Experiments were carried out with colonized polystyrene beads (diameter 4 mm) sampled from the nitrification biologically active filters (BAFs) of a domestic WRRF (Seine Centre, France). In this WRRF, wastewater (240 000 m3 d-1) passes through a pre-treatment stage, followed by physicochemical decantation and tertiary biological treatment. The latter is composed of three biofiltration processes: (i) carbon elimination (24 Biofor^®), (ii) nitrification (29 Biostyr^®) and (iii) denitrification (12 Biofor^®). Nitrifying Biostyrs^® are submerged fixed-bed biofilm reactors with a unitary section of 111 m2 and a filter bed of 3 m high. This unit is operated to receive a nominal load of 0.7 kg NH4+-N m-3 d-1.

A lab-scale reactor with a working volume of 9.9 L (colonized Biostyrene^® beads and interstitial volume) and a headspace of 1.4 L was operated in continuous down-flow counter-current mode for 7 weeks (i.e., solution was down-flowing, while air was up-flowing; Fig. S1 in the Supplement). Mass flow meters (F-201CV, Bronkhorst, France) sustained the inflow gas rate at 0.5 L min-1. A peristaltic pump (R3425H12B, Sirem, France) pumped feeding solution from a feeding tank into the reactor at 0.2 L min-1, in order to maintain a hydraulic retention time (HRT) of 27.8±0.6 min. A water jacket monitored by a cryogenic regulator (WK 500, Lauda, Germany) controlled the reactor temperature. The feeding solution consisted of ammonium chloride (NH4Cl) as substrate, monobasic potassium phosphate (KH2PO4) as phosphorus source for bacterial growth, and sodium hydrogen carbonate (NaHCO3) as pH buffer and inorganic carbon source in 100 or 150 L of tap water (average 0.2±0.4, 2.4±1.1, and 2.5±1.3 mg N L-1 of NO2-, NO3- and sum of both NOx- molecules, respectively).

The influence of environmental conditions on the ammonium oxidation rates and the N2O emissions from various combinations of oxygenation levels, temperatures and ammonium concentrations were tested in 24 experiments (Table 1). Note that two of them were used twice: as oxygenation tests and as concentration tests. The oxygenation tests were carried out by mixing compressed air and pure nitrogen gas to reach 0 % to 21 % O2 in the gas mixture (Fig. S2a). The tests were performed at five substrate concentrations and at a temperature between 19.2 and 20.6 ∘C. The temperature tests were carried out by cooling the feeding solution directly in the feeding tank (22.3 to 13.5 ∘C), with an inflow ammonium concentration close to the nominal load that received the nitrifying biomass, i.e., 20.3–21.1 mg NH4+-N L-1. The ammonium concentration tests were run at an increase (6.2, 28.6 and 62.1 mg NH4+-N L1) and a decrease (56.1, 42.9, 42.7 and 20.2 mg NH4+-N L-1) of NH4+ concentrations in the feeding solution, at temperatures ranging from 19.0 to 19.8 ∘C. The atmospheric oxygenation level (i.e., 21 % O2 in the gas mixture) was imposed for both tests (Fig. S2b and c). This gas mixture using compressed air with 21 % O2 was considered hereafter as optimal as compared to the oxygen-depleted atmosphere used during the oxygenation tests. Noticeably, the atmospheric oxygenation level is the condition that represents the most optimal conditions of oxygenation applied in nitrification BAFs of domestic WRRF.

Dissolved oxygen, temperature (Visiferm DO Arc 120, Hamilton, Switzerland) and pH (H8481 HD, SI Analytics, France) were continuously measured at the top of the reactor and data were recorded at 10 s intervals. The N2O concentration was continuously analyzed by an infrared photometer (Rosemount™ X-STREAM X2GP, Emerson, Germany) in outflow reactor gas after drying through a condenser and a hydrophobic gas filter (0.2 µm). Minute averages are used for monitored data hereafter. Gas samples were taken for N2O isotopic signature determination by an outlet gas pipe derivation into a sealed glass vial of 20 mL. The vial was first flushed with the sampling gas for >45 s prior to 1–5 min sampling. Gas samples were then stored in the dark at room temperature until analysis. Note that gas sampling was lacking for 5 of the 13 oxygenation tests.

