The problem of measuring surface height and snowpack characteristics from satellite radar altimeter echoes is investigated. In this paper, we perform an analysis of the ERS1 altimeter dataset acquired during a 3 day repeat orbit. The analysis reveals that there are temporal variations in shapes of the radar altimeter echo and that these variations are linked to meteorological phenomena. The time- and space-scales over which these variations apply are a few to tens of days and a few hundred kilometres, respectively. This phenomenon, if not accounted for, can create error in the height measurement. A numerical echo model is used to recover snowpack characteristics by taking advantage of the temporal variations of the radar echoes. A map of penetration depth of the radar waves in the Ku band over the Antarctic continent is obtained and suggests that grain-size produces the dominant effect on radar extinction in the snowpack at this frequency. Finally, a procedure is proposed to correct the height measurement within the context of ice-sheet mass-balance survey.

Changes in the Earth’s gravity field with time have important applications to a broad range of disciplines. Any process that involves a large enough horizontal redistribution of mass, either within the Earth or on or above its surface, is potentially detectable. In particular, when ice sheets grow or shrink, gravity changes as mass is redistributed in the solid earth and between the oceans and the ice sheets. The sources of global sea-level rise (about 2 mm a−1 over the last century) and in particular the contribution of the Antarctic ice sheet thereto are not well understood. Gravity measurements can help to diminish this uncertainty.

The technology currently exists to measure gravity with high accuracy by a dual-satellite mission in which the distance between the satellites is precisely monitored. We estimate from recent studies that temporal changes in the gravity field as determined by a satellite gravity mission lasting 5 years at an orbital height of 400 km would be sensitive to changes in the overall mass of the Antarctic ice sheet to a precision corresponding to better than 0.01 mm a−1 of sea-level change. However, the effects of three other phenomena that could each produce a temporally varying gravity signal with characteristics comparable to that caused by a change in Antarctic ice—postglacial rebound, inter-annual variability in snowfall, and atmospheric pressure trends — also need to be evaluated. Postglacial rebound could be partly separated from ice-mass changes with the aid of global positioning system campaigns and numerical models of rebound that use improved determinations of mantle viscosity also provided by the gravity mission. Determination of inter-annual ice-mass changes will be aided by measurements of moisture-flux divergence around the perimeters of the ice sheets and direct observations of inter-annual changes by the gravity satellite itself. The removal of pressure effects over Antarctica will become more effective as the number of automatic weather stations in the interior of the continent increases.

Even after corrections are made for these factors, the uncertainties they cause limit the accuracy in the détermination of the contribution of the Antarctic ice sheet to sea-level change to about 0.5 mm a−1. However, there is a strong complementarity between gravity measurements and the surface-height measurements that will be produced by NASA’s laser altimeter mission early next century. Together, they should be able to determine that contribution to an accuracy of about 0.1 mm a−1.

For glaciological and meteorological reasons Mount Elbrus, Caucasus, was chosen as a site for physical and chemical pilot studies of ice cores. This study was the first step towards systematic studies of impurities in glacier ice on Mount Elbrus. In 1900 two ice cores, each 17 m deep and spaced 10 m apart, were taken at an elevation of 4100 m on the Bolshoy Azau glacier on the western slopes of Mount Elbrus. The cores were used for different physical and chemical analyses. Structure, texture and ice microstructure were studied. Chemical analyses of major ions (SO42−, NO3−, K+ and Na+) and measurements of insoluble light-absorbing material and radioactivity (137Cs and total β activity) were made. With the results of the physical and chemical analyses of these two ice cores, the possibilities of utilising the ice for the study of trace substances deposited after long-range transport from Europe were explored. Ice-stratigraphic methods made it possible to establish the annual accumulation rate. A reference horizon was established from the depth variation of 137Cs and total β activities that showed a well-defined peak of their activities coinciding in time with the 1986 Chernobyl accident. The results of this study show that Mount Elbrus is a useful archive for atmospheric composition downwind of Europe.

