An analysis is made of the steady-state size of a two-dimensional ice sheet whose base is below sea-level and which terminates in floating ice shelves. Under the assumption of perfect plasticity it is found that an ice sheet placed on a bed whose surface was initially flat cannot exist if the depth of the bed below sea-level exceeds a critical depth. If this depth is less than the critical level, the ice sheet extends out to the edge of the continental shelf. Similar results are found with more realistic assumptions about the laws governing the flow of ice. If the bed slopes away from the centre, the ice sheet can have a stable width that increases in value as the accumulation rate increases or as sea-level is lowered. It is not possible to decide whether or not the West Antarctic ice sheet is in stable equilibrium. It is entirely possible that this ice sheet is disintegrating at present, as suggested by Hughes.

Ice unquestionably exists on Mars. Annual polar-region frost blankets are principally solid CO2, and perennial residual ice caps near each pole are probably water ice, except for a part of the north polar cap which may consist of a 1 km thick mass of solid CO2. Minor amounts of carbon-dioxide clathrate (CO2 · ≈ 6H2O) presumably accompany the solid CO2. The annual frost blankets may have a concentric banding with an outermost very thin layer of water frost, an intermediate narrow zone of clathrate, and a major central core of solid CO2.

Layered deposits and underlying homogeneous materials mantle large areas within both polar regions. These blankets are probably composed of dust, volcanic ash, or both, and possibly contain frozen volatiles. They may comprise the largest reservoir of water substance on the Martian surface.

Ground ice formed by the freezing of ascending de-gassed water substance may underlie the surface of Mars. Localized collapse of small areas may be due to ground-ice deterioration, and recession of steep slopes may have been caused by ground-ice sapping.

If liquid water ever existed in significant quantities on the Martian surface, intense frost shattering, widespread creep, and prolific development of patterned structures should have occurred because the thermal regimen of the surface is highly favorable to the freeze–thaw process. It is ineffective at present owing to the lack of liquid water.

No evidence suggests that the residual ice caps have ever acted like terrestrial glaciers in terms of erosion and deposition. Currently, they are too thin, too cold, and presumably frozen to their substrates. Their most important function is to buffer the atmosphere in terms of its H2O and CO2 content, thereby exerting a modifying influence on the surface environment of the entire planet.

Detailed measurements of the positions of stakes along the center-line of the lower Nisqually Glacier were made over a period of two years. Variations in the basal sliding speed were calculated from the measured changes in surface speed, surface slope, and thickness, using the glacier flow model of Nye (1952) and allowing for the effect of the valley walls, longitudinal stress gradients, and uncertainties in the flow law of ice. The flow is predominantly by basal sliding and has a pronounced seasonal variation of approximately ±25%. Internal deformation contributes progressively less to the total motion with distance up-glacier. Neither the phase nor the magnitude of the seasonal velocity fluctuations can be accounted for by seasonal variations in the state of stress within the ice or at the bed, and the variations do not correlate directly with the melt-water discharge from the terminus. A seasonal wave in the ice flow travels down the glacier at a speed too high for propagation by internal deformation or the pressure melting/enhanced creep mechanism of basal sliding.

The rate of sliding appears to be determined primarily by the amount of water in temporary storage in the glacier. The peak in sliding speed occurs, on the average, at the same time as the maximum liquid water storage of the South Cascade Glacier. The data support the idea that glaciers store water in the fall, winter and spring and then release it in the summer. This temporary storage may be greatest near the equilibrium line. The amount of stored water may increase over a period of years and be released catastrophically as a jökulhlaup. Any dependence of sliding on the basal shear stress is probably masked by the effect of variations in the hydrostatic pressure of water having access to the bed.

A statistical analysis has been made of the annual balances collected during 16 consecutive years at 32 sites on the ablation area of the Glacier de Saint-Sorlin (French Alps). Only 38% of the 32 × 16 balances are known; moreover in 8 cases only the total balance for 2 consecutive years is known, and in one case the balance for 4 consecutive years. A comprehensive study of the errors leads us to assume the following linear model for the annual balance xjt at site j for year t:

where αj and βt are parameters depending upon the site and the year respectively, ηjt and η’jt are random errors with a Gaussian distribution and standard errors σ and σ’ respectively. Assuming some known value for σ’2/σ2 = ρ, the parameters αj and βt, their variance–covariance matrix, and the variance covariance matrix of the residuals are estimated in the most general case. The estimators being stable against variations in ρ, the value ρ = o may be assumed; this value docs not conflict with the behaviour of the estimates of the residuals. A test of the linear model derived from Tukey’s non-additivity test is positive. Although a much more general, non-linear model

gives a better representation of 13 × 6 balances forming a complete table of data, the linear model with σ ≈ 0.20 m is good enough to be used in theoretical studies or in routine work.

