Three CRDS analysers of the same model (G5131-i, Picarro Inc., USA) were used in this study for N2O concentration and isotopic analysis. The availability of three individual analysers, referred to as CRDS-I, CRDS-II and CRDS-III, in the same set of experiments facilitates the comparison of analyser specimen-specific correction functions to speculate on the possibility of generalised model-specific corrections. CRDS-I (serial number 5080-DAS-JDD S5089, year of production 2018) was provided by Empa (Dübendorf, Switzerland), CRDS-II (serial number 5056-PPU-JDD S5065, year of production 2017) was contributed by the Thünen Institute of Climate-Smart Agriculture (Braunschweig, Germany) and CRDS-III (serial number 5070-PVU-JDD S5079, year of production 2018) by the Karlsruhe Institute of Technology (Garmisch-Partenkirchen, Germany). CRDS-III was already applied in an earlier study (Harris et al., 2020) and therefore results can be compared to evaluate stability of correction terms on longer timescales. Aside the G5131-i model analysers, a G2401 gas concentration analyser (Picarro Inc., USA) for CO, CO2, CH4, and H2O was used to derive accurate trace gas concentrations in all experiments. Operational consistency of all three G5131-i instruments during the experimental period was not achieved, due to failure of individual analysers, which indicates challenges when working with this analyser model. The experimental period spanned from August 2023 to May 2025. Within this period, CRDS-I was operational from August 2023 till May 2024, whereafter it was sent for repair, while CRDS-II was operational from December 2023 throughout the rest of the experimental period. Lastly, CRDS-III was included in this study somewhat later to expand the dataset and confirm observed analyser-specific and universal corrections. It was operational at the interval from July until August 2024 and April to May 2025.

Allan-Werle experiments were conducted regularly throughout the entire experimental period to check the analyser status and assess optimal integration times for acquiring data with sufficient precision but also drift effects of the analysers over longer time intervals (Werle et al., 1993). These experiments were performed analysing pressurised ambient air (Cal 1.2_330 ppb; Table 1) over approximately 24 h. From the acquired data, three different datasets were generated and subsequently evaluated using the Allan variance technique (Fig. 1), a standard method for assessing frequency stability over varying timescales (Werle et al., 1993; Barnes and Allan, 1966). The first dataset consisted of the raw, uncorrected analyser output, but binned to 15 s temporal resolution. To cover experiments in which distinct samples, such as bag samples, are analysed, the original dataset was segmented into consecutive 15 min intervals, and these intervals were identified as alternating between reference and sample gas measurements. For each interval, the first 10 min were discarded, and the final 5 min were averaged. Based on this procedure, the second dataset (referred to as sliced data in Fig. 1) consisted of those 5 min averages identified as sample gas measurements, while for the third dataset (referred to as drift-corrected data in Fig. 1) the sample gas measurements were drift-corrected using the 5 min averages identified as reference gas measurements. The latter approach is expected to provide superior performance as it involves intermittent drift correction as applied in replicate analysis of a sample. The Allan variance analysis indicates maximum precision (square root of the Allan variance) for CRDS-I and -II at 0.1 ‰–0.2 ‰, averaging up to 10 000 s (104 s), for CRDS-III somewhat lower, around 0.3 ‰, integrating measurement data for only 1000 s (103 s). The Allan precision for the tested analysers was found to be superior to the manufacturer's specification at near ambient N2O concentrations, i.e. <1.0 ‰ for δ15Nα, δ15Nβ and δ18O, respectively (5 min averaging, ∼330 ppb). 5 min averaging and consideration of 10 min stabilisation periods provide similar precision but at longer integration times. Drift correction is an efficient method for providing high-precision data for integration intervals that exceed the Allan minimum, which is particularly evident for CRDS-III. The Allan precision of the 5 min averaged and drift corrected data shown in Fig. 1 was in the range of 0.2 ‰–0.8 ‰, similar to standard errors plotted in Figs. 5–8 for the respective CRDS systems.

Figure 2 shows a simulated spectrum for typical ambient concentrations of trace gases, i.e. 300 ppb N2O, 400 ppm CO2 and 2 ppm CH4, together with a spectrum measured by the CRDS-I instrument in ambient air, both for the wavenumber window of 2195.7 to 2196.3 cm-1, where the Picarro G5131-i spectrometer operates.

