A meteorological experiment was carried out during the summer months of 1990 and 1991 near the mean equilibrium-line altitude (ELA) on the western slope of the Greenland ice sheet (ΕΤΗ Camp; 69° 34’ N, 49° 17’ W; 1155 m a.s.l.). As a part of the project, the energy fluxes at the surface, including all components of the radiation balance, atmospheric profiles with a tower and radiosondes, and the cloud conditions were investigated in detail. Results from the radiative fluxes are compared with observations made at other locations in order to derive general characteristics of the radiation conditions on the Greenland ice sheet and their relation to the climate cf the ice sheet.

At ΕΤΗ Camp, albedo values obtained at ground level (2 m) and from a high tower (27 m) are similar during the melt season (late May to mid-August) and slightly different during pre- and post-melt seasons due to the interplay of inhomogeneous surface conditions and solar elevation. During the melt period, the decrease in global radiation due to increasing cloud amount is compensated for by an increase, m longwave incomine, radiation. Because of the steady values of longwave outgoing radiation, net radiation at the surface is characterized mainly by the albedo and its variation. The regional net radiation for summer months on the Greenland ice sheet is determined mainly by three facts: (1) a strong increase in alhedo from the ablation area to the ELA and a smaller increase Gom the ELA to the accumulation area: (2) a large increase in longwave outgoing radiation in the ablation area and at the ELA in June and July compared to the accumulation area: (3) a larger amount of cloud of the stratus type at lower areas.

The climate-modeling problems associated with global change underline the importance of understanding paleoclimates. The available evidence, which suggests that the Earth has never been fully glaciated, poses an especially serious problem for the early Earth when the Sun was about 20–30% fainter than today. In conventional explanations of this “faint young Sun paradox”, presumed very high levels of atmospheric greenhouse gases are required to prevent runaway glaciation of the Earth. Here we explore other possible explanations of this paradox. As an extension of our previous work on this subject, we illustrate how-dynamical beat-flux feed backs may have prevented the early Earth from freezing. Our simulations are carried out using a two-dimensional, seasonal-climate model with physically based parameterizations for atmospheric meridional-heat transport and sea ice. It ís found that dynamical heat-flux feed backs alone may have protected the Archean Earth against a runaway glaciation to a considerable degree.

During the LeadEx main field experiment, held in April 1992 in the Alaskan Beaufort Sea, a number of large ice stalactites were observed growing under young lead ice. Formation of the stalactites was associated with rafting of the thin, highly saline ice. The rafting caused the brine to drain rapidly from the ice at a temperature well below the freezing point of the surrounding water, which in turn caused ice to form in a hollow cylinder around the brine plume. Within a 15 h period after the rafting event, the stalactites, which were located approximately 10 m apart in a line along the upwind edge of a 150 m wide lead, had grown to a length of 2 m. A detailed structural analysis of the upper part of one of these stalactites revealed that the interior channel, down which the brine flowed, was bounded by a zone of frazil ice that developed into a shell of columnar ice. The growth of the columnar ice was directed radially outward and the c axes of these crystals were oriented perpendicular to their growth direction. Development of the stalactites illustrates the impact ice deformation can have on the process of brine rejection in freezing leads and potentially on the thermohaline structure of the upper ocean in the immediate vicinity of the lead.

By fitting a very simple atmospheric impurity model to high-resolution data on ice accumulation and contaminant fluxes in the GISP2 ice core, we have estimated changes in the atmospheric concentrations of soluble major ions, insoluble particulates and 10Be during the transition from glacial to Holocene conditions. For many species, changes in concentration in the ice typically overestimate atmospheric changes, and changes in flux to the ice typically underestimate atmospheric changes, because times of increased atmospheric contaminant loading are also times of reduced snowfall. The model interpolates between the flux and concentration records by explicitly allowing for wet- and dry-deposition processes. Compared to the warm Preboreal that followed, we estimate that the atmosphere over Greenland sampled by snow accumulated during the Younger Dryas cold event contained on average four–seven times the insoluble particulates and nearly seven times the soluble calcium derived from continental sources, and about three times the sea salt but only slightly more cosmogenic 10Be.

