (∼7200 m), assuming an average longitudinal groundwater velocity of 120 m/yr [Shapiro et al., 1999].
 Synoptic sampling of a large-scale array of wells in 1990, 1994, and 1998 provided direct evidence for movement of the NH4+ cloud over time (Figure 5). The apparent horizontal velocities of the leading edges of the NH4+ concentration contours over the 7.7-year period range from about 19 to 44 m/yr (average = 30 m/yr) and are inversely proportional to the magnitudes of the concentrations. These apparent rates of advance of the NH4+ cloud are approximately 0.16 to 0.37 times (average = 0.25 times) the average groundwater velocity of 120 m/yr. Heterogeneities in the shape of the NH4+ cloud and its rate of advance may be related in part to local variations in the groundwater velocities, which range from at least 110 to 220 m/yr [LeBlanc et al., 1991; Böhlke et al., 1999] (this study).
 Detailed vertical profiles at F168 and F593 include the upper and lower boundaries of the NH4+ cloud behind its leading edge (Figure 6). At these sites, NH4+ concentrations were low (<1 μmol/L) in the upper parts of the profiles where O2 concentrations ranged from near air saturation values in the overlying recharge water to <10 μmol/L near the plume boundary. NH4+ concentrations increased abruptly below the O2-bearing zone, peaked at >400 μmol/L, then decreased again to <1 μmol/L. The vertical spacing of the multiport samplers was such that measurable O2 and NH4+ both were present in only one sample in each profile. The thickness of the zone in which O2 and NH4+ might coexist measurably is <0.6 m.
3.2. Isotopic Composition of Ammonium
 Despite the large variation in NH4+ concentrations, there was essentially no variation in the δ15N[NH4+] values among the anoxic samples from the NH4+ cloud at F168, F593, F471, and F472 (+12.6 ± 0.4‰, n = 23) (Figures 6 and 7). When compared to the Rayleigh fractionation equation [Clark and Fritz, 1997],
with [NH4+]o equal to the peak concentration of NH4+ in F593 and F168 (520 μmol/L), the anoxic samples yield an apparent isotope fractionation factor (α) of 1.0000 ± 0.0003 (Figure 7) for processes associated with the major NH4+ gradients within the main body of the NH4+ cloud.
 Relatively high values of δ15N[NH4+] were obtained in the upper transition zone where concentrations of NH4+ were low and measurable amounts of O2 were present. In that narrow zone, NH4+ concentrations and δ15N values were inversely correlated (Figure 7), consistent with a fractionating NH4+-consuming process such as nitrification. Limited data from F168 yield apparent isotope fractionation factors (α) of around 0.980 to 0.991. Because of dispersion and uncertainty about the initial NH4+ concentrations of individual samples, the apparent fractionation effect may not be equal to the intrinsic fractionation, which may have had a smaller value of α. Nevertheless, the existence of a substantial isotope effect that occurred only in the vicinity of the O2 gradient is evidence for aerobic NH4+ oxidation near the upper boundary of the NH4+ cloud.
3.3. Concentrations and Isotopic Compositions of Nitrate and Nitrogen Gas
 Other major N species that coexist with NH4+ are NO3− and N2. NO3− concentrations at F168 and F593 ranged from about 40 to 240 μmol/L (Figure 6), typical of the wastewater plume in areas more than about 500 m from the source (Figure 3). Near the upper boundary of the NH4+ cloud, there was a small peak in the NO3− concentrations as might be expected if nitrification had occurred (Figure 6). Except for that minor peak, the concentrations of NO3− were moderately variable but did not change systematically through the contaminated part of the profile.
 Above the wastewater plume, where NH4+ concentrations were low, the NO3− had an average δ15N of +6 ± 1‰. This NO3− is attributed to nonwastewater sources in recharge areas downgradient from the wastewater infiltration beds. Values of δ15N[NO3−] increased to around +10 to +15‰ near the upper boundary of the wastewater plume where O2 was present, then increased further to almost +40‰ deeper in the plume (Figure 6). Within the plume, values of δ18O[NO3−] and δ15N[NO3−] were positively correlated, with an average slope (Δδ18O/Δδ15N) of 0.73 (Figure 8). The δ15N and δ18O values of the NO3− within the wastewater plume are too high to be a result of nitrification of the coexisting NH4+, which would be expected to yield NO3− with δ15N ≤ 13‰ and δ18O ≈ 0‰ [Hübner, 1986; Amberger and Schmidt, 1987]. Instead, the NO3− isotopic variations within the plume are consistent with wastewater NO3− in varying stages of denitrification [Smith et al., 1991; Böhlke et al., 2000]. Concentrations of NO2− were below the detection limit (<1 μmol/L) throughout the profile at F168 and concentrations of N2O ranged from <0.01 μmol/L to approximately 0.09 μmol/L. These values are lower than the concentrations of these intermediate species commonly observed in the upgradient area of active denitrification (R. L. Smith, unpublished data, 2005).