Spectral simulations were performed using proprietary software written in LabVIEW. The software utilises spectral line data from the HITRAN2020 database (Gordon et al., 2022) to simulate the absorption spectrum, accounting for Doppler broadening of the spectral lines. In addition, pressure broadening by the matrix gas, pressure shift of the spectral lines as well as temperature dependence of the line intensity and line broadening effects were considered. Spectra were simulated for the actual experimental conditions of 313 K gas temperature, 100 hPa gas pressure and 20 km absorption path length. The simulated spectra were fitted using a self-developed algorithm using the Fityk software (Wojdyr, 2010). While the simulations were performed using all spectral lines listed in the HITRAN 2020 database, in the fitting, we only considered those lines that have a measurable contribution to the spectrum within the spectral window of 2195.70–2196.3 cm-1. The fitting approach followed the same principles as described in our recent publication (Pogány et al., 2025). The fitted lines included 19 N2O lines. Nine lines of the main N2O isotopic species were fitted as one line set, i.e. the relative line positions as well as ratios of the line intensities were calculated and used as fixed parameters in the fitting, together with Gauss and Lorentz line widths, leaving only the line area and position of the line at 2196.209 cm-1 as free parameters. Three lines of the 15Nα isotopic species were fitted as a second line set, three lines of both the 15Nβ and the 14N14N17O isotopologue as the third line set, and one 14N14N18O line as a fourth line set. Furthermore, 12 CO2 lines corresponding to different isotopic species were fitted as a fifth line set. In the line sets numbers 2–5, all line positions are given as fixed parameters relative to the position of the N2O line at 2196.209 cm-1. The CH4 lines are so weak compared to the N2O and CO2 lines that they cannot be fitted independently; i.e., their influence on the spectrum cannot be considered in the fitting process.

Isotope ratios were calculated from the ratio of the line areas obtained from the spectral fitting, and the line intensities calculated for a temperature of 313 K, according to the following equation: Δδ=αi⋅Smαm⋅Si-αi330⋅Smαm330⋅Si⋅1000 where αi is the line area (in cm-2) and Si the line intensity in cm-1(molec.cm-2)-1, for the minor, i.e. 15Nα, 15Nβ or 14N16O18O isotopic species, and am the line area and Sm the line intensity for the main N2O isotopologue. The superscript 330 corresponds to values determined from the spectrum simulated for a gas composition of 330 ppb N2O in synthetic air containing no CO2 or CH4, which we chose as a reference point for the delta values. Relative delta values were calculated as the difference between simulated results for the experimental conditions and reference conditions (330 ppb N2O in synthetic air), and compared to the experimental results.

We developed a customised MATLAB App for correction and calibration of experimental data. While our specific focus was N2O isotope analysis on ambient air samples with contributions from soil emissions, the approach can be adapted to any application with sequential analysis of gas samples, intermitted by reference gas analyses, such as bag analyses or on-line sampling from a laboratory or field setup.

The main functionalities of the code, outlined in Fig. 4, include: data import and pre-processing of N2O isotope data from a Picarro G5131-i analyser, as well as trace gas concentrations of, CO2 and CH4 from a supportive Picarro G2401 analyser, instrumental parameters check, correction and calibration of concentration data, and correction and calibration of δ-values. All corrections are optional and can be individually activated by the user via a graphic user interface. In addition, the code can also provide a propagated uncertainty on the reported δ-values. The approach used for the data treatment, correction and calibration is described below, while a full description of the mathematical model, including all equations, can be found in Appendix A.

Although the three tested CRDS analysers are the same analyser model, they offer different N2O operation ranges, i.e. CRDS-II and -III displayed increasing data loss already above ∼700–800 ppb N2O, which most probably is related to enhanced absorption of the empty cavity (e.g. by dust particles) and therefore partial saturation of the absorption features at higher N2O concentrations. Therefore, only CRDS-I was tested in between 330 and 1200 ppb N2O, while CRDS-II and -III were only operated up to 800 ppb N2O. Figure 5 provides dependencies of apparent δ-values of N2O isotopologues (Δδ15Nα, Δδ15Nβ, Δδ18O) on inverse N2O concentrations for all three G5131-i analysers as well as for simulated results. The experimentally determined regression slopes mN2O are applied to parametrise the developed MATLAB algorithm. Consistency of apparent δ-values from triplicate analyses for individual analysers confirms reproducible offsets, within short timeframes, between measured and true δ-values for N2O concentration changes between sample and calibration gases (Fig. 5). A linear relationship between apparent delta values and the inverse N2O concentration has already been observed by Harris et al. (2020). A closer look at the results of spectral simulations displays a slightly non-linear behaviour of the apparent isotope effect. For the experimental data, this effect is masked by instrumental precision, and therefore a linear correction was applied.

