A one-dimensional time-dependent flowline model of Rhonegletscher, Switzerland, has been used to test the glacier’s response to climatic warming. Mass-balance variations over the last 100 years are obtained from observations of the equilibrium-line altitude (ELA) and a reconstruction of the ELA based on a statistical correlation between temperature and ELA. For the period prior to AD 1882, for which no reliable climate data exist, we chose equilibrium-line altitudes that enabled us to simulate accurately the glacier length from AD 1602.

The model simulates the historical glacier length almost perfectly and glacier geometry very well. It underestimates glacier-surface velocities by 1-18%. Following these reference experiments, we investigated the response of Rhonegletscher to a number of climate-change scenarios for the period AD 1990-2100. For a constant climate equal to the 1961-90 mean, the model predicts a 6% decrease in glacier volume by AD 2100. Rhonegletscher will retreat by almost 1 km over the next 100 years at this scenario. At a warming rate of 0.04 K a-1, only 4% of the glacier volume will be left by AD 2100.

During the last few decades, the lake-terminating glaciers in the Himalaya have receded faster than the land-terminating glaciers as proglacial lakes have exacerbated the mass loss of their host glaciers. Monitoring the impacts of glacier recession and dynamics on lake extent and water volume provides an approach to assess the mass interplay between glaciers and proglacial lakes. We describe the recession of Longbasaba Glacier and estimate the mass wastage and its contribution to the water volume of its proglacial lake. The results show that the glacier area has decreased by 3% during 1988–2018, with a more variable recession prior to 2008 than in the last decade. Longbasaba Lake has expanded by 164% in area and 237% in water volume, primarily as a result of meltwater inflow produced from surface lowering of the glacier. Over the periods 1988–2000 and 2000–18, the mass loss contributed by glacier thinning has decreased from 81 to 61% of the total mass loss, accompanied by a nearly doubled contribution from terminus retreat. With the current rate of retreat, Longbasaba glacier is expected to terminate in its proglacial lake for another four decades. The hazard risk of this lake is expected to continue to increase in the near future because of the projected continued glacier mass loss and related lake expansion.

To understand the dynamics of ice shelves, a knowledge of their internal and basal structure is very important. As the capacity to perform local surveys is limited, remote sensing provides an opportunity to obtain the relevant information. We must prove, however, that the relevant information can be obtained from remote sensing of the surface. That is the aim of this study. The Jelbart Ice Shelf, Antarctica, exhibits a variety of surface structures appearing as stripe-like features in radar imagery. We performed an airborne geophysical survey across these features and compared the results to TerraSAR-X imagery. We find that the stripe-like structures indicate surface troughs coinciding with the location of basal channels and crevasse-like features, revealed by radio-echo sounding. HH and VV polarizations do not show different magnitude. In surface troughs, the local accumulation rate is larger than at the flat surface. Viscoelastic modelling is used to gain an understanding of the surface undulations and their origin. The surface displacement, computed with a Maxwell model, matches the observed surface reasonably well. Our simulations show that the surface troughs develop over decadal to centennial timescales.

The distribution of velocity along a vertical line in Greenland is calculated. Almost all the relative shear motion is concentrated at and very near to the bottom, and this result is thought to apply generally in Greenland and Antarctica. It is due to the relatively high temperature of the lowest layers and the strong dependence of creep rate on temperature. The outward velocity being thus almost constant with depth, it is assumed proportional to the mth power of the shear stress on the bed; the results previously obtained by the approximation of perfect plasticity then correspond to m→∞. Steady-state solutions for finite m are derived, and non-steady states are discussed by use of Weertman’s perturbation method. The steady-state height of an ice sheet is found to be very insensitive to the rate of accumulation. Surface waves in Antarctica are attributed to mountains buried beneath the ice, and it is shown how the height and form of a buried mountain ridge may be calculated from the associated surface disturbance.

