Evaluation of Data Processing Strategies for Methane Isotopic Signatures Determined During Near-Source Measurements

2.1. Controlled release set up

The controlled release experiment allows an evaluation of the accuracy and precision of mobile near-source measurements of CH₄ emission rates, ethane to methane ratios and δ¹³CH₄. Our experiment took place over 5 days in September 2019 at Bedford Aerodrome, UK. Pure methane was released from a manifolded multi-cylinder pack of twelve cylinders containing 999.6 ± 10.0 mmol mol^–1 methane, with an initial pressure of about 200 bars. The impurities in the cylinders came from ethane (48 ± 10 µmol mol^–1) and propane (0.149 ± 0.30 µmol mol^–1). All 12 cylinders were filled at the same time from the same CH₄ source, ensuring δ¹³CH_{4 source} remained stable over the entire measurement period. The methane release rate varied from 25 L min^–1 to 70 L min^–1. During the release, CH₄ was mixed with ethane (C₂H₆) in a varying ratio, giving C₂H₆:CH₄ ratios from 0.00 to 0.07. The purity of the C₂H₆ was 999.9 ± 10.0 mmol mol^–1, with impurities mostly from methane (2.27 ± 0.46 µmol mol^–1) and propane (7.5 ± 1.5 µmol mol^–1). To reach the required CH₄ emission rate, CH₄ was released simultaneously from all 12 cylinders, using a transportable flow control system (details in Gardiner et al., 2017). Briefly, the flow control system is designed and configured for the creation of ‘real-life’ gaseous emission scenarios, in a range of industrial settings. It allows for validation of methods for emission monitoring applied during typical field conditions. The control system is built on six mass flow controllers (MFC), (Brooks Instrument, Hatfield, PA, USA). Four primary MFCs provide independent emission sources, while two secondary MFCs allow for the introduction of purge and interferant gases into the primary flow. The flow control system is computer operated, allowing for the implementation of pre-written operational programs and the post-test analysis (Gardiner et al., 2017).

Here, the controlled release experiment involved 26 releases, each lasting about 45 minutes. The number of releases per day varied between 2 and 8. The smallest number of releases was conducted during day 1 (3 releases) and day 5 (2 releases). As well as controlling emission fluxes and the ratio of C₂H₆:CH₄, wind speed and direction were measured during all releases. Details of individual gas releases during controlled release experiment are presented in Table A1.

2.2. Measurement technique

During the mobile near-source measurements, the sampling method was based on driving through a plume of CH₄. Throughout each release, a vehicle intersected the multiple times plume perpendicular to the wind direction. The controlled release experiment gave the opportunity to validate the mobile laboratories of Royal Holloway, University of London (RHUL) and of the Laboratory for Sciences of Climate and Environment (LSCE). Details of evaluated mobile laboratories are presented in appendix A, with instrument characteristics in Table A2. Briefly, the RHUL mobile laboratory used for this experiment was in operation between 2013 and 2020 (Lowry et al., 2020). This vehicle was equipped with a Picarro CRDS G2301 analyzer, capable to measure mole fractions of CO₂, CH₄ and H₂O, a Los Gatos Research Ultraportable Methane Ethane Analyzer (LGR UMEA), and a manually operated diaphragm pump for filling air sample bags. Three air cylinders were measured and calibrated against the NOAA scale by the Max-Plank Institute for Biogeochemistry Jena, which were used to calibrate the Picarro CRDS G2301 before and after the measurement campaign to the WMO X2004 A CH₄ scale (Lowry et al., 2020; France et al., 2016; Zazzeri et al., 2015).

