With the conclusion of the Last Glacial Maximum (LGM), about 20 000 years ago, ended the most recent long-lasting cold phase in Earth history. This last glacial advance left a strong observable imprint on the landscape, such as moraines, trimlines and other glacial geomorphic features. These features reflect the extent of former glaciers and ice caps, which in turn provides information on past temperature and precipitation conditions. Here we present an inverse approach to reconstruct the equilibrium line altitudes (E) from observed ice extents. The ice-flow model is developed solving the mass conservation equation using the shallow ice approximation and implemented using Graphical Processing Units (GPUs). We present the theoretical basis of the inversion method, which relies on a Tikhonov regularization, and demonstrate its ability to constrain spatial variations in mass balance with idealized and real glaciers.

Ice IV, a wholly metastable ice phase, has a structure based on a framework of tetrahedrally hydrogen-bonded water molecules in a rhombohedral unit cell. The structure involves two non-equivalent types of water molecules and four non-equivalent types of hydrogen bonds. A novel structural feature is a hydrogen bond that passes through the center of a 6-ring of water molecules and links non-adjacent structural layers. The bond network is proton-disordered, even after quenching.

A method is described for preparing the surface of ice and for forming etch pits on the prismatic surfaces with whisker replicas that correspond to basal dislocations. The technique removes the ambiguity sometimes associated with etch pits and dislocations, and allows direct observation of dislocation glide, pile-up against barriers, and other features in deformed ice.

The structure and flow field in the margin of the Barnes Ice Cap was determined through observations on the ice-cap surface, in four bore holes, and in a 125 m ice tunnel. A band of fine bubbly white ice with a single maximum fabric appears at the glacier surface about 160 m from the margin. This band is overlain by coarse blue ice with a four-maximum fabric, and underlain by alternating bands of fine ice with a single-maximum fabric and moderately coarse ice with a two or three-maximum fabric.

The effective strain rate was determined from the bore-hole and tunnel deformation data, and possible variations in the other three parameters in Glen’s flow law, , were studied. It appears that τxy is independent of depth near the surface, and that relative to the coarse blue ice, A is 40 to 50% lower in the white ice and possibly 10% lower in the fine blue ice.

Dips of foliation planes decrease rapidly with increasing depth and distance from the margin. This foliation is assumed to have developed near and parallel to the bed some distance from the margin. An analysis based on this assumption predicts the observed change in dip, but suggests that it did not develop under the present flow field. The ice cap was probably thicker a few tens of years ago, and the observed foliation pattern may be a relict from that time.

A common technique for simulating non–Newtonian fluid dynamics, such as snow avalanches, is to solve the Shallow Water Equations (SWE), together with a rheological model describing the momentum dissipation by shear stresses. Friction and cohesion terms are commonly modelled using the Voellmy friction model and, recently, the Bartelt cohesion model. Here, an adaptation of the Roe scheme that ensures the balance between the flux and pressure gradients and the friction source term is presented. An upwind scheme was used for the discretisation of the SWE numerical fluxes and the non–velocity-dependent terms of the friction–cohesion model, whereas a centred scheme was used for the velocity-dependent source terms. The model was tested in analytically solvable settings, laboratory experiments and real cases. In all cases, the model performed well, avoiding numerical instabilities and achieving stable and consistent solution even for an avalanche stopping on a sloping terrain.

We have adapted inexpensive ultrasonic rangefinders to measure ablation rates on the surface of a glacier. While ultrasonic rangers are commercially available for this purpose, our goal was to utilize rangefinders typically used in hobby robotics without significantly compromising performance. To correct for environmental factors that affect the speed of sound we use two ultrasonic rangefinders, one focused on a fixed target. Measurements of ablation correlate well with manual measurements with an uncertainty of about ±3 cm, suggesting an accuracy comparable with other non-manual methods of recording ablation. The limitations of our rangefinder include those inherent in commercially available units as well as having less acoustical power, which results in a reduced effective range of the sensor (~2 m) and difficulties in detecting surfaces lying below low-density snow. Our sensor design provides a cost-effective means of increasing the spatial coverage of ice ablation measurements.

