Isotopic Techniques to Measure N₂O, N₂ and Their Sources

Abstract

GHG emissions are usually the result of several simultaneous processes. Furthermore, some gases such as N₂ are very difficult to quantify and require special techniques. Therefore, in this chapter, the focus is on stable isotope methods. Both natural abundance techniques and enrichment techniques are used. Especially in the last decade, a number of methodological advances have been made. Thus, this chapter provides an overview and description of a number of current state-of-the-art techniques, especially techniques using the stable isotope ¹⁵N. Basic principles and recent advances of the ¹⁵N gas flux method are presented to quantify N₂ fluxes, but also the latest isotopologue and isotopomer methods to identify pathways for N₂O production. The second part of the chapter is devoted to ¹⁵N tracing techniques, the theoretical background and recent methodological advances. A range of different methods is presented from analytical to numerical tools to identify and quantify pathway-specific N₂O emissions. While this chapter is chiefly concerned with gaseous N emissions, a lot of the techniques can also be applied to other gases such as methane (CH₄), as outlined in Sect. 5.3.

7.1 Introduction

In this chapter, we are presenting techniques utilising the stable isotope ¹⁵N to better understand the N cycle but more importantly to determine GHG gas fluxes that cannot be quantified or are difficult to quantify with any non-isotopic technique. The stable isotope ¹⁵N was discovered in the 1920s (Naudé 1929a, b) and the advantage of using this isotope in agriculture, for the determination of the N use efficiency has been recognised and applied since 1943 (Norman and Werkman 1943). Also, microbiologists have utilised the new possibilities that ¹⁵N can offer, to quantify the turnover rates of individual processes in the N cycle (Hiltbold et al. 1951) based on dilution principles (Kirkham and Bartholomew 1954). Moreover, ¹⁵N allowed for the first time the development of techniques to quantify the loss of N₂ against a huge atmospheric N₂ background (Hauck et al. 1958). Also, the identification which of the processes contributing to total N₂O emissions (Butterbach-Bahl et al. 2013) is unthinkable without the use of advanced ¹⁵N tracing techniques (Müller et al. 2014). With the development of new and advanced analytical techniques, it is now possible to also use information on the position of the ¹⁵N (i.e. central, alpha and terminal, beta position) in N₂O, i.e. the isotopomers (of one isotopologue), providing information on the origin without the addition of ¹⁵N labelled fertiliser. Note, isotopologues are molecules that differ in their isotopic composition, isotopomers are molecules with the same isotopic atoms but differing in their position, and isotopocules is the generic term for both isotopologues and isotopomers. There is a wealth of information that we can obtain from using diverse isotopic approaches based on ¹⁵N or ¹⁸O labelling but also on natural abundance techniques that take advantage of the different metabolism with which for instance N₂O is produced. Thus, ¹⁵N provides us with a toolbox to identify emission pathways and in turn provides information on effective mitigation techniques.

7.2 ¹⁵N Gas Flux Method (¹⁵N GFM) to Identify N₂O and N₂ Fluxes from Denitrification

7.2.1 Background

N₂O reduction to N₂ is the last step of microbial denitrification, i.e. anoxic reduction of nitrate (NO₃⁻) to dinitrogen (N₂) with the intermediates NO₂⁻, NO and N₂O (Firestone and Davidson 1989; Knowles 1982). Commonly applied non-isotopic techniques enable us to quantitatively analyse only the intermediate product of this process including NO and N₂O, but not the final product, N₂, a non-greenhouse gas. The challenge to quantify denitrification rates is largely related to the difficulty in measuring N₂ production due to its spatial and temporal heterogeneity and the high N₂-background of the atmosphere (Groffman et al. 2006). There are three principal ways to overcome this problem: (i) adding NO₃⁻ with high ¹⁵N enrichment and monitoring ¹⁵N labelled denitrification products (¹⁵N gas flux method, ¹⁵N GFM) (e.g. (Siegel et al. 1982)); (ii) adding acetylene to block N₂O reductase quantitatively and estimating total denitrification from N₂O production (acetylene inhibition technique, AIT) (Felber et al. 2012); (iii) measuring denitrification gases during incubation of soils in absence of atmospheric N₂ using gas-tight containers and an artificial helium/oxygen atmosphere (HeO₂ method; (Butterbach-Bahl et al. 2002; Scholefield et al. 1997; Senbayram et al. 2018)). Each of the methods to quantify denitrification rates in soils has various limitations with respect to potential analytical bias, applicability at different experimental scales and the necessity of expensive instrumentation that is not available for routine studies. Today the AIT is considered unsuitable to quantify N₂ fluxes under natural atmosphere, since its main limitation among several others is the catalytic decomposition of NO in presence of O₂ (Bollmann and Conrad 1997), resulting in unpredictable underestimation of gross N₂O production (Nadeem et al. 2012). The ¹⁵N gas flux method requires homogenous ¹⁵N-labelling of the soil (Mulvaney and Vandenheuvel 1988) and under natural atmosphere, it is not sensitive enough to detect small N₂ fluxes (Lewicka-Szczebak et al. 2013). Direct measurement of N₂ fluxes using the HeO₂ method is not subject to the problems associated with ¹⁵N-based methods (Butterbach-Bahl et al. 2013) but the need for sophisticated gas-tight incubation systems limits its use. When applying ¹⁵N GFM in the laboratory, sensitivity can be augmented by incubation under an N₂-depleted atmosphere (Lewicka-Szczebak et al. 2017; Meyer et al. 2010; Spott et al. 2006). In the following, the basic principle, limitations, bias and application examples are presented and discussed.

7.2.2 Principles of the ¹⁵N Gas Flux Method

The ¹⁵N gas flux method consists of quantifying N₂ and or N₂O emitted from ¹⁵N-labelled NO₃⁻ applied to soil in order to quantify fluxes from canonical denitrification (Mulvaney and Vandenheuvel 1988; Stevens et al. 1993), where N₂ and N₂O are formed from the combination of two NO precursor molecules. Under certain preconditions, it is also possible to identify the production of hybrid N₂ or N₂O (i.e. molecules formed from the combination of N atoms from one source of oxidised N, e.g. NO₂⁻), and another source of reduced N (e.g. NH₃ or NH₂OH) via anaerobic ammonia oxidation (annamox) or co-denitrification (Laughlin and Stevens 2002; Spott and Stange 2007; Spott et al. 2011). To quantify canonical denitrification, experimental soil is amended with NO₃⁻ highly enriched with ¹⁵N. The ¹⁵N gases evolved are collected in closed chambers and ¹⁵N emission is calculated from the abundance of N₂ and N₂O isotopologues in the chamber gas. ¹⁵N enrichment of N₂ in the gas samples are typically close to natural abundance because the amount of N emitted from the ¹⁵N-labelled soil is small compared to the atmospheric background. Precise techniques of isotope analysis are, therefore, necessary.

7.2.2.1 The Non-random Distribution of Atoms in the N₂ Molecule

The ¹⁵N gas flux method is based on the assumption that within N₂ or N₂O from a single source of a given ¹⁵N abundance, the N₂O isotopologues of a distinct number of ¹⁵N substitutions follow a random (binomial) distribution, as given by the terms in (Eq. 7.1):

$$ (p + q)^{2} = p^{2} + 2pq + q^{2} $$

(7.1)

where p is the atom fraction of ¹⁴N, q the atom fraction of ¹⁵N and p + q is equal to unity (Hauck et al. 1958).

If N₂O or N₂ from two different N pools, one background pool of natural ¹⁵N abundance (0.3663 atom %) and the second enriched in ¹⁵N are mixed, the distribution deviates from the binomial pattern. Given the distribution of N₂ or N₂O isotopologues emitted from the first (background) N pool (a_bg) including non-labelled N₂ and N₂O (derived from the atmosphere and possibly non-labelled N₂O from non-labelled N sources in soil) and the resulting mixture (a_m), the ¹⁵N abundance in the ¹⁵N-labelled second pool (a_p) and the fraction of N₂O or N₂ originating from that labelled pool (f_p) can be determined (e.g. Bergsma et al. 2001; Spott et al. 2006). To calculate f_p values, the nitrogen isotope ratios ²⁹R(²⁹N₂/²⁸N₂) and ³⁰R(³⁰N₂/²⁸N₂) are used. In case of N₂, the three isotopologues ¹⁴N¹⁴N and ¹⁴N¹⁵N and ¹⁵N¹⁵N are detected. For N₂O, one option is to directly analyse intact N₂O molecules, consisting of N and oxygen (O) and analysing molecular masses 44, 45 and 46. It has to be taken into account that these molecular masses include not only N- but also O-substituted isotopocules and thus the following 6 species: ¹⁴N¹⁴N¹⁶O with mass-to-charge (m/z) 44, ¹⁴N¹⁴N¹⁸O (m/z 46), the isotopomers ¹⁴N¹⁵N¹⁶O and ¹⁵N¹⁴N¹⁶O (both m/z 45), ¹⁴N¹⁴N¹⁷O (m/z 45) and ¹⁵N¹⁵N¹⁶O) (m/z 46). To calculate ¹⁵N pool-derived N₂O, ²⁹R and ³⁰R of the N₂O–N is calculated taking into account the natural abundance of ¹⁷O- or ¹⁸O-substituted isotopocules (¹⁴N¹⁴N¹⁸O and ¹⁴N¹⁴N¹⁷O) due to their mass overlap with the ¹⁵N-substituted isotopocules (Bergsma et al. 2001). Alternatively, N₂O can be reduced to N₂ prior to IRMS analysis (Lewicka-Szczebak et al. 2013), thereby allowing direct determination of ²⁹R and ³⁰R of N₂O–N.

There are various calculation procedures that have evolved over time (Hauck et al. 1958; Mulvaney 1984; Arah 1992; Nielsen 1992, Well et al. 1998; Spott et al. 2006). In Eqs. 7.2 and 7.3 we show one example (Spott et al. 2006), where the fraction of N₂ or N₂O evolved from the ¹⁵N-labelled NO₃⁻ pool (f_p) is calculated:

$$ f_{p} = \frac{{a_{m} - a_{bg} }}{{a_{p} - a_{bgd} }} $$

(7.2)

where $a_{m}$ is the ¹⁵N abundance of the total gas mixture

$$ {a}_{{m}} = \frac{{^{{{{29}}}}\!{R} + {{2}}{*}^{{{{30}}}}\!{R}}}{{{{2}}\left( {{{1}} +\,\,^{{{{29}}}}\!{R} +\,\,^{{{{30}}}}\!{R}} \right)}} $$

(7.3)

and a_bg is the ¹⁵N abundance of atmospheric background N₂.

The ¹⁵N abundance of the ¹⁵N-labelled nitrate pool undergoing denitrification is

$$ {a}_{{p}} = \frac{{^{{{{30}}}} {x}_{{m}} - {a}_{{{bgd}}} *{a}_{{m}} }}{{{a}_{{m}} - {a}_{{{bgd}}} }} $$

(7.4)

where $^{30} x_{m}$ is the measured fraction of m/z 30 in the total gas mixture:

$$ ^{{{{30}}}} {x}_{{m}} = \frac{{^{{{{30}}}}\!{R}}}{{{{1}}\,\,+\,\,^{{{{29}}}}\!{R}\,\,+\,\,^{{{{30}}}}\!{R}}} $$

(7.5)

The same calculations can be used for N₂ and N₂O, resulting in respective values for fractions of pool-derived N (f_{p_N2}; f_{p_N2O}) and for the respective ¹⁵N abundances of the active N pools (a_{p_N2}; a_{p_N2O}).

If only m/z = 28 and m/z = 29 are determined during isotope analysis of N₂, then emission of ¹⁵N₂ is underestimated (Hauck et al. 1958). The extent of underestimation is related to the ¹⁵N atom fraction of the NO₃⁻ pool from which N₂ is emitted (Well et al. 1998) and f_p can thus be calculated if the ¹⁵N enrichment of the denitrified N pool is known (Mulvaney 1984):

$$ {f}_{{p}} = \left( {^{{{{29}}}} {R}_{{{{sa}} }} -{}^{{{{29}}}}{{R}}_{{{{bg}}}} } \right)/\left( {{{2}}\,{a}_{{p}} \left( {{{1}} - {a}_{{p}} } \right)} \right) $$

(7.6)

where lower case sa and bg denote sample and background (typically ambient air), respectively. An alternative equation yielding f_p from ²⁹R that is more complex, but also more precise, is given by Spott et al. (2006).

In many studies, a ¹⁵N atom fraction of 0.99 was selected for the ¹⁵N enrichment of applied NO₃⁻ (¹⁵a_NO3) in order to maximise ³⁰R (see Fig. 7.1), thus yielding better ³⁰R signals. However, there are also reasons to keep ¹⁵a_NO3 between about 0.6 and 0.4, since ³⁰R is only detectable with high fluxes due to a typical high IRMS background signal at m/z 30 (see next section), so that f_p has to be calculated from ²⁹R only using Eq. 7.6. But f_p calculated from Eq. 7.6 with a given ²⁹R is relatively insensitive to changes in a_p between 0.4 and 0.6 since the nominator yields, e.g. for a_p between 0.4 and 0.6, values between 0.48 and 0.5. Hence, uncertainty in the estimation of a_p within that range causes minor uncertainty in calculated f_p (Well and Myrold 1999).

Fig. 7.1

Abundance of ²⁸N₂, ²⁹N₂ und ³⁰N₂ in air, in soil-emitted N₂ evolved from NO₃⁻ with 50 atom% ¹⁵N, and in a 1:1000-mixture without and with randomisation of isotopologues by N₂ dissociation, respectively

To illustrate how the combination of denitrification rates (i.e. f_p) and homogenous or non-homogenous ¹⁵N enrichment of the soil NO₃⁻ pool affect instrumental raw data as well as calculated f_p and a_p values, some theoretical data are shown (Table 7.1). Three cases are represented, (1) the soil is homogenously labelled with ¹⁵N, (2) non-labelled soil-derived NO₃⁻ dilutes the labelled pool to a different extent in the 0 to 10 and 10 to 20 cm layers, but N₂ and N₂O production rates in both layers are equal and (3) like case (2) except that production rates of both layers differ. It can be seen that only case (1) calculated using Eq. 7.4 yields results identical to ideal a_p and f_p. Equation 7.6 gives deviating results when used with ¹⁵a_NO3 as this value differs from a_p. In the case of (2) and (3), all calculations lead to some deviation due to the non-homogeneity in label distribution. Moreover, isotope ratios show that even at the high denitrification rate assumed (case 2, 542 g N ha⁻¹ 20 cm⁻¹ d⁻¹), the increase in ²⁹R (²⁹Rm–²⁹Ra) and ³⁰R (³⁰Rm–³⁰Ra) was 9.2 × 10⁻⁶ and 3 × 10⁻⁶, respectively, and thus only about one order of magnitude above typical instrumental precision (see Table 7.2).

Table 7.1 Mole fractions (X) of ²⁸N₂, ²⁹N₂ und ³⁰N₂ in air (subscript a), in soil-emitted N₂, N₂O or N₂ + N₂O evolved from ¹⁵N-labelled NO₃⁻ pool (subscript p), and of their mixture (subscript m), resulting isotope ratios (²⁹R, ³⁰R) and calculated (Spott et al. 2006) values of a_p and f_p. Values are computed for individual fluxes from two soil layers (0–10 and 10–20 cm) and the mixed flux from both layers. The ratio of soil NO₃⁻-N to added ¹⁵NO₃⁻-N (at 60 at % ¹⁵N) is varied to obtain differing ¹⁵a_NO3 and a_p values. Denitrification rates are calculated from f_p assuming micro-plots size of 30 cm diameter, chamber height of 10 cm and 1 h closing time

Table 7.2 Typical precision (standard deviation, SD) for the nitrogen isotope ratios ²⁹R (²⁹N₂/²⁸N₂) and ³⁰R (³⁰N₂/²⁸N₂) by IRMS

Table 7.3 Detection limit of the ¹⁵N GFM determined by Monte-Carlo modelling. Detection limit for the fraction of pool derived N₂ (f_p of N₂) is given as 1 standard deviation (SD) in dependence of ¹⁵N enrichment of active labelled NO₃-pool (ap) and magnitude of f_p in atmospheres with 100% or 2% N₂ and assuming IRMS precision of ²⁹R and ³⁰R according to the first instrument in Table 2

Table 7.4 Overview of current ¹⁵N- labelling techniques

7.2.3 Identifying the Formation of Hybrid N₂ and/or N₂O

When N₂ and N₂O are formed from denitrification, both N atoms are derived from the ¹⁵N labelled pool, and in hybrid N₂ or N₂O only one N atom comes from the labelled pool (N oxides, i.e. NO₂⁻) and the other one comes from non-labelled reduced N (e.g. NH₃, NH₂OH or organic N). Hence, the contribution of hybrid processes is reflected by an increase in ²⁹R only, while denitrification increases both ²⁹R and ³⁰R (Clough et al. 2001). Laughlin and Stevens (2002) derived equations to calculate the fraction of hybrid and non-hybrid N₂, assuming that the measured ¹⁵N atom fraction of NO₃⁻ also reflected the enrichment of the NO₂⁻ that contributed one N atom to the hybrid molecules, and that the ¹⁵N abundance of the non-labelled sources (atmospheric N and non-labelled reduced N) were identical. An extended approach was developed allowing to take into account different ¹⁵N enrichment for all contributing sources, i.e. different values for atmospheric and reduced N (Spott and Stange 2007; Spott et al. 2011). Spott et al. (2011) used those equations to calculate co-denitrification in a soil slurry but pointed out that the approach would be subject to possible bias due to difficulty and inaccuracy when determining the ¹⁵N enrichment of the nitrite (NO₂⁻) pool contributing to the hybrid formation. For N₂O mixtures consisting of N₂O from only two sources, i.e. hybrid and non-hybrid N₂O, the authors, therefore, suggest to use the indicator value R_binom to assess the contribution of hybrid N₂O. R_binom reflects the fact that N₂ or N₂O isotopocules of each non-hybrid source contributing to a gas mixture are following a random (binomial) distribution, whereas this is not the case for the hybrid N₂O. R_binom values >1 indicate a significant hybrid contribution. While fluxes excluding hybrid N₂O would always yield R_binom ≤ 1, respective R_binom values would not exclude the possibility of some hybrid contribution. Hence, R_binom can only prove the existence (but not the absence) of hybrid fluxes. The limitation of this approach is that it does not work in the presence of additional sources, e.g. if there is N₂O from unlabelled sources including atmospheric N₂O. Thus, R_binom does not work for N₂ because there is always a high background of atmospheric N₂. To our knowledge, systematic and quantitative studies on hybrid fluxes from soils, including quantification of average pool enrichment and its homogeneity or non-homogeneity, and estimation of resulting uncertainties, have not yet been accomplished.

7.2.4 Analysis of N₂ and N₂O Isotopologues

Precise quantification of N₂ and N₂O isotopocules requires isotope ratio mass spectrometry (IRMS) where ²⁹R and ³⁰R are obtained from ion current ratios detected at Faraday collectors tuned for m/z 28, 29 and 30 (e.g. Lewicka-Szczebak et al. 2013). A double collector IRMS was used before multi-collector IRMS became available. Double collector IRMS required two measurements with the IRMS so that either ²⁹N₂ or ³⁰N₂ is positioned on the first collector (Siegel et al. 1982). Emission spectroscopy has also been used in the past to detect ²⁸N₂, ²⁹N₂ and ³⁰N₂ (Kjeldby et al. 1987), but its relatively low precision enabled only detection of large N₂ fluxes. While dual inlet IRMS had been used with manual measurement of samples in glass containers that were sealed (Well et al. 1993) or isolated by stopcocks (Siegel et al. 1982), continuous flow IRMS enables automated injection of samples from septum capped vials since the 1990s (Stevens et al. 1993). Recently, further progress was obtained by automated analysis of N₂, N₂+N₂O and N₂O in one run, including N₂O reduction to N₂ (Lewicka-Szczebak et al. 2013). The latter enables the analysis of N₂O-N at m/z 28, 29 and 30, thus excluding the need to conduct ¹⁷O and ¹⁸O corrections, yielding better precision, since O corrections are biased to some extent by natural variation of ¹⁷O and ¹⁸O (Deppe et al. 2017).

While quantification of ²⁹R is quite robust, ³⁰R is affected by the mass overlap of ³⁰N₂ with the most abundant isotopocule of NO (¹⁴N¹⁶O), since NO⁺ is formed at the hot filament in the ion source of the IRMS (Brand et al. 2009, Siegel et al. 1982) due to the omnipresence of oxygen traces. NO⁺ formation can be quantified by the ratio between ideal and measured ³⁰R of standard gases, giving values of 0.15 to 0.06 for atmospheric N₂ analysed in the instrumentation proposed by Lewicka-Szczebak et al. (2013). NO⁺ formation can be minimised by removal of all O sources (O₂, H₂O) from the samples and also from the carrier and reference gases. In some types of IRMS the NO⁺ background is too high and associated with extreme tailing of the m/z 30 peak. This makes it impossible to quantify ³⁰R (Well et al. 1993). To overcome this limitation, a procedure to quantify ³⁰R indirectly from ²⁹R was developed where ²⁹R had to be analysed twice, (i) in samples where the non-random distribution of N₂ isotopocules was randomised by the temporary splitting up of N₂ molecules during a gas discharge (see change in ²⁹R due to randomisation in Fig. 7.1). Discharge was actuated using a microwaves source, initially offline in sealed glass tubes, later with online continuous flow IRMS, where the discharge occurred in the gas circuit connecting and IMRS (Well and Meyer 1998). An overview of the IRMS precision for ²⁹R and ³⁰R in N₂ standard gases is given in Table 7.2, showing that repeatability for ²⁹R varied significantly between instruments, but ³⁰R is comparable. However, it is also evident that during the last 35 years (Siegel et al. 1982) there has been no substantial improvement in the measurement precision.