The feeding solutions were characterized of one to five replicate samples collected in the feeding tank. For each tested condition, the outflow was characterized within 5 d of 1 to 14 replicate samples immediately filtered through a 0.2 µm syringe filter and stored at 4 ∘C. Outflow sampling started after at least one hydraulic retention time (28±1 min). Ammonium was analyzed using the Nessler colorimetric method, according to AFNOR NF T90-015 (DR 2800, Hach, Germany). Nitrite and nitrate were measured by ionic chromatography (IC25, Dionex, USA).

Atmospheric N2 and Vienna Standard Mean Ocean Water (VSMOW) are the references used for the nitrogen and oxygen isotopes ratios, respectively, expressed in conventional δ notation, in per mil (‰). Nitrogen and oxygen isotope ratios of nitrate and nitrite were determined separately following a modified protocol of McIlvin and Altabet (McIlvin and Altabet, 2005; Semaoune et al., 2012). Nitrogen isotope ratios of ammonium were determined following the protocol of Zhang et al. (2007). These methods consist in the conversion of the substrate (ammonium or nitrite or nitrate) into dissolved N2O. δ15N and δ18O for ammonium, nitrite and nitrate were hence determined from a calibration curve created with a combination of nitrate or ammonium standards that underwent the same chemical conversion as the samples (USGS-32, δ15N-NO3- = 180 ‰, δ18O-NO3- = 25.7 ‰; USGS-34, δ15N-NO3- = -1.8 ‰, δ18O-NO3- = -27.9 ‰ and USGS-35 δ15N-NO3- = 2.7 ‰, δ18O-NO3- = 57.5 ‰; IAEA-N1, δ15N-NH4+ = 0.4 ‰, IAEA-305A, δ15N-NH4+ = 39.8 ‰, USGS-25, δ15N-NH4+ = -30.4 ‰). The quality of calibration was controlled with additional international standards (IAEA-NO-3, δ15N-NO3- = 4.7 ‰, δ18O-NO3- = 25.6 ‰; IAEA-N2, δ15N-NH4+ = 20.3 ‰). Basically, an analytical sequence was comprised of triplicate standards for calibration, and quality controls and duplicate samples. The average of the analytical replicates was then used for calibration, for quality control and as a result.

Since no international standards were available for N2O isotopes, these were determined the same day as nitrate or ammonium standard analysis ensuring correct functioning of the method and analysis. In addition to this, the internal N2O standards were previously calibrated by exchange with the laboratory of Naohiro Yoshida and Sakae Toyoda at the Tokyo Institute of Technology. All isotope measurements were determined using an isotope ratio mass spectrometer (IRMS, DeltaVplus; Thermo Scientific) in continuous flow with a purge and trap system coupled with a Finnigan GasBench II system (Thermo Scientific). The precision was 0.8 ‰, 1.5 ‰ and 2.5 ‰ for δ15N, δ18O and 15N-SP, respectively.

The effects of environmental conditions on nitrification were assessed from four indices. The ammonium oxidation rate (AOR) was estimated in each experiment for time ≥1 HRT from the difference between influent and effluent NH4+ concentrations multiplied by the liquid flow rate (kg NH4+-N d-1). The nitrification efficiency was defined as the ratio between AOR and influent ammonium load. The N2O emission rate (N2O-ER) was calculated by multiplying the measured N2O concentration by the gas flow rate (mg N2O-N min-1). The N2O emission factor (N2O-EF) was defined as the ratio between N2O-ER and AOR (% of oxidized NH4+-N). The measurements related to liquid or gas samples were averaged by experiment, i.e., the average of data obtained from the samples collected after one hydraulic retention time.

Statistical analysis were performed using the R software (R Development Core Team, 2014). The value of 0.05 was used as significance level for Spearman correlations (cor.test function) and linear regressions (lm function). Adjusted r2 was provided as r2 for the latter.

As shown in Fig. 1, the pairwise relationships between δ15N, δ18O and 15N-SP assist the determination of the producing and consuming pathways at play. The N atoms that compose the N2O molecule originate from NH4+ molecules when produced by hydroxylamine oxidation, while originating from the N atoms of NO3- or NO2- molecules when produced by nitrite reduction (NOx- molecules). However, the nitrogen isotope ratio of N2O does not equal those of its substrates as it depends on isotope effects associated to each reaction step of N2O-producing process. The isotope effect of the reaction step can be determined from the isotope composition of substrates or products. Although performed on a few tests here, the obtained value can only be applied to a limited number of environmental conditions. The use of estimates from the literature seems therefore suitable.