 Dissolved gas data indicate that denitrification or some other process yielding excess N2 had occurred in the samples containing isotopically fractionated NO3 (Figure 9). The concentration of excess N2 in each sample (N2,excess) was estimated from
where the expression in parentheses is the concentration of N2 in air-saturated water (ASW) at the temperature indicated by the Ar concentration [Weiss, 1970]. The δ15N value of the N2,excess component in each sample was estimated from
where δ15N[N2, ASW] = 0.7‰ and (Ar/N2)ASW is defined as above. In oxic groundwaters overlying the wastewater plume, the concentrations of Ar and N2, and the values of δ15N[N2], were similar to those of air-saturated waters with <2 cm3STP/L of excess air (Figure 9) [Böhlke et al., 1999]. Within the plume at F593, N2 concentrations ranged from air saturation values up to about 850 μmol/L and were consistent with 0 to 250 μmol/L of N2,excess (0 to 500 μmol/L denitrified NO3−). Samples with detectable N2,excess had values of δ15N[N2] ranging from 0.0 to +4.7‰. The combined gas and NO3− data from the anoxic parts of the F593 profile are consistent with moderate to advanced stages of denitrification of NO3− with initial isotopic composition (δ15N[NO3−]°) of +9 ± 2‰. All samples had CH4 < 0.1 μmol/L, consistent with persistence of NO3−.
3.4. Ammonium Sorption and Isotopic Fractionation From Extraction Experiments
 Paired samples of NH4+ in groundwater and NH4+ extracted from core samples were approximately consistent with a linear sorption coefficient (K′d) of 0.46 gH2O/gsolid (Figure 10). This K′d value is within the range of values reported by Ceazan et al.  for sorption experiments with uncontaminated aquifer sediments from the MMR site (0.34 gH2O/gsolid) and for paired groundwaters and extracts from within the contaminated plume at F347 (0.87 gH2O/gsolid) and F262 (0.59 gH2O/gsolid). A volumetric (dimensionless) Kd value, giving the ratio of (NH4+)solid/(NH4+)aqueous in a representative aquifer volume, was derived from K′d [Appelo and Postma, 1996]:
where ρsolid is the grain density (assumed to be 2.65 g/cm3, equal to that of quartz), and n is the aquifer porosity (0.4 on average at the MMR plume site). The corresponding NH4+ retardation factor (R) is given by
where R = VH2O/VNH4+ (V = linear velocity). For a K′d value of 0.46 gH2O/gsolid (Figure 10), the corresponding Kd value would be 1.8 and the retardation factor R would be 2.8, meaning that dissolved NH4+ would move through the aquifer approximately 0.36 times as fast as the water.
 Although these data indicate that the majority of the NH4+ in a given aquifer volume resides in the solid phase, the maximum solid NH4+ concentrations in the plume are much lower than concentration of available exchange sites, as indicated by linearity of sorption isotherms to higher aqueous NH4+ concentrations (>1400 μmol/L) [Ceazan et al., 1989]. Estimates of the total cation exchange capacity of glacial outwash aquifers on Cape Cod range from about 5 to 20 μeq/gsolid [Ceazan et al., 1989; DeSimone and Howes, 1996, 1998].
 There was no consistent evidence for stable N isotope fractionation between aqueous and sorbed (extracted) NH4+. The average δ15N difference between the matched pairs was −0.2 ± 0.6‰ (Figure 10). Uncertainties in the depths of collection of the different sample types (cores versus water samples) could be partly responsible for some of the variability in this comparison, as there were gradients in the δ15N values of both NH4+ components.
3.5. Ammonium Retardation From Isotope Tracer Tests
 The in situ natural gradient isotope tracer tests resulted in 15NH4+ breakthrough curves that were delayed substantially with respect to the corresponding Br− breakthrough curves (Figure 11). Complete breakthrough curves were obtained in 1997 for the deep tracer at multiport M06-06, port 9 (−8.2 m elevation and 6.0 m downgradient from the injection port, with NH4+ ≈ 340–460 μmol/L) and in 1998 for the shallow tracer at multiport M08-06, port 4 (−6.2 m elevation and 9.1 m downgradient from the injection port, with NH4+ ≈ 30–50 μmol/L). A partial breakthrough curve in 1997 at the shallow port at M08-06 (with NH4+ ≈ 60–90 μmol/L) was similar to the 1998 curve at the same site.
 The steady state nonreactive numerical simulations based on constant average NH4+ concentrations give reasonable approximations to the observed Br− and 15N[NH4+] breakthrough curves for each of the tracer tests, but the results from the different experiments indicate a range of responses (Table 1 and Figure 11). Simulated groundwater velocities range from 0.36 to 0.56 m/d and steady state NH4+ retardation factors range from 4.0 to 6.4. The shallow tracer tests (with lower NH4+ concentrations) indicate higher groundwater velocities and larger NH4+ retardation factors than the deep tracer test (with higher NH4+ concentrations). Previous studies have indicated similar variations in horizontal flow velocities in the MMR wastewater plume [LeBlanc et al., 1991]. The retardation factors from the isotope tracer tests are larger than the average value of 2.8 derived from the sediment-water desorption tests and the value of 3.5 reported by Ceazan et al.  for the results of a small-scale (1.5 m, 12–27 hour) forced-gradient tracer test involving enrichment of the groundwater NH4+ concentration in an uncontaminated part of the aquifer.
