Accurate modeling of calving glaciers relies on knowledge of many processes (ice flow, surface/submarine melting, calving, mélange interaction) and glacier-specific factors (air temperature, ocean circulation, precipitation rate, glacier geometry) that remain challenging to assess. Iceberg calving, especially, is important to glacier mass loss and difficult to resolve in currently-available models. Given these challenges facing even the most sophisticated models, there is value in simple, computationally-efficient models that can capture first-order effects. In this study we derive a simple model, extending Nye's perfect plastic approximation to include a yield surface at the calving front. With one climate-related input—either an upstream glacier thinning rate or glacier-wide accumulation—this model is able to simulate the advance and retreat of marine-terminating glaciers on annual to decadal scales. Our model requires knowledge of only two glacier-specific factors: glacier bed topography and basal shear strength, both reasonably constrained by laboratory and field observations. We apply the model to a case study of Columbia Glacier, Alaska and show that, despite its simplicity, the model succeeds in reproducing observed centerline profiles and rates of terminus retreat up to 2007.

The ERTS satellite’s sun-synchronous orbit covers the entire Earth horn lat. 81° N. to 81° S. every 18 d at approximately 10.00 a.m. ground time. The scanners on board have continued to relay images to Earth from the launch on 23 July 1972 to the present (summer 1974). Images from four spectral bands (0.5-1.I μm), with ground resolution of about 100 m. cover an area 185 km on a side. The resulting images have proved to be very useful for collecting certain basic data from glaciers.

Long-term surface velocities are readily determined by comparison of recent ERTS images with maps that have been produced from earlier data. Images have been used 10 measure velocities on the Malaspina Glacier over a 10 year period, surge displacements on the Lowell, Tenas Tikke. and Tweedsmuir Glaciers and Lednik Medvezhiy, and velocity at the margin of the Hubbard Glacier. Many surging glaciers are readily identifiable on (he images. Coverage from the satellite will allow surging glaciers to be identified world-wide which may help glaciologists to understand their peculiar geographical distribution. Images of large glaciers taken under conditions of low sun angle and complete snow cover show previously undetected subtle slope changes which can be interpreted as dynamic How features or reflections of subglacial topography.

ERTS imagery is providing new glacier data for several reasons: very large areas are covered repetitively with sufficient consistency to show subtle tonal changes, conditions of maximum and minimum snow cover, subtle morphologic features at low sun angle, and changes in position of glaciers.

The loss of methanesul phonic acid (MSA) from stored ice cores can be significant over typical storage times, with diffusion to the ice-core surface controlling the loss. Methods for minimizing this loss are discussed and it is shown how measurements can be corrected by calculating the amount of MSA lost. A revised diffusion coefficient for MSA in solid ice, (4.1 × 10−13) ± (2.5 × 10−14) m2 s−1, is derived to improve such MSA loss corrections.

It is well known that an empty hole in a glacier will fill in if it is more than some 15 to 20 m. deep, due to the rapid variation of strain rate with shear stress. It is pointed out that a water-filled hole or lake will tend to enlarge itself by the same mechanism, if it is more than 150 to 200 m. deep. This phenomenon is believed to be responsible for the periodical and complete emptying of some glacier lakes, such as has been reported for the Tulsequah Lake in British Columbia, and Graenalón and Grilmsvötn in Iceland.

Deglaciated bedrock surfaces in limestone areas often exhibit extensive patterning by solutional furrows and carbonate deposits that occur in close association with undulations in the bed topography. These features clearly result from subglacial dissolution and precipitation of calcite on the bed — induced, for instance, by melting and freezing in a regelation water film — but little is known about the observed morphology. In particular, it is intriguing that (i) the solutional furrows, whose formation requires explanation, are collectively organized into arcuate patterns, with characteristic spacing, and (ii) a fluted or “spiculed” surface texture is ubiquitous on the calcite deposits. Herein, we propose specific mechanisms for such patterning based on a theory where chemical processes in the water film are coupled to regelation physics. Solutional furrows reflect locally enhanced dissolution along stoss surfaces, where CO2-rich bubbles advected in the ice from up-glacier come into contact with the bed. The bubbles form as CO2 is exsolved from freezing film water at the lee of bed bumps. The flutings on the deposit are inherently the manifestation of a spatial instability at the interface where calcite precipitation occurs. Complex interactions underlie some of the striking glacier-bed features shaped by subglacial chemical processes.