The LSCE mobile laboratory was previously used during mobile studies (e.g., Defratyka et al., 2021), and it is similar to other mobile laboratories equipped with a Picarro CRDS G2201-i (henceforth referred to as CRDS), capable of in-situ measurements of CH₄ mole fractions and δ¹³CH₄ (e.g. Rella et al. 2015; Lopez et al. 2017; Hoheisel et al. 2019). The LSCE mobile set-up also comprises of an active AirCore sampler for tripling the sampling frequency during in-situ measurements of δ¹³CH₄ (Defratyka et al., 2021). The LSCE instrument was calibrated using a 3-point mole fraction and isotopic composition calibration, just before shipping the instrument to the UK. After calibration, CH₄ mole fractions were reported on the WMO X2004 A scale and δ¹³CH₄ is reported relative to the international Vienna Pee Dee Belemnite (VPDB) standard (Craig, 1957). Due to logistical restrictions, the calibration cylinder or known working gas could not be used during the controlled release experiment. However, an additional working gas was measured in the laboratory before and after the experiment, and no significant drift was observed.

The CRDS measurements were made in a high precision mode, in CO₂-CH₄ simultaneous mode. CO₂ measurement acquisition was kept for additional trouble shooting of analytical artifacts. To resolve short temporal variabilities, the flow rate was adjusted to 100 cc min^–1 for faster instrument response during the mobile measurements. Significant cross sensitivities between C₂H₆ and δ¹³CH₄ in the absorption spectrum have been shown to lead to biases in the measured δ¹³CH₄ by CRDS (details in Appendix A). The effect is inversely proportional to the CH₄ mole fraction and proportional to the C₂H₆ mole fraction in the sample and has been previously quantified (e.g., Rella et al. 2015; Assan et al. 2017).

3.1. Keeling and Miller-Tans methods

During mobile near-source measurements, the observed CH₄ (hereafter CH_{4 obs}) mole fraction and δ¹³CH₄ signature (hereafter δ¹³CH_{4 obs}) are a mixture of atmospheric background CH₄ (hereafter CH_{4 bckg}) and the CH_{4 source} from the source. To determine δ¹³CH_{4 source} the Keeling or the Miller-Tans methods can be applied (e.g. Hoheisel et al. 2019; Menoud et al., 2020; Defratyka et al., 2021; Fernandez et al., 2022). In the Keeling method (Keeling, 1961; Pataki et al., 2003), δ¹³CH_{4 obs} is plotted against the inverse of CH_{4 obs} mole fraction and the y-intercept of the fitted linear regression is interpreted as the δ¹³CH_{4 source} of the observed source:

where subscripts obs, bckg, and source refer to observed, background, and source values. Notably, parameter CH_4bckg∙(δ¹³CH_4bckg – δ¹³CH_4source) does not affect δ¹³CH_{4 source} determined as intercept of Eq. 1, and it can remain as an unknown parameter.

The Miller-Tans method (Miller and Tans, 2003) is another mass conservation approach, where the mole fraction and the isotopic signature of atmospheric background are assumed to be well known. The isotopic signature of the source is represented by the slope of a fitted linear regression, where, after background subtraction, δ¹³CH_{4 obs} multiplied by CH_{4 obs} mole fraction is plotted against CH_{4 obs} mole fraction:

The Miller-Tans method can be useful to interpret studies, where the Keeling method assumption of stable background is unfulfilled or unknown, e.g., when studies are conducted over a long period of time (Al-Shalan et al., 2022; Lowry et al., 2020).

