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.
A wide variety of spectacular shapes and patterns formed through differential ablation can be found in nature: surface patterns known as
On ice and snow surfaces, similar structures can be found: slender snow blades known as penitentes
On a temperate glacier, the ice ablation rate is influenced by the
presence of debris on its surface. Indeed, a dense debris layer
covering an ice surface can, when thin enough (less than 0.5 cm),
enhance the ice melting compared to a bare-ice surface or, if thick
enough, act as an insulation layer and reduce the melting
rate
Glacier tables (see Fig.
In this article, we report field observations made on the Mer de Glace (French Alps) of the formation dynamics of glacier tables monitored over the course of a few days, as well as a systematic measurement of already-formed tables on a given day. The Mer de Glace is a temperate glacier, meaning that the ice temperature is always given by the melting temperature of water:
In this article, we report two sets of observations made on the Mer de Glace: a time-resolved camera recording of the formation and evolution of four glacier tables and a field observation of 80 glacier tables.
The lower part of the Mer de Glace (below a 2100 m altitude) is
largely covered with granitic debris, with sizes ranging from
submillimetric up to several metres. In the following, their
dimensions are characterized by their thickness
Time-lapse images were obtained using an autonomous solar-powered camera (Enlaps Tikee) placed on three 1.5 m long wood rods set into the ice. Pictures (
The surface temperature of rock 4 was measured every 5 min during period B using thermocouples and a homemade battery-powered device (Arduino MKR ZERO and EVAL-CN0391-ARDZ Shield). The wind speed
On 3 June 2021, we systematically measured, in an area of
Characteristics of the rocks studied.
Raw data of the observation made at location 1 (see Fig.
In the following, we characterize the heat flux balance on the glacier surface by linking the ablated ice thickness to local meteorological data in the same way as it has previously been carried out in the literature
In
For the sake of simplicity, the following main assumptions are made in the model: (1) the rocks are considered cuboids (see Fig.
The energy balance of a rock, taking into account its 3D structure, is summarized in the schematic of Fig.
The quasi-static assumption implies that the flux balance is verified at each time
The heat flux transmitted from the rock to the ice underneath can be estimated using a 1D conduction model as
From Eqs. (
The dashed black lines in Fig.
Rocks 1 and 2 formed glacier tables over the course of approximately a week (see Fig.
Temperature
Figure
Figure
In Fig.
The snow layer covering that part of the glacier finished melting on
26 May, leaving the ice exposed. The meteorological data of the time
period C (from 26 May until 3 June), alongside the previously
adjusted parameters
The critical diameter, corresponding to the transition between the two regimes described in the previous section (the rock sinks into the ice or forms a table), is denoted as
From our model, given a set of meteorological data and an aspect ratio
A rock forms a glacier table when the heat flux reaching the ice underneath is reduced compared to that received by the bare-ice surface around it. If, on the contrary, this heat flux is amplified, the rock will sink into the ice surface. Depending on the rock size, both phenomena are observed on temperate glaciers. During summer, the main source of heat flux causing the ice to melt is the short-wave radiation coming from the sun. Due to the lower albedo of the rock, this flux is slightly amplified compared to what is received by a similar area of bare ice and thus does not directly favour the formation of glacier tables. However this induces a heat flux across the thickness of the rock that elevates its surface temperature
The formation of glacier tables in the natural environment of a temperate glacier results from a more complex energy balance than the idealized lab-controlled study conducted previously
While the heat transfer across the rock controls the formation dynamics, the end of life of glacier tables and in particular the maximum height reached by ice feet will likely result from lateral melting of the ice column. This process is expected to be affected by the rock shape and size that would prevent radiative melting due to shading effects, leaving only turbulent flux and long-wave balance. Note also that when the ice pedestal becomes very slender, a heavy rock could also cause the ice column to creep.
We studied the formation of four glacier tables over the course of a week, and we measured the characteristics of 80 glacier tables on the Mer de Glace (Alps). We developed a simple model taking into account the infrared and solar radiation and turbulent heat flux received by a rock and by the glacier ice surface using local meteorological data, allowing us to quantitatively reproduce the glacier table formation dynamics and to identify the physical effects at its origin. The table formation is controlled by the ice melting under the rocks, and the ice foot growth rate is proportional to the ice ablation rate at the glacier surface. The size of the rocks is a determinant factor governing table formation: the bigger the rock, the higher and faster the ice foot supporting it will grow. Under a critical size, rocks show the opposite behaviour of sinking into the ice surface. The ability of a rock to form a table is controlled by the balance between two opposing effects: a thermal insulation effect, which depends strongly on the rock size, and a geometrical amplification effect linked to the fact that the external surface on which the rock receives an external heat flux is larger than its contact area with the ice. This second effect becomes dominant only for rocks smaller than a few tens of centimetres. The insulation effect originates from the warmer temperature of the rock surface compared to the ice, which reduces, even sometimes changing the sign of, the net long-wave and turbulent flux, ultimately reducing the heat available for ice melting under the rock. While a rock receives a slightly larger net short-wave flux (the main source of heat at the glacier surface) than ice because of the difference in albedo, this effect is too weak to compensate for the insulation effect for large rocks. The solar radiation, by inducing a strong thermal gradient across the thickness of the rock, raises the rock surface temperature, which also contributes to the insulation effect. To summarize, we identified three main parameters controlling the dimensionless growth rate of the ice foot
The graphical user interface (GUI) developed to extract the data from the raw images is available at
The S2M data used in this work provided by Météo-France
CNRS, CNRM Centre d'Etudes de la Neige, through AERIS, are available at
The supplement related to this article is available online at:
MH, VL, JV, NP and NT conceived the study and performed the fieldwork. MH performed the data analysis, developed the model and drafted the manuscript. All authors contributed to the data interpretation, discussion of the results and writing of the manuscript.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors acknowledge technical support and useful scientific discussion with Marine Vicet and Thierry Dauxois. The S2M data are provided by Météo-France CNRS, CNRM Centre d'Etudes de la Neige, through AERIS.
This research has been supported by the Fédération de Recherche André-Marie Ampère and Laboratoire de Physique at ENS de Lyon.
This paper was edited by Chris R. Stokes and reviewed by Adrien Gilbert and two anonymous referees.