Investigations of isotopic and temperature profiles in polar ice sheets were mostly carried out independently of one another until 1973 when a workshop dealing with both topics was held in Cambridge. Studies of temperature profiles show the approximate validity of theoretically derived temperature distributions for steady-state models of ice sheets, while other analyses help to determine departures from the steady state. The review gives some idea of the degree of accuracy of various solutions arising from studies of the heat flow and temperature distribution of ice sheets. Much of this knowledge is directly applicable to interpretation of isotopic profiles if a direct correspondence between mean isotopic δ values and mean annual temperatures can be established. The paper therefore reviews various methods of comparing δ values and temperatures, and shows that for central regions of polar ice sheets a reasonably consistent relationship between these factors does exist.

The microwave emission from a model snow field, consisting of randomly spaced ice spheres which scatter independently, is calculated. Mie scattering and radiative transfer theory are applied in a manner similar to that used in calculating microwave and optical properties of clouds. The extinction coefficient is computed as a function of both microwave wavelength and ice-particle radius. Volume scattering by the individual ice particles in the snow field significantly decreases the computed emission for particle radii greater than a few hundredths of the microwave wavelength. Since the mean annual temperature and the accumulation rate of dry polar firn mainly determine the grain sizes upon which the microwave emission depends, these two parameters account for the main features of the 1.55 cm emission observed from Greenland and Antarctica with the Nimbus-5 scanning radiometer. For snow particle sizes normally encountered, most of the calculated radiation emanates from a layer on the order of 10 m in thickness at a wavelength of 2.8 cm, and less at shorter wavelengths. A marked increase in emission from wet versus dry snow is predicted, a result which is consistent with observations. The model results indicate that the characteristic grain sizes in the radiating layers, dry-firn accumulation rales, areas of summer melting, and physical temperatures, can be determined from multispectral microwave observations.

Application of thermal convection theory to polar ice sheets (Hughes, 1970, 1971. 1972[a],[c]) is reviewed and expanded. If it occurs, thermal convection is mainly concentrated near the bed of the ice sheet; resulting in active and passive convective flow, respectively below and above the ice density inversion. Convection begins as transient creep when a stress-independent critical Rayleigh number is exceeded, and stabilizes as steady-state creep when a stress-dependent critical Rayleigh number is exceeded. Transient- creep convection begins as unstable ripples in isotherms near the bed, with some ripples becoming upward bulges of basal ice which rapidly shrink laterally and grow vertically to become ascending dikes of recrystallized basal ice during steady-state creep. Sills of basal ice are injected horizontally between weakly coupled layers in the strata of cold ice slowly sinking en masse between dikes. Convection begins under domes of thick ice toward the ice-sheet center and a stable polygonal array of dikes may form if frictional heat creates hot ice at the bed as rapidly as convection flow redistributes hot basal ice in dikes and sills, Advective flow transports the converting ice toward the margin of the ice sheet where dikes converge at the heads of ice streams. Dike—sill convection then becomes ice-stream convection in which the entire ice stream behaves like a dike, uncoupling from the bed, and rising en masse. This would help explain why ice streams flow at surge velocities.

It appears to be possible to identify certain conditions of thermal regime at the base of a glacier through the seismic reflection method. In some cases layers of water or wet rock debris may be identifiable. The procedure is based upon the reversal of phase of reflected dilatational waves at the interface between ice and a substratum of lower acoustic impedance. Illustrations of the method are given from the west Antarctic ice sheet, and suggestions are made for the improvement of the technique.

Disposal of the the radioactive waste from the peaceful use of nuclear energy in the central region of the ice sheet of Greenland or Antarctica has been proposed. This paper demonstrates that an area only 100 km2 on the ice divide is sufficient to dispose of the high-level waste of the whole world for the next 30 years without hazard. The thermal power of the radioactive decay makes the waste containers melt down to a depth of 2 km. Thus the total disintegration heat is spread through a volume of 100 km2 × 2 km. The mean temperature increase in this volume is a few degrees. The temperature increase does not influence the rheology of the ice sheet at any time: for a few ten-thousand years after the dumping the area concerned is too small; later the temperature increase is too small.

