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Calibration strategies for FTIR and other IRIS instruments for accurate #13C and #18O measurements of CO2 in air Edgar Flores, Joele Viallon, Philippe Moussay, David W.T. Griffith, and Robert Ian Wielgosz Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b05063 • Publication Date (Web): 15 Feb 2017 Downloaded from http://pubs.acs.org on February 16, 2017

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Analytical Chemistry

Calibration strategies for FTIR and other IRIS instruments for accurate δ13C and δ18O measurements of CO2 in air Edgar Flores*1, Joële Viallon1, Philippe Moussay1, David W.T. Griffith2, and Robert Ian Wielgosz1. 1

Bureau International des Poids et Mesures (BIPM), Pavillon de Breteuil, F-92312 Sèvres Cedex, (33) 1 45 07 70 92, [email protected]

2

University of Wollongong, Wollongong NSW 2500 Australia

This paper describes calibration strategies in laboratory conditions that can be applied to ensure accurate measurements of the isotopic composition of the CO2 in ultra-dry air, expressed as δ13C and δ18O on the VPDB scale, with either FTIR (in this case a Vertex 70V (Bruker)) or an Isotope Ratio Infrared Spectrometer (IRIS) (in this case a Delta Ray (Thermo Fisher Scientific)). In the case of FTIR a novel methodology using only two standards of CO2 in air with different mole fractions but identical isotopic composition was demonstrated to be highly accurate for measurements of δ13C and δ18O with standard uncertainties of 0.09 ‰ and 1.03 ‰ respectively, at a nominal CO2 mole fraction of 400 µmol mol-1 in air. In the case of the IRIS system, we demonstrate that the use of two standards of CO2 in air of known but differing δ13C and δ18O isotopic composition allows standard uncertainties of 0.18 ‰ and 0.48 ‰, to be achieved for δ13C and δ18O measurements respectively. The calibration strategies were validated using a set of five traceable Primary Reference Gas Mixtures. These standards, produced with whole air or synthetic air covered the mole fraction range of (378- 420) µmol mol-1 and were prepared and/or value assigned either by the National Institute of Standards and Technology (NIST) or the National Physical Laboratory (NPL). The standards were prepared using pure CO2 obtained from different sources, namely: combustion; Northern Continental and Southern Oceanic Air and a gas well source, with δ13C values ranging between -35‰ and -1‰. The isotopic composition of all standards was value assigned at the Max Planck Institute for Biogeochemistry Jena (MPI-Jena).

Introduction According to the World Meteorological Organization (WMO), in spring 2015 the global average mole fraction of carbon dioxide (CO2) crossed the 400 µmol mol-1 threshhold1. The global carbon cycle includes carbon sinks on both land and in the ocean, offsetting increases in atmospheric CO2 from fossil fuel and biomass burning and other sources. To better understand the carbon cycle, clear identification of sources and sinks of CO2 is required as well as the ability to quantify their relative contribution to the atmosphere at a variety of spatial scales. The study of isotopic composition of CO2 in the atmosphere permits the identification of sources and sinks of carbon at local, regional, and global scale1-4. Over recent years the introduction of Isotope Ratio Infrared Spectroscopy (IRIS), based on various spectroscopic techniques, has revolutionized stable isotope analysis in the atmosphere, allowing in-situ field measurements of the isotope ratio of CO2 in air, performed in real time directly on the air sample without separation of CO2 from air. The technology therefore provides an alternative to isotope ratio mass spectrometers (IRMS) for the measurement of stable isotope ratios5. Techniques that can be used include tunable diode laser absorption spectroscopy (TDLAS), quantum cascade laser absorption spectroscopy (QCLAS), cavity ring down spectroscopy (CRDS), off-axis integrated cavity output spectroscopy (OA-ICOS) and Fourier transform infrared spectroscopy (FTIR). Instruments based on these techniques have been reported to operate with precisions of ±(0.04 to 0.25) ‰ for δ13C and ±(0.05 to 2.0) ‰ for δ 18O for field measurements, and thus approaching the ±0.01‰ levels reported for IRMS in a

