  A glacier table consists of a rock supported by a slender column of ice.
These structures form naturally on glaciers through differential melting of the
ice. In this paper, we investigate the onset of their formation by reproducing
glacier tables at a smaller scale, using model materials in a controlled
environment. We show that in the lab the melting process of an ice block in air
is controlled by both the infrared radiations form the environment and by the
natural convection of air. Using cylindrical caps made of materials of various
thermal conductivities, one can initially observe either the formation of a
table standing on an ice foot, or the sinking of the cap into the ice block. A
one-dimension model shows that the differential ice ablation rate is controlled
by the thermal conduction through the cap leading to a competition between two
effects: a geometrical amplification of the heat flux on the one hand, and a
heat flux reduction due to the higher temperature of the cap compared to that
of the ice. Our model captures the transition between the two regimes and
identifies a dimensionless number which control the onset of the formation in
its early stages.
