A simple mechanism for irreversible tidewater glacier retreat

[1] Tidewater glacier retreat is abrupt and typically irreversible. The mechanics of abrupt onset are evaluated by considering the behavior of a sliding law that depends inversely upon effective pressure ( p(ice) - p(water)); for such a law, flux can increase with decreasing thickness if the loss of bed traction exceeds the loss of driving stress. Characteristic values of increased flux and glacier thinning are shown to propagate upstream if ice flux increases with decreasing thickness below an ice thickness threshold determined by the chosen sliding law. Upstream propagation leads to instability, described in earlier literature, in which increased flow leads to thinning, loss of bed traction, and continued acceleration. In simplest terms, the instability arises when alterations in glacier geometry act to reduce resistive stresses more than driving stresses. The effects of diffusion are also analyzed, and it is shown that for the form of sliding law considered here, diffusion will not necessarily eliminate upstream-propagating instabilities. Application of this theory shows that a transition from stable to unstable conditions occurred at Columbia Glacier, Alaska, near the time of onset of its retreat in the early 1980s. The theory also successfully predicts stable or rapidly retreating states for 12 other Alaska tidewater glaciers, and its applicability to Greenland outlet glaciers is discussed.