A simple model for crystal growth in the ice shell of Europa has been made in order to estimate the size of ice crystals at Europa’s surface. If mass is lost from the surface of Europa due to sputtering processes, and the ice thickness is constant in time, ice crystals will be transported upwards in the ice shell. The crystals will therefore grow under varying conditions through the shell. The model predicts that ice crystals are 4 cm– 80 m across at the surface. For the preferred parameter values, a crystal size of the order of 7 m is calculated.

A one-dimensional numerical thermodynamic model is used to study the effects of strain heating on temperature profiles along the flowline of two outlet glaciers in Dronning Maud Land, Antarctica, flowing down a steep escarpment. Measurements of ice surface velocities on the glaciers show higher speeds than surface speeds calculated using Glen’s flow law. These calculations are based on ice-temperature distributions excluding strain heating in the general heat equation. The incorporation of strain heating in the general heat equation produces higher ice temperatures, and calculated ice surface speeds that are close to the measured values. It is found that relatively short-scale temporal and spatial steps in basal topography are enough to drive the ice flow into a positive feedback loop as long as the bedrock step produces a stress that overcomes the advection of cool ice from the surface. In this case, where surface temperatures are –25°C, stresses of 0.4 MPa are enough to drive the base of the ice to the melting point within 102 years.

The recent fluctuation of the central Asian climate, and its effect on the region’s glaciers, is poorly known, largely because of a lack of knowledge of the dynamic behaviour of so-called summer-accumulation-type glaciers. In this study, a one-dimensional numerical glacier model is used to simulate the dynamic response of Sofiyskiy glacier, Altai mountains, Russia, to climate forcing. A successful simulation of the observed historical front variations was accomplished by dynamic calibration. This resulted in a reconstruction of the recent mass-balance history of the glacier, showing a distinct decline in surface mass balance in the second half of the 19th century, a slightly higher mass balance at the beginning of the 20th century, followed by a steady decline towards present conditions. The future response of Sofiyskiy glacier was projected for six 21st-century climate scenarios. Under a “no-change” scenario, the glacier will retreat > 2 km by 2100. If air temperature gradually rises by > 5°C during this century, the glacier will vanish around 2100. Basic response characteristics of Sofiyskiy glacier were determined. These indicate rather low mass-balance sensitivity to temperature change, but a strong front reaction due to geometric conditions.

Accurate dating in ice sheets is required for a correct interpretation of palaeoclimatic records and for incorporation of material characteristics in the flow law which depend on ice age. In this paper, we make a comparison between a Lagrangian and Eulerian approach to the ice advection problem in numerical ice-sheet models. This comparison is first performed for a schematic two-dimensional ice sheet of Nye–Vialov type with a prescribed stationary velocity field. Severalcases are examined which incorporate basal melting, basal sliding and an undulating bed. A further comparison is made with an analytical solution for the ice divide. Both methods are also applied in a thermomechanical model of the Antarctic ice sheet for steady-state present-day conditions. Our main conclusion is that, for similar discretization parameters, the Lagrangian method produces less error than an Eulerian approach using a second-order upwinding finite-difference scheme, though the difference is small (<1%) for the largest part of the model domain. However, problems with the Lagrangian approach are introduced by the dispersion of tracers, necessitating the use of interpolation procedures that are a main source of additional error. It is also shown that a cubic-spline approximation of Lagrangian trajectories improves accuracy, but such a method is computationally hardly applicable in large-scale ice-sheet models.

The aim of this study is to derive basic ice dynamics for Nivlisen, a relatively small ice shelf in Dronning Maud Land, East Antarctica, and its drainage area. Therefore, the adaptation of an existing three-dimensional numerical flow model (Sandhäger, 2000) was undertaken, which had been applied previously to Ekstromisen and its drainage system. Compared to that region, Nivlisen and its drainage area represent a significantly more complicated geometrical situation. This has consequently large impacts on the flow regime, i.e. several modifications are necessary and reasonable. The diagnostic modelling is carried out in order to derive the current ice dynamics. The resulting ice-flow velocities seem to be too small compared to typical values for such glaciers. Therefore, the basal temperature at some gridpoints was set to pressure-melting point to obtain more realistic results. Furthermore, the use of a spatially varying parameter to describe basal sliding is advisable. Presenting the numerical results, the focus lies on the modelled ice-velocity field. The mass-balance quantities are calculated from the simulated velocity distribution and the underlying ice-geometry models derived from different datasets. The diagnostic results will serve as the basis for future prognostic modelling studies.