By 1969 considerable data had been collected over Law Dome from surface measurements. These included surface elevation, ice thickness, accumulation rates, ice movement and strain-rates, surface mean temperatures, and several temperature-depth gradients. Since then core drilling up to 380 m in depth has been carried out from the summit to the coast where the cores reached close to the bed. The bore holes have been concentrated on two main flow lines: one to Cape Folger and the other to Cape Poinsett. The bore-hole temperatures give a clear indication of the temperature distribution throughout the ice cap.

Numerical modelling shows that the measured deep temperatures closely match the steady-state temperature distribution calculated from the present regime. The variations in the temperature profiles over the dome are primarily associated with the flow regime.

The Cape Folger line has low accumulation rates and low velocities which results in positive surface temperature-depth gradients increasing towards the coast. By contrast the Cape Poinsett line has high accumulation rates and high velocities which result in a large negative temperature-depth gradient there. The profile at the Dome summit is close to isothermal primarily due to the high accumulation rates and lack of horizontal motion.

Ten-meter temperatures on the Ross Ice Shelf increased by I deg between 1958 and 1974. Surface temperatures at the “Byrd” and McMurdo stations have also risen during this period and the observed change is consistent with the 10m temperature increase. This rising trend in temperature appears to have an anti-phase relationship with northern hemisphere cooling.

The 10 m temperatures were measured over several years at 16 sites on the White Glacier (lat. 80° N.), Axel Heiberg Island, Canadian Arctic Archipelago. At three sites deep profiles were made using a new drilling technique, reaching a maximum depth of 280 m. Large differences in the 10 m temperatures between locations and from year to year were observed. The deviations of these temperatures from the almost isothermal mean annual air temperature over the glacier are discussed. The heating effect of the melt water in the lower percolation zone was found to be very important. A conceptual model is developed to assess the influence of these irregularities in the energy input at the upper boundary on the thermal regime of the entire glacier. So far a quantitative analysis has been made only for the relatively simple 30 m temperature profile measured on the tongue of the glacier.

The formation of superimposed ice in the accumulation area of sub-polar glaciers plays an important role in the heat and mass balance of the glaciers. In order to study the process of superimposed ice formation in detail, field observations were conducted on McCall Glacier, a sub-polar glacier in Arctic Alaska. It was found that the approximate thickness of superimposed ice formed in a whole summer was 20 cm in the upper region and 30—40 cm in the lower region of the accumulation area of the glacier. This difference in thickness may be attributed to the difference in the temperature of the underlying ice and the rate of supply of melt water. The ratio of the amount of superimposed ice formed in the accumulation area from May to July in 1972 to the total amount of melt was determined. Approximately 50% of the total melt water was discharged from the glacier as run-off water, and the remainder contributed to the formation of superimposed ice.

An experimental study on the artificial formation of superimposed ice was conducted in the cold laboratory to obtain the ratio of superimposed ice, that of run-off water, and that of free water suspended between snow grains, to the total amount of melt water produced in the snow. The ratios obtained in the laboratory experiment agree fairly well with those derived from the observational data on McCall Glacier.

Numerical calculations were conducted to examine the relationship between the growth rate of superimposed ice, the rale of snow melting, the rate of discharge of excess melt-water, and the temperature of the underlying ice. Calculations were made in reference to both the laboratory experiment and the field observations on McCall Glacier. It was found that the predominant factors controlling the growth rate or the total amount of superimposed ice in a sub-polar glacier are the rate of supply of melt water to the snow-ice interface and the initial temperature distribution in the underlying ice. By using the present calculation, it may be possible to estimate the growth rate, the total amount of superimposed ice, and the ratio of superimposed ice to the total amount of melting in the accumulation area of any sub-polar glacier, if observational data on the initial temperature distribution in ice and the rate of snow melting at the snow surface are available.