Blue Glacier has an area of 4.3 km.2, a volume of 0.57 km.3, a mean density of 0.88 g. cm.−3 and an altitude range of 1,275 to 2,350 m. above sea-level. It is an active temperate glacier in a strongly maritime climate where the net budget gradient varies from 10 mm. m.−1 in the ablation zone to 7 or 8 mm. m.−1 in the accumulation zone. There is a very large snow accumulation each winter and a large snow melt each summer which exceeds by several times the ice melt. The annual mass budget is strongly influenced by altitudes of the freezing level during spring and autumn storms, for these determine whether the heavy precipitation falls as rain or snow. Recent glacier variations are quantitatively consistent with climate trends but there is no clear cause-and-effect relation. Since 1958 the glacier has been gaining mass by an average of 0.4 per cent per year.

We have mapped the full crystallographic orientation of sea ice using electron backscatter diffraction (EBSD). This is the first time EBSD has been used to study sea ice. Platelet ice is a feature of sea ice near ice shelves. Ice crystals accumulate as an unconsolidated sub-ice platelet layer beneath the columnar ice (CI), where they are subsumed by the advancing sea–ice interface to form incorporated platelet ice (PI). As is well known, in CI the crystal preferred orientation comprises dominantly horizontal c-axes, while PI has c-axes varying between horizontal and vertical. For the first time, this study shows the a-axes of CI and PI are not random. Misorientation analysis has been used to illuminate the possible drivers of these alignments. In CI the misorientation angle distribution from random pairs and neighbour pairs of grains are indistinguishable, indicating the distributions are a consequence of crystal preferred orientation. Geometric selection during growth will develop the a-axis alignment in CI if ice growth in water is fastest parallel to the a-axis, as has previously been hypothesised. In contrast, in PI random-pair and neighbour-pair misorientation distributions are significantly different, suggesting mechanical rotation of crystals at grain boundaries as the most likely explanation.

Our knowledge of ice avalanches is very limited in comparison to snow avalanches, for obvious reasons. Ice avalanches are restricted to remote areas with glaciers, whereas snow avalanches may occur in the middle of inhabited regions. Consequently, the economic importance of the two types of avalanches is quite different. Also the efforts and expenditure required to study them are different.

Two classes of ice avalanches may be discerned (with no sharp dividing line between them). A common form occurs on steep glacierized slopes below ice cliffs, from which ice breaks off at intervals. The avalanche debris remains on the glacier and can either be reincorporated or can form a regenerated glacier tongue. This is the type of ice avalanche primarily noticed by mountaineers because of the hazards involves, although little seems to have been done in the way of glaciological studies. A second class of ice avalanches consists of events more akin to landslides where a considerable portion of a glacier falls off a steep part of the bed and moves beyond the original position of the glacier onto ice-free ground, sometimes with disastrous effects. Through such glacier catastrophes, which are fortunately very scarce, more intensive glaciological studies have been initiated. The individual case histories serve best to illustrate the various problems related to ice avalanches.

The Altels avalanche of 11 September 1895, thoroughly documented by Heim (1896), can be regarded as a slab of ice sliding off a uniform inclined plane. It is remarkable for its size of 4.5 × 106 m3, its simple geometry at the origin, its equally simple trajectory involving a jump through the air, and the fact that in 1782 a similar avalanche had occurred. The slope of the bed at the origin was 30° to 32°, the mean ice thickness was 25 m (with a maximum of 40 m). No apparent signs had been noticed in the days preceding the catastrophe. The Altels avalanche provides one of the few sources of reliable empirical parameters in relation to ice stability and ice-avalanche dynamics.

The Allalingletscher avalanche of 30 August 1965 hitting the Mattmark construction site was of a very different origin. It occurred when about 106 m3 of ice broke off at the snout of the glacier during a surge-like active phase of a larger mass of some 3×106 m3. Since this event, it has been established that such active phases occur periodically at Allalin once every 1-3 years, alternating with quiescent periods. During the active phase, the fast motion sometimes starts in summer or autumn and comes to a halt in November or December. The active phase seems to depend on the presence of melt water and also on mass distribution. A direct effect of high water pressure in a communicating drainage system at the bed can be excluded, however. The surge-like motion appears to have been a prerequisite for the ice avalanche of 1965, but it does not give a sufficient explanation of the event, when one considers the frequent occurrence of active phases without a concurrent major ice avalanche at Allalin and elsewhere. It is conceivable that in 1965 a large dome-shaped cavity had formed below a particular rock knob and that the collapse of the dome then triggered the avalanche, but other forms of static instability at high speed of bed slip, developing because of a specific bed morphology and mass distribution, may equally be envisaged.

