Evidence as to the potential roles of marine ice flows in the dramatic climatological changes which have occurred from the late Pleistocene to the present is reviewed, indicating the need for careful modeling studies to evaluate several crucial hypotheses. A scale analysis of the flow of a marine ice stream coupled to a freely floating ice shelf is presented, in two dimensions and ignoring thermodynamic effects. With these limitations, the most important control of the dynamics of the ice stream is associated with first-order buoyancy effects related to the density contrast ∆ρ/ρw between ice and sea-water. It is shown that longitudinal stretching, arising from large gradients in basal sliding velocity, dominates shearing deformation provided the aspect ratio ω2 « ∆ρ/ρw. The buoyancy control is established through the necessity of having continuously varying longitudinal strain-rates in the neighborhood of the grounding line.

The scale analysis is the basis for derivation of a simplified model of a fast-flowing ice stream coupled to a freely floating ice shelf. The distance in the ice stream up-stream from the grounding line over which the above dynamic regime extends is estimated and found to be relatively insensitive to the basal sliding velocity and to the rheological constant of ice. A further potentially important feed-back mechanism between ice stream and ice shelf is associated with buoyancy corrections to the longitudinal deviatoric stress field.

We present a model for the determination of a sliding law in the presence of subglacial cavitation. This law determines the basal stress at a clean ice‒bedrock interface in terms of the velocity and effective pressure. The method is based on an exact solution of the Nye—Kamb (linearly viscous) sliding problem with cavities, and uses ideas of Lliboutry (1979) to construct, via renormalization methods, an approximate law for general bedrock form. We show that, for a bedrock whose spectrum has a power‒law behaviour, one obtains a sliding law which gives the basal shear stress proportional to a power of the velocity, and to a power of the effective pressure.

The effect of subglacial cavitation on the drainage system is examined, using recent ideas of Kamb. For sufficiently high velocities, drainage through a Röthlisberger tunnel system is unstable, and drainage takes place through the linked system of cavities. This leads to a reduction of the effective pressure, and by taking account of this, one can rewrite the sliding law in terms of stress and velocity only.

This sliding law can be multi‒valued, and it is suggested that this underlies the dynamic phenomenon of surges.

A contradiction has existed in the literature as to the conditions favoring formation of “ablation hollows” (“suncups”) on a melting snow surface. Some experiments find that these features grow under direct sunlight and decay in overcast, windy weather; whereas others find just the opposite result, that they grow best under cloudy, windy conditions and decay if exposed to direct sunlight. We find that the hidden variable in past experiments, which acts as a switch to determine which mode of formation can operate, is the absence or abundance of dark insoluble impurities in the snow. Direct sunlight causes ablation hollows to grow in clean snow and to decay in dirty snow (for dirt content below a critical value), because the dirt migrates to the ridges between the hollows, lowering the albedo at the ridges. By contrast, when ablation is dominated by turbulent heat exchange, the presence of dirt favours development of ablation hollows because the dirt migrates to the ridges and insulates them; albedo reduction has a negligible effect on ablation.

This hypothesis is supported by an experiment which showed that the presence of a thin layer of volcanic ash on the snow inhibited formation of ablation hollows under direct sunlight.

McTigue and others (1985) identified a possible problem in the type of constitutive equation usually used for modeling the creep behaviour of polycrystalline ice. They pointed out that Glen’s flow law necessarily excludes the consideration of normal stress effects, which are of great significance in other disciplines that consider non-Newtonian fluids. Using the second-order fluid (with material parameters evaluated from laboratory data) as a tentative model for ice, they reached the conclusion that normal stress effects may be discernible in natural glacier flow. But, as noted by McTigue and others, the second-order fluid “fails to represent the non-linear rate dependence of ice in shear”; therefore it is in fact not a suitable constitutive model for glacier ice in shearing flow. In this note, parallel to what McTigue and others did for the second-order fluid, we present a similar analysis for (I) the modified second-order fluid and (II) the power-law fluid of grade 2, both of which are constitutive models recently proposed by Man as a tentative generalization of Glen’s flow law. Both models (I) and (II) can represent normal stress effects, and both agree with Glen’s flow law in the prediction of the depth profile of velocity in the steady laminar flow of glaciers. For ease of comparison, the same creep data of McTigue and others are used in quantifying the material parameters in these two models. Both models (I) and (II) predict far less pronounced normal stress effects in glaciers than those estimated by McTigue and others (whose data analysis in fact suffered from inconsistencies and over-parameterization).

