There is now much geological evidence that the Earth was fully glaciated during several periods in the geological past (about 700Myr ago) and attained a so-called Snowball Earth (SBE) state. Additional support for this idea has come from climate models of varying complexity that show transitions to SBE states and undergo hysteresis under changes in solar radiation. In this paper, we apply large-scale bifurcation analyses to a novel, fully-implicit Earth System Model of Intermediate Complexity (I-EMIC) to study SBE transitions. The I-EMIC contains a primitive equation ocean model, a model for atmospheric heat and moisture transport, a sea ice component and formulations for the adjustment of albedo over snow and ice. With the I-EMIC, high-dimensional branches of the SBE bifurcation diagram are obtained through parameter continuation. We are able to identify stable and unstable equilibria and uncover an intricate bifurcation structure associated with the ice-albedo feedback. Moreover, large-scale linear stability analyses are performed near major bifurcations, revealing the spatial nature of destabilizing perturbations.