3.2. Background subtraction for Miller-Tans method

On the small scale, the diurnal variation of CH₄ mole fraction can be observed. Additionally, some local CH₄ enhancements can exist and affect the background determination. Under these circumstances and regarding available instrumentation, one needs to decide how to define the background, which is defined as a part of the Miller-Tans method. To evaluate the impact of a chosen CH_{4 bckg} mole fraction and δ¹³CH_{4 bckg} isotopic signature, defined backgrounds are subtracted for the Miller-Tans method. For bag samples measured by IRMS, as a first attempt, an ‘individual background’ was subtracted, defined from a background bag sample collected directly after the release, when bag samples were collected within CH₄ enhancement. For example, for all bag samples collected during the first day, the background sample collected on the first day was subtracted. For the next calculation, an ‘averaged background’ is subtracted, which is defined as the average of all background bag samples collected over whole experiment. Next, to verify the sensitivity of Miller-Tans method for a subtracted background, calculations for two arbitrary chosen backgrounds with lower CH_{4 bckg} mole fraction and δ¹³CH_{4 bckg} than during the experiment were conducted: ‘arbitrary I’ and ‘arbitrary II’ background. For arbitrary I background, CH_{4 bckg} mole fraction is defined as an average global CH₄ mole fraction observed in September 2019, equal to 1.871 ± 0.001 µmol mol^–1 (Dlugokencky, 2022), while δ¹³CH_{4 bckg} is defined using value from Brownlow et al., as –47.2 ± 0.2‰ (2017). For arbitrary II background, the CH_{4 bckg} mole fraction is set up the same as the arbitrary I background, but the δ¹³CH_{4 bckg} set to –42.7 ± 0.2 ‰.

For bag samples measured by CRDS, the Miller-Tans method is implemented three times, while defined backgrounds are subtracted. The backgrounds have been chosen similarly as for the IRMS analysis. Thus, the analysis is implemented three times where individual, averaged, and arbitrary I background are subtracted. The CH_{4 bckg} mole fraction and δ¹³CH_{4 bckg} for bag samples measured on IRMS and CRDS are presented in Appendix A.

In the case of in-situ AirCore sampling, for the Miller-Tans method, data were analyzed twice to examine possible impact of subtracted background. First, subtracted background is calculated individually for each AirCore, as an average of AirCore background data of an individual AirCore sample, observed directly before and after CH_{4 obs} elevation (defined for later as Miller-Tans 1). Second, averaged background of all bag samples measured on CRDS was subtracted for each individual AirCore sample (Miller-Tans 2) to evaluate sensitivity of Miller-Tans method for subtracted background.

3.3. Data averaging

3.4. Linear Fitting method

Both Keeling and Miller-Tans methods rely on linear regression fitting. Potentially, using different linear fitting methods can introduce discrepancies between determined δ¹³CH_{4 source} and impede its comparison (Menoud et al., 2022; Zobitz et al., 2006). Here we aim the first intercomparison of all broadly used linear regression methods to verify potential biases introduced by different linear fittings: Ordinary Least Squares (OLS) (Defratyka et al., 2021), Major Axis (MA) (Menoud et al., 2022), York fitting (Hoheisel et al., 2019) and Bivariate Correlated Errors and Intrinsic Scatter (BCES) Orthogonal (e.g., Fernandez et al., 2022), adding verification of BCES (Y|X) (Figure 1). Also, we implement comparison between methods including measurements uncertainty (York and BCES) and not including uncertainties (OLS and MA), as OLS method is still the most used linear fitting method.

Most of the tested fittings are calculated using built in packages and functions in the R programming language: OLS using lm() function, MA using lmodel2() function and York fitting using York() function from package IsoplotR. As there is no available package to calculate BCES fitting in R, BCES fitting is calculated using the lnr module in the Python programming language. Throughout the paper, uncertainties of δ¹³CH_{4 source} determined using different linear regressions are presented as one standard error.

OLS method minimizes the distance only on the y-axis between the fitted line and the data points, using the principle of least squares to minimize the sum of the vertical distances from the regression line, what is also known as model I regression method (Legendre and Legendre, 1998, p. chapter 10). According to Legendre and Legendre (1998), if the error rate on y-axis is more than three times than on x, OLS is the most efficient method to estimate the slope of a linear fitting.

If both x and y variables are not controlled by the researcher or measured with an error, using OLS can cause an underestimation of the slope inferred by the linear regression (Legendre and Legendre, 1998, chapter 10). Thus, the model II linear regression methods are recommended, as they minimize the distance both of x and y from the regression line. The MA method, tested in this study is an example of the model II linear regression. MA method is also known as Orthogonal Distance Regression (ODR) or Deming regression. The MA method minimizes the sum of the squared Euclidean distances (x and y distances) from the regression line. Geometric mean regression (GMR) is another model II linear regression method, but is not tested in this study as it is expected to deliver similar results to the MA method (Zobitz et al., 2006). Details about the standard errors of OLS and MA methods are presented in Appendix A.