In the case of a hanging glacier on the Weisshorn, the village of Randa was severely damaged in 1819 by a very large avalanche approximately 13 x 106 m3 consisting mainly of snow but having been triggered by falling ice. This led to a detailed study in 1972/73 of a seemingly threatening situation. A volume of approximately 5 × 106 m3 of ice (firn) was accelerating in a characteristic way on a very steep slope of about 45°. Rough estimates showed that the acceleration was too large to be accounted for by frictional heating alone; a fracture mechanism had instead to be invoked to play the decisive role (besides possible recrystallization). A hyperbolic law has been found to fit best the data on change of velocity with time (Flotron, see the following abstract).

The Huascaran catastrophes of 1962 and 1970 have been some of the most disastrous events in glaciological history. In 1962 a true ice avalanche appears to have been the cause of a giant mudflow (Morales, 1966). For the first time in at least several hundred years a large volume, estimated at 2.5 to × 106 m3, broke off simultaneously over the full length of an ice cliff, 800 m long and 50 to 60 m high. It is an open question as to how this could happen. The mudflow was formed by mixing of the ice with rock and soil picked up along the course of the avalanche, bringing the total volume ot some 13 × 106 m3. In this process part of the ice was melted. The 1970 incident was not an ice avalanche proper, but rather a giant landslide caused by an earthquake, in which the ice played an important role in the form of a source of water causing lubrication and liquefaction.

The above examples constitute a diversity of problems which could be augmented further by additional cases. A certain order may nevertheless be brought to the subject of ice avalanches by looking at it from a practical point of view. The main objective is to look for means by which damage to property can be reduced and loss of life avoided.

The basic question is the one of stability of a large ice mass on a steep slope. The problem seems to be simple enough, but a closer inspection shows that the time scale and the unknown factors are such that laboratory results of, for example, strength are of no avail. On an empirical basis it can be noticed that temperate glaciers have become unstable on a slope of about 30°, while the limiting slope of cold glaciers is about 45°. The distribution and development of crevasses and, more generally, the flow pattern can help to delineate an acutely unstable ice mass. A special condition is the occurrence of a surge-like active phase which should be taken as an indication that part of the fast moving ice may slide off. There is a basic rule applicable to all types of ice avalanches, that if a particular one has occurred once it will happen again in a similar way; unfortunately our records do not extend sufficiently far back to allow us to depend on this rule very often.

The probable extent of the danger zone is of equal practical importance. Experience has shown that after an initial phase the ice becomes completely broken up so that snow-avalanche dynamics can be applied to estimate how far the debris will move, possibly with some modifications for large masses of landslide dimensions. The possibility that snow and loose rock and soil may be added along the path must be taken into account. Secondary effects must also be considered. Amongst these are an air blast, or the formation of destructive water waves in a lake or fjord, or the blockage of a river by a huge ice mass leading to a flood from an ice-dammed lake.

A warning by the glaciologist is hardly taken seriously unless it includes a forecast of the time of final rupture. At present the most promising approach for such a prediction is the almost perfect regularity by which certain large ice masses accelerate for a very long time prior to the instant when the avalanche starts to fall (see the Weisshorn case). The limitation of the forecasts lies as much in short-term irregularities as in the extreme difficulties of obtaining sufficiently accurate data without interruptions, and further in the lack of experience on the critical velocity that is reached immediately before final breakage. The physical explanation of the observed law is another question. Using a finite-element computational model for the analysis of stress and flow in a somewhat different case, Iken (1977) has shown that a stepwise crack extension alternating with phases of flow leads to the observed form of velocity–time relationship.

There are various possibilities in the way of preventive measures; none of them is completely satisfactory, however. The most certain consists in avoiding the danger zone altogether, a solution usually not acceptable to those involved. In view of the requirements necessary for withstanding an impact of exceptional magnitude, protective structures are generally not practical either. A stepwise elimination of the unstable ice mass by blasting could be considered, though the realization would be difficult and not without danger—not to speak of the legal problem encountered if the blasting should trigger the full-size avalanche. Consequently a certain calculated risk will occasionally have to be accepted whereby the dangers during an operation on the glacier and the extreme costs have to be weighed against the severity and small probability of a catastrophe. Viewed in proportion to other risks in everyday life (especially in road and air traffic, but also in relation to earthquakes), the dangers of ice avalanches should not be exaggerated.

