Nitrogen isotopic fractionations during nitric oxide production in an agricultural soil

Nitric oxide (NO) emissions from agricultural soils play a critical role in atmospheric chemistry and represent an important pathway for loss of reactive nitrogen (N) to the environment. With recent methodological advances, there is growing interest in the natural-abundance N isotopic composition (δ¹⁵N) of soil-emitted NO and its utility in providing mechanistic information on soil NO dynamics. However, interpretation of soil δ¹⁵N-NO measurements has been impeded by the lack of constraints on the isotopic fractionations associated with NO production and consumption in relevant microbial and chemical reactions. In this study, anoxic (0 % O₂), oxic (20 % O₂), and hypoxic (0.5 % O₂) incubations of an agricultural soil were conducted to quantify the net N isotope effects (¹⁵η) for NO production in denitrification, nitrification, and abiotic reactions of nitrite (${\mathrm{NO}}_{\mathrm{2}}^{-}$) using a newly developed δ¹⁵N-NO analysis method. A sodium nitrate (${\mathrm{NO}}_{\mathrm{3}}^{-}$) containing mass-independent oxygen-17 excess (quantified by a Δ¹⁷O notation) and three ammonium (${\mathrm{NH}}_{\mathrm{4}}^{+}$) fertilizers spanning a δ¹⁵N gradient were used in soil incubations to help illuminate the reaction complexity underlying NO yields and δ¹⁵N dynamics in a heterogeneous soil environment. We found strong evidence for the prominent role of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation under anoxic conditions in controlling the apparent ¹⁵η for NO production from ${\mathrm{NO}}_{\mathrm{3}}^{-}$ in denitrification (i.e., 49 ‰ to 60 ‰). These results highlight the importance of an under-recognized mechanism for the reversible enzyme ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidoreductase to control the N isotope distribution between the denitrification products. Through a Δ¹⁷O-based modeling of co-occurring denitrification and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation, the ¹⁵η for ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction to NO and NO reduction to nitrous oxide (N₂O) were constrained to be 15 ‰ to 22 ‰ and −8 ‰ to 2 ‰, respectively. Production of NO in the oxic and hypoxic incubations was contributed by both ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption, with both processes having a significantly higher NO yield under O₂ stress. Under both oxic and hypoxic conditions, NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation proceeded with a large ¹⁵η (i.e., 55 ‰ to 84 ‰) possibly due to expression of multiple enzyme-level isotopic fractionations during ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ that involves NO as either a metabolic byproduct or an obligatory intermediate for ${\mathrm{NO}}_{\mathrm{2}}^{-}$ production. Adding ${\mathrm{NO}}_{\mathrm{2}}^{-}$ to sterilized soil triggered substantial NO production, with a relatively small ¹⁵η (19 ‰). Applying the estimated ¹⁵η values to a previous δ¹⁵N measurement of in situ soil NO_x emission (NO${}_x=\mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}$) provided promising evidence for the potential of δ¹⁵N-NO measurements in revealing NO production pathways. Based on the observational and modeling constraints obtained in this study, we suggest that simultaneous δ¹⁵N-NO and δ¹⁵N-N₂O measurements can lead to unprecedented insights into the sources of and processes controlling NO and N₂O emissions from agricultural soils.

1 Introduction

Agricultural production of food has required a tremendous increase in the application of nitrogen (N) fertilizers since the 1960s (Davidson, 2009). In order to maximize crop yields, N fertilizers are often applied in excess to agricultural soils, resulting in loss of reactive N to the environment (Galloway et al., 2003). Loss of N in the form of gaseous nitric oxide (NO) has long been recognized for its adverse impacts on air quality and human health (Veldkamp and Keller, 1997). Once emitted to the atmosphere, NO is rapidly oxidized to nitrogen dioxide (NO₂), and these compounds (collectively referred to as NO_x) drive production and deposition of atmospheric nitrate (${\mathrm{NO}}_{\mathrm{3}}^{-}$) (Calvert et al., 1985) and play a critical role in the formation of tropospheric ozone (O₃) – a toxic air pollutant and potent greenhouse gas (Crutzen, 1979). Despite the observations that emission of NO from agricultural soils can sometimes exceed that of nitrous oxide (N₂O) – a climatically important trace gas primarily produced from reduction of NO in soils (Liu et al., 2017), NO is frequently overlooked in soil N studies due to its high reactivity and transient presence relative to N₂O (Medinets et al., 2015). Consequently, the contribution of soil NO emission to contemporary NO_x inventories at regional to global scales is highly uncertain (e.g., ranging from 3 % to >30 %) (Hudman et al., 2010; Vinken et al., 2014) and remains the subject of much current debate (Almaraz et al., 2018; Maaz et al., 2018).

As the central hub of the biogeochemical N cycle, NO can be produced and consumed in numerous microbial and chemical reactions in soils (Medinets et al., 2015). Among these processes, nitrification and denitrification are the primary sources responsible for NO emission from N-enriched agricultural soils (Firestone and Davidson, 1989). Denitrification is the sequential reduction of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and nitrite (${\mathrm{NO}}_{\mathrm{2}}^{-}$) to NO, N₂O, and dinitrogen (N₂) and can be mediated by a diversity of soil heterotrophic microorganisms (Zumft, 1997). The enzymatic system of denitrification comprises a series of dedicated reductases whereby ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reductase (NIR) and NO reductase (NOR) are the key enzymes that catalyze production and reduction of NO, respectively (Ye et al., 1994). As such, NO is often viewed as a free intermediate of the denitrification process (Russow et al., 2009). In comparison, nitrification is a two-step aerobic process in which oxidation of ammonia (NH₃) to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ is mediated by ammonia-oxidizing bacteria (AOB) or archaea (AOA), while the subsequent oxidation of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ is performed by nitrite-oxidizing bacteria (NOB) (Lehnert et al., 2018). Although production of NO during the nitrification process has been linked to NH₃ oxidation (Hooper et al., 2004; Caranto and Lancaster, 2017) and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction by AOB/AOA-encoded NIR (Wrage-Mönning et al., 2018), the metabolic role of NO in AOB and AOA remains ambiguous, making it difficult to elucidate the enzymatic pathways driving NO release by nitrification (Beeckman et al., 2018; Stein, 2019). Additionally, NO can also be produced from abiotic reactions involving soil ${\mathrm{NO}}_{\mathrm{2}}^{-}$ or its protonated form – nitrous acid (HNO₂) (Venterea et al., 2005; Lim et al., 2018). However, despite empirical evidence for the dependence of soil NO emission on soil N availability and moisture content (Davidson and Verchot, 2000), the source contribution of soil NO emission across temporal and spatial scales is poorly understood (Hudman et al., 2012). This is largely due to the lack of a robust means for source partitioning soil-emitted NO under dynamic environmental conditions.

Natural-abundance stable N and oxygen (O) isotopes in N-containing molecules have long provided insights into the sources and relative rates of biogeochemical processes comprising the N cycle (Granger and Wankel, 2016). The unique power of stable isotope ratio measurements stems from the distinct partitioning of isotopes between chemical species or phases, known as isotopic fractionation. Thus, in order to extract the greatest information from the distributions of isotopic species, a rigorous understanding of the direction and magnitude of isotopic fractionations associated with each relevant transformation is required. Both kinetic and equilibrium isotope effects can lead to isotopic fractionations between N-bearing compounds in soils (Granger and Wankel, 2016; Denk et al., 2017). During kinetic processes, isotopic fractionation occurs as a result of differences in the reaction rates of isotopically substituted molecules (i.e., isotopologues), leading to either enrichment or, in a few rare cases, depletion of heavy isotopes in the reaction substrate (Fry, 2006; Casciotti, 2009). The degree of kinetic isotope fractionation can be quantified by a kinetic isotope fractionation factor (α_k), which is often represented by the ratio of reaction rate constants of light isotopologues to that of heavy isotopologues. In this definition, α_k is larger than 1 for normal kinetic isotope fractionation. For equilibrium reactions, equilibrium isotope fractionation arises from differences in the zero-point energies of two species undergoing isotopic exchange, leading to enrichment of heavy isotopes in the more strongly bonded form (Fry, 2006; Casciotti, 2009). In this case, the isotope ratios of two species at equilibrium are defined by an equilibrium isotope fractionation factor (α_eq), which is also related to the kinetic isotope fractionation factors of forward and backward equilibrium reactions (Fry, 2006). By convention, isotopic fractionation can be expressed in units of per mill (‰) as an isotope effect $\left(\mathit{ϵ}\right):\mathit{ϵ}=(\mathit{\alpha }-\mathrm{1})\times \mathrm{1000}$. Nevertheless, in a heterogeneous soil environment, expression of intrinsic kinetic and equilibrium isotope effects for biogeochemical N transformations is often limited due to transport limitation in soil substrates, the multi-step nature of transformation processes, and the presence of diverse soil microbial communities that transform N via parallel and/or competing reaction pathways (Maggi and Riley, 2010). As such, interpretation of N isotope distribution in soils has largely relied on measuring net isotope effects (η), which are often characterized by incubating soil samples under environmentally relevant conditions, that favor expression of intrinsic isotope effects for specific N transformations (Lewicka-Szczebak et al., 2014). For example, it has been shown that the net N isotope effects for N₂O production in soil nitrification, denitrification, and abiotic reactions are distinctively different under certain soil conditions (Denk et al., 2017), rendering natural-abundance N isotopes of N₂O a useful index for inferring sources of N₂O in agricultural soils (Toyoda et al., 2017).

While the isotopic dynamics underlying soil N₂O emissions has been extensively studied, there has been little investigation into the N isotopic composition (notated as δ¹⁵N in units of ‰; $\mathit{\delta }=\left(\right(R_{\text{sample}}/R_{\text{standard}})-\mathrm{1})\times \mathrm{1000}$) of soil-emitted NO due to measurement difficulties (Yu and Elliott, 2017). Using a tubular denuder that trapped NO released from urea and ammonium (${\mathrm{NH}}_{\mathrm{4}}^{+}$)-fertilized soils, Li and Wang (2008) revealed a gradual increase in δ¹⁵N-NO from −49 ‰ to −19 ‰ and simultaneous ¹⁵N enrichment in soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ over a 2-week laboratory incubation. Similar δ¹⁵N variations (i.e., −44 ‰ to −14 ‰) were recently reported for in situ soil NO_x emission in a manure-fertilized cornfield (Miller et al., 2018). Moreover, the magnitude of δ¹⁵N-NO_x measured in this study depended on manure application methods, implying that NO_x was mainly sourced from nitrification of manure-derived ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (Miller et al., 2018). Based on a newly developed soil NO collection system that quantitatively converts soil-emitted NO to NO₂ for collection in triethanolamine (TEA) solutions, our previous work demonstrated substantial variations in δ¹⁵N-NO (−54 ‰ to −37 ‰) in connection with changes in moisture content in a forest soil (Yu and Elliott, 2017). Furthermore, the measured in situ δ¹⁵N-NO values spanned a wide range (−60 ‰ to −23 ‰) and were highly sensitive to added N substrates (i.e., ${\mathrm{NH}}_{\mathrm{4}}^{+}$, ${\mathrm{NO}}_{\mathrm{3}}^{-}$, and ${\mathrm{NO}}_{\mathrm{2}}^{-}$), indicating that NO produced from different sources may bear distinguishable δ¹⁵N imprints (Yu and Elliott, 2017). Nevertheless, despite the potential of δ¹⁵N-NO measurements in providing mechanistic information on soil NO dynamics, interpretation of δ¹⁵N-NO has been largely impeded by the knowledge gap as to how δ¹⁵N-NO is controlled by N isotopic fractionations during NO production and consumption in soils.

To this end, we conducted a series of controlled incubation experiments to quantify the net N isotope effects for NO production in an agricultural soil. Replicate soil incubations were conducted to measure the yield and δ¹⁵N of soil-emitted NO under anoxic (0 % O₂), oxic (20 % O₂), and hypoxic (0.5 % O₂) conditions, respectively. A sodium ${\mathrm{NO}}_{\mathrm{3}}^{-}$ fertilizer mined in the Atacama Desert, Chile (Yu and Elliott, 2018), was used to amend the soil in all three incubation experiments. This Chilean ${\mathrm{NO}}_{\mathrm{3}}^{-}$ originated from atmospheric deposition and thus contained an anomalous ¹⁷O excess (quantified by the Δ¹⁷O notation) as a result of mass-independent isotopic fractionations during its photochemical formation in the atmosphere (Michalski et al., 2004). Because isotopic fractionations during biogeochemical ${\mathrm{NO}}_{\mathrm{3}}^{-}$ production and consumption are mass-dependent, Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ is a conservative tracer of gross nitrification and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption and provides a quantitative benchmark for disentangling isotopic overprinting on δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ during co-occurring nitrification and denitrification (Yu and Elliott, 2018) (see Sect. S1 in the Supplement for more details). As additional tracers, three isotopically different ${\mathrm{NH}}_{\mathrm{4}}^{+}$ fertilizers were used in parallel treatments of the oxic and hypoxic incubations to quantify the nitrifier source contribution of NO production with changing O₂ availability. By integrating multi-species measurements of N and O isotopes in an isotopologue-specific modeling framework, we were able for the first time to unambiguously link the yield and δ¹⁵N variations of soil-emitted NO to nitrification and denitrification carried out by whole soil microbial communities and to characterize the net isotope effects for NO production from soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NH}}_{\mathrm{4}}^{+}$, and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ under different redox conditions. The quantified isotope effects are discussed in the context of chemical and enzymatic pathways leading to net NO production in the soil environment and are applied to a previous field study (Miller et al., 2018) to provide implications for tracing the sources of NO emission from agricultural soils.

