Comparative analysis of carbon cycle models via kinetic representations

The pre-industrial state of the global carbon cycle is a significant aspect of studies related to climate change. In this paper, we recall the power law kinetic representations of the pre-industrial models of Schmitz (Chem Eng Educ 36(4):296–309, 2002) and Anderies et al. (Environ Res Lett 8(4):044–048, 2013) from our earlier work. The power law kinetic representations, as uniform formalism, allow for a more extensive analysis and comparison of the different models for the same system. Using the mathematical theories of chemical reaction networks (with power-law kinetics), this work extends the analysis of the kinetic representations of the two models and assesses the similarities and differences in their structural and dynamic properties in relation to model construction assumptions. The analysis includes but is not limited to the coincidence of kinetic and stoichiometric spaces of the networks, capacity for equilibria multiplicity and co-multiplicity, and absolute concentration robustness in some species. We bring together previously published results about the power law kinetic representations of the two models and consolidate them with new observations here. We also illustrate how the pre-industrial model of Anderies et al. may serve as a building block in the analysis of a kinetic representation of a global carbon cycle with carbon dioxide removal intervention.