number of laboratories. However, non negligible dependencies of measured isotopic ratios on the CO2 mole fraction have been reported6, requiring a full calibration process with appropriate standards that are value assigned on internationally recognized scales, both for mole fraction and isotopic composition. In addition, whereas IRMS instruments make measurements on small amounts of pure CO2, IRIS instruments operate and need to be calibrated with gas standards of CO2 in air at ambient levels, with flows of gas in the range of 0.1 L/min to 1 L/min. Therefore, a new range of standards is required to properly calibrate IRIS instruments, with consideration given to the composition of the standards that are needed, as well as the number required for an accurate calibration, and the appropriate calibration procedure to be applied. In this paper we applied a calibration strategy for δ13C and δ18O measurements for a FTIR instrument. The strategy is based on the calibration of the instrument response to predetermined CO2 isotopologue mole fractions focusing on the minimum number of standards, their composition and the level of accuracy required for an accurate calibration. The achievable measurement uncertainty is discussed in detail. The method is compared with another calibration approach used with a laser absorption analyser (Delta Ray), based on a two-point calibration of the delta values. Although both instruments measure the absorbance of CO2 minor isotopologues in the same mid-infrared region (4.3 µm or 2325 cm-1), they differ in the approach developed for their calibration, with the Delta Ray being equipped with calibration standards consisting of two pure CO2 cylinders with different δ13C and δ18O values.

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We demonstrate the effectiveness of the calibration strategies using a set of five standards accurately characterized for CO2 mole fraction and isotopic composition, which are presented in detail in the first section of the paper. A second section describes the FTIR calibration procedure and associated uncertainties. The other approach used for the Delta Ray instrument is presented in a third section, before comparing the performances of both instruments.

CO2 in air standards The standards used in this study were produced with ultra-dry whole air containing CO2 in the mole fraction range of (380420) µmol mol-1 and were prepared and/or certified either by the National Institute of Standards and Technology (NIST) or by the National Physical Laboratory (NPL). Table 1 lists the set of standards used in the study. Particular attention was paid to the composition of the matrix gas, especially the major components (N2, O2 and Ar) which were targeted to be within 0.01 % of atmospheric values to avoid biases that could be introduced into spectroscopic measurements due to pressure broadening effects (details of the matrix composition are provided in Supporting Information Table S- 1.). Cylinders 1 and 2 were produced by Scott Marrin Gases using the gravimetric blend technique to add pure CO2 (assumed to be a product of combustion) in cryogenic ultra-pure air. The mixtures were further analyzed by NIST to certify the mole fraction of CO2, methane (CH4) and nitrous oxide (N2O). The certification of these gas mixtures was performed against a suite of CO2 in synthetic air references prepared by gravimetry, following NIST standard procedures (see Rhoderick et al.13). Cylinders 3 and 4 were produced by NIST to mimic atmospheric air: cylinder 3 was made of Southern Oceanic Air (SRM 1721)14 and cylinder 4 of Northern Hemisphere Air (SRM 1720)15. The quantification of traces gases followed the same NIST standard procedures used for cylinders 1 and 2. Cylinder 5 was produced by NPL (NPL1788) by gravimetry following the procedure described by Brewer et al.16 This mixture was prepared using pure CO2 from a gas well source provided by the BIPM to NPL for that purpose. The δ13C values in these standards covered the range -35‰ to -1‰ using CO2 from specific sources, namely: from air (both Northern Continental and Southern Oceanic Air); from a combustion source; and from a gas well source. The isotope ratio analysis of all standards was performed by the MPI-Jena12 using a Finnigan MAT 252 (ThermoFinnigan, Bremen, Germany) mass spectrometer (CORA) with a homemade CO2 extraction system (BGC-AirTrap) for automatic analysis of carbon and oxygen isotope ratios of CO2 in air samples. Table 1 lists the isotopic composition of each mixture reported on the j-RAS06 realization of the VPDB-CO2 scale12, maintained by MPI-Jena in its quality of WMO-endorsed Central Calibration Lab (CCL) for CO2 isotopic analysis. As all delta values considered here are anchored to the realization of the VPDB-CO2 scale by MPI-Jena, either directly or indirectly via calibrated IRIS instruments, any bias in those values would be fully correlated. Therefore values provided by

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MPI-Jena were considered un-biased relative to the VPDBCO2 scale. The uncertainty in the IRMS measurements was estimated from the reported calibration results provided by MPI-Jena for a set of ten standards sent for delta value assignment during 2014 and 2015. The uncertainty budget was constructed from two components, the first related to the repeatability of the measurement results at MPI-Jena, and the second related to the stability and homogeneity of the isotope ratio values in different standards containing nominally the same CO2 gas. The first uncertainty component was calculated from the standard deviation of repeated measurements on the same standard. For this, the standard deviation of a time series reported of one cylinder measured over several hours was used. The standard deviation of the instrument response was 0.015 ‰ for δ13C and 0.27 ‰ for δ18O. For the second component, three secondary standards made of the same pure CO2 produced under identical conditions were analysed. The standard deviation of the delta values was 0.002 ‰ and 0.187 ‰ for δ13C and δ18O, respectively. It was expected that the second component would capture the variation occurring between different standards containing the same CO2. Both contributions were then combined in quadrature resulting in standard uncertainties of the values assigned by MPI-Jena of u(δ13CMPI-Jena)=0.015 ‰ and u(δ18OMPI-Jena) =0.328 ‰. The resulting uncertainty in δ13C was comparable to that reported by Werner et al. 18 however the uncertainty calculated for δ18O was one order of magnitude larger. These uncertainties were used and considered to provide conservative values for the variation in isotopic ratios expected in the standards.

