Early-warning signals for the small ice cap instability.

In certain mathematical models of Earth's climate, the non-linear temperature response of the ice-albedo feedback will cause a sudden and irreversible shift to an ice-free Arctic Ocean. From the theory of stochastic dynamical systems we expect that this tipping point will be preluded by early-warning signals (EWS). Such EWSs are observable near critical transitions in a low-dimensional stochastic dynamical systems, where as equilibrium states becomes unstable, the characteristic relaxation times becomes longer and the systems experience "critical slowing down". However, it is not clear how "critical slowing down" is observable in models with more degrees of freedom, or in systems with complex spatial structures. In this presentation we will explore how EWSs are presented in energy-balance models with diffusive spatial heat transport and seasonal variability, as well as in models with multiple characteristic time scales caused by the thermal inertia of the deep oceans. The results show that EWS may, in some cases, only be seen in certain observable quantities and in specific frequency bands.