7.2.5 Detection Limit for a_p and f_p

Because f_p is calculated from two quantities, ²⁹R and ³⁰R, and the relationship between them depends on the ¹⁵N enrichment of the active N pool (a_p, see Fig. 7.1), the limit of detection (LOD) for f_p at given repeatability of ²⁹R and ³⁰R is variable. LOD for f_p was thus determined for varying conditions using equations from Spott et al. (2006) using Monte Carlo modelling assuming a normal distribution of ²⁹R and ³⁰R errors (Standard deviation of repeated analysis of standard gas samples). The MS-Excel function norm.inv was used to create the normal distribution of values but allowing only a maximum deviation of 3 standard deviations, otherwise unrealistic outlier of ²⁹R or ³⁰R yield unrealistically high uncertainty. Different scenarios were tested (f_p = 1 to 100 ppm; a_p = 0.055 to 0.75 using repeatability for ²⁹R and ³⁰R of the first IRMS listed in Table 7.1). LOD is obtained for two cases: 1. Both ²⁹R and ³⁰R are taken into account to calculate both a_p and f_p; 2. f_p is calculated using only ²⁹R (using Eq. 7.4 in (Spott et al. 2006)) and a_p is estimated either from soil extract analysis or from a_p of N₂O (e.g. Stevens and Laughlin 2002). Note that a_p of N₂O is usually much more reliable than a_p of N₂ since f_p of N₂O is typically large (often between 0.1 and 1) due to the fact that, in contrast to N₂, N₂O is an atmospheric trace gas. Conversely, f_p of N₂ is typically very small (usually <10⁻⁵ in ambient atmosphere).

The first calculation is preferable because a_p of N₂ and N₂O can be different (see Fig. 7.3) and a_p of N₂O can only be obtained if N₂O can be directly measured by IRMS, which is only the case if concentrations are high enough (about 0.3 to 3 ppm necessary, depending on ¹⁵N enrichment of N₂O). Since incubation under N₂-depleted atmosphere improves f_p sensitivity, LOD is also given for an artificial gas mixture containing 2% N₂.

LOD results are as follows (Table 7.3): with high f_p (i.e. ≥10 ppm) and high a_p (i.e. ≥0.5) and ideal IRMS performance (Table 7.2) both calculations yield precise results. Under N₂-depleted atmosphere, LOD is excellent (2 to 7 ppb N₂, last columns). With lowering of a_p, LOD gets worse if a_p has to be calculated using ³⁰R. But without using ³⁰R and assuming an ideal a_p value or estimating a_p of N₂ from direct determination of a_p of N₂O, LOD of f_p is still excellent. This is because with decreasing a_p, abundance of ¹⁵N¹⁵N (³⁰N₂), and thus ³⁰R, decreases exponentially whereas the decrease of ²⁹R (²⁹N₂) is much slower (see Fig. 7.2).

Fig. 7.2

Abundance of ²⁸N₂, ²⁹N₂ and ³⁰N₂ in N₂ evolved from the ¹⁵N–labelled NO₃^– depending on a_p (Siegel et al. 1982)

7.2.6 Limitations of the ¹⁵N Gas Flux Method (¹⁵N GFM)

The following factors limit the applicability of the ¹⁵N GFM

7.2.6.1 Inaccurate Definition of the Soil Volume Represented by Denitrification Measurements and Incomplete Recovery of Denitrification Gases

The denitrifying soil volume is clearly defined if soil cores are entirely labelled with ¹⁵N and are incubated in closed systems. However, in situ measurement of denitrification in surface soils or subsoils with approaches other than the core methods do not include complete enclosure of the investigated soil. It is not possible to control the application of ¹⁵NO₃⁻ accurately. Consequently, the soil volume represented by the detected denitrification gases is not exactly defined, and calculated denitrification rates are associated with uncertainty. Partial enclosure of the investigated soil is typically achieved by driving cylinders into surface soils. This option reduces the problem to a certain extent. Moreover, measuring the spatial distribution of the ¹⁵N label at the end of experiments (Well and Myrold 2002) helps to constrain the soil volume contributing to soil N₂ fluxes that can be “seen” by ¹⁵N analysis of headspace gases.

An additional problem of open systems is the difficulty to determine the direction and strength of diffusional gas transport. When chamber methods are used to determine denitrification of surface soils, a significant fraction of the denitrification gases produced in the ¹⁵N-labelled soil diffuses into the subsoil and is thus not recovered in the chambers. Principally, this can be solved by modelling diffusion of ¹⁵N labelled gaseous denitrification products (see Sect. 7.2.7).

7.2.6.2 The Problem of Non-homogenous ¹⁵N Enrichment of the NO ⁻₃ Pool

An overview of techniques to supply ¹⁵N-labelled NO₃^– to the soil is given in Table 7.4. The ¹⁵N GFM is based on the assumption of an isotopically homogenous NO₃^– pool. Because this condition is rarely achieved in soils, underestimation of denitrification rates up to 30% can result (Arah 1992; Mulvaney and VandenHeuvel 1988). An initial homogeneity can be obtained by intensive mixing of the soil, but this is a massive disturbance with huge potential effects on N processes including denitrification dynamics and is only adequate to simulate soil tillage with similar disturbance. But even with initially ideal tracer distribution, non-homogeneity inevitably develops over time, since N transformations including nitrification, denitrification and immobilisation are never homogenous in structured soil where aerobic and anaerobic domains coexist and organic matter fractions of varying reactivity are unevenly distributed. Injection of ¹⁵N tracer solution (Wu et al. 2012) increases moisture and inevitably produces non-homogeneity with maximum label concentration at the injection spots. Saturation and drainage (Nõmmik 1956) or soil water displacement by irrigation of lysimeters (Well et al. 1993) leads to an interim increase in moisture and causes loss of DOC. Labelling with gaseous NO₂ was not a suitable way to achieve high and homogenous enrichment of soil NO₃⁻ (Stark and Hart 1996). Consequently, non-homogeneity of the label distribution is probably the main source of bias of the ¹⁵N GFM. Often ¹⁵N tracer has been applied to the surface similar to conventional fertilisation (Baily et al. 2012). However, in this case, only fertiliser derived fluxes are detected initially, while during ongoing diffusion and leaching of NO₃⁻, the ¹⁵N labelled NO₃⁻ pool rapidly changes its dimensions and thus non-homogeneity complicates the interpretation of results.

Table 7.5 Treatments (TR) used for the dual isotope method

Possible causes and consequences of non-homogenous distribution of the ¹⁵N-label and denitrification /nitrification dynamics is illustrated using two conceptual models (Well et al. 2015). The first model shows how a_p of N₂ and N₂O can differ due to non-homogeneity in ¹⁵N enrichment and also non-homogeneity in N₂ and N₂O production rates (Fig. 7.3). Even if equal amounts of ¹⁵N tracer solution could be applied to each soil layer, ¹⁵N enrichment of NO₃⁻ would be variable due to the different dilution of the label via soil-derived NO₃⁻. Additionally, production rates of N₂ and N₂O and their ratio are typically spatially variable, which results in differing a_p values for N₂ and N₂O (Fig. 7.4). The development of spatial heterogeneity in ¹⁵N enrichment and the consequences arising from the fact that nitrification and denitrification typically occur in different soil niches is shown with the second conceptual model (Fig. 7.4) that had been used to explain observations (Deppe et al. 2017). In that study, the soil had been mixed with ¹⁵N labelled NO₃⁻ and non-labelled NH₄⁺ and isotopic values of initial NO₃⁻ and final NO₃⁻ and N₂O had been compared. Results showed that a_p of N₂O was similar to initial enrichment of soil NO₃⁻ (13 atom% ¹⁵N), but final NO₃⁻ enrichment of the bulk soil was much lower (about 3 atom% ¹⁵N) whereas a_p of N₂O did not change significantly. This was postulated to result from the dilution of the label only in aerobic domains where nitrification occurred, whereas in anaerobic microsites there was no nitrification, and hence no dilution of the label. But the undiluted microsites produced all or most of the N₂O whereas there was negligible N₂O flux from aerobic domains. While this discrepancy between ¹⁵N enrichment of NO₃⁻ in the bulk soil and a_p of N₂O was certainly extreme in that study, similar process dynamics can be expected in many cases. Such non-homogeneity in label distribution and its dilution as well as N₂ and N₂O production leads to uncertainties in calculation of f_p (see Table 7.1). But these examples also show that comparison of a_p of N₂ and a_p of N₂O can be used to identify heterogeneity in labelling and thus stress the importance of using analytical methods including ²⁹R and ³⁰R of N₂ and N₂O-N (Lewicka-Szczebak et al. 2013). Moreover, it shows that calculating f_p based on ¹⁵N enrichment of bulk NO₃⁻ from soil extraction (Eq. 7.6) can lead to severe bias, since the ¹⁵N enrichment of the active pool can strongly deviate from the bulk pool. Moreover, an advantage of the non-random distribution approach with N₂ and N₂O is that non-homogeneity is indicated by discrepancies between a_p of N₂, a_p of N₂O and ¹⁵a_NO3, which is quite useful (Lewicka-Szczebak and Well 2020). But it also shows that hybrid fluxes are difficult to identify if label distribution is non-homogenous.

Fig. 7.3

Model 1 to explain why N₂ and N₂O from denitrification can originate from different effective ¹⁵N pools: In the lower pool with a higher ¹⁵N enrichment, N₂ fluxes dominate over N₂O,whereas the opposite is the case for the shallow pool with lower enrichment. Hence, emitted N₂ is more enriched compared to emitted N₂O

Fig. 7.4

Model 2 to explain possible non-homogeneity in ¹⁵N-labelling of NO₃⁻ in NH₄⁺-fertilised soil (Deppe et al. 2017). Colours represent enrichment (blue = nat abundance, red = max. ¹⁵N enrichment). a. Initial enrichment of NO₃⁻ results from mixing of soil NO₃⁻ and added ¹⁵N-NO₃⁻. b. Initial homogenous distribution of labelled NO₃⁻ and non-labelled NH₄⁺ in the soil matrix. c. In anaerobic microsites, nitrification is inhibited and the NO₃⁻ pool of initial ¹⁵N enrichment is denitrified and produces N₂O of identical enrichment. In aerobic domains, nitrification of non-labelled NH₄⁺ produces non-labelled NO₃⁻, thus diluting the initial labelled NO₃⁻ pool and emitting unlabelled N₂O. Note that the ¹⁵N enrichment of NO₃⁻ undergoing denitrification is larger than the average ¹⁵N enrichment of extracted NO₃⁻ and of emitted N₂O

Further limitations of the ¹⁵N GFM have been reviewed previously (Aulakh et al. 1991; Groffman et al. 2006; Sgouridis et al. 2016). They include enhancement of denitrification by NO₃⁻ application in unfertilised systems, gas entrapment in very wet or fully water-saturated soils or sediment, and limited residence time of applied ¹⁵NO₃⁻-N due to plant uptake and leaching.

7.2.6.3 Combining the ¹⁵N GFM with Modelling of Gross N Transformation

The current model to analyse data for the ¹⁵N GFM cannot be used to solve situations that include multiple labelled pools and heterogeneity of process activity and thus yield variable results in terms of flux quantification. Therefore, more complex models are needed to fill this gap. A ¹⁵N tracing model had been developed to analyse N₂O dynamics in terrestrial ecosystems, which builds on previous tracing models for the quantification of the main mineral N transformations and soil nitrite (NO₂⁻) dynamics (Müller et al. 2014). This model is thus a first step in taking more complex dynamics into account. Extending this approach to model heterogeneity of processes and pools might be a promising way to solve current limitations of the ¹⁵N GFM. For more information on the tracing technique see Sect. 7.5 of this chapter.

7.2.7 Evaluation of the ¹⁵N GFM

While quantification of N₂ and N₂O fluxes from distinct N pools remains a challenge after several decades of method development and improvement, this is even more the case for robust evaluation of methods, as this requires that the reference method is quantitative and is applied under the same conditions as the tested method. From that perspective, all previous tests included some uncertainties to our knowledge and were thus not fully able to evaluate the ¹⁵N GFM. There have been several comparisons between ¹⁵N GFM and AIT with controversial results, i.e. reporting general agreement (Aulakh et al. 1991) and severe underestimation by AIT (Arah et al. 1993; Sgouridis et al. 2016). Aulakh et al. (1991) compared ¹⁵N GFM and AIT in the field and found that ¹⁵N fertiliser derived N₂ + N₂O fluxes were comparable to total N₂O fluxes in presence of acetylene (C₂H₂), suggesting that both methods were in general agreement. However, in all comparisons, ¹⁵N fertiliser was surface applied, so only the soil volume reached by the fertiliser contributed to the surface flux, unlike the AIT, were a larger soil volume was reached by the gaseous acetylene supplied by perforated pipes or buried calcium carbide. Hence comparisons did not reflect equal parts of the soil profile. Interestingly, in most comparisons denitrification was enhanced by soil compaction or glucose amendment, to achieve detectable ¹⁵N₂ fluxes against the atmospheric N₂ background. Sgouridis et al. (2016) compared closed chamber ¹⁵N GFM using needle injection to distribute K¹⁵NO₃⁻ evenly with the AIT “soil core” variant finding 3 to 5 times higher rates with ¹⁵N GFM. Kulkarni et al. (2014) conducted an extensive comparison of the HeO₂ method using small cores (5 cm diameter × 5 cm height, incubated under HeO₂ in the lab) with in situ measurement using the ¹⁵N GFM where KNO₃⁻ with 99 atom% was sprayed on the soil surface. Authors discussed difficulties to compare measurements in view of O₂ manipulation in the lab and uneven label distribution in the field as well as variable moisture and temperature conditions in the field, and also that there are N₂ fluxes from sources other than NO₃⁻ (Butterbach-Bahl et al. 2013). What is still needed for a quantitative evaluation of the ¹⁵N GFM is to incubate ¹⁵N-labelled soil in a HeO₂ setup to allow direct comparison of GC- and IRMS based N₂ fluxes.

If ¹⁵N GFM is conducted under conditions maximising sensitivity and minimising bias, it can be used to evaluate other methods as for example the N₂O isotopocule approach to determine N₂O reduction (Lewicka-Szczebak et al. 2017, Buchen et al. 2018) (see Sect. 7.3).

7.2.8 Lab and Field Experiments

Initial application of ¹⁵N GFM in lab incubations was carried out in closed vessels (Melin and Nõmmik 1983; Siegel et al. 1982). Recently, some studies used N₂-depleted atmosphere to increase sensitivity in soil incubations (Lewicka-Szczebak et al. 2017; Schorpp et al. 2016) achieving sensitivities for pool-derived N₂ of approximately 50 ppb which is thus comparable to GC sensitivity for N₂O and two order of magnitude more sensitive compared to ¹⁵N GFM under ambient atmosphere. Important to note is that this also improves precision for quantifying a_p and thus yields more precise estimates for the dilution of the denitrified pool by soil-derived NO₃⁻.

A key feature of ¹⁵N GFM is in situ measurement of denitrification and today it must be considered the only available field method, since AIT has been found unsuitable (Felber et al. 2012; Nadeem et al. 2012; Sgouridis et al. 2016). But ¹⁵N GFM has been used far less compared to the AIT probably due to its low sensitivity and high effort and expense to keep high ¹⁵N labelling in the field for extended periods, and also because of the multiple sources of bias. ¹⁵N GFM has thus been primarily used for soil types and/or conditions with high denitrification potential, e.g. due to abundant organic C (e.g. in organic soils or after soil compaction Arah et al. 1993). Typically, experiments covered only certain phases of the year. Maybe the most extensive study (including an extensive review of past in situ measurements) was by Sgouridis et al. (2016) who conducted ¹⁵N GFM in 4 sites monthly during about 18 months. But it has recently been found that during field application of the ¹⁵N GFM, denitrification is severely underestimated because a large fraction of the labelled N₂ and N₂O produced is not emitted from into the soil surface but diffuses to the subsoil or accumulates in pore space (Well et al. 2019a). This was confirmed experimentally and production–diffusion modelling showed that under typical experimental conditions, denitrification rates would be underestimated by more than 50%. It was concluded that field surface fluxes of ¹⁵N-labelled N₂ and N₂O have been severely underestimated in the past, but that diffusion modelling can be used to correct data. Moreover, to overcome the poor sensitivity of in situ ¹⁵N GFM, a new procedure was developed to conduct the ¹⁵N gas flux method using artificial N₂‐depleted atmosphere also for field application (Well et al. 2019b), giving a sensitivity for N₂ + N₂O fluxes up to 80‐fold better compared to the conventional ¹⁵N GFM under ambient atmosphere. Consequently, recent methodical improvements are promising to yield good progress in the study of denitrification control at the field scale. ¹⁵N GFM has been used extensively with water saturated cores of aquatic sediments, e.g. Enrich-Prast et al. (2015), where sensitivity is less critical due to the possibility to measure ¹⁵N-labelled N₂ dissolved in pore water where atmospheric N₂ background is small.

7.2.8.1 In Situ Measurement in Subsoil and Groundwater

Some modifications of the ¹⁵N GFM for subsurface applications had been proposed and applied. For water saturated subsoil of hydromorphic soils or deeper groundwater, the “push–pull” type experimental setup (Istok et al. 1997) was combined with ¹⁵N tracing (Addy et al. 2002; Well et al. 2003; Well and Myrold 1999), where ¹⁵N tracer solution is injected in groundwater wells and groundwater samples are subsequently extracted over time and analysed for ¹⁵N labelled N₂ and N₂O. Similar to using ¹⁵N GFM in water saturated sediment in the lab (see above, Enrich-Prast et al. 2015), this approach is quite sensitive since produced N₂ mixes with the small N₂ background of N₂ dissolved in groundwater. The ¹⁵N push–pull approach has been compared to slurry incubations of aquifer samples in the lab (Eschenbach et al. 2015; Well et al. 2005) finding good agreement between both approaches. It has also been successfully applied for deeper groundwater up to 90 m depth (Eschenbach et al. 2015).

In the unsaturated zone, subsoil denitrification has been quantified in situ from the steady-state ¹⁵N₂ + ¹⁵N₂O concentration within a defined ¹⁵N-labelled soil volume (Well and Myrold 2002). Diffusion-reaction modelling has been used to quantify rates by fitting measured and modelled f_p values, but accuracy of this approach was limited by the difficulty to quantify the volume of ¹⁵N-labelled soil, its gas diffusivity and its distribution in ¹⁵N enrichment.

7.2.9 Conclusions and Outlook

The ¹⁵N GFM is a powerful approach to quantify soil denitrification and its N₂O/(N₂ + N₂O) mole ratio, to distinguish N₂O fluxes derived from NO₃⁻ and other N sources and, under certain conditions, also to identify the formation of hybrid N₂ and N₂O fluxes. It is applicable in the lab as well as in the field. But it is based on a variety of assumptions and prerequisites that are not always easy or possible to validate or to fulfil. Therefore, and because of its high expense for isotope tracers, IRMS analysis and demanding experimental setups, it has until now rarely been used routinely to study denitrification. Moreover, systematic evaluation using independent methods, e.g. using the HeO₂ method, is still pending. Progress has been made in automated IRMS approaches that can be established using commercially available devices with some custom-made modifications. While sensitivity was clearly improved in the lab by incubation under N₂ depleted atmosphere, this has not yet been fully realised for field conditions. These are good reasons to intensify the use of ¹⁵N GFM in future N cycle research, since despite large efforts during preceding decades, the magnitude of denitrification is still the big unknown of the N cycle (Butterbach-Bahl et al. 2013; Müller and Clough 2014).

7.3 Isotopocule Techniques to Identify Pathway-Specific N₂O Emissions

7.3.1 Introduction

N₂O isotopocules are the chemically identical N₂O molecules but differing either in the atomic mass due to a substitution of one atom with heavy isotope ¹⁵N or ¹⁸O (isotopologues: ¹⁴N¹⁴N¹⁶O; ¹⁵N¹⁴N¹⁶O; ¹⁴N¹⁴N¹⁸O), or in the location of ¹⁵N substitution (isotopomers: ¹⁴N¹⁵N¹⁶O; ¹⁵N¹⁴N¹⁶O) (Toyoda et al. 2017). Thus, the asymmetric NNO molecule has in total twelve distinct isotopocules, representing all possible combinations of the N isotopes ¹⁴N and ¹⁵N and the oxygen isotopes ¹⁶O, ¹⁷O and ¹⁸O and providing a wealth of interpretation perspectives. Most commonly the three isotopic characteristics (δ¹⁸O, δ¹⁵N^α and δ¹⁵N^β) are measured, reporting the relative differences of isotope ratios of the four most abundant N₂O isotopocules ¹⁴N¹⁴N¹⁸O/ ¹⁴N¹⁴N¹⁶O (δ¹⁸O), ¹⁴N¹⁵N¹⁶O/ ¹⁴N¹⁴N¹⁶O (δ¹⁵N^α) and ¹⁵N¹⁴N¹⁶O/ ¹⁴N¹⁴N¹⁶O (δ¹⁵N^β) in relation to a measurement standard defined on an international isotope ratio scale, Air-N₂ for ¹⁵N/¹⁴N and Vienna Standard Mean Ocean Water (VSMOW) for ¹⁸O/¹⁶O. The average of δ¹⁵N^α and δ¹⁵N^β is referred to as δ¹⁵N^bulk and the difference between δ¹⁵N^α and δ¹⁵N^β (i.e. δ¹⁵N^α–δ¹⁵N^β) is called δ¹⁵N-site preference (δ¹⁵N^SP), or commonly as SP (Toyoda and Yoshida 1999).

Natural abundance isotopic signatures can be used as an alternative approach to ¹⁵N tracing to constrain N₂O transformations in the environment. Variations in stable isotope abundances are due to the fact that for many biotic and abiotic processes, the reaction rates differ between isotopic species, e.g. reduction of ¹⁵NO₂⁻ versus ¹⁴NO₂⁻, leading to a so-called isotopic fractionation. As the isotopic fractionation is distinct for certain reaction pathways, isotopic signatures of particular production pathways and reduction fractionation factors determined in laboratory pure culture studies can be used to differentiate processes from each other. Distinct process information is provided by the difference in ¹⁵N substitution between the central and terminal position within the N₂O molecule (SP), which is independent of the precursor’s isotopic composition and characteristic of specific reaction mechanisms or enzymatic pathways. The most common interpretation strategy used to date is the dual isotope plot, also known as “mapping” approach, presenting the relationship between two isotopic parameters–commonly δ¹⁸O/ δ¹⁵N^bulk, δ¹⁵N^SP/ δ¹⁵N^bulk or δ¹⁵N^SP/ δ¹⁸O. From such figures, estimates can be made about trends, probable dominance of particular pathways, or reduction progress (Toyoda and Yoshida 1999; Lewicka et al. 2017; Koba et al. 2009; Ibraim et al. 2019) (Fig. 7.5).

N₂O isotopocules at natural abundance levels can be analysed by isotope ratio mass spectrometry (IRMS) (Toyoda and Yoshida 1999) and more recently mid-infrared (MIR) laser spectroscopic techniques.