The application of a law of sliding to glaciers leads to an expression for the longitudinal strain-rate, hitherto an undetermined parameter.

In the summers of 1993, 1994 and 1995, video and Global Positioning System location data and 35 mm photographs were collected in a series of systematic survey flights undertaken over the Bering Glacier and Bagley Ice Field system (Alaska) in an effort to characterize surge-crevasse patterns and surge propagation. During survey flights in late August 1995, we observed that the 1993–94. Bering Glacier surge was continuing and still expanding affecting new areas farther up in Bagley Ice Field. New crevasse fields, similar in pattern to the first surge crevasses we had observed in June 1993 below Khitrov Hills and in other isolated areas of central Bering Glacier and in July 1994 near the head of Bering Glacier (near the junction of Bering Glacier and Bagley Ice Field, in both upper Bering Glacier and Bagley Ice Field), were opening in eastern Bagley Ice Field and in the “Stellet” side of Bagley Ice Field. The type of crevasses seen in the new fields suggested that the surge was propagating into these areas. By analysis and interpretation of the brittle-deformation patterns apparent in the crevasse patterns, some aspects of the past kinematic framework of the surge can be deduced. This approach may lead to a more general classification of ice-surface structures and to their linkage to ongoing processes.

Water is present in glaciers in the form of veins at the three-grain junctions. This water remains unfrozen even many degrees below the normal freezing point, mainly because it contains much of the soluble impurity content of a glacier, but also because of the microscopic curvature of the ice–water interfaces. As the temperature is lowered and the veins shrink, the concentration of impurities in them increases, and the curvature effect also increases. The predicted relation between vein size and temperature has now been verified by laboratory experiments.

Because of the latent heat of the vein water, the ice behaves macroscopically as a continuum with an anomalous specific heat capacity that depends strongly on temperature. From this point of view, a polythermal glacier is a single medium with continuously varying properties, rather than consisting of distinct cold and temperate phases with sharp boundaries between them. The paper sets up differential equations for heat diffusion in such a continuum. To explain the local uniformity of the vein system seen under the microscope, it is found necessary to include the effect of diffusion of solutes along the veins.

Solutions are presented for a model in which two semi-infinite slabs, initially having different temperatures, impurity concentrations and vein sizes, are instantaneously brought into contact. In this way, transition thicknesses between cold and temperate ice are estimated, and also the velocities of various kinds of waves that are generated from the original discontinuity at the interface.

During the North Water Project of the late F. Müller, glaciological studies were carried out on Laika ice cap. In addition to the main climatological investigations, surveying, mapping, mass-balance studies, and englacial temperature measurements were carried out. The mass-balance distribution is strongly determined by the orography. Strong westerly winds erode and transport snow from exposed surfaces, whereas prevailing easterly winds, during precipitation, deposit snow on lee slopes. The balance is negative under the present climate. The history of the glacier-tongue geometry is reconstructed using geomorphological observations and photogrammetric mapping for 1959 and 1971. Englacial temperature measurements revealed a finite layer of temperate basal ice in the ablation zone. The temperature distribution in the accumulation area around the summit of the ice cap is not stationary.

A simple model uses once-daily meteorological values in the U.S. National Centers for Environmental Prediction and U.S. National Center for Atmospheric Research (NCEP–NCAR) re-analysis database to estimate summer balance of South Cascade Glacier, Washington, U.S.A., each year over 1959–99. The rms error, 0.30 m w.e. (r2 = 0.71), is comparable to measurement error. The model relates summer balance linearly to temperature T > 0°C at 2000 m andto snow flux at 1650 m, the altitudes in recent years of the equilibrium line and terminus. The snow flux is the product of the humidity and westerly wind component at 850 hPa when temperature T <+2°C at 1650 m. Temperatures are interpolated linearly between the 850 and 700 hPa levels. Both the positive 2000 m temperature and the snow flux are summed from 26 April to 4 October. When the summer estimates are combined with those from a winter balance model using the same database, the rms error in estimating net balance is 0.40 m (r2 = 0.81). The indicated sensitivities of balance to warming of 1°C are −0.51 m for summer and −0.24 m for winter. On the assumption that the total −0.75 m °C−1 sensitivity exists at all altitudes, a warming of only 0.7°C would be sufficient to overcome the 1986–98 average net balance +0.5 m at the top of the glacier.