FTIR Measurement principle A vacuum Bruker Vertex 70v FTIR Spectrometer equipped with a RockSolid interferometer (vacuum better than 0.2 hPa), with 1 cm-1 resolution (0.16 optional), a 40 mm beam diameter, a globar source and CaF2 beam splitter was used for the study. The spectrometer was configured with a liquid N2cooled mid-infrared Indium Antimonide (InSb) detector and a 10.01 m multi-pass White-type gas cell of volume 0.75 L (Gemini Scientific Instruments, USA). The wetted surfaces of the gas cell were electro-polished stainless steel treated with silconert 2000 (Silcotek) and gold (mirror coatings) to minimize surface adsorption and desorption effects for CO2. The interferometer was scanned at 64 scans min-1 and spectra coadded for five minutes to obtain an acceptable signal-to-noise ratio. The transmission spectra of gas reference standards obtained following this procedure had a very high signal to noise ratio of typically ~1 x 104 peak-peak from (2240–3380) cm-1. In order to prevent nonlinear responses produced by excess photon flux reaching the InSb detector special care was put into adjusting the instrument parameters of the software to ensure that the apparent intensity from the InSb detector was zero at 1850 cm-1. The spectrometer user interface was controlled using a BIPM developed software named B-FOS, that allowed the automatic setting of all instrument parameters into Bruker’s proprietary OPUS software for control, spectral acquisition and on-line analysis through the use of MALT (Multiple Atmospheric Layer Transmission) spectrum analysis software, version 5.56. MALT retrieves concentrations of each trace gas in the sample


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from a least-squares fit to the measured spectrum based on a model calculation and Hitran line parameters. This code is the basis for quantitative analysis of open and closed path FTIR trace gas measurements and has been compared with other codes such as SFIT for ground based solar FT-IR measurements with agreement of better than 0.7% (Griffith et al.).

CO mole 2

fraction

Mixture

Standard uncertainty

u(

CO2 -1

CO2

13

_

18

δ C

δ O

VPDB-CO2 (j-RAS06)

VPDB-CO2(jRAS06)

(‰)

(‰)

_

_

) -1

(µmol mol )

(µmol mol )

1

378.90

0.09

-35.685

2

420.43

0.1

3

393.97

4 5

-1

-1

-1

(µmol mol )

(µmol mol )

(µmol mol )

-34.478

373.06

4.02202

1.50445

-35.682

-34.115

413.95

4.46287

1.66998

0.07

-8.636

-1.436

387.73

4.29736

1.61709

388.16

0.06

-8.295

-0.241

382.01

4.23540

1.59514

380.00

0.19

-1.384

-7.148

373.96

4.17507

1.55075

13

18

Table 1. Mole fraction, uncertainty, δ C, δ O, x626_R, x636_R and x628_R for the five CO2 in air standards. For more details regarding mole fractions and associated standard uncertainties of all components in the set of 5 CO2 in air standards see Table S-1 (supporting material).

The spectra were constructed by co-adding up to 320 scans recorded in about 5 minutes to provide a single spectrum of a sample. This single spectrum was ratioed with a similar spectrum of ultra-pure N2 collected under similar conditions to provide an absorbance or transmission spectrum of the gas sample (relative to ultra-pure N2) in the gas cell. The sample flow rates were kept at ~400 mL min−1. Assuming perfect mixing in the cell it was estimated that 99.9 % of the sample was replaced after 10 min of flow, and 99.998 % replaced after 20 min26. In order to ensure the complete exchange of samples, only the measured spectra obtained after flowing the sample through the White-type cell for 35 min (99.99999% gas replacement) were used for mole fraction determinations. The sample pressure was measured by means of the calibrated barometer Mensor Series 6000. The relative uncertainty of this pressure sensor was u(P) = 0.02 %. The sample temperature was measured with a calibrated 100 Ω RTD temperature probe introduced into the outlet gas of the White-type gas cell with a standard uncertainty u(T)=0.02 K. The recorded spectra were analysed online by non-linear least squares fitting in two sections of the spectra, 3500–3800 cm-1 (plotted in Figure 1) and 2200–2310 cm-1 (plotted in Figure 2), with modelled spectra calculated by MALT using absorption line parameters from the HITRAN database version 2012. As previously described by Griffith et al.11, the first region shows peaks that are due to the major isotopologue 12C16O16O, whereas the second region can be used to analyse the two other isotopologues 13C16O16O and 12C16O18O. In order to correctly account for interferences, N2O mole fractions were also calculated from measurements in the second spectral region. Since all standards used during this work were ultra-dry