In contrast to OLS and MA methods, York fitting (York et al., 2004) and BCES regression (Akritas and Bershady, 1993) allow inclusion of x and y uncertainties. Overall, York fitting can be treated as a general linear regression method, while OLS and MA are special cases valid in particular conditions and can be obtained mathematically from the York fitting method, when appropriate circumstances appear (York, 1966; York et al., 2004). In the York fitting method, the best slope fit is searched iteratively, where the initial slope value is assumed, e.g., using OLS. Then, computations are weighted based on x and y measurement errors. Finally, computations are repeated until differences between iteration are smaller than tolerance level (e.g., 10^–15) (York et al., 2004).

The BCES method is a direct extension of the OLS method and was the final linear fitting method evaluated. Within BCES, four sub-methods can be employed: BCES (Y|X), BCES (X|Y), and two symmetric lines: BCES Bisector and BCES Orthogonal (Akritas and Bershady, 1993). BCES (Y|X) assume x as the independent variable. BCES Bisector was shown to be self-inconsistent and should not be used (Hogg et al., 2010). Finally, BCES Orthogonal is a line that minimizes orthogonal distances and should be used when it is not clear which variable should be treated as the independent variable. Our study focuses on the application of BCES Orthogonal, as this method has been broadly implemented in previous studies using IRMS instruments (e.g., Fernandez et al., 2022; Lowry et al., 2020; Zazzeri et al., 2015). Additionally, to examine the difference between the two BCES methods, BCES (Y|X) is also tested, as both methods could be implemented to determine δ¹³CH₄.

To arrive at the final uncertainty of the x- and y-axis, error propagation was applied for both for Keeling and Miller-Tans methods. Details of used error propagation are presented in Appendix A.

3.5. Rejection criteria for AirCore samples

The determined δ¹³CH_{4 source} is rejected if the standard error of the fitted regression line (intercept for the Keeling method and slope for the Miller-Tans method) is greater than 5‰ (based on the Picarro CRDS performance). Based on previous studies (Defratyka 2021), an additional criterion was applied to the Miller-Tans method, where δ¹³CH_{4 source} is also rejected if coefficient of determination, r², is less than 0.85. This additional criterion was not previously applied to the Keeling method, so we examined the variance of the r² in the Keeling method to determine whether the r² criterion could also be applied.

Eventually, all retained AirCore δ¹³CH_{4 source} values from one data processing strategy (mass conservation approach (Sect. 3.1), background (Sect. 3.2), averaging (Sect. 3.3), and linear fitting (Sect. 3.4)) are averaged to obtain a final δ¹³CH_{4 source} value for each strategy. These final values are then used to compare results from different analytical approaches, presented in the flow chart on Figure 1. Additionally, for releases where bag samples for IRMS and in-situ AirCore sampling occurred simultaneously, the average AirCore results are compared with IRMS results.

4.1. Measurement technique

For bag samples measured on IRMS, a sample collected during the first day of the experiment, containing 11 µmol mol^–1 of CH₄, biased results toward more¹³C enriched values and was rejected from further analysis. Potentially, observed biased came from the necessary sample dilution to obtain CH₄ mole fraction in IRMS operational range (details in Appendix B).

Due to the low mole fraction enhancement above the background, bag samples from day 2 exhibited scattered values with bias toward more ¹³C depleted values, and were rejected from further analysis. Using remaining 18 bag samples measured on IRMS, determined δ¹³CH_{4 source} varied from –40.55 ± 0.12‰ (day 1) to –39.87 ± 0.10‰ (day 5), reaching treatment 1 average equal to –40.23 ± 0.14‰ and it is treated as a reference value for the other atmospheric results. In the case of samples measured with CRDS, those from day 2 were also rejected from further analysis, thus only bags collected during first day of the experiment (releases 1.1 and 1.2) were analyzed. For in-situ CRDS sampling using the AirCore tool, 3 out of 31 collected samples were rejected, due to CRDS cavity pressure and temperature instability.

