Hysteresis and Temporal Scales of Ice Stream Variability

Understanding the mechanisms governing temporal variability of ice stream flow remains one of the major barriers to developing accurate models of ice sheet dynamics and ice-climate interactions. Previous efforts considered the effects of heating at the bed and consequent basal melting on ice stream dynamics, as well as the effect of a dynamic drainage system on ice flow. We consider the effects of both basal heating and dynamic drainage on ice stream flow for the first time, and model ice dynamics, melt water production and drainage evolution. We determine which processes contribute to ice stream variability and the physical controls on the temporal scales of ice stream stagnation and activation. Our tools of choice are both simple and intermediate complexity models of subglacial processes and simple ice dynamics. Analytic and numerical results from the simple model indicate that there are two major modes of ice stream behavior: steady-streaming and binge-purge-like variability. The steady-streaming mode arises either from drainage- or friction-mediated subglacial meltwater production. The binge-purge mode arises from a sufficiently cold environment sustaining successive cycles of thinning-induced basal cooling and stagnation. We characterize both the parameter regimes that produce each of the modes as well as the period of ice stream variability. Modern Siple Coast ice streams are found to reside in the binge-purge parameter regime near a transition to the steady-streaming mode. Changing the prescribed atmospheric temperature can lead to a transition between these modes through a subcritical Hopf bifurcation. The properties of this type of bifurcation and our numerical experiments indicate that this may lead to significant hysteresis in ice stream variability as the surface temperature is varied. Upon atmospheric warming, modern Siple Coast ice streams would transition from binge-purge behavior to steady-streaming at a very different temperature than the reverse transition during a cooling. We will discuss the implications of these findings for our understanding of ice streams, ice sheet modeling and various paleoclimatic phenomena.