Researchers in France have pinned down the conditions under which “glacier tables” – large rocks perched atop thin columns of ice – form within retreating glaciers. Their results, which highlight the importance of the rocks’ surface area and heat conductance, could give scientists an alternative way of estimating the rate at which glaciers melt.

Glacier tables can appear strange, even unnatural, when seen for the first time. They form when a rock lying on top of a glacier shields the ice directly underneath it, decreasing the rate at which the ice melts. The un-melted ice then forms a column that can grow up to two metres tall as the rest of the glacier melts around it. When the column can no longer support the rock’s weight (usually after a few months), the rock topples over.

Miniature glaciers

Glacier tables are mainly found on low-altitude glaciers, where summer temperatures are high enough to melt ice. Only large rocks can create them since smaller ones invariably sink into the ice as it melts. Beyond these rough rules, however, little was known about the details of how they form. To better understand this phenomenon, physicists led by Nicolas Taberlet from the University of Lyon created miniature glaciers consisting of slabs of clear ice inclined at various angles. They left these slabs on a bench in their lab and measured the rate at which the slabs melted by monitoring how their thickness decreased over time. Under these circumstances, the main drivers of ice melting were infrared radiation coming from the walls of the lab and natural air convection.

Taberlet and colleagues then repeated the experiment using fresh slabs of ice, but this time they placed cylinders measuring between 4 and 14 cm in diameter and between 0.5 and 7 cm in height on top of them. These “rocks” were made of materials with different thermal conductivities and included polystyrene and granite.

The researchers observed that while some of the cylinders formed tables, others did not. For example, ice columns formed readily under cylinders made of polystyrene, but never under those made of granite. This is because polystyrene is a much worse heat conductor than granite, so it acts as an insulator, shielding the ice from the warmer environment.

Taberlet and colleagues also observed that thinner cylinders formed tables more easily than thicker ones. This is because a thicker structure has a greater surface area in contact with its environment, allowing it to absorb more heat, which causes the ice underneath to melt at a faster rate than the ice under a thinner cylinder.

One-dimensional conduction model

By inputting these observations into a one-dimensional conduction model that determines how quickly ice under a rock will melt relative to uncovered ice, the team estimated that the minimum size for a table-forming rock is between 10 and 20 cm. This is on par with the size of glacier tables observed in nature.

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The model shows that ice-melting rates under different types of cylinders are controlled by a competition between two effects: the size and shape of the cylinder and a reduction in heat flux due to the higher temperature of the cylinder relative to the ice. The model also takes into account the transition between the two regimes and identifies a dimensional number, h_effR=λ (where h_eff is the effective heat transfer coefficient between the cylinder and the ice, R is the radius of the cylinder and λ is its thermal conductivity) that controls the onset of glacier table formation.

This model might make it possible to develop new “benchmarks” for glaciology, Taberlet tells Physics World. For instance, glaciologists might be able to visit a site once a year, at the same time each year, and estimate glacier melting rates by measuring the height of the glacier tables, rather than by making repeated trips in a single season. He and his colleagues now plan to extend their study to the entire lifetimes of glacier tables and compare the results of their model with new field measurements.

The present study is detailed in Physical Review Letters.