CO2/air gas mixtures the cross sensitivity with H2O was not considered. 1.00 0.95

Transmitance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.90

Measured Fitted

0.85 0.80 0.75 0.70 3500 0.002

3550

3600

3650

3700

3750

3800

3550

3600

3650

3700

3750

3800

Residual

0.000 -0.002 3500

-1

Wavenumber/cm

Figure 1. Typical measured and fitted spectra (upper part), and residual signal (lower part) in the region 3500–3800 cm-1 obtained on a standard of CO2 in air at 384.33 µmol mol-1. The absorption feature is due to the major isotopologue 626.


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Transmitance


1.00 0.95 0.90 0.85 0.80

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O =

O =

(4)

Measured Fitted

0.75 0.70

(5)

where:

0.65 0.60 0.55 0.50 2200 0.002

2250

2300

Residual

0.000 -0.002 2200

2250

2300 -1

Wavenumber/cm

Figure 2. Typical measured and fitted spectra (upper part), and residual signal (lower part) in the region 2200–2310 cm-1 obtained on a standard of CO2 in air at 395 µmol mol-1. The absorption feature is due to the isotopologues 626, 636 and 628, and to N2O when present.

Calibration procedure The FTIR calibration procedure is based on the calibration of the instrument’s responses to the individual 12C16O16O, 13 16 16 C O O and 12C16O18O isotopologues (the Hitran/Air Force Geophysics Laboratory (AFGL) shorthand notation, 626, 636 and 628 respectively, is also used in the paper to refer to these28). As isotopologue mole fractions are measured, the standards were chosen so as to bracket each of the three expected isotopologue mole fractions in the samples. As a result, the two standards were prepared from the same CO2 gas, and almost identical δ13C and δ18O values, but different CO2 mole fractions, as can be seen in Table 1. The calibration procedure is a further development of the principles introduced by Griffith et al.11, and also compared with three other methods on other IRIS instruments by Wen6, who referred to this method as “two-points mixing ratio gain and offset calibration”, but did not provide an uncertainty budget for its application, and was unable to implement it accurately due to a lack of appropriate standards. A slightly different terminology being used here, the notation and the equations are redefined below. Starting with standards of known CO2 mole fractions and isotopic composition, the mole fraction of each individual isotopologue needs to be calculated, as these quantities are the ones measured by the FTIR. At first the atomic isotopic abundances in each of the calibration gas mixtures must be calculated using equations 1 to 5, where R is the isotope ratio in the CO2 gas, with the superscripts denoting whether these are 13C/12C, 18 O/16O or 17O/16O ratios):

C =

C =

O =

(1)

(2) (3)

1 + 10 # C$ =

(6)

1 + 10 # O$^& =

(7)

1 + 10 # O$ =

(8)

and δ13C and δ18O are the delta values expressed in per mil, which in this case were measured by the MPI-Jena (realization of the VPDB-CO2 scale). '()*+, , '()*+, and +,'()* values were taken from Brand et al for VPDB-CO2 ( = 0.011180, = 0.0003931 and = 0.00208835) since those correspond to parameters used by the MPI-Jena (&=0.528). Then each carbon dioxide isotopologue mole fraction in the reference gas was calculated according to its composition using equations 6 to 8: x626_R=- C ∗ O ∗ O / ∗ +,

(9)

x636_R=- C ∗ O ∗ O / ∗ +,

(10)

x628_R=- C ∗ O ∗ O / ∗ 2 ∗ +,

(11)

Where +, is the CO2 mole fraction, the shorthand notations for isotopologues is used (626, 636 and 628) and the subscript R is used to identify the reference values. These calculated reference isotopologue mole fraction values were used, together with the MALT generated mole fractions from the FTIR measurements of the references, to determine three calibration equations, one per isotopologue. The calibration curves were established to ensure that the isotopologue mole fractions in the two calibration standards bracketed the isotopologue mole fractions to be measured in unknown mixtures. This was the case in this work as displayed in Table 1, where the isotopologue mole fractions calculated in all standards are listed. The measured FTIR spectrum was fitted with MALT to produce 626, 636 and 628 isotopologue mole fractions (using the MALT isoscale=1 option). The predicted mole fraction xiso of the isotopologue iso (where iso stands for 626, 636 or 628) in an unknown sample was then deduced from the corresponding calibration equation: 123 = 4123 − 6789 $/;123

(12)

where 4123 is the mole fraction of the same isotopologue given by MALT, aiso and biso are the slope and intercept of each calibration equation (see calibration lines in supporting material Figure S-1).


