An error in ice-temperature measurement

An analysis is made of the disturbance in conductive heat flow caused by drilling a bore hole in ice in which there is a vertical temperature gradient. The model used is that of a perfectly insulating hole placed in a linear temperature gradient; it is shown that the temperature measured at the bottom of the hole deviates from its value before drilling by an amount of order —0.6aU where a is the bore-holt radius and U is the temperature gradient. The deviation takes effect in a few hours. The error is typically between 0.005 and 0.1 deg and is therefore significant only where very high accuracy is required. It should not be present in temperate glaciers, nor where the thermometer is properly frozen in, nor if temperatures are measured at the bore-hole walls far above the bottom

Thermal stresses near the surface of a glacier

Stresses occur in the uppermost 10 m of a glacier as a result of temperature fluctuations at the surface. A model is set up of a typical year's surface temperature variation, and the progress of temperature waves through the glacier is calculated using Fourier theory of heat conduction. Short-period fluctuations are rapidly attenuated, and at 10 m depth the annual cycle is reduced to 5% of its surface amplitude. As the temperature of the ice varies it undergoes small volume changes; stresses are calculated on the assumption that any tendency of the ice to expand or contract laterally results in the creation of just enough stress to cause the ice to remain unstrained. It is found that in the top 2 or 3 m stresses of thermal origin are generally in excess of those due to gross deformation or overburden pressure. For the case of high-density ice Glen's flow law is used, and conditions are found to be favourable for the formation of surface rumples of wavelength about 10 m. For the case of firm or snow a Newtonian flow law is assumed, and it is found that under cold conditions fracture under tension can occur. Cracks of thermal origin may be responsible for the initial formation of crevasses, and they also provide an explanation for background noise encountered when seismic shooting at low temperatures. Calculations are made of the strain-rate field surrounding a crack and it is found that thermal effects can lead to appreciable Strain-rate anomalies for strain-rate measurements near cracks. The magnitude of the effect is easily sufficient to account for anomalous fluctuating strain-rates found by workers using wire strainmeters on the Barnes Ice Cap

Equilibrium profile of ice shelves

Using expressions for ice-shelf creep derived by Weertman (1957) and Thomas (1973[b]) a general method is developed for calculating equilibrium thickness profiles, velocities, and strain-rates for any ice shelf. This is done first for an unconfined glacier tongue and the result agrees well with data for Erebus Glacier tongue (Holdsworth, 1974). Anomalies occur within the first 3 km after the hinge zone and these are too great to be the result of local bottom freezing; they are probably due to disturbance of the velocity field. Secondly, profiles are calculated for bay ice shelves. Thickness gradients are largely independent of melt-rate or flow parameters but are inversely proportional to the width of the bay. Data from Antarctic ice shelves agree with this result both qualitatively and quantitatively. The theory is readily extended to ice shelves in diverging and converging bays. An ice shelf in a diverging bay can only remain intact if it is thick enough and slow enough to creep sufficiently rapidly in the transverse direction. If it cannot, it will develop major rifts or will come adrift from the bay walls. It is then likely to break up. The presence of ice rises or areas of grounding towards the seaward margin can radically alter the size of the ice shelf which can form. The theory could be used as a starting point to study non-equilibrium behaviour

Is vertical shear in an ice shelf negligible?

Vertical shear stress in ice shelves cannot be precisely zero, since the upper and lower surfaces are generally not parallel. By performing stress balance on a vertical column in an ice shelf we calculate what its magnitude must be. This is done for an unconfined glacier tongue and for a confined bay ice shelf; first, using the assumption of constant temperature and density with depth, and secondly, using realistic data and profiles for Erebus Glacier tongue and for the Amery ice shelf. Shear stresses increase almost linearly with depth and are proportional to surface slope. For Erebus Glacier tongue the shear stress is at most 5% of the magnitude of the direct stress deviators and its action through the ice shell should result in differential movement of 1.8 cm a−1 between the top and bottom of the ice shelf. For the Amery ice shelf, the shear stress is at most 0.4% of the magnitude of the direct stress deviators and this should lead to differential movement of 2.5 cm a−1 between the top and bottom of the ice shelf. Shear stresses are therefore generally negligible in comparison with direct stress deviators and can be ignored when considering the overall dynamics of ice shelves. Differential movement is unlikely to be detectable