The influence of snow structure on the liquid water distribution is recorded by measuring the high-frequency relative permittivity. The structure is characterized by the size and the shape of the ice grains, which are derived by analyzing the static dielectric constant and by analyzing photographs of the surface of the snow samples. The liquid distribution is very sensitive to the liquid saturation and to the shape of the ice grains; it is unaffectcd by the grain size. A transition from the pendular into the funicular mode of liquid distribution occurs in the range of 7 to 18% saturation. This transitional zone is very sensitive to the structure of snow; it decreases from approximately 13 to 18% liquid saturation for new snow to 7 to 12% saturation for old, coarse-grained snow.

The seasonal distribution of snow at the South Pole and its relationship to stratigraphy was investigated to pits dug beside a number of four-year-old accumulation stakes. Results show that conventional stratigraphic methods yield thoroughly reliable values of accumulation rates. Even hiatuses in accumulation can be identified from the intensity of sublimation of layers of depth hoar in the stratigraphic section. Such hiatuses are due almost invariably to the prolonged absence of accumulation rather than to widespread scouring of pre-existing layers of snow. The bulk of the year’s accumulation is deposited as dunes during winter. The majority of dunes are subsequently transformed into linear sastrugi by wind with the result that the amplitude of surface relief observed at the end of winter frequently exceeds the average thickness of snow accumulated annually. Such gross relief does not persist to the end of summer, however. Instead the dunes and sastrugi arc gradually worn down by a process of sublimation-deflation. It is this leveling of the surface relief in summer and the resultant redistribution of snow more uniformly over the surface that are believed to be the significant factors in the formation of the systematic stratigraphy observed in pits at the South Pole.

Deformation characteristics of polycrystalline ice and their dependence on time, temperature, and stress have been analysed on the basis of a phenomenological relation which describes creep in terms of initial elastic, delayed elastic, and permanent strain. It is shown that the effective modulus of ice observed in the laboratory or in the field can be examined on the basis of this model. The model also provides a basis on which the observed flow law of ice can be examined conveniently. Some apparent inconsistencies in the results of earlier investigations of the mechanical property of ice appear of be reconciled by the model.

This paper presents the distribution of average δD andδ18O values for the top 1 m of surface snow for a large area of Antarctica. The samples were collected on the 1990 International Trans-Antarctica Expedition which crossed the continent from the northern tip of the Antarctic Peninsula to Mirny Station. The empirical relationships between the isotopes, temperature and elevation are computed. The slopes of δD with respect to the surface temperature for the segments west (Patriot Hills-Vostok) and east of Vostok (Komsomolskaya-Mirny) are not significantly different to that observed between Dumont d’Urville and Dome C (Lorius and Merlivat, 1977) which are often used to interpret deep ice-core isotopic profiles. There is, however, a noticeable shift between the two regression lines with, for a given temperature, higher isotopic values west of Vostok. The deuterium excess values increase sharply at 3000 m.a.s.l. on the plateau, confirming the results of Petit and others (1991).

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.

Ice-sheet simulations of Antarctica extending to the year 3000 are analysed to investigate the long-term impacts of 21st-century warming. Climate projections are used as forcing until 2100 and afterwards no climate trend is applied. Fourteen experiments are for the ‘unabated warming’ pathway, and three are for the ‘reduced emissions’ pathway. For the unabated warming path simulations, West Antarctica suffers a much more severe ice loss than East Antarctica. In these cases, the mass loss amounts to an ensemble average of ~3.5 m sea-level equivalent (SLE) by the year 3000 and ~5.3 m for the most sensitive experiment. Four phases of mass loss occur during the collapse of the West Antarctic ice sheet. For the reduced emissions pathway, the mean mass loss is ~0.24 m SLE. By demonstrating that the consequences of the 21st century unabated warming path forcing are large and long term, the results present a different perspective to ISMIP6 (Ice Sheet Model Intercomparison Project for CMIP6). Extended ABUMIP (Antarctic BUttressing Model Intercomparison Project) simulations, assuming sudden and sustained ice-shelf collapse, with and without bedrock rebound, corroborate a negative feedback for ice loss found in previous studies, where bedrock rebound acts to slow the rate of ice loss.