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Note that the calibration model adopted here assumes linearity of the response of the instrument. This is normally the case with FTIR providing the gas cell path length is properly chosen, and was tested formally and confirmed in this work. It is only in a last step that the predicted (or calibrated) responses were used to determine the isotope ratios of the measured samples: < = < =

=>>

(13)

=>?> =>?

(14)

=>?> ∗

and that finally, the δ13C and δ18O values of the unknown mixture(s) were calculated on the VPDB-CO2 scale using equations 15 and 16: # JKL C=@

A

BCDEFGH?

# JKL O=@

A BCDEFGH?

− 1I ∗ 1000

(15)

− 1I ∗ 1000

(16)

Equations 1 to 11 are only valid for ultra-dry and well isotopically equilibrated CO2/air mixtures. If such conditions are not satisfied new validations should be done.

Uncertainty budget Because of the innovative use of FTIR and Delta Ray for δ13C measurements only a very limited amount of information has been published on the uncertainty of these measurements, and most of it has focused solely on the precision and stability of the measurements. In the case of FTIR, Griffith et al.11 and Hammer et al.30 reported long term reproducibility values in their instrumentation and methodology of ±0.05 ‰ for δ13C measurements. Vardag et al. also reported comparable values for δ13C reproducibility measurements, ±0.02 ‰. Additionally, Vardag et al. reported the first stability value for δ18O FTIR measurements (±0.15 ‰ after 30 minutes of measurements). Those values reflect the stability of the instrument and were estimated from statistical analysis. However when proposing a calibration procedure, it is also important to take into account the uncertainty of the calibration standards. Here, the uncertainties on the reference isotopologue mole fraction values xiso were first estimated, and then used in an uncertainty budget reflecting a two point calibration process for each isotopologue, as described below. All calculations were performed according to the Guide for Uncertainty in Measurements32, using the software GUM workbench. Values obtained with this standard approach were further confirmed using a sensitivity study, in which the influence of each input parameter (mole fraction of the calibration standards, the δ13C and δ18O value assigned by the MPI-Jena and the 626, 636 and 628 FTIR responses) on the resulting δ13C and δ18O was analyzed independently. As a final test we also analyzed the stability of the δ13C and δ18O measurements, similarly to Griffith et al.11, Hammer et al. and Vardag et al.31, in order to demonstrate why this manner of determining uncertainties may underestimate the final δ13C and δ18O uncertainties by FTIR measurements.

Standard approach by GUM In a standard approach, the standard uncertainty of the result of the calibration is derived from a model equation. Noting that each individual isotopologue mole fraction is obtained by a two-point calibration process, the model equation for each of them is equation 12 in which the slope aiso and intercept biso were explicitly deduced from the two calibration standards’ reference values and FTIR responses. The model equation for the isotopic ratio is then equation 13. Standard uncertainty on δ13C Using the estimation of δ13C as an example, a total of four reference values were required, two (x626R, x636R) for each calibration standard. From equations 9 and 10, one can easily conclude that their standard uncertainty uiso is linked to the CO2 mole fraction relative uncertainty by MNOP = QNOPR MR QSTU $, as the contributions from the abundances reflect the uncertainty on the δ13C measured by MPI-Jena and are negligible. However the 636 and 626 reference values in each calibration standard are highly correlated via the isotopic ratio R13 (or the value δ13C). In our model a correlation factor of one between those values was included. The stability of the FTIR response impacts a total of six measured values, one for each of the two isotopologues 626 and 636, for the two calibrations standards plus the sample. The FTIR stability is not exactly the same for 636 and 626. Those values have been estimated from the Allan deviations at an averaging time of five minutes on each response, resulting in the values ustab1 = 6 nmol mol-1 for 626 and ust-1 ab2 = 0.07 nmol mol for 636. The Allan Variance analysis was applied using the Stable 32 software (a frequency stability analysis software that allows the entry and editing of phase and frequency data, the calculation of stability statistics, and the plotting of phase, frequency and stability data)33. In addition, the correlation between the response to 626 and 636 was also evaluated from the same time series analysis, resulting in a correlation factor of 0.29.



