Modelling Chemical Speciation in Seawater pH Buffers, Standard Seawater and Other Natural Waters: Applications and Uncertainties

The pH of Tris buffers in artificial seawater, and the stoichiometric equilibrium constants (K*) of the carbonate system in seawater, have been quantified as functions of T (temperature) and S (salinity) by experiments carried out over many decades. However, the results are valid only for natural waters of seawater stoichiometry. Trace metal complexation has mostly been measured as a function of ionic strength in simple media such as NaCl(aq) or NaClO₄(aq). Chemical speciation models can potentially calculate buffer pH, K*, and complexation directly as functions of the total concentrations of the individual ions present. This offers the possibility of application to a much wider range of natural waters, without the burden of experimental measurement for every composition. Such models (e.g., those developed by Millero and co-workers) have existed for some time, but are hampered by both a lack of many of the interaction parameters needed and, critically, a lack of understanding of the sources and magnitude of likely uncertainty in the results. We have therefore studied the influence of various sources of uncertainty for two current models (those of Waters and Millero (2013), and a subset of Pierrot and Millero (2017)) using a combined Monte Carlo simulation and error propagation approach. We find that the major sources of uncertainty, affecting calculations of pH and K* for carbonate equilibria, are some of the thermodynamic equilibrium constants (notably that for HSO₄^– dissociation) and a relatively small number of parameters for interactions between the trace species of interest (e.g., H⁺, HSO₄^– CO₃^2–, HCO₃^–) and the major ions. This suggests that improving the models, and quantifying the key uncertainties in variables of oceanographic importance like pH, may be relatively simple tasks. Our results provide a much-needed focus for future modelling work and experiments, which are now underway.