Several equations enable us to approximate the isotope effect and its effect on the isotope ratios of substrate and product pools involved in a reaction. These equations vary according to the assumptions made on the system boundaries (Denk et al., 2017).

The nitrifying reactor used in this study can be described as an open system continuously supplied by an infinite substrate pool with constant isotopic composition (NH4+,in). A small amount of the infinite substrate pool is transformed into a product pool (NOx-,p) or a residual substrate pool (NH4+,res) when flowing through the system. The equations describing the input, output and processes considered here are presented in Fig. 2 after Fry (2006). Note that the definitions of f and Δ are inverse to the cited literature and that Δ1 and Δ4 are null because no fractionation alter the residual substrate exiting the reaction (Fry, 2006).

The balance between input and output of each reactional step allows us to propose equations for calculation of the nitrogen isotope ratio of compounds in the inflow and outflow of the system (Denk et al., 2017; Fry, 2006). These equations can be simplified under the assumption that a limited amount of N compounds are transformed into N2O, i.e., f2 close to 0 and f3 close to 1. Therefore, the N isotope ratios of the residual substrate pool can be approximated from Eq. (1). 1δ15N-NH4+,res≈δ15N-NH4+,in-Δ21-f1, where f1 is the remaining substrate fraction leaving the reactor (i.e., remaining fraction of ammonium), ranging from 0 to 1 (0 % to 100 %), and Δ2 is the N isotope enrichment factor associated with ammonium oxidation. In their review, Denk et al. (2017) reported a mean value of -29.6±4.9 ‰ for Δ2. Therefore, δ15N is higher for residual than the initial substrate pool (δ15N-NH4+,in<δ15N-NH4+,res). Consequently, the pool of product is depleted in heavier isotope (i.e., nitrite and nitrate hereafter defined as NOx- pool; δ15N-NOx-,in>δ15N-NOx-,int). It is estimated from Eqs. (2)–(4): 2δ15N-NOx-,p≈δ15N-NH4+,in+Δ2f1, Where δ15N-NOx-,p is the nitrogen isotope ratio of the product pool produced by nitrification. The nitrogen isotope ratio of the overall intermediate NOx- exiting this process results from mixing between initial and produced NOx- pools (δ15N-NOx-,int) and can be estimated from Eqs. (3) and (4): 3δ15N-NOx-,in=(δ15N-NO2-,in×[NO2-]in+δ15N-NO3-,in×[NO3-]in)([NO3-]in+[NO2-]in),4δ15N-NOx,int≈(δ15N-NOx-,in×([NO3-]in+[NO2-]in)+δ15N-NOx-,p×(1-f1)×[NH4+]in)([NO3-]in+[NO2-]in+(1-f1)×[NH4+]in). Note that δ15N-NOx-,out equals δ15N-NOx-,int when f3 is close to 1, which means that nitrifier denitrification and heterotrophic denitrification are negligible. Finally, two options must be considered to approximate the nitrogen isotope ratio of N2O that exits the reactor. On the one hand, δ15N-N2O can be estimated from Eq. (5), when hydroxylamine oxidation is the producing process of N2O: 5δ15N-N2O≈δ15N-NH4+,res-Δ21-f1+Δ3. In addition to the influence of the nitrogen isotope composition of the substrate, δ15N-N2O depends therefore on the difference between the isotope effects related to the oxidation of NH4+ to NO2- and the oxidation of NH2OH to N2O for complete nitrification (f1=0), while depending only on the latter for limited nitrification (f1=1). On the other hand, δ15N-N2O can be estimated from Eq. (6), when the nitrite reduction is the producing process of N2O: 6δ15N-N2O≈δ15N-NOx-,int1-f1-1+Δ5. In addition to the influence of the nitrogen isotope composition of the substrate, when negligible amounts of N2O are produced by nitrite reduction during nitrifier denitrification or heterotrophic denitrification, its nitrogen isotope ratio depends on isotope effect related to this process (Δ5).