Clearly, the different analyser specimens (CRDS-I, CRDS-II, CRDS-III) and simulated results show contrasting regression slopes (mN2O) (Table 4). Repetitive tests of individual analysers over longer timescales, such as several weeks or months, indicate that the N2O non-linearity correction is not only analyser-specific but also variable over time. CRDS-III tested here was already included in an earlier study (CRDS II in Harris et al., 2020), but with substantially different non-linearity behaviour. Similarly, dependencies of delta values on N2O concentration changed significantly for CRDS-II, which was tested several times. The situation is complicated by the fact that the analyser software has a built-in post-correction to minimise N2O non-linearities, which is parametrised analyser-specific by Picarro Inc.

Figure 6 shows the effect of CH4 concentration changes, between 0 and 10 ppm, on apparent N2O delta values (Δδ15Nα, Δδ15Nβ, Δδ18O) for three different N2O concentrations (330, 660 and 990 ppb). Delta values display a linear relationship on CH4/N2O concentration ratios, i.e., the interference effect doubles for samples with either a twofold CH4 concentration or halving the N2O concentration. Dependencies of apparent delta values on CH4 concentrations are most substantial for δ15Nα, intermediate for δ18O and weakest for δ15Nβ (Table 5). Results are generally consistent for repeated experiments (n=3) and between analyser specimens (CRDS I, CRDS II, CRDS-III) as well as with literature data (Harris et al., 2020), which indicates that corrections might be specific for this particular CRDS analyser model (G5131-i) and constant over time. For analysers CRDS-II and CRDS-III, the upper N2O concentration limit for obtaining precise measurement data is 800 ppb due to enhanced background signals (see Sect. 3.1); therefore, experimental data obtained at 990 ppb were excluded from data analysis. Our spectral simulations underpin the experimental results, although correction slopes for δ15Nα are significantly smaller compared to experimental results (Table 5).

The strong spectral interference, observed for δ15Nα, can be explained by two CH4 spectral lines at 2195.762 cm-1 and 2195.764 cm-1, with line intensities of 1.02×10-24 cm-1 and 4.49×10-25 cm-1, respectively (see Fig. 2). The spectral interference on δ18O is a factor of two (for simulations) to three (for experimental results) weaker and caused by a single CH4 line at 2195.95 cm-1 with a line intensity of 4.26×10-25 cm-1, overlapping with the N218O line. In the case of the 15Nβ isotopologue, the overlapping CH4 line is approximately an order of magnitude weaker with a line intensity of 5.148×10-26 cm-1; thus, the observed spectral interference and its effect on the δ-values are negligible. The main analytical challenge with respect to the CH4 interference is the fact, that all CH4 lines co-evolve with N2O lines, so no specific CH4 concentration analysis is feasible within the wavelength region implemented in the G5131-i analyser. Therefore, the most straightforward approach is an empirical post-correction using an independent CH4 concentration analyser, as suggested and implemented in this manuscript.

Figure 7 displays the effect of CO2 concentration changes in the range 0 to 2000 ppm on apparent δ-values for experimental results (CRDS-I and II) and spectral simulations. Experiments were conducted for three different N2O concentrations, 330, 660 and 990 ppb, with each experiment repeated three times. CRDS-II was not capable to analyse gas mixtures at 990 ppb due to enhanced background and saturation effects (see Sect. 3.1). Overall, no consistent and significant effect of CO2/N2O concentration changes on apparent δ-values was observed for the two analyser specimens (Fig. 7; Table 6). These results are in agreement with observations made by Harris et al. (2020) and imply that the interfering CO2 absorption lines are either well enough separated or the CRDS quantification algorithm is able to correct effects appropriately. In contrast, spectral simulations indicate a stronger, significant spectral interference of CO2 concentrations on the apparent isotopic delta values for δ15Nβ and δ18O, and a minor effect on δ15Nα. Apparent effects of up to 8 ‰ for δ15Nβ and δ18O values are most probably due to computational differences between the spectral simulation and the analyser's fitting software.