Accurately estimating winter surface mass balance on glaciers is central to assessing glacier health and predicting glacier run-off. However, measuring and modelling snow distribution is inherently difficult in mountainous terrain. Here, we explore rigorous statistical methods of estimating winter balance and its uncertainty from multiscale measurements of snow depth and density. In May 2016, we collected over 9000 manual measurements of snow depth across three glaciers in the St. Elias Mountains, Yukon, Canada. Linear regression, combined with cross-validation and Bayesian model averaging, as well as ordinary kriging are used to interpolate point-scale values to glacier-wide estimates of winter balance. Elevation and a wind-redistribution parameter exhibit the highest correlations with winter balance, but the relationship varies considerably between glaciers. A Monte Carlo analysis reveals that the interpolation itself introduces more uncertainty than the assignment of snow density or the representation of grid-scale variability. For our study glaciers, the winter balance uncertainty from all assessed sources ranges from 0.03 to 0.15 m w.e. (5–39%). Despite the challenges associated with estimating winter balance, our results are consistent with a regional-scale winter-balance gradient.

The high-Alpine ice-core drilling site Colle Gnifetti (CG), Monte Rosa, Swiss/Italian Alps, provides climate records over the last millennium and beyond. However, the full exploitation of the oldest part of the existing ice cores requires complementary knowledge of the intricate glacio-meteorological settings, including glacier dynamics. Here, we present new ice-flow modeling studies of CG, focused on characterizing the flow at two neighboring drill sites in the eastern part of the glacier. The3-D full Stokes ice-flow model is thermo-mechanically coupled and includes firn rheology, firn densification and enthalpy transport, and is implemented using the finite element software Elmer/Ice. Measurements of surface velocities, accumulation, borehole inclination, density and englacial temperatures are used to validate the model output. We calculate backward trajectories and map the catchment areas. This constrains, for the first time at this site, the so-called upstream effects for the stable water isotope time series of the two ice cores drilled in 2005 and 2013. The model also provides a 3-D age field of the glacier and independent ice-core chronologies for five ice-core sites. Model results are a valuable addition to the existing glaciological and ice-core datasets. This especially concerns the quantitative estimate of upstream conditions affecting the interpretation of the deep ice-core layers.

Until now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

We use a simple energy-conservation model and a model based on Röthlisberger’s theory for steady-state water flow in a subglacial conduit to model water movement between lakes in the Adventure subglacial trench region of East Antarctica during a 1996–98 jökulhlaup. Using available field evidence to constrain the models suggests that water flow would likely be accommodated in a tunnel with a cross-sectional area of 36 m2 and a value for k (the reciprocal of Manning’s roughness parameter) larger than the 12.5 m1/3 s−1 previously calculated. We also use Nye’s theory for time-dependent conduit water flow to model the temporal evolution of conduit discharge, cross-sectional area, water pressure and lake draining and filling during the flood. We initially assume one source and one sink lake. We perform sensitivity tests on the input parameter set, matching modeled source- and sink-lake depth changes with measured surface elevation data. Using a simple function for vertical ice deformation in which surface deformation scales linearly to the lake depth change, we find the scaling factor is of the order 4 × 10−3 of the ice thickness. The most likely value of k lies in the range 55–68 m1/3 s−1, and the ratio of source to sink-lake radii is approximately 1 : 1.4. Finally, we experiment using Nye’s theory to model water movement between one source and three sink lakes. The model fails to produce the observed patterns of water movement as indicated by the surface deformation data.

