N 2 O isotopocule measurements using laser spectroscopy: analyzer characterization and intercomparison

. For the past two decades, the measurement of nitrous oxide (N 2 O) isotopocules – isotopically substituted molecules 14 N 15 N 16 O, 15 N 14 N 16 O and 14 N 14 N 18 O of the main isotopic species 14 N 14 N 16 O – has been a promising technique for understanding N 2 O production and consumption pathways. The coupling of non-cryogenic and tuneable light sources with different detection schemes, such as direct absorption quantum cascade laser absorption spectroscopy (QCLAS), cavity ring-down spectroscopy (CRDS) and off-axis integrated cavity output spectroscopy (OA-ICOS), has enabled the production of commercially available and ﬁeld-deployable future analyzer models and instruments focusing on isotopic species of other molecules.

Abstract. For the past two decades, the measurement of nitrous oxide (N 2 O) isotopocules -isotopically substituted molecules 14 N 15 N 16 O, 15 N 14 N 16 O and 14 N 14 N 18 O of the main isotopic species 14 N 14 N 16 O -has been a promising technique for understanding N 2 O production and consumption pathways. The coupling of non-cryogenic and tuneable light sources with different detection schemes, such as direct absorption quantum cascade laser absorption spectroscopy (QCLAS), cavity ring-down spectroscopy (CRDS) and offaxis integrated cavity output spectroscopy (OA-ICOS), has enabled the production of commercially available and fielddeployable N 2 O isotopic analyzers. In contrast to traditional isotope-ratio mass spectrometry (IRMS), these instruments are inherently selective for position-specific 15 N substitution and provide real-time data, with minimal or no sample pretreatment, which is highly attractive for process studies.
Here, we compared the performance of N 2 O isotope laser spectrometers with the three most common detection schemes: OA-ICOS (N 2 OIA-30e-EP, ABB -Los Gatos Research Inc.), CRDS (G5131-i, Picarro Inc.) and QCLAS (dual QCLAS and preconcentration, trace gas extractor (TREX)-mini QCLAS, Aerodyne Research Inc.). For each instrument, the precision, drift and repeatability of N 2 O mole fraction [N 2 O] and isotope data were tested. The analyzers were then characterized for their dependence on [N 2 O], gas matrix composition (O 2 , Ar) and spectral interferences caused by H 2 O, CO 2 , CH 4 and CO to develop analyzerspecific correction functions. Subsequently, a simulated twoend-member mixing experiment was used to compare the accuracy and repeatability of corrected and calibrated isotope measurements that could be acquired using the different laser spectrometers.
Our results show that N 2 O isotope laser spectrometer performance is governed by an interplay between instrumental precision, drift, matrix effects and spectral interferences. To retrieve compatible and accurate results, it is necessary to include appropriate reference materials following the identical treatment (IT) principle during every measurement. Remaining differences between sample and reference gas compositions have to be corrected by applying analyzer-specific correction algorithms. These matrix and trace gas correction equations vary considerably according to N 2 O mole fraction, complicating the procedure further. Thus, researchers should strive to minimize differences in composition between sample and reference gases. In closing, we provide a calibration workflow to guide researchers in the operation of N 2 O isotope laser spectrometers in order to acquire accurate N 2 O isotope analyses. We anticipate that this workflow will assist in applications where matrix and trace gas compositions vary considerably (e.g., laboratory incubations, N 2 O liberated from wastewater or groundwater), as well as extend to

Introduction
Nitrous oxide (N 2 O) is a long-lived greenhouse gas with a 100-year global warming potential nearly 300 times that of carbon dioxide (CO 2 ; Forster et al., 2007) and is the largest emission source of ozone-depleting nitrogen oxides in the stratosphere (Ravishankara et al., 2009). In 2019, the globally averaged [N 2 O] reached approximately 332 ppb compared to the pre-industrial level of 270 ppb (NOAA/ESRL, 2019). While this increase is known to be linked primarily to increased fertilizer use in agriculture (Bouwman et al., 2002;Mosier et al., 1998;Tian et al., 2015), understanding the underlying microbial processes producing and consuming N 2 O has proved more challenging, and individual source contributions from sectors such as agricultural soils, wastewater management and biomass burning to global bottom-up estimates of N 2 O emissions have large uncertainties (Denman et al., 2007). Stable isotopes are an effective tool for distinguishing N 2 O sources and determining production pathways, which is critical for developing appropriate mitigation strategies (Baggs, 2008;Ostrom and Ostrom, 2011;Toyoda et al., 2017).
The N 2 O molecule has an asymmetric linear structure (NNO), with the following most abundant isotopocules: 14 (Yoshida and Toyoda, 2000). The terms 15 N α and 15 N β refer to the respective central and terminal positions of nitrogen (N) atoms in the NNO molecule (Toyoda and Yoshida, 1999). Isotopic abundances are reported in δ notation, where δ 15 N = R( 15 N/ 14 N) sample /R( 15 N/ 14 N) reference − 1 denotes the relative difference in per mil (‰) of the sample versus atmospheric N 2 (AIR-N 2 ). The isotope ratio R( 15 N/ 14 N) equals x( 15 N)/x( 14 N), with x being the absolute abundance of 14 N and 15 N, respectively. Similarly, Vienna Standard Mean Ocean Water (VSMOW) is the international isotope-ratio scale for δ 18 O. In practice, the isotope δ value is calculated from measurement of isotopocule ratios of sample and reference gases, with the latter being defined on the AIR-N 2 and VSMOW scales. By extension, δ 15 N α denotes the corresponding relative difference of isotope ratios for 14 N 15 N 16 O/ 14 N 14 N 16 O, and δ 15 N β for 15 N 14 N 16 O/ 14 N 14 N 16 O. The site-specific intramolecular distribution of 15 N within the N 2 O molecule is termed 15 Nsite preference (SP) and is defined as SP = δ 15 N α − δ 15 N β (Yoshida and Toyoda, 2000). The term δ 15 N bulk is used to express the average δ 15 N value and is equivalent to δ 15 N bulk = (δ 15 N α + δ 15 N β )/2. Extensive evidence has shown that SP, δ 15 N bulk and δ 18 O can be used to differentiate N 2 O source processes and biogeochemical cycling (Decock and Six, 2013;Denk et al., 2017;Heil et al., 2014;Lewicka-Szczebak et al., 2014Ostrom et al., 2007;Sutka et al., 2003Sutka et al., , 2006Toyoda et al., 2005Toyoda et al., , 2017Wei et al., 2017). Isotopocule abundances have been measured in a wide range of environments, including the troposphere (Harris et al., 2014;Röckmann and Levin, 2005;Toyoda et al., 2013), agricultural soils (Buchen et al., 2018;Ibraim et al., 2019;Köster et al., 2011;Mohn et al., 2012;Ostrom et al., 2007;Park et al., 2011;Pérez et al., 2001Pérez et al., , 2006Toyoda et al., 2011;Verhoeven et al., 2018Verhoeven et al., , 2019Well et al., 2008;Well and Flessa, 2009;Wolf et al., 2015), mixed urban-agricultural environments , coal and waste combustion (Harris et al., 2015b;Ogawa and Yoshida, 2005), fossil fuel combustion (Toyoda et al., 2008), wastewater treatment (Harris et al., 2015a, b;Wunderlin et al., 2012Wunderlin et al., , 2013, groundwater (Koba et al., 2009;Minamikawa et al., 2011;Nikolenko et al., 2019;Well et al., 2005Well et al., , 2012, estuaries (Erler et al., 2015), mangrove forests (Murray et al., 2018), stratified water impoundments (Yue et al., 2018), and firn air and ice cores (Bernard et al., 2006;Ishijima et al., 2007;Prokopiou et al., 2017). While some applications like laboratory incubation experiments allow for analysis of the isotopic signature of the pure source, most studies require analysis of the source diluted in ambient air. This specifically applies to terrestrial ecosystem research, since N 2 O emitted from soils is immediately mixed with background atmospheric N 2 O. To understand the importance of soil emissions for the global N 2 O budget, two-end-member mixing models commonly interpreted using Keeling or Miller-Tans plots are frequently used to back-calculate the isotopic composition of N 2 O emitted from soils (Keeling, 1958;Miller and Tans, 2003). N 2 O isotopocules can be analyzed by isotope-ratio mass spectrometry (IRMS) and laser spectroscopic techniques, with currently available commercial spectrometers operating in the mid-infrared (MIR) region to achieve highest sensitivities. IRMS analysis of the N 2 O intramolecular 15 N distribution is based on quantification of the fragmented (NO + , m/z 30 and 31) and molecular (N 2 O + , m/z 44, 45 and 46) ions to calculate isotope ratios for the entire molecule ( 15 N/ 14 N and 18 O/ 16 O) and the central (N α ) and terminal (N β ) N atom (Toyoda and Yoshida, 1999). The analysis of N 2 O SP by IRMS is complicated by the rearrangement of N α and N β in the ion source, while analysis of δ 15 N bulk (45/44) involves correction for NN 17 O (mass 45). IRMS can achieve repeatability as good as 0.1 ‰ for δ 15 N, δ 18 O, δ 15 N α and δ 15 N β (Potter et al., 2013;Röckmann and Levin, 2005), but an interlaboratory comparison study showed substantial deviations in measurements of N 2 O isotopic composition, in particular for SP (up to 10 ‰) .
The advancement of mid-infrared laser spectroscopic techniques was enabled by the invention and availability of noncryogenic light sources which have been coupled with different detection schemes, such as direct absorption quantum cascade laser absorption spectroscopy (QCLAS; Aerodyne Research Inc. (ARI); Wächter et al., 2008), cavity ring-down spectroscopy (CRDS; Picarro Inc.; Berden et al., 2000) and off-axis integrated cavity output spectroscopy (OA-ICOS; ABB -Los Gatos Research Inc.; Baer et al., 2002) to realize compact field-deployable analyzers. In short, the emission wavelength of a laser light source is rapidly and repetitively scanned through a spectral region containing the spectral lines of the target N 2 O isotopocules. The laser light is coupled into a multi-path cell filled with the sample gas, and the mixing ratios of individual isotopic species are determined from the detected absorption using Beer's law. The wavelengths of spectral lines of N 2 O isotopocules with distinct 17 O, 18 O or position-specific 15 N substitution are unique due to the existence of characteristic rotational-vibrational spectra (Rothman et al., 2005). Thus, unlike IRMS, laser spectroscopy does not require mass-overlap correction. However, the spectral lines may have varying degrees of overlap with those of other gaseous species, which, if unaccounted for, may produce erroneous apparent absorption intensities. One advantage of laser spectroscopy is that instruments can analyze the N 2 O isotopic composition in gaseous mixtures (e.g., ambient air) in a flow-through mode, providing realtime data with minimal or no sample pretreatment, which is highly attractive to better resolve the temporal complexity of N 2 O production and consumption processes (Decock and Six, 2013;Heil et al., 2014;Köster et al., 2013;Winther et al., 2018).
Despite the described inherent benefits of laser spectroscopy for N 2 O isotope analysis, applications remain challenging and are still scarce for four main reasons: 1. Two pure N 2 O isotopocule reference materials (USGS51, USGS52) have only recently been made available through the United States Geological Survey (USGS) with provisional values assigned by the Tokyo Institute of Technology (Ostrom et al., 2018). The lack of N 2 O isotopocule reference materials was identified as a major reason limiting interlaboratory compatibility .
2. Laser spectrometers are subject to drift effects (e.g., due to moving interference fringes), particularly under fluctuating laboratory temperatures, which limits their performance (Werle et al., 1993).
3. If apparent δ values retrieved from a spectrometer are calculated from raw uncalibrated isotopocule mole fractions, referred to here as a δ-calibration approach, an inverse concentration dependence may be introduced. This can arise if the analyzer measurements of isotopocule mole fractions are linear, yet the relationship between measured and true mole fractions has a non-zero intercept (e.g., Griffith et al., 2012;Griffith, 2018), such as due to baseline structures (e.g., interfering fringes; Tuzson et al., 2008).
4. Laser spectroscopic results are affected by mole fraction changes of atmospheric background gases (N 2 , O 2 and Ar), herein called gas matrix effects, due to the difference of pressure-broadening coefficients (Nara et al., 2012) and potentially by spectral interferences from other atmospheric constituents (H 2 O, CO 2 , CH 4 , CO, etc.), herein called trace gas effects, depending on the selected wavelength region. The latter is particularly pronounced for N 2 O due to its low atmospheric abundance in comparison to other trace gases.
Here, we present an intercomparison study of commercially available N 2 O isotope laser spectrometers with the three most common detection schemes: (1) OA-ICOS (N 2 OIA-30e-EP, ABB -Los Gatos Research Inc.); (2) CRDS (G5131-i, Picarro Inc.); (3) QCLAS (dual QCLAS and trace gas extractor (TREX)-mini QCLAS, ARI). Performance characteristics including precision, repeatability, drift and dependence of isotope measurements on [N 2 O] were determined. Instruments were tested for gas matrix effects (O 2 , Ar) and spectral interferences from enhanced trace gas mole fractions (CO 2 , CH 4 , CO, H 2 O) at various [N 2 O] to develop analyzer-specific correction functions. The accuracy of different spectrometer designs was then assessed during a laboratory-controlled mixing experiment designed to simulate two-end-member mixing, in which results were compared to calculated expected values, as well as to those acquired using IRMS (δ values) and gas chromatography (GC, N 2 O concentration). In closing, we provide a calibration workflow that will assist researchers in the operation of N 2 O and other trace gas isotope laser spectrometers in order to acquire accurate isotope analyses.