Ranges of δ15N for N2O produced by different processes were hypothesized from Eqs. (1)–(5) for pairwise relationships with reviewed data of δ18O and 15N-SP. To this aim, measurements of isotope ratios of the different nitrogen species were required. The δ15N values of inflow ammonium, nitrite and nitrate were -3±0.1 ‰ (n=3), -15±0.1 ‰ (n=2) and 6.9±0.3 ‰ (n=3), respectively, during ammonium concentration experiments (Fig. S3 and Table S2). The δ15N of residual NH4+ and intermediate NOx- were estimated from Eqs. (1)–(4) with f1=0.1 or 0.9 (Fig. S2d–f), Δ2=-30 ‰, the highest [NH4+]in (62.1 mg N L-1) and the lowest [NOx-]in (1.4 mg N L-1). They ranged from -3 ‰ to 27 ‰ and from -32 ‰ to 7 ‰, respectively, which encompasses a few isotope compositions measured in the outflow during ammonium concentration tests (Fig. S3 and Table S2).

Prior to pairwise comparisons with δ18O and 15N-SP, ranges of δ15N values for N2O produced by the hydroxylamine oxidation and nitrite reduction pathways were estimated from Eq. (5). The net isotope effect of N2O production by ammonium oxidation via hydroxylamine can be estimated by combining the isotope effects of ammonium oxidation and hydroxylamine oxidation to N2O. The net isotope effect associated with ammonium oxidation to nitrite ranges from -38.2 ‰ to -14.2 ‰ (Casciotti et al., 2003) and can approximate the nitrogen isotope ratio of hydroxylamine transitory produced. The isotope effect related to hydroxylamine oxidation to N2O ranging from -26.0 ‰ to 5.7 ‰ from data in Sutka et al. (2003, 2004, 2006); the net isotope effect of N2O production by ammonium oxidation via hydroxylamine (Δ3) can range from -64.2 ‰ (-26.0+(-38.2)) to -8.5 ‰ (5.7+(-14.2)). Considering the range of the nitrogen isotope ratio of residual ammonium, this method provided a broad range of δ15N values, from -65 ‰ (δ15N-NH4+,res=-3 ‰, Δ2=-30 ‰, f1=0.9 and Δ3=-64.2 ‰) to 46 ‰ (δ15N-NH4+,res=27 ‰ , Δ2=-30 ‰, f1=0.1 and Δ3=-8.5 ‰), for N2O produced from ammonium by hydroxylamine oxidation, according to Eq. (5). These values encompassed the values proposed by others (-46.5 ‰ and -32.9 ‰; Sutka et al., 2006; Yamazaki et al., 2014).

A higher range of the net nitrogen isotope effect for nitrite reduction than hydroxylamine oxidation pathway was estimated for N2O production (Fig. 3a and b). Prior to being reduced to N2O through the nitrite reduction pathway, NOx- was mainly derived from ammonium oxidation in the nitrifying system (Eqs. 1–4); the resulting intermediate δ15N-NOx- ranges from -32 ‰ to 7 ‰. In addition to this, the net isotope effects related to the N2O production through nitrite reduction performed by nitrifiers or heterotrophic denitrifiers (Δ5) ranges from -52.8 ‰ to -6 ‰ (Lewicka-Szczebak et al., 2014; Sutka et al., 2008). Consequently, the δ15N of N2O produced by nitrite reduction ranged from -89 ‰ (δ15N-NOx-,int=-32 ‰, f1=0.1 and Δ5=-52.8 ‰) to 64 ‰ (δ15N-NOx-,int=7 ‰, f1=0.9 and Δ5=-6 ‰) , according to Eq. (6). This is consistent with previous findings reporting δ15N-N2O between -112 ‰ and -48 ‰ for nitrifier denitrifying systems (Mandernack et al., 2009; Pérez et al., 2006; Yamazaki et al., 2014; Yoshida, 1988). However, a similar range of nitrite-derived δ15N-N2O is suggested for nitrifiers and heterotrophic denitrifiers, because ammonium oxidation influences both processes in the system used in this study where there is a low initial amount of NO2- and NO3-.