With N₂O isotopic analysis, the qualitative information can be added to the quantitative information gained from the concentration measurements. This is to naturally occurring differences between N₂O from various origins as a result of isotopic fractionation, which causes enrichment or depletion of the reaction product in heavy isotope. Typically, for biochemical reactions we deal with the product depleted in heavy isotopes, but different biochemical pathways show characteristic isotope fractionation, which results in larger or smaller isotope effects (ε, difference between substrate and product (Eq. 7.7)), including also possible inverse isotope effects (product enriched in heavy isotopes, negative ε).

$$ {\varepsilon}\cong{\delta}_{{\text{product}}} -{\delta}_{{\text{substrate}}} = {{\varDelta}}_{{\text{product}/\text{substrate}}} $$

(7.7)

Isotope effect is often expressed as Δ values, representing the difference between δ values of product and substrate. The values of ε should be used for a particular chemical reaction or physical transformation and describe the characteristic isotopic fractionation for this process (so-called intrinsic isotope effects), whereas Δ values may also be applied to describe an isotopic change between initial substrate and the final product, which may be due to a chain of following reactions and diffusion. This is the case e.g. for denitrification where we can mostly only determine the overall observed isotope effect between NO₃⁻ and N₂O (also called apparent or net isotope effect, Δ¹⁵N^bulk_N2O/NO3⁻) but without insight into intermediate products (NO₂⁻, NO) we cannot determine the ε values of individual reduction steps.

Due to distinct isotopic fractionation for various biochemical reactions, the N₂O isotopic studies have been often used to distinguish between different N₂O production pathways, e.g., nitrification and denitrification (Cardenas et al. 2017; Deppe et al. 2017; Köster et al. 2015; Toyoda et al. 2011; Wolf et al. 2015), or between different microorganisms involved in N₂O production, e.g. fungal and bacterial denitrification (Kato et al. 2013; Schorpp et al. 2016; Zou et al. 2014). Moreover, also N₂O reduction can be potentially monitored by N₂O isotopic data. The possible reduction of N₂O to N₂ during denitrification is associated with isotopic fractionation, which changes the isotopic signature of the residual N₂O. Therefore, isotopic analyses of residual N₂O can be used to estimate the magnitude of its reduction and thereby the N₂ production (Kato et al. 2013; Lewicka-Szczebak et al. 2017; Toyoda et al. 2011). Comprehensive reviews on the use of N₂O isotopocules to estimate N₂O dynamics are given by Ostrom and Ostrom (2011), Decock and Six (2013), Toyoda et al. (2017) and Yu et al. (2020). The main problem in the interpretation of isotopocule analysis of emitted N₂O is the parallel production, possibly from various pathways, and consumption due to reduction to N₂.

7.3.2 Principles

For a proper interpretation of the analysed isotopic values of emitted N₂O, both the possible production pathways and consumption due to N₂O reduction to N₂ must be taken into account.

To be able to identify potential production pathways, we need the basic data of the characteristic isotopic signatures for particular pathways, so called endmember values. These are obtained from the pure culture studies, where specific microorganisms are incubated separately and N₂O is collected and analysed. Numerous pure culture studies are summarised in detail in the recent review papers (Denk et al. 2017; Toyoda et al. 2017). N₂O isotopic signatures for specific pathways were also determined in controlled incubation of the whole soil by applying conditions favouring specific pathways. Such experiments were also summarised before (Denk et al. 2017; Toyoda et al. 2017). Here we present an overview of the most common pathways including results from pure culture studies and controlled soil incubations with some necessary critical selection explained below (after (Denk et al. 2017; Lewicka-Szczebak et al. 2017; Toyoda et al. 2017, Yu et al., 2020)). For each isotopic signature (δ¹⁵N^sp, δ¹⁸O, and δ¹⁵N^bulk) the rules how to properly use endmember values are explained and for each N₂O production process the range of values (minimal and maximal literature reported value), the mean (of all literature reported values) and the median (of all literature reported values) is given.

δ¹⁵N^bulk of the produced N₂O depends on the precursor isotopic signature, i.e. on soil NO₃⁻ for denitrification and soil ammonium for nitrification. Therefore, to compare any results with literature endmember values we need to calculate the N isotopic signature of the N₂O in relation to the precursor, i.e. Δ¹⁵N^bulk_N2O/NO3− for denitrification and Δ¹⁵N^bulk_NH4+ for nitrification. Some pure culture denitrification studies also reported the isotope effect between nitrite and N₂O (Δ¹⁵N^bulk_N2O/NO3−), especially for fungal denitrification, but for field studies, we usually analyse soil NO₃⁻. By calculating isotope effects between N₂O and N precursors one should be aware that the reaction progress changes the isotopic signature of the precursor: the more substrate is consumed, the more ¹⁵N enriched gets its residual pool. Therefore, the precursor N isotopic signature at the beginning and at the end of an experiment may differ depending on the reaction progress. Moreover, the δ¹⁵N of the measurable bulk N pools (by soil extraction) may deviate from the δ¹⁵N of the active N₂O producing pools if the fractionating processes are heterogeneously distributed. This is especially the case in unsaturated soils where NO₃⁻ in anoxic microsites is denitrified and thus progressively enriched in ¹⁵N, while in aerobic domains nitrification adds NO₃⁻ at a lower ¹⁵N^bulk NO₃₋ enrichment. Substantial deviation between bulk soil and active pool enrichment has been recently shown in tracer studies in the laboratory (Deppe et al. 2017) and in the field (Buchen et al. 2016). This indicates that the interpretation based on δ¹⁵N^bulk values is very complex and requires a good understanding of N transformation processes in the soil (see also Sect. 7.5).

The following endmember values can be considered:

• heterotrophic bacterial denitrification: Δ¹⁵N^bulk_N2O/NO3- determined in pure culture studies from −37 to −10‰, mean −25‰, median −23‰ (Barford et al. 1999; Granger et al. 2008; Sutka et al. 2006; Toyoda et al. 2005). The controlled soil incubation experiments targeted for bacterial denitrification (the sole contribution from bacterial Denitrification was confirmed by δ¹⁵N^SP values and ¹⁵N tracing) show much lower values from −52.8 to −39.2‰ (Lewicka-Szczebak et al. 2014).

• nitrifier denitrification: Δ¹⁵N^bulk_NH4+ from −60.7 to −53.1‰, mean −56.9‰ (Frame and Casciotti 2010);

• nitrification: Δ¹⁵N^bulk_NH4+ from −64 to −47‰, mean −57‰, median −57‰ (Mandernack et al. 2009; Sutka et al. 2006; Yoshida 1988);

• fungal denitrification: Δ¹⁵N^bulk_N2O/NO3– from −46 to −31‰, mean −38‰, median −38‰ (Rohe et al. 2014). The study of Maeda et al. (2015) provides only data of the produced δ¹⁵N^bulk and not the isotope effect, therefore is not summarised here.

δ¹⁵N^sp of the produced N₂O is independent of the precursor isotopic signature. Hence, unlike δ¹⁵N^bulk, the endmember values are identical in δ¹⁵N^sp of the produced N₂O. Therefore, the measured N₂O δ¹⁵N^sp values can be directly compared with the following endmember values:

• heterotrophic bacterial denitrification: determined in pure culture studies from −7.5 to +3.7‰, mean −1.9‰, median −1.9‰ (Sutka et al. 2006; Toyoda et al. 2005). The values obtained in the controlled soil incubation experiments targeted for bacterial denitrification from −4.7 to +1.7‰ fit within the range given by pure culture studies (Lewicka-Szczebak et al. 2014);

• nitrifier denitrification: from −13.6 to +1.9‰, mean −5.9‰, median −5.9‰ (Frame and Casciotti 2010; Sutka et al. 2006);

• fungal denitrification: from 27.2 to 39.9‰, mean 33.5‰, median 33.6‰ (Maeda et al. 2015; Rohe et al. 2014, 2017; Sutka et al. 2008). A recent study indicated also a lower δ¹⁵N^sp value for one individual fungal species, which was disregarded here due to its very low N₂O production: C. funicola showed δ¹⁵N^sp of 21.9‰ but less than 100 times lower N₂O production with nitrite compared to other species, and no N₂O production with NO₃⁻ (Rohe et al. 2014). Similarly, from the study of Maeda et al. (2015), only the values of strains with higher N₂O production were accepted for this summary (>10 mg N₂O-N g⁻¹ biomass).

• nitrification: from 32.0 to 38.7‰, mean 35.0‰, median 34.6‰ (Frame and Casciotti 2010; Heil et al. 2014; Sutka et al. 2006).

δ¹⁸O depends on the isotopic signature of several possible precursors: NO₃⁻, NO₂⁻, H₂O and O₂. For oxic processes like nitrification the incorporation of O₂ is important (Snider et al. 2011) whereas for anoxic processes the O of the substrate or of soil water can be incorporated in N₂O. Theoretically, during nitrification (hydroxylamine oxidation) O in N₂O originates from O₂ and during denitrification O from NO₃⁻ should be transferred to N₂O. But this is additionally complicated by the exchange of O atoms between soil water and denitrification intermediates (Kool et al. 2007). The extent of this exchange differs for various bacterial and fungal species (Rohe et al. 2017), but it has been shown recently that for soil incubations it is rather high (Lewicka-Szczebak et al. 2016). Therefore, soil water isotopic signatures show the largest impact on the final δ¹⁸O values of N₂O, hence it was suggested to present the results as Δ¹⁸O_N2O/H2O if dealt with denitrification (Lewicka-Szczebak et al. 2016). However, in pure culture studies, this rule works for fungal denitrification but not very well for bacterial denitrification where NO₃⁻ plays an important role as a precursor for O atoms in N₂O (Rohe et al. 2017). Because of different patterns for different processes, we present a summary of the measured, uncorrected δ¹⁸O values and additionally for denitrification we also show Δ¹⁸O_N2O/H2O values.

• heterotrophic bacterial denitrification based on controlled soil incubations: from 4.8 to 18.4‰, mean 10.4‰, median 10.2‰ (Lewicka-Szczebak et al. 2016, 2014). For heterotrophic bacterial denitrification, it is more reasonable to use the values of the controlled soil incubations (from 4.8 to 18.4‰) because pure culture studies show a large range of possible values (from 7.3 to 46.5‰ (Rohe et al. 2017; Sutka et al. 2006; Toyoda et al. 2005)) due to variable O-exchange with ambient water depending on the bacterial strain, whereas soil incubations indicated that this exchange is high (Kool et al. 2007; Snider et al. 2013) and the isotope effect between water and formed N₂O quite stable (Lewicka-Szczebak et al. 2016). The values calculated versus soil water (Δ¹⁸O_N2O/H2O) show a much narrower range from 16.7 to 23.3‰, mean 19.2‰, median 19.0‰ (Lewicka-Szczebak et al. 2016, 2014).

• nitrifier denitrification was determined in two pure culture studies (Frame and Casciotti 2010; Sutka et al. 2006). Frame and Casciotti (2010) provide the value in relation to nitrite δ¹⁸O_N2O/NO2 of −8.4 ± 1.4‰. However, δ¹⁸O of N₂O originating from nitrifier denitrification is mostly governed by δ¹⁸O_H2O due to reaction stoichiometry and additional O-exchange between water and nitrification intermediates (Frame and Casciotti 2010; Kool et al. 2010), and hence it is reasonable to express the isotope effect in relation to water, similarly as for bacterial denitrification. Based on the values presented in supplementary materials of Frame and Casciotti (2010) this value can be recalculated in relation to water giving the range of δ¹⁸O_N2O/H2O from 12.4 to 19.4‰ (Frame and Casciotti 2010). Sutka et al. (Sutka et al. 2006) provide a raw δ¹⁸O_N2O of 10.8 ± 0.5‰. Assuming the probable δ¹⁸O_H2O between −8 and −4‰, the calculated δ¹⁸O_N2O/H2O between 14.3 and 19.3‰ fits well within the defined range from (Frame and Casciotti 2010).

• fungal denitrification from 31.2 to 45.7‰, mean 36.8‰, median 36.6‰ (Maeda et al. 2015; Rohe et al. 2014, 2017; Sutka et al. 2008). The values calculated versus soil water (Δ¹⁸O_N2O/H2O) range from 42.0 to 55.1‰, mean 47.2‰, median 46.9‰ (Rohe et al. 2014, 2017; Sutka et al. 2008). The study of Maeda et al. (2015) provide only data of the produced δ¹⁸O without the O isotope signature of water, therefore the Δ¹⁸O_N2O/H2O values cannot be given.

• nitrification determined in nitrifier cultures incubated with NH₃ reported the δ¹⁸O_N2O values close to atmospheric oxygen of 23.5 ± 1.3‰ (Sutka et al. 2006). Frame and Casciotti (2010) determined a slight isotope effect resulting in δ¹⁸O_N2O/O2 of −2.9‰. Hence, for this process, the δ¹⁸O_N2O range of 23.5 ± 3‰ can be accepted (Frame and Casciotti 2010; Sutka et al. 2006). For the plots in Fig. 7.5, the δ¹⁸O_N2O values are shown, which were determined in experiments utilising the air δ¹⁸O_O2 of 23.5‰. For each case study where deviations from the typical O₂ value are known (e.g. due to consumption in water column), these values should be expressed relative to the actually measured δ¹⁸O_O2.

The most common way of identifying various N₂O producing pathways is a graphical presentation of the measured values together with the literature endmember values. From the graphs, we can often identify the dominant pathway. To obtain more precise quantitative information, the contribution of a pathway (A) can be calculated based on the measured N₂O isotopic signature (δ_N2O) using the isotope mass balance:

$$ {\delta}_{{{N}2{O}}} ={\delta}_{{\text{pathway A}}} \cdot {a} +{\delta}_{{\text{pathway B}}} \cdot \left( {1 - {a}} \right) $$

(7.8)

It must be noted that for this calculation (Eq. 7.8), the δ_N2O value may not be changed due to N₂O reduction. This is only fulfilled if reduction is inhibited, measured to be negligible or included in calculations as described below. Using one isotope signature (δ¹⁵N^bulk, δ¹⁵N^spor δ¹⁸O), we are able to determine the mixing ratios of two pathways. Applying more isotopic signatures can theoretically enable quantification of more pathways. However, the results are not very exact due to the sometimes wide ranges of possible isotopic values for different pathways and overlapping of these ranges for more pathways. For both, δ¹⁵N^sp and δ¹⁸O, the ranges for heterotrophic bacterial denitrification and nitrifier denitrification. Additional interpretation of δ¹⁵N^bulk can further help but is often problematic due to lacking information on precursor isotope values (Lewicka-Szczebak and Well 2020). To increase precision of such calculations, controlled soil incubations with the soil under study may help to determine more narrow ranges of endmember values characteristic for the particular soil (Lewicka-Szczebak et al. 2017).

But besides the mixing processes also isotopic fractionation during N₂O reduction changes the final isotopic value of the residual N₂O. During N₂O reduction to N₂ (the last step of bacterial denitrification) preferentially the N-O bonds between light isotopes (¹⁴N and ¹⁶O) are broken and as a result the residual unreduced N₂O is enriched in ¹⁵N^α and ¹⁸O. In consequence, δ¹⁵N^sp, δ¹⁸O and δ¹⁵N^bulk values of residual N₂O increase with progressing reduction. The magnitude of the shift towards higher values depends on the amount of reduced N₂O and the isotopic fractionation factor associated with the N₂O reduction. Hence, if we know the fractionation factor and the δ value of initially produced N₂O before reduction (δ₀), we can calculate the amount of reduced N₂O and thereby determine the magnitude of N₂ flux based on the measured δ value of the residual N₂O after reduction (δ_r). This is calculated according to the following isotopic fractionation Eqs. 7.9 to 7.11 by applying Rayleigh model that is valid for closed systems, either in its exact form (Mariotti et al. 1981):

$$ \frac{{1 + \delta_{r} }}{{1 + \delta_{0} }} = \left( {r_{N2O} } \right)^{{\varepsilon_{N2 - N2O} }} $$

(7.9)

or in simplified, approximated form:

$$ \delta_{r} \cong \delta_{0} + \varepsilon_{N2 - N2O} \cdot \ln \left( {r_{N2O} } \right) $$

(7.10)

where δ_r is the residual N₂O isotopic signature, after reduction, δ_o is the initial N₂O isotopic signature, before reduction, ε_N2-N2O is the isotopic fractionation factor associated with N₂O reduction and r_N2O is the residual unreduced N₂O fraction (r_N2O = y_N2O/(y_N2 + y_N2O); (y: mole fraction))

The application of the closed system model has been confirmed by several studies (Köster et al. 2015; Lewicka-Szczebak et al. 2017, 2014). However, it was also suggested that an isotopic fractionation model for open systems could be suitable (Decock and Six 2013), which is associated with smaller apparent isotope effects during N₂O reduction:

$$ \delta_{r} = \delta_{0} - \varepsilon_{\text{red}} \left( {1 - r_{N_{2}O} } \right) $$

(7.11)

To be able to determine r_N2O from N₂O isotopic values of individual samples according to the above equations, isotopic fractionation factor associated with N₂O reduction to N₂ (ε_N2-N2O) must be known. They were determined in numerous studies in controlled soil incubations (Jinuntuya-Nortman et al. 2008; Lewicka-Szczebak et al. 2014; Menyailo and Hungate 2006; Ostrom et al. 2007; Well and Flessa 2009) and the following ranges were obtained:

• ε¹⁵N^bulk_N2-N2O from −11.0 to −1.8‰ with a mean of −7.1‰ and median −7.0‰

• ε¹⁵N^sp_N2-N2O from −8.2 to −2.9‰ with a mean of −5.9‰ and median −6.0‰

• ε¹⁸O_N2-N2O values from −25.1 to −5.1‰ with a mean of −15.4‰ and median −15.9‰

In the summary, we disregarded one study which provided an inverse isotope effect for ε¹⁵N^bulk_N2-N2O and ε¹⁸O_N2-N2O (Lewicka-Szczebak et al. 2014). These values might have been a result of untypical reduction conditions in the experiment or an experimental artefact (Denk et al. 2017), therefore, they are neglected here. From the study of Lewicka-Szczebak et al. (2015) only the data of moderate reduction (from Pool1) were summarised here, because it was shown that by very intensive reduction the results can be strongly affected by N₂O diffusion. This depends on the balance between diffusive and enzymatic fractionation during N₂O reduction (Lewicka-Szczebak et al. 2014). By nearly complete N₂O reduction, we observe a relatively large impact of diffusive N₂O fractionation, resulting in residual N₂O more depleted in heavy isotopes, hence the apparent isotope effects are significantly lower, i.e. −2.7‰, −1.5‰, and −2.0‰ for ε¹⁵N^bulk_N2-N2O, ε¹⁵N^sp_N2-N2O, and ε¹⁸O_N2-N2O, respectively (Lewicka-Szczebak et al. 2015).

It is often problematic to separate the impact on the final N₂O isotopic values by the mixing endmember for the produced N₂O and by the isotopic fractionation due to N₂O reduction. The interpretations and calculations based on N₂O isotopic studies are difficult when we deal with the simultaneous variations in r_N2O and δ₀ values. Usually, to calculate r_N2O a stable δ₀ is assumed (Lewicka-Szczebak et al. 2015) and to precisely determine temporal changes in δ₀, we need independent data on r_N2O (Köster et al. 2015). In field studies, both r_N2O and δ₀ cannot be determined precisely, but the possible ranges for each parameter can be given (Zou et al. 2014).

It is often attempted to distinguish between mixing and fractionation processes by using the changes in the isotopic signatures and their relations: δ¹⁵N^sp/δ¹⁸O, δ¹⁵N^sp/δ¹⁵N^bulk, δ¹⁸O/δ¹⁵N^bulk. These relations differ for the N₂O reduction process and for mixing processes due to differences in the respective isotope effects. From literature data on N₂O reduction fractionation factors (Jinuntuya-Nortman et al. 2008; Lewicka-Szczebak et al. 2014; Menyailo and Hungate 2006; Ostrom et al. 2007; Well and Flessa 2009) the following ratios are determined:

• ε¹⁵N^sp_N2-N2O/ε¹⁸O_N2-N2O from 0.23 to 0.98 with a mean of 0.45 and median 0.36

• ε¹⁵N^sp_N2-N2O/ ε¹⁵N^bulk_N2-N2O from 0.51 to 2.78 with a mean of 0.96 and median 0.77

• ε¹⁸O_N2-N2O/ ε¹⁵N^bulk_N2-N2O values from 1.02 to 3.83 with a mean of 2.21 and median 2.25.

Although the range of possible ε_N2-N2O variations is quite large, it has been shown recently that the mean values and typical ε¹⁵N^sp_N2-N2O/ ε¹⁸O_N2-N2O ratios are well applicable for oxic or anoxic conditions unless N₂O reduction is almost complete, i.e. the ratio N₂O/(N₂ + N₂O) < 0.1, meaning more than 90% of N₂O was reduced (Lewicka-Szczebak et al. 2015).

For comparison, here are the relations between isotopic signatures of emitted N₂O resulting from mixing processes calculated based on literature ranges for mixing endmembers given above. Because of the overlapping endmember ranges, we cannot distinguish between all individual pathways, and we determine the slopes of mixing lines between selected endmember values (Figs. 7.5 and 7.6) as follows:

Fig. 7.5

Scheme of the δ¹⁵N^sp/ δ¹⁸O mapping approach to simultaneously estimate the possible range of N₂O reduction and the admixture of nitrification. The endmember values are shown according to the citations provided in the text. Note that δ⁵N values are given in relation to N substrate, which should be determined for the particular study (here 0‰ for both NO₃⁻ and NH₄⁺ was assumed). Here the mixing of bacterial denitrification and nitrification is considered. The method can be applied for other selected processes (Zou et al. 2014)

Fig. 7.6

Scheme of the δ¹⁵N^sp/ δ¹⁸O mapping approach to simultaneously estimate the magnitude of N₂O reduction and the admixture of fungal denitrification (or nitrification). The endmember values are shown according to the citations provided in the text. Note that δ¹⁸O values are given in relation to water and to air oxygen (for nitrification). Here the mixing of bacterial denitrification and fungal denitrification is considered. The method can be applied for other selected processes

• mixing between heterotrophic bacterial denitrification and nitrification:

  • δ¹⁵N^SP/ δ¹⁸O from −10.5 to 4.8 with a mean of 6.1;

  • δ¹⁵N^SP/ δ¹⁵N^bulk from −4.6 to −0.5 with a mean of −1.2;

  • δ¹⁸O/ δ¹⁵N^bulk from −1.0 to 0.1 with a mean of −0.1.