Analytical techniques
Operational details of the laser spectrometers tested in this study, including wavenumber regions, line positions and line strengths of N 2 O, are provided in Table 1. In Fig. 1, selected N 2 O rotational lines are shown in combination with the absorption lines of the atmospheric most abundant IR-active trace gases (H 2 O, CO 2 , CH 4 , CO and O 3 ) within the different wavenumber regions used by the analyzers. Figure 1 can be used to rationalize possible spectral interferences within different wavenumber regions.

OA-ICOS (ABB -Los Gatos Research Inc.)
The N 2 OIA-30e-EP (model 914-0027, serial number 15-830, ABB -Los Gatos Research Inc., USA) tested in this study was provided by the University of New South Wales (UNSW Sydney, Australia) and is herein referred to as OA-ICOS I ( Table 1). The instrument employs the OA-ICOS technique integrated with a quantum cascade laser (QCL) (Baer et al., 2002). In short, the QCL beam is directed off axis into the cavity cell with highly reflective mirrors, providing an optical path of several kilometers. For further details on the OA-ICOS technique, the reader is referred to the webpage of ABB -Los Gatos Research Inc. (ABB -Los Gatos Research Inc., 2019) and Baer et al. (2002).
The specific analyzer tested here was manufactured in June 2014 and has had no hardware modifications since then. It is also important to note that a more recent N 2 OIA-30e-EP model (model 914-0060) is available, that in addition quantifies δ 17 O. We are unaware of any study measuring N 2 O isotopocules at natural abundance and ambient mole fractions with the N 2 OIA-30e-EP. The only studies published so far reporting N 2 O isotope data apply the N 2 OIA-30e-EP either at elevated [N 2 O] in a standardized gas matrix or using 15 N labeling, including Soto et al. (2015), Li et al. (2016), Kong et al. (2017), Brase et al. (2017), Wassenaar et al. (2018) andNikolenko et al. (2019).

CRDS (Picarro Inc.)
Two G5131-i analyzers (Picarro Inc., USA) were used in this study: a 2015 model (referred to as CRDS I, serial number 5001-PVU-JDD-S5001, delivered September 2015) provided by the Niels Bohr Institute, University of Copenhagen, Denmark; and a 2018 model (referred to as CRDS II, serial number 5070-DAS-JDD-S5079, delivered June 2018) provided by Karlsruhe Institute of Technology, Germany (Table 1). In CRDS, the beam of a single-frequency continuous wave (cw) laser diode enters a three-mirror cavity with an effective pathlength of several kilometers to support a continuous traveling light wave. A photodetector measures the decay of light in the cavity after the cw laser diode is shut off to retrieve the mole fraction of N 2 O isotopocules. For more details, we refer the reader to the webpage of Picarro Inc. (Picarro Inc., 2019) and Berden et al. (2000).
Importantly, the manufacturer-installed flow restrictors were replaced in both analyzer models, as we noted reduced flow rates due to clogging during initial reconnaissance testing. In CRDS I, a capillary (inner diameter, ID: 150 µm, length: 81 mm, flow: 25.2 cm 3 min −1 ) was installed, while CRDS II was equipped with a critical orifice (ID: 75 µm, flow: 12.5 cm 3 min −1 ). Both restrictors were tested and confirmed leakproof. Both analyzers had manufacturer-installed permeation driers located prior to the inlet of the cavity, which were not altered for this study. In December 2017, CRDS I received a software and hardware update as per the manufacturer's recommendations. The CRDS II did not receive any software or hardware upgrades as it was acquired immediately prior to testing.
To the best of our knowledge, the work presented in Lee et al. (2017) and Ji and Grundle (2019) discusses the only published uses of G5131-i models. A prior model (the G5101-i), which employs a different spectral region and does not offer the capability for δ 18 O, was used by Peng et al. (2014), Erler et al. (2015), Li et al. (2015), Lebegue et al. (2016) and Winther et al. (2018).

QCLAS (Aerodyne Research Inc.)
Three QCLAS instruments (ARI, USA; CW-QC-TILDAS-SC-D) were used in this study. One instrument (QCLAS I, serial number 046), purchased in 2013, was provided by Karlsruhe Institute of Technology, Germany, and two instruments, purchased in 2014 (QCLAS II, serial number 065) and 2016 (QCLAS III, serial number 077), were supplied by ETH Zürich, Switzerland (Table 1). QCLAS I was used in all experiments presented in this study, while QCLAS II and III were only used to assess the reproducibility of drift reported in Sect. 3.1.
All instruments were dual-cw QCL spectrometers, equipped with mirror optics guiding the two laser beams through an optical anchor point to assure precise coincidence of the beams at the detector. On the way to the detector, the laser beams are coupled into an astigmatic multipass cell with a volume of approximately 2100 cm 3 in which the beams interact with the sample air. The multiple passes through the absorption cell result in an absorption path length of approximately 204 m. The cell pressure can be selected by the user and was set to 53.3 mbar as a trade-off between line separation and sensitivity. This set point is automatically maintained by the TDL Wintel software (version 1.14.89 ARI, MA, USA), which compensates for variations in vacuum pump speed by closing or opening a throttle valve at the outlet of the absorption cell.
QCLAS instruments offer great liberty to the user as the system can also be operated with different parameter settings, such as the selection of spectral lines for quantification, wavenumber calibration, sample flow rate and pressure. Thereby, different applications can be realized, from high-flow eddy covariance studies or high-mole-fraction process studies to high-precision measurements coupled to a customized inlet system. In addition, spectral interferences and gas matrix effects can be taken into consideration by multi-line analysis, inclusion of the respective spectroscopic parameters in the spectral evaluation or adjustment of the pressure-broadening coefficients. The spectrometers used in this study (QCLAS I-III) were tested under standard settings but were not optimized for the respective experiments. The mini QC-TILDAS spectrometer is used in combination with a preconcentration device (Ibraim et al., 2018); the indicated N QCLAS I was operated as a single laser instrument using laser 1, to optimize spectral resolution of the frequency sweeps. It is important to note the mixing ratios returned by the instrument are solely based on fundamental spectroscopic constants (Rothman et al., 2005), so that corrections such as the dependence of isotope ratios on [N 2 O] have to be implemented by the user in the postprocessing. To our knowledge, QCLAS instruments have so far predominately been used for determination of N 2 O isotopic composition in combination with preconcentration (see below) or at enhanced mole fractions (Harris et al., 2015a, b;Heil et al., 2014;Köster et al., 2013), except for Yamamoto et al. (2014), who had used a QCLAS (CW-QC-TILDAS-SC-S-N2OISO; ARI, USA) with one laser (2189 cm −1 ) in combination with a closed chamber system. To achieve the precision and accuracy levels reported in their study, Yamamoto et al. (2014) corrected their measurements for mixing ratio de-pendence and minimized instrumental drift by measuring N 2 gas every 1 h for background correction. These authors also showed that careful temperature control of their instrument in an air-conditioned cabinet was necessary for achieving optimal results.

