An alternative approach to determine source stable carbon isotope composition for closed-transient chamber measurements using TDLAS analyzers

Closed-transient chamber systems are widely used to measure the transport of non-reactive greenhouse gases (GHGs) and their stable isotopes between the soil and atmosphere. Technologies used to measure GHGs in chamber-based systems have advanced since their first introduction. In many early systems, gas analysis was performed off-line using gas chromatography and/or mass spectrometry. The introduction of non-dispersive infrared gas analyzers suitable for field deployment allowed CO₂ to be measured on-line, but for other GHGs on-line analysis was not possible until the more recent introduction of tunable diode laser absorption spectroscopy (TDLAS)- based gas analyzers. The most recent generations of TDLAS analyzers have extended measurement capabilities from reporting total concentration of a given GHG, to separating concentrations of its most abundant stable isotopologues. For CO₂, this advancement makes possible near real-time estimation of isotopic signature (δ¹³C) of the carbon source pool.

Linear mixing model-based approaches are used to separate the isotopic signature of a source pool from background condition observed during soil chamber measurements. The most common, those proposed by Keeling (1958) and Miller and Tans (2003), uses the relationship between the normalized isotopic ratio (δ) and total concentration, or some derivate term of either, to estimate the source pool conditions. Keeling’s methodology is widely cited but requires extrapolation well beyond measured conditions. The Miller-Tans approach is predicated on the same underlying mass balance as Keeling but uses a solution that estimates the source pool only over measured conditions, reducing uncertainty in final estimates. Both approaches require independent measurement of the total concentration and normalized isotopic ratio, which is not possible with TDLAS based analyzers. TDLAS analyzers measure individual isotopologue mole fractions and use the same set of individual measurements to calculate both total concentration and the normalized isotopic ratio, introducing an inherent autocorrelation between them. Additionally, the δ exhibits a bias as a function of total measured CO₂ concentration, introducing an apparent concentration dependence error (CDE) in d reported from TDLAS.

We present an alternative approach to estimating the source pool isotopic composition specific to TDLAS measurements. This alternative approach relies only on measurements of individual isotopologue mole fractions, avoiding autocorrelation, and does not require extrapolation beyond measurement conditions. We include a sensitivity analysis of mixing model approaches and errors common to TDLAS based instruments, using a chamber dataset synthesized from field-based measurements of environmental conditions and physical properties of gas transport.