• mixing between heterotrophic bacterial denitrification and fungal denitrification:

  • δ¹⁵N^SP/ δ¹⁸O from 1.1 to 1.4 with a mean of 1.3;

  • δ¹⁵N^SP/ δ¹⁵N^bulk from −3.9 to 7.9 with a mean of −2.7;

  • δ¹⁸O/ δ¹⁵N^bulk from −2.8 to 6.4 with a mean of −2.2.

Fungal denitrification cannot be distinguished from relations including δ¹⁵N^bulk because of the overlapping range with bacterial denitrification (see Fig. 7.5). Anyway, relations including δ¹⁵N^bulk are difficult to use due to dependence of this isotope value on the precursor, which differ for nitrification and denitrification. Here the relationships must be determined with isotope effect for δ¹⁵N^bulk, i.e. using Δ¹⁵N^bulk(N₂O/NH ⁺₄ ) for nitrification and Δ¹⁵N^bulk( N₂O/NO ⁻₃ ) for denitrification (see x-axis in Fig. 7.5). Often the isotopic signatures of the precursors are not known, which make the interpretation of δ¹⁵N^bulk values rather ambiguous. Nevertheless, some studies apply the δ¹⁵N^sp/ δ¹⁵N^bulk isotope maps for distinction of mixing and fractionation processes, but for such isotope maps, systematic changes in δ¹⁵N^bulk induced by systematic changes in the N isotopic composition of one of the precursors NH₄⁺ or NO₃⁻ could be misinterpreted as reduction events (Well et al. 2012; Wolf et al. 2015). Hence, the careful monitoring of precursor isotopic signatures is needed (Zou et al. 2014).

A δ¹⁵N^sp/ δ¹⁵N^bulk isotope mapping approach allowing for assessment of minimal and maximal reduced N₂O fraction and nitrification and denitrification mixing ratios was proposed by Zou et al. (2014) (Fig. 7.5). Such an approach is most often used for distinguishing between nitrification and bacterial denitrification only. However, other cases have also been analysed (Zou et al. 2014). The calculation method presented (Fig. 7.5) assumes first mixing of N₂O from different endmembers and afterwards its partial reduction. Two mixing lines are defined–for the minimum and maximum values for both endmembers as well as two reduction lines–with maximal and minimal slope. From the intercept 1 the maximal denitrification contribution is determined whereas from the intercept 2 the minimal one. Based on the difference between the sample point and intercept 1 or 2 the reduction contribution, respectively, maximal and minimal, is also determined. However, it must be noted that in case of significant admixture of fungal denitrification or nitrifier denitrification the results may be biased.

The application of δ¹⁵N^sp/ δ¹⁸O isotope mapping approach may be easier since δ¹⁵N^sp and δ¹⁸O values are more stable in time (Lewicka-Szczebak et al. 2017; Wu et al. 2019), and δ¹⁸O values show narrower endmember ranges when compared to δ¹⁵N values. The distinction of mixing and fractionation processes is based on the different slopes of the mixing lines and the reduction line (Fig. 7.6).

Isotopic values of the samples analysed are typically located between these two, reduction and mixing, lines. Here we defined only one mixing line for the median values of bacterial and fungal denitrification and one reduction line with a mean slope. From sample’s, location, we can estimate the impact of fractionation associated with N₂O reduction and admixture of N₂O originating from fungal denitrification. We can deal with two scenarios:

• (i) Scenario 1: the N₂O emitted due to bacterial denitrification is first reduced (point move along reduction line up to the intercept 1 with dashed mixing line) and then mixed with the second endmember (point move along dashed mixing line to the measured sample point).

• (ii) Scenario 2: the N₂O from two endmembers is first mixed (point move along mixing line up to the intercept 2 with dashed reduction line) and only afterwards the mixed N₂O is reduced (point move along dashed reduction line to the measured sample point).

While both scenarios yield identical results for the admixture of N₂O from fungal denitrification, the resulting reduction shift, and hence the calculated r_N2O value, is higher when using Scenario 2. It is still not clear which scenario is more realistic. The uncertainty analysis of this method has been recently presented by Wu et al. (2019) and this approach has been successfully applied in the field case studies (Buchen et al. 2018; Ibraim et al. 2019; Verhoeven et al. 2019). However, after the appearance of those publications, it has been found that other δ¹⁸O values should be applied for nitrification (Yu et al., 2020). This summary reports the most current choice of endmember ranges, which differ from those presented recently (Buchen et al. 2018; Ibraim et al. 2019; Lewicka-Szczebak et al. 2017; Verhoeven et al. 2019; Wu et al. 2019).

7.3.3 Analysis of N₂O Isotopocules by IRMS

The most common method for N₂O isotopocule analysis is isotope ratio mass spectrometry (IRMS). In order to perform N₂O isotopic analysis the gas samples need to be purified, and N₂O must be separated and pre-concentrated. First, water and CO₂ are removed by chemical traps, and then N₂O is concentrated with liquid N traps. Afterwards, the gases are separated with gas chromatography and finally introduced in the isotope ratio mass spectrometer.

In the mass spectrometer, N₂O isotopocule values are determined by measuring m/z 44, 45 and 46 of the intact N₂O⁺ ions as well as m/z 30 and 31 of NO⁺ fragment ions. This allows the determination of average δ¹⁵N (δ¹⁵N^bulk), δ¹⁵N^α (δ¹⁵N of the central N position of the N₂O molecule), and δ¹⁸O (Toyoda and Yoshida 1999). δ¹⁵N^β (δ¹⁵N of the peripheral N position of the N₂O molecule) is calculated from δ¹⁵N^bulk = (δ¹⁵N^α + δ¹⁵N^β) / 2 and ¹⁵N site preference (δ¹⁵N^sp) from δ¹⁵N^sp = δ¹⁵N^α–δ¹⁵N^β. Since the IRMS approach was developed simultaneously by two groups (Brenninkmeijer and Röckmann 1999; Toyoda and Yoshida 1999), two different nomenclatures had been introduced for the two positions of N₂O-N. Hence, in some studies, the peripheral (β) position is referred to as 1- and the central (α) as 2-position (Brenninkmeijer and Röckmann 1999). The scrambling factor resulting from the exchange of ¹⁵N atoms on the ion source must be taken into account. The magnitude of the scrambling factor should be determined individually for each mass spectrometer (Röckmann et al. 2003). Also, ¹⁷O-correction should be taken into account, because ¹⁷O substitution is indistinguishable from ¹⁵N, therefore typical terrestrial ¹⁷O content (0.528) is assumed (Kaiser and Röckmann 2008).

Up to now, there are still no internationally agreed gaseous N₂O reference materials for N₂O isotopocule analyses. Usually, the laboratories calibrated pure N₂O gas for isotopocule analyses in the laboratory of the Tokyo Institute of Technology according to the method of Toyoda and Yoshida (1999). Recently, the first interlaboratory comparison has been performed and now the standards from this study (REF1, REF2) are available for the laboratories and allow the performing of two-point calibration for δ¹⁵N^sp values (Mohn et al. 2014). This intercalibration study has shown that the two-point calibration method is necessary to obtain accurate δ¹⁵N^sp values. Recently, two N₂O standards had been tested in a further interlaboratory comparison (Ostrom et al. 2018) and is available from United States Geological Survey (USGS).

The sample volume needed for the N₂O isotopocule depends on the concentration and is about 100 ml for ambient N₂O concentration samples (about 300 ppb) and about 10 ml for N₂O concentration of above two ppm.

7.3.4 Laser Spectroscopic Analysis of N₂O Isotopomers to Differentiate Pathways

The invention and availability of non-cryogenic light sources in the mid-infrared (MIR) spectral range (Brewer et al. 2019) coupled with different detection schemes such as direct absorption quantum cascade laser absorption spectroscopy (QCLAS) (Mohn et al. 2010, Mohn et al. 2012, Wächter et al. 2008), cavity ring down spectroscopy (CRDS) (Erler et al. 2015) and off-axis integrated-cavity-output spectroscopy (OA-ICOS) (Wassenaar et al. 2018) has provided sensitive and field-deployable laser spectroscopic analysers for N₂O isotopocule analysis. These instruments can analyse the N₂O isotopic composition in gaseous mixtures (e.g. ambient air) in a flow-through mode, providing real-time data with minimal or no sample pre-treatment, which is highly attractive to better resolve the temporal complexity of N₂O production and consumption processes. Most importantly, MIR laser spectroscopy is selective for ¹⁷O, ¹⁸O and position-specific ¹⁵N substitution due to the existence of characteristic rotational-vibrational spectra (Gordon et al. 2017).

Therefore, laser spectroscopy has the potential to open a new field of research in the N₂O biogeochemical cycle, but, applications remain challenging and are still scarce for the following main reasons: (1) laser spectrometers as any analytical instrument are subject to drift effects, in particular under fluctuating environmental conditions, limiting their performance (Werle et al. 1993); (2) changes in N₂O concentration affect N₂O isotope results when using the δ-calibration approach (Griffith 2018); (3) laser spectroscopic results are affected by mole fraction changes of atmospheric background gases (N₂, O₂, and Ar), called gas matrix effects, due to the difference of pressure-broadening coefficients, and potentially by spectral interferences from other atmospheric constituents (H₂O, CO₂, CH₄, and CO, etc.), called trace gas effects, depending on the wavelength region used in an instrument. Spectral interferences are particularly pronounced for N₂O due to its low atmospheric abundance in comparison to other trace gases; (4) only since recently two pure N₂O isotopocule reference materials (USGS51, USGS52) have been made available through the United States Geological Survey (USGS) (Ostrom et al. 2018), which was identified as a major reason limiting interlaboratory compatibility (Köster et al. 2013; Mohn et al. 2014, 2016).

In a recent study, the most common commercially available N₂O isotope laser spectrometers were carefully characterised for their dependence on N₂O concentration, gas matrix composition (O₂, Ar) and spectral interferences caused by H₂O, CO₂, CH₄ and CO to develop analyser-specific correction functions. In addition, the authors suggest a step-by-step workflow that should be followed (Fig. 7.7) by researchers to acquire trustworthy N₂O isotopocule results using laser spectroscopy (Harris et al. 2020).

Fig. 7.7

Workflow to acquire trustworthy N₂O isotopocule results using laser spectroscopy (Harris et al. 2020)

7.3.5 Hands-on Approach to Use a CRDS Isotopic N₂O Analyser

Introduction

As an example, the Picarro G5101-i analyser can be used to determine N₂O concentration, ¹⁵N^bulk isotope ratios and isotopomer values (¹⁵N^α and ¹⁵N^β) by continuous or discrete sample measurement. Small volume discrete samples (≤20 ml) can be measured using the SSIM (small sample isotope module) (see also Sect. 5.3.) peripheral unit in conjunction with the Picarro G5101-i analyser. The G5101-i analyzer is the predecessor of the current G5131-i analyzer which also measures δ¹⁸O in addition to δ¹⁵N^bulk, δ¹⁵N^α and δ¹⁵N^β. The SSIM can also be used to dilute samples. Larger volume samples (e.g. Tedlar bags) can be measured by direct input into the G5101-i analyser or through the 16-port distribution manifold. The 16-port distribution manifold allows for partial automation of measurement and can be used in conjunction with the SSIM for smaller volume samples (see also Fig. 5.5 that illustrates the coupling of a 16-port manifold and a SSIM). The SSIM can also be used to dilute samples.

Principle

Samples are measured using mid-IR laser by CRDS (cavity ring down spectroscopy). Measurement precision increases with measurement time. Several options are available for delivery of N₂O samples into the analyser and how long measurements take. Sample volume and the required precision of measurements should be considered to decide which operational set up is the most appropriate.

Apparatus

• Picarro G5101-i isotopic N₂O analyser and pump.

• Picarro SSIM peripheral unit.

• Picarro 16-port distribution manifold.

• Gas-tight syringe.

• Pressure regulators.

• Stainless steel tubing.

• Swagelock fittings.

• Injector nut for SSIM.

Consumables

• Zero Air.

• N₂O working standards.

• Septa for injector nut on SSIM.

• Septa capped vials for discrete gas samples.

• Tedlar bags for larger volume gas samples.

• Side port needles for sample injection to SSIM.

Sampling

For discrete gas samples follow a suitable sampling procedure as outlined by De Klein and Harvey (2012). Small volume samples (≤20 ml) should be stored in septum capped vials, ensuring to overpressure when filling to prevent inward contamination by ambient air. Vials can be stored in a cool dry place. Larger volume samples in Tedlar bags should be measured ASAP as storage reliability decreases greatly after 24–48 h.

Operational Procedure

• To start the analyser, ensure the power switches are on for the pump, analyser and monitor. Turn the power switch at the rear of the analyser from O to I. NB: the power switch on the pump should always be in the on position, the pump will power up when the analyser is turned on. To turn on the analyser press the button on its front. Windows will load on the monitor and the analyser software will run through the system checks.

• When the analyzer is in startup mode, monitor the liquid coolant at the back of the analyzer. You should observe little to no bubbles and the fluid should be flowing. If the bubbles have not disappeared after a few minutes or the liquid is not flowing, refer to the troubleshooting section in this document.

• After the system checks are complete, the GUI (Graphical User Interface) will appear. It will begin by measuring the Cavity Pressure, DAS (Data Acquisition System, i.e. the analyser) temperature and Etalon temperature. Once the correct temperatures and pressures are reached a message will appear on the bottom of the GUI screen; e.g. “Pressure locked”, “Cool Box Temperature locked”, “Preparing to measure”, Measuring…”. The GUI will then begin to show the continuous N₂O measurements in real time. It may take up to 1 h for the analyser to begin N₂O measurements. Before measuring samples, allow the laser to stabilise for up to 24 h by measuring room air.

• Continuous samples (e.g. incubation experiments) can be measured by directly connecting a piece of tubing from the sampling container to the inlet at the back of the analyser and segmenting the data into the respective time periods.

Discrete samples (≤20 ml)

• To measure small volume discrete samples (≤20 ml) allow the laser to run continuously for 24 h to ensure that the laser has been given sufficient time to stabilise.

• Before operating the SSIM check that the “Valve Seqeuncer MPV” is turned off. To do this click Shutdown on the GUI and select “Software Only”. Double click on the Picarro Utilities icon located on the desktop and double click on “Setup Tool”. Under the “Port Manager” tab check that the “Valve Sequencer MPV” is turned off. If necessary change this setting to off and close the Picarro Utilities folder.

• Restart the GUI software by double clicking on the Picarro Switcher Mode icon located on the desktop and select the Isotopic N₂O option followed by clicking Launch.

• In the standard GUI mode, the H₂O parameter is not available from the Data Key drop-down menus. This is necessary to check for pressure leaks in the system. To access this, log into the service GUI mode under the settings tab of the GUI. The password is “picarro”.

• In the cylinder cabinet open the zero air (ZA) cylinder followed by opening the valve to the lab (do not open the exhaust valve–this will drain the ZA cylinder). Record the overall pressure remaining in the cylinder before and after each use. The pressure regulator in the cabinet should be set to 3.5 bar when the cylinder and line valve are open. This will drop to around 3 bar when the pressure regulators at the lab bench are opened.

• At the lab bench, open the black valve at the first pressure regulator on the ZA line to the SSIM and adjust slowly to 1.5 bar. This will rise to 2 bar when it meets the resistance of the SSIM.

• The second pressure regulator has been set to 3 psi (following Picarro’s recommendations), check to ensure this is the case and only adjust if necessary. Never allow the final pressure into the SSIM to go above 8 psi. The indicator on the valve may flicker during operation due to valve switching within the SSIM.

• Connect the stainless steel tubing from the SSIM to the analyser. Finger tighten and then apply a ¼ turn using the adjustable spanner.

• Connect the grey (valve switching controls) and black (pressure detector) cables from the analyser to the SSIM. This will power on the SSIM, indicated by the green light on the front of the unit.

• NB Turn on the SSIM vacuum pump. This must be done before launching the SSIM software.

• Launch the SSIM software by double clicking on the “SSIM Pressure Detector” icon. This locates the COM port (COM 7) of the analyser that the SSIM is connected to. Leave this software window open while using the SSIM.

• Measure the Zero Grade Air only for 30 min before beginning sample analysis. This is to obtain the average N₂O concentration, ¹⁵N^bulk, ¹⁵N^α and ¹⁵N^β of the Zero Grade Air, necessary for correcting concentration dilution and isotope mixing.

• Double click on the “SSIM Coordinator” from the desktop and select G5101-i. Configure the settings to suit the measurement procedure required. There are nine parameters (1–9) to be set.

• 1. Multi-Port Valve: 1 = Use 16 Port Distribution Manifold; 2 = Don’t Use 16 Port Distribution Manifold. [Select 2 for SSIM only].

• 2. If using Multi-Port Valve: Number of Sample Ports (between 1 and 8). [Select 1 for SSIM only].

• 3. Number of Repeats per Sample (between 0 and 5). [Select 1].

• 4. Number of Repeats per Standard (between 0 and 5). [Select 0].

• 5. Standard Mode: 1 = Between Each Sample; 2 = Beginning and End. [Select 2].

• 6. Measurement Mode: 1 = One Time; 2 = Continuous Loop. [Select 2].

• 7. Measurement Speed: 1 = Standard, 2 = Fast. [Select 2] (Fast is approximately 10 min per sample/ Standard is approximately 15 min per sample).

• 8. Sample Loading: 1 = Manual; 2 = Automatic; 3 = Syringe. [Select 3].

• 9. Sample Dilution: 1 = No Dilution; 2 = Dilute Sample with ZA. [Select 2 for samples < 20 ml. Select 1 for samples >20 ml].

  • Click OK. Select G5101-i for reference standard.

  • SSIM pressure measurements should be available in the GUI data key drop-down tabs. Select this parameter to monitor SSIM pressure visually on the left side of the GUI.

Note: Under vacuum, the SSIM pressure should be ~8 Torr or below. When a sample is injected the max pressure is reached upon filling the cavity with sample/ ZA. The max pressure should read between 980 and 1000 Torr. If the pressure is too high down-regulate the second pressure regulator. If the pressure is too low up-regulate the second pressure regulator being very careful not to exceed 8 psi.

• Overlay the SSIM Coordinator screen on to the bottom right corner of the GUI screen. This allows the user to monitor the parameters on the left side of the GUI while following the prompts of the SSIM Coordinator.

• Follow the steps indicated on the SSIM Coordinator screen to process each sample.

• The first prompt requires the operator to inject the sample syringe with the valve closed and to click “Resume” under “Control”. The SSIM coordinator will then run through several valve sequencing steps.

• The next prompt to the operator is to open the syringe valve and to click “Resume” under “Control”. The SSIM coordinator will then run through several valve sequencing steps.

• The operator will then be prompted to inject the sample. The sample will begin to draw itself in but the operator may be required to manually complete the injection depending on the sample volume. Once the sample is fully injected, close the syringe valve. Allow the SSIM pressure reading to settle and record this pressure value followed by clicking “Resume” under “Control”. NB–Always manually record the SSIM pressure as it settles after sample injection, and record the max SSIM pressure when the ZA dilution is carried out. This is used to work out the actual volume of a sample using the pressure vs volume calibration curve.

• The SSIM coordinator will then begin the dilution process. NB–watch the SSIM pressure readings and record the maximum pressure reached during the dilution step.

• The SSIM will then begin the sample measurement. At this stage, the syringe can be removed from the injector nut to prepare for the next sample injection.

• Before each measurement day, complete a pressure vs volume calibration curve. Use room air injected at the following volumes: 0 ml, 5 ml, 10 ml, 15 ml and 20 ml. To complete the 0 ml point do not inject the syringe, instead allow the zero air to fill 20 ml (cavity volume) into the SSIM.

Note: The calibration curve should be almost perfectly linear with a R² = 0.99 +. Deviations from the curve or lower R² values may indicate a leak. Check the injector nut and septum, change septum if necessary. Check the ZA line connections from the SSIM unit to the analyser. Tighten loose connections if necessary by finger tightening + ¼ turn with an adjustable spanner. Never over tighten as this can lead to leaks.

• To check the instrument precision and to avoid measurement drift, it is recommended that a room air/zero blank is run after every 10 samples. A reference standard or working standard may also be used if available.

• To discontinue SSIM use and return to continuous measurement reverse the order of the SSIM setup steps. Close the SSIM Coordinator window. (Note: a system alarm will appear on the GUI, this is normal) Close the SSIM pressure detector window. Turn off the SSIM vacuum pump. Disconnect the grey and black cables from the SSIM. Disconnect the stainless steel tubing from the SSIM output. Close the black valve on the first pressure regulator at the lab bench and close this regulator by turning in the decrease direction. Close the valve and the ZA cylinder in the cylinder cabinet.

Note: A system alarm will probably appear on the top left of the GUI and a message stating “Pressure unlocked”. This results from the SSIM being disconnected. To resolve: click Shutdown and select “Stop Analyser Software Only”. Wait a couple of minutes and relaunch the analyser software by double clicking on the Picarro Switcher Mode icon on the desktop and selecting G5101-i Isotopic N₂O and click launch. Monitor the system as it relaunches and wait until it begins measuring N₂O parameters.

• To turn off the instrument completely click shutdown on the GUI.

NB: Never leave the analyser measuring ZA overnight, this will lead to drift.

Expression of Results

• N₂O concentration is expressed as ppb.

• δ ¹⁵N^bulk is expressed as permil (‰).

• δ ¹⁵N^α is expressed as permil (‰).

• δ ¹⁵N^β is expressed as permil (‰).

Quality Assurance

• Prior to taking gas samples in the field (i.e. from static chamber) ensure vials are properly sealed and that they have been flushed and evacuated three times.

• Ensure samples are injected with slight overpressure (e.g. 20 ml into 12 ml vial) to avoid inward contamination that would dilute the sample concentration.

• Ensure samples are stored in a cool dry place. Process samples as quickly as possible. Vials lose pressure over time. Avoid storing in direct sunlight.

• The laser should be given sufficient time to stabilise. 24 h is recommended prior to measuring samples.

• Before each measurement day, complete a pressure vs volume calibration curve as described above. Check for leaks based on any variation detected.

• Ensure the septum in the injector nut is replaced approximately every 100 injections.

• Use side bore needles to reduce the damage caused to the septum.

