A first-order global model of late Cenozoic climatic change II. Further analysis based on a simplification of CO₂ dynamics

Abstract

A model developed recently for the long-term variations of global ice mass, carbon dioxide, and mean ocean temperature through the late Cenozoic is simplified by hypothesizing a new equation for the CO₂ variations containing one less adjustable parameter, but retaining the essential physical content of the previous equation (including nonlinearity and the potential for instability). By assuming plausible time constants for the glacial ice mass and global mean ocean temperature, and setting the values of six adjustable parameters (rate constants), a solution for the last 5 My is obtained displaying many of the features observed over this period, including the transition to the near-100 ky major ice-age oscillations of the late Pleistocene. In obtaining this solution it is also assumed that variations in tectonic forcing lead to a reduction of the equilibrium CO₂ concentration (perhaps due to increased weathering of rapidly uplifted mountain ranges over this period). As a consequence of this CO₂ reduction, the model dynamical system can bifurcate to a free oscillatory ice-age regime that is under the “pacemaker” influence of earthorbital (Milankovitch) forcing. Expanded discussions are given of the surface temperature variations accompanying the evolution of ice, CO₂, and ocean temperature, and of the bifurcation properties of the model from both mathematical and physical viewpoints.