The geographical distribution of firn temperature, annual accumulation rate as well as deuterium and oxygen-18 content in the firn were determined along an east-west transect through central Greenland. This study is based on isotopic and chemical analyses of shallow firn cores at 18 sites along the EGIG line and high-precision firn-temperature measurements m 17 steam-drilled boreholes along the eastern part of the transect. The firn temperatures at 15 m depth range from -31.6°C at Dome GRIP (3230 m a.s.l.) to -11.4°C at Caecilia Nunatak (eastern ice margin at 1600 m a.sl.) and -18°C at T05 (near the western ice margin at 1900 m a.s.l.). The temperature/altitude gradient changes from -0.7°C (100 m)−1 in the ice divide region to -1.1 °C (100 m)−1 in the eastern part of the dry-snow zone. The temperature/latitude gradient in the central part of the EGIG line is -0.7° C lat−1 The average annual accumulation decreases significantly from the west (~47 cm a−1 water equivalent at T05) towards the ice divide (20–25 cm a−1 water equivalent from T99 to T43). Accumulation rates are constantly low east of the ice divide (−23–17 cm a−1 water equivalent), thus dividing central Greenland into two climatologically different regions. The average δ18O and δD values along the whole EGIG line reflect the well-known temperature-dependence for Greenland very well (e.g. ∂18O/∂Tm = 0.69%ₒ °C–1 Different regression lines for the western and eastern part, however, should be applied. Unlike the mean annual temperature, the isotopic minimum along the EGIG line lies east of the ice divide. This geographical distribution supports the choice of different water-vapour trajectories in central Greenland for the west and for the east. Significant parts of the water precipitated over the western slope are attributed to cyclonic systems entering Greenland from the west. The deuterium excess shows no significant geographical trend but a uniform seasonal variation at all sites along the EGIG line, suggesting equal contributions from vapour-source areas of the water precipitated over central Greenland.

A finite-element model that solves the stress-balance equations for glacier dynamics in three dimensions has been developed by extending previous flow-plane models. This model retains all terms of the stress tensor and uses a Glen-type power law for viscosity calculations. In the paper, the model is applied to Storglaciären, Sweden, to explore both the glacier’s dynamics and the model’s characteristics. Values of the stiffness parameter B of 0.20–0.22 MPa year1/n were required to match observed strain rates on Storglaciären. Overall velocities required imposition of a problematically small sliding speed. Stress fields implied by the model simulation showed that the glacier receives its largest driving force from a high-slope zone near the equilibrium line, and that a large proportion of the resistive stress comes from lateral drag. Lateral drag is enhanced on this glacier by being frozen to its sidewalls and by a turning of the main flow as it comes out of the main, or northern, cirque.

The paleoglaciological concept that during the Pleistocene glacial hemi-cycles a super-large, structurally complex ice sheet developed in the Arctic and behaved as a single dynamic system. as the Antarctic ice sheet does today, has not yet been subjected to concerted studies designed to test the predictions of this concept. Yet, it may hold the keys to solutions of major problems of paleoglaciology, to understanding climate and sea-level changes. The Russian Arctic is the least-known region exposed to paleoglaciation by a hypothetical Arctic ice sheet but now it is more open to testing the concept. Implementation of these tests is a challenging task, as the region is extensive and the available data are controversial. Well-planned and coordinated field projects are needed today, as well as broad discussion of the known evidence, existing interpretations and new field results. Here we present the known evidence for paleoglaciation of the Russian Arctic continental shelf and reconstruct possible marine ice sheets that could have produced that evidence.

Flexural strength of iceberg and glacier ice was determined from Four-point beam-bending experiments. A large quantity of glacial ice was collected from four icebergs and one glacier, and a detailed ice-characterization program was performed on samples from the five sources. Beam-bending experiments were conducted at four temperatures in the range −1 ° to-16 °C and at strain rates of 10 −3 and 10−5 s−1. The flexural strength was found to increase with increasing strain rate (based on extreme fibre strain and decreasing temperature. The data suggest than air-bubble inclusions play an important role in determining the flexural strength of glacial ice and this can explain the significant differences in mean strength of the ice from the five sources. At a strain rate of 10−3 s−1 and temperature of —11 °C, the flexural strength was found to increase as the number of bubbles per unit volume increased. Reduction of crack-initiating stresses at grain boundaries by “softening” of grains due to intragranular air-bubble inclusions is thought to be the mechanism.

