Heinrich-type glacial surges in a low-order dynamical climate model

Recent studies suggest the occurrence of sporadic episodes during which the ice streams that discharge ice sheets become enormously active, producing large numbers of icebergs (reflected in North Atlantic sea cores as Heinrich events) and possibly causing the partial collapse of the ice sheets. To simulate the mechanism of internal thermo-hydrodynamical instability implied by such behavior in the context of a more general paleoclimate dynamics model (PDM), we introduce a new sliding-catastrophe function that can account for ice-sheet surges. In particular, using simple scaling estimates derived from the equations of motion and thermo-conductivity for ice flow, we express this function in terms of the thickness, density, viscosity, heat-capacity, and heat-conductivity of ice. Analysis of the properties of this function suggests that these Heinrich-type instability events might be of three possible kinds: the first type of event occurs in periods of glacial maximum when temperature conditions on the ice surface are extremely cold, but internal friction within bottom boundary layer is also at its maximum and is strong enough to melt ice and cause its surge. The second type of event may happen during an interglacial, when the ice thickness is small but relatively warm climatic conditions on the upper surface of ice can be easily advected with the flow of ice to the bottom where even a small additional heating due to friction may cause melting. The third and, perhaps, most interesting type of event is one that may occur during ice sheet growth; in this period particles of ice reaching the bottom still remember the warm temperature conditions of the previous interglacial and additional heating due to increasing friction associated with the growing ice sheet may again cause melting. To the extent that the upper glacier surface temperature depends on atmospheric carbon dioxide concentration, this third case introduces the interesting possibility that earlier CO₂ concentrations may be as important for the present-day climate as its current value. We present results of numerical experiments demonstrating how these three kinds of instability can originate and interact with other components of the global climate system to produce variations of the Heinrich-event type. In particular, according to our model the climate system seems more vulnerable to surges during the penultimate interglacial period than in the present one, which may contribute to an explanation of the recent results of the Greenland Ice Core Project.