Pairwise comparisons of δ15N, δ18O and 15N-SP estimates of the different experiments are presented in Fig. 3. These comparisons provided ranges of plausible isotope compositions for N2O produced by nitrifying or heterotrophic denitrifying bacteria through the hydroxylamine oxidation and nitrite reduction pathways (red and blue boxes, respectively). The measured N2O isotope compositions were compared to these estimates to identify the N2O-producing and N2O-consuming pathways likely at play in oxygenation, temperature and ammonium concentration tests.

This approach suggests that the nitrite reduction pathway was the main contributor to N2O emissions. Heterotrophic denitrification likely influenced N2O emissions, as shown by oxygen isotope ratios higher than 35 ‰ (Snider et al., 2013; Fig. 3a and c). However, this conclusion depends highly on δ18O-N2O ranges. Furthermore, the application of atmospheric oxygen δ18O (23.5 ‰; Kroopnick and Craig, 1972) to estimate the oxygen isotope ratio of N2O produced by hydroxylamine oxidation remains uncertain since respiratory activity and air stripping might drive isotopic fractionations and increase δ18O of residual dissolved oxygen (Nakayama et al., 2007). To date, the oxygen isotope fractionation related to air stripping has not been investigated. Note that this estimate relies on the assumption that there is no accumulation of NH2OH and that its oxidation to N2O occurs before or independently of its oxidation to NO2-.

Ammonium concentrations decreased from 20.2–37.3 to 11.4–31.1 mg N L-1, with 45 % to 89 % of the inflow ammonium remaining in the outflow during the oxygenation tests (Fig. S2d). When measured, the cumulated concentrations of NO2- and NO3- ([NOx-]) increased from 2.4–4.1 to 4.7–11 mg N L-1 between inflow and outflow and were composed by at least 74 % and 82 % of NO3-, respectively. The mass balance between N compounds that enter and exit the reactor evidenced a default of up to 5 mg N and impacted each test. No significant amounts of NO were detected during any tests (data not shown), whereas NH2OH, N2 and N mineralization/assimilation in the biofilm were not quantified. The accumulation of such amounts of NH2OH is unlikely. Heterotrophic denitrification, i.e., the reduction of NOx- and more particularly of N2O to N2, may explain the incomplete N mass balance. However, the measurement of small N2 variations in the gas mixture exiting the reactor and comprising at least 79 % N2 was not performed.

The oxygenation level had contrasting effects on ammonium oxidation rates, and N2O emission rates and factors (Fig. 4a–c). Between an oxygenation of 0 % to 10.5 % O2 in the gas mixture, no clear trend in ammonium oxidation rates was observed although it was rather low (1.1±0.5 mg NH4+-N min-1). In the same oxygenation level interval, the N2O emission rate increased for two of three inflows [NH4+] tested. It increased from 0.35×10-3 to 0.73×10-3 mg N min-1 between 0 % and 10.5 % O2 at 25.3 mg NH4+-N L-1, and from 1.34×10-3 to 1.4×10-3 mg N min-1 between 4.2 % and 10.5 % O2 at 23.8 mg NH4+-N L-1; it decreased from 2.86×10-3 to 2.04×10-3 mg N min-1 between 4.2 % and 10.5 % O2 at 37.3 mg NH4+-N L-1. Finally, the N2O emission factor globally increased from 0.05 % to 0.16 % in the 0 %–10.5 % O2 interval. At oxygenation levels from 10.5 % to 21 % O2, the ammonium oxidation rates increased from 0.9±0.2 to 2.1±0.4 mg N min-1, with N2O emission rates remaining stable at 1.2×10-3±0.6×10-3 mg N min-1 and the emission factors decreasing from 0.15±0.03 % to 0.06±0.03 %.