The set of ten values set of ten values (four reference and six measured values) and associated uncertainties were entered in GUM workbench as input quantities. The two calibration standards 1 and 2 were used with the sample 3 for this exercise. This resulted in a standard uncertainty uR13 = 1.03×10-6 on the ratio R13, or u_FT_ δ13C = 0.09 ‰ on δ13C. Contributions of all input quantities are displayed in Table 2. The uncertainty is largely dominated by uncertainties on all isotopologue reference mole fraction values xiso, hence by the CO2 mole fraction uncertainties of the calibration standards.

To perform this study the FTIR calibration method was executed using cylinders 1 and 2 as calibration mixtures and cylinder 3 as the sample. The quantities required to perform the FTIR calibration and for which the impact on the final δ13C and δ18O uncertainty was estimated were the CO2 gravimetric mole fractions values and uncertainties assigned to the mixtures 1 and 2, the δ13C and δ18O values assigned by the MPIJena and the individual isotopologue mole fractions estimated from the FTIR spectra using MALT (for each isotopologue, Allan variance analysis).

Table 2: Uncertainty budget for R13, showing the input quantity q, its value qv, standard uncertainty u(qv), and the contribution to the standard uncertainty on R13 for the two calibration standards 1, 2, and the sample 3.

qv / (µmol mol-1)

Sample

q

1

x636

2

x636

3

y636

2

y636

1

y636

1

x626

2

x626

3

y626

2

y626

1

y626

18

Standard uncertainty on δ O The model for δ18O is very similar as the one just described, except that the two calibrations lines are made from the reference values in 626 and 628, together with the FTIR responses to those values. The standard uncertainties on x626R and x628 are also dominated by the uncertainty on CO2 mole fraction, and highly correlated.

Using the same kind of calculation in GUM workbench as described previously, a standard uncertainty uR18 = 2.16×10-6 was obtained on the ratio R18, or u_FT_ δ18O = 1.03 ‰ on δ18O. A similar budget as displayed in Table 2 was obtained, and can be found in the supporting material (Table S- 2), but in this case the major contributor is the stability of the FTIR 628 response (y628), rather than the uncertainty of reference mole fraction value. Sensitivity study The uncertainty in the δ13C and δ18O determined from the FTIR method was assessed by varying the calibration input parameters, as described in the GUM (see supporting material) and studying the effect on the predicted δ13C and δ18O values. Each input parameter variation was chosen according to a range delimited by its standard uncertainty xi - u(xi) to xi + u(xi). The contribution to the total standard uncertainty was considered equal to half the variation (∆Y) observed in the delta values. Table S- 3 of the supporting material lists the assumed distribution, standard uncertainties u(xi) and the contribution ∆Y to the combined uncertainty of all considered parameters.

626 calibration

The stability of the FTIR response is unchanged for the isotopologue 626, ustab1 = 6 nmol mol-1. For the isotopologue 628, the Allan deviation at an averaging time of five minutes provides the value of 0.8 nmol mol-1. An additional instability on measurements repeated over three days was noted for the 628 response and it was decided to add a second contribution. Observing a noise of 2 nmol mol-1 peak-to-peak and considering a rectangular distribution, the value unoise = (2)/(√3) = 1.15 nmol mol-1 was estimated. The combination of both uncertainty components results in a standard uncertainty on the FTIR response to 628 of ustab3 = 1.40 nmol mol-1. The correlation between the response to 626 and 628 was also evaluated from the time series analysis, resulting in the same correlation factor of 0.29.

636 calibration

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R

u(qv) / (µmol mol-1)

Uncertainty Contribution/ (10-6)

4.02202

0.00096

0.960

4.46287

0.00106

1.700

4.20550

0.00007

0.180

4.37383

0.00007

-0.110

3.93919

0.00007

-0.071

373.06740

0.08860

-1.700

413.95380

0.09830

-0.980

381.40250

0.00600

-0.170

407.75810

0.00600

0.060

367.40560

0.00600

0.110

13

0.01108365

1.03×10-6

The results of the sensitivity study confirmed that in the case of δ13C the main uncertainty contributor comes from the uncertainty of the mole fraction of both CO2/air mixtures used to calibrate the FTIR, which contributed together 90 % of the index for the total uncertainty. In the case of δ18O the main uncertainty contributor comes from the FTIR response to 628 isotopologue, which contributed to up to 93 % of the index for the total uncertainty when combining the measurements of cylinders 1, 2 and 3. In conclusion according to this sensitivity study the standard uncertainty of the FTIR methodology for the determination of δ13C values was 0.09 ‰ and 1.07 ‰ for δ18O. Stability of the delta values Allan Variance analysis was applied to the δ13C and δ18O time series obtained by the FT-IR spectrometer using the Stable 32 software. White noise behaviour was observed for measurement averaging times up to at least top = 300 s for both (δ13C and δ18O, supporting material), with Allan deviation at top equal to 0.02 ‰ for δ13C 0.5 ‰ for δ18O, comparing favourably with values reported previously for other IRIS instruments6.


