Onset of glacier tables

A glacier table consists of a rock supported by a slender column of ice and form naturally on glaciers. We investigate the onset of their formation at a smaller scale in a controlled environment. Depending on the size and thermal conductivity of a cap, it can either form of a table standing on an ice foot, or sink into the ice block. A one-dimension conduction model shows that the differential ice melting is controlled by a competition between two effects: a geometrical amplification, and a heat flux reduction due to the higher temperature of the cap as compared to the ice. Our model captures the transition between the two regimes and identifies a dimensionless number which controls the onset of glacier tables formation.