In a temperate glacier ice the water content results from the past history of the ice, and the temperature adjusts itself to the appropriate value. Results obtained by the Laboratoire de Glaciologie are summarized. Several facts seem to prove some migration of the liquid phase and a coalescence of liquid inclusions. The enthalpy flux is calculated, but it cannot be proved that a spontaneous gathering together of liquid inclusions could occur. The water-rich, small grain-size layers should come from the lowering of the viscosity when the water content increases, as discovered by Duval. The form of Weertman’s sliding law without cavitation can be derived from simple dimensional considerations. Numerically, it cannot account for high sliding velocities, for which subglacial cavitation must be introduced. The cavities are infilled with more stagnant regelation ice than water. Two subglacial hydraulic regimes are distinguished: autonomous and interconnected. The effect which the salt content may have on cavitation is estimated.

Gas bubbles in core samples from the Blue Glacier, Washington, were observed to be partially filled with liquid. The time and spatial dependence of liquid content in the bubbles demonstrates that the in situ liquid content of the bubbles was small and liquid appeared in the bubbles as a consequence of heat flow into the sample after collection. An effective bulk heat capacity for wet bubbly ice is derived and used to analyze the relaxation process and it is shown that the warming of samples is controlled by an effective heat capacity two or more orders of magnitude larger than for pure ice. The relaxation process presents a practical difficulty for measurement of in situ water content from core samples and the behavior of the bubbles indicates that at positions in a temperate glacier where bubbles have pressure in excess of the ice stress, bubbles may control the ice temperature and significantly restrict water flow through veins.

Total impurity content of salt plus carbon dioxide was estimated as a function of grain size and depth in polycrystalline ice samples cored from a temperate glacier by measuring the electrical conductivity of the melt with air excluded. Conductivity decreased with increasing depth and grain size and ranged from × 10-5 to 0.4 × 10-5 Ω -1 m-1 at 0°C. The conductivity of pure water at 0°C is 0.1 × 10-5 Ω -1 m-1 Studies of the configuration of the three phases and of in situ temperature were also made. Thermodynamic constraints indicate that these impurities are probably concentrated as follows: about 5 mol m-3 in the liquid in the veins along three-grain intersections, roughly 1 × 10-6 mol m-2 associated with grain-boundary area exclusive of veins, and about 0.7 × 10-3 mol m-3 in volume exclusive of veins and grain boundaries. The last of these categories seems to account for most of the impurities in coarse ice (grain size about 20 mm), but all three categories seem significant in fine ice (grain size about 2 mm). Differences in bulk impurity content possibly indicate different histories of flushing by water.

Certain aspects of the flow of glaciers suggest that molecular adhesion contributes to basal friction of glaciers sliding at speeds below those of surging glaciers. Laboratory experiments indicate that this will only occur if some part of the ice-rock contact is “cold”, that is below the pressure melting point (p.m.p.), a few tenths of a degree being sufficient. Field evidence is scanty, but suggests that such cold patches may exist at the base of a temperate glacier.

Discussion of pressure-melting within the basal ice mass, as distinct from processes at the ice-rock contact, indicate that excess water is formed in zones of high-pressure ice up-stream of obstacles. If this water is squeezed out of the ice by the pressure, we have a simple heat pump that will tend to cool the basal ice. The ice will warm again as the result of thermal conduction and internal friction, but before reaching the p.m.p. it can produce "cold" patches of the ice-rock contact, roughly estimated to be from 0. 1 to 1.0 m in extent.

Another factor that could cause intermittent cold patches at the ice-rock interface arises from changes of basal water pressures with time beneath a glacier. If a major part of the weight of a glacier is supported by a thin water film at a relatively low pressure and by a small proportion of water film in which pressures are high, then over a large area the water pressures must balance the weight of ice. If however the pressure in the low-pressure film rises, the smaller high-pressure areas of stress concentration will suffer a proportionately greater decrease of pressure to maintain the total balance between pressure and weight, If changes take place rapidly, in a matter of hours, then in areas of stress concentration of the order of a metre or more across, the water film will freeze to the bed as stresses are relieved. This could cause stick-slip motion in a temperate glacier.

Pressure-temperature effects at the ice-rock interface can help to explain certain features of glacial erosion, such as intense grinding on the top surface of a roche moutonée and plucking on the down-stream side.