Lake-ice properties at Lake Abashiri, Hokkaido, Japan, were examined using field observations and a 1-D thermodynamic model to clarify formation processes at mid-latitudes subject to significant snowfall as well as moderate air temperature. At all lake sites examined, the ice comprised two distinct layers: a snow ice (SI) layer on top and a congelation ice (CI) layer below. The SI layer occupied as much as 29–73% of the total ice thickness, a much greater fraction than that reported for lakes at Arctic high latitudes. In the model, the CI growth rate was estimated using the traditional heat budget method, while the SI growth rate was calculated assuming the excessive snowfall from the isostatic balance is converted to SI by a snow compression rate (β) with the surface melting rate added when the surface heat budget becomes positive. By tuning the value of β to the observational results of SI thickness, the model outcome successfully reproduced the observational thicknesses of CI and SI, and the break-up date of the lake. Essentially, the model findings show how snow and its formation into SI reduce, by about half, the seasonal variability of total ice thickness.

Creep tests on homogeneous, isotropic polycrystalline ice gave an apparent activation energy for creep of 16.4 kcal/mol (68.8 kJ/mol) over the temperature range −10° to −60° C. Above −10° C the Arrhenius relation for temperature dependence is invalid, and creep rate becomes progressively more temperature dependent as the melting point is approached. Between −20° and −50° C the apparent activation energy for creep of a single crystal of ice was found to be 16.5 kcal/mol (69.1 kJ/mol). A complete creep curve for a single crystal loaded in uniaxial compression parallel to the basal plane was qualitatively similar to the classical creep curve; creep rate at all stages was very much faster than for polycrystalline ice under the same conditions. Creep tests on polycrystalline ice at 0° C gave a stress/strain-rate relation for that temperature, but its precise meaning is unclear, since recrystallization complicated the results.

A linear stability analysis of a two-dimensional flow of an isothermal ice sheet interacting with the ocean is considered. The set of boundary conditions determining motion of the grounding line is adopted to describe hydrostatic equilibrium of ice in water and a cubic dependence of the mass flow rate on ice thickness. The numerical analysis shows that the zero-growth (zero-eigenvalue) mode found for linear bed slopes and constant accumulation rates indeed determines neutral equilibrium and separates stable and unstable solutions. It is also argued that, provided some conditions of regularity of the solutions are satisfied, finding only one stable and one unstable solution would be enough to ascertain that the condition determining a zero eigenvalue also determines neutral equilibrium. This supports the intuitive understanding of ice-sheet stability: ice sheets are stable on bed slopes that ensure that the mass flow rate at the grounding line increases faster than the cumulative ice accumulation rate at the surface when the grounding line is perturbed; and ice sheets are unstable otherwise.

Large-scale melting phenomena such as meltwater drainage channels and meltwater accumulation basins of frozen lakes were surveyed on the land ice mass in Jutulgryta, Dronning Maud Land, Antarctica, during the Norwegian Antarctic Research Expedition in 1989–90 (NARE 1989–90). The largest frozen lake that was observed was close to 1 km in width. These melting features were also detected in a Landsat Thematic Mapper image recorded on 12 February 1990. Then, during NARE 1993–94, a 5year glaciological programme was started in this area. In spite of negative air temperatures and the presence of a frozen ice surface, sub-surface melting and runoff were found within the uppermost metre in blue-ice fields. The sub-surface melting is a consequence of solar radiative penetration and absorption within the ice, i.e. the “solid-state-greenhouse effect”. Temperatures in blue ice were about 6°C higher than for snow. Internal melt and meltwater transport were observed throughout the 1 month of measurements. The conditions for active melting in Jutulgryta are probably marginal. A slight increase of air temperatures can result in more “classical” surface melting, whereas a cooling may disable sub-surface melting. Studies of how the extent and characteristics of the melting features change with time can be particularly valuable as indicators of climate change. This ongoing programme clearly identifies the importance of analyzing how these melting features originate, of mapping their present areal distribution, of determining how sensitive they are to climate change and of Studying changes in the past and possible changes in the future.