A “tethered stake” apparatus is used to measure basal sliding in a borehole on Ice Stream B, West Antaretica, about 300 km upstream (east) from its grounding line near the head of the Ross Ice Shelf. A metal stake, emplaced at the top of a laver of unfrozen till underlying the ice, is connected by a tether line to a metering unit that measures the tether line as it is pulled out from the borehole by the stake as a result of basal sliding. The measured sliding motion includes any actual slip across the ice–till interface and may include in addition a possible contribution from shear deformation of till within about 3 cm of the interface. This 3 cm figure follows from a qualitative model of the movements of the stake in the course of the experiment, based on features of the record of apparent sliding. Alternative but less likely models would increase the figure from 3 cm to 10 cm or 25 cm. In any case it is small compared to the seismically inferred till thickness of 9 m. Measured apparent sliding averages 69% of the total motion of 1.2 m d−1 over 26 days of observation if a 3.5 day period of slow apparent sliding (8% of the total motion) is included in the average. The occurrence of the slow period raises the possibility that the sliding motion switches back and forth between c.80% and c. 8% of the total motion, on a time-scale of a few days. However, it is likely that the period of slow apparent sliding represents instead a period when the stake got caught on the ice sole. If the slow period is therefore omitted, the indicated average basal sliding rate is 83% of the total motion. In either case, basal sliding predominates as the cause of the rapid ice-stream motion. In the last 2 days of observation the average apparent sliding rate reached 1.17 m d−1, essentially 100% of the motion of the ice stream. If till deformation contributes significantly to the ice-stream motion, the contribution is concentrated in a shear zone 3 cm to possibly 25 cm thick at the top of the 9 m thick till layer. These observations, if applicable to the West Antaretic ice sheet in general, pose complications in modeling the rapid ice-streaming motion.

We analyse data on solar radiation measured with an automatic weather station on Morteratschgletscher, Switzerland, for the period 1 October 1995–30 September 1996. The station is in the lower ablation zone. Due to shading by surrounding mountains and atmospheric attenuation, only 49% of the annual extraterrestrial irradiance (mean: 292 W m−2) reaches the glacier surface. About 48% of this is absorbed at the surface (mean: 79 W m−2; annual albedo of 0.53).

We present a simple albedo scheme for use in glacier mass-balance models. We fit the model to the 1 year dataset by optimizing five control parameters (optimal values in brackets): albedo of snow (0.75), albedo of firn (0.53), albedo of ice (0.34), e-folding constant for effect of ageing on snow albedo (21.9 days) and e-folding constant for effect of snow depth on albedo (3.2 cm). The input consists of daily albedo, snow depth and dates of snowfall events. The correlation coefficient between observed and simulated albedo is 0.931, the corresponding rms difference being 0.067.

Reconnaissance energy-balance studies were made for the first time at two sites in North Greenland to compare with conditions in West Greenland. The field experiments were planned to save weight because it is expensive to operate in North Greenland. The larger energy components (incoming radiation and ablation) were measured for 55 days altogether, and the smaller components were evaluated by indirect methods, e.g. turbulent fluxes are calculated from air temperature, humidity and wind speed, to save the weight of instruments. The energy-balance model is “tuned" by choosing surface roughness and albedo to reduce the mean error between measured ablation and modelled daily melting. The error standard deviation for ablation is only ± 5 kg m −2 d−1’, which is much lower than found in West Greenland, due to better instruments and modelling in the present study. Net radiation is the main energy source for melting in North Greenland but ablation is relatively low because sublimation and conductive-heat fluxes use energy that would otherwise be available for melting. There is a strong diurnal variation in ablation, mainly forced by variations in shortwave radiation and reinforced by nocturnal cooling of the ice surface by outgoing longwave radiation and sublimation. The model frequently predicts a frozen glacier surface at night even when air temperatures are positive.

Numerical models for sea-ice thickness distribution and velocity are used for ice-dynamics research and ice forecasting. In the modeling work, ERS-1 SAR is an excellent tool, in particular by providing spatial ice-velocity fields as described in the present Baltic Sea study. Ice velocities were extracted from SAR data with 3 and 6 day time intervals using the optical-flow method. A considerable stiffening of the ice pack was observed due to the change in the character of ice déformation under compression from rafting to ridging as the minimum ice thickness increased from 10 to 3O cm. The coastal alignment was strong in the ice motion and the coastal boundary layer width was 20-30 km. An analysis of the SAR data with an ice-dynamics model showed that the observed overall ice-velocity field could be produred using the Hibler viscous-plastic ice rheology. The compressive strength of the ice (over 10 km sc ales) was 2.5x 104 N m−2 ±50% for ridging and negligible for rafting of very thin ice. The shear strength was significant and the normal yield ellipse aspect ratio of 2 was valid. The 3 day time interval is val id for updating an ice model but for detailed ice-dynamics investigations a data frequency of 1 d−1 or higher would be preferable.