Transient temperature variations in a vertical column of ice with horizontally uniform conditions, constant vertical strain-rate and specified surface temperature, and basal heat flux can be calculated analytically. The solution consists of eigenfunctions which are forms of the confluent hypergeometric function. This solution shows that advection and diffusion have clearly separated areas of dominance, with diffusion being a sufficient approximation for small-scale perturbations in the temperature profile and advection placing an upper limit on the response time of the ice sheet as a whole. This solution is useful for analysis and testing of numerical models, for evaluation of the response time of an ice sheet and for exploratory analysis of real bore-hole data. The lowest eigenvalue of the solution determines the time-scale for transient decay of temperature anomalies. The time-scale can be determined for more general strain-rates using a finite-difference approximation to the linearized energy-balance equation.

Apparent ice-surface topography is observed at several scales on Landsat multi-spectral scanner (MSS) imagery. Digitally enhanced MSS scenes from Antarctica and Nordaustlandet, Svalbard, are compared with ice-surface elevations from aircraft altimetry (relative accuracy 2–3 m) to show that this apparent topography is real. Apparent ice divides on Landsat images fit closely with divides on altimetric records. Ice-surface irregularities within drainage basins are also shown to be real. On Byrd Glacier, Antarctica, apparent “flow lines” coincide with ridges on altimetric records. Synoptic Landsat data, calibrated by information from aircraft altimetric flight lines, are used to classify the surface roughness of the ice caps on Nordaustlandet and 40% of the Antarctic ice sheet. On Nordaustlandet, the roughest ice is of amplitude 15–25 m and wavelength 3–4.5 km. Drainage basins with such rough surface characteristics may be associated with ice streams or possibly past surge activity. The most rough Antarctic terrain is up to 60 m in amplitude, with wavelengths of <10 km. The roughness of the Antarctic ice sheet increases with distance from ice divides, reflecting changes in the parameters affecting the transfer of basal stresses to the ice surface.

Scientific investigations on valley glaciers engaged some of the greatest natural philosophers of the nineteenth century. Among these, Louis Agassiz has unique importance for he personifies the transition from the protoscientific period of de Saussure and Scheuchzer to the scientific one of Forbes and his successors. In this brief history I have attempted to connect the achievements of the past 50 years with the aspirations of our predecessors.

The principal objectives of glacial geology over the last 50 years have been to establish and explain the history of ice, and in particular glaciation, on Earth and to understand the origin of the erosional and depositional products of ice. One of its major successes has been to establish the tempo and magnitude of change in the global glacier mass during the late Cenozoic ice age, and to demonstrate Earth orbital forcing of these changes. On the larger time-scale of the whole geological record, there has been steady elucidation of the frequency of ice ages since the first evidence of glaciation in rocks 2700 Ma old.

There has also been considerable progress in identifying the processes of glacial erosion and deposition and systematizing their products. It is now important that glacial geologists and glaciologists attempt to establish ways in which glacier behaviour is related to sedimentary processes, and via the geological product of those processes to relate the dynamics of glaciers in the past to processes in the lithosphere, hydrosphere, and atmosphere.

The energy budget of a snow or ice surface is determined by atmospheric variables like solar and atmospheric long-wave radiation, air temperature, and humidity; the transfer of energy from the free atmosphere to the surface depends on the stability of the atmospheric boundary layer, where vertical profiles of wind speed and temperature determine stability, and on surface conditions like surface temperature (and thus surface humidity), roughness, and albedo.

This paper investigates the conditions exactly at the onset or the end of melting using air temperature, humidity, and as the radiation term the sum of global and reflected short-wave plus downward long-wave radiation. For the turbulent exchange in the boundary layer, examples are computed with a transfer coefficient of 18.5 W m−2 K−1 which corresponds to the average over the ablation period on an Alpine glacier. Ways to estimate the transfer coefficient for various degrees of stability are indicated in the Appendix.

It appears from such calculations that snow may melt at air temperatures as low as –10°C and may stay frozen at +10°C.

Meteorological observations on and around a small, exposed plateau ice cap on north-eastern Ellesmere Island, N.W.T., Canada, were carried out in the northern summers of 1982 and 1983. The objective was to assess the effect of the ice cap on local climate as the melt season progressed. In 1982, seasonal net radiation totals were lowest on the ice cap and greatest at the site farthest from the ice cap. The ice-cap site received only 35% of net radiation totals on the surrounding tundra. This reflects a gradient in albedo; albedo changed most markedly away from the ice cap as the summer progressed. A thermal gradient was observed along a transect perpendicular to the ice-cap edge; this gradient was greatest at low levels (15 cm) and was maximized under cloud-free conditions. The “cooling effect” of the ice cap was less at the start of the ablation season than later. Low-level inversions occurred more frequently over the ice cap than over the snow-free tundra. Overall, melting degree days on the ice cap were only 40–65% of those on the adjacent tundra. A model of interactions between the atmosphere and a snow and ice cover, or a snow-free tundra/felsenmeer surface is proposed. Observations indicate that the ice cap has a cooling effect on the lower atmosphere relative to the adjacent snow-free tundra; this effect is absent when snow cover is extensive (as in 1983).

