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Glacier tables are structures frequently encountered on temperate glaciers. They consist of a rock supported by a narrow ice foot which forms through differential melting of the ice. In this article, we investigate their formation by following their dynamics on the Mer de Glace (the Alps, France). We report field measurements of four specific glacier tables over the course of several days, as well as snapshot measurements of a field of 80 tables performed on a given day. We develop a simple model accounting for the various mechanisms of the heat transfer on the glacier using local meteorological data, which displays a quantitative agreement with the field measurements. We show that the formation of glacier tables is controlled by the global heat flux received by the rocks, which causes the ice underneath to melt at a rate proportional to the one of the surrounding ice. Under large rocks the ice ablation rate is reduced compared to bare ice, leading to the formation of glacier tables. This thermal insulation effect is due to the warmer surface temperature of rocks compared to the ice, which affects the net long-wave and turbulent fluxes. While the short-wave radiation, which is the main source of heat, is slightly more absorbed by the rocks than the ice, it plays an indirect role in the insulation by inducing a thermal gradient across the rocks which warms them. Under a critical size, however, rocks can enhance ice melting and consequently sink into the ice surface. This happens when the insulation effect is too weak to compensate for a geometrical amplification effect: the external heat fluxes are received on a larger surface than the contact area with the ice. We identified the main parameters controlling the ability of a rock to form a glacier table: the rock thickness, its aspect ratio, and the ratio between the averaged turbulent and short-wave heat fluxes.

In this article, the formation of Zen stones on frozen lakes and the shape of the resulting pedestal are elucidated. Zen stones are natural structures in which a stone, initially resting on an ice surface, ends up balanced atop a narrow ice pedestal. We provide a physical explanation for their formation, sometimes believed to be caused by the melting of the ice. Instead, we show that slow surface sublimation is indeed the physical mechanism responsible for the differential ablation. Far from the stone, the sublimation rate is governed by the diffuse sunlight, while in its vicinity, the shade it creates inhibits the sublimation process. We reproduced the phenomenon in laboratory-scale experiments conducted in a lyophilizer and studied the dynamics of the morphogenesis. In this apparatus, which imposes controlled constant sublimation rate, a variety of model stones consisting of metal disks was used, which allows us to rule out the possible influence of the thermal conduction in the morphogenesis process. Instead, we show that the stone only acts as an umbrella whose shade hinders the sublimation, hence protecting the ice underneath, which leads to the formation of the pedestal. Numerical simulations, in which the local ablation rate of the surface depends solely on the visible portion of the sky, allow us to study the influence of the shape of the stone on the formation of the ice foot. Finally, we show that the far-infrared black-body irradiance of the stone itself leads to the formation of a depression surrounding the pedestal., Competing Interests: The authors declare no competing interest.