The Analysis of the Glacial Cycles: Approch for the Simplified Climate-Ice Sheet Model

The marine records of glacial cycle (δ18O) after 0.8Ma show large-amplitude 100kyr period oscillations, which are not direct linear response to the Milankovich cycle, with an asymmetric profile, a long stage of slow buildup of glacier followed by abrupt decrease by melting. Previous studies have proposed a variety of mechanisms that caused these features such as the fluidity effect of ice sheet, time-lag due to isostatic adjustments of the lithosphere under the weight of the glaciers, etc. However, these studies of modeling approach little considered about hydrological processes which are important factors for ice mass balance. In this study, we developed a coupled climate-ice sheet model that explicitly includes the fluidity effects of ice sheet and hydrological processes in order to reveal the mechanisms of glacial cycles. Our coupled model is the meridional one-dimensional model, consisting of three sub-models: the atmospheric energy balance model, atmospheric moisture balance model, and ice sheet model. These sub-models are formed with balance equations of the diffusive transfer and the surface fluxes for heat and water (e.g. short- wave radiation, long-wave radiation, and so on for energy balance and precipitation and evaporation for moisture balance). The ice sheet sub-model includes the non-linear fluidity effect (the meridional velocity is assumed to be proportional to the third power of the gradient of the ice sheet height). The ablation of ice sheet depends on intensity of short-wave radiation as well as temperature. We inputted superimposed two sinusoidal insolations with periods of 19kyr and 23kyr, which imitate the Milankovich forcing, to the model. The power spectrum of resultant global ice volumes shows a stronger sharp peak at about 100kyr than those at 19kyr and 23kyr. A single sinusoidal input never induces the 100kyr oscillation. The 100kyr period corresponds to the envelope of the two input sinusoids, so that some non-linear processes of the model induced the 100kyr period. The ablation process is responsible for non-linear effects. As the ablation also depends on ice mass balance itself, the large ice sheet volume in the ablation zone plus strong insolation led to the abrupt melting.