The top of Mont Blanc is a dry snow zone. The cold infiltration zone extends between about 4 300 and 3 800 m. Its lower limit is lined by large cracks and ice cliffs, similar to bergschrunds. Near rock faces this limit is the bergschrund, which can descend as far as the 0°C isotherm of the mean annual air temperature, 3 100-3 200 m- At Col du Dôme (c, 4 250 m), 15 m deep temperature has increased 1.8 deg between the years 1911 and 1973, probably due to infiltration which happened there in the last few years. The ice in the ablation area is entirely temperate, while in dryer areas of the Alps it may be at 1°C to — 3°C in the vicinity of the firn line.

Bore-hole drilling techniques have been used to connect with the subglacial water system of the temperate South Cascade Glacier. The water level in a connecting bore hole probably represents a direct measurement of the basal water pressure over an area at least to m in extent. Fluctuations of up to 40 m in bore-hole water levels occur typically over periods of several days and often peak about 2 d after large changes in water input at the glacier surface. The long-term trend in bore-hole water levels supports the idea of seasonal storage and release of liquid water.

The Columbia Icefield rests upon limestones containing natural caves that drain waters from the glacier sole. The principal cave is sealed at one end by an extrusion of glacier ice 300 m below the icefield surface. The hydrologic regime of the cave indicates that the modern icefield is temperate in character and that water is present at the glacier sole throughout the year. An interpretation of the air temperature pattern in the cave suggests that the geothermal flux to the glacier is only 10-40% of the expected value because heat is abstracted by melt water circulating through the rock. U, Th and O isotopic analyses of calcite speleothems further indicate that the base of the icefield has probably been temperate throughout the past 150000 years. The cave was inundated when glaciers expanded during the classical Wisconsinan main Würm period. The inundation implies maintenance of a permanent water table at some hundreds of meters above the base in a valley glacier 750—800 m in depth.

A necessary condition for a glacier to surge by thermal instability is that the glacier be cold with basal ice at or near the melting point. Deep temperature measurements show that two small surge-type glaciers in the Yukon Territory meet this requirement, but shallow measurements in three other surge-type glaciers suggest a temperate regime. If the latter observations are accepted, not all surges are thermally controlled: if a single mechanism accounts for all surges it cannot be thermal instability.

In this paper it is argued that thermal instability remains a viable mechanism for explaining surges of many cold glaciers, and that regardless of the underlying mechanism, thermal processes must at least have a major influence on the surge behavior of cold glaciers.

Two numerical modelling experiments are described. The first involves a one-dimensional model which shows that thermal control can account for the remarkably constant surge cycle found in some glaciers. The second, a two-dimensional model of the time-dependent temperature structure of a surge-type glacier, shows that the relative amounts of temperate and cold basal ice can change considerably as the surge cycle progresses. This variation alone may be sufficient to explain surges, but even if this is not the case, thermal processes must affect the timing of surges in many cold glaciers.

A compelling feature of the thermal instability mechanism is that it offers an explanation of the factors controlling the non-random geographical distribution of surge-type glaciers. For a glacier to have a cold surface and near-temperate bed, the ice thickness, temperature, and geothermal flux must be fortuitously related.

Recent measurements of near-surface temperature and surface velocity from the Variegated Glacier are presented. Temperature was measured with thermocouples at nine sites spaced along the length of the glacier. Maximum measurement depths ranged from 8 m in the lower ablation area to 20 m in the accumulation area. Accuracy of measurement was about 0.1 deg. By the end of summer the temperature at all measured sites and depths was not measurably different from zero, indicating that practically all of the near-surface ice of the glacier is temperate. The distribution of surface velocity along the length of the glacier shows distinct variations with time which cannot be explained by internal deformation in the glacier as influenced by changes in ice depth and slope. This indicates that the glacier is sliding over much of its length, which requires that the base of the glacier is temperate. Taken together, the near-surface temperature and velocity data provide good evidence that Variegated Glacier is temperate throughout and also indicate that the surge behavior of this glacier cannot be explained by thermal triggering.

Deep ice temperatures measured at four widely spaced sites on Steele Glacier show that the thermal regime was profoundly influenced by the 1965-66 surge advance. Three of four measured temperature profiles are "anomalous" in that the upper 100 m of ice is far from thermal equilibrium. Water penetration during the surge is the probable cause of these anomalies. Insufficient data are available to predict the basal ice temperature.