TREX-QCLAS
A compact mini QCLAS device (CW-QC-TILDAS-76-CS, serial number 074, ARI, USA) coupled with a preconcentration system (TREX) was provided by Empa, Switzerland. The spectrometer comprises a continuous-wave mid-infrared quantum cascade laser source emitting at 2203 cm −1 and an astigmatic multipass absorption cell with a path length of 76 m and a volume of approximately 620 cm 3 (Ibraim et al., 2018) (Table 1). The TREX unit was designed and manufactured at Empa and is used to separate the N 2 O from the sample gas prior to QCLAS analysis. Thereby, the initial [N 2 O] is increased by a factor of 200-300, other trace gases are removed, and the gas matrix is set to standardized conditions. Before entering the TREX device, CO is oxidized to CO 2 using a metal catalyst (Sofnocat 423, Molecular Products Limited, GB). Water and CO 2 in sample gases were removed by a permeation dryer (PermaPure Inc., USA) in combination with a sodium hydroxide (NaOH)/magnesium perchlorate (Mg(ClO 4 ) 2 ) trap (Ascarite: 6 g, 10-35 mesh, Sigma Aldrich, Switzerland, bracketed by Mg(ClO 4 ) 2 , 2 × 1.5 g, Alfa Aesar, Germany). Thereafter, N 2 O is adsorbed on a HayeSep D (Sigma Aldrich, Switzerland) filled trap, cooled down to 125.1 ± 0.1 K by attaching it to a copper baseplate mounted on a high-power Stirling cryocooler (Cry-oTel GT, Sunpower Inc., USA). N 2 O adsorption requires 5.080 ± 0.011 L of gas to have passed through the adsorption trap. For N 2 O desorption, the trap is decoupled from the copper baseplate, while slowly heating it to 275 K with a heat foil (diameter 62.2 mm, 100 W, HK5549, Minco Products Inc., USA). Desorbed N 2 O is purged with 1-5 cm 3 min −1 of synthetic air into the QCLAS cell for analysis. By controlling the flow rate and trapping time, the [N 2 O] in the QCLAS cell can be adjusted to 60-80 ppm at a cell pressure of 35.6 ± 0.04 mbar. A custom-written LabVIEW program (Version 18.0.1, National Instruments Corp., USA) allows remote control and automatic operation of the TREX. So far, the TREX-QCLAS system has been successfully applied to determine N 2 O emission, as well as N 2 O isotopic signatures from various ecosystems (e.g., Mohn et al., 2012;Harris et al., 2014;Wolf et al., 2015;Ibraim et al., 2019).

GC-IRMS
IRMS analyses were conducted at ETH Zürich using a gas preparation unit (Trace Gas, Elementar, Manchester, UK) coupled to an IsoPrime100 IRMS (Elementar, Manchester, UK). [N 2 O] analysis using gas chromatography was also performed at ETH Zürich (456-GC, Scion Instruments, Livingston, UK). GC-IRMS analyses were conducted as part of experiments described further in Sect. 2.4.8. Further analytical details are provided in Sect. S1 in the Supplement. Table 2 provides O 2 , Ar and trace gas mole fractions of matrix gases and interference test gases used during testing. The four matrix gases comprised synthetic air (matrix a Messer Schweiz AG, Switzerland); synthetic air with Ar (matrix b, Carbagas AG, Switzerland); synthetic air with Ar, CO 2 , CH 4 and CO at near-ambient mole fractions (matrix c, Carbagas AG, Switzerland); and high-purity nitrogen gas (N 2 , Messer Schweiz AG, Switzerland). Matrix gases were analyzed in the World Meteorological Organization (WMO) Global At-mosphere Watch (GAW) World Calibration Center at Empa (WCC Empa) for CO 2 , CH 4 , H 2 O (G1301, Picarro Inc., USA), and N 2 O and CO (CW-QC-TILDAS-76-CS; ARI, USA) against standards of the National Oceanic and Atmospheric Administration/Earth System Research Laboratory/Global Monitoring Division (NOAA/ESRL/GMD). The [N 2 O] in all matrix gases and N 2 were below 0.3 ppb. The three gas mixtures used for testing of spectral interferences contained higher mole fractions of either CO 2 , CH 4 or CO in matrix gas b (Carbagas AG, Switzerland), which prevented spectroscopic analysis of other trace substances.

Matrix and interference test gases
2.2.2 Reference gases (S1, S2) and pressurized air (PA1, PA2) Preparation of pure and diluted reference gases Two reference gases (S1, S2) with different N 2 O isotopic composition were used in this study. Pure N 2 O reference gases were produced from high-purity N 2 O (Linde, Germany) decanted into evacuated Luxfer aluminum cylinders (S1: P3333N, S2: P3338N) with ROTAREX valves (Matar, Italy) to a final pressure of maximum 45 bar to avoid condensation. Reference gas 1 (S1) was high-purity N 2 O only. (2) condensation of NH 3 and reaction controlled by LN 2 ; and (3) thermal decomposition of NH 4 NO 3 in batches of 1 g in 150 mL glass bulbs with a breakseal (Glasbläserei Möller AG, Switzerland) to produce NN 18 O. The isotopic enrichment was analyzed after dilution in N 2 (99.9999 %, Messer Schweiz AG) with a Vision 1000C quadrupole mass spectrometer (QMS) equipped with a customized ambient pressure inlet (MKS Instruments, UK). Triplicate analysis provided the following composition: 36.25 ± 0.10 % of NN 16 O and 63.75 ± 0.76 % of NN 18 O.
High [N 2 O] reference gases (S1-a 90 ppm , S1-b 90 ppm , S1c 90 ppm , S2-a 90 ppm ) with a target mole fraction of 90 ppm were prepared in different matrix gases (a, b, c) using a twostep procedure. First, defined volumes of S1 and S2 were dosed into Luxfer aluminum cylinders (ROTAREX valve, Matar, Italy) filled with matrix gas (a, b and c) to ambient pressure using N 2 O calibrated mass flow controllers (MFCs) (Vögtlin Instruments GmbH, Switzerland). Second, the N 2 O was gravimetrically diluted (ICS429, Mettler Toledo GmbH, Switzerland) with matrix gas to the target mole fraction. Ambient [N 2 O] reference gases (S1-c 330 ppb , S2-c 330 ppb ) with a target mole fraction of 330 ppb were prepared by dosing Table 2. O 2 , Ar content and trace gas concentrations for matrix and interference test gases. Trace gas concentrations of matrix gases were analyzed by WMO GAW WCC Empa against standards of the NOAA/ESRL/GMD. For trace gas concentrations of interference test gases, manufacturer specifications are given. Reported O 2 and Ar content is according to manufacturer specifications. The given uncertainty is the uncertainty stated by the manufacturer or the standard deviation for analysis of n cylinders of the same specification.

Gas
Abbreviation S1-c 90 ppm or S2-c 90 ppm into evacuated cylinders with a calibrated MFC, followed by gravimetric dilution with matrix c. O] isotope reference gases in synthetic air (S1-a 90 ppm , S2-a 90 ppm ) was analyzed in relation to N 2 O isotope standards (Cal1-Cal3) in an identical matrix gas (matrix a) using laser spectroscopy (CW-QC-TILDAS-200; ARI, Billerica, USA). The composition of Cal1-Cal3 is outlined in Sect. S2. For high-mole-fraction reference gases in matrix b and c (S1-b 90 ppm , S1-c 90 ppm , S2-c 90 ppm ), the δ values acquired for S1-a 90 ppm and S2-a 90 ppm were assigned, since all S1 and S2 reference gases (irrespective of gas matrix) were generated from the same source of pure N 2 O gas. Direct analysis of S1b 90 ppm , S1-c 90 ppm and S2-c 90 ppm by QCLAS was not feasible, as no N 2 O isotope standards in matrix b and c were available. The absence of significant difference (< 1 ‰) in N 2 O isotopic composition between S1-b 90 ppm and S1-c 90 ppm in relation to S1-a 90 ppm (and S2-c 90 ppm to S2-a 90 ppm ) was assured by first statically diluting S1-b 90 ppm , S1-c 90 ppm and S2-c 90 ppm to ambient N 2 O mole fractions with synthetic air. This was followed by analysis using TREX-QCLAS (as described in Sect. 2.1.4) against the same standards used for S1-a 90 ppm , S2-a 90 ppm isotope analysis. Ambient mole fraction N 2 O isotope reference gases (S1c 330 ppb , S2-c 330 ppb ) and PA1 and PA2 were analyzed by TREX-QCLAS (Sect. 2.1.4) using N 2 O isotope standards (Cal1-Cal5) as outlined in Sect. S2.

Laboratory setup
All experiments were performed at the Laboratory for Air Pollution/Environmental Technology, Empa, Switzerland, during June 2018 and February 2019. The laboratory was air conditioned to 295 K (±1 K), with ±0.5 K diel variations (Saveris 2, Testo AG, Switzerland), with the exception of a short period (7 to 8 July 2018), where the air conditioning was deactivated to test the temperature dependence of analyzers. Experiments were performed simultaneously for all analyzers, with the exception of the TREX-QCLAS, which requires an extensive measurement protocol and additional time to trap and measure N 2 O (Ibraim et al., 2018) and thus could not be integrated concurrently with the other analyzers. Figure 2 shows a generalized experimental setup used for all experiments. Additional information for specific experiments is given in Sect. 2.4, and individual experimental setups are depicted in Sect. S3. Gas flows were controlled using a set of MFCs (model high-performance, Vögtlin Instruments GmbH, Switzerland) integrated into a MFC control unit (Contrec AG, Switzerland). All MFCs were calibrated by the manufacturer for whole air, which according to Vögtlin Instruments is valid for pure N 2 and pure O 2 as well. Operational ranges of applied MFCs ranged from 0-25 to 0-5000 cm 3 min −1 and had reported uncertainties of 0.3 % of their maximum flow and 0.5 % of actual flow. To reduce the uncertainty of the flow regulation, the MFC with the smallest maximum flow range available was selected. The sum of dosed gas flows was always higher than the sum of gas consumption by analyzers, with the overflow exhausted to room air. Gas lines between gas cylinders and MFCs, as well as between MFCs and analyzers, were 1/8 stainless steel tubing (type 304, Supelco, Sigma Aldrich, Switzerland). Manual two-way (SS-1RS4 or SS-6H-MM, Swagelok, Switzerland) or three-way valves (SS-42GXS6MM, Swagelok, Switzerland) were used to separate or combine gas flows.