Table 1. Summary of Ammonium Transport and Reaction Parameters
3.6. Ammonium Reaction Rates From Isotope Tracer Tests
 In addition to the delayed 15N[NH4+] transport, the shallow isotope tracer tests also yielded evidence for minor nitrification near the upper boundary of the NH4+ cloud (Figure 11). Values of δ15N[NO3−] as high as 1240‰ (1997) and 880‰ (1998) were obtained from samples collected near the Br− breakthrough peak, and values as high as 66‰ (1997) and 36‰ (1998) were present midway between the Br− and 15N[NH4+] breakthrough peaks. Values as high as 42‰ also were obtained in samples collected after the 15N[NH4+] peak in 1998. In each of these situations, δ18O[NO3−] analyses of selected samples were used to resolve the effects of tracer 15N[NH4+] nitrification from preexisting background variations in the effects of denitrification (Figure 8). In each case, 15N enrichment of the NO3− by oxidation of tracer 15N[NH4+] was confirmed by 15N[NO3−] excess over the background variations attributable to denitrification.
 According to the reactive transport simulations, nitrification should have resulted in relatively high and constant values of δ15N[NO3−] throughout the interval between the arrival of the Br− peak and the arrival of the 15N[NH4+] peak at the downgradient sampling site, with low values before the Br− peak and after the 15N[NH4+] peak (Figure 11). The relatively constant theoretical elevation of 15N in NO3− arriving throughout this interval presumably reflects the offsetting effects of decreasing the peak values of δ15N[NH4+] while increasing the length of the high 15N[NH4+] flow path in which the 15N-enriched NO3− was produced, both of which result from the dispersion of the 15N[NH4+] peak. Comparisons of simulations with measurements indicate similarities, as well as some important differences (Figure 11).
 The early high δ15N[NO3−] values associated with the Br− peak at the shallow downgradient site are similar to those obtained from the injection port within 0–1.5 days after the 1998 injection [Smith et al., 2006]. The injection port data were interpreted to indicate oxidation of NH4+ to [NO2− + NO3−] in the early stages of the experiment at a rate of approximately 20 μmol/m3 aquifer/h, equivalent to 1.2 μmol/L/d in the aqueous phase. In contrast, the rates indicated by the persistent δ15N[NO3−] values between the Br− and 15N[NH4+] peaks at the downgradient site according to the steady state simulations are about 0.15 μmol/L/d in 1997 and 0.09 μmol/L/d in 1998. The order-of-magnitude difference between the results from the injection port (and early downgradient breakthrough peak) and the later downgradient breakthrough results is consistent with transient stimulation of NH4+ oxidation in the early stages of the experiment [Smith et al., 2006], followed by a lower (relatively undisturbed) rate of oxidation as the tracer NH4+ migrated to the downgradient sampling site.
 In 1998, although some of the measured values of δ15N[NO3−] appear to match the simulated values between the Br− and 15NH4+ peaks, there is an equivalent amount of variation before and after the 15NH4+ peak that is not consistent with the simulation. The arrival after day 140 of a second peak of elevated δ15N[NO3−] values in the 1998 shallow experiment is not consistent with the simple flow system assumed in the model, nor are some relatively low values between days 30 and 50 (Figure 11c). These anomalies may be related to minor changes in the flow path trajectories in the aquifer over time. Heterogeneities in the hydraulic properties of the aquifer, combined with variations in the slope of the water table, may have separated some of the isotopically labeled NO3− from its labeled NH4+ source laterally as well as longitudinally as the isotope monitoring continued for more than 5 months. This interpretation is supported by variations in the concentrations of NO3− and NH4+ at the collection site that indicate lateral (horizontal or vertical) shifts in the flow paths being monitored, and by a factor-of-two variation in the Br− flushing times from ports near the injection (R. L. Smith, unpublished data, 2005). In any case, the rates of NH4+ oxidation indicated by the isotope measurements were sufficiently low that systematic changes in the concentrations of NH4+ and NO3− between the injection port and the downgradient sampling ports were difficult to detect.