Bakaninbreen, Svalbard, started surging in 1985 and developed a steep surge front where fast-moving ice impinged on stagnant non-surging ice. This front, which was 20- 25 m high in 1985, became a steep and heavily crevassed feature about 60 m high. The surge continued through 1986-95. Annual surge-front propagation rate was 1.0 1.8 km a−1 during 1985-89; this rate dropped considerably during 1989 95 and the front became less steep. Front propagation occurred largely by longitudinal compression and vertical extension of the ice and the effects of over-riding appear minor. Ice velocities were slower than the average propagation rate of the front. The surge affected Bakaninbreen in four zones: (1) Upper region where extensive flow, fast propagation rates and negative vertical strain occurred, resulting in widespread crevassing and stranded blocks tens of metres above the post-surge ice surface, (2) Mid-glacier region where initial strong compression was associated with ice thickening which started before the arrivai of the surge front. Horizontal strain rates were very low but vertical strain rates were tip to 300 mmd−1. As (he front passed, the horizontal velocity increased and about 500 m behind it became extensive. Negative vertical strain and ice down-draw occurred as ice velocities dropped, (3) Surge front where ice velocity was high but vertical strain remained positive associated with compression. (4) Lower region below the iront where only compression occurred, resulting in the formation of a fore bulge, a thickening of the ice of up to 50 m above pre-surge levels. The fore bulge affected the whole 1.7 km below the, now halted, surge front. The glacier has not advanced, Bakaninbreen’s surge was characterized by a long active phase, approximately 10 years, low ice velocities and low basal shear stresses compared to glaciers in lower latitudes, and an indistinct surge termination.

If it were possible to properly extract seasonal information from ice-core isotopic records, paleoclimate researchers could retrieve a wealth of new information concerning the nature of climate changes and the meaning of trends observed in ice-core proxy records. It is widely recognized, however, that the diffusional smoothing of the seasonal record makes a “proper extraction" very difficult. In this paper, we examine the extent to which seasonal information (specifically the amplitude and shape of the seasonal cycle) is irrecoverably destroyed by diffusion in the firn. First, we show that isotopic diffusion firn is reasonably well understood. We do this by showing that a slightly modified version of the Whillans and Grootes (1985) theory makes a tenable a priori prediction of the decay of seasonal isotopic amplitudes with depth at the GISP2 site, though a small adjustment to one parameter significantly improves the prediction. Further, we calculate the amplitude decay at various other ice-core sites and show that these predictions compare favorably with published data from South Pole and locations in southern and central Greenland and the Antarctic Peninsula. We then present numerical experiments wherein synthetic ice-core records are created, diffused, sampled, reconstituted and compared to the original. These show that, alter diffusive mixing in the entire fini column, seasonal amplitudes can be reconstructed to within about 20% error in central Greenland but that all information about sub-annual signals is permanently lost there. Furthermore, most of the error in the amplitude reconstructions is due to the unknowable variations in the sub-annual signal. Finally, we explore how these results can be applied to other locations and suggest that Dye 3 has a high potential for meaningful seasonal reconstructions, while Siple Dome has no potential at all. An optimal ice-core site for seasonal reconstructions has a high accumulation rate and a low temperature.

A perturbation method is used to analyse the stability of a thin till layer overlain by a deep ice layer. Ice is modelled as a linearly viscous fluid, while the till viscosity has power-law dependence on stress and effective pressure. A linearized set of equations yields descriptions of the coupling of the ice flow with the sediment flow and reveals parameter ranges where the till-perturbation amplitude can grow. This sheet-flow instability is an essential part of any theory of drumlin formation and shows that viscous models of till have the ability to explain typical deforming-bed features. This is of great significance for large-scale ice-sheet modelling.

Glacially induced flow naturally tends to thin and extended till cover through shock formation, even in the absence of longitudinal gradients in the applied stress. Thicker till cover has an increased effective pressure at its surface and base, a lower sliding velocity or deformation rate and above a critical thickness, a decrease in wave velocity with thickness, leading to reverse-facing shocks moving downstream. For sliding and for some theologies of internal deformation, a decrease in sediment flux with thickness occurs, implying backward-moving kinematic waves and reverse-facing, reverse-moving shock.