A new and efficient algorithm for computing the three-dimensional stress and velocity fields in grounded glaciers includes the role of deviatoric stress gradients. A consistent approximation of first order in the aspect of ratio of the ice mass gives a set of eight field equations for the five stress and three velocity components and the corresponding boundary conditions. A coordinate transformation mapping the local ice thickness on to unity and approximating the derivatives in the horizontal direction by centered finite-differences yields five ordinary differential and three algebraic equations. This allows use of the method of lines, starting the integration with prescribed stress and velocity components at the base, and a simple iteration procedure converges rapidly.

The algorithm can be used for a wide rangе of stress-strain-rate relations, as long as strain only depends on deviatoric and shear stresses and on temperature. Sensitivity tests using synthetic and realistic ice geometries show the relevance of normal deviatoric stresses in the solutions for the velocity components even for ice sheets. Stress and velocity fields may deviate substantially from the widely used shallow-ice approximation.

Triaxial experiments, at confining pressures in the range 0–13.79 MPa, have been performed on glacial ice collected from four icebergs and one glacier. Tests were conducted at strain rates in the range of 5 × 10−5 to 5 × 10−5s−1 and at four temperatures in the range of −1° to −16°C. Depending on test conditions, the ice failed by one of four possible modes ductile deformation, due to extensive non-interacting microcracks; fracture along a shear plane followed by continuous or stick-slip sliding; large-scale brittle fracture; and combined ductile and shear-plane fracture and slip The strength Increased with decreasing temperature, increasing strain rate up to 5 × 10−3s−1 and increasing confining pressure at the lower temperatures. The strength at 5 × 10−2s−1 was lower than at 5 × 10−3s−1 probably because extension and interaction of microcracks is enhanced at the higher rate. For higher confining pressures at −1°C, the strength decreased due to freezing-point depression. The ice from the different sources exhibited different mean uniaxial compressive strengths. The mean number of air bubbles per unit volume correlated with the mean uniaxial compressive strengths and this may be the dominant factor distinguishing the strengths of the various ice types.

Freezing of water-filled boreholes drives water into the subglacial bed and the associated pressure effects yield information about subglacial hydraulic properties. A numerical model describing the mechanical response of an unconnected borehole and the bed beneath it to this freezing forcing was developed, using a nonlinear transient visco-elastic ice-flow law and an approximate model of top-down freezing. The resulting system of equations was solved using the method of lines. Results agreed well with analytic solutions, when parameters were correctly chosen. Forward modelling of pressure records from three 1992 boreholes and three from other years indicated that the till underlying Trapridge Glacier has a hydraulic conductivity of 1.35-7.0 × 10 −9m s −1. The model was also used to investigate the response of a borehole to sudden pressure changes. The response is very fast compared to pressure-sensor sampling rates; thus, the true basal signal is essentially unaffected by the presence of the borehole, except during the initial freeze-in.

Using radio-echo soundings and seismic reflections, we measured cross-sections of Taku Glacier, near Juneau, Alaska, to resolve inconsistencies in previous measurements and to understand better the glacier’s dynamics. The maximum thickness is about 1477 m and the minimum bed elevation is about 600 m below sea level, which establishes Taku Glacier as the thickest and deepest temperate glacier yet measured. Our data indicate that, during the 19th century, the terminus of Taku Glacier may have begun its rapid advance at a position where the ice bed was greater than 300 m below sea level and more than 25 km from the inland end of its submarine trough; this behavior is uncharacteristic of temperate tide-water glaciers. The glacier, which no longer calves, has eroded a sediment layer 100 m thick since 1890 at an average rate of about 3 m a−1 since 1948; this high erosion rate retards advance by entrenching the glacier into the terminal moraine. Calculations based on ice-deformation theory indicate significant basal ice motion near the terminus and high basal shear stress (140–220kPa) along much of its length. Estimated differences between ice flux and balance flux are consistent with observed thickening and positive net mass balance; these data indicate that ice volume is increasing and that further advance is likely.