Velocity and strain-rate patterns in a small temperate valley glacier display flow effects of channel geometry, ice thickness, surface slope, and ablation. Surface velocities of 20–55 m/year show year-to-year fluctuations of 1.5–3 m/year. Transverse profiles of velocity have the form of a higher-order parabola modified by the effects of flow around a broad bend in the channel, which makes the velocity profile asymmetric, with maximum velocity displaced toward the outside of the bend. Marginal sliding rates are 5–22 m/year against bedrock and nil against debris. Velocity vectors diverge from the glacier center-line near the terminus, in response to surface ice loss, but converge toward it near the firn line because of channel narrowing. Plunge of the vectors gives an emergence flow component that falls short of balancing ice loss by about 1 m/year. Center-line velocities vary systematically with ice thickness and surface slope. In the upper half of the reach studied, effects of changing thickness and slope tend to compensate, and velocities are nearly constant; in the lower half, the effects are cumulative and velocities decrease progressively down-stream. Where the slope increases down-stream from 7° to 9°, reflecting a bedrock step, there is localized longitudinal extension of 0.03 year–1 followed by compression of 0.08 year–1 where the slope decreases. Marginal shear (up to 0.5 year–1) is strongly asymmetric due to flow around the bend: the stress center-line, where one of the principal axes becomes longitudinal, is displaced 150 m toward the inside of the bend. This effect is prominently visible in the crevasse pattern. Ice fluxes calculated independently by “laminar” flow theory and by continuity disagree in a way which shows that internal deformation of the ice is controlled not by local surface slope but by an effective slope that is nearly constant over the reach studied.

On the McCall Glacier, an Arctic glacier in the eastern Brooks Range, northern Alaska, a heat balance study was carried out during the summer of 1970 to investigate quantitatively the relationship between energy transfer, climatic parameters and melting processes. Considering the individual energy balance terms, it was found that radiation is the most important heat source for snow and ice melt. The melting period itself is only 11 weeks long, which is quite short. The evaporation overcompensates for what little condensation occurs, and amounts to about 2% of the total ablation. Evaporation is more important in the spring, but becomes decreasingly so during the summer. The melt water which percolates into the snow-pack and refreezes at a lower level is a more effective way of transporting energy into the ground than conduction, and is of importance during the beginning of the melt period. The summer balance is considerably less energetic than over the tundra north of the Brooks Range. The main difference is a higher surface albedo, and to a lesser extent the protected nature of the glacier in a deep valley on a N–S axis, which reduces the duration of possible sunshine by 39% in summer. These are the important factors in maintaining the McCall Glacier and other similar glaciers in an otherwise low precipitation area.

Examination of the past and present behaviour of the Erebus Glacier tongue over the last 60 years indicates that a major calving from the tongue appears to be imminent. Calculations of the regime of the tongue indicate that bottom melt rates may exceed 1 m a−1. By successive mapping of the ice tongue between the years 1947 and 1970, longitudinal strain-rates were determined using the change in distance between a set of 15 teeth, which are a prominent marginal feature of the tongue. Assuming a flow law for ice of the form where τ is the effective shear stress and is the effective shear strain-rate, values of the exponent n = 3 and B = 1 × 108 N m−2 are determined. These are in fair agreement with published values.

The McCall Glacier is located in the Brooks Range, north Alaska. Most of its slopes have a northerly exposure with an inclination between 5°and 15°. The reduction in direct solar radiation owing to this northerly exposure is small (1.7%) in summer (ablation period, solar declination 20°), as the reduction in radiation received on a north slope during the noon hours is mostly compensated by the increase of energy during the “night” hours, as the sun does not set at that latitude in summer. With the shortening of the solar path, the decrease in direct solar radiation as compared with a horizontal surface becomes more important. At the equinox the loss is 24.8%, and at a solar declination of —10° (20 October or 24 February) even higher with 32.6%.

A further reduction in solar radiation is caused by the steep mountains, which surround the McCall Glacier. The duration of sunshine is reduced during the ablation period by nearly 40%, which, however, represents an energy loss of only 13.4%, as the screening effect of the mountains is most important with low solar angles, i.e. at times when the total energy received at the surface is small. The screening effect of the mountains becomes more severe with lower sun angles and shorter paths of the sun. During the equinox a loss in duration of 67.6%, and in energy of 55.7% is observed. For a solar declination of —10°, there is hardly any direct sunshine on the glacier at all. There is then a loss in duration of 93.6%, resulting in a loss of energy of 87.8%.

Together, these two components reduce the direct solar radiation by about 15% in the ablation period, 67% at the equinox and more than 90% at a solar declination of —10°.