2 Materials and methods

2.1 Soil characteristics and preparation

Soil samples used in this study were collected in July 2017 from a conventional corn–soybean rotation field in central Pennsylvania, USA, managed by the USDA (Agricultural Research Service, University Park, PA, USA). The soil is a well-drained Hagerstown silt loam (fine, mixed, semiactive, mesic Typic Hapludalfs) with sand, silt, and clay content of 21 %, 58 %, and 21 %, respectively. The sampled surface layer (0–10 cm) had a bulk density of 1.2 g cm⁻³ and a pH (1:1 water) of 5.7. Total N content was 0.2 % and δ¹⁵N of total N was 5.3 ‰. Soil C:N ratio was 11.4 and organic carbon content was 1.8 %. In the laboratory, soils were homogenized and sieved to 2 mm (but not air-dried) and then stored in resealable plastic bags at 4 ^∘C until further analyses and incubations. Gravimetric water content of the sieved and homogenized soils was 0.14 g H₂O g⁻¹. Indigenous ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations were 0.7 and 19.8 µg N g⁻¹, respectively. Throughout this paper, soil N concentrations, NO fluxes, and N transformation rates are expressed on the basis of soil ovendry (105 ^∘C) weight.

2.2 Net NO production and collection of NO for δ¹⁵N analysis

The recently developed soil dynamic flux chamber (DFC) system was used to measure net NO production rates and to collect soil-emitted NO for δ¹⁵N analysis (Yu and Elliott, 2017). A schematic of the DFC system is shown in Fig. 1a. Detailed development and validation procedures for the NO collection method were presented in Yu and Elliott (2017). Briefly, custom-made flow-through incubators modified from 1 L Pyrex medium bottles (13951 L, Corning, USA) were used for all the incubation experiments (Fig. 1b). Each incubator was stoppered with two 42 mm Teflon septa secured by an open-topped screw cap and equipped with two vacuum valves for purging and closure of the incubator headspace. To measure net NO production from enclosed soil samples, a flow of NO-free air with desired O₂ content was directed through the incubator into a chemiluminescent NO–NO_x–NH₃ analyzer (model 146i, Thermo Fisher Scientific) (Fig. 1a) (Yu and Elliott, 2017). Outflow NO concentration was monitored continuously until steady, and then the net NO production rate was determined from the flow rate and steady-state NO concentration. To collect NO for δ¹⁵N analysis, a subsample of the incubator outflow was forced to pass through a NO collection train (Fig. 1a) where NO is converted to NO₂ by excess O₃ (∼3 ppm) in a Teflon reaction tube (9.5 mm i.d., ca. 240 cm length) and subsequently collected in a 500 mL gas washing bottle containing a 20 % (v∕v, 70 mL) TEA solution (Yu and Elliott, 2017). The collection products were about 90 % ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and 10 % ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Yu and Elliott, 2017). Results from comprehensive method testing showed that the NO collection efficiency was 98.5 %±3.5 % over a wide range of NO concentrations (12 to 749 ppb) and environmental conditions (e.g., temperature from 11 to 31 ^∘C and relative humidity of the incubator outflow from 27 % to 92 %) (Yu and Elliott, 2017). Moreover, it was confirmed that high concentrations of ammonia (NH₃) (e.g., 500 ppb) and nitrous acid (HONO) (removed by an inline HONO scrubber, Fig. 1a) in the incubator outflow do not interfere with NO collection (Yu and Elliott, 2017).

2.3 Anoxic incubation

To prepare for the anoxic incubation, the soil samples were spread out on a covered tray for pre-conditioning under room temperature (21 ^∘C) for 24 h. Next, the soil was amended with the Chilean ${\mathrm{NO}}_{\mathrm{3}}^{-}$ fertilizer (${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}=\mathrm{0.3}\mathrm{‰}\pm \mathrm{0.1}\mathrm{‰}$, ${\mathit{\delta }}^{\mathrm{18}}\mathrm{O}=\mathrm{55.8}\mathrm{‰}\pm \mathrm{0.1}\mathrm{‰}$, ${\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}=\mathrm{18.6}\mathrm{‰}\pm \mathrm{0.1}\mathrm{‰}$) to achieve a fertilization rate of 35 µg ${\mathrm{NO}}_{\mathrm{3}}^{-}$-N g⁻¹ and a target soil water content of 0.21 g H₂O g⁻¹ (equivalent to 46 % water-filled pore space, WFPS). The fertilized soil samples were thoroughly homogenized using a glass rod in the tray. A total of 100 g (dry-weight equivalent) of soil was then weighed into each of eight incubators, resulting in a soil depth of about 1.5 cm. The incubators were connected in parallel using a Teflon purging manifold (Fig. 1c), vacuumed and filled with ultra-high-purity N₂ for three cycles, and incubated in the dark with a continuous flow of N₂ circulating through each of the eight incubators at 0.015 standard liters per minute (SLPM). The sample fertilization and preparation procedures were repeated three times to establish three batches of replicate samples, leading to 24 soil samples in total for the anoxic incubation.

Figure 1 (a) Schematic of the DFC system (not to scale) consisting of the following: (1) zero air tank, (2) N₂ tank, (3) mass flow controller, (4) Nafion moisture exchanger, (5) flow-through incubator, (6–9) needle valves for controlling vacuum and flushing of the DFC system, (10) HONO scrubber, (11) diaphragm pump, (12) Teflon reaction tube, (13) gas washing bottle containing TEA solution, (14) NO–NO_x–NH₃ analyzer, (15) O₃ generator, and (16) in-line PTFE particulate filter assembly. (b) Photo of the flow-through incubator. (c) Photo of the Teflon purging manifold for connection of the incubators in parallel.

The first NO measurement and collection event was conducted 24 h after the onset of the anoxic incubation, and daily sampling was conducted thereafter. At each sampling event, one incubator from each replicate sample batch was isolated by closing the vacuum valves, removed from the purging manifold, and then measured using the DFC system. To prevent O₂ contamination by residual air in the DFC system, the DFC system was evacuated and flushed with N₂ five times before the vacuum valves were re-opened. A flow of N₂ was then supplied at 1 SLPM for continuous NO concentration measurement and collection. Samples from the replicate batches were measured successively.

Following the completion of measurement and collection of each sample, the incubator was opened from the top and the soil was combined with 500 mL deionized water for extraction of soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (McKenney et al., 1982). Because ${\mathrm{NO}}_{\mathrm{2}}^{-}$ accumulation was found in pilot experiments, deionized water, rather than routinely used KCl solutions, was used for the extraction to ensure accurate ${\mathrm{NO}}_{\mathrm{2}}^{-}$ determination (Homyak et al., 2015). To extract soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$, the soil slurry was agitated vigorously on a stir plate for 10 min and then centrifuged for 10 min at 3400 g. The resultant supernatant was filtered through a sterile 0.2 µm filter (Homyak et al., 2015). In light of high ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentrations observed in the pilot experiments, the filtrate was divided into two 60 mL Nalgene bottles, with one of the bottles receiving sulfamic acid to remove ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (Granger and Sigman, 2009). This ${\mathrm{NO}}_{\mathrm{2}}^{-}$-removed sample was used for ${\mathrm{NO}}_{\mathrm{3}}^{-}$ isotope analysis, while the other sample without sulfamic acid treatment was used for determining ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations and combined δ¹⁵N analysis of NO${}_{\mathrm{2}}^{-}+{\mathrm{NO}}_{\mathrm{3}}^{-}$. Two important control tests, based on ${\mathrm{NO}}_{\mathrm{2}}^{-}$∕${\mathrm{NO}}_{\mathrm{3}}^{-}$ spiking and acetylene (C₂H₂) addition, were conducted to evaluate the robustness of the adopted soil incubation and extraction methods. The results confirmed that the water extraction method was robust for determining concentrations and isotopic composition of soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and that aerobic ${\mathrm{NO}}_{\mathrm{3}}^{-}$ production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation was negligible during the soil incubation and extraction procedures (Tables S1 and S2 in the Supplement; see Sect. S2 for more details).

2.4 Oxic and hypoxic incubations

The same pre-conditioning and fertilization protocol described for the anoxic incubation was used for the oxic and hypoxic incubations. Three isotopically different ${\mathrm{NH}}_{\mathrm{4}}^{+}$ fertilizers were used in parallel treatments of each incubation experiment: (1) δ¹⁵N-NH${}_{\mathrm{4}}^{+}=\mathrm{1.9}$ ‰ (low ¹⁵N enrichment), (2) δ¹⁵N-NH${}_{\mathrm{4}}^{+}=\mathrm{22.5}$ ‰ (intermediate ¹⁵N enrichment), and (3) δ¹⁵N-NH${}_{\mathrm{4}}^{+}=\mathrm{45.0}$ ‰ (high ¹⁵N enrichment). An off-the-shelf ammonium sulfate ((NH₄)₂SO₄) reagent was used in the low-δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatment, while the fertilizers with intermediate and high enrichment of ¹⁵N were prepared by gravimetrically mixing the (NH₄)₂SO₄ reagent with ${\mathrm{NH}}_{\mathrm{4}}^{+}$ reference materials IAEA-N2 (δ¹⁵N-NH${}_{\mathrm{4}}^{+}=\mathrm{20.3}$ ‰) and USGS26 (δ¹⁵N-NH${}_{\mathrm{4}}^{+}=\mathrm{53.7}$ ‰). In both oxic and hypoxic incubations, each of the three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments consisted of three replicate sample batches where each batch consisted of eight samples, resulting in 72 samples for each incubation experiment.

At the onset of each incubation experiment, soil samples (100 g dry-weight equivalent) were amended with the desired ${\mathrm{NH}}_{\mathrm{4}}^{+}$ fertilizer (90 µg N g⁻¹) and the Chilean ${\mathrm{NO}}_{\mathrm{3}}^{-}$ fertilizer (15 µg N g⁻¹) to the target soil water content of 0.21 g H₂O g⁻¹ (46 % WFPS). Following the amendment, two soil samples from each replicate batch were immediately extracted – one with 500 mL of deionized water for soil ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ using the extraction method described above and the other one with 500 mL of a 2 M KCl solution for determination of soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$. The remaining samples were incubated under desired O₂ conditions until further measurements. In the oxic incubation, the incubators were connected in parallel using the purging manifold and continuously flushed by a flow of zero air (20 % O₂+80 % N₂). In the hypoxic incubation, a flow of synthetic air with 0.5 % O₂ content (balanced by 99.5 % N₂) was used to incubate the soil samples. The synthetic air was generated by mixing the zero air with ultra-high-purity N₂ using two mass flow controllers (model SmartTrak 50, Sierra Instruments).

Replicate NO measurement and collection events were conducted at 24, 48, and 72 h following the onset of the oxic and hypoxic incubations. Because net NO production rates were low under oxic and hypoxic conditions, all remaining soil samples in each replicate batch were connected in parallel for NO measurement and collection using the DFC system. This parallel connection ensured high outflow NO concentrations (i.e., >30 ppb) required for quantitative NO collection (Yu and Elliott, 2017). The flow rate of purging air (20 % O₂ for the oxic incubation and 0.5 % O₂ for the hypoxic incubation) during the DFC measurement was 0.25 SLPM to each incubator. Following the NO measurement and collection, two soil samples from each replicate batch were extracted for determination of soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ (500 mL deionized water) and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (500 mL 2M KCl), respectively. Because NO concentrations were too low for reliable NO collection at 72 h after the onset of the incubations, only net NO production rates were measured using the remaining two soil samples in each replicate batch.

2.5 Abiotic NO production

The potential for NO production from abiotic reactions was assessed using sterilized soil samples. Soil samples (100 g dry-weight equivalent) were weighed into the incubators and then autoclaved at 121 ^∘C and 1.3 atm for 30 min. The autoclaved samples were pre-incubated under oxic and anoxic conditions, respectively, for 24 h and then fertilized with the Chilean ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (35 µg ${\mathrm{NO}}_{\mathrm{3}}^{-}$-N g⁻¹) or the lab (NH₄)₂SO₄ (90 µg ${\mathrm{NH}}_{\mathrm{4}}^{+}$-N g⁻¹). The fertilizer solutions were added to the soil surface through the Teflon septa using a sterile syringe equipped with a 25-gauge needle. These samples were then measured periodically for net NO production. Because ${\mathrm{NO}}_{\mathrm{2}}^{-}$ was found to accumulate during the anoxic incubation (see below), four soil samples were sterilized, pre-incubated under anoxic condition, and then fertilized with a NaNO₂ solution (δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}=\mathrm{1.4}\mathrm{‰}\pm \mathrm{0.2}\mathrm{‰}$) (8 µg N g⁻¹) for immediate NO measurement and collection. These ${\mathrm{NO}}_{\mathrm{2}}^{-}$-amended samples were thereafter incubated under anoxic conditions and measured periodically for net NO production until undetectable.

2.6 Chemical and isotopic analyses

Soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations were determined using a Dionex ion chromatograph ICS-2000 with a precision of (1σ) of ±5.0 µg N L⁻¹. Soil ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentrations were analyzed using the Griess–Ilosvay colorimetric reaction with a precision of ±1.2 µg N L⁻¹. Soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$ concentrations were measured using a modified fluorometric o-phthaldialdehyde (OPA) method for soil KCl extracts (Kang et al., 2003) with a precision of ±7.0 µg N L⁻¹. NO${}_{\mathrm{2}}^{-}+{\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration in the TEA collection samples was measured using a modified spongy cadmium method with a precision of ±1.6 µg N L⁻¹ (Yu and Elliott, 2017).