• For acceptable precision and accuracy ensure that sample concentrations are within the stated operating range of the analyser (300–1500 ppb N₂O).

• Minimise moisture (H₂O) in samples. Use drying tubes to introduce samples to the analyser if necessary.

• Use a gas-tight syringe to inject discrete samples into the SSIM. If using a plastic syringe and with a three-way valve, replace when necessary due to wear and tear.

• Never leave the analyser measuring ZA overnight. This will cause measurement drift.

Reporting of Results

Raw data files are automatically generated by the analyser and are stored on the instrument’s computer as a DataLog_User file. These raw data files can be found by following the file path: C:\UserData\DataLog_User\Year\Month\Day. An example of the file naming convention is JBDS5030-20170331-140739Z-DataLog_User. JBDS5030 refers to the instrument serial number. 20170331 is the Year, Month and Date the file was started. 140739 is the Hour, Minute and Second of when the file was started. There are a number of values available for the N₂O parameters measured. The dry corrected values are the appropriate values to select for analysis.

When measuring discrete samples using the SSIM there is sufficient time between samples to record the real-time values on a separate spreadsheet that has been premade with sample reference numbers included.

Safety

• When using syringes and needles for sampling and analysis, take extra care to avoid needle stick injuries.

• Regularly check the pressure reading of the instrument and the pressure regulators on the ZA line.

• Never handle pressurised gas cylinders without the appropriate safety training and certification.

• If moving the instrument, always ensure it is shut down so that the cavity returns to ambient pressure and does not remain under vacuum.

• There are a number of valve sequences during operation of the SSIM. Ensure to follow the prompts carefully to avoid loss of sample or pressure build ups.

• Read and follow the information in the Risk Assessments for the Stable Isotope Analysis lab.

Trouble Shooting

• Start-up:

If the chiller line contains large air bubbles this may stop the circulation of water in the line. This can lead to the baseplate temperature being exceeded which causes the analyser to enter safe mode (error message appears in GUI). This problem should be avoided by keeping the cooling agent LIQ-702 (propylene glycol) in the buffer tank (externally mounted on the chiller cover) topped up to 90% of its full volume with deionised water. To do this unscrew the black cover and use a wash bottle to add in fresh deionised water. This can be done while the analyser is running. If the error message does appear this may require the instrument to be shut down and for the chiller line be flushed following the instructions provided in the installation manual for the installation of the water buffer tank.

7.3.6 Accuracy, Precision and Bias

The analytical precision for IRMS measurements determined as standard deviation (1σ) of the internal standards for measurements of δ¹⁵N^bulk, δ¹⁸O and δ¹⁵N^sp is typically 0.1, 0.1 and 0.5‰, respectively. Commercially available laser spectrometers at ambient N₂O concentrations offer a precision of 0.2 to 1 ‰ for δ¹⁵N^α, δ¹⁵N^β and δ¹⁸O, which can be reduced to 0.1 ‰ at higher concentrations, or by using a preconcentration device. However, from the inter-comparison study, we see that the bias may be much larger, up to: for δ¹⁵N^bulk 0.8 and 2.8‰, and for δ¹⁵N^sp 4.3 and 3.7‰ for mass spectrometry and for laser spectroscopy, respectively (Mohn et al. 2014). But these potentially large errors can be minimised by a proper data calibration using two points standardisation with the reference gases that bracket the measurement range. Care must be also given when samples with high concentrations are diluted as the dilution matrix (typically Helium or N₂) may apparently have an impact on the final result. The rule of identical treatment of standards and samples should be held, including identical dilution matrix and similar concentration range (Mohn et al. 2014).

Possible bias is also associated with calculations applied for data interpretation. Due to large ranges of literature data, the N₂O source partitioning cannot be done precisely, but rather the ranges of possible results can be given. To increase precision of such methods controlled soil incubation can be applied to determine the soil specific endmember isotopic values or fractionation factors (Lewicka-Szczebak et al. 2017).

7.3.7 Examples of Laboratory Applications

Köster et al. (2015)

This experiment applied an N₂O isotopocule approach combined with conventional N₂O and N₂ flux measurements to study microbial pathways after different organic fertiliser applications. The direct determination of emitted N₂ was used to take isotope effects during N₂O reduction to N₂ into account. The measured isotope signatures were corrected for isotope effects during N₂O reduction with Eq. 7.10 using previously determined fractionation factor ranges. Based on the corrected values the isotope mass balance equations (Eq. 7.8) for δ¹⁵N^sp and δ¹⁸O were applied. The ranges for different pathways contribution were given for δ¹⁵N^sp- and δ¹⁸O-based results and the common area for both was accepted as most probable. Two mixing scenarios were considered: bacterial denitrification and nitrification or bacterial and fungal denitrification. Although the range of possible results for endmembers contribution varied up to 30%, a clear increase in nitrification contribution with the incubation time has been documented.

Schorpp et al. (2016)

In this experiment, incubations with soil fauna were applied to check the impact on N₂O and N₂ emission of anecic earthworms and euedaphic collembola. Isotopocule approach was applied together with ¹⁵N tracing. Interpretation of the isotopocule results based on the δ¹⁸O-δ¹⁵N^sp isotope map, similar as presented in Fig. 7.6, including three possible mixing endmembers: bacterial and fungal denitrification and nitrification (hydroxylamine oxidation) and taking N₂O reduction into account. Isotope data allowed concluding that the presence of collembolans shifted the process pathways towards bacterial denitrification although no change in N₂O concentration could be noted.

Deppe et al. (2017)

In this incubation experiment high NH₄⁺ concentrations in soil were established to check the supposed inhibition of nitrification. An isotopocule approach, together with ¹⁵N tracing and acetylene inhibition approach, was applied to gain insight into N₂O production processes. Interpretation of the isotopocule results based on the δ¹⁸O-δ¹⁵N^sp isotope map, similar as presented in Fig. 7.6, including two mixing endmembers: denitrification and nitrification (hydroxylamine oxidation) and N₂O reduction. This assumption of the mixing conditions appeared incorrect, since some data were located outside of the mixing and reduction lines. This indicated a substantial contribution of nitrifier denitrification and/or coupled nitrification-denitrification (10–40%) to total N₂O production.

Cardenas et al. (2017)

Laboratory incubation was carried out at different saturation levels for a grassland soil and emissions of N₂O and N₂ were measured as well as the N₂O isotopocules. Thanks to direct measurements of N₂ flux, the extent of N₂O reduction was known. Hence, the measured δ values were mathematically corrected to obtain the δ values of the produced N₂O before reduction applying Eq. 7.9. An endmember mixing model (Eq. 7.8) was then used to calculate the percentage of bacterial N₂O in the total N₂O flux based on δ¹⁵N^sp and δ¹⁸O. To assess the uncertainty of this approach the ranges of possible endmembers isotopic signatures and reduction fractionation factors were taken into account. The variations of the bacterial N₂O contribution due to assumed ranges of input values reached up to 40%. But still it allowed to distinguish the dominant pathways for different water saturation levels and indicated that only when the micropores become partially dry, the more aerobic soil conditions allow a higher contribution of nitrification. The dryer conditions in soil macropores did not result in significant changes in bacterial denitrification contribution.

7.3.8 Examples of Field Applications

Toyoda et al. (2011)

N₂O emitted from agricultural soils planted with rice, wheat, soybean, and vegetables, and treated with synthetic (urea or ammonium) and organic (poultry manure) fertilisers was analysed. The observed isotopic values for Δ¹⁵N and δ¹⁵N^sp were compared with literature endmembers of nitrifying and denitrifying bacteria. A characteristic relationship between δ¹⁵N^bulk and δ¹⁵N^sp during N₂O reduction by denitrifying bacteria was used to quantify N₂O reduction. The relative fraction of N₂O derived from nitrification and the approximate progress of N₂O reduction were calculated by a Monte Carlo method. Different scenarios for pairs of mixing endmembers were tested (nitrification and denitrification; nitrification and nitrifier–denitrification; fungal denitrification and denitrification; fungal denitrification versus nitrifier–denitrification) but due to overlapping ranges for δ¹⁵N^sp values it was chosen to consider only the mixing between bacterial nitrification and denitrification. It was found that the contribution from nitrification was relatively high (40%–70%) in soils amended with synthetic ammonium fertiliser, while denitrification was dominant (50%–90%) in the same soils amended with poultry manure.

Kato et al. (2013)

In this study, field samples from static flux chambers located on alpine meadow, shrub and wetlands were collected and analysed. Interpretation of results based on the relationship between δ¹⁵N^bulk and δ¹⁵N^sp (similar as presented in Fig. 7.5). A mixing of two endmembers was assumed: bacterial and fungal denitrification and subsequent N₂O reduction. Applying literature values for endmembers and fractionation during reduction the contribution of fungal denitrification (from 23 to 41%) and degree of reduced N₂O (from 83 to 93%) was calculated. The calculations were performed with Monte Carlo simulations and the assessed uncertainty of the results ranged from 17 to 23% for contribution of mixing endmembers and from 10 to 19% for degree of reduced N₂O.

Zou et al. (2014)

Soil gas was collected from a highly fertilised tea field at 10–50 cm depths using a silicone tube. δ¹⁵N^sp –Δ¹⁵N^bulk isotope maps (Fig. 7.5) were applied for interpretations. The precursor isotopic signatures were determined, and the endmember ranges have been recalculated according to the measured precursor values for bacterial and fungal denitrification, nitrification and nitrifier denitrification. For the N₂O reduction two scenarios were taken into account: assuming reduction after mixing and applying closed system dynamics and assuming reduction preceding mixing and applying open system dynamics. Predictions of δ¹⁵N^sp values for different scenarios, reduction degrees and mixing ratios were presented and compared to the measured results. The study identified the bacterial denitrification as the dominant process and allowed for indication of the particular events when the contribution of nitrification or fungal denitrification increased pronouncedly.

Wolf et al. (2015).

N₂O isotopic analyses were done directly from the atmospheric surface layer (at 2.2 m height) applying a laser spectrometer connected to an automated N₂O pre-concentration unit. The isotopic signatures of soil-emitted N₂O were derived using the Keeling plot approach, where δ values measured in the atmosphere surface layer are plotted versus the inverse of N₂O mole fractions (for a background on Keeling plot analysis see Pataki et al 2003). The intercept of the linear regression line is interpreted as the isotopic composition of soil-emitted N₂O. The interpretation of the results is based on isotope maps of δ¹⁵N^sp vs. δ¹⁵N^bulk and δ¹⁵N^sp vs. δ¹⁸O. These isotope maps allowed concluding that N₂O was predominately formed by bacterial denitrification and that variations in isotopic composition may have been caused predominately by N₂O reduction to N₂. The study did not attempt to quantify the mixing ratios or N₂O reduction. The high-frequency isotope data was combined with a biogeochemical model Landscape DNDC with a stable isotope model for nutrient cycles (SIMONE) to identify and address weaknesses in N cycling of the model (Denk et al. 2019).

7.3.9 Outlook

N₂O isotopocule analyses provide a unique possibility to get insight into processes contributing to N₂O production as well as to assess the magnitude of N₂O reduction and thereby also N₂ flux. However, the information is still rather indicative than strongly quantitative. The calculation methods presented allow estimates of ranges of possible mixing ratios and reduction contribution rather than precise numbers. However, such information is also quite precious hence often not attainable by any other methods. ¹⁵N tracing, which is often a more precise tool, is much more expensive and laborious, moreover applicable only on a very limited space and time scale, hence much more constrained in application potential.

A promising perspective is to apply the N₂O isotopocule analyses in combination with other methods, like with ¹⁵N tracing (Deppe et al. 2017; Schorpp et al. 2016) (see also Sect. 7.5.) or with process modelling (Bai and Houlton 2009; Denk et al. 2017) which vastly increases the interpretation potential of such studies. Moreover, more quantitative estimates can be expected if the isotopocule approach is calibrated using controlled incubations where endmember values and isotopic fractionation factors are determined for specific conditions using independent estimates of contributing processes, e.g. by direct measurement of N₂ production or ¹⁵N tracing (Lewicka-Szczebak et al. 2017; Wu et al. 2019). The most recent idea for interpretation of N₂O isotope data is the application of a N₂O isotopocule model which incorporates all three measured isotopic signatures (δ¹⁵N^bulk, δ¹⁵N^sp and δ¹⁸O) (Lewicka-Szczebak and Well 2020).

7.4 Dual Isotope Method for Distinguishing Among Sources of N₂O

Various microbial processes can produce N₂O (for a simplified overview, see Fig. 7.8). These may occur simultaneously in distinct soil microhabitats or take place temporally separated with fluctuating soil conditions. Often, only nitrification and denitrification are considered to be the main sources. However, the methods often applied cannot distinguish among all sources. For example, using ¹⁵N tracing with labelled ammonium or NO₃⁻ does not allow a distinction among N₂O produced by nitrifiers either via hydroxylamine (termed here nitrification, N) or via nitrite reduction (nitrifier denitrification, ND), or by denitrifiers using NO₃⁻ produced by nitrifiers (nitrification-coupled denitrification, NcD). All N₂O produced by these sources is summarised as ‘nitrification’ by authors using this method. No method based on ¹⁵N alone can so far separate the sources shown in Fig. 7.5. However, a distinction is important, as ND can under certain conditions produce all N₂O derived from NH₄⁺ and has been reported to cause up to 90% of total N₂O emissions (Kool et al. 2010).

Fig. 7.8

Overview of N₂O producing processes carried out by nitrifiers and denitrifiers in soils. Shown is also the use of O₂ versus H₂O as source of oxygen. Please note that the distinction between nitrification-coupled denitrification and fertiliser denitrification is purely methodological, as the organisms and pathways are identical, but the source of NO₃⁻ differs. Within brackets, abbreviations of the pathways as used in the text are shown. DNRA: Dissimilatory NO₃⁻ reduction to NH₃ (Wrage-Mönnig et al. 2018)

A distinction between ND and other sources of N₂O is possible if ¹⁸O labelling is used in addition to ¹⁵N labelling (Kool et al. 2011). As seen in Fig. 7.8, nitrifiers use distinct sources of O₂ for the oxidation of NH₃ and the subsequent oxidations of NH₂OH and NO₂⁻. This is used in the dual isotope method, where ¹⁸O-labelled H₂O is applied on top of ¹⁵N tracers. However, care has to be taken to account for O-exchange, which can occur between H₂O and N oxides in all reactions of N oxides shown in Fig. 7.8. This is accomplished using the enrichment ratio retention (ERR) approach, where the enrichment ratio of ¹⁸O:¹⁵N of N₂O is compared to that of NO₃⁻ in incubations with either ¹⁵N- or ¹⁸O-labelled NO₃⁻. Then, we can differentiate among N₂O produced by N, ND, NcD and fertiliser denitrification (FD).

The preparation of soil samples proceeds in a similar way as for other stable isotope methods. However, one has to keep in mind that water needs to be added as tracer, so that the water content during conditioning needs to be a bit less than intended for the incubation. So far, conditioning has been done at 40% water-filled pore space (of samples dried at 40°C), and incubation at 80%, but this is adaptable as long as the requirements for tracer additions are kept. Soil samples of 75–100 g have been incubated in glass jars of about 300 ml for 24–28 h. These ratios and times may be adapted, but care must be taken to ensure linear N₂O production over the incubation period, as well as stable concentrations of substrates (including O₂ and H₂O). Much longer incubations are difficult, as the ¹⁸O enrichment of the soil H₂O might change locally due to evaporation and addition of H₂O. The occurrence of NO₃⁻ assimilation and DNRA needs to be checked (indicated by enrichment of NH₄⁺ in incubations with ¹⁵N-NO₃⁻) and accounted for if necessary, as in other ¹⁵N methods.

The treatments (TR) are established (Table 7.5) with proper replication (at least five times) after conditioning of the soil as needed. So far, added label has been enriched at 1.0 atom% for ¹⁸O and 40 atom% for ¹⁵N, but higher enrichments may be desirable to reduce the amount of substrates added, especially concerning the N-substrates in natural systems. Usually, 100 mg N kg⁻¹ soil has been applied, half each as NO₃⁻ and as NH₄⁺. When applying less NO₃⁻, one has to consider that if NO₃⁻ becomes limiting, the underlying assumption of the method that only NO₃⁻ and no NO₂⁻ is used in NcD and FD becomes invalid. This would result in an underestimation of NcD and an overestimation of ND. Additional incubations with ¹⁸O-NO₂⁻ (which is currently not commercially available, though) or analysis of the ¹⁸O enrichment of the NO₂⁻ pool may help to overcome this.

Table 7.6 Oxygen sources of N₂O in the different processes and pathways distinguished using the dual isotope method

Immediately after establishing the treatments, the jars are closed, and samples are taken for N₂O content and isotopic signature as explained in Chap. 3 and above. At the end of the incubation, soil samples are taken for analysis of mineral N and its isotopic signature (the latter only in TR 3 and 4), as well as the soil moisture content to verify that this did not change during incubation. Consider that the label added with ¹⁸O-H₂O is diluted when mixed with moist soil.

For quantifying the O-exchange between N oxides and ¹⁸O-H₂O, the ERR approach is used. It is assumed that the O-exchange is similar for denitrifiers and nitrifiers. This need not be true, as O-exchange by nitrifiers has often been found to be less than in denitrifiers. Such a discrepancy would lead to an underestimation of the N₂O produced by ND and NcD. No O-exchange is assumed to affect N₂O derived from N. The ERR is calculated in Eqs. 7.12 to 7.17 as follows:

$$ ERR \left[ \% \right] = 100 \frac{{^{18} {\text{O}}\left( {{\text{N}}_{2} {\text{O}}_{TR2} } \right)}}{{^{15} {\text{N}}\left( {{\text{N}}_{2} {\text{O}}_{TR3} } \right)}}/\frac{{^{18} {\text{O}}\left( {{\text{NO}}_{{3_{TR2} }}^{ - } } \right)}}{{^{15} {\text{N}}\left( {{\text{NO}}_{{3_{TR3} }}^{ - } } \right)}} $$

(7.12)

where ¹⁸O(Y_TRx) and ¹⁵N(Y_TRx) denote the ¹⁸O or ¹⁵N enrichment, respectively, of substance Y from treatment x. Without O-exchange, ERR is 100%. O-exchange (O_ex) is then quantified as

$$ O_{ex} = 100 - ERR $$

(7.13)

Next, the percentage of N₂O derived from NO₃⁻ $\left( {{\text{N}}_{2} {\text{O}}_{{{\text{NO}}_{3}^{ - } }} } \right)$ and NH₄⁺ $\left( {{\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }} } \right)$ is calculated. ${\text{N}}_{2} {\text{O}}_{{{\text{NO}}_{3}^{ - } }}$ is defined as N₂O from FD, whereas N₂O_NH4+ comprises the other three sources.

$$ {\text{N}}_{2} {\text{O}}_{{{\text{NO}}_{3}^{ - } }} \left[ \% \right] = FD = 100\frac{{^{15} {\text{N}}\left( {{\text{N}}_{2} {\text{O}}_{TR3} } \right)}}{{^{15} {\text{N}}\left( {{\text{N}}_{2} {\text{O}}_{TR3} } \right) +^{15} {\text{N}}\left( {{\text{N}}_{2} {\text{O}}_{TR4} } \right)}} $$

(7.14)

$$ {\text{N}}_{2} {\text{O}}_{{NH_{4}^{ + } }} \left[ \% \right] = {\text{N}} + {\text{ND}} + {\text{NcD}} = 100\frac{{^{15} {\text{N}}\left( {{\text{N}}_{2} {\text{O}}_{TR4} } \right)}}{{^{15} {\text{N}}\left( {{\text{N}}_{2} {\text{O}}_{TR3} } \right) +^{15} {\text{N}}\left( {{\text{N}}_{2} {\text{O}}_{TR4} } \right)}} $$

(7.15)

If the ¹⁵N enrichment of N₂O in TR4 does not exceed the ¹⁵N enrichment of NO₃⁻ in the same treatment, all ${\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }}$ might have been derived from NcD (maximum contribution of ${\text{NcD}},{\text{NcD}}_{\text{max} } = {\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }}$, implying that ND and N were equal to zero). If not, NcD_max is calculated as follows:

$$ {\text{NcD}}_{\text{max}} \left[ \% \right] = {\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{ + } }} \times \frac{{^{15} {\text{N}}\left( {{\text{NO}}_{{3_{TR4} }}^{ - } } \right)}}{{^{15} {\text{N}}\left( {{\text{NO}}_{{3_{TR4} }}^{ - } } \right) + {^{15}} {\text{N}}\left( {{\text{NH}}_{{4_{TR4} }}^{ + } } \right)}},\,{\text{if}}\,^{15} {\text{N}}({\text{N}}_{2} {\text{O}}_{{{\text{TR}}4}} ) >^{15} {\text{N}}\left( {{\text{NO}}_{3} {^{ - }} {_{{{\text{TR}}4}}} } \right) $$

(7.16)

To distinguish among the other N₂O producing pathways considered, the actual O incorporation from H₂O into N₂O (AOI) is determined from TR1:

$$ AOI \left[ \% \right] = 100 \frac{{^{18} O\left( {N_{2} O_{TR1} } \right)}}{{^{18} O\left( {H_{2} O_{TR1} } \right)}} $$

(7.17)

This AOI may come from O_ex quantified as shown above and the reaction stoichiometry of the different pathways as shown in Table 7.6.

A large AOI may thus be caused either by a larger contribution of pathways with a larger incorporation of ¹⁸O-H₂O (ND or NcD) or by a larger O_ex. For further evaluation, O_ex is maximised, i.e. assumed to take place in the NH₄⁺-derived pathways to the same extent as in FD (Scenario A) or minimised, i.e. assumed to be absent in nitrification pathways (Scenario B). Furthermore, in Scenario A, the contributions of N and NcD are maximised, while in Scenario B, ND is maximised. Under both scenarios, a theoretical O incorporation (TOI) is calculated and compared to the AOI.