This paper presents and discusses the results of constant deformation-rate tests on laboratory-prepared polycrystalline ice. Strain-rates ranged from 10−7 to 10−1s−1, grain–size ranged from 1.5 to 5.8 mm, and the test temperature was −5°C.

At strain-rates between 10−7 and 10−3 s−1, the stress-strain-rate relationship followed a power law with an exponent of n = 4.3 calculated without regard to grain-size. However, a reversal in the grain-size effect was observed: below a transition point near 4 × 10−6 s−1 the peak stress increased with increasing grain-size, while above the transition point the peak stress decreased with increasing grain-size. This latter trend persisted to the highest strain-rates observed. At strain-rates above 10−3 s−1 the peak stress became independent of strain-rate.

The unusual trends exhibited at the lower strain-rates are attributed to the influence of the grain-size on the balance of the operative deformation mechanisms. Dynamic recrystallization appears to intervene in the case of the finer-grained material and serves to lower the peak stress. At comparable strain-rates, however, the large-grained material still experiences internal micro-fracturing, and thin sections reveal extensive deformation in the grain-boundary regions that is quite unlike the appearance of the strain-induced boundary migration characteristic of the fine-grained material.

Over the past 50 years, ideas relating to the physical features and dynamics of ice sheets have evolved materially, primarily due to modern technological advances in the acquisition of basic data. This paper therefore does not review contemporary knowledge but records how our perception of ice sheets has changed with time. Rather than dealing with individual contributions to the understanding of ice sheets, major topics and concepts are considered against a background of earlier ideas and theories.

Both the form and extent of the surface features of ice sheets have been defined more clearly by the relatively recent use of satellite studies (imagery and altimetry). In an analogous way, radio echo-sounding has enabled the accurate calculation of ice thicknesses and the mapping of the sub-ice bedrock contours, and hence estimation of the ice volume. Studies on the dynamics of ice sheets have been enhanced by bore-hole sampling of deep ice and the determination of ice-temperature distributions, coupled with measurements of mass balance and both surface and internal ice movement. Internal deformation of ice sheets, surging, and various flow theories are considered in relation to recent modelling studies. Global geophysics inevitably includes the role of ice sheets, and therefore climatological studies and new atmospheric chemistry data, together with information on the distribution of meteorites on the Antarctic ice sheet, are considered critically.

Modern concepts of the evolution of ice sheets have substantially modified earlier ideas of the glacial geologists and have explained much that had previously mystified them.

The flow of a glacier along a channel of constant longitudinal curvature is analyzed using analytical and finite-element methods. Channels of various cross–sectional shape are investigated, ranging from a simple rectangular form with zero shear traction along the bed to realistic profiles taken from Blue Glacier, Washington. Terms in the equilibrium and rate-of-deformation equations which are inversely dependent on radius and a body force which varies transversely across the glacier introduce several characteristic features into the stress and velocity fields of the curving glacier. The stress center line is shifted toward the inside of the bend, causing an asymmetric crevasse pattern and non‒zero stress magnitude at the surface on the geometric center line of the channel. The stress field is dependent on the stress exponent in the flow law and is non-linear across the surface. The surface–velocity pattern shows a “tilting” of the usual high‒order parabolic form, being skewed toward the inside of the bend. There is a shift in the velocity maximum from the deepest part of the channel. All of these curvature‒induced features are dependent on the radius of curvature, actual channel geometry, and stress exponent in the flow law. Model results show excellent agreement with the velocity and crevasse patterns on the curving Blue Glacier.

The dihedral angle of water at a grain boundary in ice is found, by measuring the optical focal length of lenticular water inclusions, to be 33.6 ± 0.7°. The new result leads to only minor revision of published experimental values of specific surface free energies in the ice–water system (Ketcham and Hobbs, 1969).