The denitrifier method (Sigman et al., 2001; Casciotti et al., 2002) was used to measure δ¹⁵N and δ¹⁸O of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ in the ${\mathrm{NO}}_{\mathrm{2}}^{-}$-removed soil extracts and the δ¹⁵N of NO${}_{\mathrm{3}}^{-}+{\mathrm{NO}}_{\mathrm{2}}^{-}$ in the extracts without sulfamic acid treatment. In brief, a denitrifying bacterium (Pseudomonas aureofaciens) lacking the N₂O reductase enzyme was used to convert 20 nmol of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ into gaseous N₂O. The N₂O was then purified in a series of chemical traps, cryo-focused, and finally analyzed on a GV Instruments Isoprime continuous flow isotope ratio mass spectrometer (CF-IRMS) at m∕z 44, 45, and 46 at the University of Pittsburgh Regional Stable Isotope Laboratory for Earth and Environmental Science Research where all isotope analyses were conducted for this study. International ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reference standards IAEA-N3, USGS34, and USGS35 were used to calibrate the δ¹⁵N and δ¹⁸O analyses. The long-term precision is ±0.3 ‰ and ±0.5 ‰, respectively, for the δ¹⁵N and δ¹⁸O analyses. Because the denitrifier method does not differentiate ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ for the δ¹⁵N analysis, δ¹⁵N of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ was estimated using an isotopic mass balance when ${\mathrm{NO}}_{\mathrm{2}}^{-}$ accounted for a significant fraction of the total NO${}_{\mathrm{3}}^{-}+{\mathrm{NO}}_{\mathrm{2}}^{-}$ pool.

Δ¹⁷O of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ was measured using the coupled bacterial reduction and thermal decomposition method described by Kaiser et al. (2007). The denitrifying bacteria were used to convert 200 nmol of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ to N₂O, which was subsequently converted to O₂ and N₂ by reduction over a gold surface at 800 ^∘C. The produced O₂ and N₂ were separated using a 5 Å molecular sieve gas chromatograph, and the O₂ was then analyzed for δ¹⁷O and δ¹⁸O using the CF-IRMS. Δ¹⁷O was calculated from the measured δ¹⁷O and δ¹⁸O using Eq. (1) (see Sect. S1) and calibrated by USGS34, USGS35, and a 1:1 mixture of USGS34 and USGS35.

$$\begin{array}{}\text{(1)}& {\displaystyle }{\mathrm{\Delta }}^{\mathrm{17}}\mathrm{O}=\left[\ln \left({\displaystyle \frac{\mathit{\delta }{}^{\mathrm{17}}\mathrm{O}}{\mathrm{1000}}}+\mathrm{1}\right)-\mathrm{0.52}\ln \left({\displaystyle \frac{{\mathit{\delta }}^{\mathrm{18}}\mathrm{O}}{\mathrm{1000}}}+\mathrm{1}\right)\right]\times \mathrm{1000}\end{array}$$

The precision of the Δ¹⁷O analysis of USGS35 and the USGS35:USGS34 mixture is ±0.3 ‰ (Yu and Elliott, 2018). Following Kaiser et al. (2007), the measured Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ was used in the reduction of molecular isotope ratios of N₂O to correct for the isobaric interference (i.e., m∕z 45) on the measured δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$.

δ¹⁵N of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ in the KCl extracts was measured by coupling the NH₃ diffusion method (Zhang et al., 2015) and the hypobromite (BrO⁻) oxidation method (Zhang et al., 2007) with the denitrifier method (Felix et al., 2013). Briefly, an aliquot of soil KCl extract with 60 nmol ${\mathrm{NH}}_{\mathrm{4}}^{+}$ was pipetted into a 20 mL serum vial containing an acidified glass fiber disk. The solution was made alkaline by adding magnesium oxide (MgO) to volatilize NH₃, which was subsequently captured on the acidic disk as ${\mathrm{NH}}_{\mathrm{4}}^{+}$. After incubation under 37 ^∘C for 10 d, ${\mathrm{NH}}_{\mathrm{4}}^{+}$ was eluted from the disk using deionized water, diluted to 10 µM, oxidized by BrO⁻ to ${\mathrm{NO}}_{\mathrm{2}}^{-}$, and finally measured for δ¹⁵N as ${\mathrm{NO}}_{\mathrm{2}}^{-}$ at 20 nmol using the denitrifier method. International ${\mathrm{NH}}_{\mathrm{4}}^{+}$ reference standards IAEA-N1, USGS25, and USGS26 underwent the same preparation procedure as the soil KCl extracts and were used along with the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reference standards to correct for blanks and instrument drift. The precision of the δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ analysis is ±0.5 ‰ (Yu and Elliott, 2018).

δ¹⁵N of NO collected in the TEA solution was measured following the method described in Yu and Elliott (2017). Briefly, the TEA collection samples were first neutralized with 12 N HCl to pH ∼7, and then 10 to 20 nmol of the collected product NO${}_{\mathrm{2}}^{-}+{\mathrm{NO}}_{\mathrm{3}}^{-}$ was converted to N₂O using the denitrifier method. In light of the low δ¹⁵N values of soil-emitted NO and the presence of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ as the dominant collection product, a low-δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ isotopic standard (KNO₂, RSIL20, USGS Reston; ${\mathit{\delta }}^{\mathrm{15}}\mathrm{N}=-\mathrm{79.6}$ ‰) was used together with the international ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reference standards to calibrate the δ¹⁵N-NO analysis. Following the identical treatment principle, we prepared the isotopic standards in the same matrix (i.e., 20 % TEA) as the collection samples and matched both the molar N amount and injection volume (±5 %) between the collection samples and the standards to minimize the blank interferences associated with the bacterial medium and the TEA solution. The precision and accuracy of the δ¹⁵N-NO analysis, determined by repeated sampling of an analytical NO tank (δ¹⁵N-$\mathrm{NO}=-\mathrm{71.4}\mathrm{‰}$) under diverse collection conditions, is ±1.1 ‰ (Yu and Elliott, 2017).

3 Results

Sixty-three NO collection samples were obtained from the incubation experiments. The NO collection efficiency calculated based on the measured NO${}_{\mathrm{2}}^{-}+{\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration in the TEA solution and the theoretical concentration based on the measured net NO production rate (Yu and Elliott, 2017) was on average 99.1 %±3.7 %. Out of the 63 collection samples, four samples had a NO collection efficiency lower than 95 %. These samples were excluded from further data analysis and interpretation. The measured N concentrations, net NO production rates, and isotope data from all the incubation experiments are available in Tables S5 to S11.

3.1 Anoxic incubation

During the anoxic incubation, soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration decreased linearly from 49.3±0.1 to 23.1±0.2 µg N g⁻¹ (Fig. 2a), while ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentration increased linearly from 0.4±0.1 to 6.9±0.1 µg N g⁻¹ (Fig. 2b). The net NO production rate (f_NO-anoxic) increased progressively from the first sampling day (72±8 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) to sampling day 5 and then stabilized at about 82 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$ (Fig. 2c).

Figure 2 Measured and modeled concentrations of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (a) and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (b); net NO production rate (c); δ¹⁵N values of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (d), ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (e), and NO (f); and δ¹⁸O (g) and Δ¹⁷O (h) of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ during the anoxic incubation.

δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and δ¹⁵N-NO values increased from 4.7 ‰±0.3 ‰ to 38.7 ‰±1.5 ‰ and $-\mathrm{44.7}\mathrm{‰}\pm \mathrm{0.3}\mathrm{‰}$ to $-\mathrm{22.8}\mathrm{‰}\pm \mathrm{2.2}\mathrm{‰}$, respectively, over the anoxic incubation (Fig. 2d and f). The difference between δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and δ¹⁵N-NO values increased significantly from 49.4 ‰ to 59.5 ‰ toward the end of the incubation (Fig. 2d and f). Based on the closed-system Rayleigh model, the apparent N isotopic fractionation during ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption was estimated to be 43.3 ‰±0.9 ‰ (Fig. S3 in the Supplement). δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ was estimated for samples collected in the last 3 sampling days where ${\mathrm{NO}}_{\mathrm{2}}^{-}$ accounted for >15 % of the NO${}_{\mathrm{3}}^{-}+{\mathrm{NO}}_{\mathrm{2}}^{-}$ pool. The estimated δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ values were $-\mathrm{6.9}\mathrm{‰}\pm \mathrm{3.7}\mathrm{‰}$, $-\mathrm{6.0}\mathrm{‰}\pm \mathrm{2.5}\mathrm{‰}$, and $-\mathrm{0.9}\mathrm{‰}\pm \mathrm{1.3}\mathrm{‰}$, respectively (Fig. 2e). Although limited to the last 3 sampling days, δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ was lower than δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ by 33.6 ‰ to 37.9 ‰ (Fig. 2d and e) but was higher than the concurrently measured δ¹⁵N-NO values by a relatively constant offset of 21.5 ‰±0.7 ‰ (Fig. 2e and f). Surprisingly, both δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values (33.4 ‰±0.2 ‰ to 23.1 ‰±0.3 ‰) and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values (10.0 ‰±0.2 ‰ to 0.7 ‰±0.2 ‰) decreased progressively over the course of the anoxic incubation and were entirely decoupled from δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Fig. 2g and h).

3.2 Oxic and hypoxic incubations

Over the oxic incubation, soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$ concentration decreased linearly with increasing ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentration under all three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments (Fig. 3a and b). In the hypoxic incubation, changes in ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations were more limited, although the linear trends were still evident (Fig. 3a and b). Under both oxic and hypoxic conditions, the total concentration of soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ remained nearly constant over the entire incubations (i.e., variations <4 %), and soil ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentration was below the detection limit in both incubations. In the oxic incubation, δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ values uniformly increased by 8.6 ‰ to 13.1 ‰ under all three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments (Fig. 3e), while δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values varied distinctly, depending on the initial δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ values (Fig. 3d). Specifically, δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values increased by 7.8 ‰ and decreased by 10.9 ‰ under the high and low δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments, respectively, and remained relatively constant under the intermediate δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatment (Fig. 3d). Limited increases in δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ values (<2 ‰) were observed under all three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments in the hypoxic incubation (Fig. 3e). Correspondingly, variations in δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values were much smaller in the hypoxic incubation compared to those revealed in the oxic incubation (Fig. 3d). In both oxic and hypoxic incubations, δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Fig. 3g) and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Fig. 3h) values decreased progressively under all three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments, although the rates of decrease were significantly higher in the oxic incubation (Fig. 3g and h).

Figure 3 Measured and modeled concentrations of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (a) and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (b); net NO production rate (c); δ¹⁵N values of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (d), ${\mathrm{NH}}_{\mathrm{4}}^{+}$ (e), and NO (f); and δ¹⁸O (g) and Δ¹⁷O (h) of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ under the three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments (differed by color) of the oxic (open symbols) and hypoxic (solid symbols) incubations.

Figure 4 δ¹⁵N-NO as a function of δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ in the oxic and hypoxic incubations.

Figure 5 (a) Net NO production rate (f_NO-abiotic) of the ${\mathrm{NO}}_{\mathrm{2}}^{-}$-amended sterilized soil as a function of time. (b) Plot of the natural logarithm of f_NO-abiotic vs. time showing first-order decay of f_NO-abiotic.

The net NO production was significantly higher in the hypoxic incubation (f_NO-hypoxic; 9.0 to 10.4 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) than in the oxic incubation (f_NO-oxic; 7.1 to 8.5 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) (Fig. 3c). The measured δ¹⁵N-NO values ranged from $-\mathrm{16.8}\mathrm{‰}\pm \mathrm{0.3}\mathrm{‰}$ to $-\mathrm{54.9}\mathrm{‰}\pm \mathrm{0.8}\mathrm{‰}$ in the oxic incubation and from $-\mathrm{21.3}\mathrm{‰}\pm \mathrm{0.0}\mathrm{‰}$ to $-\mathrm{51.4}\mathrm{‰}\pm \mathrm{0.4}\mathrm{‰}$ in the hypoxic incubation (Fig. 3f). Pooling all the δ¹⁵N-NO measurements, we found that δ¹⁵N values between ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and NO differed from 58.9 ‰ to 70.7 ‰ across the three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments in the oxic incubation and from 50.4 ‰ to 69.6 ‰ in the hypoxic incubation (Fig. 4). In both incubations, the largest difference was observed under the high-δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatment, while the smallest difference was observed under the low δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatment. Under both oxic and hypoxic conditions, there was a significant linear relationship between the measured δ¹⁵N-NO and δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ values from all three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments (Fig. 4). The slope of the linear relationship is 0.78±0.03 (±1 SE) and 0.61±0.05 for the oxic and hypoxic incubations, respectively (Fig. 4).

3.3 Abiotic NO production

Addition of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ or ${\mathrm{NH}}_{\mathrm{4}}^{+}$ to the sterilized soil did not result in detectable NO production under either oxic or anoxic condition. Immediate NO release was, however, triggered by ${\mathrm{NO}}_{\mathrm{2}}^{-}$ addition under anoxic conditions (Fig. 5a). The abiotic NO production rate (f_NO-abiotic) reached a steady level of 83±5 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$ several minutes after the ${\mathrm{NO}}_{\mathrm{2}}^{-}$ addition and then decreased exponentially to <3 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$ over the following 8 d (Fig. 5a). The natural logarithm of f_NO-abiotic showed a linear relationship with time (Fig. 5b). The NO produced following the ${\mathrm{NO}}_{\mathrm{2}}^{-}$ addition had a δ¹⁵N value of $-\mathrm{17.8}\mathrm{‰}\pm \mathrm{0.4}\mathrm{‰}$, giving rise to a δ¹⁵N offset between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and NO of 19.2 ‰±0.5 ‰.