A three-dimensional thermomechanically coupled ice-sheet model including calculation of the first-order stress gradients is developed to perform numerical studies on the effects of stress components neglected in the zeroth-order shallow-ice approximation. Steady-state solutions are obtained with both a shallow-ice and a first-order ice-sheet model for several idealistic, radially symmetric ice-sheet configurations. The results show that the effects of the normal deviatoric-stress gradients on ice thickness are generally small, but the influence on basal temperatures and age profiles at an ice divide is significant.

Mechanisms that determine time-dependent changes of the marine ice margin in dynamic ice-sheet models are important but poorly understood. Here we derive an empirical formulation for changes in the marine extent when modelling the Northern Hemisphere ice sheets over the last glacial cycle in a three-dimensional thermomechanically coupled ice-sheet model. We assume that the strongest control on changes in marine extent is ice calving, and that the variable most crucial to calving is water depth. The empirical marine-extent relationship is tuned so that the major marine-retreat history of the Laurentide and Eurasian ice sheets is modelled accurately in time and space. We find that this empirical treatment relating marine extent to water depth is sufficient to reproduce the observations, and discuss the implications for the physics of marine margin changes and the dynamics of the Northern Hemisphere ice sheets since the Last Glacial Maximum.

Measurements of surface dynamics on polythermal John Evans Glacier, Nunavut, Canada, over two winter periods and every 7–10 days throughout two melt seasons (June–July 2000, 2001) provide new insight into spatio-temporal patterns of High Arctic glacier dynamics. In the lower ablation zone, mean annual surface velocities are 10–21 m a–1, but peak velocities up to 50% higher are attained during late June/early July. In the upper ablation zone and lower accumulation zone, mean annual surface velocities are typically 10–18 m a–1, and peak velocities up to 40% higher occur during late July. In the upper accumulation zone, mean annual surface velocities are 2–9 m a–1, and motion in mid- to late July exceeds this by up to 10%. Rapid drainage of ponded supraglacial water in the upper ablation zone to an initially distributed subglacial drainage system in mid-June may force excess surface motion in the warm-based lower glacier. The data indicate that the duration of the velocity response may be related to the rate of channelization of the basal drainage, and the velocity response may be transmitted up-glacier by longitudinal coupling. An increase in surface velocities in the middle glacier in late July occurs in conjunction with the opening of two further moulins in the accumulation zone.

A non-linear regression model describing the mass-balance distribution of the whole Vatnajökull ice cap, Iceland, for the years 1992–2000 is presented. All available data from some 40 locations over this 9 year period were used to determine the parameters of the model. The regression model uses six adjustable parameters which all have a clear physical interpretation. They are the slope, direction and the height of the equilibrium-line altitude (ELA) plane, two altitude mass-balance gradients, and a maximum value of the surface mass balance. It is found that the temporal variation of the observed mass-balance distribution can be accurately described through annual shifts of the ELA. Annual shifts in ELA are on the order of 100 m, which is of the same magnitude as the change expected to be caused by the climate variation predicted during the next decades. A slight trend towards a more negative mass balance is detected during this 9 year period.

Snow radar profiles were measured in Dronning Maud Land, East Antarctica, in the vicinity of the Finnish research station Aboa during austral summer 1999/2000. The aim was to study the annual layering in the upper 50 m of the snowpack and to compare the results obtained by three radar antenna frequencies (50, 100 and 800 MHz). Intercomparison of the radar profiles measured by the three frequencies shows that some individua linternal layers are visible with different antennas. Sparse accumulation-rate data from stake measurements and snow pits are compared with layer depths. The comparison reveals a great deal of scatter due to the large interannual variability in accumulation patterns. Using the radar layers as isochrones together with a model of depth–density–radar-wave velocity allows the individual accumulation data to be integrated, and a better estimate of accumulation patterns is obtained. Using the radar layering seems to be a much better method of estimating accumulation rate in this region than using a short series of stake measurements, even in the absence of deep ice cores to directly date the radar layering.

Ice surface roughness is a parameter of importance to many glaciological studies. Surface roughness, a derivative of microtopography, provides the high-resolution information necessary to characterize morphological types of ice surfaces and complements satellite data in investigations of surface features across scale. There has been a gap in observational scale between high-resolution satellite data, aircraft data and analyses at microscopic scale, the latter investigating material properties rather than micromorphology. To fill this gap, we designed and built the Glacier Roughness Sensor (GRS), a towed instrument that collects surface roughness data mechanically in swath-survey style with 0.1 m along-track spacing, 0.2 m across-track spacing, and sub-centimeter accuracy for areas typically 100 m by 175 m. As a result of this instrument development, the variable ice surface roughness has been added as a geophysical observable in the study of glaciers and ice sheets. The method utilized for analysis of GRS surface roughness data is geostatistical classification employing a range of parameters extracted from vario functions, which are generalized spatial structure functions. In a seasonal comparison of data from spring (May 1997) and summer (late July 1999), characteristic parameters of the spring and summer ice surface were calculated, and, as a result, an answer to the morphogenetic question of ice surface processes could be derived: in this part of the Jakobshavn Isbræ drainage basin, ice-surface structures develop in an interplay of ablation, refreezing, snowfall, wind and (distant) crevassing, each process yields characteristically different components of the surface structure, and ablat ion is the dominant morphogenetic process.