 In contrast to the shallow tracer tests, the deep experiment in 1997 indicated no detectable nitrification within the anoxic core of the NH4+ cloud. Simulations based on the maximum observed 15N variation would indicate a maximum rate of NO3− production from tracer NH4+ of about 0.00016/d, or 0.016 μmol/L/d (Figure 11a). This estimate can be improved by observing that the variations in δ15N[NO3−] during the tracer test were correlated positively with δ18O[NO3−] and inversely with NO3− concentration in the same way as the pretracer profile samples (Figure 8). Therefore much of the variation in δ15N[NO3−] at the downgradient site during the deep tracer test can be attributed either to longitudinal variations in the background characteristics of the wastewater plume [Smith et al., 2004] or to lateral or vertical shifts in the flow paths being monitored. The data summarized in Figure 8 indicate that the enrichment of 15N in the NO3− caused by oxidation of tracer 15N[NH4+] was less than or equal to about 2‰. Simulations permitting this amount of enrichment indicate that the maximum rate of NO3− production from tracer NH4+ deep within the NH4+ cloud was of the order of 0.008 μmol/L/d. There was no evidence for an early breakthrough of 15N-enriched NO3− in the deep tracer test comparable to the early peaks in the shallow tests.
 Production of N2 by NH4+ oxidation reactions such as anammox was investigated by analyzing δ15N[N2] in a limited number of tracer breakthrough samples from 1997 (Figures 9 and 11). Samples from the 1997 deep tracer test between the Br− and 15NH4+ peaks had δ15N[N2] values that were constant to within the precision of the analyses (Figure 11a). The average value of +1.8 ± 0.07‰ is similar to some of the background values in the pretracer profile, but possibly higher by about 0.2–0.4‰ than average projected background samples with comparable Ar/N2 ratios (Figure 9). Selected samples from the 1997 shallow tracer test had apparent δ15N[N2] values that decrease slightly from +2.2‰ near the Br− breakthrough peak to +1.1–1.2‰ after the beginning of the 15NH4+ breakthrough peak (Figure 11). The higher values near the Br− peak may be attributable to the use of Ar as the headspace gas during the tracer preparation because (1) high Ar/N2 causes a slight increase of the apparent value of δ15N[N2] in the mass spectrometer, and (2) partial degassing of N2 during gas reequilibration in the tracer bladder may have altered the δ15N[N2] values of the tracer mixture. The later shallow tracer breakthrough samples with normal Ar/N2 ratios all had relatively uniform δ15N[N2] values with an average of +1.2 ± 0.1‰, which is slightly higher than the projected background value of around 0.8 ± 0.1 at comparable Ar/N2 in the pretracer profile (Figure 9). If these modest apparent differences reflect tracer 15N enrichment of the N2, then the steady state reaction simulations indicate that rate constants for N2 production from tracer 15NH4+ could have been as high as 0.000016/d for the deep tracer and 0.000007/d for the shallow tracer, assuming a maximum 0.4‰ increase of δ15N[N2] in each case (Figure 11). For anammox with the stoichiometry of equation (2), given the average measured N2 concentrations, these rate constants for N2 production would correspond to maximum NH4+ oxidation rates of approximately 0.027 μmol/L/d for the deep tracer and 0.009 μmol/L/d for the shallow tracer in 1997. However, given the normal heterogeneity of the NO3− and N2 isotopic profiles in the vicinity of these tests (Figure 6), it is not certain whether the apparent elevation of breakthrough δ15N[N2] values was caused by tracer reactions.
4.1. Relation of Ammonium to Other Nitrogen Species in the Wastewater Plume
 One of the important implications of the retardation of NH4+ transport (Table 1) is that NH4+ and the other major dissolved N species in any given groundwater sample may not have come from the same source at the same time, and they may not be related to each other biogeochemically. Evidence for denitrification (concentrations and isotopic compositions of NO3− and N2) in samples from the NH4+ cloud does not necessarily mean that this reaction was occurring where the samples were collected, as similar features have been observed in parts of the plume near the wastewater source where denitrification was actively occurring [Smith et al., 1991; Böhlke et al., 2000; Smith et al., 2004].
 Geochemical and isotopic studies indicate that denitrification in the vicinity of the wastewater plume largely depended on labile organic C (LOC) from the wastewater as an electron donor [Smith et al., 1991; Böhlke et al., 1999]. Denitrification coupled with C oxidation removed most of the NO3− in the plume within about 0.5 km of the source, then slowed down and essentially ceased farther downgradient [Smith and Duff, 1988; Smith et al., 1991, 2004] (Figure 3). Beyond that distance, concentrations of NO3− within the plume fluctuated between 0 and around 300 μmol/L, and excess N2 was ubiquitous. These observations indicate either LOC or NO3− may have become a limiting substrate for denitrification in different parts of the plume near its source. One possible explanation for this phenomenon is that the ratio of NO3−:LOC in the infiltrating wastewater fluctuated in such a way that one or the other was consumed first in the aquifer, depending on the time of infiltration. These fluctuations could result from variations in the elemental ratio of N:C, the efficiency of nitrification during wastewater treatment, or the composition and reactivity of the C in the wastewater being recharged over time. Other studies have shown that the total DOC in the plume included substantial but variable amounts of relatively unreactive compounds that persist beyond the region of most active denitrification [Barber et al., 1988]. Alternatively, if accumulated wastewater-derived C sorbed onto aquifer sediments was an important electron source, then perhaps the amount or reactivity of the sorbed C, or the rate of movement of NO3− bearing water through the sorbed C reservoir, may have fluctuated in such a way that denitrification was more or less complete before the contaminated groundwater moved out of the reactive part of the aquifer. Either way, it appears that NO3− was reduced completely in some parts of the plume whereas some NO3− remained in other parts of the plume after labile C became limiting. As a result, in the anoxic part of the NH4+ cloud near F593 and F168, groundwaters containing isotopically fractionated NO3− and nonatmospheric excess N2 from previous denitrification near the plume source were passing rapidly through a region containing large amounts of isotopically unfractionated NH4+ that was moving more slowly and where denitrification was largely inactive. Thus the relative concentrations and isotopic compositions of the coexisting N species cannot be interpreted as a closed system. Nevertheless, because there is no evidence locally for NO3− reduction to NH4+ or of NH4+ oxidation to NO3− (except near the upper plume boundary), the N speciation, isotope effects, and reaction history, can be resolved.