Under Scenario A, the TOI (TOI_A) is calculated (Eq. 7.18) as

$$ TOI_{A} = N_{2} O_{{NO_{3}^{ - } }} \times O_{ex} + NcD_{\text{max}} \left( {2/3 + 2/3O_{ex} - 1/3\left( {O_{ex} } \right)^{2} } \right) $$

(7.18)

This calculation comprises O_ex occurring during D (${\text{N}}_{2} {\text{O}}_{{{\text{NO}}_{3}^{ - } }} \times {\text{O}}_{\text{ex}}$) as well as from NcD stoichiometry (2/3 O from H₂O) and O_ex occurring during N to NO₃⁻ and NcD (for further explanation, see Appendix 1 in Kool et al. 2009). If TOI_A ≥ AOI, no contribution by ND is necessary to explain the AOI. The minimal contribution of ND, ND_min, is then set to zero, and the maximum contribution of N, ${\text{N}}_{\text{max} } = {\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }} {-}{\text{NcD}}_{\text{max} }$. If not, ND must have contributed to N₂O production (ND_min > 0), which implies at the same time a maximum contribution of N, N_max $\left( {{\text{N}}_{\text{max} } < {\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }} {-}{\text{NcD}}_{\text{max} } } \right)$. In this case, we can calculate the contribution of ND_min (Eq. 7.19) as follows:

$$ ND_{\text{min}} = \frac{{AOI - (N_{2} O_{{NO_{3}^{ - } }} \times O_{ex} )}}{{2/3 + 2/3O_{ex} - 1/3(O_{ex} )^{2} }} - NcD_{\text{max}} $$

(7.19)

N_max is then equal to ${\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }} {-}{\text{NcD}}_{\text{max} } {-}{\text{ND}}_{\text{min} }$.

Under Scenario B, ND is maximised by assigning ${\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }}$ to ND and assuming no O_ex during this pathway, and in Eq. 7.20 TOI_B is calculated as

$$ TOI_{B} = N_{2} O_{{NO_{3}^{ - } }} \times O_{ex} + N_{2} O_{{NH_{4}^{ + } }} \times 0.5 $$

(7.20)

If TOI_B > AOI, not all ${\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }}$ can have been derived from ND $\left( {{\text{ND}}_{\text{max} } < {\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }} } \right)$. In that case, some N₂O must have originated from N (i.e. the minimum contribution of N, N_min > 0), which will lower the TOI. However, if TOI_B ≤ AOI, all ${\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }}$ may have come from ND $\left( {{\text{ND}}_{\text{max} } = {\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }} } \right)$ and the contribution of N_min was zero. A larger AOI (TOI_B < AOI) may either come from a contribution of NcD or O_ex during ND, which was assumed not to take place under this scenario. As both may equally well explain the numbers, NcD_min is set to zero in this case and O_ex assumed to have occurred during ND.

If N_min was found to be larger than zero, we can calculate ND_max from this scenario as follows (Eq. 7.21):

$$ ND_{\text{max}} = \frac{{AOI - N_{2} O_{{NO_{3}^{ - } }} \times O_{ex} }}{0.5} $$

(7.21)

In that case, ${\text{N}}_{\text{min} } = {\text{N}}_{2} {\text{O}}_{{{\text{NH}}_{4}^{+} }} {-}{\text{ND}}_{\text{max} }$.

Thus, in the dual isotope method, the contribution of NcD is always maximised, and consequently minimum and maximum contributions of N and ND are estimated based on Scenario A and B. Applying this method allows insight into these three potential sources of N₂O plus fertiliser denitrification. However, in soils, further microbial processes can lead to N₂O production. In the following, we will briefly discuss potential effects of nitrification by heterotrophs and archaea, fungal denitrification, as well as DNRA and co-denitrification.

If N₂O of nitrification by heterotrophs and archaea is produced by the same sources and similar pathways as in autotrophic nitrifiers, this should not interfere with the calculations. The contribution of N would then comprise that of other nitrifiers. However, archaea have also been suggested to produce N₂O in a pathway similar to ND (Jung et al. 2014). If so, this would be included in the contribution of ND. However, the pathway of N₂O production by archaea is not clear yet and needs further study (Stieglmeier et al. 2014), the outcome of which will also affect the calculations presented here. In soils where fungal denitrification occurs, this is counted as FD using the dual isotope method, if the fungi use added NO₃⁻ as a source in a reaction similar to denitrification. Fungal denitrification may be quantified using the isotopomer method (Sect. 7.3), calling for a combination with the dual isotope method.

The occurrence of DNRA should be tested for as explained above. Should it lead to N₂O production (Stevens et al. 1998), this would lead to an overestimation of N₂O from FD. As DNRA may be important in soils (Rütting et al. 2011), this pathway should always be considered by checking for enriched NH₄⁺ in incubations with added ¹⁵N-NO₃⁻.

Co-denitrifiers combine NO₃⁻ or NO₂⁻ with other nitrogenous compounds to produce N₂O or N₂. The occurrence of such a process could be quantified using the triple labelling ¹⁵N tracing model (Müller et al. 2014) in combination with non-random ¹⁵N distribution (Laughlin and Stevens 2002). Incorporating this would be an improvement of the dual isotope method, as co-denitrification could interfere with the source estimations presented above.

The dual isotope method could be further developed by incorporating better rates of O_ex for the pathways starting from NH₄⁺. Despite potential for improvements, however, this method allows an estimation of the contributions of N, ND, NcD and FD to N₂O production and should be applied to a range of soils to further our understanding of these sources of N₂O and potential mitigation strategies.

7.5 Quantification of Gross N Transformation Rates and Process Specific N₂O Pathways via ¹⁵N Tracing

7.5.1 Background

The N cycle is a conceptual model that illustrates where and in which form N is present in the environment and how N is transformed and exchanged between organic, mineral and gaseous N forms. Since the N cycle is a dynamic system not only the sizes of the different N pools, e.g. NH₄⁺, NO₃⁻ or organic N but also the rates between the pools provide an understanding of the dynamic nature of this important elemental cycle in soils and aquatic systems (Ryabenko 2013). The most common and easiest approach to understand the dynamic nature of the N pools is the determination of net process rates, such as net mineralisation rates by calculating the difference in the size of the mineral N pool between two time points. If this rate is positive, we refer to a net mineralisation, if it is negative then we call it net immobilisation. Thus, a net rate always refers to the difference between the production and consumption of the N pools in question. It can easily be shown that different pairs of production and consumption rates will lead to exactly the same net result. Thus, the analyses of net rates do not provide a measure of the individual rates that are contributing to the observed net rate. The individual rates associated with the N pool in question are called gross transformation rates. However, the quantification of these individual rates is not trivial because they cannot be measured directly. The most commonly used method to quantify the gross rates is the isotopic dilution technique (Stark 2000). The principle of this technique relies on the ¹⁵N labelling of a certain N pool so that the gross rate entering this pool can be quantified by taking into account the change in pool size and ¹⁵N enrichment of at least two times after label addition (Fig. 7.9).

Fig. 7.9

Illustration of the dilution technique by considering pool size and ¹⁵N abundance at two time points according to Kirkham and Bartholomew (1954)

The example in Fig. 7.9 shows that the pool size is decreasing which means that a net immobilisation of N occurred. However, the decline in ¹⁵N abundance of the pool N during the same period also shows that N at natural abundance or low ¹⁵N abundance must have entered the pool N. Thus, via visual inspection of the data we can say that N must have entered but also left the pool and that the rate leaving the pool must have been faster than the rate entering the pool. To quantify the individual rates requires a numerical analysis via a suitable N cycle model. Based on a simple two-pool N model, Kirkham and Bartholomew (1954) were the first to derive analytical equations that allowed the calculations of the two rates between two-time points, i.e. the gross mineralisation and immobilisation rates. The underlying assumptions are (i) ¹⁵N is homogeneously labelled and no preferential usage of either ¹⁵N or ¹⁴N occurs in the soil, (ii) immobilised N will not re-mineralise and (iii) N transformation rates follow zero-order kinetics (constant rates). The conceptual model of the Kirkham and Bartholomew approach and the equations derived for their model are illustrated in Fig. 7.10.

Fig. 7.10

The conceptual model, the differential equations of the various pools and the closed-form analytical solutions for the individual gross rates (m and i) according to Kirkham and Bartholomew (1954). Note, N_org (assumed to contain only ¹⁴N) depicts the organic N pool which mineralises into mineral N (M) which consist of H (¹⁵N) and N (¹⁴N), M = H +N. The subscript 0 refers to the concentrations of the pools at time zero

Since Kirkham and Bartholomew’s pioneering work in the 1950s, analyses techniques have been developed which are based on more realistic conceptual N models. These include the division of the mineral N pool into NH₄⁺ and NO₃⁻ pools with separate immobilisation rates, the consideration of more than one organic N pool and additional N loss rates such as ammonia volatilisation and denitrification (Myrold and Tiedje 1986). The dilution technique works well in simple systems where the inflow into a pool occurs via a single gross N transformation rate. However, in reality, often more than one pathway contributes to the buildup of a pool size. This can be illustrated by the NO₃⁻ pool in soil. Production of NO₃⁻ can occur via oxidation of NH₄⁺ to NO₃⁻ (usually termed autotrophic nitrification), and via oxidation of organic N to NO₃⁻ (usually termed heterotrophic nitrification) (Fig. 7.11).

Fig. 7.11

Conceptual model for nitrification

Following the principles of the dilution technique, the total gross rate of NO₃⁻ production can be quantified by labelling the NO₃⁻ pool and following the concentrations and ¹⁵N dilution of this pool over time. This total NO₃⁻ production rate includes both, autotrophic (oxidation of NH₄⁺) and heterotrophic nitrification (oxidation of N_org). To separate the two processes, in addition to the ¹⁵NO₃⁻ label also the NH₄⁺ pool should be labelled in a separate ¹⁵N labelling treatment. To keep the conditions in the two ¹⁵N labels the same, it is important to also apply NH₄⁺ in the soil that has received the ¹⁵NO₃⁻ label while NO₃⁻ should be applied in the ¹⁵NH₄⁺ treatment. Now, the ¹⁵N enrichment in the NO₃⁻ when only NH₄⁺ has been labelled will provide a measure of autotrophic nitrification while heterotrophic nitrification can be calculated by difference: N_h = N_tot–N_a where N_tot, N_a and N_h refer to total, autotrophic and heterotrophic nitrification, respectively. In practice, to quantify N_tot the dilution of the ¹⁵N labelled NO₃⁻ pool (Fig. 7.10) can be used while N_h and N_a can only be estimated via a simulation model that takes into account both nitrification rates (Barraclough and Puri 1995). A parameter optimisation technique can also be used to estimate N_a or N_h (Myrold and Tiedje 1986). Thus, in modern ¹⁵N tracing applications dilution-enrichment principles will be taken into account which we refer to as tracing.

In models with several simultaneous N transformations, it is impossible to derive analytical solutions. Therefore, the development of ¹⁵N tracing models which use numerical solutions has become the state-of-the-art approach (Mary et al. 1998). These models rely on a set of differential equations for example of a simple system that describes the N cycle. Transformation rates between the various pools can be constant (zero-order kinetics) or are dependent on the pool size where the rate is originating from (first-order kinetics) or follow enzyme kinetics (i.e. Michaelis–Menten kinetics). While zero and first-order kinetics are described by one parameter, rates calculated via Michaelis–Menten kinetics are dependent on two parameters, i.e. the maximum velocity of the reaction rate and the half-saturation constant (Müller 2000). The determination of the parameters in such equation systems rely on parameter optimisation tools. A whole range of parameter optimisation tools are available and different algorithms have been used in ¹⁵N tracing models (Mary et al. 1998; Myrold and Tiedje 1986). More recently, parameter optimisation tools based on Bayesian probability have become more common because they allow the simultaneous optimisation of a large number of parameters (for more details see Müller et al. 2007). It should be noted that the sole purpose of tracing models is to quantify gross transformation rates and are therefore data analysis tools and should not be confused with simulation models.

In the following sections, current ¹⁵N tracing techniques are illustrated. This includes the description of experimental requirements to obtain suitable data sets and the subsequent model analysis. A number of ¹⁵N tracing models have been developed (e.g. FLUAZ, Mary et al. 1998), and here, the data analysis will be illustrated by the Ntrace model. This model is based on the tool presented by Müller et al. (2007) and has since been developed further to analyse data sets from a range of differently complex setups, including dynamics of nitrite, gaseous N emissions, soil–plant interactions, biochar, etc. An advantage of Ntrace is its flexibility to adapt to various conditions and models because it is programmed in MatLab with code that can easily be changed and amended.

7.5.2 Stable Isotope Tracing Technique

A stable isotope tracing study consists of two parts, an experimental study where one or more pools are isotopically labelled and a data analysis tool (e.g. Ntrace) to quantify individual gross transformation rates. The technique can be regarded as a calculation procedure to quantify gross rates which cannot be quantified via any other means. Thus, both the tracing experiment and the numerical tool are building an analysis unit and it is important that the experimental approach is taking into account the requirements of the numerical analysis and vice versa. What is also important is that the quality of the final results critically depends on the data quality and therefore on the careful execution of the experimental part of the tracing study. For instance, data with high uncertainties may also result in gross N rates that are associated with large errors.

7.5.3 Setup of Tracing Experiments

To be able to analyse experimental data with the Ntrace model, the experiment needs to be set up in a certain way. Based on the research questions both field and laboratory experiments can be carried out. The research question usually requires the setup of several treatments (e.g. effect of various soil amendments). To quantify the individual gross N transformation rates in each treatment usually a set of at least two ¹⁵N labels should be employed per treatment (i.e. ¹⁵N-labelled NH₄⁺ and ¹⁵N-labelled NO₃⁻, typically applied as NH₄NO₃ to ensure the application of equal quantities of each N species). However, often multiple labels are used (e.g. very common is a triple labelling approach with NH₄NO₃ where either NH₄⁺, NO₃⁻ or both moieties are ¹⁵N labelled).

Ideally the ¹⁵N label should be applied without enhancing the concentration because this will also have an impact on the N transformations. Thus, in ecosystems that are not used to receive large N concentrations often a high ¹⁵N enrichment (e.g. 99 atom% ¹⁵N) is applied at a very low application rate. However, in agricultural soils which receive N in the form of fertiliser, this is less of a problem. The advantage of applying a reasonable, but not unrealistically high, N concentration is that it can more homogenously be applied to the soil. In most cases, a ¹⁵N enrichment of a few percent (e.g. 10 atom% ¹⁵N) is sufficient to determine gross rates. However, in situations where, for instance, the nitrite or gaseous N species such as N₂O are analysed, the labelled N pool (e.g. NO₃⁻) should ideally be enriched by approximately 50 atom% ¹⁵N which allows most precise analysis based on the expected 29/28 iron current (Stevens et al. 1993). The ¹⁵N solutions are made up according to standard calculations which are, for instance, summarised by Cabrera and Kissel (1989). To homogeneously label the soil a variety of application techniques are described in the literature ranging from application via side port needles in different depth, multiple needle applicators and automated techniques (Buchen et al. 2016) (Table 7.4). In field tracing studies often an application via a watering can is preferred, simply, because under field conditions when large plots of several m² have to be treated, it is critical that the solutions are applied within a short time window to ensure the same starting conditions (Plate 7.1). This is particularly important if dynamically changing N species such as N₂O should be compared among treatments (Moser et al. 2018). However, the application rate should be slow enough to avoid by-pass in cracks and fissures down the soil profile because this would cause uneven distribution of the ¹⁵N.

Plate 7.1

Application of ¹⁵N solution (¹⁵NH₄NO₃, NH ¹⁵₄ NO₃) on plots in the field with a small watering device (a), and soil incubation in a climate chamber in suitable incubation jars (b)

The time of labelling should be carefully noted because the difference between ¹⁵N application and soil analysis during the experiment provides the time after N supply which is required for the model analysis. If both, soil extractions and gaseous measurements are planned then in the field an area for the gas sampling and an adjacent soil sampling area should be setup (in Plate 7.1, gas measurement are in the forefront, and the area for soil sampling is at the top). In laboratory incubations usually one set of jars is reserved for gaseous measurements (which will be extracted at the end of the experiment) while for each analysis day, separate sets of jars are prepared for destructive sampling. The question arises for how long we need to carry out a typical incubation study. Since the application of N may cause a stimulation of microbial activity resulting in faster gross N rates shortly after N application, the duration of a typical tracing study should be continued until after this initial stimulation has subsided. A typical duration of such a study is approximately 14 days. To characterise the non-linear dynamics of the gross N rates over time it is necessary to determine the N pool sizes and their ¹⁵N enrichment at least 5 times throughout that period. Gas analysis should be carried out more frequently but at least at the times when soils are extracted.

Soil incubations have typically been carried out under controlled conditions at a pre-defined moisture content (set to a certain water filled pore space (WFPS) or water holding capacity (WHC)) and temperatures in a climate chamber (Plate 7.1).

Case study

To investigate the effect of a nitrification inhibitor in two soils on gross N transformations the following setup is realistic (using a triple ¹⁵N labelling approach, numbers in brackets refer to the number of entities):

Soils (2) × Inhibitors (2) × ¹⁵N labels (3) × Replicates (3) × Time of soil extraction (5) = 180 jars.

Thus, a total of 180 jars (i.e. 36 jars per extraction day) need to be prepared. The label needs to be applied with minimal disturbance while providing an equal distribution in the soil. This can be done using a long needle with side ports. If 150 g of dry soil equivalent should be used per jar, then approximately 14 kg of soil is required from each soil.

The extraction times should be timed in such a way that the first extraction happens as soon as possible after ¹⁵N labelling (typically after 2 h), then on day 1, 3, 7 and 15. Note, soils can react quite differently, therefore, the times and duration of the experiment should be adjusted accordingly.

7.5.4 Analyses of Experimental Data

7.5.4.1 Soil Extraction

If nitrite concentrations should be investigated it is recommendable to carry out the blending procedure of Stevens and Laughlin (1995). They discovered that nitrite is chemically reduced to N₂ in the KCl extract at pH below 5.5. They recommended a soil extraction at pH 7 and fast soil extraction. The blending procedure of Stevens and Laughlin (1995) is typically carried out at a soil: solution ratio of 1:1 in a blender for 90 s (Plate 7.2).

Plate 7.2

Extraction procedure for quick soil extraction (a) and glass filter unit for glass fibre filter papers (b)

Immediately after the blending, the soil suspension needs to be centrifuged at 2000 × g for 5 min, and the supernatant filtered sequentially through a GF/D and GF/F (Plate 7.2).

The extracts have to be analysed for NO₃⁻ and NH₄⁺ and possibly for NO₂. Based on the concentration a certain µmol of N of each N species will then be converted to ¹⁵N-N₂O or via a diffusion approach.

7.5.4.2 Chemical Conversion of Mineral N to ¹⁵N-N₂O

A precise method to determine the ¹⁵N content of ammonium, NO₃⁻ and nitrite is via a method that converts the N species to nitrous oxide (N₂O). The reduction of NO₃⁻ to N₂O is described by Stevens and Laughlin (1994). For this, sulphamic acid (2.5 ml of 0.2 M solution) is added to 50 ml soil extract and shaken by hand for 5 s to ensure conversion of NO₂⁻ to N₂. Then 5 ml of 1 M sodium acetate- 1 M acetic acid buffer has to be added to increase the pH to 4.7. Then a CD-Cu reductor has to be placed in the bottle (Plate 7.3).

Plate 7.3

Soil extracts are transferred to medical flasks for conversion of NO₂⁻ and NO₃⁻ to N₂O; gas samples are taken through the septa with syringes and then are transferred to pre-evacuated exetainers (from left to right)

The flask, capped, has to be laid flat in an orbital incubator at 20°C and shaken at 120 rpm with an orbit diameter of 50 mm for 2 h. A gas sample of the headspace is analysed with an IRMS for the ¹⁵N content of the N₂O. The ¹⁵N content of the NO₃⁻ is considered to be the same as that of the N₂O.

The production of N₂O from NH₄⁺ is described in Laughlin et al. (1997). Firstly, the ammonium must be diffused into (NH₄)₂SO₄. For this, 50 ml of the soil extract has to be pipetted in the diffusion unit (Plate 7.4). Above this liquid, a small flask containing 3 ml of H₂SO₄ has to be placed. Before the diffusion jar is closed, 0.2 g of heavy MgO must be added. The MgO has to be brought into suspension by gentle swirling for 30 s. After this, the diffusion jar has to be left for 4 days. After diffusion of the NH₃, the (NH₄)₂SO₄-H₂SO₄ has to be poured into a 12 ml glass exetainer and evaporated to dryness in a 150 °C oven, before cooling it in a desiccator and sealing it with a septum and cap. Then the vial has to be evacuated and filled with He to atmospheric pressure. One ml of NaOBr, with the molarity of NaOH adjusted to 10 M has to be injected through the septum. The vial has to be tilted and the solution gently swirled to ensure that the NaOBr reacts with as much of the (NH₄)₂SO₄ as possible. The concentration and ¹⁵N content of the N₂O in each vial has to be determined by an IRMS system.

Plate 7.4

Glass equipment used for the conversion of NH₄⁺ to NH₃ which is trapped in the acid contained in the small hanging flask

For the Ntrace_Nitrite model, data on NO₂⁻ concentration and ¹⁵N content are also necessary. The NO₂⁻ concentrations can be determined by a manual photometer method.

The ¹⁵N content of the NO₂⁻ extracts can also be determined by a method based on conversion to N₂O as described by Stevens and Laughlin (1994). For this 50 ml of the soil extract has to be pipetted into a bottle. One ml of 1 M HCl and 0.5 ml of 0.04 M NH₂OH has to be added to the bottle. The bottle should then be capped and laid flat in an orbital incubator and shaken at 120 rpm with an orbit of 50 mm for 16 h. A 12 ml sample of the headspace has to be transferred to an evacuated septum-capped glass vial, and the ¹⁵N content of the N₂O in each vial can be determined by IRMS. The atom% excess in ¹⁵N in NO₂⁻ is calculated as two times the ¹⁵N atom% excess in N₂O minus the ¹⁵N atom% excess in NH₂OH.

The specific steps of the conversion method to N₂O are summarised below.