Figure 8 shows the effect of O2 concentration changes in the range 12 % to 21 % on apparent δ-values. Experiments were repeated thrice for a constant N2O concentration of 330, 660 and 990 ppb (CRDS-I) or 330 and 660 ppb (CRDS-II). The experimental data fits well to a linear model, and the regression coefficients, their corresponding uncertainties and the adjusted R2 values are provided in Table 7. The coefficient values are in agreement for the two analyser specimens, for different N2O concentrations and also with results from Harris et al. (2020). Based on the results, it can be inferred that an instrument-specific correction is applicable for O2 effects on apparent delta values. However, corrections for Δδ15Nβ andΔδ18O at 330 ppb N2O should be applied with caution, as our experimental data indicate low adjusted R2 values for both CRDS-I and CRDS-II (Fig. 8). A correction term for the O2 matrix gas effect was not included in the MATLAB code, as no relevant oxygen concentration changes are expected for the target application, N2O emissions from soils.

Experiments involving the simultaneous addition of two interfering gases (CH4 and CO2) at two different N2O concentrations (330 ppb (Exp. 5a) and 660 ppb (Exp. 5b)) were conducted to assess the practicality of the developed MATLAB code and test whether the established correction functions are additive or require a more complex correction algorithm. Apparent delta values were corrected for CH4 and CO2 spectral interference as well as N2O non-linearity using the mathematical formalism described in Appendix A and analyser specific average, i.e. combined, corrections factors given in Tables 4–6. For CO2 interference correction of CRDS-III, correction factors of CRDS-II were applied, which was justified by consistent results for two analyser specimen (CRDS-I and II). Figures 9 and 10 illustrate the combined effects of simultaneously increasing CH4 (0–10 ppm) and CO2 (0–2000 ppm) concentrations on apparent δ-values at two different N2O concentrations (330 ppb, Fig. 9, 660 ppb, Fig. 10) for the two tested analysers (CRDS-II and III). CH4 and CO2 concentrations were increased stepwise from 0 to 10 ppm (2.5 ppm per step) and 0 to 2000 ppm (500 ppm per step), respectively (see Tables S11 and S12 in the Supplement for further details). Our basic assumption was that spectral interferences by the combined addition of CH4 and CO2 for δ15Nα and δ18O are predominantly driven by CH4, while interference effects of CH4 and CO2 on δ15Nβ are more balanced. However, the apparent effects on δ-values resulting from simultaneous CH4 and CO2 addition (Fig. 9, black squares) deviate significantly from the predetermined correction function for CH4-only addition (Fig. 6; Table 5). As a result, the fully corrected delta values (black squares) deviate from actual δ-values for all isotopologues. It is also noteworthy that the correction function for CH4/N2O is well-defined with respect to δ15Nα and δ18O but less substantial for δ15Nβ (Fig. 6). However, in the validation experiment with simultaneous increases of CH4 and CO2 concentrations, the spectral interference on apparent δ15Nβ values is substantial (Fig. 9). Another notable observation in this validation experiment is that the observed non-corrected data for δ15Nα agrees substantially better with CH4/N2O correction function derived from spectral simulation than with the one obtained in experiment 2 (CH4 addition without CO2) (not shown). The reasoning for this connection, however, is unclear.

Validation experiments carried out at 660 ppb N2O show an even more complex interplay of interference effects (Fig. 10). Our working hypothesis was, that interferences by N2O non-linearity and CH4 as well as CO2 spectral artifacts, induced by changes in N2O, CH4 and CO2 concentrations of the sample relative to the reference gas, are additive. Experimental results (grey symbols) and δ-values corrected assuming additivity of interferences (black symbols) for CRDS-II display a consistent offset in delta values of up to 15 ‰ for δ15Nα and δ15Nβ but 20 ‰–40 ‰ for δ18O. In fact, two datasets were collected on two different measurement dates (20 March and 20 May 2025). The datasets were corrected using identical CH4 and CO2 regression factors but for the N2O nonlinearity correction the correction function determined closest to the measurement date were applied (Table 4). Interestingly, measurements at 20 May 2025 (black squared symbols) were corrected with a N2O non-linearity correction slope, which was determined just a few days before (16 May 2025), and resulted in a better agreement with target values than the second dataset, where N2O non-linearity (10 April 2025) and validation measurements (20 March 2025) were separated by a longer time interval. For CRDS-III offsets are somewhat smaller for δ15Nα and δ15Nβ but indicate a decreasing trend with increasing CH4 and CO2 concentrations, similar to measurements at 330 ppb N2O. Corrected results for δ18O analysed by CRDS-III show an approximately 25 ‰ offset. We speculate, that persistent offsets between corrected delta values to the target are linked to the observed changes in the N2O non-linearity correction function over time (Fig. 5; Table 4).