4 Discussion

Because interpretations of the results from the incubation experiments build upon each other, here we discuss the results from incubation of the sterilized soils (hereafter, abiotic incubation), anoxic incubation, and oxic/hypoxic incubations successively.

4.1 Reaction characteristics and N isotopic fractionation during abiotic NO production

The immediate release of NO upon the addition of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ highlights the chemically unstable nature of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and the critical role of chemical ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reactions in driving soil NO emissions (Venterea et al., 2005; Lim et al., 2018). The strong linearity between ln(f_NO-abiotic) and time (Fig. 5b) suggests apparent first-order kinetics for the abiotic NO production from ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (Eqs. 2 and 3) (McKenney et al., 1990).

$$\begin{array}{}\text{(2)}& {\displaystyle }& {\displaystyle }{f}_{\text{NO-abiotic}}=s_{\text{abiotic}}\times k_{\text{abiotic}}\times [{\mathrm{NO}}_{\mathrm{2}}^{-}{]}_t\text{(3)}& {\displaystyle }& {\displaystyle }[{\mathrm{NO}}_{\mathrm{2}}^{-}{]}_t=[{\mathrm{NO}}_{\mathrm{2}}^{-}{]}_{\mathrm{0}}{e}^{-k_{\text{abiotic}}\times t}\end{array}$$

In Eqs. (2) and (3), t is time; k_abiotic is the pseudo-first-order rate constant for ${\mathrm{NO}}_{\mathrm{2}}^{-}$ loss; s_abiotic is the apparent stoichiometric coefficient for NO production from ${\mathrm{NO}}_{\mathrm{2}}^{-}$; and [${\mathrm{NO}}_{\mathrm{2}}^{-}$]_t and [${\mathrm{NO}}_{\mathrm{2}}^{-}$]₀ are ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentration at time t and t=0 in the sterilized soil, respectively. Combining Eqs. (2) and (3) and then log-transforming both sides yield

$$\begin{array}{ll}{\displaystyle }\ln \left(f_{\text{NO-abiotic}}\right)=& {\displaystyle }-k_{\text{abiotic}}\times t\\ \text{(4)}& {\displaystyle }& {\displaystyle }+\ln (s_{\text{abiotic}}\times k_{\text{abiotic}}\times [{\mathrm{NO}}_{\mathrm{2}}^{-}{]}_{\mathrm{0}}).\end{array}$$

According to Eq. (4), k_abiotic and s_abiotic are estimated using the slope and intercept of the linear regression of ln (f_NO-abiotic) vs. time (Fig. 5b). Given [${\mathrm{NO}}_{\mathrm{2}}^{-}$]₀=8 µg N g⁻¹, s_abiotic and k_abiotic are estimated to be 0.52±0.05 (±SE) and 0.019±0.002 h⁻¹, respectively, suggesting that NO accounted for 52 %±5 % of the reacted ${\mathrm{NO}}_{\mathrm{2}}^{-}$ during the abiotic incubation. The estimated k_abiotic is within the range (i.e., 0.00055 to 0.73 h⁻¹) derived by a recent study based on soil samples spanning a wide range of pH values (3.4 to 7.2) (Lim et al., 2018). Based on the estimated k_abiotic, 97 % of the added ${\mathrm{NO}}_{\mathrm{2}}^{-}$ was lost by the end of the abiotic incubation.

Several reaction pathways with distinct stoichiometry have been proposed for abiotic NO production from ${\mathrm{NO}}_{\mathrm{2}}^{-}$ in soils. Under acidic soil conditions, self-decomposition of HNO₂ produces NO and nitric acid (HNO₃) with a stoichiometric HNO₂-to-NO ratio ranging from 0.5 to 0.66 (i.e., 1 mole of HNO₂ produces 0.5 to 0.66 moles of NO) (Van Cleemput and Samater, 1995). Although at pH 5.7 HNO₂ constituted <1 % of the NO${}_{\mathrm{2}}^{-}+{\mathrm{HNO}}_{\mathrm{2}}$ pool in this soil, HNO₂ decomposition can occur on acidic clay mineral surfaces, even though bulk soil pH is circumneutral (Venterea et al., 2005). However, given the complete ${\mathrm{NO}}_{\mathrm{2}}^{-}$ consumption in the abiotic incubation, HNO₂ decomposition confined to acidic microsites could not account for all observed NO production. Under anoxic conditions, ${\mathrm{NO}}_{\mathrm{2}}^{-}$∕HNO₂ can also be stoichiometrically reduced to NO by transition metals (e.g., Fe(II)) and diverse organic molecules (e.g., humic and fulvic acids, lignins, and phenols) in a process termed chemo-denitrification (Zhu-Barker et al., 2015). The produced NO from chemo-denitrification can undergo further reduction to form N₂O and N₂ (Zhu-Barker et al., 2015). In addition, both ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and NO in soil solution can be consumed as nitroso donors in abiotic nitrosation reactions, resulting in N incorporation into soil organic matter (Heil et al., 2016; Lim et al., 2018). Therefore, our observation that about half of the reacted ${\mathrm{NO}}_{\mathrm{2}}^{-}$ was recovered as NO may result from multiple competing ${\mathrm{NO}}_{\mathrm{2}}^{-}$ sinks, parallel NO-producing pathways, and possibly abiotic NO consumption in the sterilized soil. The other half of the reacted ${\mathrm{NO}}_{\mathrm{2}}^{-}$ that could not be accounted for by the measured NO was likely present in the forms of N₂O, N₂, and/or nitrosated organic compounds in the soil.

The observed δ¹⁵N difference between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and NO (i.e., ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}\text{(abiotic)}}=\mathrm{19.2}\mathrm{‰}\pm \mathrm{0.5}\mathrm{‰}$) likely reflects a combined N isotope effect for all of the competing NO production pathways during the abiotic incubation. While very little isotope data exist for abiotic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reactions in the literature, the measured ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}\text{(abiotic)}}$ in this study is consistent with reported N isotope effects (i.e., 15 ‰ to 25 ‰) for abiotic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction by Fe(II) at similar ${\mathrm{NO}}_{\mathrm{2}}^{-}$ consumption rates to this study (0.02 to 0.05 h⁻¹) (Buchwald et al., 2016). On the other hand, the measured ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}\text{(abiotic)}}$ is lower than the reported δ¹⁵N offsets between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and N₂O (i.e., ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/{\mathrm{N}}_{\mathrm{2}}\mathrm{O}\text{(abiotic)}}$) for chemo-denitrification (24 ‰ to 29 ‰) (Jones et al., 2015; Wei et al., 2019). This seems to suggest that the observed abiotic NO production was mainly driven by chemo-denitrification and that accumulation of NO as an chemo-denitrification intermediate may explain why the observed ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/{\mathrm{N}}_{\mathrm{2}}\mathrm{O}\text{(abiotic)}}$ was larger than the N isotope effect for Fe(II)-catalyzed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction in previous batch experiments (Jones et al., 2015; Buchwald et al., 2016). Future studies adopting simultaneous δ¹⁵N-NO and δ¹⁵N-N₂O measurements will be required to elucidate the role of NO as the N₂O precursor during chemo-denitrification.

It is important to note that the autoclaving is a harsh sterilization method and can substantially alter soil physical and chemical properties. For example, Buessecker et al. (2019) recently showed that autoclaved peat soil had 10-fold-higher total fluorescence compared to non-sterilized controls, indicating dramatic increases in solubility and lability of organic molecules by autoclaving. Furthermore, autoclaving has also been shown to substantially increase abiotic N₂O production from ${\mathrm{NO}}_{\mathrm{2}}^{-}$-amended soils (Wei et al., 2019). Conversely, milder sterilization methods (e.g., gamma-irradiation) that presumably cause less alteration of soil properties may not completely inactivate biological NO production due to the high diversity of biological NO production pathways in soils (e.g., non-specific reactions catalyzed by extracellular enzymes) (Medinets et al., 2015). Further research is warranted to compare different sterilization methods for their effects on abiotic NO production and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}\text{(abiotic)}}$.

4.2 Reaction reversibility between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and N isotope distribution between ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NO}}_{\mathrm{2}}^{-}$, and NO during the anoxic incubation

The measured f_NO-anoxic (72 to 82 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) (Fig. 2c) is well within the range reported for anoxic soil incubations (e.g., 5 to 500 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) (Medinets et al., 2015) and is about two-thirds of the net consumption rate of NO${}_{\mathrm{3}}^{-}+{\mathrm{NO}}_{\mathrm{2}}^{-}$ during the anoxic incubation. That the majority of consumed NO${}_{\mathrm{3}}^{-}+{\mathrm{NO}}_{\mathrm{2}}^{-}$ was recovered as NO supports the emerging notion that NO can be the end product of denitrification once limitations on gas diffusion are lifted in soils (Russow et al., 2009; Loick et al., 2016). Applying the derived k_abiotic and s_abiotic in the abiotic incubation to the measured ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentrations under anoxic condition produced a range of f_NO-abiotic from <4 to 68 $\mathrm{ng}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$ (Fig. S4). While this modeled f_NO-abiotic appears to contribute up to 80 % of the measured f_NO-anoxic (Fig. S4), f_NO-anoxic was high and remained stable even without any significant accumulation of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ in the soil (Fig. 2b and c), suggesting that k_abiotic was likely overestimated in the abiotic incubation (see above). Assuming that net biological NO production was maintained at the level of f_NO-anoxic measured during the first sampling event and that s_abiotic was constant and equal to 0.52, a back-of-the-envelope calculation based on the difference in f_NO-anoxic between the first and last sampling events and the ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentration measured at the end of the anoxic incubation indicates that k_abiotic was likely on the order of 0.0027 h⁻¹, or about 7 times lower than the k_abiotic derived in the abiotic incubation. Although qualitative, this calculation suggests a minor contribution of abiotic NO production to the measured f_NO-anoxic (<12 %; Fig. S4).

The large increases in δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and δ¹⁵N-NO values over the anoxic incubation (Fig. 2d and f) are congruent with strong N isotopic fractionations during microbial denitrification (Mariotti et al., 1981; Granger et al., 2008). However, the observed net isotope effect for NO production from ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (i.e., ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$; 49.4 ‰ to 59.5 ‰) is larger than the apparent N isotope effect for ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption (43.3 ‰±0.9 ‰) (Fig. S3). The large magnitude and increasing pattern of ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$, together with the accumulation of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ in the soil, point to complexity beyond single-step isotopic fractionations and highlight the need to carefully examine fractionation mechanisms for all intermediate steps leading to net NO production (i.e., ${\mathrm{NO}}_{\mathrm{3}}^{-}$ to ${\mathrm{NO}}_{\mathrm{2}}^{-}$, ${\mathrm{NO}}_{\mathrm{2}}^{-}$ to NO, and NO to N₂O). Moreover, it is surprising that both δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values decreased over the anoxic incubation (Fig. 2g and h). Interestingly, similar decreasing trends in δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values (e.g., up to 4 ‰ over 25 h) have been reported by Lewicka-Szczebak et al. (2014) for two anoxically incubated agricultural soils amended with a high-δ¹⁸O Chilean ${\mathrm{NO}}_{\mathrm{3}}^{-}$ fertilizer similar to ours (i.e., δ¹⁸O-NO${}_{\mathrm{3}}^{-}=\mathrm{56}$ ‰), although Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ was not reported in this previous study. The decreasing δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values, observed here and by Lewicka-Szczebak et al. (2014), appear to contradict the well-established paradigm that variations in δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values follow a linear trajectory with a slope of 0.5 to 1 during dissimilatory ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction (Granger et al., 2008). Furthermore, as Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ is in theory not altered by microbial denitrification – a mass-dependent fractionation process (Michalski et al., 2004; Yu and Elliott, 2018), the decreasing Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values observed in this study indicate that processes capable of diluting or erasing the Δ¹⁷O signal may occur concurrently with denitrification during the anoxic incubation. Importantly, if this dilution or removal of the Δ¹⁷O signal was accompanied by N isotopic fractionations, there may be cascading effects on the distribution of N isotopes between ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NO}}_{\mathrm{2}}^{-}$, and NO.

The decreasing δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values could be potentially explained by an O isotope equilibration between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and soil H₂O, catalyzed either chemically or biologically via a reversible reaction between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (Granger and Wankel, 2016). However, it has been shown in controlled laboratory experiments that dissimilatory ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction catalyzed by bacterial nitrate reductase (NAR) is irreversible at the enzyme level (Treibergs and Granger, 2017) and that abiotic O isotope exchange between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and H₂O is extremely slow (half-life >10⁹ years at 25 ^∘C and pH 7) and therefore irrelevant under natural soil conditions (Kaneko and Poulson, 2013). Although fungi use a distinct enzyme system for denitrification (Shoun et al., 2012), there is no evidence for enzymatic reversibility of fungal NAR in the literature. Furthermore, by converting ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ simultaneously to N₂ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$, anaerobic ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation (anammox) could dilute the Δ¹⁷O signal by producing ${\mathrm{NO}}_{\mathrm{3}}^{-}$ with Δ¹⁷O=0 (Brunner et al., 2013). However, due to the low indigenous ${\mathrm{NH}}_{\mathrm{4}}^{+}$ concentration, anammox is considered not pertinent during the anoxic incubation. Given the complete recovery of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations and isotopes in the control experiments (Tables S1 and S2), as well as the significantly increased δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values during the anoxic incubation, we excluded ${\mathrm{NO}}_{\mathrm{3}}^{-}$ production from aerobic ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation as a possible explanation for the observed declines in δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values.