Measurement procedures, data processing and calibration
With  (Werner and Brand, 2001). Each experiment was performed over the course of 1 d and consisted of three phases: (1) an initial calibration phase; (2) an experimental phase; and (3) a final calibration phase. During phases (1) and (3), reference gases S1-c 330 ppb and S2-c 330 ppb were analyzed. On each occasion (i.e., twice a day), this was followed by the analysis of PA1, which was used to determine the long-term (day-to-day) repeatability of the analyzers. Phase (2) experiments are outlined in Sect. 2.4. Throughout all three phases, all measurements were systematically alternated with an Anchor gas measurement, the purpose of which was two-fold: (1) to enable drift correction and (2) as a means of quantifying deviations of the measured [N 2 O] and δ values caused by increasing [N 2 O] (Sect. 2.4.4), the removal of matrix gases (O 2 and Ar in Sect. 2.4.5) or addition of trace gases (CO 2 , CH 4 and CO in Sect. 2.4.6). Accordingly, the composition of the Anchor gas varied across experiments (see Sect. 2.4) but remained consistent throughout each experiment. A drift correction was applied to the data if a linear or non-linear model fitted to the Anchor gas measurement over the course of an experiment was statistically significant at p < 0.05. Otherwise, no drift correction was applied.
In Sect. 2.4.3 (repeatability experiments) and 2.4.8 (twoend-member mixing experiments), trace gas effects were corrected according to Eqs. (1), (2) and (3) using derived analyzer-specific correction functions because the CO 2 , CH 4 and CO composition of PA1 in Sect. 2.4.3 and the gas mixtures in Sect. 2.4.8 varied from those of the calibration gases S1-c 330 ppb (S1) and S2-c 330 ppb (S2): and and [x] S2 are the mole fractions of trace gas x in reference gases S1-c 330 ppb and S2-c 330 ppb . It is important to note that the differences in CO 2 and CH 4 mole fractions in S1-c 330 ppb and S2-c 330 ppb are 2 orders of magnitude smaller than the differences with PA1. Thereafter, δ values of trace-gas-corrected, mole-fractioncorrected (Sect. 2.4.8 only) and drift-corrected measurements from the analyzers were normalized to δ values on the international isotope-ratio scales using a two-point linear calibration procedure derived from values of S1-c 330 ppb (S1) and S2-c 330 ppb (S2) calculated using Eq. (4) (Gröning, 2018): where δ Cal, G is the calibrated δ value for sample gas G normalized to international isotope-ratio scales; δ ref, S1 and δ ref, S2 are the respective δ values assigned to reference gases S1-c 330 ppb and S2-c 330 ppb ; δ corr, S1 and δ corr, S2 are the respective δ values measured for the reference gases S1c 330 ppb and S2-c 330 ppb which, if required, were drift corrected; and δ corr, G is the trace-gas-corrected, mole-fractioncorrected (Sect. 2.4.8 only) and drift-corrected (if required) δ value measured for the sample gas G.

Testing of instruments
An overview of all experiments performed in this study, including applied corrections and instruments tested, is provided in Table 4. Trace gas concentrations of high concentration reference gases were retrieved from the composition of matrix gases used for their production (see Table 2); trace gas concentrations in ambient concentration reference gases and pressurized air were analyzed by WMO GAW WCC Empa against standards of the NOAA/ESRL/GMD. The N 2 O isotopic composition was quantified by laser spectroscopy (QCLAS) and preconcentration -laser spectroscopy (TREX-QCLAS) against reference gases previously analyzed by the Tokyo Institute of Technology.

Allan precision
The precision of the laser spectrometers was determined using the Allan variance technique (Allan, 1966;Werle et al., 1993 O], S1-c 90 ppm was dynamically diluted to 1000 or 10 000 ppb [N 2 O] with matrix gas c for 10 h. CRDS I and II were disconnected for the 10 000 ppb measurement because [N 2 O] exceeded the specified measurement range. Daily drifts were estimated using the slope of the linear regression over the measurement period normalized to 24 h (i.e., ppb d −1 and ‰ d −1 ).

Temperature effects
To investigate instrumental sensitivities to variations in ambient temperature, PA1 was simultaneously and continuously measured by all analyzers in flow-through mode for a period of 24 h, while the air conditioning of the laboratory was turned off for over 10 h. This led to a rise in temperature from 21 to 30 • C, equating to an increase in temperature of approximately 0.9 • C h −1 . The increase in laboratory room temperature was detectable shortly after the air conditioning was turned off due to considerable heat being released from several other instruments located in the laboratory. Thereafter, the air conditioning was restarted and the laboratory temperature returned to 21 • C over the course of 16 h, equating to a decrease of roughly 0.6 • C h −1 , with most pronounced effects observable shortly after restart of air conditioning when temperature changes were highest.

Repeatability
Measurements of PA1 were taken twice daily over ∼ 2 weeks prior to and following the experimental measurement period to test the long-term repeatability of the analyzers. Measurements were sequentially corrected for differences in trace gas concentrations (Eqs. 1-3), drift (if required) and then δ calibrated (Eq. 4). No matrix gas corrections were applied because the N 2 , O 2 and Ar composition of PA1 was identical to that of S1-c 330 ppb and S2-c 330 ppb . TREX-QCLAS I measurements for long-term repeatability were collected separately from other instruments over a period of 6 months. Repeatability over shorter time periods (2.5 h) was also tested for each analyzer by acquiring 10 repeated 15 min measurements at different N 2 O mole fractions: ambient (PA1), 1000 and 10 000 ppb N 2 O.

N 2 O mole fraction dependence
To determine the effect of changing [N 2 O] on the measured δ values, S1-c 90 ppm was dynamically diluted with matrix c to various [N 2 O] spanning the operational ranges of the instruments. For both CRDS analyzers mole fractions between 300 to 1500 ppb were tested, while for the OA-ICOS I and QCLAS I mixing ratios ranged from 300 to 90 000 ppb. Between each [N 2 O] step change, the dilution ratio was systematically set to 330 ppb N 2 O to perform an Anchor gas measurement. For each instrument, the effect of increasing [N 2 O] on δ values was quantified by comparing the measured δ values at each step change to the mean measured δ values of the Anchor gas and was denoted δ such that δ = δ measured − δ Anchor and δ Anchor = 0. The experiment was repeated on three consecutive days to test day-to-day variability.

Gas matrix effects (O 2 and Ar)
Gas matrix effects were investigated by determining the dependence of [N 2 O] and isotope δ values on the O 2 or Ar mixing ratio of a gas mixture. For O 2 testing, Gases 1, 2 and 3 (N 2 ) were mixed to incrementally change mixing ratios of O 2 (0 %-20.5 % O 2 ) while maintaining a consistent [N 2 O] of 330 ppb (Table 5). As an Anchor gas, Gas 1 (S1-a 90 ppm ) was dynamically diluted with Gas 2 (matrix a) to produce 330 ppb N 2 O in matrix a. O 2 mole fractions in the various gas mixtures were analyzed with a paramagnetic O 2 analyzer (Servomex, UK) and agreed with expected values to within 0.3 % (relative). For Ar testing, Gas 1 (S1-b 90 ppm ) was dynamically diluted with Gas 2 (matrix b) to produce an Anchor gas with ∼ 330 ppb N 2 O in matrix b. Gases 1, 2 and 3 (N 2 + O 2 ) were then mixed to incrementally change mixing ratios of Ar (0.003 %-0.95 % Ar), while a consistent [N 2 O] of 330 ppb was maintained. Ar compositional differences were estimated based on gas cylinder manufacturer specifications and selected gas flows. In addition, O 2 and Ar effects were derived for N 2 O mole fractions of ∼ 660 and ∼ 990 ppb. These experiments were undertaken in a way similar to those described above, except Anchor gas measurements were conducted once (not triplicated).

Trace gas effects (CO 2 , CH 4 , CO and H 2 O)
The sensitivity of [N 2 O] and δ values on changing trace gas concentrations was tested in a similar way to those described in Sect. 2.4.5. In short, Gas 1 (S1-b 90 ppm ) was dynamically diluted with Gas 2 (matrix b) to create an Anchor gas with 330 ppb N 2 O in matrix b. Gases 1, 2 and 3 (either CO 2 , CH 4 or CO in matrix gas b) were mixed to incrementally change the mixing ratios of the target substances (1.7-2030 ppm CO 2 , 0.01-10.25 ppm CH 4 and 0.14-2.14 ppm CO) while maintaining a consistent gas matrix and [N 2 O] of 330 ppb (Table 5). Trace gas mole fractions in the produced gas mixtures were analyzed with a Picarro G2401 (Picarro Inc., USA) and agreed with predictions within better than 2 %-3 % (relative  The sensitivity of the analyzers to water vapor was tested by firstly diluting Gas 1 (S1-c 90 ppm ) with Gas 2 (matrix c) to produce an Anchor gas with 330 ppb N 2 O. This mixture was then combined with Gas 3 (also matrix c) which had been passed through a humidifier (customized setup by Glasbläserei Möller, Switzerland) set to 15 • C (F20 Julabo GmbH, Germany) dew point. By varying the flows of Gases 2 and 3, different mixing ratios of water vapor ranging from 0 to 13 800 ppm were produced and measured using a dewpoint meter (model 973, MBW, Switzerland). H 2 O effects were quantified as described above, but [N 2 O] results were additionally corrected for dilution effects caused by the addition of water vapor into the gas stream. Water vapor dependence testing was not performed on the TREX-QCLAS I, as the instrument is equipped with a permeation dryer at the inlet.

CO 2 and CO removal using NaOH (Ascarite) and Sofnocat
The efficiency of NaOH and Sofnocat for removing spectral effects caused by CO 2 and CO was assessed by repeating CO 2 and CO interference tests (Sect. 2.4.6) but with the respective traps connected in line. These experiments were triplicated but only undertaken at ∼ 330 ppb N 2 O. NaOH traps were prepared using stainless steel tubing (OD 2.54 cm, length 20 cm) filled with 14 g Ascarite (0-30 mesh, Sigma Aldrich, Switzerland) bracketed by 3 g Mg(ClO 4 ) 2 (Alfa Aesar, Germany) each separated by glass wool. The Sofnocat trap was prepared similarly using stainless steel tubing (OD 2.54 cm, length 20 cm) filled with 50 g Sofnocat (Sofnocat 423, Molecular Products Limited, GB) and capped on each side with glass wool.

