Non-target analysis using gas chromatography with time-of-flight mass spectrometry: application to time series of fourth generation synthetic halocarbons at Taunus Observatory (Germany)

Abstract. Production and use of many synthetic halogenated trace gases are regulated internationally because of their contribution to stratospheric ozone depletion or to climate change. In many applications they have been replaced by shorter-lived compounds which have become measurable in the atmosphere as emissions increased. Non-target monitoring of trace gases rather than targeted measurements of well-known substances is needed to keep up with such changes in the atmospheric composition. We regularly deploy gas chromatography (GC) coupled to time-of-flight mass spectrometry (TOF-MS) for analysis of flask air samples and in situ measurements at the Taunus Observatory, a site in central Germany. TOF-MS record data over a continuous mass range enable a retrospective analysis of the data set, which can thus be considered a type of digital air archive. This archive can be made use of if new substances come into use and their mass spectrometric fingerprint is identified. However, quantifying new replacement halocarbons can be challenging, as mole fractions are generally low, requiring high measurement precision and low detection limits. In addition, calibration can be demanding, as calibration gases may not contain sufficiently high amounts of newly used substances or the amounts in the calibration gas have not been quantified. This paper presents an indirect data evaluation approach for TOF-MS data, where the calibration is linked to another compound which could be quantified in the calibration gas. We also present an approach to evaluate the quality of the indirect calibration method and to select periods of stable instrument performance and well suited reference compounds. The method is applied to three short-lived synthetic halocarbons: HFO-1234-yf, HFO-1234ze(E), and HCFO-1233zd(E). They represent replacements for longer-lived HFCs and exhibit increasing mole fractions in the atmosphere. The indirectly calibrated results are compared to directly calibrated measurements using data from TOF-MS canister sample analysis and TOF-MS in situ measurements, which are available for some periods of our data set. The application of the indirect calibration method on several test cases can result into accuracies around 13 % to 20 %. For H(C)FOs accuracies up to 25 % are achieved. The indirectly calculated mole fractions of the investigated H(C)FOs at Taunus Observatory range between measured mole fractions at urban Dübendorf and Jungfraujoch stations in Switzerland.



Data evaluation
For both measurement set-ups, the integration of the chromatographic peaks is performed in a similar way as described in Schuck et al. (2018). The signal areas A of each substance are divided by the enriched sample Volume V to yield a response 120 R. A relative response rR of each analysed substance is calculated by dividing the response of a substance in an air sample measurement (R air ) by the linearly interpolated response of the bracketing calibration gas measurements (R cal ): Thereafter, rR is used to determine the mole fractions of the analysed substances if these are known in the calibration gas. In case of a linear detector response, the mole fraction in an air sample, χ air , is determined by multiplying the relative response 125 with the mole fraction of the calibration gas, χ cal : For the measurements of the weekly whole air sampling programme, an automated procedure is used to filter the data based on the double analysis of samples and parallel sampling into two canisters to ensure a high-quality dataset, as described in Schuck et al. (2018). For the in situ measurements, only one measurement and one preceding and subsequent calibration gas 130 measurement are available. The standard gas measurements are used to determine the measurement precision by comparing each standard with the bracketing standard measurements. An average weekly precision value for each substance is derived from this. If a calibration gas measurement differs more than the average weekly 1 σ-precision range from the previous or subsequent calibration gas measurements, the air measurements between those differing calibration measurements will be neglected.

Method concept
The need of an indirect calibration approach for short-lived H(C)FOs arises from the fact that these compounds were measurable with the TOF-MS already before calibration standards were used that contained measurable amounts of these substances.
As such, when these compounds were detectable in ambient air, the peak areas cannot be converted to mole fractions using 140 Eq. 2 because neither numbers for A cal nor rR are available. Therefore, a mathematical relation between a compound which is measurable in the standard and the target compounds (i. e. the H(C)FOs) is needed. Ideally, the sensitivity of the analytical system for the two different species behaves similarly, that means that the ratio of signal per amount of analyte for the two compounds is constant with time. If this is the case, the ratio of responses R of two species is close to constant. In case of equal amounts of sample (V cal = V air ), the ratio can also be computed from the ratio of the signal areas (A). If the responses and areas are further normalised to the mole fractions of the two species, this ratio should be the same for any sample. We refer to this ratio as relative response factor rRF : This relation applies to both ambient air measurements and calibration gas measurements. Eq. (3) can be rearranged to yield: Combining Eq. 4 with Eq. 2 and Eq. 1 for ambient air measurements, the mole fraction of species 2 can then be derived by Using Eq. 5, only measurements of ambient air are evaluated for species 2 and therefore that compound does not have to be present in the calibration gas in detectable amounts. The rRF can be evaluated independently, but it must be stable in time.
For a full retrospective analysis of archived data, the assumption of temporal stability or rRF needs to be validated first. This 155 can be achieved by evaluating the ratios of peak areas for species present in a sample with constant mole fractions, which is measured repeatedly in time. Thus it can be evaluated based on the peak areas in the calibration gas used for the measurement.
If the rRF between different species is stable in time for a given measurement system, it is possible to apply the indirect calibration method. The rRF for the species of interest which is not present in the standard relative to a compound which is detectable in the standard can then be derived from measurements of another sample which has detectable amounts and known 160 mole fractions of both species using Eq. (3).

