Perturbation analysis is applied to the heat balance at the EGIG line (West Greenland) with respect to climatic changes. The shift of the equilibrium-line altitude is obtained for perturbations of temperature, absolute humidity, cloudiness and annual accumulation. The total net ice ablation at the EGIG line increases by 45% with a perturbation of + 1 K. Applying this figure to the entire ice sheet, the total ablation equals the total accumulation at a warming of + 2 K, if refreezing of melt water is neglected.

The pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

Several holes were drilled to depths of 1500–1630 m along a profile across Jakobshavns Isbræ, 50 km upstream from the calving front. Drilling was by hot water and required approximately 20 h. The holes were rapidly closed by refreezing, but it was possible to instrument them with thermistors and tilt sensors before this occurred.

Near the margins of the ice stream the holes reached the bed and connected with the subglacial drainage system. Water-level changes recorded in these holes are discussed in terms of the basal hydraulic system. The temperature measurements show that the glacier is temperate-based. Moreover, extrapolation of a measured temperature profile and its curvature suggests that a temperate layer of substantial thickness may exist at the bed near the center of the ice stream. There is a striking difference in the shapes of temperature profiles measured at different locations: beneath the center line the temperature minimum is at a considerably smaller relative depth than near the margins, but it is nearly the same in magnitude (−22.1°C). This may indicate a disproportionately large vertical stretching of the basal ice in the center of the ice stream. Since the basal ice is warmer and much less viscous than the ice above, a thickening of that layer would cause a corresponding increase of surface velocity. We presume that this mechanism contributes to the fast flow of Jakobshavns Isbræ.

A theory of subglacial consolidation is developed which shows how the meltwater flux beneath a glacier leaves a consolidation signature from which many important glacier-dynamic properties can be inferred. Conditions under which water is discharged through channels or in a thin film at the ice—bed interface or by ground-water flow are discussed, and it is concluded that glaciers flowing over aquifers of high transmissibility can induce deep circulation patterns quite different from non-glacial circulation. Examples of glacial pre-consolidation profiles in sediments from The Netherlands and England are used to illustrate how basal melting rates, subglacial ground-water flow patterns, ice overburden, basal shear stress, ice-surface profile and the amount of sediment removed by erosion can be inferred.

A two-dimensional model which links the atmosphere, the mixed layer of the ocean, the sea ice, the continents, the ice sheets and their underlying bedrock has been used to test the Milankovitch theory over the last glacial—interglacial cycle. It was found that the orbital variations alone can induce, in such a system, feed-backs sufficient to generate the low-frequency part of the climatic variations over the last 122 kyear. These simulated variations at the astronomical time-scale are broadly in agreement with ice volume and sea-level reconstructions independently obtained from geological data. Imperfections in the simulated climate were the insufficient southward extent of the ice sheets and the too small hemispheric cooling during the last glacial maximum. These deficiencies were partly remedied in a further experiment (Gallée and others, in press) by using the time-dependent CO2 atmospheric concentration given by the Vostok ice core in addition to the astronomical forcing. For this second experiment, the main mechanisms and feedbacks responsible for the glaciation and the deglaciation in the model are discussed here.

Temperate glacier ice is neither dry nor impermeable, as the standard theory of glacier sliding assumes. This fact leads to the already published concept of locally stress-controlled temperatures. Why the temperature is determined by the highest principal pressure, why the microscopic stress equals more or less the macroscopic one, and why water may flow in the capillary network even when water lenses at grain boundaries are freezing is explained. The new concept is applied to ice sliding on a hard bed having a sine profile, without cavitation. First, the stress field for a Newtonian viscous material and a vanishing roughness are used; next, an improved one, that takes into account the non-linear viscosity of ice and the finite amplitude of the micro-relief. It appears that water migrates from the stoss sides of the bumps to the lee sides within a bottom layer of thickness hw. Moreover, there is less ice melting at the sole on the former ones than ice accretion on the latter, a fact that yields a trend of ice accretion at the glacier sole. It is balanced by internal melting near the bed and water oozing at the interface from the soaked ice. Consequently, a thin layer of accreted regelation ice with a constant mean thickness hi should exist at the interface. Modelling realistically mountain glaciers, hw ∼ 20 cm and hi ∼ 3.5 cm are found.