15N-SP varied between -9 ‰ to 2 ‰ over the range of imposed oxygenation levels, with a marked increase when oxygenation increased from 16.8 % to 21 % O2 (Fig. 4d). A similar marked change in nitrogen and oxygen isotope ratios of N2O (decrease and increase, respectively) was observed when oxygenation increased from 16.8 % to 21 % O2 (Fig. 4e and f). Note that to observe the latter variations the effect of ammonium concentration was not included. One way to do so is to compare the isotope composition average at 21 % O2 with the isotope composition measured for 23.8 NH4+-N L-1 at 16.8 % O2. The 15N-SP values were close to the range of -11 ‰ to 0 ‰ reported for N2O produced by nitrifying or denitrifying bacteria through nitrifier denitrification and heterotrophic denitrification (Toyoda et al., 2017; Yamazaki et al., 2014). Additional suggestions can be made from the 15N-SP dynamics between and variations within the oxygenation levels. If an increase in the hydroxylamine oxidation contribution to the N2O emission might explain the higher 15N-SP observed at 21 % O2 as compared to lower oxygenation levels, an additional mechanism can explain the variations observed for the experiments with oxygen-depleted atmosphere. The 15N-SP dynamics suggest a higher amount of N2O was reduced to N2 at 4.2 % than 16.8 % O2. The reduction of N2O to N2 can increase the 15N-SP of residual N2O (Mothet et al., 2013). In heterotrophic denitrifying bacteria however, the nitrous oxide reductase involved in this reaction is highly sensitive to inhibition by oxygen (Betlach and Tiedje, 1981; Otte et al., 1996). This might explain the decrease in 15N-SP from -3.8±4.4 ‰ to -7.2±1.7 ‰ when O2 increased from 4.2 % to 16.8 %. This is also consistent with a possible onset of anoxic microsites within the reactor biomass more likely at 4.2 % than 16.8 % O2. The dissolved oxygen (DO) concentration never decreased below 1.5 mg O2 L-1 in the bulk solution at the top of the reactor (Fig. S2). However, DO decreased from the bulk reactor solution toward the deeper layers of biofilm due to the activity of ammonium oxidizers (Sabba et al., 2018). This is further exacerbated by heterogeneous and varying distribution of air circulation within the static bed. Therefore, oxygen depletion can be assumed within the biofilm. Finally, the N2O reduction to N2 likely explains the overall decrease in N2O emission between 16.8 % and 0 % O2 (Fig. 4b).

In general the N2O reduction to N2 is accompanied by an increase in nitrogen and oxygen isotope ratios of N2O (Ostrom et al., 2007; Vieten et al., 2007). However, our results show a decrease in δ15N-N2O, and δ18O-N2O remained stable between 30.5 ‰ and 34.7 ‰, when the N2O reduction is thought to increasingly constraint the N2O isotopocules with decreasing O2 from 16.8 % to 4.2 % (Fig. 4e and f). The independence of samples taken during the oxygenation test can explain this. The N2O sampled at 4.2 % O2 is not a residual fraction of N2O produced at 16.8 % O2 that would have undergone a partial reduction. The oxygenation level can alter the isotope fractionation factors through the control of reaction rates, as evidenced for the reduction of N2O to N2 by Vieten et al. (2007). These authors reported lower reaction rates and increased isotope fractionation factors with increasing oxygenation levels. In our case, a similar phenomenon might have influenced both oxidative and reductive processes leading to the production of N2O and occurring before its ultimate reduction to N2. However, knowledge regarding controls, such as the oxygenation level, on the net isotope effect related to a sequence of non-exclusive oxidative and reductive processes is still lacking and requires further investigations. Additionally, with δ18O below 35 ‰ for all but one experiment the oxygenation tests did not provide evidence for the heterotrophic denitrifier contribution to N2O emissions, likely due to oxygen exchange with water (Snider et al., 2015, 2012, 2013).

Ammonium concentrations decreased from 6.2–62.1 to 0.9–54.1 mg N L-1 and from 18 % to 79 % of the inflow ammonium remaining in the outflow during the temperature and ammonium concentration tests (Fig. S2e and f). This remaining fraction was positively correlated to ammonium concentrations (r=0.96) and negatively correlated to temperature within a lower range of values (61 %–67 %; r=-0.94). In the ammonium tests, the cumulated concentrations of NO2- and NO3- ([NOx-]) increased from 1.4–6.1 to 5.1–19.6 mg N L-1 between inflow and outflow and were composed by at least 74 % and 91 % of NO3-, respectively. Noticeably, the nitrite concentrations in the outflow linearly increased with temperature (r2=0.95; Fig. S2h).