Some flutes which occur on the surface of a series of glacio-fluvial sediments at the margin of Blomstrandbreen, north-west Spitsbergen, are described. A section in one has revealed a complex internal structure, in which originally horizontal beds have been folded into an anticline whose axis is normal to the ice margin, and whose structure is related to the morphology of the flute.

Comparison of the observed deformation with the theoretical distribution of stresses around the base of a subglacial tunnel shows that this deformation could have resulted from How under such a stress system. It is considered that these observations support the hypothesis that flutes are formed when unfrozen, water-soaked materials deform subglacially due to the pressure differences which exist in the vicinity of an ice tunnel formed in the lee of some rigid obstruction to ice flow.

Surface slopes of ice lobes can be estimated from the gradients of their margins as shown by ice limits, by contemporaneous recessional moraines, or by lateral melt-water channels, with allowance being made for the dip of an ice lobe laterally, as well as forward, toward its extremities. Profiles can be fitted approximately to a parabola with the equation in which h is the height above and x the distance up-stream from the terminus, in the same units, and A is a coefficient which varies from glacier to glacier. The coefficient A has a value of 4.7 m1 for both the Antarctic ice sheet inland from Mirny and the west central Greenland ice sheet. Several examples of late Pleistocene ice lobes within mountainous terrain of North America and New Zealand have values of A ranging from 2.9 ml to about 4.1 m1. For several ice lobes in the south-western part of the late Pleistocene Laurentide ice sheet, however, values are from about 0.3 to 1.0 m1, corresponding to basal shear stress of from about 0.07 to 0.22 bar. A major problem exists in accounting for the active movement of ice here under such low surface gradients and basal shear stresses. Evidence of basal slip, aided by high subglacial water pressure, should be looked for in the field. Alternatively, other possibilities for the explanation of such low surface gradients should be sought.

As part of the feasibility study for the development of an open-pit mine at the edge of the Greenland ice sheet, a study is made of the ice flow toward the proposed pit. The flow is analyzed by considering the two-dimensional flow along seven cross-sections. The most favorable profile is determined for each cross-section and its flow calculated. The excavation necessary to expose the ore is 106 × 106 m3 of ice. 66 × 106 m3 of ice will have to be removed in order to establish favorable profiles and an additional 7.9 × 106 m3 of ice will have to be removed each year in order to prevent the glacier from thickening and advancing into the mine. Many other glaciological problems must be considered, and field work continues in order to provide more information about the area.

The combined heat, ice and water balance was calculated for the McCall Glacier basin (30.6 km²) for a 36 day period in summer of 1971. This period represents about half the ablation period in this region. The heat balance was measured by detailed observations over ice, and secondary stations were established over snow and moraine surfaces. The heat balances calculated for stations located respectively on ice and snow surfaces were assumed to be representative of all such surfaces. The moraine station was only used to obtain evaporation data for areas of the basin not covered by glacier (totalling about 70%). Corrections were made to the radiative fluxes owing to screening of the surrounding mountains and the exposure of the glacier. The ice balance was calculated using 80 ablation/accumulation stakes and the discharge was measured with a water-level recorder, which was calibrated with a current meter. The precipitation was measured with seven rain gauges. Compared with the direct run-off measurements, the values calculated from the heat balance gave a value 5.5% higher, and the stake measurements a value 8.9% lower. This agreement is considered satisfactory and strengthens confidence in the methods employed in each of the three individual calculations.

Ice temperature measurements have been made in Steele Glacier to a depth of 114 m. All measured temperatures were below 0° C, the coldest being –6.5° C at a depth of 114 m. The temperature profile indicates an anomalously warm layer of ice between 30 m and 50 m, which is probably due to the freezing of water in crevasses opened during the 1965–66 surge. A two-dimensional model of a cold glacier with partially water-filled crevasses predicts temperature profiles very similar to that observed.

The Yarmouth drumlinized area is a relatively small field of about 150 drumlins located south and south-east of the town of Yarmouth, Nova Scotia. An analysis of the drumlin shapes indicates that in the majority of cases the stoss end is on the southern extremity of the drumlin. This would suggest that the ice moved in from the south, a concept which is contradictory to pebble lithology and fabric analysis of the till in the drumlins and surrounding ground moraine. The drumlin field is anomalous in other respects in that the drumlin density is very low compared with other fields, and granulometric analysis shows that the drumlins are composed of coarse-grained material with only minor amounts of clay.

It is suggested that the drumlins were originally formed by south to south-easterly flowing ice but during a later phase of glaciation a local centre of outflow, probably short-lived, developed south of Yarmouth on the continental shelf, and the drumlins were reshaped by ice flowing toward the north prior to the disappearance of this centre. Thus this area of drumlins was presumably not affected by the later area of outflow centred on the interior upland of western Nova Scotia which was hitherto believed to account for the Yarmouth drumlins.

