Inclusion of MyAMI-derived Mg/Ca corrections to the marine carbonate system in the cGENIE.cookie Earth system model (v.0.9.90)

Abstract. The concentrations of the major cations (esp., Ca²⁺, Mg²⁺) in Earth's oceans have undergone large-scale fluctuations in the geological past. This is important because the key geochemical properties of the marine environment that underpin the global carbon cycle – the aqueous carbonate system equilibria and solubility of solid calcium carbonate (CaCO₃) – are heavily influenced by ion-pairing, which in turn depends on the activity of the major cations and anions. An accurate interpretation of marine proxies as well as the reconstruction of past states of ocean geochemistry and carbon cycle dynamics across geologic events requires that these effects are considered. However, most current global carbon cycle models use empirical carbonate system dissociation constants (K) fitted to laboratory experiments with present-day seawater major cation and anion concentrations. When simulations of global carbon cycling in the geologic past have been made, only relatively simplified empirical adjustments of the equilibrium constants (from Ben-Yaakov and Goldhaber [1974], Tyrrell and Zeebe [2004]) have been implemented when seawater composition differs from modern (e.g., Panchuk et al. [2008]). More commonly, no correction is made at all.

Here we develop and evaluate a new scheme in the cGENIE Earth system model for correcting carbonate system equilibrium constants and account for variations in the dissolved calcium and magnesium concentrations in the ocean. We base our new parameterization on the MyAMI specific ion interaction model of Hain et al. [2015] and implement this in cGENIE by means of linear interpolation within a 4-dimensional parameter look-up table of pre- calculated carbonate system equilibrium constants. For modern SW composition, our implementation of MyAMI-based equilibrium constants yields no significant deviation from model results using empirically-based equilibrium constants, validating our look-up/interpolation approach. However, for simulations conducted under non-modern Mg/Ca, we find significant differences in carbon chemistry and CaCO₃ saturation when using our new MyAMI-based equilibrium constants as compared to the existing (default) correction scheme. Specifically, our new MyAMI-based correction scheme exhibits a much lower sensitivity of surface ocean pH and calcite saturation state to a change in Mg/Ca from modern to Eocene, which were overestimated by the previous correction scheme. We can also expect that any bias in carbonate chemistry and CaCO₃ saturation will affect the preservation and burial of CaCO₃ in deep-sea sediments. We illustrate this by contrasting the ocean carbon inventory arising under Eocene Mg/Ca with the same total weathering (and hence CaCO₃ burial) flux for the different possible equilibrium constant corrections. We find that the new MyAMI-based and previous default corrections give rise to a dissolved inorganic ocean carbon inventory 348 PgC higher and 950 PgC lower, respectively, relative to the same experiment conducted using empirical equilibrium constants without any Mg/Ca correction. Applying no correction at all for a different-from-modern Mg/Ca ratio in the ocean would appear to be better than applying a 'bad' correction but explicitly accounting for past dissolved calcium concentrations remains of fundamental importance. We provide this new carbonate system equilibria correction as an option in cGENIE.muffin version 0.9.64, and as standard in a completely new cGENIE code release – cGENIE.cookie v.0.9.