Table 1 presents the comparison of determined δ¹³CH_{4 source} for individual releases, where sampling using two different methods was done simultaneously, and for the averaged δ¹³CH_{4 source} using treatment 1 averaging for all measurements techniques. Due to better instrument precision and accuracy, δ¹³CH_{4 source} determined using IRMS has lower uncertainty than CRDS results. From all tested measurement techniques, the uncertainty associated with bags measured by CRDS is the largest.

Averaged δ¹³CH_{4 source} estimates using different data processing strategies, and the result of direct δ¹³CH_{4 source} measurements, are presented in Figure 2, showing constant δ¹³CH_{4 source} from IRMS measurements using different data processing strategies. δ¹³CH_{4 source} measured on CRDS is more variable, depending on chosen data processing strategy (Figure 2). Using York fitting scheme as the reference linear fitting (argumentation in Sect. 4.5), for both CRDS measurement techniques, residuals from IRMS results are smaller than CRDS uncertainties. Thus, results from CRDS and IRMS instruments are in good agreement within the uncertainty. The agreement is observed for δ¹³CH_{4 source} determined from both individual releases and averaged δ¹³CH_{4 source} (Table 1).

Figure 2

Direct δ¹³CH_{4 source} measurements were more depleted (–41.36 ± 0.17‰) comparing to the atmospheric measurements. The uncertainties of direct measurements and IRMS technique are smaller than the observed discrepancy of 1.1‰ between direct and atmospheric IRMS measurements of δ¹³CH_{4 source}. The averaged CRDS results (both for bags and AirCore samples without C₂H₆ on δ¹³CH₄ correction) are enriched about 0.3‰ comparing to direct measurements, but due to larger uncertainty of CRDS results, observed discrepancy is irrelevant within uncertainty (Figure 2).

The impact of C₂H₆ on δ¹³CH₄ correction was tested for all data processing strategies and the same trend is observed for all strategies. Thus, for simplicity the results are discussed and presented on Figure 3 only for non-clustered York fitting strategy. Applying C₂H₆ on δ¹³CH₄ corrections shifts AirCore values toward more depleted¹³C values, both comparing to IRMS results and to direct measurement of the cylinder batch. The residual reaches –3.2‰), and –2.05‰), comparing to bags on IRMS and direct measurements, respectively. As observed bias is significant, and deep examination of C₂H₆ on δ¹³CH₄ correction is out of scope of this study, hereafter we will mostly focus on results from AirCore samples where C₂H₆ on δ¹³CH₄ correction was not applied.

Figure 3

4.2. Keeling and Miller-Tans methods

Estimates of δ¹³CH_{4 source} determined using Miller-Tans and Keeling methods from bags measured on IRMS demonstrated insignificant difference for all applied linear fittings (Figure 2).

Results from bag samples measured with CRDS, using the York fitting, the δ¹³CH_{4 source} showed a negligible difference of 0.02‰ between δ¹³CH_{4 source} values determined using the Miller-Tans and Keeling method. The observed difference in determined δ¹³CH_{4 source} and its uncertainty varies depending on the chosen linear fitting approach. The largest discrepancy is observed when MA or BCES Orthogonal fittings are used (Figure 2).

For AirCore samples, the determined δ¹³CH_{4 source} showed a negligible difference of 0.2‰ for York fitting between δ¹³CH_{4 source} determined using the Miller-Tans and Keeling method. Similar to results from bag samples measured with CRDS, the observed difference of δ¹³CH_{4 source} and its uncertainty varies depending on the chosen linear fitting approach. The largest discrepancies are observed when MA (–20‰) or BCES Orthogonal (11‰) fittings are used (Figure 2). This trend is consistent regardless of whether a C₂H₆ correction on δ¹³CH₄ is applied or not (Figure 2).