A transverse profile of velocity was measured across Ice Stream B, West Antarctica, in order to determine the role of the margins in the force balance of an active ice stream. The profile extended from near the ice-stream center line, through a marginal shear zone and on to the slow-moving ice sheet. The velocity profile exhibits a high degree of shear deformation within a marginal zone, where intense, chaotic crevassing occurs. Detailed analysis of the profile, using analytical and numerical models of ice flow, leads to the following conclusions regarding the roles of the bed and the margins in ice-stream dynamics:

• (i) The overall resistive drag on the ice stream is partitioned nearly equally between the margins and the bed and, thus, both are important in the force balance of the ice stream.

• (ii) The ice within the chaotic zone must be about 10 times softer than the ice in the central part of the ice stream.

• (iii) The average basal shear stress is 0.06 × 105 Pa. This implies that the entire bed cannot be blanketed by the weak, deformable till observed by Engelhardt and others (1990) near the center of the ice stream — there must be regions of increased basal drag.

• (iv) High strain rates and shear stresses in the marginal zones indicate that strain heating in the margins may be significant.

While the exact quantitative values leading to these conclusions are somewhat model and location-dependent, the overall conclusions are robust. As such, they are likely to have importance for ice-stream dynamics in general.

We have developed a miniature high-power impulse transmitter for radio-echo sounding of glaciers. It features two synchronous second break-down pulse generators operating in a differential configuration. Specifications include bipolar 550 V pulses having rise times less than 2 ns, 512 Hz repetition rate, 180 mA at 10-14 V d.c. operating power, 5 mA standby current and maximum dimension of 12 cm. Because of its small size and low power consumption, the transmitter is suitable for back-portable systems and for towed arrays. The transmitter first saw service in 1990 on Trapridge Glacier, Yukon Territory. Subsequent copies have been used on Agassiz Ice Cap, Northwest Territories, Bering Glacier, Alaska and elsewhere. To date, the maximum ice thickness measured using this transmitter is 825 m, on temperate Bering Glacier.

We assess the accuracy and precision of the U.S. National Science Foundation’s Support Office for Aerogeophysical Research (SOAR) laser profiling system for mapping topography and detecting surface elevation changes of West Antarctic ice streams. The procedures used to process, calibrate and validate the laser, navigation and global positioning system (GPS) data are presented. The primary objective is to produce surface elevations with the best possible resolution. Repeat surveys of a grid of lines over Whillans Ice Stream and Ice Streams C and E were conducted in the 1997/98 and 1999/2000 seasons. The procedure has been calibrated using special test flights conducted over areas that have been surveyed with precise geodetic GPS equipment mounted on snow-mobiles. After calibration, agreement between the two surfaces is ±10 cm rms. The accuracy and precision of the procedure have been evaluated at points where laser flight-lines cross over one another. The accuracy of the system is found to range from 0.09 to 0.22 m.

Differential spaceborne radar interferometry observations of West Bagley Icefield are used to measure surface velocity and topography. Bagley Icefield is the accumulation area fur Bering Glacier which surged in two phases from spring 1993 through summer 1905. The observations presented are based on data collected during the winter of 1992, prior to the surge, and during winter 1994 while the surge was in full progress. Both observation intervals correspond to 3 day repeat orbit phases of the ERS-I C-band SAR. This paper gives an overview of the algorithms used to derive surface-velocity vector fields and topography for valley glaciers from SAR images. The resulting high-resolution velocity data clearly show West Bagley Icefield accelerating from its quiescent pre-surge velocity by a factor of 2.7 in response to the Bering Glacier surge. Persistence of lnterfero-metric phase coherence and the relatively moderate degree of acceleration on the western arm of Bagley Icefield suggest that the velocity increase may have been caused by increased longitudinal stress gradients resulting from coupling to the surging main trunk of Bering Glacier.