Improved isotopic model based on 15N tracing and Rayleigh‐type isotope fractionation for simulating differential sources of N2O emissions in a clay grassland soil

Rationale Isotopic signatures of N2O can help distinguish between two sources (fertiliser N or endogenous soil N) of N2O emissions. The contribution of each source to N2O emissions after N‐application is difficult to determine. Here, isotopologue signatures of emitted N2O are used in an improved isotopic model based on Rayleigh‐type equations. Methods The effects of a partial (33% of surface area, treatment 1c) or total (100% of surface area, treatment 3c) dispersal of N and C on gaseous emissions from denitrification were measured in a laboratory incubation system (DENIS) allowing simultaneous measurements of NO, N2O, N2 and CO2 over a 12‐day incubation period. To determine the source of N2O emissions those results were combined with both the isotope ratio mass spectrometry analysis of the isotopocules of emitted N2O and those from the 15N‐tracing technique. Results The spatial dispersal of N and C significantly affected the quantity, but not the timing, of gas fluxes. Cumulative emissions are larger for treatment 3c than treatment 1c. The 15N‐enrichment analysis shows that initially ~70% of the emitted N2O derived from the applied amendment followed by a constant decrease. The decrease in contribution of the fertiliser N‐pool after an initial increase is sooner and larger for treatment 1c. The Rayleigh‐type model applied to N2O isotopocules data (δ15Nbulk‐N2O values) shows poor agreement with the measurements for the original one‐pool model for treatment 1c; the two‐pool models gives better results when using a third‐order polynomial equation. In contrast, in treatment 3c little difference is observed between the two modelling approaches. Conclusions The importance of N2O emissions from different N‐pools in soil for the interpretation of N2O isotopocules data was demonstrated using a Rayleigh‐type model. Earlier statements concerning exponential increase in native soil nitrate pool activity highlighted in previous studies should be replaced with a polynomial increase with dependency on both N‐pool sizes.


| INTRODUCTION
Agricultural soils rely on external nitrogen (N) inputs and constitute a major source of nitrous oxide (N 2 O) and nitric oxide (NO) emissions, accounting for around 10% of greenhouse gas (GHG) emissions from human activities 1 and contributing to the formation of acid rain, eutrophication and ground level ozone. 2 In soil, nitrification and denitrification are the most important microbial processes involved in the production of N 2 O, requiring high and low oxygen (O 2 ) concentrations for the activation of each process, respectively.
Moreover, when denitrification occurs, N applied to soils can be emitted back to the atmosphere as dinitrogen (N 2 ). Many observations have suggested that sequential synthesis of denitrification enzymes is responsible for the delay in N 2 appearance relative to N 2 O. [3][4][5] Amongst the strategies to identify N 2 O sources in the soil and their variation in space and time, the study of the natural abundance of stable isotopic signatures of N 2 O, 6,7 such as the δ 15 N and δ 18 O values and the 15 N site preference (SP), have gained attention ever since the early 2000s. [8][9][10] The N 2 O produced from denitrification in soils tends to be associated with δ 15 N signatures with values in the range of −13 to −54‰ 11,12 while those derived from nitrification are up to −60‰. 11,13 Moreover, reduction of N 2 O to N 2 from denitrifying bacteria can be determined by isotopic discrimination as a consequence of the difference in reaction rates of the isotopically light ( 14 N, 16 O) and heavy ( 15 N, 18 O) molecules of N 2 O. [14][15][16] Interpretation of N 2 O isotopomers as indicators of source processes has also been developed. 17,18 This approach is based on the difference in 15 N occupation of the peripheral (β) and central N-positions (α) of the linear molecule that defines the intra-molecular 15 N SP. 19,20 The SP is not dependent on the isotopic signature of the precursor, 21  fertiliser. [24][25][26][27] The isotope fractionation during N 2 O production 7,12 and reduction, 15,16 or when both processes take place simultaneously, 26 has been previously reported. Moreover, a comprehensive review of isotope effects and isotope modelling approaches was recently presented by Denk et al. 28 Previously, using a Rayleigh equation to describe isotopic fractionation, 29 Well and Flessa 12 concluded that the isotopic fingerprint of soil-emitted N 2 O is a useful parameter to evaluate the contribution of different processes to the N 2 O flux in soils. However, the spatial extent and specific denitrification rates of hypothesized pools could only be constrained by fitting measured and modelled δ 15 N bulk values, which were associated with considerable uncertainties on the volume and denitrification rates of the assumed pools. Modelling the isotope fractionation during production and reduction based on the measured temporal pattern of the δ 15  design tightly constrained several factors to study the effects of nutrient concentration and fertiliser application area as previously described. 27 The soil moisture was adjusted to 85% water filled pore space (WFPS) to promote denitrification conditions, taking the amendment with nutrient solution into account. Before starting the experiment, the soil was preincubated to avoid the pulse of respiration associated with wetting dry soils. 31 For this, the required soil was spread to 3-5 cm thickness. Then, while being mixed continuously, the soil was primed by spraying it with water containing 25 kg N ha −1 of potassium nitrate (KNO 3 ), which is a typical yearly rate of N deposition through rainfall in the UK. 32,33 The soil was then left for 3 days at room temperature before being packed into cores and the incubation being started. This was done to promote the growth of denitrifying organisms and prevent a long lag-phase, therefore reducing the length of the experiment.
The incubation experiment was carried out in a specialised gas-flow-soil-core incubation system (DENItrification System

| Isotopic analysis of N 2 O in 15 N-labelled treatments
Gas samples for 15 N analysis were taken just before (0 h) and 4 h after amendment application and then daily for the first week, followed by a final sampling at day 11. The sampling dates were chosen to cover changes in isotopic ratios during the main period of NO and N 2 O fluxes, and after the emissions returned to background levels.

