The Small Ice Cap Instability in Diffusive Climate Models

Abstract

Simple climate models employing diffusive heat transport and ice cap albedo feedback have equilibrium solutions with no stable ice cap smaller than a certain finite size. For the usual parameters used in these models the minimum cap has a radius of about 20 degrees on a great circle. Although it is traditional to remove this peculiar feature by various ad hoc mechanisms, it is of interest because of its relevance to ice age theories. This paper explains why the phenomenon occurs in these models by solving them in a physically appealing way. If an ice-free solution has a thermal minimum and if the minimum temperature is just above the critical value for formation of ice, then the artificial addition of a patch of ice leads to a widespread depression of the temperature below the critical freezing temperature; therefore, a second stable solution will exist whose spatial extent is determined by the range of the influence function of a point sink of heat, due to the albedo shift in the patch. The rang... Abstract Simple climate models employing diffusive heat transport and ice cap albedo feedback have equilibrium solutions with no stable ice cap smaller than a certain finite size. For the usual parameters used in these models the minimum cap has a radius of about 20 degrees on a great circle. Although it is traditional to remove this peculiar feature by various ad hoc mechanisms, it is of interest because of its relevance to ice age theories. This paper explains why the phenomenon occurs in these models by solving them in a physically appealing way. If an ice-free solution has a thermal minimum and if the minimum temperature is just above the critical value for formation of ice, then the artificial addition of a patch of ice leads to a widespread depression of the temperature below the critical freezing temperature; therefore, a second stable solution will exist whose spatial extent is determined by the range of the influence function of a point sink of heat, due to the albedo shift in the patch. The rang...