Periods of dramatically accelerated motion, in which the flow velocity increases suddenly from about 55 cm/d to a peak of 100–300cm/d and then decreases gradually over the course of a day, occurred repeatedly during June and July 1978–81 in Variegated Glacier (Alaska), a surging-type glacier that surged in 1982–83. These “mini-surges” appear to be related mechanistically to the main surge. The flow-velocity peak propagates down-glacier as a wave at a speed of about 0.3 km/h, over a reach of about 6 km in length. It is accompanied by a propagating pressure wave in the basal water system of the glacier, in which, after a preliminary drop, the pressure rises rapidly to a level greater than the ice-overburden pressure at the glacier bed, and then drops gradually over a period of 1–2 d, usually reaching a new low for the summer. The peak velocity is accompanied by a peak of high seismic activity due to widespread fresh crevassing. It is also accompanied by a rapid uplift of the glacier surface, amounting to 6–11 cm, which then relaxes over a period of 1–2 d. Maximum uplift rate coincides with the peak in flow velocity; the peak in accumulated uplift lags behind the velocity peak by 2 h. The uplift is mainly due to basal cavitation driven by the high basal water pressure, although the strain wave associated with the mini-surge motion can also contribute. Basal cavitation is probably responsible for the pulse of high turbidity that appears in the terminal outflow stream in association with each mini-surge. In the down-glacier reach, where the mini-surge waves are attenuating, the observed strain wave corresponds to what is expected for the propagating pulse in flow velocity, but in the reach of maximum mini-surge motion the strain wave has a form quite different, possibly related to special features in the mini-surge initiation process from that point up-stream. The flow acceleration in the mini-surges is due to enhanced basal sliding caused by the high basal water pressure and the consequent reduction of bed friction. A preliminary velocity increase shortly before the pressure wave arrives is caused by the forward shove that the main accelerated mass exerts on the ice ahead of it, and the resulting preliminary basal cavitation causes the drop in water pressure shortly before the pressure wave arrives. The mini-surge wave propagation is controlled by the propagation of the water-pressure wave in the basal water-conduit system. The propagation characteristics result from a longitudinal gradient (up-glacier increase) in hydraulic conductivity of the basal water system in response to the up-glacier increase of the basal water pressure in the mini-surge wave. The mini-surge waves are initiated in a succession of areas situated generally progressively up-glacier during the course of the summer season. In these areas, presumably, melt water that has accumulated in subglacial (?) reservoirs is released suddenly into the basal water system immediately below, generating a pressure rise that propagates down-stream from there. Relationships of the mini-surges to the main surge are seen in the role of high basal water pressure in causing the rapid glacier motion in both phenomena, in the pulse-propagation features of both, and in the high outflow turbidity associated with both. The mini-surges of Variegated Glacier have a strong resemblance to movement and uplift events observed in Unteraargletscher and Findelengletscher, Switzerland. This bears on the question whether the mini-surges are a particular characteristic of surge-type glaciers prior to surge.

An opportunity to analyse the mechanism for the formation of a basal ice layer was provided by Glacier de Tsanfleuron in the Swiss Alps. This glacier has some lateral subglacial cavities in which a basal ice layer forms on the bedrock floor and is subsequently incorporated at the base of the glacier. Petrographic and crystallographic analyses of the different types of ice have provided a means of investigating the successive stages of the process. These analyses show major structural changes which provide field confirmation of the deformation mechanisms studied by several authors in laboratory experiments.

Victoria Lower Glacier is a complex structure of ice from two distinct sources (Schultz Glacier to the north and a local névé of Victoria Lower Glacier) that join at a broad median shear zone. Evidence from the margins suggest that both are currently retreating. Algae in a block of frozen stratified sediment from within the ice of the terminal margin has a radiocarbon age of 20 200 ± 2400 year BP (NZ 6531 A), indicating that the glacier has advanced since that time. Superposition of ice levels of Ross Sea I glaciation on a radio echo–sounding profile of bedrock beneath the glacier indicates that it is unlikely that Ross Sea I ice entered the valley. The radiocarbon date supports this finding.

The practical motivations for research on sea ice are discussed and an historical outline given of work carried out in the interval 1936-86. Advances in understanding the physical properties of sea ice and atmosphere–ice–ocean energy exchanges are listed. It is shown how these factors, together with an increasing ability to formulate changing ice-thickness distributions, have led to the eventual production of sophisticated models of ice movement having a useful predictive capability.

Hourly measurements of incoming short-wave and long-wave radiation, surface albedo, and net radiation were made on and around a plateau ice cap on north-eastern Ellesmere Island during the summers of 1982 and 1983. These data were stratified by cloud type and amount. All cloud types increased incoming long-wave radiation, especially low dense clouds, fog, and clouds associated with snowfall. Relative transmission of incoming short-wave radiation, expressed as a percentage of clear-sky radiation receipts, was high for all cloud types compared to clouds at lower latitudes. With high surface albedo (≥0.75), net radiation was strongly and positively correlated with net long-wave radiation but showed little relationship to net short-wave radiation. By contrast, with low surface albedo (≤0.20) net radiation was negatively correlated with net long-wave radiation but positively correlated with net short-wave radiation. Under high-albedo conditions, an increase in cloudiness led to higher values of net radiation but under low-albedo conditions net radiation decreased as cloud cover increased. Survival of a snow cover would seem to be favoured if the seasonal decline in albedo is accompanied by a corresponding increase in cloudiness.