Several analyses are given for the flexure of a floating polar ice tongue with the general dimensions of several kilometers wide by 200 in in thickness. The lengths considered are from 2 km to in excess of 10 km which is referred to as a long slab. The analyses are made under the separate assumptions that ice behaves as (1) an elastic material, (2) an elastic-plastic material, and (3) a fully plastic material, when reacting to flexure due to changes in sea-level. The elastic analysis shows that hinge-line stresses could become very high of the order of 15 bar) for slab lengths up to about 3·5 km reacting to sea-level changes of the order of ±50 cm. For slab lengths greater than this, the stresses at the hinge, as well as being significantly less than before, become independent of the length of the slab, dependent only on the slab thickness and the amount of deflection of sea-level. In the elastic-plastic analysis, the hinge-line stress cannot exceed a value of about 2 bar. This yield value is reached when sea-level departs about 50 cm from the mean. The fully plastic analysis requires more accurate knowledge of the constants in the flow law and their variation with density, temperature and salinity within the ice. However, the theory may be tested by measuring the diurnal change in strain-rate across the hinge-line zone. The process of calving of large tabular icebergs from such glacier tongues may demand sea-level changes of more than ± 1 m, or bending about more than one axis of the shelf.

Recent theoretical studies of glacier hydrology have assumed that subglacial conduits are completely filled with water under steady-state conditions. This, however, is not necessarily the case. Where discharges are larger than a few tens of liters per second and the down-glacier slope of the bed is more than a few degrees, the potential energy released by water descending this slope may be capable of melting the walls of a subglacial conduit many times faster than the conduit can close by plastic flow of the ice. As a result, the pressure in such tunnels may normally be atmospheric, or possibly even at the triple-point pressure if there is no open connection to the glacier surface. Simple calculations suggest that such pressures in subglacial conduits may be more common than heretofore anticipated.

The positions of such “open” conduits may be unstable to small perturbations in discharge or ice velocity. This is because the mechanical energy available in excess of that needed to balance closure can instead offset the general flow of the ice. Conduits can thus trend diagonally across the direction of ice flow. If an increase in the angle which such a conduit makes with the ice flow direction also results in an increase in slope of the conduit, more mechanical energy will become available, resulting in a positive feedback process.

Subglacial channels at atmospheric pressure may influence the origin and morphology of certain glacial landforms, such as eskers and “plastically-molded” features.

New and felt-like snow was sieved and sintered at a constant temperature in order to produce homogeneous samples of fine, rounded-grain snow with a density in the range 270–340 kg m−3. The structure of single samples was changed in stages by non-destructive uniaxial compression. This deformation, which amounted to 30%, took place within 8 hours (thus limiting temperature metamorphism). At each stage the Young’s modulus was measured quasi-statically and the creep behaviour under constant uniaxial compression was recorded. Stereological analysis of sections from the samples provided mean values for both grain-bond and grain properties. The Young’s modulus increased with density slightly more strongly than linearly, whereas the low-stress viscosity in unconfined compression increased nearly exponentially for densities less than 380 kg m−3. The maximum densification resulted in a 15-fold increase in the measured visco-elastic properties. However, the number of grain bonds per unit mass increased linearly by a factor in the range 1.5 to 2 while the average grain-bond size remained constant. It is concluded that only a fraction of the grain bonds in a snow sample transmit an applied stress, and that the new grain bonds formed during the deformation of a snow sample determine the visco-elastic properties of snow. The hypothesis that chains, defined as series of stress-bearing grains, are the basic units of snow structure is developed. Semi-quantitative calculations developed from the chain concept explain the observed variations in the visco-elastic properties.