An increase in temperature and inflow ammonium concentrations both positively influenced the rates of NH4+ oxidation and N2O emissions and the emission factor (Fig. 5). The NH4+ oxidation rate linearly increased from 1.3 to 1.5 mg NH4+-N min-1 with temperature (r=0.89; Fig. 5a) and increased from 0.97 to 3.49 mg NH4+-N min-1 with a 10-fold increase in the inflow ammonium concentration (r=0.82; Fig. 5b). These positive correlations are well known in the temperature range investigated here and are likely due to enhanced enzymatic activity and Michaelis–Menten kinetics, respectively (Groeneweg et al., 1994; Kim et al., 2008; Raimonet et al., 2017). Similarly, the N2O emission rates increased from 80.4×10-6 to 2.5×10-3 mg N2O-N min-1, and from 83.6×10-6 to 6.2×10-3 mg N2O-N min-1 upon changes in temperature and the ammonium concentrations, respectively. These results are in agreement with positive correlations between N2O emissions with temperature and ammonium concentration observed from modeling and experimental studies on partial nitrification and activated sludge systems (Guo and Vanrolleghem, 2014; Law et al., 2012a; Reino et al., 2017). Altogether this confirms a correlation between the N2O emission rates and the ammonium oxidation rates. Interestingly, the increase in the N2O emission factor indicates a stronger effect of temperature and ammonium concentration on the N2O emission rate than on NH4+ oxidation. The N2O emission factor increased from 0.07 % to 0.16 %, and from 0.01 % to 0.29 % with temperature and inflow ammonium concentration, respectively (r>0.94; Fig. 5e and f). Both experiments suggest that the increase in N2O emissions results from the increasing production of N2O by hydroxylamine oxidation or nitrite reduction in combination with a slow rate or the absence of N2O reduction to N2. Furthermore, no nitrite accumulation was observed with increasing ammonium oxidation rate (Fig. S2i). Therefore, if N2O emission results mainly from the nitrite reduction pathway, this suggests that the nitrite reduction pathway is more responsive to the increasing ammonium oxidation rate than the nitrite oxidation pathway; the latter remains the main pathway of nitrite consumption.

The range of nitrogen isotopomer site preference observed during the temperature and concentration tests (from -8 ‰ to 2.6 ‰) was similar to those measured during the oxygenation tests, confirming the high contribution of the nitrite reduction pathway to N2O emissions (Fig. 6a). This is consistent with previous findings based on the 15N-SP of N2O emitted from aerobic activated sludge (Toyoda et al., 2011; Tumendelger et al., 2016; Wunderlin et al., 2013), although authors reported 15N-SP as high as 10 ‰. This can suggest a higher oxygen limitation being favorable to the contribution of the nitrite reduction to N2O production in the nitrifying reactor studied here. Hydroxylamine oxidation can even be the main N2O-producing pathway, as evidenced by Tumendelger et al. (2014) in an aerated tank.

Furthermore, 15N-SP increased with temperature between 13.5 and 19.8 ∘C. Our data suggest that temperature was the main control on the change in N2O-producing pathways within this temperature range (Fig. 6a). This could explain higher SP obtained with a 28.6 mg N L-1 inflow ammonium concentration than with 42.8. The temperature control seems to mitigate here the effect that ammonium concentration can have on the N2O-producing pathways evidenced elsewhere. Wunderlin et al. (2012, 2013) observed an increase in 15N-SP from -1.2 ‰ to 1.1 ‰ when inflow [NH4+] increased from 9 to 15 mg N L-1. They also observed 3 ‰–6 ‰ decreases in 15N-SP over the course of ammonium oxidation experiments and suggested that the NH2OH oxidation contribution to N2O production increased when conditions of NH4+ excess, low NO2- concentrations and high nitrogen oxidation rate occur simultaneously. Our findings are consistent with the observation of Groeneweg et al. (1994) showing that temperature rather than ammonium concentration influenced the ammonium oxidation rate.