Therefore, having ruled out the above possibilities led us to postulate that the decreasing δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values may result from anaerobic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation mediated by NOB in the soil. The enzyme catalyzing ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ in NOB – ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidoreductase (NXR) – is metabolically versatile and has been shown to catalyze ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction under anoxic conditions by operating in reverse (Friedman et al., 1986; Freitag et al., 1987; Bock et al., 1988; Koch et al., 2015). Moreover, during NXR-catalyzed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation, the required O atom originates from H₂O molecules (Reaction R1), so that ${\mathrm{NO}}_{\mathrm{2}}^{-}$ can in theory be oxidized to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ without the presence of O₂ by donating electrons to redox-active intracellular components (Wunderlich et al., 2013) or alternative electron acceptors in niche environments (Babbin et al., 2017).

$$\begin{array}{}\text{(R1)}& {\displaystyle }{\displaystyle }{\mathrm{NO}}_{\mathrm{3}}^{-}+\mathrm{2}{\mathrm{H}}^{+}+\mathrm{2}{\mathrm{e}}^{-}\iff {\mathrm{H}}_{\mathrm{2}}\mathrm{O}+{\mathrm{NO}}_{\mathrm{2}}^{-}\end{array}$$

In a denitrifying environment, anaerobic oxidation of denitrification-produced ${\mathrm{NO}}_{\mathrm{2}}^{-}$ back to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (i.e., ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation) can dilute δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values by incorporating a “new” O atom from H₂O into the reacting ${\mathrm{NO}}_{\mathrm{3}}^{-}$ pool (Reaction R1) (Granger and Wankel, 2016). Under acidic and circumneutral pH conditions, this dilution effect can be further enhanced by chemically and perhaps biologically catalyzed O isotope equilibration between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and H₂O (Casciotti et al., 2007; Buchwald and Casciotti, 2010), which effectively erases the isotopic imprints of denitrification on ${\mathrm{NO}}_{\mathrm{2}}^{-}$ prior to its re-oxidation. The reversibility of NXR and its direct control on O isotopes in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ have been convincingly demonstrated by Wunderlich et al. (2013) using a pure culture of Nitrobacter vulgaris. By incubating N. vulgaris in a ${\mathrm{NO}}_{\mathrm{3}}^{-}$ solution under anoxic conditions, Wunderlich et al. (2013) showed that ${\mathrm{NO}}_{\mathrm{2}}^{-}$ was produced in the solution by N. vulgaris and that N. vulgaris promoted incorporation of amended ¹⁸O-H₂O labels into ${\mathrm{NO}}_{\mathrm{3}}^{-}$ through a re-oxidation of the accumulated ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (Wunderlich et al., 2013).

Importantly, there is mounting evidence from the marine N cycle community that ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation plays a critical role in the N isotope partitioning between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$. At the process scale, ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation co-occurring with dissimilatory ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction can lead to a large δ¹⁵N difference between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ beyond what would be expected to result from ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction alone (Gaye et al., 2013; Dale et al., 2014; Dähnke and Thamdrup, 2016; Peters et al., 2016; Martin and Casciotti, 2017; Buchwald et al., 2018). This large δ¹⁵N difference is thought to arise from a rare, but intrinsic, inverse kinetic isotope effect associated with ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation (e.g., −13 ‰) (Casciotti, 2009). As such, in a net denitrifying environment, ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation functions as an apparent branching pathway along the sequential reduction of ${\mathrm{NO}}_{\mathrm{3}}^{-}$, preferentially re-oxidizing ¹⁵${\mathrm{NO}}_{\mathrm{2}}^{-}$ back to ${\mathrm{NO}}_{\mathrm{3}}^{-}$. At the enzyme scale, the bidirectional NXR enzyme has been proposed to catalyze intracellular coupled ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation (i.e., bidirectional interconversion of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$), facilitating expression of an equilibrium N isotope effect between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (Reaction R2) (Wunderlich et al., 2013; Kemeny et al., 2016).

$$\begin{array}{}\text{(R2)}& {\displaystyle }{\displaystyle }{}^{\mathrm{14}}{\mathrm{NO}}_{\mathrm{2}}^{-}+{}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}^{-}\iff {}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{2}}^{-}+{}^{\mathrm{14}}{\mathrm{NO}}_{\mathrm{3}}^{-}\end{array}$$

Evidence from pure culture studies of anammox bacteria carrying the NXR enzyme (Brunner et al., 2013) and theoretical quantum calculations (Casciotti, 2009) suggest that this N isotope equilibration favors partitioning of ¹⁴N into ${\mathrm{NO}}_{\mathrm{2}}^{-}$ with an equilibrium isotope effect ranging from −50 ‰ to −60 ‰ (negative sign is used to denote that this N isotope equilibration partitions ¹⁴N to the left side of Reaction R2). This NXR-catalyzed ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ interconversion was invoked to explain the extremely low δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ values relative to δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ (up to 90 ‰) in the surface Antarctic Ocean, where aerobic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation is inhibited by low nutrient availability (Kemeny et al., 2016). Hypothetically, if expressed at either the process or the enzyme level, the N isotope effect for ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation could propagate into denitrification-produced NO, giving rise to an increased δ¹⁵N difference between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and NO (${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$).

To test whether ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation can explain the observed declines in δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values and δ¹⁵N distribution between ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NO}}_{\mathrm{2}}^{-}$, and NO, we modified an isotopologue-specific (i.e., ¹⁴N, ¹⁵N, ¹⁶O, ¹⁷O, and ¹⁸O) numerical model previously described by Yu and Elliott (2018) to simulate co-occurring denitrification and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation in two steps. Without a clear identification of the alternative electron acceptors that coupled with anaerobic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation in the studied soil, we followed the reaction scheme proposed by Wunderlich et al. (2013) and Kemeny et al. (2016) (Reaction R1) to parameterize the NXR-catalyzed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation as the backward reaction of a dynamic equilibrium between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (Fig. 6) – that is, the NXR-catalyzed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation (backward reaction) is balanced by an NXR-catalyzed ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction (forward reaction), leading to no net ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation or ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction in the soil. Importantly, this representation is consistent with the observation that both ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ accumulation followed a pseudo-zero-order kinetics over the anoxic incubation (Fig. 2a and b), which implies no net contribution from the ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ interconversion. Given previous findings that the NXR-catalyzed O exchange between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ depends on ${\mathrm{NO}}_{\mathrm{2}}^{-}$ availability (Wunderlich et al., 2013), the backward ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation was assumed to be first order (with respect to ${\mathrm{NO}}_{\mathrm{2}}^{-}$), defined by a first-order rate constant, k_NXR(b). With respect to the O isotope equilibration between H₂O and the reacting ${\mathrm{NO}}_{\mathrm{2}}^{-}$ pool, we considered two extreme-case scenarios: (1) no exchange and (2) complete exchange. In the no-exchange scenario, the imprints of denitrification on δ¹⁸O-${\mathrm{NO}}_{\mathrm{2}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{2}}^{-}$ values are preserved, such that only one H₂O-derived O atom is incorporated into ${\mathrm{NO}}_{\mathrm{3}}^{-}$ with each ${\mathrm{NO}}_{\mathrm{2}}^{-}$ molecule being re-oxidized (Reaction R1). In the complete-exchange scenario, δ¹⁸O and Δ¹⁷O values of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ always reflect those of soil H₂O (δ¹⁸O-${\mathrm{H}}_{\mathrm{2}}\mathrm{O}\approx -\mathrm{10}$ ‰, Δ¹⁷O-H₂O=0 ‰) (Fig. 6), and therefore all three O atoms in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ produced from ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation originate from H₂O. Furthermore, we considered both abiotic NO production and denitrification as the source of NO during the anoxic incubation (Fig. 6). To account for the potential overestimation in k_abiotic(see above), we used a reduced k_abiotic (0.0027 h⁻¹) to model net abiotic NO production from ${\mathrm{NO}}_{\mathrm{2}}^{-}$, while s_abiotic and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}\text{(abiotic)}}$ were fixed at 0.52 ‰ and 19.2 ‰, respectively. With respect to δ¹⁵N of denitrification-produced NO, we assumed that NIR-catalyzed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction to NO and NOR-catalyzed NO reduction to N₂O were each associated with a kinetic N isotope effect (¹⁵η_NIR and ¹⁵η_NOR). The closed-system Rayleigh equation was then used to simulate the coupled NO production and reduction in denitrification at each model time interval (Lewicka-Szczebak et al., 2014). Detailed model derivation and formulation are provided in the Supplement (Sect. S3.1).

Figure 6 Model structure of co-occurring denitrification and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation and associated N isotope effects. Nitrogen transformations driven by denitrifiers and nitrifiers are shown by solid black and red arrows, respectively, and abiotic O exchange between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and H₂O by the solid blue arrow. The dashed blue arrow denotes net NO yield from abiotic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reactions.

With this model of co-occurring denitrification and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation, we first solved for the rates of denitrifier-catalyzed ${\mathrm{NO}}_{\mathrm{3}}^{-}$ (R_NAR), ${\mathrm{NO}}_{\mathrm{2}}^{-}$ (R_NIR), and NO (R_NOR) reductions and k_NXR(b) (four unknowns) using the measured ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentrations, f_NO-anoxic, and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values (four measured variables). This first modeling step was robustly constrained by the measured Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$, which essentially functions as a ¹⁵${\mathrm{NO}}_{\mathrm{3}}^{-}$ tracer (Yu and Elliott, 2018) and is therefore particularly sensitive to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation. In the second modeling step, the measured δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$, δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$, and δ¹⁵N-NO values (three measured variables) were used to optimize the kinetic N isotope effects for NAR-catalyzed ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction (¹⁵η_NAR), ¹⁵η_NIR, ¹⁵η_NOR, and the equilibrium N isotope effect for NXR-catalyzed ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ interconversion (¹⁵η_NXR(eq)) (Reaction R2; Fig. 6) (four unknowns). This modeling system is under-determined (number of measured variables is less than the number of unknowns) and thus cannot be solved uniquely. Thus, instead of definitively solving for the four unknown isotope effects, we explored their best combination to fit the measured δ¹⁵N values of ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NO}}_{\mathrm{2}}^{-}$, and NO. Specifically, to reduce the number of unknowns for model optimization, ¹⁵η_NAR and ¹⁵η_NXR(eq) were treated as known values, and ¹⁵η_NIR and ¹⁵η_NOR were solved by mapping through the entire space of ¹⁵η_NAR and ¹⁵η_NXR(eq) (at a resolution of 1 ‰), defined by their respective widest range of possible values. We used a range of 5 ‰ to 55 ‰ for ¹⁵η_NAR, consistent with a recent compilation based on soil incubations and denitrifier pure cultures (Denk et al., 2017). Given the existing observational and theoretical constraints (Casciotti, 2009; Brunner et al., 2013), a range of −60 ‰ to 0 ‰ was assigned to ¹⁵η_NXR(eq), which is equivalent to the argument that the impact of ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ interconversion on the N isotope distribution between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ can vary from null to a strong partitioning of ¹⁴N to ${\mathrm{NO}}_{\mathrm{2}}^{-}$. We further defined the lower percentile 2.5 of the error-weighted residual sum of squares (RSS) between simulated and measured δ¹⁵N values of ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NO}}_{\mathrm{2}}^{-}$, and NO as the threshold for selection of the best-fit models. Detailed information regarding model optimization can be found in the Supplement (Sect. S3.2).

Table 1 Means and 95 % confidence intervals of modeled denitrification rates and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation rate constants under the no-exchange and complete-exchange scenarios.