Classical mixture concepts are the appropriate vehicle for describing the dynamics of ice masses containing some water. We review and derive, respectively, the theoretical formulations of cold, polythermal and temperate ice masses, emphasize the peculiarities of the model equations and point to difficulties that were encountered with the proposed models. The focus is both on the adequate physical motivation of the models and the consistency of their mathematical representation. The paper also has a tutorial character.

As usual, cold ice is treated as a single-component incompressible heat-conducting viscous fluid, while two different models are presented for temperate ice. When it arises in a polythermal ice mass, the water content is small and a simple diffusive model for the moisture content suffices. This diffusive model is further simplified by taking its appropriate limit, when the moisture diffusivity tends to zero. Temperate ice in a wholly temperate — Alpine — glacier is treated as a two-phase flow problem, i.e. the momentum-balance laws of both constituents ice and water are properly accounted for. Such Darcy-type models are suggested because the water arises in a greater proportion; so its dynamic role can no longer be ignored.

The constituent ice is treated as an incompressible non-linearly viscous isotropic body with constitutive properties similar to those of cold ice. The interstitial water is a density-preserving ideal or perfect fluid. The two interact with an interaction force that is proportional to the “porosity” and the seepage velocity. Internal melting that arises will lead to a generalization of the familiar Darcy law.

When water is present, the boundary and transition conditions across internal singular surfaces take special, more complicated forms and involve statements on drainage to the base. These conditions are also discussed in detail.

The net mass balance (1986/87–1989/90) was calculated for a small cirque glacier in the Italian Alps (Ghiacciaio della Sforzellina, 0.42 k m2, Ortles–Cevedale Group). Four annual mass balances are presented here. All four balances were negative (mean value: –0.90 m year−1), with a maximum deficit of –1.16 m year−1 in 1989–90. The climatic conditions (which are analyzed using data from the S. Caterina Valfurva Station) consisted of a succession of cold, dry winters with little snowfall. Frontal-variation data available since 1925 show a constant retreat until 1966, followed by a brief advance period which has already terminated.

Control methods are recommended as an efficient means to estimate undetermined physical parameters and boundary conditions and, in so doing, to improve the fidelity of a given ice-sheet flow model to specific ice-sheet velocity observations. To accomplish this task, the underlying dynamics of the model are inverted. This permits model-tuning adjustments to be represented explicitly in terms of model/observation misfit. Advantages of the control method over trial-and-error techniques in common use are: (1) it is readily automated with little additional programming effort, (2) the tuning parameters and boundary conditions it achieves are assured to give the best possible fit between model and observation, and (3) it quantifies the uncertainty of tuning parameters and boundary conditions in situations where they are not uniquely determined.

Observations of temperature maxima at about 10 cm depth in cold Antarctic snow during summer have previously been explained by proposing that solar heating is distributed with depth whereas thermal infrared cooling is localized at the surface (the “solid-state greenhouse”). An increase in temperature from the surface to 10 cm depth (ΔΤ ≈ 4 K) found by Rusin (1961) on the Antarctic Plateau was successfully reproduced by Schlatter (1972) in a combined radiative-transfer and heat-transfer model. However, when we improve the model’s spectral resolution, solving for solar radiative fluxes separately in 118 wavelength bands instead of just one “average” wavelength, ΔΤ shrinks to 0.2 Κ and moves toward the surface, indicating that the solid-state greenhouse is largely an artifact of inadequate spectral resolution. The agreement between Schlatter’s broad-band model and Rusin’s measurement suggests that the measurement is inaccurate, perhaps due to solar heating of the buried thermistors. Similar broad-band models which have been applied to the icy surface of Jupiter’s satellite Europa are also shown to overestimate the solid-state greenhouse by a factor of about 6.