Two-end-member mixing
The ability of the instruments to accurately extrapolate N 2 O source compositions was tested using a simulated two-endmember mixing scenario in which a gas with high N 2 O concentration, considered to be a N 2 O source gas (SG), was dynamically diluted into a gas with ambient N 2 O concentration (PA2), considered to be background air. N 2 O mole fractions were raised above ambient levels (denoted as N 2 O) in three different scenarios ranging (1) 0-30 ppb, (2) 0-700 ppb and (3) 0-10 000 ppb. In each scenario, two isotopically different source gases with high N 2 O concentration were used; one source gas (SG1-a 90 ppm ) was 15 N depleted compared to PA2, and a second source gas (SG2-a 90 ppm ) was 15 N enriched compared to PA2 (Table 3). The three different mixing scenarios and two different source gases resulted in a total of six mixing scenarios (referred to as Exps. 1-6). During each experiment, PA2 was alternated with PA2 + SG in four different mixing ratios to give a span of N 2 O concentrations and isotopic compositions required for Keeling plot analysis. Each experiment was triplicated. OA-ICOS I and QCLAS I were used in all experiments (Exps. 1-6), CRDS was used for N 2 O 0-30 ppb and 0-700 ppb (Exps. 1-4) and TREX-QCLAS was only used for N 2 O 0-30 ppb (Exps. 1-2).
To test the robustness of trace gas correction equations derived for each analyzer in Sect. 3.6, NaOH and Sofnocat traps were placed in line between the PA2 + SG mixtures and the analyzers such that we could ensure a difference in CO 2 and CO mole fractions between the measured gas mixture and reference gases (S1-c 330 ppb , S2-c 330 ppb ). The experiments were also bracketed by two calibration phases (S1-c 330 ppb , S2-c 330 ppb ) to allow for δ calibration, followed by two phases where the N 2 O concentration dependence was determined.
Gas samples for GC-IRMS analysis were taken in the same phase (last 5 min of 15 min interval) used during the minute prior to the final 5 min used for averaging by the laser-based analyzers. The gas was collected at the common overflow port of the laser spectrometers using a 60 mL syringe connected via a Luer lock three-way valve to the nee-dle and port. The 200 mL samples were taken at each concentration step. A 180 mL gas sample was stored in preevacuated 110 mL serum crimp vials for isotopic analysis using IRMS. IRMS analyses were conducted at ETH Zürich using a gas preparation unit (Trace Gas, Elementar, Manchester, UK) coupled to an IsoPrime100 IRMS (Elementar, Manchester, UK). The remaining 20 mL were injected in a pre-evacuated 12 mL Labco exetainer for [N 2 O] analysis using gas chromatography equipped with an electron capture detector (ECD) performed at ETH Zürich (Bruker, 456-GC, Scion Instruments, Livingston, UK). After injection, samples were separated on HayeSep D packed columns with a 5 % CH 4 in Ar mixture (P5) as carrier and make-up gas. The GC was calibrated using a suite of calibration gases at N 2 O concentrations of 0.393 (Carbagas AG, Switzerland), 1.02 (PanGas AG, Switzerland) and 3.17 ppm (Carbagas AG, Switzerland). For further analytical details, see Verhoeven et al. (2019) and Sect. S1.
For the laser-based analyzers, data were processed as described in Sect. 2.3.2 using the following sequential order: (1) analyzer-specific correction functions, determined in Sect. 3.6, were applied to correct for differences in trace gas concentrations (CO 2 , CO) between sample gas and calibration gases; (2) the effect of [N 2 O] changes was corrected using a three-point correction; (3) a drift correction based on repeated measurements of PA2 was applied if necessary; and (4) δ values standardized to international scales (Eq. 4) using S1-c 330 ppb and S2-c 330 ppb .

Results
Note that due to the large number of results acquired in this section, only selected results are shown in Figs. 3 to 14. The complete datasets (including [N 2 O], δ 15 N α , δ 15 N β and δ 18 O acquired by all instruments tested) are provided in Sect. S4.

Allan precision
Allan deviations (square root of Allan variance) for 5 and 10 min averaging times, often reported in manufacturer specifications, at ∼ 327, 1000 and 10 000 ppb [N 2 O] are shown in Table 6.
At near-atmospheric N 2 O mole fractions of ∼ 326.5 ppb, both CRDS analyzers showed the best precision and stability for the measurement of δ 15 N α , δ 15 N β and δ 18 O (0.32 ‰-0.41 ‰, 0.41 ‰-0.45 ‰, 0.41 ‰-0.46 ‰ at 300 s averaging time, respectively), while for the precision of [N 2 O], the OA-ICOS I and the CRDS II showed best performance (1.7 × 10 −2 ppb at 300 s averaging time) (Figs. 3 and S4-1; Table 6). The Allan precision of CRDS and OA-ICOS analyzers further improved with increasing averaging times, and optimal averaging times typically exceeded 1.5-3 h. The precision and daily drift of the OA-ICOS I and both CRDS analyzers were in agreement with manufacturer specifications (ABB -Los Gatos Research Inc., 2019; Picarro Inc., 2019). The CRDS II outperformed the CRDS I for precision, presumably due to manufacturer upgrades/improvements in the newer model. The QCLAS spectrometers exhibited significant differences between instruments, which might be due to differences in the instrument hardware/design, as instruments were manufactured between 2012 and 2016, or in the parameter setting (such as cell pressure and tuning parameters) of different analyzers.
Generally, short-term (approximately up to 100 s) precision of QCLAS instruments was compatible or superior to CRDS or OA-ICOS, but data quality was decreased for longer averaging times due to drift effects. Nonetheless, the performance of QCLAS I, II and III generally agrees with Allan precision measurements executed by Yamamoto et al. (2014), who reported 1.9 ‰-2.6 ‰ precision for δ values at ambient N 2 O mole fractions and 0.4 ‰-0.7 ‰ at 1000 ppb N 2 O. QCLAS I, which was tested further in Sect. 3.2-3.7, displayed the poorest performance of all QCLAS analyzers, in particular for δ 15 N β . The primary cause of the observed excess drift in QCLAS I was fluctuating spectral baseline structure (ARI, personal communication, 2019), which can be significantly reduced by applying an automatic spectral correction method developed by ARI. This methodology is currently in a trial phase and thus not yet implemented in the software that controls the QCLAS instruments. A brief overview of the methodology is provided in Sect. S5, and corrected results for QCLAS I are provided in Table 6. This methodology is not discussed in detail here as it is beyond the scope of this work. Nonetheless, QCLAS I achieved Allan deviations of ∼ 0.4 ‰ at 300 s averaging time for δ 15 N α and δ 15 N β at ambient N 2 O mole fractions when this correction method was applied by ARI.
At [N 2 O] of 1000 ppb, the precision of δ values measured by all analyzers, except CRDS I, significantly improved due to greater signal-to-noise ratios. Whilst the performance of OA-ICOS I was similar to that of CRDS II for δ 15 N α and δ 15 N β (0.24 ‰ and 0.24 ‰ for CRDS II; 0.28 ‰ and 0.37 ‰ for OA-ICOS I at 300 s averaging time), CRDS II displayed the best precision for δ 18 O (0.21 ‰ at 300 s averaging time). Also notable was the improved performance of the 2018 model (CRDS II) compared to the 2015 model (CRDS I). QCLAS analyzers showed the best 1 s precision for δ values, but beyond 100 s, δ measurements were still heavily affected by instrumental drift resulting in lower precision, especially for QCLAS I. When the spectral correction method described in Sect. S5 was applied, QCLAS I achieved Allan deviations of ∼ 0.2 ‰ at 300 s averaging time for δ 15 N α and δ 15 N β at 1000 ppb N 2 O.
At [N 2 O] of 10 000 ppb, all analyzers showed excellent precision, with QCLAS I, II and III outperforming OA-ICOS I for precision of δ 15 N α and δ 15 N β (collectively better than 0.10 ‰ at 300 s averaging time for both δ 15 N α and δ 15 N β ). QCLAS II had the best precision for [N 2 O] (1.2 ppb at 300 s averaging time). OA-ICOS I and QCLAS III were the only analyzers tested in this study that could be used to measure δ 18 O at 10 000 ppb N 2 O. OA-ICOS I attained a precision of 0.17 ‰, while QCLAS III attained a precision of 0.48 ‰, both with 300 s averaging time. QCLAS I achieved Allan deviations of ∼ 0.02 ‰-0.03 ‰ at 300 s averaging time for δ 15 N α and δ 15 N β at 10 000 ppb N 2 O when the spectral correction method (Sect. S5) was applied.
The precision of instruments on [N 2 O] measurements at 1000 and 10 000 ppb N 2 O might not be representative because of small fluctuations in the final gas mixture produced by the MFCs, which were likely amplified due to the small dilution ratios. Moreover, the different relative increases in Allan deviation compared to measurements at 326.5 ppb might have been caused by the different internal plumbing volumes, flow rates and spectral fits used for the analyzers, which could scale or add to the increased Allan deviation introduced via the MFCs. Therefore, the indicated [N 2 O] precisions should be considered as a pessimistic estimate. Nonetheless, the observed decline in [N 2 O] precision for all analyzers was around 1 order of magnitude when changing from atmospheric N 2 O mole fractions to 1000 ppb N 2 O and from 1000 ppb to 10 000 ppb N 2 O.

Temperature effects
All instruments tested showed significant effects, albeit to varying degrees, on their measurements due to the change in laboratory temperature (Figs. 4 and S4-2). The OA-ICOS I displayed no clear temperature effects for [N 2 O], δ 15 N α and δ 15 N β but displayed a moderate temperature dependence for δ 18 O measurements (up to 14 ‰ deviation from the mean), with measurement drift closely paralleling the laboratory temperature (r 2 = 0.78). Both CRDS instruments displayed smaller shifts in [N 2 O] (up to 0.14 ppb deviation from the mean), δ 15 N α , δ 15 N β and δ 18 O that occurred particularly when the laboratory temperature had an acute change. QCLAS I showed a strong temperature dependence on δ 15 N α (r 2 = 0.85) and δ 15 N β (r 2 = 0.96).