| Soil analyses
where δ S is the isotopic signature of the remaining NO 3 − (δ 15 N NO3-r ); δ S0 the isotopic signature of the initial NO 3 − (δ 15 N NO3-i ), i.e., fertiliser or soil NO 3 -l ; and η P-S the Net Isotope Effect (NIE) between product and substrate.
In this study, we determined the δ 15 N value of the applied fertiliser whereas that of soil NO 3 − was adapted from the literature 26 f , the fraction of unreduced NO 3 − N, was determined by subtracting the initial NO 3 − concentration and the cumulative N loss as denitrification products (N 2 + N 2 O) for each time step of the process: It was assumed that the NO and NO 2 − pools were negligible in the overall N balance, as these represent very reactive intermediate The isotopic signature of the reduced N 2 O was calculated according to Equation 1, where δ S is the isotopic signature of the remaining

| Statistical analysis
Data were analysed to determine normality (Kolmogorov-Smirnov test) and equality of variance (Levene test) conditions. To fulfil these assumptions, the data were log-transformed before analysis, if needed. Statistical analysis was performed using GenStat 16th edition (VSN International Ltd, Hemel Hempstead, UK). Cumulative emissions were calculated after linear interpolation of the area between sampling points. Differences in total emissions between treatments for each gas measured were assessed by analysis of variance (ANOVA) at p <0.01.

| Fluxes and cumulative gas emissions
The fluxes and cumulative emissions of NO, N 2 O, N 2 as kg N ha −1 and CO 2 are shown in Figure 2 and Table 1, respectively. The NO emissions from treatments 1c and 3c increased immediately after amendment application with a peak lasting just over 2 days and a maximum on day 1 ( Figure 2) The mean cumulative NO emissions from treatment 3c (same shape) was about 2.3 times greater over the time of the incubation than that from treatment 1c ( Table 1).
Emissions of NO from the Control treatment were negligible.
Similarly to the observed NO emissions, the N 2 O emissions increased immediately after amendment application (Figure 2  In treatment 1c one of the three cores inside a vessel was amended with KNO 3 and glucose (the other two received water); in treatment 3c, all three of the cores inside a vessel were amended with KNO 3 and glucose (each core received the same N and C rate as treatment 1c); in the Control treatment, only water was applied to each of the three cores treatment 1c and the Control treatment, whereas significant higher N 2 cumulative emissions were measured in treatment 3c ( Table 1).
The total denitrification was calculated as the sum of all the N emitted (Table 1) and was significantly higher in treatment 3c than in treatment 1c (2.8-fold) and the Control (6.1-fold) treatment.
The CO 2 fluxes showed similar trends to the N 2 O fluxes. In treatments 1c and 3c, the CO 2 emissions increased immediately after amendment application ( Figure 2) and peaked after about 3 days in both treatments. The cumulative emissions of CO 2 (

| Soil mineral N
The results of the soil analysis at the end of the incubation are given in

| 15 N site preference of N 2 O
An where f(X) is the contribution of fertiliser N to N 2 O in % and x is the time after amendment (d).
The Rayleigh model fit adapted to 15 N data for the unlabelled treatments 1c and 3c was evaluated in all vessels, assuming one-pool and two-pool emissions. Only two vessels per treatment (n = 4) showed a good polynomial fit (R 2 >0.89) of the modelled data to the measured data and an average of them is shown in Figure 6. The equations and R 2 values of all the vessels for each N pool are shown in Table S1 (supporting information). The Rayleigh model applied to the δ 15 N bulk -N 2 O data showed poor agreement with the measurements using the original model for treatment 1c, with the two-pool model giving better results when using the polynomial equation determined above ( Figure 6). In contrast, for treatment 3c little difference was observed between the modelling approaches ( Figure 6).

| Soil data and gaseous emissions
Our findings are in agreement with those of Wang et al 36  treatments. It has been demonstrated that many denitrifiers lack one or more of the denitrification enzymes involved in all reduction steps from NO 3 − to N 2 , 37 particularly N 2 O reductase (NosZ) the enzyme reducing N 2 O to N 2 . In addition, the last step in denitrification is also the least energetically favourable. 38 Therefore, denitrifiers would preferentially reduce NO 3 − to N 2 O rather than N 2 O to N 2 .
We hypothesised that these reasons explain the accumulation of  where the latter is also confirmed by flux data (Figure 3).

| Isotopocules model
The Rayleigh model 25,26 was applied to account for the importance of N 2 O emissions from the one-pool and two-pools using the δ 15 N bulk values of N 2 O. Until now, this model has been used to simulate the δ 15 N values of N 2 O using process rates and associated fractionation factors, but assumptions had to be made for some of the model parameters due to lack of available data. 25 In this study, we carried out two incubation experiments in order to parameterise the model.   25,26 should be replaced with a polynomial increase with dependence on both pool sizes. Our results show the value of parameterising models under controlled laboratory conditions using experimental data but further work is required to apply the findings to other soil types and improve the refinement of model parameters.