The recovery of past climatic conditions from ice-sheet borehole temperatures can best be accomplished using the calculus of variations (control methods) to minimize mismatch between the observed profile and a solution of the heat equation which depends on the unknown climate history. Here, we use control methods and a simple one-dimensional heat equation and the temperature depth profile observed at Dye-3 to infer the surface temperature of south Greenland over the last 30 000 years. This history illustrates the virtues that recommend control methods for future use in borehole-temperature analysis, namely: (i) it meets objective performance criteria, and (ii) its uncertainty can be established quantitatively. Our inferred climate history displays what may be the Younger Dryas cold event at about 9000 years BP. Borehole paleothermometry by control methods may thus resolve the controversy concerning the interpretation of Greenland ice-core isotope records.

Fifteen synthetic aperture radar (SAR) images of the Ronne Ice Shelf (also referred to as the Filchner-Ronne Ice Shelf), Antarctica, obtained by the European remote-sensing satellites ERS-1 and -2, are used to study ice-shelf dynamics near two ends of the iceberg-calving front. Interferograms constructed from these SAR images are used to resolve the ice-shelf displacement along several directions in response to both ocean tide and long-term creep flow. Tidal motion is separated from creep flow using differential interferometry, i.e. two or more interferograms in which fringe patterns common to all are predominantly associated with creep flow. Creep-flow velocities thus determined compare well with prior ice-shelf velocity surveys. Using these data, we studied the influence of large-scale rifts, ice rises and coastal separation on the ice-shelf flow. Many of the large rifts that appear to form the boundaries where tabular icebergs may eventually detach from the ice shelf are filled with a melange of sea ice, ice-shelf debris and wind-blown snow. The interferograms show that this melange tends to deform coherently in response to the ice-shelf flow and has sufficient strength to trap large tabular ice-shelf fragments for several decades before the fragments eventually become icebergs. In many instances, the motion of the tabular fragments is a rigid-body rotation about a vertical axis that is driven by velocity shear within the melange. Tfhe mechanical role of the rift-filling melange may be to bind tabular ice-shelf fragments to the main ice shelf before they calve. This suggests two possible mechanisms by which climate could influence tabular iceberg calving. First, spatial gradients in oceanic and atmospheric temperature may determine where the melange melts and, thus, the location of the iceberg-caking margin. Second, melting or weakening of ice melange as a consequence of climate change could trigger a sudden or widespread release of tabular icebergs and lead to rapid ice-shelf disintegration.

Measurements of ice deformation at the surface and at depth in the Athabasca Glacier, Canada, reveal for the first time the pattern of flow in a nearly complete cross-section of a valley glacier, and make it possible to test the applicability of experimental and theoretical concepts in the analysis of glacier flow. Tilting in nine bore holes (eight holes essentially to the bottom at depth about 300 m) was measured with a newly developed electrical inclinometer. The new instrument permitted bore-hole configurations to be determined with greater speed and accuracy than possible with earlier methods. The measurements define the distribution of the velocity vector and the strain-rate tensor over about 70% of the area of the glacier cross-section.

The main longitudinal component of flow has the following general features: (1) basal sliding velocity which exceeds 70% of the surface velocity over half of the width of the glacier, (2) marginal sliding velocity (not more than a few meters per year) much less than basal sliding velocity at the center-line (about 40 m a-1), (3) marginal shear strain-rate near the valley walls two to three times larger than the basal shear strain-rate near the center-line (0.1 a-1).

The observed longitudinal flow is significantly different from that expected from theoretical analysis of flow in cylindrical channels (Nye, 1965). The relative strength of marginal and basal shear strain-rate is opposite to that expected from theory. In addition, the longitudinal flow velocity averaged over the glacier cross-section (which determines the flux of ice transported) is larger by 12% than the average flow velocity seen at the glacier surface, whereas it would be essentially the same if the theoretical prediction were correct. These differences are caused to a large extent by the contrast between the actual distribution of sliding velocity and the constant sliding velocity for which the theoretical analysis holds. The observed relation between marginal and basal sliding velocity is probably a general flow feature in valley glaciers, and may be caused by lateral variation of water pressure at the ice-rock contact. The observed pattern of longitudinal velocity over the section also shows in detail certain additional features incompatible with the theoretical treatment, even after the difference in boundary conditions (distribution of sliding velocity) is taken into account.