From temperature measurements down through the 3001 m deep borehole at the North Greenland Icecore Project (NorthGRIP) drill site, it is now clear that the ice at the base, 3080 m below the surface, is at the pressure-melting point. This is supported by the measurements on the ice core where the annual-layer thicknesses show there is bottom melting at the site and upstream from the borehole. Surface velocity measurements, internal radio-echo layers, borehole and ice-core data are used to constrain a time-dependent flow model simulating flow along the north-northwest-trending ice-ridge flow-line, leading to the NorthGRIP site. Also time-dependent melt rates along the flowline are calculated with a heat-flow model. The results show the geothermal heat flow varies from 50 to 200 mW m–2 along the 100km section of the modeled flowline. The melt rate at the NorthGRIP site is 0.75 cm a–1, but the deep ice in the NorthGRIP core originated 50 km upstream and has experienced melt rates as high as 1.1 cm a–1.

Accumulation and ablation rates over an Antarctic blue-ice area spanning the 14year period 1988–2002 are presented. Data were obtained by direct stake measurements. Large spatial and temporal variations in the net balance were observed without any clear trend over the entire period. There are marginally significant increases in snow accumulation, and in ablation in the blue-ice area farthest from the equilibrium zone (both at the 95% confidence level). The snow/blue-ice transition zone shows no change over the entire period of observation,and the blue-ice area near the zone shows no change in ablation rate over the 14 year period. The mass-balance gradient in Scharffenbergbotnen may have increased during the period 1988–2002. However, the changes are small, especially when compared with the changes observed elsewhere in Antarctica even relatively close to the blue-ice area. This may indicate that the blue-ice areas are relatively stable to changes in accumulation rate, and possibly temperature.

High-resolution ground-penetrating radar surveys at 50 MHz on the polythermal glaciers Hornbreen, Hambergbreen and several surrounding glaciers in southern Spitsbergen, Svalbard, are presented and interpreted. Accurate positioning was obtained using differential global positioning system (DGPS). Digital elevation models (DEMs) of the bedrock and surface were constructed. Comparison of DGPS data and surface DEMs with data from the topographic mappings from 1936 oblique stereoscopic aerial photographs and from Mission Russe in 1899–1901 shows that the Hornbreen and Hambergbreen surfaces are about 60–100 m thinner today in the upper part than at the beginning of the 20th century. Hornbreen has retreated by 13.5 km from the central part of the front, and Hambergbreen by 16 km. All the fronts of the nearby east-coast glaciers in this area have retreated. The bedrock DEM shows that the Hornbreen and Hambergbreen beds lie at –25 to 25 m a.s.l. The combination of sub-sea-level fronts and increasing steepness of the glaciers suggests that the low-lying glaciated valley filled by Hornbreen and Hambergbreen may become a partially inundated ice-free isthmus within perhaps 100 years.

Knowledge of the spatial distribution of bed lubrication regimes, i.e. frozen vs wet conditions, is crucial for understanding ice-sheet flow. Radar sounding can probe differing reflectivities between wet and frozen beds, but is limited by uncertainty in attenuation within the ice of bed echoes. Here we present two methods to estimate attenuation: (1) wide-angle radar sounding, in which source and receiver locations are varied so as to vary propagation path length, and thus echo amplitude; and (2) profiling, inwhich similar variations are obtained by sounding through varying ice thicknesses (assuming constant bed reflectivity). Siple Dome, West Antarctica, provides unusually favorable circumstances for application of these methods: the bed beneath Siple Dome is flat and uniform in its radar reflectivity, while ice thickness varies by several hundred meters. Wide-angle data 4 km from the summit yield an estimate for characteristic attenuation length of 124 m (35 dB km–1 loss), whereas profiling yields an estimate of 168 m.The difference between estimates is modest compared to the range of attenuation lengths reported in the literature. It may nonetheless prove informative by bounding effects of two ice properties to which the methods respond differently: (1) wide-angle sounding sampled relatively warm (lossy) ice beneath the summit, whereas the profiling method sampled relatively cold ice beneath the flanks as well; and (2) strain-induced crystal orientation fabrics and resulting dielectric anisotropy in the ice would vary from summit to flank, and may influence wide-angle sounding more strongly than profiling.