4.3. Background subtraction for Miller-Tans method

Using four separately defined backgrounds (individual, averaged, arbitrary I, and arbitrary II), no significant differences are observed for δ¹³CH_{4 source} from bag samples measured with IRMS. For δ¹³CH_{4 source} determined from bag samples measured with CRDS, where three different backgrounds (individual, averaged, and arbitrary I) were tested, also no impact of subtracted background was observed for all analytical strategies, except for BCES Orthogonal. A similar dependency was observed for δ¹³CH_{4 source} determined from AirCore samples, where individual and averaged backgrounds were subtracted. Tables of determined δ¹³CH_{4 source} are presented in Appendix B for bag samples and in Appendix C for AirCore samples.

4.4. Data averaging and clustering

4.4.2. Data averaging AirCore in-situ sampling

Subsequently, the impact of clustering data (using both CH₄ mole fraction and time averaging clusters) on the final, averaged δ¹³CH_{4 source} for AirCore samples, is presented on Figure 4. The details about clustering impact for analysis using different mass conservation methods and linear fittings can be found in Appendix C. Overall, clustering causes a changeable bias for AirCore samples, which depends on the chosen clustering strategy and the linear fitting. Additionally, clustering increases the uncertainty of the final averaged δ¹³CH_{4 source}. Furthermore, depending on the clustering method and the linear fitting, the amount of rejected individual AirCore samples varies. For example, for York fitting, for 50 nmol mol^–1 and 100 nmol mol^–1 CH₄ mole fractions clusters, only one individual AirCore result remains for each cluster. The largest discrepancies between raw and clustered data are observed for the MA and BCES Orthogonal linear fitting methods, possibly due to forced symmetry applied in both methods, with δ¹³CH_{4 source} reaching up to –7.6 ± 2.4‰ (Figure 4).

Figure 4

4.5. Linear fitting

Regarding the results from bag samples measured on IRMS, differences between determined δ¹³CH_{4 source} using different fitting methods are insignificant (Figure 2). The largest uncertainty is observed for MA linear fitting, where uncertainty is calculated from 95% confidence intervals converted to standard error. The smallest uncertainty is observed for York fitting for both averaging approaches.

In the case of bag samples measured with CRDS, differences between determined δ¹³CH_{4 source} using different fitting methods are insignificant, except for results where BCES Orthogonal was used (δ¹³CH_{4 source} equals to –36.9 ± 3.0‰) (Figure 2). For bag samples measured on CRDS, the largest uncertainties are observed for MA and York linear fitting.

For AirCore samples, for OLS, York, and BCES (Y|X) methods, insignificant differences were observed between the Keeling and the Miller-Tans method with two distinct backgrounds, considering raw data clustering (Table 2). The results from these three linear fittings are in good agreement within each other, indicating them as good methods for AirCore data treatment. Similar to bag samples measured with CRDS, larger, and significant discrepancies were observed using MA and BCES Orthogonal methods, reaching –45.0 ± 1.7‰ and –35.5 ± 2.3‰), for raw data. Notably, only for the BCES Orthogonal fitting, the results from Miller-Tans methods with two differently defined backgrounds were significantly different.

4.6. Rejection criteria

Previous research using the Miller-Tans method proposed to reject individual AirCore sample results if their uncertainty is greater than 5‰), and if r² is less than 0.85 (Defratyka et al., 2021). The fraction of rejected AirCore predictably varied with the data processing strategy (Table 2 and more details in Appendix C). For example, using the reference analytical strategy, 12 out of the 28 AirCore samples remained, after applying the rejection criteria.

We investigated whether the same rejection criteria can be applied to the Keeling method. For the CRDS AirCore studies, the r² values remain scattered, regardless of whether determined δ¹³CH_{4 source} agreed with IRMS reference value or not. Also, r² remains systematically low, mostly ranging between 0.1 and 0.3. Thus, it was not possible to find a satisfying r² rejection criterion for Keeling method. Applying only the uncertainty criterion leads to fewer rejections and a wider spread of δ¹³CH_{4 source} among individual AirCore samples using the Keeling method, which therefore increases the uncertainty of the final, averaged δ¹³CH_{4 source} (Figure 4).

