[Paper Review] Onset of glacier tables

Marceau Hénot, Nicolas Plihon+1 more|arXiv (Cornell University)|Mar 17, 2021

Cryospheric studies and observations41 references14 citations

TL;DR

This study investigates the onset of glacier table formation through controlled laboratory experiments and a one-dimensional thermal conduction model. It identifies that the competition between geometrical amplification of melting and heat flux reduction due to a warmer cap determines whether a cap sinks into or forms a stable table on ice; a dimensionless number based on thermal conductivity and geometry controls the transition between these regimes.

ABSTRACT

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.

Motivation & Objective

• To determine the physical conditions under which a cap on ice either sinks or forms a stable glacier table.
• To isolate the dominant heat transfer mechanisms governing differential ice melting in air.
• To develop a predictive model for the onset of glacier table formation based on cap properties and geometry.
• To identify a dimensionless number that controls the transition between sinking and table formation regimes.

Proposed method

• Conducted controlled experiments with cylindrical caps (XPS, PVC, plaster, cement, granite) on flat ice blocks under constant temperature, humidity, and still air.
• Measured ice surface melting velocity profiles using time-lapse imaging and image processing with Python.
• Developed a 1D thermal conduction model accounting for radiative and convective heat fluxes to the ice surface.
• Quantified the thermal conductivity of cap materials using a steady-state heat transfer setup with calibrated thermocouples and resistive heating.
• Fitted experimental data to a theoretical convective heat flux model (q_conv ∝ (gβΔT sinθ / x)^{1/4}) to isolate convection as the dominant heat source.
• Derived a dimensionless number combining cap thermal conductivity, geometry, and ice properties to predict the formation regime.

Experimental results

Research questions

• RQ1 Under what conditions does a cap on ice sink into the ice rather than form a stable table?
• RQ2 What physical mechanisms—geometrical amplification or heat flux reduction—dominate the differential melting process?
• RQ3 How do the thermal conductivity and size of the cap influence the onset of glacier table formation?
• RQ4 Can a single dimensionless number predict the transition between sinking and table formation?
• RQ5 What role does air convection play in enhancing melting near the leading edge of inclined ice plates?

Key findings

• The dominant heat source for ice melting is natural convection, not condensation or water film effects, with convective heat flux scaling as (sin θ / x)^{1/4} and matching experimental data with a prefactor A = 0.61.
• The radiative heat flux from room-temperature walls contributes ~110 W·m⁻², accounting for roughly half the total heat flux at the ice surface.
• The thermal conductivity of caps strongly influences the formation outcome: low-conductivity caps (e.g., XPS, λ = 0.03 W·m⁻¹·K⁻¹) promote table formation, while high-conductivity caps (e.g., granite, λ = 2.82 W·m⁻¹·K⁻¹) lead to sinking.
• A dimensionless number, based on cap thermal conductivity, radius, and ice properties, controls the transition between sinking and table formation, with a critical threshold identified.
• The model successfully predicts the experimental transition between sinking and table formation across diverse cap materials and sizes.
• The onset of glacier table formation is governed by a competition between geometrical amplification of melting and heat flux reduction due to the cap’s higher temperature, with convection being the dominant energy transfer mechanism.