Glaciological research can obviously contribute in a variety of ways to the solution of practical problems with ice avalanches, and there are ample opportunities for future studies. Of urgent need are more and better observations on almost every aspect of the problem, extending to phenomena hitherto not observed such as frequency and intensity of seismic signals. The inherent difficulty with the more interesting large-scale events is their scarcity, precluding proper experimentation. Advances in the theoretical treatment are also to be hoped for. There is also room for new ideas, for instance on how to prevent a particular ice mass from forming.

The marginal areas of the Greenland ice sheet develop streams and lakes each summer, documenting that surface runoff of meltwater is a major component of ice-sheet mass balance. Here we map the slush limit, a proxy for the extent of surface runoff, using daily MODIS data for the years 2000–2021. We develop an automated algorithm capable of detecting daily slush limits, provided sufficient image quality. The algorithm is applied to the ice sheet's western flank (61.7 $^{\circ }$N to 76.5 $^{\circ }$N). We find significant increasing trends in maximum slush limits until the year 2012, but not thereafter. We show that the slush limit typically rises quickly early in the ablation season but stabilizes before melting ceases. The data provide evidence that upward migration of surface runoff in summer 2012 stopped early at the upper margin of the ice slabs. These thick and continuous ice layers are located close to the surface, in the firn, and impede percolation of melt into deeper pore space. Had the ice slabs extended higher, the summer 2012 provided sufficient energy to raise the slush limit by another $\sim$300 m in elevation.

Glacier surface albedo dominates glacier energy balance, thus strongly affecting the glacier mass balance. Glaciers in the Western Nyainqentanglha Mountains (WNM) experienced large mass losses in the past two decades, but long-term changes of glacier albedo and its drivers are less understood. In this study, we retrieved glacier albedo with MODIS reflectance data to characterize the spatiotemporal variability of albedo from 2001 to 2020. Air temperature, rainfall, snowfall and deposition of light-absorbing impurities (LAIs) were evaluated as potential drivers of the observed variability in glacier albedo. The results showed that: (1) the glacier albedo experienced large inter-annual fluctuations, with the mean albedo being 0.552 ± 0.002 and a clear decreasing trend of 0.0443 ± 2 × 10−4 dec−1 in the WNM. The fastest decline was observed in autumn and in the vicinity of the equilibrium line altitude, indicating an extended melt season and an expansion of the ablation region to higher elevation; (2) local meteorology and LAIs deposition are the main drivers of glacier albedo change, but their effects on seasonal albedos are different due to different glacier processes. Both air temperature and the balance between liquid and solid precipitation affect summer and autumn albedos due to glacier ablation. Air temperature is the main driver of spring and winter albedos due to sublimation and metamorphism of snow, while snowfall carried by westerlies has limited influence on these two seasonal albedos due to less snowfall. LAIs mainly affect spring albedo due to high concentration coupled with the southerly wind in spring. These findings highlight the significance of changes in glacier albedo and the key role of local meteorology and LAIs deposition in determining such changes, which play an important role in glaciological and cryosphere processes.

Kilometer-scale variations in ice velocity and surface topography are used to investigate the style of glacier deformation in the main body of Ice Stream B, West Antarctica. The pattern is very different from that reported for other glaciers. For the 250 km2 area studied on Ice Stream B, most of the observed deformation occurs within two narrow bands, in which there is large across-flow compression and slow lateral shearing. The bands underlie valleys in the ice-surface topography. Measured upward displacement of ice adjacent to the rapidly compressing bands appears to be linked to the creation of the ice stream’s topography. The most likely cause for the observed pattern of strain rates and surface topography, and their changes over time, is deformation guided by longitudinal bands of ice with an aligned crystal fabric.

Apparatus was built for deforming ice crystals under hydrostatic pressures up to 350 atmospheres. Single crystals were placed in the mounts in such a way that the deformation occurred by gliding on the basal glide plane. It was found that the shear strain rate increased as the pressure was increased at constant temperature, but that the rate is practically independent of hydrostatic pressure when the difference between the ice temperature and the melting temperature is kept constant.