Comparison of the distribution of seasonal variations in surface elevation derived from a firn-densification–elevation model with observed variations derived from ERS-1/-2 satellite radar altimetry shows close similarity in the patterns of the amplitude of the variations over the North Greenland ice sheet. The amplitudes of the seasonal variations decrease from west to east and from south to north, determined by the accumulation rate and the surface-temperature distribution pattern. Several methods of estimating the amplitude of the seasonal variation in the observations are compared, including the use of a three-frequency sinusoidal function derived from the modeled seasonal variation that is asymmetric. The resulting correlation coefficient between the observed amplitude, estimated with the three-frequency function, and the modeled amplitude is 0.66 and the slope is 0.7. Residual differences may be caused by interannual variability in accumulation and temperature and other approximations in the model.

We investigate whether the recent slow-down of Whillans Ice Stream (WIS), West Antarctica, may lead to its complete stoppage in the near future, using a numerical model. Basal resistance to ice-stream motion is represented by a continuous till layer whose strength changes in response to basal melting and freezing. We implement a basal drainage system, which acts to hinder ice-stream stoppage through supply of extra water to those parts of the bed that are experiencing freezing. The ice module is a standard flowline model with parameterized key out-of-plane effects (Raymond, 1996). The most important result of our modeling effort is that we never obtained a slow-down that would not be followed by a complete stoppage within <100 years. WIS slow-down can be avoided in the model if large basal water-input rates are assumed, to satisfy basal freezing. In comparison, the tested perturbations in WIS width and mass balance had a relatively small effect on the tendency of the simulated ice stream to slow down. These results underscore the need for more quantitative constraints on the efficiency of sub-ice-stream water drainage. We conjecture that the present-day slow-down of WIS will evolve to shut-down in the next few decades, unless an addition of basal water prevents freeze-on-driven bed strengthening.

A plane, gravity-driven, steady flow of a polar ice sheet over a horizontal bedrock, with no-slip basal conditions, is considered. The ice is modelled as a linearly viscous, incompressible and anisotropic fluid, with evolving orthotropic fabric depending on local strain rates and deformations. For prescribed free-surface elevation and non-uniform temperature field, the ice velocities required to maintain the assumed geometry are calculated by using the finite-element method. The focus is on the mechanism of dynamic (migration) recrystallization occurring near the base ofan ice sheet and leading to significant weakening, and ultimately to the complete loss, of the anisotropic fabric developed in the upper part of the ice cap. The weakening of the fabric with increasing strain rate and temperature is modelled by means of a scaling function depending continuously on a single effective strain-rate invariant. The results of numerical calculations demonstrate the effect of the recrystallization process on the overall flow rate of the ice sheet, and normalized velocity and strain-rate depth profiles are compared for flows with and without recrystallization involved to illustrate the effect of this mechanism on the large-scale behaviour of polar ice sheets.

Precise topography from European Remote-sensing Satellite radar altimetry and high density of airborne radio-echo sounding in the area surrounding Dome C, Antarctica, show a link between surface features and subglacial lakes. In this paper, we extend the study to fine structures by computing a curvature-based coefficient (cy) related to surface undulations. These coefficient variations reveal many surface undulations, and some elongated features of this parameter seem to link known subglacial lakes. A population of high values of this coefficient, assumed to correspond to transitions between sliding and non-sliding flow regime, strengthen the appearance of a network which would link most of the lakes in the area. The existence of such a network impacts on ice-flow dynamics and on subglacial-lake studies.

Three debris-bearing ice facies were recognized at the base of Suess Glacier, a cold-based glacier damming a lake in Taylor Valley, South Victoria Land, Antarctica. These facies are termed “amber ice”,“solid facies” and “basal stratified facies”. This paper uses stable-isotope composition (δD and δ18O), gas content and gas composition (CO2, O2 and N2) to develop an understanding of the processes responsible for the formation of these facies. The basal ice is characterized by a striking difference in ice properties between the innermost end of a 25 m long tunnel dug 200 m upstream from the glacier front and the front itself. At the glacier front, co-isotopic data plot along a well-defined freezing slope (S = 5.6), whereas, inside the tunnel, the isotopic data offset from the freezing slope and from the local meteoric water-line (which has a slope of 8.2). CO2 concentrations rise from a minimum of about 1000 ppmv in the tunnel to about 220000ppmv at the front. Taken together, these characteristics strongly suggest an increasing contribution of liquid water in the formation of basal ice towards the glacier terminus. We therefore conclude that visually similar basal ice facies can have different origins.