The results of airborne radio-echo (R/E) depth sounding over Wilson Piedmont Glacier, Mackay, Ferrar and Taylor outlet glaciers, and over the ice sheet bordering the mountains, provide ice thicknesses and subglacial topography accurate to 20 m and to 1 km areally. The R/E records show that flours of the Debenham, Wright and Victoria Valleys occur beneath the Wilson Piedmont at elevations of –260 m, and up to 260 and 670 m, respectively. The 670 m “threshold” may have blocked easterly marine and glacial invasions experienced by lower valleys. Profiles along the outlet glaciers display large depressions, some below sea-level. These are associated with erosion by tributaries and with glacial erosion through thick dolerite sills. Elevated ridges thought to be sills submerged beneath the heads of these glaciers also limit nourishment from the adjacent part of the ice sheet. The subglacial west flank of the mountains is formed by a series of high steep-sided plateaux with gentle west-sloping surfaces. Block faulting, west-dipping dolerite and sandstone units, and glacial erosion must explain this topography.

Measurements of the concentrations of Na+ K+, Mg2+, and Ca2+ were made on 28 samples from the 255 m deep ice core from Little America V. All concentrations decrease sharply with depth from the firn–ice transition at 52 m to somewhere between 125 m and 150 m. From 150 m to 250 m the cationic concentrations are relatively constant. This is interpreted to indicate that the ice above 125 m fell as snow on the Ross Ice Shelf and that ice below 150 m originated inland on Marie Byrd Land.

The relative importance of the principal elements of the thermal balance above snow during a period of melting has been evaluated using recent studies of the turbulent transfer in the boundary layer. Several anomalies in the profiles prove the continuing presence, near to the surface, of a thick layer of air apparently re-heated by the radiative flux. It is shown that the upper surface of this “exchange layer” ought to be considered as the new level for the origin of profiles, and taken as the exchange surface. The importance of nocturnal refreezing has been quantified. Excellent correlations have been found between mean air temperature and total energy balance; they have allowed the establishment of an approximate, non-linear expression for the effective daily ablation of snow as a function of mean air temperature. This relation gives satisfactory results at high and intermediate altitudes, in horizontal uncovered terrain. The measurements were made in the French Alps at 3550 m and in Spain at the latitude of Madrid à 1860 in.

The two medial moraines of the Glacier de Tsidjiore Nouve are nourished by rock debris revealed at the surface by progressive ablation down-glacier. The sources of the moraine appear to be rock outcrops marginal to or above the Pigne d’Arolla ice fall, much of the detritus entering the glacier via crevasses either at the summit or the base of the ice fall. The role of differential ablation in the emergence of the moraines as relief features is illuminated by measurements made in the late summers of 1971 and 1972. The eventual decline of the moraines down-glacier is related to factors of reducing debris supply, lateral sliding and accelerated ablation due to attenuation of the detrital cover to a mean thickness of 1 cm or less. A model of moraine development, different in several respects from that proposed by Loomis (1970) for the Kaskawulsh Glacier, Alaska, is outlined.

A series of minor moraine ridges lying on a lodgement till surface in front of the glacier Austre Okstindbreen are described. The available chronological control suggests that from 1957 through to 1970 a new ridge was formed each winter and that this pattern of annual production is probably also applicable to the period back to circa 1950. During the winter months of 1970/71 and 1971/72 the glacier advanced and deformed the ice cover of a marginal lake which now isolates the till areas from the ice margin. It is concluded that the ridges are true “annual” moraines formed primarily by ice push although the operation of a squeeze process during their genesis is not rejected.

Measurements of mesoscale sea-ice deformation over a region approximately 20 km in diameter were carried out over a five-week period in the spring of 1972 at the main AIDJEX camp in the Beaufort Sea. They have been analyzed to determine non-linearities in the ice velocity field (due to the discrete small-scale nature of the ice pack), as well as a continuum mode of deformation represented by a least-squares strain-rate tensor and vorticity. The deformation-rate time series between Julian day 88 and 112 exhibited net areal changes as large as 3% and deformation rates up to 0.16% per hour. In the principal axis co-ordinate system, the strain-rate typically exhibited a much larger compression (or extension) along one axis than along the other. Persistent cycles at ≈ 12 h wavelengths were observed in the divergence rate.

A comparison of the average residual error with the average strain-rate magnitude indicated that strains measured on a scale of 10 km or greater can serve as a valid measure of the continuum motion of the sea ice. This conclusion is also substantiated by a comparison between the mesoscale deformation, and macroscale deformation measured over a ≈ 100 km diameter region.

Regarding pack-ice rotation, vorticity calculations indicate that at low temporal frequencies (0.02 h−1), the whole mesoscale array rotates essentially as an entity and consequently the low-frequency vorticity can be estimated accurately from the rotation of a single floe.