Longitudinal strain-rate (a compression of about 0.02 a-1 at the surface) decreases with depth, becoming nearly o at the bed in the center of the glacier, which confirms a prediction by Savage and Paterson (1963). The depth variation cannot be explained completely by overall bending of the ice mass as a result of a longitudinal gradient in the curvature of the bed, and is at variance with existing theories, which require the longitudinal strain-rate to be constant with depth.

Motion transverse to the longitudinal flow occurs in a roughly symmetric pattern of diverging margin-ward flow, with most of the lateral transport occurring at depth in a fashion reminiscent of extrusion flow. The observed lateral velocities averaged over depth (up to 1.9 m a-1) are compatible with the lateral flux required to maintain equilibrium of the marginal portions of the glacier surface under ablation (about 3.7 m of ice per year) and are driven by the convex lateral profile of the ice surface.

During the June-August 1976 Quelccaya ice cap expedition, global, SW↓, and net long-wave radiation, LW↑↓, were measured through several complete day-night cycles, and for a wide range of cloudiness conditions. Field work further included albedo measurements along representative transects across the ice cap and lysimeter-type estimates of ablation. Automatic stations recording wind, temperature and sunshine duration were also installed.

Daily totals of SW↓ and LW↑↓ representative of completely clear and overcast days are derived. On this basis, empirical relationships allow the computation of monthly totals of radiation fluxes for an entire year from records of sunshine duration and temperature expected from the automatic stations.

The larger part of the plateau is situated above 5400 m and has an albedo mostly in excess of 80%. Sub-freezing temperatures essentially limit ablation to the energetically expensive sublimation. For clear sky, daily totals of SW↓and LW↑↓ are of the order of 312 and 53 W m–2, respectively. With the albedo found, net short-wave radiation SW↑↓ becomes of the same general magnitude as LW↑↓, and the energy left for ablation is near to nil. Cloudiness would reduce both SW↑↓ and LW↑↓, thus largely compensating the effect on the residual net radiation, SWLW↑↓. This is consistent with ablation measurements. Over the larger area of the ice plateau, ablation may be close to zero in a first approximation; some ablation, including melting, takes place near the lower-lying rim of the ice cap, and calving off steep cliffs seems to provide a major mechanism for the disposal of the ice mass.

The rapid formation of glacial lakes is one of the most conspicuous landscape changes caused by atmospheric warming in glacierised regions. However, relatively little is known about the history and current state of glacial lakes in the High Arctic. This study aims to address this issue by providing the first inventory of glacial lakes in Svalbard, focusing in particular on the post-Little Ice Age evolution of glacial lakes and their typology. To do so, we used aerial photographs and satellite imagery together with archival topographic data from 1936 to 2020. The inventory comprises the development of 566 glacial lakes (146 km2) that were still in direct contact with glaciers during the period 2008–2012. The results show a consistent increase in the total area of glacial lakes from the 1930s to 2020 and suggest an apparent link between climatic and geological factors, and the formation of specific lake dam types: moraine, ice, or bedrock. We also detected 134 glacial lake drainage events that have occurred since the 1930s. This study shows that Svalbard has one of the highest rates of glacial lake development in the world, which is an indicator of the overall dynamics of landscape change in the archipelago in response to climate change.

Complex unconformable englacial stratigraphy, including a segment of distinctive cosets of bed sequences, occurs throughout the thickness of a 3.2 MHz ice-sheet radar profile we acquired across the upper Byrd Glacier (East Antarctica) catchment. Some cosets span >10 km, are >100 m thick and are delineated by distinct horizons. At 40-90 m depth in firn, comparisons between 200 MHz and specially processed 3.2 MHz profiles reveal that the delineating horizons result from density-modified layers produced by decades to millennia of subaerial exposure, as detailed in our related paper (Part I). These comparisons, together with reflected waveforms at depth, also reveal that the modified layers retain their chemical stratification, and therefore the original unconformable surface. Two profile segments show high-amplitude transverse folds spanning much of the ice-sheet thickness. The parallel nature of most of them suggests basal sliding beneath long-term up-ice-flow accumulation zones, which we identify in satellite images as the likely sources for the cosets. The unconformable stratigraphy at depths greater than 2000 m shows that antidunal deposition and intense firn recrystallization zones have persisted for tens of thousands of years in this region of East Antarctica.