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The ice-covered Earth instability in a model of intermediate complexity

The ice-covered Earth instability found in energy balance models is studied with a zonal mean statistical dynamical atmospheric model coupled to a global mixed layer ocean model. The response of the model to changes in solar constant is examined in two parallel studies, one with and one without a fixed meridional heat transport (a Q-flux) being included in the ocean model. The Q-flux is derived so as to make the climate with the current value of the solar constant resemble the earth’s current climate. In both cases the climate displays a hysteresis loop as the solar constant decreases and then increases, with two equilibrium states being possible for a range of values of the solar constant. In the case without a Q-flux, as in energy balance models, one state corresponds to an ice-covered Earth, and the other is partially covered. In the case with a Qflux, because the poleward Q-flux is stronger in the Southern Hemisphere, one state corresponds to an icecovered Northern Hemisphere, but a Southern Hemisphere that is only partially ice-covered; the other state has much reduced ice-cover in both hemispheres. In the case when the Q-flux is present, the sensitivity of the state with smaller ice-cover is about half as much, and the hysteresis loop extends over a smaller range of values of the solar constant. Also in this case there is a strong ice-covered Earth instability that sets in when the solar constant is about 13–14% below the current value. However in the case without a Q-flux the ice-covered Earth instability virtually disappears. The different behavior is attributed to the much lower efficiency of the meridional heat transport in the case with no Q-flux. The behavior in this case may be more realistic for cold climates. The results in both cases confirm the simple analytical relation between global mean surface temperature and global ice area found in energy balance models.