Downstream-facing shocks are also formed which move upstream if the till is sliding and downstream if the till is deforming internally. Eventually, shocks coalesce, leaving an upstream-lacing shock for sliding and a downstream-facing shock for internal deformation. It is observed that some drumlins have downstream blunt ends only.

Fairly realistic three-dimensional drumlin shapes can be produced from symmetric sediment bodies and barchan shapes can be produced from linear forms perpendicular to the ice-sheet flow.

The fact that viscous theories produce drumlinoid forms suggests that on this scale till behaves viscously and the the lower length scale for drumlins represents the plastic/viscous transition scale.

Small glaciers appear to have been at equilibrium or shrinking very slightly during 1961–90, according to analysis of an essentially complete set of published measurements. Simple calculations give an average annual mass balance of –195 ± 59 mm a−1 (water equivalent) but this is too low because of systematic errors. Neglect of internal accumulation is responsible for some tens of millimeters of underestimate. Uneven spatial coverage, with fewer measurements where mass balances are less negative, accounts for about 50 mm a−1 of underestimate. This figure derives from spatial interpolation based on global data on ice extent and on an analysis of correlations between balance time series. The correlogram shows exponential decay, the scale length being about 600 km. The largest bias is due to a newly detected dependence of mass balance on glacier size. Among the 231 measured glaciers, many are small and belong to a restricted size range in which balance is negative, but much of the small-glacier extent is accounted for by larger glaciers in a size range where balance is indistinguishable from zero. Correcting for this size bias increases the average balance to –35 ± 89 mm a−1. Inspection of time series for 1940–95 (251 glaciers) shows that mass balance was least negative during the 1960s, and has varied in broad agreement with Northern Hemisphere temperature anomalies; smaller small glaciers (A < 16 km2) appear to be more sensitive than larger small glaciers to changes in thermal forcing. The small-glacier contribution to sea-level rise implied by this assessment is only 0.06–0.32 mm a−1, consistent with glaciers in general making little or no contribution to sea-level change during 1961–90.

A new technique for characterizing the structure of firn and bubbly ice is presented. This technique, based on observation of etched (sublimation) surfaces in coaxial reflected light, enables une to see simultaneously the pore network of the firn or bubbles in the ice and the crystal boundaries. At the same time, the main stages of image processing used to transform the initial photographs into clean binary images are described.

McCall Glacier has the only long-term mass-balance record in Arctic-Alaska. Average annual balances over the periods 1958–72 and 1972–93 were –15 and –33cm, respectively; recent annual balances (1993–96) are about –60 cm, and the mass-balance gradient has increased. For an Arctic glacier, with its low mass-exchange rate, this marks a significant negative trend.

Recently acquired elevation profiles of McCall Glacier and ten other glaciers within a 30 km radius were compared with topographic maps made in 1956 or 1973. Most of these glaciers had average annual mass balances between –25 and –33 cm, while McCall Glacier averaged –28 cm for 1956–93, indicating that it is representative of the region. In contrast, changes in terminus position for the different glaciers vary markedly. Thus, mass-balance trends in this region cannot be estimated from fractional length changes at time-scales of a few decades.

We developed a simple degree-day/accumulation mass-balance model for McCall Glacier. The model was tested using precipitation and radiosonde temperatures from weather stations at Inuvik, Canada, and Barrow, Kaktovik and Fairbanks, Alaska, and was calibrated with the measured balances. The Inuvik data reproduce all measured mass balances of McCall Glacier well and also reproduce the long-term trend towards more negative balances. Data from the other stations do not produce satisfactory model results. We speculate that the Arctic Front, oriented east–west in this region, causes the differences in model results.

Based on glacier mass-balance records collected, compiled and published by the World Glacier Monitoring Service (WGMS), an attempt is made here to determine whether there were abrupt decadal-scale changes in annual balance on glaciers in the Tien Shan Mountains. There appears to have been an abrupt change in the mid-1970s; two-thirds of the change was caused by an increase in annual ablation and the other one-third by a decrease in the annual accumulation. Thus, the change was caused mainly by a summer-temperature increase, supplemented by a decrease in annual snowfall. Climate records suggest that this event, in effect, is in response to a shift hi the background state of the coupled Ocean -atmosphere system over the Tropical Pacific during the mid-1970s.