15N-SP increased from -6.5 ‰ to 2.6 ‰ with increasing temperature from 13.5 to 19.8 ∘C (Fig. 6a). This 15N-SP increase may either result from an increase in the N2O production by the hydroxylamine oxidation pathway or the N2O reduction to N2. Since an optimal oxygenation level was imposed and increased emissions were observed, the increasing 15N-SP is more likely due to N2O production by the hydroxylamine oxidation pathway. Reino et al. (2017) also observed an increase of N2O emissions for temperatures above 15 ∘C in a granular sludge airlift reactor performing partial nitritation. The authors suggested two hypothesis to explain their results: (i) the difference in the kinetic dependency with temperature of enzymes involved in ammonium and hydroxylamine oxidation; (ii) the temperature dependency of the acid–base equilibrium ammonium–ammonia. The changes in 15N-SP observed here are consistent with the former hypotheses. Hydroxylamine oxidation likely becomes the limiting step at temperatures above 15 ∘C, while being faster than ammonium oxidation at lower temperatures (Fig. 7). At temperatures above 15 ∘C, hydroxylamine therefore accumulates and leads to a higher contribution of the hydroxylamine oxidation pathway to N2O emissions. It would thus be interesting to determine the temperature dependency of the hydroxylamine oxidase.

The change in nitrous oxide-producing and nitrous oxide-consuming pathways had contrasting effects on the nitrogen and oxygen isotope ratios of nitrous oxide (Fig. 6b and c). δ15N-N2O decreased from -2.5 ‰ to -40.9 ‰ with an increasing contribution of hydroxylamine oxidation to the N2O emissions, i.e., when temperature increased from 13.5 to 19.8 ∘C. This is in contrast with the expected net lower isotope effect for N2O produced by hydroxylamine oxidation than nitrite reduction, and points out that further investigations are needed (Snider et al., 2015; Yamazaki et al., 2014). The changes in δ18O-N2O were less straightforward, likely influenced by changes in the reaction rates in addition to changes in the contribution of N2O-producing pathways. The values decreased from 41.1 ‰ to 34.3 ‰ with an increasing contribution of hydroxylamine oxidation to the N2O emissions when temperature increased from 13.5 to 18.2 ∘C. It decreased linearly from 38.2 ‰ to 31.8 ‰ with increasing reaction rate when inflow ammonium concentration increased from 20.2 to 62.1 mg NH4+-N L-1 (r2=0.83).

The oxygenation, temperature and ammonium concentration tests revealed a strong control of nitrite-oxidizing activity and the contribution of the nitrite reduction pathway to N2O production. No relationship was observed between NO2- concentrations and oxygenation (Fig. S2g). In addition to this, higher 15N-SP at 21 % compared to the 10.5 %–16.8 % O2 was observed while the temperature remained below 20 ∘C (Fig. 4d). This is most likely due to higher nitrite oxidation than nitrite reduction rates in response to increasing oxygenation levels to 21 % O2, which is consistent with the nitrite oxidation step sensitivity to oxygen limitation (Pollice et al., 2002; Tanaka and Dunn, 1982). Additionally, 15N-SP close to 0 ‰ observed at the highest oxygenation level indicates a decreasing contribution to N2O production of nitrite reduction over hydroxylamine oxidation pathway. The highest oxygenation level thus limits the reduction pathways (i.e., NO2- reduction to N2O and N2O reduction to N2) while favoring the ammonium and nitrite oxidation pathways.

During the temperature and ammonium concentration tests, the contribution of the hydroxylamine oxidation pathway to N2O emissions increased with a temperature between 13.5 and 19.8 ∘C (Sect. 3.3) and decreased in favor of the nitrite reduction pathway when the temperature exceeded 20 ∘C (Fig. 6a). 15N-SP was low when the temperature exceeded 20 ∘C (-7.3±1 ‰), while being higher than -5 ‰ (-1.3±2.4 ‰) when the temperature ranged from 18.2 to 19.8 ∘C. At temperatures above 20 ∘C, ammonium oxidation rates exceed nitrite oxidation rates (Fig. 7; Kim et al., 2008; Raimonet et al., 2017). This most likely explains the increased contribution of the nitrite reduction pathway to N2O emission, as more nitrite becomes available for nitrifier denitrification and/or heterotrophic denitrification. As little nitrite accumulated (Fig. S2h), lower rates of nitrite-consuming processes than nitrite-producing processes can be inferred (nitrite reduction and oxidation vs. ammonium oxidation). Additionally, values of δ18O>35 ‰ measured during these tests suggest a significant contribution of heterotrophic denitrifiers to N2O emissions (Snider et al., 2013). This seems to occur at the lowest hydroxylamine oxidation contribution to N2O production below 18 ∘C and at 20.3 ∘C. Furthermore, the denitrifiers were impacted to a larger extent by temperature than ammonium concentration.