A degree-day glacier mass-balance model is applied to three glaciers in Iceland, Norway and Greenland for which detailed mass-balance measurements are available over a period of several years. Model results are in good agreement with measured variations in the mass balance with elevation over the time periods considered for each glacier. In addition, the model explains 60-80% of the year-to-year variance in the elevation-averaged summer season mass-balance measurements on the glaciers, using a single parameter set for each glacier.

The increase in ablation on the glaciers due to a warming of 2° C is predicted to range from about 1 m w.e. year−1 at the highest elevations to about 2.5 m w.e. year−1 at the lowest elevations. Predicted changes in the winter balance (measured between fixed date) are relatively small, except at the lowest elevations on the Icelandic and Norwegian glaciers where the winter balance is significantly reduced. Equilibrium-line altitudes are raised by 200-300 m on the Icelandic and Norwegian glaciers. Except at the highest elevations, the winter balance of the Icelandic and Norwegian glaciers is predicted to decrease even if the warming is accompanied by a 10% increase in the precipitation.

No firm evidence of a climate-related variation in the degree-day factors or in the temperature lapse rate on the same glacier could be found. The model, furthermore, reproduces large variations in the mass balance with elevation and from year to year on each glacier using the same parameter set. We assume, therefore, that these parameters will not change significantly for the climate scenarios considered here.

The prediction of run-up and run-out of dry-flowing avalanches is very important for land-use planning, design of run-out zone defenses and construction of risk maps in avalanche terrain. In this paper, we present a numerical dynamics model to predict the stop position of the tip of these avalanches when friction coefficients (internal and external), initial flow depth and incoming speed are specified for known path geometry in the run-out zone. We also compare our model to that in the Swiss guidelines and to field examples. The results of these calculations clearly define model differences and the implications of different choices of friction coefficients.

By using a simple parameterized model of thermomechanically coupled flow in cold ice sheets, together with a physically based sliding law which includes a description of basal drainage, we show that relationships between ice flux and ice thickness can realistically be multi-valued, and hence that hydraulically induced surges can occur. We term this mechanism hydraulic run-away, as it relies on the positive feed-back between sliding velocity and basal melt production. For this feedback to operate, it is essential that water pressure increases with water storage. This is consistent with various recent ideas concerning drainage, under ice sheets, be it through a system of canals, a distnbuted film or a subglacial aquifer. For confined flows, such as valley glaciers (e.g. Trapridge Glacier) or topographically constrained ice streams (e.g. Hudson Strait in the Laurentide ice sheet), which are underlain by sufficiently deformable sediment, we can expect thermally regulated surges to occur, while in a laterally unconfined drainage basin (such as that which flows into the Ross Ice Shelf), we might expect ice streams to develop.

Ice-sheet surfaces have scales of fluctuation that arc similar to the diameter of the area illuminated by a satellite radar altimeter. The present theory of altimeter, developed to describe scattering from the ocean surface, does not deal properly with the geometry of ice-sheet surfaces. In this paper, the theory of altimeter is extended to cover this geometry. A general relation for the altimeter echo from a surface of unknown geometry is developed, including the effects of the penetration of the surface by the radar waves. This expression is linearized, using the characteristic operating geometry of satellite altimeters and the gentle nature of ice-sheet gradients. From this expression, an integral equation is derived, from whose solution the spatial average of the height of the surface relative to a spherical datum can be determined. The integral equation is of a Volterra type, which permits the uniqueness of the solution for the average height to be investigated simply. The method is extended to provide a solution for the spatial average of the height of a local region of the ice sheet, provided the region remains large in comparison with the area illuminated by the altimeter, and to deal with variations in the antenna bore-sight alignment. The results have a number of implications for the collection and reduction of echoes in an experiment to determine the average height of an ice sheet. The unique determination of the average height requires the echo to be known over a time interval that depends on the extrema of the surface, which therefore must be known a priori. The average height itself can be determined by the operation on the echo of a linear operator whose kernel is derived from the solution of the Volterra-type equation. This marks a change from the procedures currently used in practice to reduce echoes from ice sheets.

