  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 (2002) and
Anderies et al. (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. Moreover, 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.