Repeatability
The best long-term repeatability for δ values was achieved by TREX-QCLAS I with 0.60 ‰ for δ 15 N α , 0.37 ‰ for δ 15 N β and 0.46 ‰ for δ 18 O, even though measurements were taken over a 6-month period ( and δ values, suggesting that these dependencies were either analyzer-specific or differences were due to hardware/software modifications between different production years. Preconcentration prior to analysis, as performed in TREX-QCLAS I, eliminated O 2 dependencies as the gas matrix was normalized to synthetic air (20.5 % O 2 ). The change in Ar composition of the matrix gas caused minor, yet measurable, interferences on [N 2 O] and δ measurements ( Fig. S4-5). The range investigated was between approximately 0 % and 0.95 % Ar, as anticipated for N 2 O in synthetic air (no Ar) reference gas versus a whole air (with Ar) sample gas. The effects observed for a 0.95 % change in [Ar] were significantly smaller than that observed for O 2 but might extend to a similar range for sample and reference gases with higher differences in [Ar]. The interference effects were found to be best described by second-order polynomial functions, though we expect that a linear fit would serve equally well if a larger change in [Ar] was investigated. Although most functions to describe the dependence on Ar across all instruments were statistically significant (p < 0.05), maximum effects did not transgress the repeata-     (Fig. S4-2). The laboratory temperature is indicated by a solid orange line and was allowed to vary over time. Cell temperatures for each instrument are also plotted for comparison. The analyzers began acquiring measurements at 00:00 CEST on 8 July 2018, capturing the end of the rising limb of the laboratory temperature. Results are plotted as the deviation from the mean, without any anchoring to reference gases. We could not adequately predict the nature in which the slopes of the interference effects scaled with N 2 O mole fractions. Overall, this suggests that interference effects were analyzer-specific and varied according to instrument-specific Measurements span the manufacturer-specified operational ranges of the analyzers. The experiment was repeated on three separate days. A linear regression is indicated by the solid line, and a residual plot is provided above each plot. Individual linear equations, coefficients of determination (r 2 ) and p values are indicated above each plot. The remaining plots for δ 15 N β and δ 18 O are provided in Sect. S4 (Fig. S4-3 (5) and (6) to fit values for the constants A and B for [N 2 O] meas, mix , and a, b and c for δ meas, mix resulted in a total of 11 analyzer-specific values (Sect. S8). With gasspecific constants established, interferences on [N 2 O] and δ measurements for a sample gas G for a given analyzer can be corrected using Eqs. (7)-(8): and δ values of sample gas G, respectively; [O 2 ] G is the difference in O 2 mole fraction between sample gas G and reference gases. Correction using Eqs. (7)-(8) removes the O 2 effect to a degree that corrected measurements from Sect. 3.5.1 are typically within the uncertainty bounds of the anchor (Sect. S8).
Although Ar effects seemingly scaled with increased N 2 O mole fractions, we did not derive scaling coefficients for Ar because the derived Ar correction equations at 330, 660 and 990 ppb N 2 O were typically not statistically significant at p < 0.05. These interferences also did not always exceed the repeatability of Anchor gas measurements. Although we could have tested for effects for [Ar] changes greater than 0.95 %, we limited our experiments to [Ar] expected in tropospheric samples.

Trace gas effects (H 2 O, CO 2 , CH 4 and CO)
3.6.1 Trace gas effects at ambient N 2 O mole fractions The apparent offset of [N 2 O] and δ values resulting from the change in CO 2 composition of the matrix gas was best described by linear functions (Figs. 7 and S4-6). OA-ICOS I exhibited discrete and well-defined linear interference effects of CO 2 on [N 2 O], δ 15 N α , δ 15 N β and δ 18 O (all r 2 > 0.95), likely due to crosstalk between CO 2 absorption lines situated near 2192.46 and 2192.33 cm −1 . Both CRDS instruments showed CO 2 interference effects of smaller magnitude for [N 2 O], δ 15 N α and δ 18 O, presumably due to CO 2 absorption lines at 2196.21, 2195.72 and 2196.02 cm −1 . QCLAS I displayed less well-defined CO 2 interference effects for δ 15 N β , which was possibly due to several overlapping absorption lines of CO 2 located near 2187.85 cm −1 . All linear functions derived for the TREX-QCLAS I were not statistically significant at p < 0.05. As shown in Figs. 7 and S4-6, the NaOH trap was effective in removing the CO 2 effect (if present) across the mole fraction ranges tested for all instruments.
Similarly, CH 4 effects on apparent [N 2 O] and δ values were well described by linear functions (Figs. 8 and S4-7). The largest effects were for CRDS I and II, which both displayed strong CH 4 dependencies for δ 15 N α and δ 18 O of similar magnitude. This might be due to crosstalk of 14 N 15 N 16 O and 14 N 14 N 18 O absorption lines with the respective CH 4 lines located at 2195.76 and 2195.95 cm −1 . For OA-ICOS I, minor CH 4 effects were observed for δ 15 N β , due to absorption line overlap at 2192.33 cm −1 . QCLAS I did not display any CH 4 interference effect over the tested [CH 4 ] range. Linear functions derived for the TREX-QCLAS I were not statistically significant at p < 0.05. The similarity between the [N 2 O] dependencies on CH 4 mole fractions for OA-ICOS I, CRDS I, II and QCLAS I suggests that the apparent effects may be due to small fluctuations in the gas mixtures produced by the MFCs, rather than a discrete spectral interference effect.
The CRDS analyzers showed minor interference effects for δ 15 N α and δ 15 N β on [CO] (0.14-2.14 ppm) (Fig. S4-8), likely due to crosstalk with CO absorption lines located at 2195.69 and 2195.83 cm −1 . The magnitude of these effects was similar for both models. QCLAS I displayed interference effects for δ 15 N α and δ 15 N β caused by a CO absorption line located near 2187.9 cm −1 , although this effect did not exceed the repeatability of the Anchor gas (containing no CO) over the measurement range. The effects of [CO] on δ values acquired using OA-ICOS I and TREX-QCLAS I were not statistically significant at p < 0.05. Similar to CH 4 , the resemblance of [CO] effects to [N 2 O] measurements for OA-ICOS I, CRDS I, II and QCLAS I suggests that the apparent effects may be due to inaccuracies in the dynamic dilution process, rather than a discrete spectral interference effect. The Sofnocat trap was effective in removing CO (if present) across the mole fraction ranges tested for all instruments.
OA-ICOS I exhibited large effects of [H 2 O] (0-13 800 ppm) on δ 15 N β (up to −10 ‰) and δ 18 O (up to −15 ‰), and minor dependencies for δ 15 N α (up to 4 ‰) and [N 2 O] (up to 1 ppb) across the range tested (Fig. S4-9). For QCLAS I, the H 2 O effect was largest for δ 15 N α (up to 20 ‰), whilst minor effects for [N 2 O] (up to 2 ppb) were observed in relation to the Anchor gas (no H 2 O). In contrast, both CRDS instruments showed no significant effects across the range tested, which is attributable to the installation of permeation dryers inside the analyzers by the manufacturer.  ] introduced to the analyzers could be described using Eqs. (9) and (10): where [N 2 O] meas, mix and δ meas, mix are the measured offsets on [N 2 O] and δ values for the gas mixtures introduced to the analyzers as reported in Sect. 3.6.1, respectively; [x] A is the difference in trace gas mole fraction between the gas mixture and Anchor gas as reported in Sect. 3.6.1; and A x , B x , a x and b x are constants that are trace gas and instrument specific. The constant b x only occurs when there is spectral overlap from the trace gas and 14 N 14 N 16 O absorption lines. For a sample gas G, the effect can then be corrected by using Eqs. (11) and (12): In Eqs. (11)-(12), the sum of the effect of all interfering gases with overlapping absorption lines is taken into account. Similar to Sect. 3.5.2, correction using Eqs. (11)-(12) removes the trace gas interference effects to the extent that corrected measurements from Sect. 3.6.1 are within the repeatability bounds of the Anchor gas (Sect. S8). Similar inverse relationships have been described by Malowany et al. (2015) for H 2 S interferences on δ 13 C−CO 2 .

Two-end-member mixing
Results for the two-end-member mixing experiment were evaluated in two different ways. First, results for individual gas mixtures acquired by laser spectroscopy and GC-IRMS were compared to expected [N 2 O] and δ values calculated from N 2 O mole fractions and isotopic composition of endmembers and mixing fractions. Second, source values were extrapolated using a weighted total least squares regression analysis, known as Keeling plot analysis (Keeling, 1958), and compared to assigned δ values of the source gas used in each experiment.

Comparison with expected [N 2 O] and δ values
Triplicate measurements (mean ±1σ ) obtained using the laser spectrometers and GC-IRMS were plotted against expected [N 2 O] and δ values calculated using MFC flow rates, N 2 O mole fractions and isotopic composition of background and source gases (Figs. 12-15). Comparisons between individual laser spectrometer measurements and GC-IRMS are plotted in Sect. S9 and are discussed only briefly below.

OA-ICOS I
Generally, there was good agreement of [N 2 O] between the OA-ICOS I and expected values, although the analyzer overestimated mole fractions at higher N 2 O during Exps. 5 and 6. There was excellent agreement between the OA-ICOS I and calculated expected δ values (all r 2 > 0.95; Figs. 9 and S4-10). Measurements for δ 15 N α were mostly within ±2.4 ‰ of expected values, while δ 15 N β , δ 15 N bulk and SP  (Fig. S4-6). The standard deviation of the Anchor gas (±1σ ) is indicated by dashed lines. Data points represent the mean and standard deviation (1σ ) of triplicate measurements. Dependencies are best described by linear fits, which are indicated by solid lines. Individual equations, coefficients of determination (r 2 ) and p values are indicated above each plot for the 330 ppb N 2 O data only.  (Fig. S4-7). Data points represent the mean and standard deviation (1σ ) of triplicate measurements. Dependencies are best described by linear fits, which are indicated by solid lines. Individual equations, coefficients of determination (r 2 ) and p values are indicated above each plot for the 330 ppb N 2 O data only.
were all within ±2 ‰ of expected values. δ 18 O measurements were the poorest performing but were typically within ±3.6 ‰ of expected values. Similarly, there was excellent agreement between OA-ICOS I and IRMS isotope values (all r 2 > 0.95), which agreed within 1.7 ‰-2.4 ‰ (Fig. S9-2). The standard deviations of triplicate isotope measurements decreased dramatically with increasing N 2 O, improving from 1 ‰ to 2 ‰ during Exps. 1 and 2 to typically better than 0.1 ‰ during Exps. 5 and 6. Conversely, the standard deviations of triplicate sample measurements for [N 2 O] increased with increasing N 2 O, rising from < 0.1 ppb during Exps. 1-4 to > 1 ppb during Exps. 5 and 6. Nonetheless, all OA-ICOS I [N 2 O] measurements had better 1σ repeatability than those acquired using GC. The repeatability of the triplicate isotope measurements with OA-ICOS I was typically better than IRMS exclusively at higher N 2 O (> 700 ppb). There was excellent agreement between CRDS I and IRMS isotope values (all r 2 > 0.93), which agreed to within 0.5 ‰-1.9 ‰ (Fig. S9-3). In general, the standard deviations of triplicate isotope measurements increased as a function of N 2 O, with the lowest deviations of 0.1 ‰-1 ‰ occurring when N 2 O < 100 ppb. However, two triplicated measurements for δ 15 N bulk had standard deviations better than 0.1 ‰. The standard deviations of triplicate measurements for [N 2 O] also increased with increasing N 2 O mole fractions, rising from 0.03-0.07 ppb when N 2 O =∼ 0 ppb (i.e., ambient conditions) to ∼ 1 ppb when N 2 O =∼ 700 ppb. With the exception of one triplicate measurement, all CRDS I [N 2 O] measurements had better 1σ repeatability than those acquired using GC. Overall, IRMS had slightly better repeatability (most ranging from 0.1 ‰ to 1 ‰) than CRDS I (most ranging from 0.1 ‰ to 2 ‰) for isotopic measurements.