4.2. Isotopic Discrimination Between Sorption and Nitrification
 Results of desorption experiments (Figure 10) and synoptic sampling (Figures 6 and 7) indicate that the major process causing NH4+ retardation and concentration gradients in the anoxic parts of the NH4+ cloud did not cause measurable isotopic fractionation. If sorption and desorption caused substantial isotopic fractionation, then the leading edges of the NH4+ cloud would be expected to differ isotopically from the middle of the cloud as a result of chromatographic isotope separation. Lack of evidence for isotope fractionation in the anoxic parts of the NH4+ cloud provides a useful contrast with the strong evidence for isotope fractionation in the suboxic part of the cloud where aerobic nitrification was occurring. Similar correlations between NH4+ concentrations and δ15N[NH4+] values should be useful for distinguishing different natural attenuation processes affecting NH4+ in other settings [Heaton et al., 2005].
 Our results are different from published experimental results indicating N isotopic fractionation factors (α) ranging from around 1.001 to 1.011 for NH4+ ion exchange [Delwiche and Steyn, 1970; Karamanos and Rennie, 1978]. Delwiche and Steyn  report that NH4+ sorbed from solutions by kaolinite and a cation exchange resin was enriched in 15N relative to the NH4+ that remained in solution by about 0.7–0.8‰. Karamanos and Rennie  report that time series experiments with clay minerals separated from soils indicated a kinetic fractionation effect initially (the clay was depleted in 15N relative to the solution), followed by an isotope reversal and approach to equilibrium (with the clay being enriched in 15N) with α = 1.003 to 1.011. Reasons for the different results could be related to the characteristics of the solid phases (e.g., clays, organics, competing cations), the mechanism of NH4+ sorption (e.g., ion exchange, surface adsorption), or possibly other fractionating processes such as partial oxidation in some of the experiments. Nevertheless, if sorption were to cause 15N depletion in the aqueous NH4+ in some situations, as indicated by the published data, this would still be in contrast to the 15N enrichment of aqueous NH4+ resulting from nitrification. Published fractionation factors (α) for nitrification range from about 0.962 to 0.983 [Delwiche and Steyn, 1970; Miyake and Wada, 1971; Mariotti et al., 1981; Casciotti et al., 2003]. The apparent α values indicated by our profiles are near the high end of that range (0.980 to 0.991), perhaps because of dispersion in the aquifer, mixing during sampling, or uncertainty about the progress of reaction in samples from the NH4+ gradient.
4.3. Importance and Controls of Nitrification
 Various types of chemical and isotopic evidence indicate that nitrification was occurring locally along the upper boundary of the contaminant plume, including: (1) intersection of O2 and NH4+ concentration gradients, indicating appropriate chemical conditions for nitrification; (2) a small peak in NO3− concentration near the intersection of O2 and NH4+ concentration gradients (Figure 6), possibly indicating NO3− production; (3) a minor decrease in pH [Smith et al., 2006], consistent with release of protons during nitrification; (4) 15N enrichment in the NH4+ in the pretracer profiles only where measurable O2 was present (Figures 6 and 7), consistent with kinetic isotope fractionation caused by nitrification; and (5) minor 15N enrichment in the NO3− during the tracer experiment consistent with nitrification rates of the order of 0.1 to 0.15 μmol N/L/d (Figures 8 and 11 and Table 1). All of these features were observed near the contact between the plume and the oxic overlying groundwater but none were observed in the anoxic core of the NH4+ cloud. Despite evidence for nitrification near the upper plume boundary, it is considered likely that relatively little of the NO3− was produced in this way. Instead, most of the NO3− is interpreted to have been recharged with the wastewater and partially denitrified within the aquifer upgradient from the NH4+ cloud.
 In contrast to the evidence for minor nitrification along the upper boundary of the plume, the isotope tracer results limit the rate of nitrification deep within the NH4+ cloud to very low values that would yield, at most, only minor changes in the concentrations of NH4+ or NO3− during the lifetime of the plume. This result is consistent with the lack of evidence for NH4+ isotopic fractionation in the main body of the NH4+ cloud, and with the lack of evidence for NO3− isotopic features in the tracer tests that were not a result of prior denitrification.