In polar deserts, depth hoar (hereinafter: DH) growth is not systematic unlike on tundra and this is critical for snowpack properties. Here, we address the spatio-temporal variability of the DH layer in the polar desert at two sites in the Canadian High Arctic: Ward Hunt Island (83° N) and Resolute Bay (75° N). Our data show that, over humid areas, DH represented a larger fraction of the snowpack and was characterized by lower density and coarser crystals than over dry gravelly areas. Increased soil moisture extends the zero-curtain period during freeze-up, leading to stronger temperature gradients in the snowpack and greater kinetic metamorphism. Our results also demonstrate that the large inter-annual variability in DH is primarily driven by wind conditions in the fall since this key variable controls the initial snow density and snow onset date. These strong controls exerted by soil moisture and meteorological conditions on DH growth in polar deserts highlight the possibility of major changes in polar snowpacks physical properties in response to the rapid climate and environmental changes currently affecting these regions.

Side-looking airborne radar (SLAR) imagery obtained in April-May 1974 from the North Slope of Alaska between Barrow and Harrison Bay indicates that tundra lakes can be separated into two classes based on the strength of the radar returns. Correlations between the areal patterns of the returns, limited ground observations on lake depths and water compositions, and information obtained from LANDSAT imagery strongly suggest that areas of fresh-water lakes giving weak returns are frozen completely to the bottom while areas giving strong returns are not. This is a reasonable interpretation inasmuch as the reflection coefficient associated with the high-dielectric-contrast ice-water interface would be roughly twelve times that associated with the low-contrast ice-soil interface. Brackish lakes also give weak returns even when they are not completely frozen. This is the result of the brine present in the lower portion of the ice cover limiting the penetration of the X-band radiation into the ice. The ability to separate tundra lakes rapidly and easily into these two classes via SLAR should be useful in understanding a wide variety of problems.

A preliminary assessment of the daily variation of ice albedo in the 285-2 800 nm range was made using field data collected over snow ice and refrozen slush. Significant diurnal variations could be attributed to changing low solar altitude under clear skies or to decay of the ice surface. Changes in albedo due to changes in cloud cover were observed for the most part to be slight. The measurements provide a base for a program of wider scope which would consider other types of ice under a variety of natural conditions.

Optical measurements have been made on the water lenses which form under pressure at grain boundaries in polycrystalline ice. Monochromatic light from a point source is focused by the lenses but, because the lenses are microscopic in size, the image is blurred by diffraction. The diffraction pattern observed under a microscope has been compared with the computed diffraction pattern to deduce the angle 2θ at the rim of each lens. This is the dihedral angle for water at a grain boundary in ice, and gives the ratio of the grain-boundary energy to that of an ice-water interface. The most sensitive measurements are those made on the rings of the virtual diffraction pattern formed on the object side of the lens. They give θ = 12.5 ± 0.5° for the grain boundary under observation, which is 26% lower than the previous value for θ found by ignoring diffraction.

Ice temperature data collected from the area of continental–type glaciers in China since 1959 are analysed. Formulae for the temperature stratification of the active layer and for annual mean temperature profiles are suggested. The temperature in continental–type glaciers in China is quite low, rising rapidly with depth. A major part of the bottom of most glaciers reaches the pressure–melting point, with basal sliding. The extreme huge valley glacier will change from a cold glacier into a temperate one when it descends to the district where the climate is temperate. The ice temperature of the lower bound of the active layer at the altitude of the equilibrium line is 1.8–3.7 deg higher than the annual mean air temperature at the same level. The western section of Ch’i–licn Shan (Qilian Shan) may be the place where the temperature of alpine glaciers is the lowest of the middle and low latitudes. The infiltration zone is warmed significantly by the infiltration and recongelation process. A scheme showing how the lower bound temperature of the active layer changes with glacial zones is drawn.