Results from the first modeling step are summarized in Table 1, and the best-fit models were plotted in Fig. 2 to compare with the measured data. Because the NXR-catalyzed ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ interconversion was assumed to result in no change in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentrations, R_NAR (0.158 $\mathrm{\mu }\mathrm{g}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$), R_NIR (0.112 $\mathrm{\mu }\mathrm{g}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$), and R_NOR (0.039 $\mathrm{\mu }\mathrm{g}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) can be well described by zero-order kinetics and are not sensitive to model scenarios for O exchange between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and H₂O (Table 1). Moreover, the observed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ accumulation and f_NO-anoxic dynamics can be well reproduced using the modeled denitrification rates and the downward adjustment of k_abiotic (Fig. 2b and c). k_NXR(b) was estimated to be 0.64 and 0.25 h⁻¹ under the no-exchange and complete-exchange scenarios, respectively (Table 1). Under both scenarios, the simulated Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values exhibit a characteristic decreasing trend and are in excellent agreement with measured Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values (Fig. 2h). The larger k_NXR(b) under the no-exchange scenario is expected and can be explained by the faster back reaction (i.e., ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation) required to reproduce the observed dilution of Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$, because only one new O atom is incorporated into ${\mathrm{NO}}_{\mathrm{3}}^{-}$ with each ${\mathrm{NO}}_{\mathrm{2}}^{-}$ molecule being re-oxidized. Although the measured δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values did not provide quantitative constraints for the model optimization, the isotopologue-specific model with the optimized denitrification rates and k_NXR(b) was run forward to test whether the decreasing δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values can also be possibly explained by co-occurring denitrification and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation (details are provided in Sect. S4). The results showed that ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction (acting to increase δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values) and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation (acting to decrease δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values) have counteracting effects on the forward-modeled δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ (Fig. S2) and that the decreasing trend in δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values can be well reproduced under both no-exchange and complete-exchange scenarios with a reasonable assumption on the net O isotope effects for denitrification and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation (Fig. S2; see Sect. S4) (Granger and Wankel, 2016). Therefore, although k_NXR(b) cannot be definitively quantified in this study due to the unknown degree of O exchange between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and H₂O, these simulation results provide confidence in our hypothesis that the observed decreases in δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values were driven by the reversible action of the NXR enzyme. It is important to note that the estimated k_NXR(b) is fairly large even under the complete-exchange scenario. Based on the ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentration measured at the end of the anoxic incubation (6.9 µg N g⁻¹), a k_NXR(b) of 0.25 h⁻¹ would require a ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation rate (1.7 $\mathrm{\mu }\mathrm{g}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) that is 1 order of magnitude higher than the estimated R_NAR and R_NIR. However, the inferred maximum ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation rate under either model scenario (1.7 to 4.4 $\mathrm{\mu }\mathrm{g}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) is still within the reported range for aerobic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation in agricultural soils (e.g., up to 6–7 $\mathrm{\mu }\mathrm{g}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$) (Taylor et al., 2019), which is indicative of high NOB activity even under anoxic conditions (Koch et al., 2015). It is also noteworthy that Δ¹⁷O analysis of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ can in theory provide quantitative constraint on the degree of O isotope exchange between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and H₂O during the anoxic incubation, as has been previously demonstrated by Δ¹⁷O analysis of N₂O to determine O exchange between N₂O and H₂O during denitrification (Lewicka-Szczebak et al., 2016). However, in this study, robust Δ¹⁷O-${\mathrm{NO}}_{\mathrm{2}}^{-}$ analysis was confounded by the low ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentrations as well as the fact that ${\mathrm{NO}}_{\mathrm{2}}^{-}$ can undergo O exchange with H₂O during sample processing and storage (Casciotti et al., 2007). Future development in soil Δ¹⁷O-${\mathrm{NO}}_{\mathrm{2}}^{-}$ analysis and calibration will benefit the use of Δ¹⁷O to disentangle ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reaction complexity in soil environments.

Figure 7 Contour maps showing variations in error-weighted residual sum of squares (RSS) between simulated and measured δ¹⁵N values, modeled ¹⁵η_NIR, and modeled ¹⁵η_NOR as a function of prescribed ¹⁵η_NAR and ¹⁵η_NXR under the no-exchange (a, c, e) and complete-exchange (b, d, f) model scenarios. Bold contour lines encompass the best-fit models defined by the lower percentile 2.5 of the error-weighted RSS.

Figure 8 Frequency distributions of the best-fit ¹⁵η_NAR (a), ¹⁵η_NXR(eq) (b), ¹⁵η_NIR (c), and ¹⁵η_NOR (d) under the no-exchange (red) and complete-exchange (blue) model scenarios. Dashed vertical lines denote the RSS-weighted mean ¹⁵η values from the best-fit models under the two model scenarios.

Based on the modeled denitrification rates and k_NXR(b), the best-fit ¹⁵η_NXR(b) was confined to a narrow range from −40 ‰ to −35 ‰ (Fig. 7a and b) and was not sensitive to model scenarios for O equilibration between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and H₂O (Fig. 8b). While the best-fit ¹⁵η_NAR and ¹⁵η_NXR(b) were positively correlated, especially under the complete-exchange scenario (Fig. 7a and b), the best-fit ¹⁵η_NAR spanned a wide range (5 ‰ to 45 ‰) and was significantly lower under the no-exchange scenario (RSS-weighted mean: 19 ‰) relative to the complete-exchange scenario (RSS-weighted mean: 30 ‰) (Fig. 8a). On the other hand, the best-fit ¹⁵η_NIR (15 ‰ to 22 ‰) and ¹⁵η_NOR (−8 ‰ to 2 ‰) did not vary substantially and were similar between the two model scenarios (Figs. 7c–d and 8c–d). Under both model scenarios, the measured δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$, δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$, and δ¹⁵N-NO values can be well simulated using the RSS-weighted mean ¹⁵η values from the best-fit models (Fig. 2d to f). Specifically, the modeled difference between δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ values increased from about 29 ‰ at the beginning of the incubation to about 38 ‰ at the end of the incubation (Fig. 2d and e), whereas a constant δ¹⁵N offset of about 20 ‰ was revealed between the modeled δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ and δ¹⁵N-NO values (Fig. 2e and f). Therefore, the modeled ¹⁵η values and δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ dynamics reveal important new information for understanding the increasing ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ over the anoxic incubation. During the early phase of the incubation, the N isotope partitioning between ${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{NO}}_{\mathrm{2}}^{-}$, and NO was mainly controlled by denitrification and its associated isotope effects (i.e., ¹⁵η_NAR, ¹⁵η_NIR, and ¹⁵η_NOR). With the increasing accumulation of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ in the soil, the dominant control on the δ¹⁵N distribution shifted to the N isotope exchange between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$, so that the difference between the δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and δ¹⁵N-${\mathrm{NO}}_{\mathrm{2}}^{-}$ values was primarily determined by ¹⁵η_NXR(eq) (−40 ‰ to −35 ‰). The revealed positive correlation between the best-fit ¹⁵η_NAR and ¹⁵η_NXR(b) (Fig. 7a and b) and the significantly lower ¹⁵η_NAR under the no-exchange scenario (Fig. 8a) essentially reflect a trade-off between ¹⁵η_NAR and ¹⁵η_NXR(b) in controlling the δ¹⁵N difference between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ – that is, when the interconversion between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ is fast and the magnitude of ¹⁵η_NXR(eq) is large (i.e., very negative), only a small ¹⁵η_NAR is required to sustain the large δ¹⁵N difference between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ over the course of the anoxic incubation.

The estimated ¹⁵η_NXR(eq) from the best-fit models is higher (i.e., closer to zero) than that derived from theoretical calculations and pure culture studies (−50 ‰ to −60 ‰) (Casciotti, 2009; Brunner et al., 2013). Given the heterogeneous distribution of substrates in soils, the lower absolute magnitude of the best-fit ¹⁵η_NXR(eq) may be due to the partial rate limitation by transport of ${\mathrm{NO}}_{\mathrm{2}}^{-}$∕${\mathrm{NO}}_{\mathrm{3}}^{-}$ to the active site of NXR. As such, the best-fit ¹⁵η_NXR(eq) should provide a conservative estimate of the intrinsic equilibrium isotope effect. Thus, the results from the anoxic incubation underscore the important, yet previously unrecognized, role of the reversible ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ interconversion in controlling the δ¹⁵N dynamics of soil ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and its denitrification products. Substantial re-oxidation of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ under anoxic conditions seems paradoxical but is underpinned by the increasingly recognized high degree of metabolic versatility of NOB, including simultaneous oxidation of an organic substrate and ${\mathrm{NO}}_{\mathrm{2}}^{-}$, as well as parallel use of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and O₂ as electron acceptors (Koch et al., 2015). In the absence of O₂, few electron acceptors exist at common environmental pH that have a higher redox potential than the ${\mathrm{NO}}_{\mathrm{3}}^{-}$∕${\mathrm{NO}}_{\mathrm{2}}^{-}$ pair (Wunderlich et al., 2013; Babbin et al., 2017). It is therefore likely that NOB would gain energy by performing the intracellular coupled oxidation of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and reduction of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ to survive periods of O₂ deprivation. Although anaerobic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation until now has been conclusively shown only in anoxic ocean water columns (Sun et al., 2017; Babbin et al., 2017) and aquatic sediments (Wunderlich et al., 2013), soils host a huge diversity of coexisting NOB (Le Roux et al., 2016) and the physiological flexibility of NOB beyond aerobic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation may contribute to the unexpected higher abundances and activities of NOB relative to AOB and AOA in agricultural soils (Høberg et al., 1996; Ke et al., 2013). Using the modified isotopologue-specific model, we demonstrate the possibility that large ¹⁵η_NAR can be an artifact of an isotopic equilibrium between ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$, occurring in connection with the bifunctional NXR enzyme. Therefore, effective expressions of ¹⁵η_NXR(eq) in concurrence with ¹⁵η_NAR may explain why ¹⁵η_NAR values estimated by some anoxic soil incubations (e.g., 25 ‰ to 65 ‰) are far larger than those reported by studies of denitrifying and ${\mathrm{NO}}_{\mathrm{3}}^{-}$-reducing bacterial cultures (e.g., 5 ‰ to 30 ‰) (Denk et al., 2017) and why the slope of δ¹⁸O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ vs. δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values during denitrification in many field studies was not constant and rarely close to unity as observed in pure denitrifying cultures (Granger and Wankely, 2016). Indeed, evidence for a reversible enzymatic pathway linking ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ under anoxic conditions has already been documented in previous soil studies (e.g., Kool et al., 2011; Lewicka-Szcebak et al., 2014), implying its wide occurrence in soils. More studies using soils from a broad range of environments are needed to pinpoint the exact mechanisms by which ${\mathrm{NO}}_{\mathrm{2}}^{-}$ can be anaerobically oxidized in soils. To that end, Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ can be used as a powerful benchmark for disentangling co-occurring ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction and ${\mathrm{NO}}_{\mathrm{2}}^{-}$ re-oxidation.

The best-fit ¹⁵η_NIR (15 ‰ to 22 ‰) falls within the range derived in anoxic soil incubations (11 ‰ to 33 ‰) (Mariotti et al., 1982) and is consistent with results based on denitrifying bacteria carrying copper-containing NIR (22 ‰) (Martin and Casciotti, 2016). Under both model scenarios, the best-fit ¹⁵η_NOR (−8 ‰ to 2 ‰) is relatively small and more normal (i.e., ¹⁵η value closer to zero) than the bulk N isotope effect for NO reduction to N₂O catalyzed by purified fungal NOR (P450nor) (−14 ‰) (Yang et al., 2014). During P450nor-catalyzed NO reduction, two NO molecules are sequentially bonded to the Fe active site of P450nor, and the observed inverse isotope effect was proposed to arise from a reversible bonding of the first NO molecule (Yang et al., 2014). To date, the N isotope effect for NO reduction catalyzed by bacterial NORs has not yet been quantified. Unlike P450nor, which contains only a single heme Fe at the active site, the active site of bacterial NORs has two Fe atoms (i.e., binuclear center). Therefore, three classes of mechanisms have been proposed for the two-electron reduction of NO by bacterial NORs, including sequential bonding of two NO molecules to either Fe catalytic center and simultaneous bonding of two NO molecules to both Fe centers (Kuypers et al., 2018; Lehnert et al., 2018). Although the precise catalytic mechanism remains uncertain, site-specific measurements of N isotopes in N₂O (i.e., N₂O isotopomers) produced from denitrifying bacteria indicate a similar magnitude for isotopic fractionations during the reduction of two NO molecules, in support of the simultaneous binding theory (Sutka et al., 2006; Yamazaki et al., 2014). Thus, if the bulk N isotope effect for bacterial NO reduction is higher than that for fungal NO reduction, the best-fit ¹⁵η_NOR may reflect a mixed contribution of bacteria and fungi to NO consumption during the anoxic incubation. Alternatively, the model-inferred ¹⁵η_NOR might reflect a balance between enzymatic and diffusion isotope effects, as has been previously demonstrated for N₂O reduction in soil denitrification (Lewicka-Szczebak et al., 2014). Because diffusion would be expected to have a small and normal kinetic isotope effect, if ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction was limited by NO diffusion out of soil denitrifying sites, the estimated ¹⁵η_NOR would be shifted toward the isotope effect for NO diffusion. Diffusion might be particularly important in this study due to the flow-through condition during the anoxic incubation and the low solubility of NO, both of which favor gas diffusion while preventing re-entry of escaped NO to denitrifying cells. Thus, the small ¹⁵η_NOR inferred from the best-fit models is likely a combination of diverse NO reduction pathways in this agricultural soil, as well as limited expression of enzymatic isotope effects imposed by NO diffusion. Regardless, the empirical finding of this study suggests that due to the small ¹⁵η_NOR, the bulk δ¹⁵N values of denitrification-produced N₂O should not be significantly altered by accumulation and diffusion of NO during denitrification.

4.3 NO source contribution and N isotope effects for NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation under oxic and hypoxic conditions

The coupled decrease in ${\mathrm{NH}}_{\mathrm{4}}^{+}$ concentrations and increase in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations (Fig. 3a and b) indicate active nitrification in both oxic and hypoxic incubations. Moreover, the two oxidation steps of nitrification were tightly coupled, resulting in no accumulation of ${\mathrm{NO}}_{\mathrm{2}}^{-}$ in the soil. Because ${\mathrm{NO}}_{\mathrm{3}}^{-}$ produced from nitrification has a zero Δ¹⁷O value, the active nitrification was also reflected in the progressive dilution of Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ under both oxic and hypoxic conditions (Yu and Elliott, 2018). Based on the measured concentrations and isotopic composition of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$, the isotopologue-specific model previously developed by Yu and Elliott (2018) was used to estimate the rates and net N isotope effects of net mineralization ($R_{\text{Org}\mathrm{N}/{\mathrm{NH}}_{\mathrm{4}}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{\text{Org}\mathrm{N}/{\mathrm{NH}}_{\mathrm{4}}}$), gross ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ ($R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$), and gross ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption ($R_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$) during the oxic and hypoxic incubations. As has been discussed above, this numerical model relies on the conservative nature of Δ¹⁷O-${\mathrm{NO}}_{\mathrm{3}}^{-}$ and its powerful application in tracing co-occurring nitrification and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption (consisting of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ immobilization and denitrification in this case) (Yu and Elliott, 2018). Detailed model derivation, formulation, and optimization have been documented in Yu and Elliott (2018) and are also briefly summarized in Sect. S5. The modeling results based on the low-δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatment in the oxic incubation were reported by Yu and Elliott (2018). Here, we used data from all three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments to more robustly constrain the N transformation rates and net N isotope effects for each incubation experiment (i.e., oxic and hypoxic).