Relative response factor
The methodology outlined in 3.1 is based on the assumption of a constant rRF in Eq. 4. In other words, the sensitivity of the GC-MS system towards different compounds should vary in the same way and the relative sensitivity should show no 165 drift in time. In reality, this will not be the case, as many factors influence the sensitivity. In particular after tuning the mass spectrometer or modifications of the analytical system such as replacement of filaments, columns or sample loops, changes in relative sensitivity and thus in the rRF are to be expected. Thus, to evaluate the approach described above, the temporal stability of the rRF needs to be investigated and periods with stable/unstable rRF need to separated. In the following we will refer to the compound which is detectable in the standard as the main reference substance. We further define an evaluation 170 substance, which is also present in the standard and which is used to identify periods of stable rRF . In order to investigate how large temporal changes of the rRF are and to determine periods of low variability of the rRF , we have investigated the Table 1. System precision (1σ) of the investigated substances of the TOF-MS used for the weekly whole air sampling (prc (TOF_Lab)) and of the TOF-MS used for the in situ measurements (prc (TOF_in situ)) and their calibration scales.  (Guillevic et al., 2018) temporal change of rRF for the combination of selected compounds listed in Table 1. Substances in Table 1 were chosen such that they have similar retention times and peak areas as the short-lived H(C)FOs of interest. In addition, we have excluded species which are known to elute close to water vapour and thus could be affected by the humidity of the sample and the 175 effectiveness of the sample drier, which is expected to lead to enhanced variability in sensitivity. This was, for example, the case for HCFC-141b (1,1-Dichloro-1-fluoroethane, CH 3 CCl 2 F, CAS 1717-00-6) and CFC-113 (1,1,2-Trichloro-1,2,2trifluoroethane, CCl 2 FCClF 2 , CAS 76-13-1) in the case of the laboratory system. with an rRF evalu that differs by not more than 10 % is counted. The measurement with the highest number of matching data points is used as a reference and all measurements that fall outside the 10 % interval are excluded (shown as grey data points in panel (b)). If more than one measurement has the same number of matching data points, the case with the lowest standard deviation is selected. In panels (c) and (d) the evaluation substance is replaced by a third substance, hereafter named test 185 substance, and the rRF test is plotted. In panel (d) the data point selection determined above is applied to the rRF between test and main substance. For comparison, panel (c) shows the selection that would be obtained if the above procedure was directly applied to the main-test-pair of substances. For three outliers with a high peak area ratio and several outliers with Panels (a) and (b) show the calculated rRF evalu of a known main reference and a known evaluation substance. Panel (b) shows which measurements will be selected, excluding measurements where the rRF differs more than 10 %. The resulting selection of measurements should represent the periods of stable rRFtest in panel (c) and (d), where the rRF is determined using the main reference substance and an arbitrary test substance. The aim is to find a main reference and an evaluation substance, which have many measurements with a constant rRF and which will represent the selection of test substances as well as possible.
low ratios a mismatch is evident. To choose the best combination of one main reference and one evaluation substance all possible combinations from the selected substances in Table 1 are investigated and tested for how well they represent known 190 test substances.

Evaluation based on weekly sample measurements
To evaluate the stability of the rRF of the laboratory GC-MS set-up used to analyse the weekly canister samples, we determined for each pair of substances from the compound selection listed in Table 1  quantify the differences between the selection of data of main reference and test substance via main reference substance and an evaluation substance we compared the relative standard deviations of the resulting filtered data sets. This is shown for all substance combinations in panels (d) and (h) (coloured points). A small range of standard deviations for a substance indicates more stable data selection and roughly correlates with a high percentage of selected data points as for example for HFC-143a.  In summary, for a good indirect calibration, the main reference and an evaluation substance should show a stable rRF for a large number of measurements and also rRF should be stable with a change of calibration gas. Finally, the rRF of data points selected via main reference and evaluation substance should not vary too much from the rRF of data points selected via main reference and test substance. Based on these criteria, we chose HFC-143a as main reference substance and HFC-125 as evaluation substance. Signal areas of HFC-143a have a high mean r 2 above 0.8 for all tested substances and one of the smallest mean values of MAPE with 19 %. After the application of the ± 10 % data selection criterion with HFC-125 as evaluation substance, HFC-143a has more than 50 % of the selected data for six out of the eight tested evaluation substances.

