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International audienceMarine scientists often use two measured or modeled carbonate system variables to compute others. These carbonate chemistry calculations, based on well-known thermodynamic equilibria, are now available in a dozen public packages. Ten of those were compared using common input data and the set of equilibrium constants recommended for best practices. Current versions of all 10 packages agree within 0.2 μatm for pCO2, 0.0002 units for pH, and 0.1 μmol kg−1 for CO32− in terms of surface zonal-mean values. That represents more than a 10-fold improvement relative to outdated versions of the same packages. Differences between packages grow with depth for some computed variables but remain small. Discrepancies derive largely from differences in equilibrium constants. Analysis of the sensitivity of each computed variable to changes in each constant reveals the general dominance of K1 and K2 but also the comparable sensitivity to KB for the AT–CT input pair. Best-practice formulations for K1 and K2 are implemented consistently among packages. Yet with more recent formulations designed to cover a wider range of salinity, packages disagree by up to 8 μatm in pCO2, 0.006 units in pH, and 1 μmol kg−1 in CO32− under typical surface conditions. They use different proposed sets of coefficients for these formulations, all of which are inconsistent. Users would do well to use up-to-date versions of packages and the constants recommended for best practices

Abstract. Modelers compute ocean carbonate chemistry often based on code from the Ocean Carbon Cycle Model Intercomparison Project (OCMIP), last revised in 2005. Here we offer improved publicly available Fortran 95 routines to model the ocean carbonate system (mocsy 2.0). Both codes take as input dissolved inorganic carbon C T and total alkalinity A T , tracers that are conservative with respect to mixing and changes in temperature and salinity. Both use the same thermodynamic equilibria to compute surface-ocean pCO 2 and simulate air-sea CO 2 fluxes, but mocsy 2.0 uses a faster and safer algorithm (SolveSAPHE) to solve the alkalinitypH equation, applicable even under extreme conditions. The OCMIP code computes only surface pCO 2 , while mocsy computes all other carbonate system variables throughout the water column. It also avoids three common model approximations: that density is constant, that modeled potential temperature is equal to in situ temperature, and that depth is equal to pressure. Errors from these approximations grow with depth, e.g., reaching 3 % or more for pCO 2 , H + , and A at 5000 m. The mocsy package uses the equilibrium constants recommended for best practices. It also offers two new options: (1) a recently reassessed total boron concentration B T that is 4 % larger and (2) new K 1 and K 2 formulations designed to include low-salinity waters. Although these options enhance surface pCO 2 by up to 7 µatm, individually, they should be avoided until (1) best-practice equations for K 1 and K 2 are reevaluated with the new B T and (2) formulations of K 1 and K 2 for low salinities are adjusted to be consistent among pH scales. The common modeling practice of neglecting alkalinity contributions from inorganic P and Si leads to substantial biases that could easily be avoided. With standard options for best practices, mocsy agrees with results from the CO2SYS package within 0.005 % for the three inorganic carbon species (concentrations differ by less than 0.01 µmol kg −1 ). Yet by default, mocsy's deep-water f CO 2 and pCO 2 are many times larger than those from older packages, because they include pressure corrections for K 0 and the fugacity coefficient.

Abstract. To study ocean acidification and the carbon cycle, marine scientists often use two measured or modeled carbonate system variables to compute others. These carbonate chemistry calculations, based on well-known thermodynamic equilibria, are now available from seven public packages: CO2SYS, csys, seacarb, swco2, CO2calc, ODV, and mocsy. We compared results from these packages using common input data and the set of equilibrium constants recommended for best practices. All packages agree within ±0.00025 units for pH and ±0.5 μmol kg−1 for CO32−, and six packages agree within ±0.2 μatm for pCO2 in terms of zonal-mean surface values. In the remaining package (csys), the surface pCO2 variable is up to 1.4 μatm lower than in other packages, but that is because it is mislabeled. When compared to surface fCO2, it differs by less than 0.2 μatm. The csys deviations in fCO2, pH, and CO32− grow with depth but remain small. Another package (swco2) also diverges significantly but only in warm deep waters as found in the Mediterranean Sea. Discrepancies between packages derive largely from their code for the equilibrium constants. Analysis of the sensitivity of each computed variable to changes in each constant showed the expected dominance of K1 and K2, while also revealing comparable sensitivity to KB, e.g., with the AT–CT input pair. Best-practice formulations for K1 and K2 are implemented consistently among packages, except those in csys deviate slightly at depth (e.g., 0.5% larger values at 4000 db) due to its pressure corrections made on the total instead of the seawater pH scale. With more recent formulations for K1 and K2 designed to cover a wider range of salinities, packages disagree more, e.g., by 8 μatm in pCO2, 1 μmol kg−1 in CO32−, and 0.006 units in pH under typical surface conditions. These discrepancies stem from packages using different sets of coefficients for the corresponding salinity dependence of the new formulations. Although each set should be equally viable after simple conversions, we show they are fundamentally inconsistent. Despite general agreement between current packages, agreement was much worse with outdated versions, e.g., differences reached up to 2.5 μatm in pCO2, 1.4 μmol kg−1 in CO32−, and 0.007 units in pH for surface zonal means when using the best-practice constants.

Abstract. Software used by modelers to compute ocean carbonate chemistry is often based on code from the Ocean Carbon Cycle Model Intercomparison Project (OCMIP), last revised in 2005. As an update, we offer here new publicly available Fortran 95 routines to model the ocean carbonate system (mocsy). Both codes take as input dissolved inorganic carbon CT and total alkalinity AT, the only two tracers of the ocean carbonate system that are unaffected by changes in temperature and salinity and conservative with respect to mixing, properties that make them ideally suited for ocean carbon models. With the same basic thermodynamic equilibria, both codes compute surface-ocean pCO2 in order to simulate air–sea CO2 fluxes. The mocsy package goes beyond the OCMIP code by computing all other carbonate system variables (e.g., pH, CO32−, and CaCO3 saturation states) and by doing so throughout the water column. Moreover, it avoids three common model approximations: that density is constant, that modeled potential temperature is equivalent to in situ temperature, and that depth is equivalent to pressure. These approximations work well at the surface, but total errors in computed variables grow with depth, e.g., reaching −8 μatm in pCO2, +0.010 in pH, and +0.01 in ΩA at 5000 m. Besides the equilibrium constants recommended for best practices, mocsy also offers users three new options: (1) a recent formulation for total boron that increases its ocean content by 4%, (2) an older formulation for KF common to all other such software, and (3) recent formulations for K1 and K2 designed to also include low-salinity waters. More total boron increases borate alkalinity and reduces carbonate alkalinity, which is calculated as a difference from total alkalinity. As a result, the computed surface pCO2 increases by 4 to 6 μatm, while the computed aragonite saturation horizon (ASH) shallows by 60 m in the North Atlantic and by up to 90 m in the Southern Ocean. Changes due to the new formulation for K1 and K2 enhance pCO2 by up to 8 μatm in the deep ocean and in high-latitude surface waters. These changes are comparable in magnitude to errors in the same regions associated with neglecting nutrient contributions to total alkalinity, a common practice in ocean biogeochemical modeling. The mocsy code with the standard options for best practices and none of the 3 approximations agrees with results from the CO2SYS package generally within 0.005%.