Global carbon cycle: model complexity and BIBO stability

The paper aims to compare linear time-invariant 1 st and 2 nd order state equation models (SMx, x=1,2) of the Global Carbon Cycle that have been estimated from global data, with mid-complexity models (MMx, x=1,2,3,4) like MAGICC and FAIR. One of the reasons is the different airborne carbon dioxide (CD) prediction, even driven by similar bell-shaped CD emission profiles like SSP245: delayed and amplitude modulated emission that of SMx, sigmoidal that of MMx. To the purpose, the LTI dynamics of MMx has been fitted to a common LTI irrational dynamics describing the vertical carbon diffusion from air to land and ocean. The fitting has proven feasible and accurate, thus providing a standard set of state equations, which can be mechanized to produce centennial predictions under CD emission profiles. Preliminary predictions only differ in amplitude, but not in shape, depending on whether diffusion-fitted LTI dynamics have been obtained either by linearization (MM4) or by extracting the LTI dynamics (MM3). A brief discussion is provided.