5.1. Comparison with previous studies

A few studies have been conducted to find the best strategy for applying the Keeling or the Miller-Tans methods to determine isotopic signatures, and they focused mostly on synthetic data or continuous measurements of CO₂ (Miller and Tans, 2003; Pataki et al., 2003; Wehr and Saleska, 2017; Zobitz et al., 2006). Furthermore, Hoheisel et al. (2019), focused on atmospheric CH₄ measurements, using both CRDS AirCore sampling and synthetic data to compare use of OLS and York fitting during the application of the Keeling and Miller-Tans method. Pataki et al. (2003) concentrated on the application of the Keeling method for δ¹³C of CO_2. However, as they highlighted in their paper, this method can be used also for other gas species or isotopes, where each application has its own constraints. Pataki et al. (2003) and Miller and Tans (2003) recommend using the model II (e.g. MA) fitting method for mass conservation because the OLS method could introduce a systematic bias, especially if the linear fitting r² value is low. However, Zobitz et al. (2006) showed that model II can also introduce some bias if the range of the CO₂ mole fraction is low (e.g., CO₂ enhancement above background is lower than 20 µmol mol^–1) and if variability on the x-axis is much lower than in the y-axis. Geometric mean regression (GMR) is another model II linear regression method that was not tested in our study, as it is expected to yield similar results to the MA method (Zobitz et al., 2006). In our study, we observed bias in the MA method for CRDS studies, where the uncertainty and fluctuation of the measured δ¹³CH_{4 obs} were greater than those for CH_{4 obs} mole fractions. As advised by Hoheisel et al. (2019), we focused on releases where the measured CH₄ mole fraction exceeded the background mole fraction by at least 0.5 µmol mol^–1. This provided a signal-to-noise ratio large enough to avoid introducing biases in high precision IRMS measurements using the model II method. However, bias due to low signal-to-noise ratio can occur when observing lower enhancements. This is typically the case for measurement stations conducting continuous measurements located at some distance from the source.

Hoheisel et al. (2019) focused on the comparison of the Keeling and Miller-Tans methods, using OLS and York fittings, for CH_{4 obs} AirCore and synthetic data. Regarding the comparison of measurement techniques, they obtained identical results for the Keeling and Miller-Tans methods when using York fitting. Using OLS fitting, they observed differences from –2‰ to 2‰ for individual AirCore samples between the Keeling and Miller-Tans methods. Hoheisel et al. (2019) showed that for AirCore studies, the results from York fitting fall between results obtained using OLS with the Keeling or Miller-Tans method for 90% of the measurements. In their study, results from York and OLS are nearly the same, but both show larger differences from the true, modeled value than from each other. The observed discrepancy between the fitted and true value reached <0.2‰ These results are consistent with our study, where we did not observe significant differences between York and OLS fittings and similar discrepancies between AirCore samples and direct δ¹³CH_{4 source}. Moreover, Hoheisel et al. (2019) investigated the influence of averaging time, examining intervals up to 1 minute. Using synthetic data, they demonstrated no significant differences between raw and 15 s averaged. They also observed improved precision of the measurements when averaging over 1 minute, but this did not enhance the determination of δ¹³CH_{4 source}. This contrasts with our results from mobile measurements, where we observed a varying bias introduced by data averaging, using different clusters, which worsens the determination of the final δ¹³CH_{4 source} (Figure 4).