The reason that the solid-state greenhouse effect is insignificant in the case of Antarctic snow is that the wavelengths which do penetrate deeply into snow (visible light) are essentially not absorbed and are scattered back to the surface, whereas the wavelengths that are absorbed by snow (near-infrared) are absorbed in the top few millimeters.

The conditions needed to obtain a significant solid-state greenhouse are examined. The phenomenon becomes important if the scattering coefficient is small (as in blue ice) or if the thermal conductivity is low (as in low-density snow, such as near-surface depth hoar).

Four boreholes in Storglaciären, a small valley glacier in northern Sweden, were inspected with a video camera. In two of the boreholes, the apparent glacier bed was filmed. In one borehole, the bed was found to be composed of soft sediment, but in the other it consisted of bedrock. In the latter, the camera moved 5.6 mm relative to the bed during an 80 min period. The recorded camera movement showed a background motion which is in the expected range of basal sliding. Superimposed on the background motion, a jerky motion of a high-speed spike was found. The jerky motion is interpreted as a stress release induced by local topography at the ice–bed interface.

Analyses of the first aircraft multi-frequency, Polarimetric synthetic aperture radar (SAR) data acquired over the southwestern Greenland ice sheet are presented. Data were collected on 31 August 1989 by the Jet Propulsion Laboratory SAR using the NASA DC-8 aircraft. Along with curvilinear patterns associated with large-scale morphologic features such as crevasses, lakes and streams, frequency and polarization dependencies are observed in the P-, L-and C-band image products. Model calculations that include firn grain-size and volumetric water content suggest that tonal variations in and between the images are attributable to large-scale variations in the snow-and ice-surface characteristics, especially snow wetness. In particular, systematic trends in back-scatter strength observed at C-band across regions of changing snow wetness are suggestive of a capability to delineate boundaries between snow facies. Ice lenses and ice pipes are the speculated cause for similar trends in P-band back-scatter. Finally, comparison between SEASAT SAR data collected in 1978 and these airborne data collected in 1989 indicate a remarkable stability of surface patterns associated with the locations of supraglacial lake and stream systems.

The trapping of bubbles of air in polar ice has provided a unique record of past atmospheric composition. However, the interpretation of measured concentrations depends on the statistics of the trapping process. Measurements of trace atmospheric constituents whose concentrations are changing steadily can be interpreted in terms of an “effective age” of the gas which differs from the age of the ice by a delay which corresponds to the mean trapping time. The statistics of bubble trapping can be modelled as a percolation model which is one of a class of models whose transitions are characterized by large critical fluctuations. These critical fluctuations cause an intrinsic sample-to-sample variability in the delay time and thus in the effective age. Monte Carlo simulations using a lattice model of the firn are presented, showing the effect of finite sample size on the age distribution of trapped gas. For samples containing more than about 103–104 bubbles, the simulations indicate that the range of variability is small compared to the average duration of the trapping process.

Tracers were injected into South Cascade Glacier to determine the flow condition and geometry of the subglacial water system. Results indicate that two distinct drainage basins on the glacier feed the two main streams flowing from the glacier. In the largest basin, two parallel drainage networks exist, one englacial and the other subglacial. The englacial system is an arboresecent network of conduits, whereas the subglacial system is a distributed flow system. Both systems connect to a single subglacial conduit which appears as a stream at the glacier’s terminus. The comparison between the travel time of the tracers and stream discharge indicated that the single conduit was pressurized in July and partly filled in August and September.

To estimate the flow geometry (e.g. path length, flow depth and velocity), the advection-diffusion equation was formulated to express the water velocity as a function of water depth. Longitudinal dispersion of the tracer was calculated from the shear in longitudinal water velocity. Results indicate that the flow is very wide compared to its depth and that the path is sinuous. The estimated flow speed in the conduits is an order of magnitude larger than the measured speed through the glacier, indicating that other flow processes, probably englacial, route the water much more slowly.

