A Second-order Dynamic Model of the Mean Global Carbon Cycle

A significant research activity is ongoing about present and future stability of the Earth’s mean global carbon cycle, which plays a key role in climate dynamics, and is perturbed by the increasing carbon emission of the fossil-fuel combustion. The paper aims to provide an answer through a second-order state equation, which is tuned on global data of surface temperature, airborne carbon dioxide (CD) concentration, solar radiation and anthropogenic carbon emissions. The state variables are temperature and airborne CD perturbations from pre-industrial equilibriums. The equilibriums, taken as unknown, are expected to approach historical estimates, thus providing a tuning validation criterion. Since state variables are linked in a closed loop, carbon cycle stability can be assessed through loop stability criteria. The state equations, being linear time invariant, neglect time variability and nonlinearity. They are revealed by a rolling time regression, whose time interval shrinks from industrial era to recent decades, when data become more accurate. The paper concludes with preliminary predictions tuned on recent data. Comparison with predictions of the well-known MAGICC model show discrepancies that are briefly discussed.