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Delta Ray Measurement principle The Delta Ray is an Isotope Ratio mid-Infrared Spectrometer (Thermo Fisher Scientific, Bremen, Germany)34 operating in the mid-infrared region (4.3 µm). The instrument, fully described elsewhere5, operates with a tuneable mid-infrared laser beam generated by two near-infrared telecommunication type lasers that are mixed in periodically poled lithium niobate (PPLN). One laser is frequency-stabilized, whilst the other is a tunable distributed feedback (DFB) laser that is used to tune the mid-infrared difference frequency. The Delta Ray works with a simple direct absorption approach since the absorption lines of the different carbon dioxide isotopologues are shifted relative to each other and allow for the calculation of their relative abundances and the stable isotope ratios from the spectrum. The laser scans over the absorption lines at 500 Hz and the signal is averaged for 1 s before the spectrum is fitted and isotope ratios are calculated from the spectrum fit. The sample gas is measured for its concentration and isotope composition by laser direct absorption in a multipass Herriot cell with temperature stability of a few mK, and the pressure is controlled at 100 hPa. The sample line runs through the temperature-controlled enclosure that allows for thermal equilibration before the sample gas enters the cell. The instrument user interface is controlled using Qtegra software. Since the quantification model and measurement procedure of the delta values by this instrument is propriety information of the Thermo company, no access to this information, including raw calibration values, was available for recalibrations. Calibration Procedure Unlike the FTIR or other IRIS instruments described in the literature6, the Delta Ray instrument is supplied with a calibration procedure and gases. The Delta Ray uses two pure CO2 standards to correct for changes in measured isotope ratio over a concentration range (linearity calibration) and for calibrating the delta values on the VPDB-CO2 scale by a two-point calibration. In addition two CO2 in air reference standards can be used to calibrate the system for CO2 concentration. This calibration procedure, named ‘Get Ready’, is performed automatically by the instrument once the Qtegra software instructions are followed, and is not accessible to the user. In this work Delta Ray calibration was performed using the ‘Get Ready’ procedure with two pure CO2 references gases: cylinder 401557 with delta values δ13C = -1.38 ‰ and δ18O = 7.14 ‰ and cylinder C11375KO with delta values of δ13C = 42.13 ‰ and δ18O = -27.7 ‰ on the VPDB-CO2 (j-RAS06) scale; the CO2 in air reference standards 1 and 2; and one dry whole air mixture scrubbed of CO2 (Scott Marrin, Inc.) which was used by the instrument to dilute the pure CO2 gas to the target concentration. The first measurements demonstrated the existence of a bias between Delta Ray instrument measured values and the values for these samples reported on the j-RAS06 realization of the VPDB-CO2 scale12. When measuring samples with reference values of δ13C = -35.69 ‰ and δ18O = -34.48 ‰ the ‘Get ready’ procedure calibrated instrument indicated δ13C = 40.65 ‰ and δ18O = -40.11 ‰. It was therefore decided to perform an additional two point calibration of the δ13C and δ18O values including a low and a high delta value CO2 in air mixture (cylinders 2 and 5) as part of the measuring sequence.

The principle of this calibration method was described by Wen et al.6 as “method 3” or “two-points delta value gain and offset calibration”. Measurement uncertainty There is little literature on the Delta Ray measurement uncertainty, with Van Geldern et al.5 being the only published work available. Van Geldern compared δ13C Delta Ray measurements against a conventional IRMS in a field measuring campaign reporting that the precision for 15 s integration time was typically better than 0.1 ‰ (Allan-Werle plot), with differences from the IRMS ranging between 0.04‰ and 1‰. Times series analysis were performed with the Delta Ray on cylinder 3, resulting in Allan deviations of 0.03 ‰ for δ13C and 0.05 ‰ for δ18O (see Figure S-4 and Figure S-5, supporting material) at the optimum averaging time of 300 s. In addition, it was further noted that the noise of the instrument was significantly higher when measuring during two hours, which is the time period of a typical calibration. Using a rectangular distribution the standard uncertainty of 0.31 ‰ for δ13C and 0.35 ‰ for δ18O was observed. This component was further combined with the Allan deviations and taken as the stability uncertainty associated with the instrument response. The two-point calibration of the delta value requires the knowledge of the uncertainty associated with them, which was in this case taken as the uncertainties deduced from MPI-Jena measurements explained in section Error! Reference source not found., equal to 0.015‰ for δ13C and 0.328‰ for δ18O. After calibration with the two additional CO2 in air standards, the standard uncertainties associated with the instrument measurement were finally equal to 0.18 ‰ for δ13C and 0.48 ‰ for δ18O. It is important to note that the uncertainties of the Delta Ray are comparable to the FTIR uncertainties, but that it was not possible to fully take into account the uncertainty contribution for the CO2 mole fraction values. This is a consequence of the calibration method being performed directly on delta values, which may result in issues when performing a Keeling analysis, as observed by Wen et al. when measuring CO2 in outside air samples.