Table 2 Means and 95 % confidence intervals of modeled gross N transformation rates, NO yields, and net N isotope effects in the oxic and hypoxic incubations.

The modeling results are summarized in Table 2. Excellent agreement was obtained between the observed and simulated concentrations and isotopic composition of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ for both oxic and hypoxic incubations (Fig. 3). $R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ can be well described by zero-order kinetics and was estimated to be 0.46 and 0.11 $\mathrm{\mu }\mathrm{g}\mathrm{N}{\mathrm{g}}^{-\mathrm{1}}{\mathrm{h}}^{-\mathrm{1}}$ for the oxic and hypoxic incubations, respectively (Table 2). The lower $R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ in the hypoxic incubation indicates that nitrification was limited by low O₂ availability. Under both oxic and hypoxic conditions, oxidation of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ was associated with a large ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ (23 ‰ to 28 ‰; Table 2), consistent with the N isotope effects for NH₃ oxidation in pure cultures of AOB and AOA (e.g., 13 ‰ to 41 ‰) (Mariotti et al., 1981; Casciotti et al., 2003; Santoro and Casciotti, 2011). On the other hand, the estimated $R_{\text{Org}\mathrm{N}/{\mathrm{NH}}_{\mathrm{4}}}$ and $R_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$ were low and not significantly different between the two incubation experiments (Table 2). Nevertheless, while $R_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$ was only 16 % of $R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ in the oxic incubation, $R_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$ accounted for a much larger fraction (63 %) of $R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ in the hypoxic incubation, mainly due to the reduced $R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ under the low-O₂ condition. Due to the low magnitude of $R_{\text{Org}\mathrm{N}/{\mathrm{NH}}_{\mathrm{4}}}$ and $R_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$, the estimated ${}^{\mathrm{15}}{\mathit{\eta }}_{\text{Org}\mathrm{N}/{\mathrm{NH}}_{\mathrm{4}}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$ are associated with large errors and not significantly different from zero (Table 2).

By using three isotopically different ${\mathrm{NH}}_{\mathrm{4}}^{+}$ fertilizers in parallel treatments, we are able to quantify the fractional contribution of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation to the measured net NO production ($f_{{\mathrm{NH}}_{\mathrm{4}}}$). Specifically, if NO was exclusively produced from soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$, we would expect to see a constant δ¹⁵N difference between ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and NO across the three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments. In fact, the observed δ¹⁵N differences were not constant, and the slope of δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ vs. δ¹⁵N-NO was significantly lower than unity under both oxic and hypoxic conditions (Fig. 4). This suggests that sources other than ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation contributed to the observed net NO production. Although NO can be produced by numerous microbial and abiotic processes (Medinets et al., 2015), we argue that the other major NO source is mostly likely related to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption. This is based on the observation of high ${\mathrm{NO}}_{\mathrm{3}}^{-}$ concentrations in both oxic and hypoxic incubations, as well as the estimated low $R_{\text{Org}\mathrm{N}/{\mathrm{NH}}_{\mathrm{4}}}$ (Table 2), which indicates a low availability of labile organic N – another potential substrate for NO production (Stange et al., 2013) – in this agricultural soil. Therefore, based on the assumption that ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption were the two primary NO sources during the oxic and hypoxic incubations, a two-source isotope mixing model was used to relate the measured δ¹⁵N-NO values to the concurrently measured δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ and δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values:

$$\begin{array}{ll}{\displaystyle }{\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\text{-NO}& {\displaystyle }=f_{{\mathrm{NH}}_{\mathrm{4}}}\times \left({\mathit{\delta }}^{\mathrm{15}}\text{N-}{\mathrm{NH}}_{\mathrm{4}}^{+}{-}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}\right)\\ \text{(5)}& {\displaystyle }& {\displaystyle }+(\mathrm{1}-f_{{\mathrm{NH}}_{\mathrm{4}}})\times \left({\mathit{\delta }}^{\mathrm{15}}\text{N-}{\mathrm{NO}}_{\mathrm{3}}^{-}{-}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}\right),\end{array}$$

where ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ are the net isotope effects for NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption, respectively. Rearranging Eq. (5) yields Eq. (6):

$$\begin{array}{ll}{\displaystyle }{\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\text{-NO}& {\displaystyle }=f_{{\mathrm{NH}}_{\mathrm{4}}}\times {\mathit{\delta }}^{\mathrm{15}}{\text{N-NH}}_{\mathrm{4}}^{+}+(\mathrm{1}-f_{{\mathrm{NH}}_{\mathrm{4}}})\times {\mathit{\delta }}^{\mathrm{15}}\text{N-}{\mathrm{NO}}_{\mathrm{3}}^{-}\\ {\displaystyle }& {\displaystyle }-[f_{{\mathrm{NH}}_{\mathrm{4}}}{\times }^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}+(\mathrm{1}-f_{{\mathrm{NH}}_{\mathrm{4}}})\\ \text{(6)}& {\displaystyle }& {\displaystyle }{\times }^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}],{}^{\mathrm{15}}{\mathit{\eta }}_{\text{comb}}& {\displaystyle }=f_{{\mathrm{NH}}_{\mathrm{4}}}{\times }^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}\\ \text{(7)}& {\displaystyle }& {\displaystyle }+(\mathrm{1}-f_{{\mathrm{NH}}_{\mathrm{4}}}){\times }^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}},\end{array}$$

$$\begin{array}{ll}{\displaystyle }{\mathit{\delta }}^{\mathrm{15}}\mathrm{N}\text{-NO}& {\displaystyle }=f_{{\mathrm{NH}}_{\mathrm{4}}}\times {\mathit{\delta }}^{\mathrm{15}}{\text{N-NH}}_{\mathrm{4}}^{+}+(\mathrm{1}-f_{{\mathrm{NH}}_{\mathrm{4}}})\times {\mathit{\delta }}^{\mathrm{15}}\text{N-}{\mathrm{NO}}_{\mathrm{3}}^{-}\\ \text{(8)}& {\displaystyle }& {\displaystyle }-{}^{\mathrm{15}}{\mathit{\eta }}_{\text{comb}}.\end{array}$$

Equation (6) essentially dictates that the δ¹⁵N-NO values can be modeled from the δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ and δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values using a hypothetical isotope effect for NO production from the combined soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ pool (¹⁵η_comb; the last term in Eq. 6) that is a mixing of ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ controlled by $f_{{\mathrm{NH}}_{\mathrm{4}}}$ (Eq. 7). Thus, assuming $f_{{\mathrm{NH}}_{\mathrm{4}}}$ and ¹⁵η_comb were constant in each incubation experiment, $f_{{\mathrm{NH}}_{\mathrm{4}}}$ and ¹⁵η_comb can be solved using the measured δ¹⁵N-NO, δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$, and δ¹⁵N-${\mathrm{NO}}_{\mathrm{3}}^{-}$ values from all three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments (Eq. 8). $f_{{\mathrm{NH}}_{\mathrm{4}}}$ was estimated to be 0.72 under the oxic incubation (Table 2), indicating that 72 % of the measured net NO production was sourced from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation, with the remainder being ascribed to ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption. Under the hypoxic condition, the share of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation decreased to 58 % (Table 2). ¹⁵η_comb was estimated to be 56 ‰ under the oxic condition and 51 ‰ under the hypoxic condition (Table 2). Combining the δ¹⁵N-based NO source partitioning with the estimated $R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ and $R_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$, we further estimated NO yield in ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption, respectively, and where the results are illustrated according to the classic “hole-in-the-pipe” (HIP) concept (Fig. 9) (Davidson and Verchot, 2000). NO yield was 1.3 % in ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and 3.2 % in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption in the oxic incubation (Fig. 9; Table 2). Under the hypoxic condition, NO yield was increased to 5.2 % in ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and 6.1 % in ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption (Fig. 9; Table 2).

Figure 9 Hole-in-the-pipe illustration of NO production from gross nitrification and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption under oxic and hypoxic conditions. “OrgN” denotes organic nitrogen.

Most previous laboratory and field studies suggest that soil NO emissions are predominately driven by nitrification, whereas NO produced from denitrification is further reduced to N₂O before it escapes to the soil surface (Kester et al., 1997; Skiba et al., 1997). The minor role of denitrification is largely deduced from the supposition that denitrification is activated only under wet soil conditions (Davidson and Verchot, 2000). However, based on our δ¹⁵N-based NO source partitioning, about 30 % of the net NO production was contributed by ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption under oxic condition, highlighting the potential importance of denitrification in driving soil NO emissions under conditions not typically conducive to its occurrence. There is growing evidence that extensive anoxic microsites can develop in otherwise well-aerated soils due to micro-scale variability of O₂ demand and soil texture-dependent gas diffusion limitations (Keiluweit et al., 2018). Although we would not predict high rates of heterotrophic respiration in this agricultural soil with low organic carbon, it is possible that rapid O₂ consumption by nitrification may outpace O₂ supply through diffusion in soil microsites, fostering development of anoxic niches in close association with nitrification hot spots (Kremen et al., 2005). Based on ¹⁵N labeling and direct ¹⁵NO measurements using a gas chromatograph–quadrupole mass spectrometer, Russow et al. (2009) demonstrated that nitrification contributed about 70 % of net NO production in a well-aerated, ${\mathrm{NH}}_{\mathrm{4}}^{+}$-fertilized silt loam, in strong agreement with our results based on natural-abundance δ¹⁵N measurements. An even lower contribution to NO production, e.g., 26 % to 44 %, has been reported for nitrification in organic, N-rich forest soils incubated under oxic conditions (Stange et al., 2013). The persistence of denitrifying microsites in the studied soil is further corroborated by the nearly doubled net NO production from ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption in the hypoxic incubation (Fig. 9). Importantly, the actual NO yield in denitrification might be much higher than those estimated for gross ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption during the oxic and hypoxic incubations (i.e., 3.2 % and 6.1 %), as denitrification occurring in anoxic niches might only comprise a small fraction of the estimated $R_{{\mathrm{NO}}_{\mathrm{3}}\text{comp}}$.

Figure 10 The three enzymatic pathways for NO production during NH₃ oxidation to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ by AOB: the NH₂OH obligatory intermediate pathway is indicated by blue circle 1, the NH₂OH∕NO obligatory intermediate pathway is indicated by blue circle 2, and the nitrifier-denitrification pathway is indicated by blue circle 3. Square brackets enclose proposed enzyme-bound intermediates [HNO-Fe] and [NO-Fe] of the NH₂OH obligatory intermediate pathway. The role of AOB-encoded nitrite reductase (NIR) in catalyzing NO oxidation to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ in the NH₂OH∕NO obligatory intermediate pathway is hypothetical.

Interestingly, while $R_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ was significantly lower in the hypoxic incubation, the net NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation was similar between the two incubation experiments, indicating a higher NO yield in nitrification when O₂ availability became limited (Fig. 9). However, mechanisms underlying the differential NO yield in nitrification are difficult to elucidate owing to the high complexity of biochemical pathways of NO production by AOB and AOA. In AOB, the prevailing view of NH₃ oxidation is that it occurs via a two-step enzymatic process, involving hydroxylamine (NH₂OH) as an obligatory intermediate (Fig. 10). The first step is catalyzed by NH₃ monooxygenase (AMO), which uses copper and O₂ to hydroxylate NH₃ to NH₂OH. Next, a multiheme enzyme, NH₂OH oxidoreductase (HAO), catalyzes the four-electron oxidation of NH₂OH to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ via enzyme-bound nitroxyl ([HNO-Fe]) and nitrosyl ([NO-Fe]) intermediates (Lehnert et al., 2018) (Fig. 10). Under this NH₂OH obligate intermediate model, NO emission was proposed to result from dissociation of NO from the enzyme-bound nitrosyl complex under high-NH₃ and/or low-O₂ conditions (Fig. 10) (Hooper et al., 2004; Beeckman et al., 2018). However, there is recent strong evidence that HAO generally catalyzes the three-electron oxidation of NH₂OH to NO under both aerobic and anaerobic conditions; the HAO-produced NO is further oxidized to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ by an unknown enzyme (Caranto and Lancaster, 2017). In this way, NO would not be a byproduct of incomplete NH₂OH oxidation but rather required as an obligatory intermediate for ${\mathrm{NO}}_{\mathrm{2}}^{-}$ production (Fig. 10). It was further proposed that AOB-encoded copper-containing NIR may catalyze the final one-electron oxidation of NO to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ by operating in reverse (Lancaster et al., 2018). Under this NH₂OH∕NO obligate intermediate model, high intracellular NO concentrations arise when the rate of NO production outpaces the rate of its oxidation to ${\mathrm{NO}}_{\mathrm{2}}^{-}$, leading to NO leakage from cells. Consequently, under O₂ stress, decreases in the rate of NO oxidation to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ might be expected, and this may explain the observed increase in nitrification NO yield in the hypoxic incubation. Additionally, some AOB strains can produce NO in a process termed nitrifier denitrification, in which NO is produced through NIR-catalyzed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction and can be further reduced to N₂O by AOB-encoded NOR (Wrage-Mönning et al., 2018) (Fig. 10). Compared to AOB, the NH₃ oxidation pathway in AOA remains unclear (Beeckman et al., 2018). The current model is that NH₃ is first oxidized by an archaeal AMO to NH₂OH and subsequently converted to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ by an unknown HAO counterpart (Kozlowski et al., 2016). NO seems to be mandatory for archaeal NH₂OH oxidation and has been proposed to act as a co-substrate for the ${\mathrm{NO}}_{\mathrm{2}}^{-}$ production (Kozlowski et al., 2016). Consequently, NO is usually produced and immediately consumed with tighter control in AOA than in AOB (Kozlowski et al., 2016).