CRDS II
Similar to results for CRDS I, [N 2 O] acquired by CRDS II were in good agreement with expected values but slightly underestimated mole fractions at higher N 2 O during Exps. 3 and 4. There was excellent agreement between the CRDS II and calculated expected isotope values (all r 2 > 0. 99;. Measurements for δ 15 N α and SP were typically better than ±0.8 ‰ of expected values, while δ 15 N β , δ 15 N bulk measurements were all within ±0.4 ‰ of expected values. δ 18 O measurements were within ±1.0 ‰ of expected values. There was excellent agreement between CRDS II and IRMS isotope values (all r 2 > 0.98), which agreed within ±0.6 ‰-1.4 ‰ (Fig. S9-4). The standard deviations of triplicate isotope measurements typically decreased as a function of N 2 O, with the lowest deviations of < 0.1 ‰-0.3 ‰ occurring when N 2 O =∼ 700 ppb. Conversely, the standard deviations of triplicate sample measurements for [N 2 O] increased with increasing N 2 O, rising from 0.04-0.09 ppb when N 2 O =∼ 0 ppb (i.e., ambient conditions) to ∼ 0.4 ppb when N 2 O =∼ 700 ppb. All CRDS II [N 2 O] measurements had better 1σ repeatability than those acquired using GC. There was no clear distinction between CRDS II and IRMS triplicate repeatability, with both achieving triplicate repeatability ranging from 0.1 ‰ to 1 ‰ for most isotopic measurements. However, the repeatability of SP CRDS II measurements was mostly better than IRMS, achieving triplicate repeatability between 0.1 ‰ and 0.6 ‰, compared to 0.2 ‰-1 ‰ for IRMS.

QCLAS I
There was good agreement of [N 2 O] between QCLAS I and expected values; however, the analyzer underestimated mole fractions at higher N 2 O during Exps. 5 and 6. Unfortunately, it is clear from the large spread of isotope values depicted in Fig. 12 that the standardized calibration scheme selected for the two-end-member mixing tests was insufficient for acquiring accurate and precise isotopic measurements using QCLAS I. For this reason, we urge researchers not to overinterpret such results, as the implementation of a QCLAS-specific calibration procedure (in line with results from Sect. 3.1 and 3.3) would improve results dramatically. Nonetheless, QCLAS I obtained accurate results at higher N 2 O mole fractions (indicated in red in Figs. 12 and S4-13), such that when N 2 O < 700 ppb measurements were excluded, δ 15 N α , δ 15 N β , δ 15 N bulk and SP were within ±3.0 ‰, 1.4 ‰, 1.4 ‰ and 3.8 ‰ of calculated expected values, respectively. Similarly, QCLAS I showed good agreement with IRMS only at higher N 2 O (> 700 ppb; Fig. S9-5). Similar to OA-ICOS I, the standard deviations of QCLAS I triplicate isotope measurements decreased dramatically with increasing N 2 O, improving from ∼ 10 ‰ during Exps. 1 and 2 to typically between 0.1 ‰ and 1 ‰ during Exps. 5 and 6. Conversely, the standard deviations of triplicate sample measurements for [N 2 O] increased with increasing N 2 O, rising from < 0.1 ppb during Exps. 1-4, to > 1 ppb during Exps. 5 and 6. All QCLAS I [N 2 O] measurements had better 1σ repeatability than those acquired using GC. QCLAS I had triplicate isotope measurement standard deviations comparable to IRMS only at higher N 2 O (> 700 ppb).

TREX-QCLAS I
There was good agreement of N 2 O mixing ratios between the TREX-QCLAS I and expected values. Similarly, there was excellent agreement between the TREX-QCLAS I and calculated expected isotope values (all r 2 > 0. 97;. Measurements for δ 15 N α , δ 15 N β , δ 15 N bulk and SP were within ±0.29 ‰, 0.32 ‰, 0.23 ‰ and 0.41 ‰ of expected values, respectively. δ 18 O measurements were typically within ±0.24 ‰ of expected values. Generally, the standard deviations of triplicate isotope measurements de-creased with increasing N 2 O, improving from typically 0.2 ‰-0.3 ‰ at low N 2 O mole fractions (ambient) to close to or better than 0.1 ‰ when N 2 O reached 30 ppb. Conversely, the standard deviations of triplicate sample measurements for [N 2 O] increased with increasing N 2 O, rising from < 0.3 to ∼ 1 ppb. No comparison could be made between TREX-QCLAS I and IRMS measurements because TREX-QCLAS measurements were undertaken separately from the other instruments.

Source identification using Keeling analysis
Despite the excellent agreement between expected and measured values across all experiments for OA-ICOS I, CRDS I and II, and TREX-QCLAS I, the extrapolated source intercept values acquired using Keeling analysis showed large standard errors, especially for Exps. 1 and 2 ( N 2 O = 30 ppb) (Figs. 14 and S4-15; Sect. S10). This was mostly due to the small mole fraction range (i.e., large inverse mole fraction range) over which the regression line was extrapo-lated in order to acquire the intercept value. The cause of the erroneous intercepts values was likely two-fold: (1) the extrapolated source was highly susceptible to measurements acquired at background levels, and due to the inherent greater uncertainty associated with measurements acquired at ambient N 2 O mole fractions, intercepts can be skewed accordingly; and (2) any further non-linearity that could not be taken into account in the three-point concentration dependence correction applied. Overall, this implies that N 2 O isotope source studies using laser spectroscopy focusing on  (Fig. S4-14). The solid black line denotes the 1 : 1 line, while the dotted line indicates ±1σ of the residuals from the 1 : 1 line. The dashed green line represents a linear fit to the data. Individual equations, coefficients of determination (r 2 ) and p values are indicated above each plot. Each data point represents the mean and standard deviation (1σ ) of triplicate measurements. The inset plots indicate the standard deviation (1σ ) of the triplicate measurements achieved at different N 2 O mole fractions, and the 1 : 1 line is similarly a solid line.
near-ambient N 2 O variations remain a challenging undertaking, and one should expect large uncertainty in source estimates over small mole fraction changes.
For Exps. 3-6, however, the accuracy of the source intercept and its standard error improved dramatically for all analyzers on account of the decreasing uncertainty in measurement. OA-ICOS I and both CRDS analyzers typically achieved within ±2 ‰-5 ‰ of the assigned values for δ 15 N α , δ 15 N β , δ 15 N bulk , SP and δ 18 O, and had performance comparable to or better than the GC-IRMS approach (Figs. 14 and S4-15). Similarly, the standard error of all intercepts decreased dramatically for Exps. 3-6, and all analyzers typically achieved better than ±1 ‰ standard error on derived intercepts in Exps. 5 and 6.

