QUODcarb: A Bayesian solver for over-determined datasets of seawater carbon dioxide system chemistry

We present QUODcarb, a new solver for the CO₂-system in seawater, designed to handle any combination of system parameter measurements, whether exactly- or over-determined. QUODcarb, which stands for Quantifying Uncertainty in an Over-Determined marine carbonate system, is formulated in terms of a Bayesian estimation problem. By combining prior thermodynamic information on the acid/base chemistry of CO₂ in seawater with measured parameters and their uncertainties, QUODcarb yields a probability distribution for the true CO₂-system state of a water parcel from which estimates of all system parameters with associated uncertainties can be obtained. By providing a single best estimate for the true CO₂-system state, QUODcarb enables a simplified, more accurate internal consistency analysis of the marine CO₂ system.

To demonstrate QUODcarb's utility, we analyze the GOMECC-3 dataset, that includes measurements of five CO₂-system parameters. A key finding is that by analyzing these high-quality, over-determined measurements with QUODcarb, we can achieve the GOA-ON 1 % uncertainty goal for carbonate ion concentration, even when accounting for the propagated uncertainty in the dissociation constants – a level of accuracy unattainable with exactly determined calculations. Using a single internal consistency metric, we rank 26 alternative measurement combinations, finding that (pH, $p{\mathrm{CO}}_2$) performs worst, while the combination with all five measurements performs best. Furthermore, the internally-consistent thermodynamic state estimates constrained by all five measurements fall within the range expected by the assumed measurement uncertainties for over 98 % of samples, with only minor adjustments to the dissociation constants, all of which remain within the reported uncertainties for their parameterized formulas.