Le régime des températures dans les glaciers de type continental en Chine. On analyse les températures de la glace recueillies sur glaciers de type continental en Chine depuis 1959. On a suggéré des formules pour rendre compte de la stratification des températures du niveau actif, et pour le profil de température moyenne annuelle. La température dans les glaciers de type continental en Chine est très basse, s’élevant rapidement en profondeur. La plus grande partie du fond, dans la plupart des glaciers atteint le point de fusion correspondant à la pression, avec glissement sur le fond. Un très grand glacier de vallée se transforme de glacier froid en glacier tempéré lorsqu’il aborde une région où le climat est tempéré. La température de la glace à la limite inférieure du niveau actif, à l’altitude de la ligne d’équilibre est de 1,8 à 3,7 deg supérieure à la température moyenne annuelle de l’air à la même altitude. La section occidentale du Ch’i–lien Shan (Qilian Shan) est peut être l’endroit où la température d’un glacier alpin est la plus basse dans les latitudes moyennes et basses. La zone d’infiltration est, de manière significative, réchauffée par un processus d’infiltration et de regel. On a dressé un schéma montrant les variations de la température de la limite inférieure du niveau actif avec les zones de glaciations.

Über den Wärmehaushalt der kontinentalen Gletscher in China. Die Beobachtungen der Eistemperaturen aus dem Gebiet der kontinentalen Gletscher in China seit 1959 werden analysiert. Formeln fūr die Temperaturschichtung im aktiven Eis und fūr ein Profil der Jahresmitteltemperalur werden vorgelegt. Hie Temperatur in den kontinentalen Gletschern Chinas ist sehr niedrig, steigt jedoch schnell mit der Tiefe. Ein Grossteil der Grundschicht in den meisten Gletschern befindet sich auf dem Druckschmelzpunkt und gleitet am Untergrund. Extrem mächtige Talgletschcr wandeln sich von kalten zu temperierten Gletschern, wenn sie in den Bereich temperierten Klimas herabfliessen. An der unleren Grenze des aktiven Schichts in Höhe der Gleichgewichtslinie ist die Temperatur 1.8-3.7 deg höher als die Jahresmitteltemperatur in derselben Höhe. Der Westteil des Ch’i-lien Shan (QMian Shan) dūrfte der Ort sein, wo alpine Gletscher der mittleren und niedrigen Breiten ihre tiefste Temperatur erreichen. Die Sickerzone wird durch das Sickerwasser und die Wiedergerrierwärme beträchtlich erwärmt. Eine schematisch Darstellung zeigt die Veränderung der Temperatur der Untergrenzc des aktiven Schichts innerhalb der vergletscherten Zonen.

The steady-state flow model of Reeh (1988) is applied to a flow line that starts at the highest point of the Devon Island ice cap, follows the surface crest for 7.6 km, and then runs down the slope for a further 3.7 km. The effects of bedrock undulations, divergence of the flow lines, the variation of temperature with depth, and a basal layer of “soft” ice-age ice are taken into account. A flow law with n = 3 and a value of A close to that of Paterson (1981) is used. Longitudinal stress variations are neglected so that shear stress is calculated by the usual formula. It is estimated that these calculated values may be in error by at most 30%. Depth profiles of effective shear stress, and of the components of velocity and normal strain-rate, are presented at selected points along the flow line. These illustrate the large variations that occur near an ice divide and over bedrock undulations of amplitude comparable with the mean ice thickness. The model gives good predictions of the surface profile and of longitudinal and transverse surface strain-rates measured at ten points along the flow line. Predicted depth profiles of horizontal and vertical velocity components are compared with those measured in a bore hole. Comparison is limited by the fact that the model works in ice equivalent, whereas about 20% of the ice column consists of firn with different rheological properties from ice. The vertical velocity prediction is good. However, the model does not reproduce well the shape of the horizontal velocity profile, although measured and calculated fluxes differ only slightly. Predicted annual-layer thicknesses are within 15% of the measured ones in the upper half of the ice column, which consists of ice deposited in the last 1000 years. Predicted thicknesses in older ice are too small and the discrepancy increases with depth. This might indicate increased precipitation or, more likely, a thinner ice cap in the climatic optimum. However, it could also result from the fact that the layer of “soft” ice has been thinning continuously since the end of the ice age, so that the ice cap has never been in a steady state.

Coefficients of absorption of visible radiation are determined for sea ice and snow as a function of porosity of the medium and wave-length of energy refracted into it. A comparison is made between the values derived and those obtained by other investigators under similar snow conditions. A difference in results suggests a significant rôle of crystal size and orientation in the absorption properties of sea ice and snow.