Factors affecting the precision and accuracy of N 2 O isotopocule measurements using laser spectroscopy
A summary of results is presented in Table 8. Our results highlight that the precision at which laser-based analyzers acquire N 2 O isotopocule measurements is a function of N 2 O mole fraction, the selected measuring and averaging times and calibration frequency according to measurement stability. The degree of accuracy obtained using different laser spectrometers is ultimately a function of the robustness of corrections aimed at removing matrix and trace gas effects, and the selected calibration procedure aimed at standardizing the data to international scales. All spectrometers tested displayed temperature effects on isotope measurements, which can be attributed to differences in the lower state energies of the probed N 2 O isotopocule lines (Sect. S11) (e.g., Wächter et al., 2008). The temperature sensitivities of all analyzers tested necessitates that, especially when deployed in the field, they be operated under temperature-controlled conditions (such as in maintained field stations).
The experiments performed in this study were undertaken using a standardized protocol. Calibration was performed on isotope δ values derived from raw uncalibrated isotopocule amount fractions, thus requiring [N 2 O] dependence corrections. Alternative approaches aimed at calibrating isotopocule amount fractions prior to deriving δ values were not included in our study but have the potential to remove the need for this correction (e.g., Wen et al., 2013;Flores et al., 2017;Griffith, 2018) if appropriate reference materials become available. Isotopocule calibration approaches would require a set of N 2 O standard gases with high-accuracy mole fractions in addition to assigned δ values.
All analyzers tested in this study showed significant effects from changing O 2 composition of the gas matrix. Although the magnitude of this effect ultimately varied across the analyzers and was dependent on N 2 O mixing ratios, the effect of a change in O 2 composition of 20.5 % was typically on the order of 10 ‰ to 30 ‰ for δ values. Similar O 2 dependencies have been reported by Erler et al. (2015) for CRDS N 2 O isotope laser spectrometers, as well as for CRDS H 2 O isotope analyzers (Johnson and Rella, 2017). The underlying reason for this effect is differences in N 2 versus O 2 (and Ar) broadening parameters of the probed N 2 O isotopocule lines. In short, the N 2 , O 2 (and Ar) broadening parameters depend on rotational quantum numbers of the respective N 2 O lines (Henry et al., 1985; Sect. S11). Thus, differences in the rotational quantum numbers for a pair of isotopocules (e.g., 14 (Fig. S4-15). Estimated Source = True Source is indicated by a solid black line at y = 0, and the dotted lines indicated ±2 ‰ deviation from y = 0. The change in concentration exceeding that of the background gas is indicated for Exps. 1-2 ( N 2 O =∼ 30 ppb), 3-4 ( N 2 O =∼ 700 ppb) and 5-6 ( N 2 O =∼ 10 000 ppb). Note that the QCLAS I results for Exps. 1 and 2 are not depicted to maintain clarity, as they exceed the selected y-axis scale. and Ar broadening parameters. Consequently, differences in the O 2 or Ar content of the sample gas matrix and that of the reference gas affect measured isotope ratios and lead to changes in apparent δ values. Nonetheless, the magnitude of effects reported for the CRDS analyzers in this study varied across CRDS I (a 2015 model) and CRDS II (a 2018 model), as well as from those reported by Erler et al. (2015). Therefore, we recommended that in applications where O 2 concentrations vary, such as groundwater, estuaries, stratified waterbodies and incubation studies, researchers test individual analyzers for their specific dependencies to allow for correction. This is especially important given that N 2 O production and reduction processes in such environments are strongly controlled by O 2 availability. Although the Ar effects characterized in this study were not large, it is nonetheless recommended as a precautionary measure that researchers ensure, where possible, the standard calibration gas Ar composition is similar to that of the sample gas. The CO 2 effects for OA-ICOS and CH 4 effects for CRDS analyzers must be considered for applications of these analyzers where CO 2 and CH 4 may also co-vary, such as during diel atmospheric monitoring, in soil-flux chamber measurements, incubation studies and even waterbodies (e.g., Erler et al., 2015). These effects need to be either characterized and corrected for by the user, or the interfering gas quantitatively removed. To our knowledge, there is currently no commercially available technique to remove CH 4 from a gas stream without affecting N 2 O, and therefore independent coanalysis of CH 4 is ultimately required to correct for these effects post-measurement. Similarly, while water vapor effects can in theory be characterized and corrected for all instruments, we recommend that researchers remove water vapor from the gas stream prior to analysis. Although not tested here, other studies have highlighted possible spectral interference effects associated with elevated H 2 S and volatile organic compounds (Erler et al., 2015;Ostrom and Ostrom, 2017), but these may also be removed from gas streams using chemical traps (e.g., Cu and activated carbon traps, respectively).
The scaling of gas matrix and trace gas effects with [N 2 O] has important implications for any measurement setup that relies on post-measurement correction equations. An equation developed to correct for CH 4 effects that was derived using a [N 2 O] of 330 ppb should not be implemented for a sample gas containing 990 ppb N 2 O. For example, as shown in Fig. 8, the measured interference effect on δ 15 N α measurements acquired using CRDS II for 10 ppm [CH 4 ] at 330 ppb N 2 O was 24.9 ‰, while at 990 ppb N 2 O it was 8.1 ‰, resulting in a 16.8 ‰ difference. The scaling of interference effects from trace gases has been reported previously for CO 2 /CH 4 laser spectrometers (Assan et al., 2017;Malowany et al., 2015). This underlines the usefulness of removing H 2 O, CO 2 and CO with scrubbers prior to measurement, as this removes the need for correction equations to begin with and the scaling of corrections that can ensue. We are unaware of any studies that have shown that O 2 interferences caused by pressure-broadening linewidth effects change as a function of N 2 O mole fraction. While we were unable to describe the scaling of the O 2 effect sufficiently using correction functions based on theoretical deductions, empirical equations based on experimental testing, such as those developed in Sect. 3.5.2 and 3.6.2, could be implemented by researchers when covariation in both O 2 and N 2 O in the sample gas is expected. Alternatively, as shown in this study, matrix and/or trace gas effects can be removed by automated N 2 O preconcentration devices such as TREX (Ibraim et al., 2018;Mohn et al., 2010), similar to IRMS. However, such devices are not commercially available, complex to build and operate, and restrict sample frequency.

Pre-measurement considerations
Our study clearly shows that knowledge/estimation of the matrix and trace gas composition of both reference standards and sample gases, and the differences between them, are critical for accurate N 2 O isotopocule analysis using laser spectroscopy. We acknowledge, however, that this may be difficult to predict in certain applications without prior testing of the sample gas, and therefore researchers should err on the side of caution.
As a prerequisite to acquiring measurements using N 2 O isotope laser spectrometers, researchers will be required to consider the accessory gas mixtures required to characterize their instrument. For applications with significant variations in matrix (O 2 , Ar) or trace gas (CO 2 , CH 4 , CO) compositions, researchers will require gas mixtures containing the gas of interest in order to characterize the associated interference effects for their laser spectrometer. This also necessitates that appropriate interference detectors are implemented, especially O 2 and CH 4 analyzers given that these effects cannot be mitigated using chemical traps.
In this study, interference effects, and the associated scaling of these effects according to the co-measured N 2 O mole fraction, were derived via dynamic dilution with various gas mixtures using MFCs. This allowed for the introduction of a wide range of gas mixtures to the analyzers for interference testing, and consequently only a small amount of gas mixtures were required for all of the experiments outlined in Sect. 2.4. In comparison, a much larger number of individual gas mixtures would have been required had they been prepared using static dilution techniques (see Erler et al., 2015). The scaling of interference effects was sufficiently distinguished by undertaking testing at three different N 2 O mole fractions (N 2 O = 330, 660 and 990 ppb), and we therefore recommend this as a minimum criterion for researchers wishing to characterize this effect.
Researchers should also consider the sample gas volume required for a given measurement application using a specific laser spectrometer. In our experience, ensuring that five laser cavity cell volumes have been flushed prior to measurement is best practice to negate any memory effects when these instruments are operated using continuous flow-through configurations (as opposed to discrete sample measurements in a closed laser cavity). By following this procedure and using the operating parameters selected in this study (Table 1), the sample gas volume required for a single 300 s measurement is approximately 80 mL for CRDS II, 150 mL for CRDS I, 600 mL for OA-ICOS I and 1200 mL for QCLAS I. By comparison, TREX-QCLAS I requires approximately 5 L of sample gas to allow for N 2 O preconcentration. These sample gas volumes represent typical numbers for atmospheric applications; however, instrument parameter settings such as flow rate and cell pressure, which ultimately change the required sample volume, can be optimized depending on the measurement application. This is particularly the case for QCLAS instruments, which can be operated with different user-adjustable settings. For applications requiring discrete sample analysis (e.g., the headspace analysis of δ 15 N and δ 18 O in N 2 O derived from dissolved NO − 3 ), high N 2 O concentration gas samples with lower volumes can be introduced to these instruments using injection ports and dilution gases (e.g., Soto et al., 2015;Wassenaar et al., 2018); however, we did not test these capabilities in our study.

Measurement workflow
In line with our results, we propose a step-by-step workflow that can be followed by researchers to acquire N 2 O isotopocule measurements (Fig. 15). This workflow seeks to cover all sources of potential error tested in our study. Not all steps will be applicable because interference effects vary across analyzers. For QCLAS analyzers, which offer high versatility, interference effects can also be approached by multi-line analysis, inclusion of interfering spectral lines or adaption of pressure-broadening parameters in the spectral fitting algorithm. For specific applications, such as incubation experiments with He, accessory injection units and setups using TREX, related actions have to be taken. While we tested several mono-variant (e.g., changes in [CH 4 ] at constant [N 2 O]) and some bi-variant (e.g., changes in [CH 4 ] and [N 2 O]) systems in our study, more complex systems (e.g., changes in [CH 4 ], [O 2 ] and [N 2 O]) were not tested, and deviations from additive behavior are to be expected. Depending on the desired precision, users may vary the measurement and averaging times, and calibration frequency.
4.4 What degree of accuracy can be achieved using this workflow?
The simulated two-end-member mixing experiments conducted in this study show that, when the workflow proposed above is applied, accuracy within ±0.5 ‰ can be achieved for TREX-QCLAS, ±0.4 ‰-1.6 ‰ for CRDS analyzers and ±1.6 ‰-3.6 ‰ for OA-ICOS analyzers. Likewise, the comparison between the laser spectrometers and IRMS highlights that cross-technique compatibility within ±1 ‰-2.5 ‰ can be achieved for most N 2 O isotopocule measurements. However, it is clear that the balanced (i.e., non-analyzer-specific) approach applied for the purpose of this comparative study did not cater to QCLAS I. Therefore, a more specific calibration protocol for the QCLAS I will likely yield better performance, as shown in Table 6. It is worth noting that, although the results of our study are representative of the performance of the instruments tested, the magnitude of reported effects and the performance are likely to vary within the same analyzer models. Whilst the laboratory-simulated mixing experiment is not fully representative of naturally occurring two-end-member mixing per se, the results are useful in comparing intercept accuracy and uncertainty amongst analyzers and against IRMS. Our results show that large uncertainties exist for N 2 O source apportionment using Keeling analysis performed at near-ambient N 2 O mole fractions. Given the amount of corrections that are required in the experiment, we have not detailed individual analyzer uncertainty budgets to quantify individual sources of error on the intercept, as it is beyond the scope of this study. Nonetheless, the reduction of uncertainty with increasing N 2 O shown in Exps. 1-6 in Sect. 3.7 has also been shown in previous studies (e.g., Wolf et al., 2015). Therefore, by extension, it is reasonable to assume that the current largest source of uncertainty for ambient N 2 O measurements using laser spectroscopy is the inherent signal-tonoise ratio of the measurement.

Conclusions
In this study, we characterized and compared N 2 O isotope laser-based analyzers with the three most common detection schemes, including OA-ICOS, CRDS and QCLAS. Our results show a number of factors that need to be carefully considered to ensure precise and accurate measurements of N 2 O isotopocules using laser spectroscopy. The performance of N 2 O isotope laser spectrometers depends on a complex interplay between instrumental precision, drift, matrix gas composition and associated spectral interferences that ultimately vary as a function of N 2 O mole fraction. On this basis, we echo recommendations from Ostrom and Ostrom (2017), who cautioned not to underestimate the need for the careful consideration of analyzer-specific corrections. These analyzers clearly do not represent "plug and play" devices -instead, one needs to carefully consider the desired application, precision and accuracy, and develop appropriate calibration strategies to achieve these outcomes.
Consequently, we recommend calibration schemes that have (1) a calibration frequency that is adequate for constraining instrument drift over experimental period/long-term measurements; (2) temperature stability during measurement, or the temperature effect adequately characterized and corrected; (3) a three-point or higher [N 2 O] effect correc- tion that spans the range of expected [N 2 O] (if calibration relies on raw δ values derived from uncalibrated isotopocule amount fractions; i.e., a δ-calibration approach); and (4) accounted for the differences in matrix and trace gas composition between the sample gas and reference gases, whereby either analyzer-specific interference corrections have been carefully characterized and applied, or where possible interfering substances (CO 2 , CO, H 2 O) removed using chemical traps. Correcting for interference effects becomes significantly more complicated once [N 2 O] exceeds ambient levels, requiring a multitude of analyzer-and gas-specific constants that inevitably increase the number of gas mixtures required