Uncertainties in Calibration of an Optical Spectrometer for Measuring Isotope Ratios in Methane

The stable isotope ratios of carbon (δ¹³C-(CH₄)) and hydrogen (δ²H-(CH₄)) in methane (CH₄) from atmospheric air samples provide a tracer that can help distinguish the relative contribution of emission sources. These can be continuously measured at atmospheric monitoring stations by optical isotope ratio spectrometer (OIRS) instruments, providing data that is complementary to isotope ratio mass spectrometry (IRMS) measurements. OIRS instruments directly measure the amount fraction of the ¹²CH₄, ¹³CH₄, and ¹²CH₃ ²H isotopologues, in contrast to the IRMS method of conversion to CO₂ and H₂, so they have different calibration needs related to reference materials (RMs) and analysis protocol. We use a single high-purity source of CH₄, which has been isotopically characterized by IRMS, to produce two calibration RMs that bracket the sample in amount fraction. The isotope ratio measurement is calibrated via the isotopologue amount fraction, which is used to derive analytical expressions for the combined uncertainty. We test this approach using a 550 μmol mol^-1 sample (representative of the amount fraction produced from air sampled by the NPL preconcentrator) prepared from a separate CH₄ source. The combined standard uncertainty for the isotope ratio of this sample is 0.19 ‰ for δ¹³C-(CH₄) and 1.1 ‰ for δ²H-(CH₄), including uncertainty contributions from the isotopic assignment of the CH₄ used for the RMs, their gravimetric preparation, and the spectrometer noise. The dominant contribution to this is from the uncertainty in isotopic assignment of the CH₄ used in RM preparation. The next largest contribution to the uncertainty budget is the measurement noise, estimated from the Allan-Werle deviation, and the smallest contribution is from the preparation uncertainty in the total CH₄ amount fraction in the RMs. We demonstrate that preparing the bracketing RMs from a common CH₄ source results in correlations between isotopologue amount fractions and that neglecting this leads to an overestimation of the isotope ratio uncertainty.