Results and discussion The calibration procedures described above were validated by the observed difference between the measurements on calibrated instruments and the reference values for δ13C and δ18O of the standards under test, taking into account all uncertainties, as presented below.

FTIR As previously described the mixtures 1 and 2 were used as calibrants and mixtures 3, 4, and 5 as samples. The measurements were repeated three times during different days. The consistency between the MPI-Jena assigned values and those obtained by FTIR, δ FT , is presented in terms of the difference between them, ∆ FT = δ FT − δ MPI-Jena . The combined standard uncertainty associated with ∆FT can be expressed as u(∆FT ) = u(δ FT )2 + u(δMPI-Jena)2 and the expanded uncertainty, at 95 % confidence level U (∆ FT ) = k ⋅ u ( ∆ FT ) where k denotes



the coverage factor, taken as k = 2 (normal distribution, approximately 95 % level of confidence). Differences observed on the three samples are plotted in Figure 3. In all cases the values agree within their stated measurement uncertainties.

1.0 st

1 nd 2 th 3

0.8 0.6

In the case of FTIR we demonstrated that using only two cylinders with the same delta values and different mole fractions, bracketing the mole fractions to be measured, δ13C and δ18O values can be measured with uncertainties of ‰ and

uδ 13C_FT=0.09

uδ 18O_FT=1.03 ‰. The uncertainty in the δ13C meas-

urement is dominated by the CO2 mole fraction uncertainty, and further reduction of these uncertainties could lead to improvements in the accuracy of the δ13C measurement. The uncertainty in the δ18O measurement is currently dominated by the noise of the FTIR.

0.4

An in depth study of the uncertainties of the FTIR measurements of δ13C and δ18O was performed using both a standard approach and a sensitivity study, producing values which were in good agreement.

∆FT_δ13C / ‰

0.2 4

0.0

5

3

-0.2 -0.4 -0.6

In the case of the Delta Ray instrument a residual bias in the δ13C and δ18O measurements, which remained following the implementation of the manufacturer’s calibration procedure, was removed by the application of an additional two point calibration (two CO2 in air standards with known but differing isotopic composition). The resulting standard uncertainty of

-0.8 -1.0 -10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

13

δ C(VPDB-CO2) / ‰

measurements achieved was

5

st

1 nd 2 th 3

4 3 2 1

∆FT_δ18O / ‰

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 10

0 5

-1

3

4

-2 -3 -4 -5 -8

-7

-6

-5

-4

-3

-2

-1

0

18

δ O(VPDB-CO2) / ‰

Figure 3. Difference between δ13C (above) and δ18O (below) values of the three samples evaluated by FTIR and by IRMS, as measured three times. The error bar represents the expanded uncertainty at a 95 % level of confidence. Note different Y axis scales.

5.2

Delta Ray

With this instrument, mixtures 2 and 5 were used as calibrants and mixtures 1, 3, and 4 as samples. The measurements were repeated three times during different days. As result the consistency between the MPI-Jena assigned values, and those obtained by the Delta Ray for δ13C and δ18O in all cases agree within their stated measurement uncertainties. The results are listed (Table S-5 and S-6) and plotted (Figure S-6) as supporting material. CONCLUSIONS Procedures for accurately calibrating both FTIR and other IRIS instruments for δ13C and δ18O measurements have been developed and their performance validated. In addition, the study has demonstrated the number and characteristic of the gas standards required for the accurate calibration of these instruments.

uδ 18O_DR

u δ 13C_DR

=0.18 ‰ and

=0.48 ‰.

Acknowledgements: The authors would like to acknowledge the Gas Analysis Working Group (GAWG) of the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology (CCQM) for the useful discussions and especially the support of George C. Rhoderick (NIST), Paul Brewer (NPL) and Willi A. Brand (MPI-Jena). Certain commercial equipment, instruments and materials are identified in order to specify experimental procedures as completely as possible. This does not imply a recommendation or endorsement by the Bureau International des Poids et Mesures nor does it imply that any of the materials, instruments, or equipment identified are necessarily the best available for the purpose. Bibliography

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