Miller et al.  report that viable nitrifying bacteria were present in core material from throughout the vertical interval spanning the plume boundary transition zone. There was not a dramatic increase in abundance of nitrifiers or nitrification potential within the zone of nitrification defined by the isotope data. This observation is consistent with the hypothesis that nitrification was limited by vertical transport of O2 and NH4+ and that the rate of reaction was less than the potential rate for the in situ bacterial community. Three-dimensional tracer tests have indicated low rates of vertical (transverse) dispersion of aqueous constituents in undisturbed parts of the wastewater plume [Garabedian et al., 1991]. Alternatively, the active reaction zone could be so small or heterogeneous that the core data do not reflect the density of the localized active population.
 Limitation of nitrification by lateral (vertical) dispersion near the plume boundary is supported by nitrification rates derived from single-well sampling during the initial stages of the isotope tracer experiments [Smith et al., 2006]. Those early rates were about an order of magnitude higher than the rates derived from the longer-term downgradient sampling and they apparently resulted in the early δ15N[NO3−] peaks that arrived at the downgradient sampling site simultaneously with the Br− peaks in the shallow tracer tests (Figures 11b and 11c). The higher initial rates may have been stimulated, in part, by induced mixing of stratified groundwaters with opposing concentration gradients of O2 and NH4+ during the tracer injection [Smith et al., 2006]. The absence of an early high δ15N[NO3−] peak associated with Br− in the 1997 deep tracer test (Figure 11a) is consistent with this interpretation, as the O2 concentrations were uniformly low near the elevation of the deep tracer.
4.4. Evaluation of Evidence for Anaerobic Ammonium Oxidation
 Coexistence of NH4+ and NO3− in parts of the MMR wastewater plume could indicate conditions favorable for anaerobic NH4+ oxidation by reactions such as anammox (equation (2)). Anammox has been reported from wastewater treatment plants [Mulder et al., 1995], marine sediments [Thamdrup and Dalsgaard, 2002; Engstrom et al., 2005], and other suboxic waters [Dalsgaard et al., 2003; Kuypers et al., 2003], but its importance as a sink for NH4+ or a source for N2 in aquifers is not known. Christensen et al.  suggest that anaerobic oxidation of NH4+ might be an important process limiting the transport of NH4+ in landfill leachate plumes, but do not provide strong stoichiometric or mechanistic evidence for it. Here we apply 3 independent approaches for determining if NH4+ oxidation might have led to production of N2 in the MMR wastewater plume.
 The most direct test of anaerobic NH4+ oxidation comes from the isotopic composition of N2 during the 15NH4+ tracer tests (Figures 9 and 11). Slight apparent differences between δ15N[N2] values in tracer breakthrough samples and normal background samples could be consistent with NH4+ oxidation at rates as high as 0.009 μmol/L/d (shallow tracer) or 0.027 μmol/L/d (deep tracer) by anammox reaction (equation (2) and Table 1) or by coupled nitrification-denitrification. At these rates, the concentration of NH4+ could have been reduced by as much as 200–600 μmol/L in the 60-year history of transport from wastewater source, but the product NO3− would have been separated continuously from its NH4+ source by advection. These estimates are considered to be upper limits on the rates of NH4+ oxidation because of variations in background δ15N[N2] values in different parts of the aquifer in the area of the tracer site.
 Another approach for detecting anaerobic NH4+ oxidation is to evaluate the concentrations and isotopic compositions of NO3− and N2 in various parts of the plume with respect to isotope fractionation and mass balance accompanying denitrification. Deviations from expected effects of upgradient denitrification could provide evidence for other reactions involving NO3− or N2. Given the different transport rate of NH4+ relative to NO3− and N2, the maximum time for coexistence of NO3− (>100 μmol/L) with NH4+ (>100 μmol/L) would be of the order of 25 years in groundwaters near the leading edge of the NH4+ cloud. Concentrations and isotopic compositions of NO3− and N2 at F593 and F168 are approximately consistent with varying degrees of denitrification in a closed system and do not indicate a major additional NO3− sink or N2 source, although variation in the calculated initial values of δ15N[NO3−] from about 7 to 11‰ could indicate minor additional processes.
 The third test of anaerobic NH4+ oxidation is to examine the isotopic data for evidence of fractionation effects between NO3− and NH4+ where the species coexist in the anoxic part of the plume. Though the isotope effects of anaerobic NH4+ oxidation reactions including anammox have not been reported, it would be reasonable to expect some 15N enrichment in the residual NH4+ and(or) NO3− by analogy with other microbial redox reactions. The combination of constant δ15N[NH4+] and rapidly increasing δ15N[NO3−] with depth in F593 and F168 indicates that anaerobic NH4+ oxidation reactions had relatively little isotope effect in comparison to the effects of upgradient denitrification.
