The isotopic composition of atmospheric trace gases such as CO2 and CH4 provides a valuable tracer for the sources and sinks that contribute to atmospheric trace gas budgets. In the past, isotopic composition has typically been measured with high precision and accuracy by isotope ratio mass spectrometry (IRMS) offline and separately from real-time or flask-based measurements of concentrations or mole fractions. In recent years, development of infrared optical spectroscopic techniques based on laser and Fourier-transform infrared spectroscopy (FTIR) has provided high-precision measurements of the concentrations of one or more individual isotopologues of atmospheric trace gas species in continuous field and laboratory measurements, thus providing both concentration and isotopic measurements simultaneously. Several approaches have been taken to the calibration of optical isotopologue-specific analysers to derive both total trace gas amounts and isotopic ratios, converging into two different approaches: calibration via the individual isotopologues as measured by the optical device and calibration via isotope ratios, analogous to IRMS.
This paper sets out a practical guide to the calculations required to perform calibrations of isotopologue-specific optical analysers, applicable to both laser and broadband FTIR spectroscopy. Equations to calculate the relevant isotopic and total concentration quantities without approximation are presented, together with worked numerical examples from actual measurements. Potential systematic errors, which may occur when all required isotopic information is not available, or is approximated, are assessed. Fortunately, in most such realistic cases, these systematic errors incurred are acceptably small and within the compatibility limits specified by the World Meteorological Organisation - Global Atmosphere Watch. Isotopologue-based and ratio-based calibration schemes are compared. Calibration based on individual isotopologues is simpler because the analysers fundamentally measure amounts of individual isotopologues, not ratios. Isotopologue calibration does not require a range of isotopic ratios in the reference standards used for the calibration, only a range of concentrations or mole fractions covering the target range. Ratio-based calibration leads to concentration dependence, which must also be characterised.