The turbulent sensible-heat flux to a melting ice surface is calculated from wind speed and air temperature at 2 m over the ice surface, assuming a certain wind profile with the appropriate surface roughness. The aerodynamic stability of the boundary layer over melting ice is examined by comparing sensible-heat fluxes for logarithmic and log–linear wind profiles, where the logarithmic profile is strictly valid only for neutral conditions. Increasing stability reduces the sensible-heat flux to the glacier surface and introduces a non-linear relation between heat flux and air temperature. The stability effect is greatest at low wind speeds and fairly small at the high wind speeds that are common over the ice sheet. Earlier estimates of ablation by energy-balance modelling may be too large due to neglect of stability but this was almost offset by using a surface roughness that was too small. The log–linear wind profile should he used in future energy-balance models to take account of stability but more research is needed on the parameters of the profile, as well as on the surface roughness.

A physically based mathematical model of the coupled lake, lake ice, snow and atmosphere system is developed for studying terrestrial-atmospheric interactions in high-elevation and high-latitude regions. The ability to model lake-ice freeze-up, break-up, total ice thickness and ice type offers the potential to describe the effects of climate change in these regions. Model output is validated against lake-ice observations made during the winter of 1992–93 in Glacier National Park, Montana. U.S.A. The model is driven with observed daily atmospheric forcing of precipitation, wind speed and air temperature. In addition to simulating complete energy-balance components over the annual cycle, model output includes ice freeze-up and break-up dates, and the end-of-season clear ice, snow-ice and total ice depths for two nearby lakes in Glacier National Park, each in a different topographic setting. Modeled ice features are found to agree closely with the lake-ice observations.

Model simulations illustrate the key role that the wind component of the local climatic regime plays on the growth and decay of lake ice. The wind speed affects both the surface temperature and the accumulation of snow on the lake-ice surface. Higher snow accumulations on the lake ice depress the ice surface below the water line, causing the snow to become saturated and leading to the formation of snow-ice deposits. In regions having higher wind speeds, significantly less snow accumulates on the lake-ice surface, thus limiting snow-ice formation. The ice produced by these two different mechanisms has distinctly different optical and radiative properties, and affects the monitoring of frozen lakes using remote-sensing techniques.

A simple numerical flow model that couples mass divergence directly to basal shear stress as the only driving force is used to study kinematic waves. Kinematic waves that result from a perturbation of the ice thickness or mass balance are compared with the linear kinematic-wave theory of Nye/Weertman. The wave velocity is calculated as a function of the wavelength and amplitude of a perturbation. The modelled wave velocity is typically 6–8 times the vertically averaged velocity in the flow direction whereas linear theory predicts a factor of only 5.

An experiment with the geometry of Hintereisferner, Austria, shows that the increase in the local ice velocity during a kinematic wave is about 10% but varies slightly depending on the position along the glacier and the amplitude of the kinematic wave. Kinematic waves are thus hard to detect from velocity measurements.

The dynamics of simple continuity models are rich enough to support a variety of kinematic-wave phenomena. Such models are a useful tool to study the response of valley glaciers to climate change.

Ice ablation is related to air temperature by the positive degree-day factor. Variations of the positive degree-day factor in West Greenland are studied using an energy-balance model to simulate ablation under different conditions. Degree-day factors for simulated and measured ice ablation at Nordbogletscher and Qamanârssûp sermia agree well with values around 8 mm d−1 °C−1. Degree-day factors for snow are less than half those for ice. Energy-balance modelling shows that degree-day factors vary with summer mean temperature, surface albedo and turbulence but there is only evidence of large positive degree-day factors at lower temperatures and with low albedo (0.3). The greatest effect of albedo variations (0.3–0.7) is at lower temperatures while variations in turbulence have greater effect at higher temperatures. Current models may underestimate runoff from the Greenland ice sheet by several tenths because they use a degree-day factor for melting ice that is too small for the colder parts of the ice sheet, i.e. the upper ablation area and the northerly margin.