Is late Quaternary climate change governed by self-sustained oscillations in atmospheric CO2?

A simple earth system model is developed to simulate global carbon and phosphorus cycling over the late Quaternary. It is focused on the geological cycling of C and P via continental weathering, volcanic and metamorphic degassing, hydrothermal processes and burial at the seabed. A simple ocean model is embedded in this geological model where the global ocean is represented by surface water, thermocline and deep water boxes. Concentrations of dissolved phosphorus, dissolved inorganic carbon, and total alkalinity are calculated for each box. The partial pressure of CO2 in the atmosphere (pCO(2A)) is determined by exchange processes with the surface ocean and the continents. It serves as key prognostic model variable and is assumed to govern surface temperatures and global sea-level. The model is formulated as autonomous system, in which the governing equations have no explicit time-dependence. For certain parameter values, the model does not converge towards a steady-state but develops stable self-sustained oscillations. These free oscillations feature pCO(2A) minima and maxima consistent with the ice-core record when vertical mixing in the ocean is allowed to vary in response to pCO(2A)-controlled temperature change. A stable 100-kyr cycle with a rapid transition from glacial to interglacial conditions is obtained when additional non-linear equations are applied to calculate deep ocean mixing, iron fertilization and the depth of organic matter degradation as function of pCO(2A)-controlled surface temperature. The delta C-13 value of carbon in the ocean/atmosphere system calculated in these model runs is consistent with the benthic delta C-13 record. However, the simulated C-13 depletion in the glacial ocean is not driven by the decline in terrestrial carbon stocks but by sea-level change controlling the rates of organic carbon burial and weathering at continental margins. The pCO(2A)-and delta C-13 oscillations develop without any form of external Milankovitch forcing. They are induced and maintained by sea-level change generating persistent imbalances in the marine carbon and phosphorus budgets. Stable oscillations are also obtained when sea-level change is allowed to lag temperature with a realistic time scale for ice-sheet adjustmen