Instability Of The Global Greenhouse Gas System As A Cause Of The Ice Ages: A Low-Order Dynamical Model

Abstract

Due to the extremely low rate at which the major glacial variations occurred during the Pleistocene it is not possible to explain these variations by direct calculation of the fundamental fluxes of heat, momentum, and water mass that must be involved. Instead, we approach the problem in a more inductive manner by trying to formulate a physically plausible dynamical system, representing the net effects of these fluxes, that can account for the observed variance with a minimum number of adjustable parameters, given the known forcing due to Earth-orbital (Milankovitch) variations. Our model involves three “slow-response” variables: the global ice mass, the concentration of atmospheric greenhouse gases (notably CO₂, methane, and water vapor), and a measure of the thermal-biological-chemical state of the ocean (perhaps measured by the stratification) that may control the Earth’s carbon cycle over the Pleistocene time period. These variables are connected by a nonlinear dynamical system comprised of three ordinary differential equations that can exhibit instability and free oscillatory behavior of a period close to 100 000 years (the period at which the maximum ice-age variability is found to exist in the late Pleistocene) despite relatively small external Earth-orbital forcing. We calculate the rate constants needed for the model to account for the main features of the ice variations, including the mid-Pleistocene transition from a period of low global ice mass devoid of the 100 000 year oscillation. The implied variations of the greenhouse gases over the past 150 000 years are in good agreement with the recent Vostok ice-core analyses.