During the 1991 94 summer held seasons, time-correlated measure-merits of water pressure and surface speed were made over and down-glacier from a major riegel on Storglaciären, Sweden. Measurements were made at sub-hourly time-scales in order to discern details in the diurnal cycle. Large water-input events, typically associated with rain storms, produced coherent, lagged surface-velocity responses that could be understood in terms of till deformation or decoupling, and these have been discussed elsewhere. The consequences of smaller diurnal water-pressure events w ere more enigmatic, in that acceleration of ice flow generally preceded the onset of the local water-pressure rise. From consideration of these data and other work done on the hydrology of Storglaciären, we infer that the ice in this area is generally pushed from behind via a relaxation in extensional strain across the riegel. Hence, accelerations occur in response to increases in water pressure that occur up-glacier and that precede local water-pressure rises. In addition, following a period of large storm events, surface speeds became more spatially coherent and were in phase with the diurnal water-pressure cycle. This suggests that the large water-pressure events lead to a spatially more homogeneous subglacial drainage system. Sliding laws need to take into account such temporal changes in spatial coherence of the subglacial drainage system.

A three-dimensional, finite-difference model based on a first-order solution of the ice-flow equations is applied to Haut Glacier d’Arolla, Switzerland. The numerical model successfully converges at horizontal resolutions down to 70 m, so a number of detailed comparisons with field data can be made. Modelled surface velocities with no basal sliding component are compared with surface velocities observed on the glacier over four different time periods. The best fit is achieved with over-winter surface velocities (R2 = 0.75) using a rate factor, A, in Glen’s flow law of 0.063 a−1 bar−3. Surface zones of maximum computed effective stress display a high level of coincidence with observed crevassing, the orientation of which is successfully predicted by the direction of the tensile component of the computed principal surface stress. Comparison of the relative magnitude and direction of computed principal stresses with principal strains measured at the ice surface also correspond closely. In an attempt to simulate the observed annual velocity distribution within a cross-section of the glacier tongue, we incorporate two basal-motion patterns into the model. By treating net annual ice motion as a time-weighted composite of three separate flow situations: normal sliding, enhanced sliding and no sliding, we are able to reproduce the key features of the observed cross-sectional ice and basal slip velocity distributions. These experiments indicate there may be substantial decoupling taking place along an elongated narrow zone at the bed of Haut Glacier d’Arolla and that this decoupling interacts in a complex manner with the englacial stress and strain field.

Under idealized conditions, when pressurized water has access to all low-pressure areas at the glacier bed, a sliding instability exists at a critical pressure, pc, well below the overburden pressure, p0. The critical pressure is given by , where l is the wave length and a is the amplitude of a sinusoidal bedrock, and T is the basal shear stress. When the subglacial water pressure, pw, approaches this critical value, the area of ice-bed contact, △l, becomes very small and the pressure on the contact area becomes very large. This pressure is calculated from a force balance and the corresponding rate of compression is obtained using Glen’s flow law for ice. On the assumption that compression in the vicinity of the contact area occurs over a distance of the order of the size of this area, Δl, a deformational velocity is estimated. The resultant sliding velocity shows the expected instability at the critical water pressure. The dependency on other parameters, such as wavelength l and roughness a/l, was found to be the same as for sliding without bed separation.

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.

Kongsvegen is a 102 km2 sub-polar (polythermal) surge-type glacier in northwest Spitsbergen, Svalbard. It surged just before 1948 and is currently in its quiescent phase. Measurements of surface geometry since 1966 show a retreat of the front and strong thinning of up to 75 m in the ablation area, and a build-up of up to 32 m in the accumulation area. Present-day annual velocities along the glacier are low, from 1.4 up to 3.6 m a-1. The measured mean net balance for the period 1987-94 and the balance reconstructed back to 1967 show a weak positive balance of about 0.1 m w.e. The measured actual ice flux is low and the mass transfer down-glacier at the ELA is only about 3-20% of that required for steady state. Thus, the glacier is building up towards a new surge. The total thickening rate on Kongsvegen is somewhat higher than in other cases from Svalbard, but it is small compared with other well-studied surge-type glaciers in Alaska and the Pamirs. This relatively low rate of change is a function of the low accumulation rate and the relatively cold climate compared to other areas and is common for surge-type glaciers in Svalbard.