The other, smaller, basin drains the water from the surface to the subglacial distributed flow system. Based on the travel time of the individual concentration peaks, the water could be flowing through a linked-cavity system or interconnected bands of highly permeable debris separated by zones of less permeability.

Basal ice stratigraphy in coastal ice cliffs at the Law Dome margin has revealed the basal accretion of clean and debris-bearing ice, marine congelation ice and granular marine ice inland of the margin. Co-isotopic analysis of δ18O and δD isotopes together with solute chemistry were applied to determine the modes of accretion and debris entrainment. The marine congelation ice and the granular marine ice were formed from the basal freezing of desalinated sea water and the episodic mixture of basal meltwater and sea water, respectively. Two different debris-entrainment mechanisms were identified. Debris-band ice with debris concentrations of 6.3–33% (by volume) was formed from proglacial raised beach and shallow marine sediment incorporated by an over-riding advance of the margin. Two other debris-bearing ice types, dispersed debris-poor ice with debris concentrations <0.3% (by volume) and laminated debris ice with debris concentrations 0.9–1.9% (by volume) were accreted further inland from the margin by basal regelation processes associated with the Robin (1976) heat-pump effect.

An exact, analytic description of the steady, downhill flow of a viscous ice stream across a no-slip to free-slip transition in basal boundary condition suggests ways in which such transitions might be detected by observations of ice-stream surface properties. We find that the best expression of this transition is in the free-surface profile, which dips over the point of transition and becomes horizontal far downstream. The streamwise velocity at the surface shows a gradual change across the transition, and this is in disagreement with previous studies which suggest a marked change. Basal shear stress and basal pressure exhibit singularities at the point of transition. As concluded in previous study, the former singularity is a likely point of strong basal erosion. The latter singularity is problematical, however, because it violates the assumptions which make the exact solution possible. It is not clear how this problem can be overcome without appealing to thermodynamics, non-Newtonian material properties, cavitation or wake separation.

Ice observations and sediment samples were collected in the Beaufort Gyre in 1988. Fine sediment occurred in very small patches of turbid ice, as thin spotty surface layers, in mud pellets or in old snowdrifts. The latter were widespread south of 74°N, containing an estimated 22 tonnes of silt and clay km−2. Average particle concentration in sea ice (40mg l−1) was much higher than in sea water (0.8 mg l−1) or in new snow, but the sediment load was significantly smaller and of finer texture compared to that observed in a shelfal source area after a major entrainment event. About 30% of the sediment consisted of small pellets. Mud in pellets has similar texture, clay minerals and organic/inorganic carbon content as dispersed mud. Particle sizes <16μm dominate, sand is less than 1%, compared to as much as 8% in four samples obtained in 1971 and 1972. Organic carbon content is about 2%, illite dominates clay minerals (~50%), and diatoms suggest a shelf sediment source. From the prevalence of wind-reworked surficial deposits, the spotty occurrence of only small patches of turbid ice in old clean ice, and the virtual lack of sand-size material, we assume the sediment had drifted at least 2 years since entrainment and was distant from its source. Assuming one-third of the load is released each year, the estimated deposition rate would equal the measured Holocene rate (~2cm 1000year−1). Therefore, modern sea-ice rafting represents a substantial fraction of the total Arctic Ocean sediment budget.

A new extraction system has been constructed and tested which allows the extraction of gases from air bubbles in ice without melting it. An ice sample of up to 20 g is crushed in a sealed container by a milling cutter and the gas escaping from the opened bubbles is flushed with helium to a Porapak column where it is stored until its injection into the gas Chromatograph. To avoid any contamination with CH4 produced by friction in the gear section, a helium-flushed rotary feed-through is used. CH4 analyses on ice samples of about 10 g from the last 1000 years give precise and reproducible results. In the future, it is planned to measure also the CO2 and N2O concentrations on the same sample.