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Its retention time of 7.15 min is close to that of the three target species HFO-1234yf (6.0 min), HFO-1234-ze(E) (6.8 min), and HCFO-1233zd(E) (9.6 min). Using HFC-125 as evaluation substance with HFC-143a, the difference standard deviations of the mean rRF selected via the test substances and selected via itself ranges between 1 and 10 %. HFC-125 also has a large mean r 2 in comparison to other substances in the calibration gas measurements, and the fifth lowest mean MAPE (22 %) (cf. Fig. 3).
The next step of the method evaluation is the application to several test substances for which results of the indirect calibration 240 can be compared to directly calibrated measurement results. As test cases to apply the indirect calibration method to we chose HFC-32, HFC-227ea, and HFC-245fa. Results are presented in Fig. 6. Shown are time series of directly and indirectly determined mole fractions (left plots) and their correlations (right plots). In this test case, mole fractions of HFC-227ea shows the best correlation with r 2 > 0.9 and a MAPE of 11 % (Fig. 6 (c) and (d) 143a as main reference substance has also less than 50 % of selected data within the 10 %-filter (cf. Fig. 5), which means that the calculation is applied to a large portion of data for which the criterion of a constant rRF was not met. This underlines how crucial the assumption of constant instrumental sensitivity is for the indirect calibration method.  substance, HFC-125 as evaluation substance to select data with constant rRF . Error bars, which indicate the measurement precisions, are included but are often smaller than symbol size.  Especially shorter-term variations are well captured, while long-term trends between the directly and indirectly calculated mole fractions are partly different between the directly determined and the indirectly determined data. This is caused by longterm drifts in the rRF . The average relative differences are given in Table 3.

Application of indirect calibration method to short-lived synthetic halocarbons
As the indirect calibration method has shown satisfactory results for the test substances, we apply it to the short-lived com-265 pounds HFO-1234yf, HFO-1234ze(E), and HCFO-1233ze(E). For these compounds, the direct calibration is limited to parts of the time series which were calibrated with gases containing these substances at sufficiently high mole fractions. The average relative differences of that comparison are given in Table 3. For HFO-1234yf, the mole fractions differ by around 24.3 %, for HFO-1234ze(E) the relative average difference is 19.5 %.
Data of the weekly flask sampling (cf. Table 4)    Non-target analysis using full-scanning mass spectrometry offers the opportunity to detect and quantify species in the atmosphere retrospectively. However, as gas chromatography is a relative measurement technique, knowledge of the mole fraction of the retrospectively analysed species in the calibration gas is required. Often the species of interest is either not detectable in the calibration gas or the mole fraction in the calibration gas is not known. For such cases we have developed an indirect calibration approach which relies on the assumption that the relative sensitivity of the analytical system to two species changes 305 in a similar way, so that their ratio would be constant in time, even if the absolute sensitivity of the system changes. In this case, quantification may be performed using the measurement of a reference species and the ratio of the relative sensitivities of target and reference compound, provided that the absolute value of the relative response of the species is derived retrospectively. In order to evaluate the stability of the relative responses of two such species, we tested the approach using species whose concentrations are known in the calibration gas. We suggest that it is useful to use an evaluation substance to select 310 periods when relative responses of the measurement system are rather stable. Further, it is likely that using reference species with similar retention times as the target species provides more stable results. By analysing correlations and variabilities of the relative responses, we identify the combination of a reference and an evaluation substance which yields good results for a range of different target gases. Furthermore, we have chosen to include only time periods where the relative response of the reference substance and the evaluation substance are stable within 10 % in the analysis. A good combination of reference and evaluation 315 substance should thus yield small deviations between direct and indirect calibration for a wide range of compounds, while also retaining a sufficient number of measurements based on the filter criterion of maximum deviation in relative response factor.
This procedure with the 10 % criterion is applied to two different data sets for testing. The first data set is a measurements time series of flask samples collected at the Taunus Observatory on the Kleiner Feldberg near Frankfurt in Germany. This data set has been evaluated for the time period from October 2013 to December 2018. The second data set is from in situ mea-320 surements at the Taunus Observatory using an automated gas chromatographic system with time-of-flight mass spectrometric detection. This data set has been evaluated for the time period from May 2018 to March 2019. For the long-term flask data, we find relative differences between directly and indirectly calibrated mole fractions of different gases ranging between 13 Based on these differences between directly calibrated and indirectly calibrated values of up to 25 %, we conclude that the indirect calibration method is not suited for detection of small trends of long lived gases in the atmosphere, which are often of the order of less than 1 % per year. However, for species with large trends where no direct measurements are available, this method can provide the correct order of magnitude of atmospheric mole fractions in the past. A further interesting application is to the measurement of short-lived gases, which are excepted to show high variability in the atmosphere. For such gases, both 330 correct orders of magnitude and also the frequency at which they are observable can be derived. In order to confirm the validity of the indirect calibration approach, it will be useful to maintain aliquots of calibration gases, so that these can be calibrated retrospectively allowing to confirm the stability of relative response factors for species which are detectable and stable in the calibration gas over a a longer time period.
Examples for species where the indirect calibration is useful are the unsaturated HFOs and HCFOs, which have recently 335 been introduced as replacement compounds for long-lived hydrofluorocarbons. These gases are short lived with local lifetimes of less than a month and are increasingly used for e.g. mobile air conditioning. The three H(C)FOs HFO-1234yf, HFO-1234ze(E) and HCFO-1233zd(E) have been detectable at an increasing frequency in our ambient air chromatograms. We have thus applied the indirect calibration method to both the flask measurements and the in situ measurements of H(C)FOs. For the flask measurements we show that the frequency at which measurable peaks are observed at Taunus Observatory increases