Figure 11 Relative magnitude of net N isotope effects for NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation (${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$) and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption (${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$) in the oxic and hypoxic incubations.

To shed further light on the inner workings of net NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$, we turn to constraining ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$. Specifically, the inherent linkage between ¹⁵η_comb, ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$, and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ (Eq. 7) allows one to probe the relative magnitude of ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ using the determined ¹⁵η_comb and $f_{{\mathrm{NH}}_{\mathrm{4}}}$. Given that ${\mathrm{NO}}_{\mathrm{2}}^{-}$ was absent in the soil and that NO reduction in denitrification was likely associated with a small isotope effect (i.e., ¹⁵η_NOR; see above), ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ in the oxic and hypoxic incubations should mainly reflect ¹⁵η_NAR. Thus, by assigning the entire possible range of the best-fit ¹⁵η_NAR derived in the anoxic incubation (5 ‰ to 45 ‰; Fig. 7a) to ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$, ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ was estimated to range from 60 ‰ to 76 ‰ in the oxic incubation and from 55 ‰ to 84 ‰ in the hypoxic incubation (Fig. 11). If we take one step further by assuming that both ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ were identical between the oxic and hypoxic incubations, then ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ could be uniquely determined to be 30 ‰ and 66 ‰, respectively (Fig. 11; Table 2). Thus, the relative magnitude of ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ provides insights into the differential relationship between δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ and δ¹⁵N-NO across the three δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatments in the oxic and hypoxic incubations (Fig. 4). In the oxic incubation, if we assume that ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}=\mathrm{66}$ ‰ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}=\mathrm{30}$ ‰, the δ¹⁵N of NO produced from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation under the low δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatment (about −60 ‰) would be much lower than the δ¹⁵N of NO from ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption (about −38 ‰). However, under the high-δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ treatment, the δ¹⁵N of ${\mathrm{NH}}_{\mathrm{4}}^{+}$-produced NO would increase to about −14 ‰ and be higher than δ¹⁵N values of ${\mathrm{NO}}_{\mathrm{3}}^{-}$-produced NO (about −26 ‰). Consequently, the production of NO from ${\mathrm{NO}}_{\mathrm{3}}^{-}$ consumption would dilute the δ¹⁵N of total net NO production, pulling it to fall below the 1:1 line between the δ¹⁵N-${\mathrm{NH}}_{\mathrm{4}}^{+}$ and δ¹⁵N-NO values in Fig. 4. This dilution effect was more pronounced in the hypoxic incubation due to the lower $f_{{\mathrm{NH}}_{\mathrm{4}}}$ (i.e., higher contribution of ${\mathrm{NO}}_{\mathrm{3}}^{-}$-produced NO) (Fig. 4).

Figure 12 (a) Comparison of net isotope effects for NO production estimated in this study to net isotope effects for N₂O production reported in the literature. (b) Comparison of in situ δ¹⁵N of NO_x emission from a manure-fertilized soil (reported by Miller et al., 2018) to nitrification and denitrification δ¹⁵N-NO end-members derived using the estimated net isotope effects for NO production in the oxic and hypoxic incubations.

Therefore, under either oxic or hypoxic condition, the net NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation proceeded with a large ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$. As NH₃ oxidation to NH₂OH was likely the rate-limiting step for the entire nitrification process, a fraction of the inferred large ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ can be accounted for by the isotope effect for NH₃ oxidation to NH₂OH, which should be similar to the estimated ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/{\mathrm{NO}}_{\mathrm{3}}}$ (e.g., 23 ‰ to 28 ‰). The residual isotope effect, on the order of 40 ‰, must therefore stem from additional bond forming/breaking during net NO production in NH₃ oxidation. This additional N isotope effect could be explained by ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction catalyzed by AOB-encoded NIR if NO was dominantly produced through the nitrifier-denitrification pathway (Fig. 10). However, provided that the two oxidation steps of nitrification were tightly coupled under both oxic and hypoxic conditions, it is unlikely that ${\mathrm{NO}}_{\mathrm{2}}^{-}$ would accumulate to high enough intracellular concentrations to trigger nitrifier denitrification (Wrage-Mönning et al., 2018). Similarly, we would not expect any substantial isotope fractionations to result from accumulation of intracellular NH₂OH or enzyme-bound intermediate species (e.g., [HNO-Fe] and [NO-Fe]). Thus, we are left with either a large and normal isotope effect for NO dissociation from its enzyme-bound precursor if NO production was mainly routed through the NH₂OH obligate intermediate pathway or an inverse isotope effect associated with NO oxidation if NO itself was an obligatory intermediate required for ${\mathrm{NO}}_{\mathrm{2}}^{-}$ production (Fig. 10). With respect to the first possibility, if NO dissociation from the Fe active site of HAO is mainly controlled by an equilibrium reaction between NO and enzyme-bound nitrosyl species, the forward and backward reactions may occur with distinctively different isotope effects, giving rise to an equilibrium isotope effect that favors partitioning of ¹⁴N to the dissociated NO. However, expression of this equilibrium isotope effect would be largely suppressed by limited isotope exchange between the two N pools due to the presumably transient presence of nitrosyl intermediate. Therefore, a partial expression of a large equilibrium isotope effect (e.g., >40 ‰) would be required to explain the residual N isotopic fractionation during NO production in NH₃ oxidation. Alternatively, in regards to the second possibility, if we assume that the enzyme-catalyzed oxidation of NO to ${\mathrm{NO}}_{\mathrm{2}}^{-}$ proceeds via an enzyme-bound transition state and that the transition state contains the newly formed N-O bond, an inverse isotope effect may result from more strongly bonded N atom in the transition state, for which there is precedent in the literature (i.e., ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation to ${\mathrm{NO}}_{\mathrm{3}}^{-}$; see above) (Casciotti, 2009). Moreover, the small NO yield observed in the oxic and hypoxic incubations would indicate a large consumption of NO (i.e., 95 % to 99 %). With this high level of NO consumption, an inverse isotope effect on the order of −13 ‰ to −9 ‰ would be sufficient to account for the residual isotope effect for net NO production from ${\mathrm{NH}}_{\mathrm{4}}^{+}$. This inferred isotope effect is of similar magnitude to that reported for NXR-catalyzed ${\mathrm{NO}}_{\mathrm{2}}^{-}$ oxidation (i.e., −13 ‰) (Casciotti, 2009). However, to unambiguously determine the mechanisms giving rise to the large ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$, further biochemical analyses will be needed to clarify the enzymatic pathways responsible for NO production by AOB and AOA under relevant soil conditions. Nonetheless, the results presented here provide evidence that production of NO with low δ¹⁵N values may be a characteristic feature of nitrification in ${\mathrm{NH}}_{\mathrm{4}}^{+}$-fertilized agricultural soils under both oxic and hypoxic conditions.

5 Implications for NO emission from agricultural soils

In this study, the net production rates and δ¹⁵N values of NO were measured under a range of controlled laboratory conditions. The results provide insights into how stable N and O isotopes can be effectively used to understand the reaction mechanisms by which NO is produced and consumed in soils. While nitrification is the commonly cited source for NO emissions from agricultural soils, the measured net NO production rates in this study highlight the great potential of abiotic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction and denitrification in driving NO production and release from agricultural soils and thus should not be overlooked when attributing field soil NO emissions. Indeed, because NO is a direct product or free intermediate in these processes, abiotic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction and denitrification may inherently have a larger NO yield – that is, a bigger “hole” for NO leaking in the HIP model (Davidson and Verchot, 2000). We conclude that the isotope-based measurement and modeling framework established in this work is a powerful tool to bridge NO production with gross N transformation processes in agricultural soils, thereby providing a quantitative way to parameterize the HIP model for modeling soil NO emissions under dynamic environmental conditions (e.g., varying temperature and soil moisture content).

The differences in the net isotope effects for NO production from abiotic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction, denitrification, and nitrification revealed in this study (Fig. 12a) suggest that δ¹⁵N-NO is a useful tracer for informing NO production pathways in agricultural soils. Specifically, the relatively small magnitude of ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{2}}/\mathrm{NO}\text{(abiotic)}}$ indicates that δ¹⁵N-NO is particularly useful in probing the relative importance of NO production from abiotic vs. microbial reactions, lending support to our previous finding based on rewetting of a dry forest soil that high δ¹⁵N values of rewetting-triggered NO pulses were mainly contributed by chemical ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction (Yu and Elliott, 2017). Moreover, the large ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ revealed in the oxic and hypoxic incubations provides an empirical basis for discerning the relative role of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction in driving soil NO production and emissions. Interestingly, comparing the measured net isotope effects for NO production from abiotic ${\mathrm{NO}}_{\mathrm{2}}^{-}$ reduction, denitrification, and nitrification with those previously quantified for N₂O production in soil incubations and pure cultures (Denk et al., 2017, and references therein; Jones et al., 2015; Wei et al., 2019), a similar pattern is evident across these three common production pathways for NO and N₂O (Fig. 12a). This similarity reflects the intimate connection between NO and N₂O turnover within each reaction pathway and provides strong evidence that simultaneous δ¹⁵N-NO and δ¹⁵N-N₂O measurements can potentially yield unprecedented insights into the sources and processes controlling NO and N₂O emissions from agricultural soils. However, on the other hand, the demonstrated reaction reversibility between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ under anoxic conditions is a new complication that needs to be considered when using δ¹⁵N to examine soil NO and N₂O emissions. As ${\mathrm{NO}}_{\mathrm{2}}^{-}$ is often accumulated in agricultural soils following fertilizer application (Venterea et al., 2020), expression of the equilibrium isotope effect between ${\mathrm{NO}}_{\mathrm{2}}^{-}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ in redox-dynamic surface soils may render δ¹⁵N-NO and δ¹⁵N-N₂O less useful in tracing NO and N₂O sources. Given that high soil ${\mathrm{NO}}_{\mathrm{2}}^{-}$ concentrations can trigger emission pulses of NO and N₂O (Venterea et al., 2020), ${\mathrm{NO}}_{\mathrm{2}}^{-}$ accumulation should be taken as a critical sign for careful evaluation of the reaction complexity underlying δ¹⁵N distributions among the denitrification products.

To further assess the potential utility of δ¹⁵N measurements in source partitioning NO emissions from agricultural soils, we applied the estimated N isotope effects to the in situ δ¹⁵N-NO_x measurements reported by Miller et al. (2018). Importantly, the soil used in this study was collected from the same farm where Miller et al. (2018) conducted their field measurements (e.g., the USDA-managed corn–soybean field in central Pennsylvania, USA). Hence, the derived isotope effects may be particularly relevant to their reported δ¹⁵N-NO_x values due to similar soil microbial community structures. Because ${\mathrm{NO}}_{\mathrm{2}}^{-}$ accumulation was not reported by Miller et al. (2018), we consider nitrification and denitrification to be the primary sources for the observed NO (and, to a much lesser extent, NO₂) emissions. Therefore, the ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NH}}_{\mathrm{4}}/\mathrm{NO}}$ and ${}^{\mathrm{15}}{\mathit{\eta }}_{{\mathrm{NO}}_{\mathrm{3}}/\mathrm{NO}}$ values derived in the oxic and hypoxic incubations (i.e., 66 ‰ and 30 ‰, respectively) were used in combination with the δ¹⁵N values of soil ${\mathrm{NH}}_{\mathrm{4}}^{+}$ and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reported in Miller et al. (2018) to calculate the δ¹⁵N end-members for NO produced from ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction. As shown in Fig. 12b, comparing the in situ δ¹⁵N-NO_x measurements with the estimated isotopic end-members provides a compelling picture of soil NO dynamics following manure application. Notably, the initial low δ¹⁵N-NO_x values reported by Miller et al. (2018) might indicate a mixed contribution of ${\mathrm{NH}}_{\mathrm{4}}^{+}$ oxidation and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ reduction to soil NO_x emissions (Fig. 12b). Nevertheless, the increase in δ¹⁵N-NO_x values measured 4 to 11 d after manure application may reflect a shift in the dominant NO production pathway to denitrification, in line with the increasing accumulation of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ supplied by nitrification in the soil (Miller et al., 2018). Although data-limited, this example provides promising initial evidence for the ability of multi-species δ¹⁵N measurements to provide mechanistic information on soil NO dynamics and its environmental controls. Further experimental constraints on soil δ¹⁵N-NO variations can build on the measurement and modeling framework developed in this study to advance our understanding of soil NO source contributions over a wide range of environmental conditions and soil types.