• 1. NH₄⁺-N: NH₄⁺-N is first oxidised to NO₂⁻-N by BrO⁻ in a vacuum with N₂O being the by-product (Eq. 7.22). The production of N₂O can be catalysed by Cu⁺ at the appropriate pH (Laughlin et al. 1997).

  $$ {\text{NH}}_{4}^{ + } + {\text{NaBrO}} \to {\text{NaBr}} + {\text{H}}_{2} {\text{O}} + {\text{N}}_{2} \uparrow + {\text{N}}_{2} {\text{O}} $$

  (7.22)

• 2. NO₃⁻–N: NO₂⁻–N must be removed by NH₂SO₃H before NO₃⁻-N is reduced. NO₃⁻–N is reduced to NO₂⁻–N and NH₂OH by copper-plating cadmium grains at a pH of 4.7. Then NO₂⁻–N reacts with NH₂OH to produce N₂O, and the production of N₂O is positively correlated to the production of NO₃⁻-N (Eq. 7.23). The ammonium and N from other sources has no effect on the determination of NO₃⁻-N; (Stevens and Laughlin 1994).

  $$ {\text{NO}}_{3}^{ - } \to {\text{NO}}_{2}^{ - } + {\text{NH}}_{2} {\text{OH}} \to {\text{N}}_{2} {\text{O}} + 2{\text{H}}_{2} {\text{O}} $$

  (7.23)

• 3. NO₂⁻-N: NO₂⁻-N reacts with NH₂OH to produce N₂O (Eq. 7.24) and the reaction is pH-dependent. When pH < 4, the reaction rate increases rapidly, and the reaction time should be at least 16 h. Because N₂O is formatted via an asymmetric intermediate (N-nitroso-hydroxyl-amine) under acidic condition, the reaction requires at least 10 µmol of NH₂OH (Stevens and Laughlin 1994).

  $$ {\text{HNO}}_{2} + {\text{NH}}_{2} {\text{OH}} \to {\text{N}}_{2} {\text{O}} + 2{\text{H}}_{2} {\text{O}} $$

  (7.24)

The amount of N₂O produced is about half of the theoretical yield. According to the isotopic distribution, the two N atoms in N₂O are formed from NO₂⁻-N and NH₂OH, respectively. Hence, the atom% in NO₂⁻-¹⁵N needs to be calculated with Eq. 7.25 (assume the atom% ¹⁵N in NH₂OH is 0.365 atom%) (Laughlin et al. 1997):

$$ ^{15} {\text{N}}\,{\text{atom}}\% \left( {{\text{NO}}_{2}^{ - } - {\text{N}}} \right) = 2 \times^{15} {\text{N}}\,{\text{atom}}\% \left( {{\text{N}}_{2} {\text{O}}} \right){-}0.365\,{\text{atom}}\% $$

(7.25)

Apparatus

PT-IRMS (purge and trap system coupled to isotope ratio mass spectrometry)

Vacuum pump

50 ml reaction vials

Glass vials with Al caps and septums

Reagents

NH ⁺₄ -N to N₂O method:

MgO: combusted at 450 °C for 4 h

0.01 M H₂SO₄ with 0.5 mM CuSO₄5H₂O

Basic NaBrO (10 M NaOH)

NO₃⁻-N to N₂O:

0.2 M NH₂SO₃H

1 M CH₃COOH- CH₃COONa (pH = 4.7)

Copper-plated cadmium granules

NO₂⁻-N to N₂O:

1 M HCl

0.04 M NH₂OH-HCl

Procedures

• 1. NH₄⁺-N:

  • (a) Pipet 15–20 ml (about 20 µg N) soil extract into a semi-micro steam distiller. Carry out steam distillation immediately after adding 0.2 g MgO. The NH₃ is absorbed by 5 ml 0.01 M H₂SO₄. After 5 min of steam distillation, the distillate is concentrated to 2–3 ml. Transfer part of the concentrate into a 50 ml reaction vial, and evaporate to dryness at 90 °C;

  • (b) Evacuate the vials and fill them with He. Then inject 1 ml NaBrO together with 10 M NaOH through the septum, and swirl the solution around the sides of the vial to ensure that NaOBr reacts with as much of the (NH₄)₂SO₄ as possible;

  • (c) Transfer a known amount of sample to an evacuated septum-capped glass vial. The ¹⁵N content of the N₂O is then determined by IRMS.

• 2. NO₃⁻-N:

  • (a) Pipet 20–25 ml (about 20 µg N) of the soil extract into a flask. Add 2.5 ml 0.2 M NH₂SO₃H, and shake the flask for 5 min to ensure conversion of NO₂⁻-N to N₂;

  • (b) Place 50 mg copper-plated cadmium granules together with 5 ml of 1 M CH₃COOH- CH₃COONa into a 50 ml reaction bottle. Keep the bottle capped tightly, evacuate and then fill with pure He;

  • (c) Inject 15–20 ml of the nitrite-free soil extract (about10 µg N) into a reaction bottle. Place the reaction bottle on a shaker at 120 rpm for 2 h;

  • (d) Transfer a known amount of sample to an evacuated septum-capped glass vial. The ¹⁵N content of the N₂O is then determined with mass spectrometry.

• 3. NO₂⁻-N:

  • (a) Pipet 10–15 ml (about 0.5–1.0 µg NO₂⁻-N) of the soil extract into a 50 ml reaction bottle. Keep the bottle capped tightly, evacuate and then fill with pure He;

  • (b) Inject 1 ml 1 M HCl and 0.5 ml 0.04 M NH₂OH-HCl into the bottle;

  • (c) Place the bottle on a shaker running at 120 rpm for 16 h;

  • (d) Transfer a known amount of sample to an evacuated septum-capped glass vial. The ¹⁵N content of the N₂O is then determined with mass spectrometry. Finally, calculate the NO₂⁻-¹⁵N using Eq. 7.25.

7.5.4.3 Inorganic Nitrogen Isotopic Analysis in Soil Extracts via the Diffusion Method

An alternative method for the determination of ¹⁵N in NO₃⁻ and NH₄⁺ is the diffusion method. The diffusion method is easier to apply and has the advantage that only a solid analysis on an IRMS is required rather than a gas measurement. These Mass spectrometers are more readily available. However, it should also be pointed out that chemical conversion method described above is quicker and is free from contamination by atmospheric N. It has very low detection limits, which are 20 µg N for NH₄⁺-N, 5 µg N for NO₃⁻-N and 0.5 µg N for NO₂⁻-N.

Principle

During diffusion, ammonium in the soil samples is converted to ammonia by the use of MgO (Eq. 7.26). Then the ammonia is absorbed by using a filter paper containing a weakly acidic absorbent liquid during the volatilisation process. For determination of NO₃⁻-N, titrate some alkaline reagent to remove NH₄⁺-N in the sample then add some Devarda’s alloy to reduce the NO₃⁻-N into NH₄⁺-N.

$$ 2{\text{NH}}_{4}^{ + } + {\text{MgO}} \to {\text{Mg}}^{ + } + 2{\text{NH}}_{3} \uparrow + {\text{H}}_{2} {\text{O}} $$

(7.26)

Apparatus need are:

EA-IRMS

Shaker

250 ml airtight containers

Perforated silicon films

Perforated filter papers

paper clips

Glass beads

Reagents:

MgO: Combusted at 450 °C for 4 h

Devarda’s alloy: crushed to allow passage through a 300-mesh sieve

1 M H₂C₂O₄

Procedures

• 1. Put clips on the perforated silicon film and place it in the cap of a flask. Then place two pieces of 6 mm-diameter filter paper (Whatman #41 ashless filter paper) which are perforated by a needle on the clip;

• 2. For soil extracts > 2 mg l⁻¹ in inorganic N concentration, only 20 ml of soil extract is needed. Put the 20 ml of soil extract into the container and add 3 glass beads before adding the MgO and Devarda’s alloy. Onto each piece of filter paper pipette 10 µl of 1 M H₂C₂O₄ solution;

• 3. Add 0.3 g MgO and close the container quickly. Swirl the container carefully for 15 s. Then incubate the sample for 24 h at 25 °C in a shaker running at 140 rpm to complete the diffusion and recovery of NH₄⁺-N;

• 4. To determine the ¹⁵N enrichment of NO₃⁻-N from the same sample, replace the used filter paper with two new pieces also spiked with H₂C₂O₄. Incubate the sample in a shaker running at 140 rpm for 48 h to remove the remaining NH₄⁺-N. Then replace the used filter paper with two new acid-spiked pieces again, add 0.3 g Devarda’s alloy, and incubate it for 24 h to complete the processes of diffusion and recovery of NO₃⁻-N;

• 5. Remove the filter papers from the clips by forceps and dry them in a desiccator containing an open container of concentrated H₂SO₄ (to remove traces of NH₃) and silica gel. Then wrap the filter papers in tin capsules and analyse them for ¹⁵N enrichment by using a coupled elemental analyser-isotope ratio mass spectrometer (EA-IRMS);

• 6. Use the amount of N measured in diffusion blanks to calculate the corrected ¹⁵N enrichment of the sample (Eq. 7.27):

$$ {{E}}_{{{s}}} = \frac{{{{E}}_{{{m}}} {{M}}_{{{{s}} + {{b}}}} - {{E}}_{{{b}}} {{M}}_{{{b}}} }}{{{{M}}_{{{{s}} + {{b}}}} - {{M}}_{{{b}}} }} $$

(7.27)

where E_s is the corrected abundance ¹⁵N enrichment of the sample, E_m is the enrichment of the sample + blank measured by mass spectrometry, M_s+b is the mass of N (sample + blank) recovered in the acid trap, M_b is the mass of N recovered in the acid trap from the diffusion blank, and E_b is the enrichment in the blank (assumed to be 0.3663 atom%).

Note, for soil extracts < 2 mg l⁻¹ in inorganic N concentration, 50 ml of extract is needed to ensure accurate determination. When the abundances of NH₄⁺-N and NO₃⁻-N are very different, it is better to diffuse NH₄⁺-N and NO₃⁻-N separately (do not use the same extract).

7.5.4.4 Inorganic Nitrogen Isotopic Analysis in Soil Extracts at Natural Abundance

The diffusion method and chemical conversion method described above are both suitable for N at high abundance, but not for N at natural abundance. They both have a high demand for N and high levels of background N can interfere with the reaction. There are two modified chemical methods for N isotopic analysis at natural abundance. These simplify the preparation procedures, reduce the preparation time and do not require large amounts of N. The chemical method for ammonium requires 2.5 µg N in a 4 ml sample volume for analysis, and its accuracy of δ¹⁵N measurements is less than 0.3‰. The method for NO₃⁻ needs only 4.5 µg N, and its accuracy of δ¹⁵N and δ¹⁸O reaches 0.31‰ and 0.55‰, respectively.

Conversion of ammonium at natural abundance

Principle

The method is to oxidise NH₄⁺-N to NO₂⁻-N by BrO⁻ instead of extraction of NH₄⁺-N in solution. Subsequently, the NO₂⁻-N is reduced to N₂O by NH₂OH-HCl, thus replacing HN₃ (Liu et al. 2014; Stedman 1959) (Eq. 7.28).

$$ {\text{NH}}_{4}^{ + } + {\text{NaBrO}} \to {\text{NO}}_{2}^{ - } + {\text{NH}}_{2} {\text{OH}} \to {\text{N}}_{2} {\text{O}} + {\text{H}}_{2} {\text{O}} $$

(7.28)

Apparatus

PT-IRMS

Shaker

20 ml headspace glass vials: Acid rinsed and combusted at 450 °C for 4 h

Reagents

10 M NaOH: Evaporate 100 ml of 5 M NaOH to 50 ml of 10 M NaOH

NaBrO:

• (a) Bromate–bromide stock solution: Mix 0.6 g NaBrO₃ and BrNa into 250 ml DIW (deionised water) (can be stored ≥ 6 months);

• (b) Take 1 ml bromate/bromide stock solution into 50 ml water, and place the solution in the dark with 3 ml 6 M HCl added for 5 min to produce Br₂;

• (c) Add 50 ml of 10 M NaOH quickly to produce BrO⁻.

NaAsO₂: Mix5.1 g NaAsO₂ and 100 ml DIW

NH₂OH, HCl:

• (a) NH₂OH-HCl stock solution: Add 0.2778 g NH₂OH-HCl in 100 ml DIW (can be stored ≤ 7 d)

• (b) Take 3 ml NH₂OH-HCl stock solution and dilute in 500 ml DIW

6 M HCl

5 M NaOH

Procedures

• 1. Take samples (1:10 (v:v) sample to NaBrO, e.g. 4 ml) and place it into 20 ml headspace glass vials. Dilute the sample to 10-20 µM to maximise oxidation yield. NO₂⁻-N must be removed by NH₂SO₃H earlier to ensure the accurate determination of NH₄⁺-N;

• 2. Add NaBrO (e.g. 0.4 ml) into the vial, shake the vial vigorously, and then let it stand for 30 min;

• 3. Pipet 0.05 ml NaAsO₂ to remove excess BrO⁻ and terminate oxidation;

• 4. Add 6 M HCl to lower pH (pH < 1) and seal the vials;

• 5. Inject NH₂OH-HCl with a gas-tight syringe (n(NH₄⁺): n(NH₂OH) = 1:2). Put the samples in a shaker running at 120 rpm at 37 °C for 16 h;

• 6. Inject 0.5 ml 5 M NaOH to absorb CO₂ in the vials and terminate the reaction;

• 7. Transfer a known amount of gas to a PT-IRMS for analysis;

• 8. Treat 3 international NH₄⁺-N standards (IAEA N1, +0.4‰; USGS 25, −30.4‰; USGS 26, +53.7‰) using the same protocol for calibration (Eq. 7.29):

$$ \updelta^{15} {\text{N}}_{{{\text{NH}}_{4}^{+} {\text{sample}}}} = (\updelta^{15} {\text{N}}_{{{\text{N}}_{2} {\text{Osample}}}} - {\text{intercept)/slope}} $$

(7.29)

where the intercept and slope are obtained from the linear regression of the δ¹⁵N measured and the δ¹⁵N assigned from N₂O produced by the standards .

Conversion of NO ⁻ ₃ at natural abundance

Principle

The NO₃⁻-N is reduced to NO₂⁻-N by copper-plated cadmium granules in a weakly alkaline environment (Eq. 7.30):

$$ {\text{NO}}_{3}^{ - } + {\text{Cd}} + {\text{H}}_{2} {\text{O}} \leftrightarrow {\text{NO}}_{2}^{ - } + {\text{Cd}}^{2 + } + 2{\text{OH}}^{-} $$

(7.30)

NO₂⁻-N is converted into N₂O by N₃⁻ in a weakly acid buffer. When pH > 2, the reaction will be (Eqs. 7.31−7.33):

$$ {\text{NO}}_{2}^{ - } + {\text{H}}^{ + } \leftrightarrow {\text{HNO}}_{2} $$

(7.31)

$$ {\text{HNO}}_{2} + {\text{H}}_{2} {\text{O}} \leftrightarrow {\text{H}}_{2} {\text{NO}}_{2}^{ + } + {\text{OH}}^{ - } $$

(7.32)

$$ {\text{H}}_{2} {\text{NO}}_{2}^{ + } + {\text{N}}_{3}^{ - } \to {\text{N}}_{3} {\text{NO}} + {\text{H}}_{2} {\text{O}} \to {\text{N}}_{2} {\text{O}} + {\text{N}}_{2} $$

(7.33)

When there is a large number of halogen ions present the reaction will be accelerated (Stedman 1959) (Eqs. 7.34, 7.35):

$$ {\text{H}}_{2} {\text{NO}}_{2}^{ + } + {\text{Cl}}^{ - } \to {\text{NOCl}} + {\text{H}}_{2} {\text{O}} $$

(7.34)

$$ {\text{NOCl}} + {\text{N}}_{3}^{ - } \to {\text{N}}_{3} {\text{NO}} + {\text{Cl}}^{ - } \to {\text{N}}_{2} {\text{O}} + {\text{N}}_{2} $$

(7.35)

N₂O is an asymmetric molecule with a molecular structure of N-N-O. The δ¹⁵N_Air of N₂O is the mean value of δ¹⁵N_Air in two N atoms (Eq. 7.36):

$$ \updelta^{15} {\text{N}}_{\text{Air}} \permille\left( {{\text{N}}_{2} {\text{O}}} \right) = \frac{{\updelta^{15} {\text{N}}_{\text{Air}} \permille(^{15} {\text{N}} - {\text{N}} - {\text{O}}) +\updelta^{15} {\text{N}}_{\text{Air}} \permille({\text{N}} -^{15} {\text{N}} - {\text{O}})}}{2} $$

(7.36)

and the N₂O produced is composed of a N atom and an oxygen atom provided by the NO₂⁻-N and a N atom provided by N₃⁻, a N source. The isotope ratio of N and oxygen of the NO₂⁻ is identical with that of NO₃⁻ in the original solution. So, the following relationships hold (Eqs. 7.37, 7.38):

$$ \updelta^{15} {\text{N}}_{\text{Air}} \permille\left( {{\text{N}}_{2} {\text{O}}} \right) = \frac{{\updelta^{15} {\text{N}}_{\text{Air}} \permille({\text{N}}_{3}^{ - } ) +\updelta^{15} {\text{N}}_{\text{Air}} \permille({\text{NO}}_{2}^{ - } )}}{2} = \frac{{\updelta^{15} {\text{N}}_{\text{Air}} \permille({\text{N}}_{3}^{ - } ) +\updelta^{15} {\text{N}}_{\text{Air}} \permille({\text{NO}}_{3}^{ - } )}}{2} $$

(7.37)

$$ \updelta^{18} {\text{O}}_{\text{SMOW}} \permille\left( {{\text{N}}_{2} {\text{O}}} \right) =\updelta^{18} {\text{O}}_{\text{SMOW}} \permille\left( {{\text{NO}}_{2}^{ - } } \right) +\updelta^{18} {\text{O}}_{\text{SMOW}} \permille\left( {{\text{NO}}_{3}^{ - } } \right) $$

(7.38)

Therefore, when the isotope ratio of N₃⁻ is constant, the N and oxygen isotope ratios of N₂O produced is linear with the N and oxygen isotope ratios of NO₃⁻, and the theoretical slopes of their correlation curves are 0.5 (N) and 1.0 (O), respectively.

Apparatus

PT-IRMS

Shaker

pH metre

Peristaltic pump: flow rate ≥ 5 ml min⁻¹

Water-thermostat

Fume hood

Filter papers

Headspace glass vials

Reagents

0.5 M NaCl

0.5 M HCl

1 M C₃H₄N₂

NaN₃- CH₃COOH:

• (a) Mix 15 ml of 20% CH₃COOH with 15 ml of 2 M NaN₃ in a fume hood;

• (b) Ultrasonic surge the mixing solution for 15 min;

• (c) Blow the solution with He (280 ml min⁻¹) for 30 min if there are impurities;

• (d) The remaining acid is neutralised with a strong base (NaOH).

6 M NaOH

Copper-plated cadmium granules

Cadmium reduction column

Procedures

• 1. Place at least 40 ml of sample into the vials to ensure that there is still 16 ml sample with 4.5 µg N for the reaction after any loss. If the concentration of NO₃⁻-N in sample is above 20 µM, dilute the sample with 0.5 M NaCl. If the concentration of Cl⁻ is below 0.5 M, add solid NaCl to ensure that the concentration of Cl⁻ is 0.5 M.

• 2. The blank must be analysed during each analysis to test the seal of vials and the reagent blank. The signal value of blank should be below 0.6 nA.

• 3. Add 0.5 M HCl into the samples to adjust pH to 2–3. The blank will only need one drop of 0.5 M HCl. Then add 1 M C₃H₄N₂ to adjust the pH to 7.8–8.0.

• 4. (a) Connect the cadmium reduction column to a peristaltic pump of which the flow rate is 5 ml min⁻¹. Plug the end of the column with foam sponge. After filling the column with copper-plated cadmium granules, also plug the other end. Rinse the pipeline with 0.5 M NaCl (pH = 8) to activate the column. Then transfer 20 ml of adjusted sample into a 25 ml beaker, and place the inflow and outflow ends of the column in the beaker. After 80 min of continuous reduction, rinse the pipeline with 40 ml 0.5 M NaCl again. When moving the column air must not enter the column to prevent oxidation of the cadmium column.

  (b) Copper-plated cadmium granules can be added directly to the samples. Place the samples in a shaker running at 200 rpm at 30 °C for 3 h to reduce NO₃⁻-N. Filter the sample into another vial.

• 5. Take a 16 ml sample and place it into a 50 ml headspace glass vial with the cap sealed. Evacuate the vial and fill it with He gas.

• 6. Inject 0.8 ml NaN₃- CH₃COOH into the vial (pH = 4.5) and shake the solution vigorously for 1.0 min. Then place the samples in a water-thermostat at 30 °C for 30 min, or in a shaker running at 200 rpm at 35 °C for 30 min.

• 7. Inject 0.5 ml 6 M NaOH (pH ≥ 10) to terminate the reaction.

• 8. Transfer a known amount of the gas to a PT-IRMS for determination of δ¹⁵N and δ¹⁸O of N₂O in the sample.

• 9. Mix 2 international NO₃⁻-N standards (USGS 32, δ¹⁵N_Air‰ = 180‰, δ¹⁸O_SMOW‰ = 25.7‰; USGS 34, δ¹⁵N_Air‰ = −1.8‰, δ¹⁸O_SMOW‰ = −27.9‰) in different proportions (e.g. 6:0, 4:2, 0:6), then treat them with the same protocol for calibration. The calibration equation shown below is

$$ \updelta^{15} {\text{N}}_{{AirNO_{3}^{ - } }} = (\updelta^{15} {\text{N}}_{{{\text{AirN}}_{2} {\text{O}}}} - {\text{intercept}})/{\text{slope}} $$

(7.39)

$$ \updelta^{15} {\text{N}}_{{(180)WNO_{3}^{ - } }} = (\updelta^{15} {\text{N}}_{{{\text{SMOWN}}_{2} {\text{O}}}} - {\text{intercept}})/{\text{slope}} $$

(7.40)

where the intercept and slope are obtained from the linear regression of the δ¹⁵N and δ¹⁸O measured from N₂O produced by the standards and the δ¹⁵N and δ¹⁸O are assigned from the standards .

7.5.5 ¹⁵N Tracing Model Analyses via Ntrace

7.5.5.1 Data Requirements for the Ntrace Model

Data obtained through the ¹⁵N tracing experiment will be further analysed by the Ntrace model to quantify gross N transformation rates and pathway-specific N₂O emissions. The various Ntrace model versions differ in their data requirements. The Ntrace_Basic model has the fewest data requirements. The other models require more data on top of the data required for the Ntrace_Basic model. The Ntrace_Basic requires the fertiliser application rate (in µmol N g⁻¹) and its ¹⁵N excess (in atom%). It also requires the average NO₃⁻ and NH₄⁺ concentration and ¹⁵N excess (in atom% excess) including their standard deviations for each data point in time. The NO₃⁻ and NH₄⁺ concentrations should be given in the same unit as the fertiliser application rate. Next to this, a one-time measurement of total organic N (in %) is required. This measurement can be taken from basic soil characteristics. The Ntrace_Plant model also requires plant N and plant ¹⁵N data, and total plant biomass data, at each time when destructive sampling was carried out, i.e. preferably the same time points when NO₃⁻ and NH₄⁺ were determined. Ideally, above- and belowground biomass (roots) should be determined. The Ntrace_Urea model requires the urea application rate and its excess, and if plants are included, it also has the additional requirements of the Ntrace_Plant model. The Ntrace_Nitrite model requires measurements at multiple time points (preferably the same as for NO₃⁻ and NH₄⁺) of the average NO₂⁻ concentration and its ¹⁵N excess (in atom%) including standard deviations.