 In summary, evaluation of the concentrations and isotopic compositions of NO3−, NH4+, and N2, both under ambient conditions and during 15N tracer experiments, provided no conclusive evidence for the anammox reaction or other anaerobic NH4+ oxidation reactions including coupled nitrification-denitrification in the NH4+-rich part of the MMR wastewater plume. The lack of measurable NO2− (<1 μmol/L), relatively low N2O (<0.1 μmol/L), and other evidence for decreasing denitrification rates along the wastewater flow path, would not favor substantial N2 production from reactions such as equation (2).
4.5. Implications for Contaminant Plume Evolution
 Given the limited distribution and rate of NH4+ oxidation, it appears that the size and position of the NH4+ cloud within the larger wastewater plume could be due to the combined effects of (1) retardation of NH4+ transport by exchange with solids and (2) a period of higher NH4+ loads in the infiltrating water during the early years of the wastewater disposal followed by lower concentrations in more recent times. Similar factors apparently have resulted in the irregular distribution and delayed movement of phosphorus through the wastewater plume [Parkhurst et al., 2003]. It may be important that the peak concentration and center of mass of the NH4+ cloud appear to have progressed only about one fifth of the distance toward the plume limits in both the vertical and horizontal directions. This pattern can be interpreted to indicate that movement of NH4+ was retarded both during the initial rapid recharge phase beneath the infiltration beds and during the subsequent longer horizontal transport phase.
 In 1994, the front of the NH4+ cloud was approaching but had not quite reached F350 at an elevation of about −8 m and total flow path distance of around 3200 m, where Shapiro et al.  obtained 3H/3He ages of around 24–26 years. The peak NH4+ concentrations were between about F411 and F262, approximately 1700–2300 m downgradient from the source, where the interpolated 3H/3He ages would be around 13–18 years. Given the retardation factors derived from (1) the deep isotope tracer test at F593, (2) the progress of the NH4+ cloud between 1990 and 1998, and (3) the sediment NH4+ extraction experiments (overall mean R ≈ 4 ± 1), it may be concluded that at least some of the NH4+ in the core of the NH4+ cloud is as much as 4 times as old as the water in which it is currently dissolved. Therefore much of the NH4+ in the core of the NH4+ cloud may be attributed plausibly to wastewater disposal during the early years of operation of the treatment plant beginning in 1936.
 Limited records indicate that the rate of treated wastewater disposal was highest (2.1 × 106 m3/yr) from about 1941 to 1945 [LeBlanc, 1984; Parkhurst et al., 2003], and it is possible that the large fluxes at that time were associated with relatively high concentrations of NH4+ that is now part of the NH4+ cloud. Wastewater fluxes also were relatively high from about 1956 to 1970, but substantially lower (averaging between 0.3 to 0.6 × 106 m3/yr) after 1970. Records of early wastewater treatment practices and effluent composition at the MMR are not available, but it is reasonable to suppose that disposal of NH4+-rich wastewater was more common in the middle of the 20th century than near the end of the 20th century, because aerobic treatment to convert NH4+ to NO3− has become increasingly common elsewhere in recent years. Within the last 20 years of operation, some of the wastewater was recycled through the MMR treatment plant, increasing the efficiency of nitrification before recharge. The average δ15N[NH4+] values in the main body of the anoxic part of the NH4+ cloud are similar to the average δ15N[NO3−] values of treated wastewater that was recharged at the MMR in the 1980s and 1990s [Smith et al., 1991; Böhlke et al., 2000]. Thus the bulk δ15N value of the wastewater N may have been similar whether recharged mainly as reduced or oxidized species, though transitional oxidation states exhibiting isotopic fractionation clearly are present in many parts of the plume.
 If the wastewater plume source were shut down without changing the redox status of the aquifer, it might be expected that B, NO3−, and other relatively mobile wastewater constituents would be flushed from the aquifer long before the NH4+ cloud, which could take well over 100 years to reach the discharge area. However, if the wastewater plume were displaced by oxic uncontaminated groundwater from upgradient recharge areas, then it is possible that the slowly moving NH4+ cloud would be nitrified efficiently by rapidly moving O2 passing through it, yielding a diminishing NH4+ cloud with a downgradient shadow of anoxic nitrate-bearing water. This process might eliminate the NH4+ cloud before it discharges, but it also could cause an increase in the discharge of NO3−, unless there is an environment favorable for denitrification closer to the discharge area. Since the wastewater disposal was ended in 1995, tracer experiments and monitoring studies have indicated that the much of the O2 carried by upgradient groundwater into the former plume area is reduced by reaction with organic and other reduced compounds that accumulated on solid phases in the aquifer while the plume was active [Mathisen et al., 2003; Repert et al., 2006]. Therefore the ultimate fate of the NH4+ cloud may depend in part on the mass of immobile electron donors left behind near the plume source, as well as the changing cation exchange properties of the eluting groundwater.