We found that implementing a C₂H₆ correction on δ¹³CH₄ (as described in other studies) introduces a possible bias, resulting in the final averaged δ¹³CH₄ to be more¹³C depleted than calculated from IRMS measurements or from measurements made directly from the cylinder batch. To our knowledge, this is the first study to directly compare CRDS AirCore results with δ¹³CH_{4 source} determined from bag samples measured on an IRMS and direct source sampling, providing evidence to exclude a C₂H₆ correction for measuring δ¹³CH₄ in these types of samples. Previous studies that implemented a C₂H₆ correction focused solely on CRDS AirCore measurements, without the comparing them to independent C₂H₆-interference free measurements (Assan et al., 2017; Hoheisel et al., 2019; Lopez et al., 2017; Rella et al., 2015).

Finally, several studies, including Wehr and Saleska (2017) and Hoheisel et al. (2019), proposed using York fitting to determine δ¹³CH_{4 source}, as it is the most general regression method, which also accounts for uncertainties of both the x- and the y-axis. Based on Monte Carlo simulations, used to determine the isotopic signatures of CO₂, Wehr and Saleska (2017) presented that York fitting produces the closest realistic results, compared to OLS and GMR methods. Their conclusion aligns with our study, as the York fitting method consistently provides robust results for all examined analytical approaches. Additionally, we observe smaller discrepancies between the OLS and York fitting methods compared to the studies of Wehr and Saleska (2017). This can be explained by the larger CH₄ enhancements relative to CO₂ enhancements experienced in our study compared to theirs. Notably, we also tested the BCES linear fitting using two sub-methods: BCES (Y|X) and BCES Orthogonal, which had not been previously tested for atmospheric applications. We demonstrated that the choice of linear fitting method does not affect IRMS results. For AirCore samples, BCES (Y|X) results are in good agreement with York fitting results, whereas BCES Orthogonal introduces significant bias and should not be used for AirCore samples.

5.2. Possible improvements and further applications

Based on our study, several analytical details warrant special attention during the determination of δ¹³CH_{4 source}. We observed that individual AirCore values for samples collected on days 4 and 5 of the controlled release experiment were more depleted compared to samples collected from days 2 and 3 (Figure 3) and from the reference IRMS value. It is possible that an unnoticed issue, such as a leak, may have occurred during those days. Therefore, we recommend measuring calibration and working target gases on each measurement day, both before and after the fieldwork.

We observed about a 1.1‰ discrepancy in IRMS results between atmospheric and directly determined δ¹³CH_{4 source}. This discrepancy could be caused by different conditions in which direct and atmospheric samples were collected. For atmospheric studies, the gas was released over 45 minutes from the cylinder at high rates (up to 70 l min^–1) and was sampled in a downwind plume up to 250 m from the release position. For direct sampling, gas was transferred from cylinder batch to 10 L cylinder in less than two minutes. During the controlled release experiment, we did not observe significant differences or trends between atmospheric δ¹³CH_{4 source} determined during different releases, even when CH₄ flow rate, wind speed, or wind direction varied. These physical phenomena alone only impact the dispersion characteristic of CH₄ from the source to the sampling location, without any plausible mechanism for isotopic fractionation within the boundary layer on these short timescales. Further studies on possible isotopic fractionation during gas release are planned in the future to verify observed discrepancy.

In our study, we focus entirely on finding the best data processing strategy for near-source mobile measurements to determine δ¹³CH_{4 source}. However, we anticipate that the results can be generalized to other applications where similar isotopic mixing lines are appropriate. For example, the same conclusions should apply for the determination of δD-CH₄ and stable isotope ratios of CO₂. Also, our conclusions should be applicable for continuous isotopic measurements, both for CO₂ and CH₄. Before expanding our conclusion to other isotopes or continuous measurement studies, it is important to consider that the range of observed mole fractions, signal-to-noise ratios, precision, and variability of the y-axis could potentially introduce biases depending on their magnitudes and on the chosen fitting methods. Based on our study, York, and BCES (Y|X) are good candidate methods to apply in different contexts, as they exhibited the least variability and incorporate uncertainties of the x- and y-axis. Furthermore, establishing rejection criteria for individual applications, such as the size of uncertainty or the r² parameter, can identify outliers and improve the accuracy and precision of determining δ¹³CH_{4 source} isotopic signatures.