Transformation can follow zero-order, first-order, or Michaelis–Menten kinetics. The type of kinetics used needs to be specified for each transformation separately. If the transformation uses N from a large pool, it is generally appropriate to use zero-order kinetics. For N transformations coming from pools that change rapidly it is generally more realistic to use first-order or Michaelis–Menten kinetics. Especially the transformations associated with the NH₄⁺ consumption (e.g. nitrification) may be most realistically represented by Michaelis–Menten kinetics. However, under conditions when microbial activities may be affected by conditions other than substrate, the N transformation rate may also follow first-order kinetics. For example, when the rate is governed by temperature or soil moisture.

7.5.5.2 The Ntrace Model System

The ¹⁵N tracing model Ntrace described by Müller et al. (2007) is a tool to quantify gross soil N transformations; this model considers five N pools and twelve simultaneously occurring N transformations (Fig. 7.12). The five soil N pools are ammonium (NH₄⁺) adsorbed NH₄⁺ (NH₄⁺_ads); labile soil organic N (N_lab); NO₃⁻, nitrate stored ( NO₃⁻_sto) and recalcitrant soil organic N (N_rec). The model considered twelve gross N transformations from these five N pools: mineralisation of recalcitrant organic-N to NH₄⁺ (M_Nrec); mineralisation of labile N to NH₄⁺ (M_Nlab); immobilisation of NH₄⁺ into recalcitrant organic-N (I_{NH4_Nrec}); immobilisation of NH₄⁺ into labile organic-N (I_{NH4_Nlab}); oxidation of NH₄⁺ to NO₃⁻ (O_NH4); oxidation of recalcitrant organic-N to NO₃⁻ (O_Nrec); immobilisation of NO₃⁻ to recalcitrant organic-N (I_NO3); dissimilatory NO₃⁻ reduction to NH₄⁺ (D_NO3); adsorption of NH₄⁺ on cation exchange sites (A_NH4); and release of adsorbed ammonia (R_NH4a), adsorption and release of NO₃⁻ on/from stored NO₃⁻, i.e. A_NO3s and R_NO3s, respectively. Ntrace is a family of ¹⁵N tracing models to quantify gross N transformations in soils and sediments. The model consists of a N transformation model that is programmed in Simulink, a graphical programming language associated to Matlab, and a parameter optimisation routine based on a Markov Chain Monte Carlo routine in combination with the Metropolis algorithm (Müller et al. 2007).

Several extensions exist of the Ntrace_Basic model, namely Ntrace_Plant (Fig. 7.13a), Ntrace_Urea (Fig. 7.13b), Ntrace_Nitrite (Fig. 7.14) and Ntrace_Gas (Fig. 7.15). The boxes represent the different N pools, and the transformations are represented by the arrows between the boxes. For each model all transformations are quantified simultaneously (Fig. 7.12).

Fig. 7.12

Conceptual Ntrace_Basic model an extended version of the model published by Müller et al. (2007), extended by additional exchange processes between N_lab and NO₃⁻ (b)

Fig. 7.13

a Ntrace _Plant model, based on Inselsbacher et al. (2013) b Ntrace_Urea model

Fig. 7.14

Ntrace_Nitrite model, based on Müller et al. (2006) and Rütting and Müller (2008)

Fig. 7.15

Ntrace_Gas model an extension to Ntrace_Nitrite as described by Müller et al. (2014)

The Matlab-Simulink files (m-files and mdl-files) alongside their description that are part of the Ntrace model are presented in Table 7.7.

Table 7.7 The different MatLab (m-files) and Simulink file (mdl-files) that are part of the Ntrace tracing system

Currently, a new optimisation routine for the Ntrace model is being implemented. This will further improve optimisation speed, and more importantly be quicker to find a global minimum as opposed to a local one. The method used for determining optimal parameters will be Matlab’s GlobalSearch algorithm (Ugray et al., 2007). Standard deviations of the optimised parameters will be determined as described by Gavin (2019).

7.5.6 Parameter Optimisation with Ntrace

7.5.6.1 Setup

After filling out an input file for the model (DataNtrace.xlsx) that contains all the required data specified in data requirements including kinetics for each transformation, initial parameters and minimum and maximum values for the parameters, the model can be run (Fig. 7.16).

Fig. 7.16

Data Ntrace Excel file that is used to setup Ntrace model runs. The sheets show: above-left: input sheet of experimental data, below-left: setup of model run with input of basic parameters, e.g. Norg content, N application and the ¹⁵N enrichment, right: parameter sheet. Note: yellow areas are input areas

7.5.6.2 Procedure

The first step of the optimisation is generally done by hand. The model is run with the initial parameter set, and graphs of modelled versus measured data are inspected. From this, parameters are adjusted until a visually reasonable fit is obtained. Thereafter, all parameters are optimised simultaneously using a Markov chain Monte Carlo (MCMC) method, and this is explained in more detail by Müller et al. (2007). For this, the parameters are slightly adjusted, and the model is run. At the end of the run, the misfit is calculated based on the difference between the modelled and measured values. If the misfit is lower compared to the previous run, i.e. a better fit between modelled and measured data, the new parameter set is accepted, and it will start again by adjusting the newly accepted parameter set and execute the next iteration. If the misfit is higher, so a worse fit, there is also a chance the parameter set is accepted via a likelihood function. By this, it is possible that the algorithm moves out of a local minimum and enters the global minimum. If a new parameter set is not accepted, the last accepted parameter set will be used for the parameter adjustment. This iterative procedure of parameter adjustment and running the model should go on till the probability density functions (PDFs) are well characterised for all parameters. If the initial parameter set is fairly close to the optimal set, PDFs are generally well characterised after 50,000 to 100,000 iterations. So, for the final run, the maximum number of iterations is generally set between 50,000 and 100,000. During the optimisation, generally three parallel sequences, each with different starting parameters, are calculated. The number of parallel sequences should be defined before running the model, but three is generally appropriate. From these parallel sequences, a reduction factor is determined, which determines the accuracy of the sampling (Gelman et al. 2003). If the reduction factor is below a pre-specified number (default 1.1) for all parameters, the optimisation will also be stopped, regardless of reaching the maximum number of iterations. The reduction factor near 1 indicates that all parallel sequences resulted in statistically the same parameter set.

Inspection of the PDFs can show that for certain parameters the peak is close to zero. This would indicate that this particular parameter can be neglected. The parameter can then be set to zero, and excluded from optimisation when the model is re-run.

7.5.6.3 Ntrace Model Output

At the end of the optimisation, the model output will be exported to an Excel file. This output contains the initial parameter value, the optimised parameter value, the standard deviation of the optimised parameter, the average N flow for each transformation, the overall R² and the AIC. The standard deviation (SD) of the transformation rate is based on the SD and average (AVG) parameter values as shown in Eqs. 7.41 to 7.43:

$$ SD_{\text{transformation rate}} = \frac{{AVG_{\text{transformation rate}} \cdot SD_{\text{parameter}} }}{{AVG_{\text{parameter}} }} $$

(7.41)

Response ratios between transformation rates can be calculated by McGeough et al. (2016):

$$ {\text{R}} = { \ln }\left( {\frac{{\overline{\text{X}}_{\text{E}} }}{{\overline{\text{X}}_{\text{C}} }}} \right) $$

(7.42)

With the associated standard deviation:

$$ sd_{R} = \sqrt {\frac{{sd_{E}^{2} }}{{n_{E} \overline{X}_{E}^{2} }} + \frac{{sd_{C}^{2} }}{{n_{C} \overline{X}_{C}^{2} }}} $$

(7.43)

where $\overline{X}_{E}$ and $\overline{X}_{C}$ are the average N transformations of the elevated and control group, sd_E and sd_C the associated standard deviations and n_E and n_C the repetitions.

To compare the effect of different treatments on transformation rates, the individual treatments have to be run separately. After this, the rates can be compared using a one-way ANOVA based on the averages and standard deviations. Pairwise comparisons can be calculated with the Holm-Šídák test.

Another way to compare gross N transformation is via the determination of least significant difference (LSD) as described by Müller et al. (2011).

Output of the correlation matrix can be used to find parameters that tend to be strongly constrained together. A correlation value of above 0.8 indicates that it is constrained. There is also another output file that gives the pool sizes and transformation rates for each time step. This output can be used to create graphs.

7.5.7 Determination of N₂O Pathways

7.5.7.1 Ntrace Approach to Quantify N₂O Pathways

Nitrous oxide (N₂O) can be emitted via a number of pathways including inorganic and also organic pathways, involving a range of microbes (e.g. bacteria, fungi) (Butterbach-Bahl et al. 2013). The Ntrace_Gas model can be applied to quantify N₂O pathways based on the underlying N transformations and especially based on the nitrite dynamics (Ntrace_Nitrite). To accurately estimate N₂O pathways via Ntrace_Gas also the N₂ production is calculated. The two predominant biological processes for N₂O production in soil are traditionally considered to be autotrophic nitrification and heterotrophic denitrification (Ambus 1998; Wrage-Mönnig et al. 2018; Wrage et al. 2001). In both processes NO₂⁻ is the key precursor to N₂O production. In nitrifier nitrification, it is rather NH₂OH or at least something before nitrite. In nitrifier denitrification, it is nitrite.

Assuming that the N₂O production is derived from a single NO₂⁻ pool, the ¹⁵N enrichments of the N₂O and the NO₂⁻ should be similar. However, experimental data show that the enrichment of the N₂O is deviating from the theoretical 1:1 line (Fig. 7.17) leading to the conclusion that the N₂O originated from various NO₂⁻ sub-pools and also from sources which were at or close to natural abundance. Based on the experimental setup, the only common unlabeled N pool in all ¹⁵N treatments is organic N. Therefore, two possible processes were included in the Ntrace_Gas model to account for such a dilution effect:

Fig. 7.17

Relationships between nitrite and nitrous oxide a as well as the ¹⁵N enrichment b (Müller et al. 2014)

(a) reduction of NO₂⁻ originating from oxidation of organic N derived (NO₂⁻_org) and

(b) hybrid-reaction for N₂O production whereby one atom of the N₂O is derived from an enriched NO₂⁻ pool and another from organic N at natural abundance.

Heterotrophic nitrifiers can also denitrify (Blagodatsky et al. 2006; Papen et al. 1989) and it is, therefore, possible that NO₂⁻_org in the Ntrace_Nitrite model (Rütting and Müller 2008) originating from N_org oxidation could be further reduced to gaseous N products. A hybrid-reaction between NO₂⁻ and organic N is also possible which occurs, for instance, in the fungus Fusarium oxysporum (Kurakov et al. 2000; Tanimoto et al. 1992) and possibly in other heterotrophic organisms (Kumon et al. 2002).

Based on the above considerations the Ntrace_Gas model analyses four N₂O processes. The entire model includes all the previous ¹⁵N tracing models (see Ntrace family above). In Ntrace_Gas NO₂⁻ sub-pools are reduced to associated N₂O pools which may further be reduced to N₂ (Eq. 7.44).

$$ 2{\text{NO}}_{2} {^{ - }} {_{\text{x}}} \to {\text{N}}_{2} {\text{O}}_{\text{x}} \to {\text{N}}_{2} $$

(7.44)

(x = nit, den or org)

In addition, a hybrid-reaction between denitrification derived NO₂⁻ (NO₂⁻_den) and recalcitrant organic N (N_rec) was introduced (Eq. 7.45).

$$ {\text{NO}}_{2} {^{ - }} {_{\text{den}}} + {\text{N}}_{\text{rec}} \to {\text{N}}_{2} {\text{O}}_{\text{cod}} \to {\text{N}}_{2} $$

(7.45)

Each soil N₂O sub-pool can be further reduced to N₂ via specific N₂O reduction rates or emitted to the atmosphere, which is governed by gas diffusion parameters. For N₂O emission a first-order notation has been implemented (Cho and Mills 1979; p. 97 in Müller 2000).

The total N₂O emission is calculated (Eq. 7.46) by

$$ \sum {E_{x} } = \sum {k_{x} } \cdot {\text{N}}_{2} {\text{O}}_{x} $$

(7.46)

where E_x is the emission rate (µmol N g⁻¹ h⁻¹), k_x is the emission rate constant (h⁻¹) and N₂O_x the soil N₂O pool concentration (µmol N g⁻¹). The symbol x stands for the process specific pools, i.e. nit, den, org and cod.

In the following section, two simplified approaches are presented that are based on the abundance of NH₄⁺, NO₃⁻, N_org and N₂O. The methods are based on the assumption that N₂O is derived from three uniformly labelled pools, i.e. NH₄⁺, NO₃⁻ and N_org. and bases the analysis on the ¹⁵N enrichments of the different N species.

7.5.8 Source Partitioning to Quantify N₂O Pathways

7.5.8.1 Three-Pool Model

Based on the two-pool source-partitioning model by Stevens et al. (1997) a three-pool solver method (Rütting et al. 2010) was developed. The solver method (Microsoft Excel 2007) calculates the N₂O fractions associated with NH₄⁺ (n) and NO₃⁻ (d) by minimisation of the absolute difference between observed and calculated ¹⁵N enrichments of N₂O according to the equation:

$$ a_{N2O} = d*a_{d} + n*a_{n} + (1 - d - n)*a_{o} $$

(7.47)

where n and d are the fractions related to the NH₄⁺ and NO₃⁻ pools, respectively, and a_d, a_n and a_o represent the ¹⁵N abundance of the NO₃⁻, NH₄⁺ and N_org (assumed to be at natural abundance) respectively. The data are setup in an Excel spreadsheet and the Excel Solver is used to minimise the difference between measured and calculated ¹⁵N N₂O enrichments (Rütting et al. 2010) (Fig. 7.18).

Fig. 7.18

Three source model for determination of N₂O pathways based on Rütting et al. (2010), see text for details

With this method, it is possible to subdivide total N₂O emission into the three sources, autotrophic nitrification, denitrification and heterotrophic nitrification.

7.5.8.2 Four-Pool Model

The three-pool model has been developed further by Jansen-Willems et al. (2016) to analyse four simultaneous processes (nitrification, denitrification, co-denitrification and oxidation of organic matter). The assumption is that isotopic discrimination is negligible. The conceptual model for this approach is illustrated in Fig. 7.19.

Fig. 7.19

Conceptual model to analyse N₂O pathways according to Jansen-Willems et al. (2016)

Background and development of the four-pool model

Each N pool contains both ¹⁵N and ¹⁴N atoms. If one N atom would be randomly selected from a pool, the chance it would be a ¹⁵N atom is equal to the ¹⁵N atom fraction of that pool. So for the NH₄⁺ pool this would be a_n, for the NO₃⁻ pool a_d, and for the organic-N pool a_o. The chance it would be a ¹⁴N atom equals 1 minus the ¹⁵N atom fraction of that pool. So, for the NH₄⁺ pool it would be 1-a_n, for the NO₃⁻ pool 1-a_d, and for the organic-N pool it would be 1-a_o.

N₂O consists of two N atoms. For nitrification, denitrification and oxidation of organic N, both N atoms come from the same pool. For these three processes:

• The chance that N₂O contains no ¹⁵N atoms is the chance that the first atom is a ¹⁴N atom multiplied by the chance that the second atom is a ¹⁴N atom (Eq. 7.48).

• The chance that N₂O contains one ¹⁵N atom is the chance that the first atom is a ¹⁵N atom, multiplied by the chance that the second atom is a ¹⁴N atom, plus the chance that the first atom is a ¹⁴N atom and the second is a ¹⁵N atom (Eq. 7.49)

• The chance that N₂O contains two ¹⁵N atoms is the chance that the first atom is a ¹⁵N atom, multiplied by the chance that the second atom is a ¹⁵N atom (Eq. 7.50)

In Eqs. 7.48 to 7.50, a_x would be a_n for nitrification, a_d for denitrification and a_o for oxidation of organic N.

$$ {\text{Chance of zero}}^{15} {\text{N atoms}}:\left( {1{-}{\text{a}}_{\text{x}} } \right)\left( {1{-}{\text{a}}_{\text{x}} } \right) = \left( {1{-}{\text{a}}_{\text{x}} } \right)^{2} $$

(7.48)

$$ {\text{Chance of one}}^{15} {\text{N atom}}:{\text{a}}_{\text{x}} \left( {1{-}{\text{a}}_{\text{x}} } \right) + \left( {1{-}{\text{a}}_{\text{x}} } \right){\text{a}}_{\text{x}} = 2\left( {1{-}{\text{a}}_{\text{x}} } \right){\text{a}}_{\text{x}} $$

(7.49)

$$ {\text{Chance of two}}^{15} {\text{N atoms: a}_{\text{x}}} {\text{a}}_{\text{x}} = {\text{a}}_{\text{x}}^{2} $$

(7.50)

For co-denitrification, one atom comes from the NO₃⁻, and one comes from the organic N pool. So, for co-denitrification, the chance that N₂O contains

• No ¹⁵N atoms, is the chance of a ¹⁴N atom from the NO₃⁻ pool, multiplied by the chance of a ¹⁴N atom from the organic N pool (Eq. 7.51).

• One ¹⁵N atom, is the chance of a ¹⁵N atom from the NO₃⁻ pool, multiplied by the chance of a ¹⁴N atom from the organic N pool plus the chance of a ¹⁴N atom from the NO₃- pool multiplied by the chance of a ¹⁵N atom from the organic N pool (Eq. 7.52).

• Two ¹⁵N atoms is the chance of a ¹⁵N atom from the NO₃⁻ pool, multiplied by the chance of a ¹⁵N atom from the organic N pool (Eq. 7.53).

$$ {\text{Chance of zero}}^{15} {\text{N atoms:}}\,\left( {1{-}{\text{a}}_{\text{d}} } \right)\left( {1{-}{\text{a}}_{\text{o}} } \right) $$

(7.51)

$$ {\text{Chance of one}}^{15} {\text{N atom:}}\,{\text{a}}_{\text{d}} \left( {1{-}{\text{a}}_{\text{o}} } \right) + \left( {1{-}{\text{a}}_{\text{d}} } \right){\text{a}}_{0} $$

(7.52)

$$ {\text{Chance of two}}^{15} {\text{N atoms: a}_{\text{d}}} {\text{a}}_{\text{o}} $$

(7.53)

The N₂O in the gas sample is assumed to come from one of four processes. The fraction that comes from nitrification is written as n, the fraction that comes from denitrification is written as d and the fraction that comes from oxidation of organic matter is written as o. The fraction that comes from co-denitrification is written as c. As these are the only four processes considered, the four fractions should add up to one. Therefore, the following two equations apply:

$$ {\text{a}} + {\text{d}} + {\text{o}} + {\text{c}} = 1 $$

(7.54)

$$ c = 1{-}a{-}d{-}o $$

(7.55)

The fraction of N₂O in the gas sample that is expected to contain zero ¹⁵N atoms can be calculated by multiplying the fraction of that sample from a specific process by the chance that the N₂O from that process contains zero ¹⁵N atoms. So for nitrification, this would be n(1–a_n)², and for co-denitrification this would be (1–n–d−o) (1–a_d) (1–a₀). This should be done for all four processes, and then should be added together (Eq. 7.56). The fraction of the N₂O in the gas sample that is expected to contain one ¹⁵N atom is calculated in the same way (Eq. 7.57), and the expected fraction containing two ¹⁵N atoms as well (Eq. 7.58)

Chance of zero ¹⁵N atoms:

$$ n\left( {1 - {\text{a}}_{\text{n}} } \right)^{2} + d\left( {1 - {\text{a}}_{\text{d}} } \right)^{2} + o\left( {1 - {\text{a}}_{\text{o}} } \right)^{2} + (1 - n - d - o)\left( {1 - {\text{a}}_{\text{d}} } \right)\left( {1 - {\text{a}}_{0} } \right) $$

(7.56)

Chance of one ¹⁵N atom:

$$ 2n\left( {1{-}{\text{a}}_{\text{n}} } \right){\text{a}}_{\text{n}} + 2d\left( {1 - {\text{a}}_{\text{d}} } \right){\text{a}}_{\text{d}} + 2o\left( {1 - {\text{a}}_{\text{o}} } \right){\text{a}}_{\text{o}} + \left( {1{-}n{-}d{-}o} \right)\left( {{\text{a}}_{\text{d}} \left( {1{-}{\text{a}}_{0} } \right) + {\text{a}}_{0} \left( {1{-}{\text{a}}_{\text{d}} } \right)} \right) $$

(7.57)

Chance of two ¹⁵N atoms:

$$ na{{\rm N}}_{2} + d{\rm{a}}_{\rm{d}}^{2} + oa{\rm{N}}_{2} + \left(1 - n - d - o \right){\rm{a}}_{\rm{d}}\, {\rm{a}}_{0} $$

(7.58)

7.5.8.3 Mass Spectrometer Measurements and Calculation of Fractions

To determine the fractions of the different processes ⁴⁵R and ⁴⁶R measurements are needed. These need to be corrected for the presence of ¹⁸O. Therefore, this means that ⁴⁵R is the fraction of N₂O molecules containing one ¹⁵N atom divided by the fraction of N₂O molecules containing zero ¹⁵N atoms, and ⁴⁶R is the fraction of N₂O molecules containing two ¹⁵N atoms divided by the fraction of N₂O molecules containing zero ¹⁵N atoms.

The expected fractions for N₂O containing zero, one or two ¹⁵N atoms are given in Eqs. 7.56−7.58. In the study published by Jansen-Willems et al. (2016), a₀ was set to 0.003663 (natural abundance), and a_n and a_d were considered to be the ¹⁵N abundance of NH₄⁺ and NO₃⁻. Using these values, n, d and o were quantified using the fminsearchbnd function in MatLab (The MathWorks Inc, Natick, MA). Thus, from this, c could be calculated according to Eq. 7.55.