5. Summary and Conclusions
 Analyses of large-scale chemical and chronologic data, laboratory exchange experiments, ambient N isotope fractionation effects, and in situ 15NH4+ isotope tracer tests, provided a comprehensive picture of processes affecting NH4+ transport in a groundwater plume contaminated by treated wastewater. Results indicate that transport of NH4+ was retarded with respect to that of water and more mobile constituents by a factor of about 3–6 (approximately 4 in the core of an NH4+-rich “cloud”). The NH4+ retardation factors were reproduced by isotope tracer simulations that incorporated equilibrium interactions between aqueous and sorbed NH4+. The distribution of δ15N values in the absence of tracer indicates that isotopic fractionation associated with sorption was undetectable (apparent α = 1.0000 ± 0.0003‰). This result is consistent with the results of the exchange experiments with local sediments, but it is in contrast to the results of some other published studies that indicated substantial isotopic fractionation from sorption and ion exchange of NH4+.
 In the anoxic core of the plume, lack of measurable isotope fractionation of the NH4+, no measurable isotope tracer transfer to NO3−, and no conclusive isotope tracer transfer to N2, all indicate that NH4+ oxidation reactions were unimportant. The isotope tracer data yield upper limits on the rates of nitrification (≤0.008 μmol/L/d) and other NH4+-oxidizing reactions such as anammox or coupled nitrification-denitrification (≤0.027 μmol/L/d).
 In contrast to the anoxic main body of the plume, the upper boundary was in contact with oxygenated water and exhibited evidence of nitrification. Nitrification is indicated by production of 15N-enriched NO3− from 15N-enriched NH4+ during the tracer tests and by fractionation of N isotopes in the NH4+ (apparent α ≤ 0.980–0.991) in the absence of tracer. However, the rate of nitrification indicated by the tracer transfer rate was small (∼0.09 to 0.15 μmol/L/d) and the reaction was highly localized within a narrow zone of mixing between contaminated and uncontaminated water. The rate at which NH4+ from the wastewater plume could interact with O2 from overlying oxic groundwater was limited severely by a low rate of vertical dispersion transverse to flow.
 The result of these processes was a well-defined cloud of NH4+-rich groundwater within the central part of the larger wastewater plume. It is proposed that this NH4+ cloud contained a relatively large proportion of NH4+ that was recharged during the earliest years of operation of the wastewater treatment plant, and that it was maintained and augmented by chromatographic separation of NH4+ throughout the history of the plume. The coexisting H2O, NO3−, and N2 gas at a given locality within the plume were substantially younger than the NH4+ and largely unrelated to the NH4+ biogeochemically. The discrepancy between the transport rates of NH4+ and other N species complicates chemical and isotope mass balance approaches to the N system in the groundwaters. The general lack of NH4+ oxidation reactions, coupled with its low transport rate with respect to mobile constituents, means that a cloud of NH4+-rich groundwater may persist in the aquifer for some time after the more mobile contaminants are flushed out, as long as the system remains suboxic. However, sustained nitrification of the NH4+ cloud could occur if the upgradient groundwater were oxic, because interaction of O2 and NH4+ then might be promoted by a faster transport rate of dissolved O2 relative to the slower NH4+.
 This study demonstrates the feasibility and some of the benefits of combining isotope fractionation studies with experiments involving moderate isotope tracer enrichments for understanding and quantifying transport and reaction of N species in contaminated environments. Some advantages of the in situ natural gradient isotope tracer method over laboratory methods include (1) the tests can be done within the NH4+ cloud without altering the NH4+ concentrations greatly; (2) the flow system is unaltered; (3) the scale of the tests is larger, so effects of small-scale heterogeneities are included; and (4) low rates of NH4+ oxidation reactions can be evaluated simultaneously with transport. Some potential difficulties in field situations involving small-scale chemical gradients include disruption of gradients during tracer injection (these disruptions may dissipate as tracers move downgradient in the aquifer, particularly as retarded tracers separate from nonretarded species), and minor changes in natural groundwater flow paths during monitoring of long breakthrough peaks. The interpretation of empirical observations reported here could be refined by additional laboratory experiments, by continued monitoring of the plume, and by coupled modeling of flow, retardation, dispersion, and isotope fractionation in nonsteady state conditions. More sophisticated reactive transport modeling could provide further insight into the long-term history and future progress of the NH4+ cloud toward discharge areas, including the potential for interactions between the NH4+ cloud and uncontaminated groundwater that moves through it after cessation of wastewater disposal.
 This study was supported by the National Research Program and the Toxic Substances Hydrology Program of the Water Resources Discipline, USGS, and by grants from the USDA National Research Initiative Competitive Grants Program (95-37101-1713) and the USEPA/NSF Partnership for Environmental Research (R824787). USGS MMR site coordinator D. LeBlanc provided field assistance and logistical support throughout the study. A. Horn performed the desorption experiments. M. Doughten, D. Repert, K. Revesz, and P. Widman assisted with sampling and chemical analyses. J. Hannon, S. Mroczkowski, and H. Qi performed isotopic analyses with assistance from T. Coplen, M. Dunbar, M. Reilly, and K. Revesz. I. Cozzarelli, J. Holloway, A. Martin, D. Parkhurst, and two journal reviewers provided helpful comments on the manuscript.