This paper presents the bed topography of Jakobshavn Isbræ, Greenland, and Byrd Glacier, Antarctica, derived from sounding these glaciers with high-sensitivity radars. To understand the processes causing the speed-up and retreat of outlet glaciers, and to enable the development of next-generation ice-sheet models, we need information on bed topography and basal conditions. To this end, we performed measurements with the progressively improved Multichannel Coherent Radar Depth Sounder/Imager (MCoRDS/I). We processed the data from each antenna-array element using synthetic aperture radar algorithms to improve radar sensitivity and reduce along-track surface clutter. We then applied array and image-processing algorithms to extract the weak bed echoes buried in off-vertical scatter (cross-track surface clutter). At Jakobshavn Isbræ, we observed 2.7 km thick ice ~30 km upstream of the calving front and ~850 m thick ice at the calving front. We also observed echoes from multiple interfaces near the bed. We applied the MUSIC algorithm to the data to derive the direction of arrival of the signals. This analysis revealed that clutter is dominated by the ice surface at Jakobshavn Isbræ. At Byrd Glacier, we found ~3.62 km thick ice, as well as a subglacial trench ~3.05 km below sea level. We used ice thickness information derived from radar data in conjunction with surface elevation data to generate bed maps for these two critical glaciers. The performance of current radars must be improved further by ~15 dB to fully sound the deepest part of Byrd Glacier. Unmanned aerial systems equipped with radars that can be flown over lines spaced as close as 5 m apart in the cross-track direction to synthesize a two-dimensional aperture would be ideal for collecting fine-resolution data over glaciers like Jakobshavn near their grounding lines.

Dynamic changes on Greenland outlet glaciers are a primary driver for increases in ice-sheet mass loss and its contribution to sea-level rise. One dramatic example of such change has been observed at Jakobshavn Isbræ, which has thinned, retreated and doubled in speed since the early 2000s. Complementary to large changes on decadal scales, we observe the glacier response on shorter timescales, driven by tidal forcing and calving events. During a 14 day period in August 2009, we documented changes in geometry and speed near the terminus. On this timescale, ice flow responds to forcing at the front from iceberg calving and ocean tides. We observe a step-increase in velocity near the terminus during a large calving event, with transient deceleration in the days following the event. A simple calving-response model explains 94–99% of variations in detrended positions at the four sites considered. During each day, variability due to tidal forcing covers 10–90% of the variability that remains after removing effects accounted for by the calving-response model. The influence of the tidal forcing on flow decays upstream with a characteristic length scale of 2 km, comparable with about two ice thicknesses.

Mapping changes in glacier extent from repeat optical satellite data has revealed widespread glacier decline in nearly all regions of the world over the past few decades. While numerous studies have documented the changes of the outlet glaciers of the Northern and Southern Patagonia Icefields (NPI/SPI), information about glacier changes in the Patagonian Andes (to the north of the NPI) is much scarcer. Here we present an assessment of area changes for glaciers mainly located in the Palena district of Chile based on glacier inventories for 1985, 2000 and 2011 that were derived from two consecutive Landsat scenes and a digital elevation model. The analysis revealed a dramatic area decline for the largest glaciers and total area loss of 25% from 1985 to 2011. The lower parts of several larger glaciers (>10 km2) melted completely. Area loss below 1000 m elevation was 50–100% in both periods, and 374 glaciers out of 1664 disappeared. The number of proglacial lakes increased from 223 to 327 and their area expanded by 11.6 km2 (59%) between 1985 and 2011. Seasonal snow persisting at high elevations in the 2011 scene was a major obstacle to glacier delineation, so the obtained area change rate of ~1% a–1 over the entire period is a lower-bound estimate. The observed climate trends (e.g. cooling in Puerto Montt) are in contrast to the observed shrinkage.

Continuous surface debris cover strongly reduces the ablation of glaciers, but high melt rates may occur at ice cliffs that are too steep to hold debris. This study assesses the contribution of ice-cliff backwasting to total ablation of Miage glacier, Mont Blanc massif, Italy, in 2010 and 2011, based on field measurements, physical melt models and mapping of ice cliffs using a high-resolution (1 m) digital elevation model (DEM). Short-term model calculations closely match the measured melt rates. A model sensitivity analysis indicates that the effects of cliff slope and albedo are more important for ablation than enhanced longwave incidence from sun-warmed debris or reduced turbulent fluxes at sheltered cliff bases. Analysis of the DEM indicates that ice cliffs account for at most 1.3% of the 1 m pixels in the glacier’s debris-covered zone, but application of a distributed model indicates that ice cliffs account for ~7.4% of total ablation. We conclude that ice cliffs make an important contribution to the ablation of debris-covered glaciers, even when their spatial extent is very small.

The analysis of historical avalanche data is important when developing accurate hazard maps. The record of snow-avalanche disasters on Sakhalin and the Kuril Islands is incomplete, due to the historical division into periods of Japanese and Russian rule. Here we combine and analyze data from Japanese and Russian sources to reconstruct a continuous record of avalanche catastrophes in the region from 1910 to 2010. Despite the relatively small scale of the majority of catastrophic avalanches, with a total vertical drop < 200 m, we document evidence that places the region among the most avalanche-affected areas in the world. In total, 756 fatalities and > 238 injuries have occurred in 275 incidents over a 100 year period (two-thirds of those killed were Japanese). This death toll is higher than that in Canada, New Zealand or Iceland, or non-recreational fatalities in France. A wave of avalanche disasters (1930s–60s) following intense colonization of Sakhalin and the Kuril Islands is evident. Although this ‘wave’ could be considered a local issue of the past, many presently developing countries may face similar situations. The fatality rate has decreased over time, due to social factors, and differs from that of any other region, in its absence of deaths through recreational activities. Although in recent years the fatality rate is lower than that of Iceland or the USA, the per capita avalanche casualty rate on Sakhalin and the Kuril Islands remains among the highest in the world.

Since the 1970s, the sudden, rapid collapse of 20% of ice shelves on the Antarctic Peninsula has led to large-scale thinning and acceleration of its tributary glaciers. The leading hypothesis for the collapse of most of these ice shelves is the process of hydrofracturing, whereby a water-filled crevasse is opened by the hydrostatic pressure acting at the crevasse tip. This process has been linked to observed atmospheric warming through the increased supply of meltwater. Importantly, the low-density firn layer near the ice-shelf surface, providing a porous medium in which meltwater can percolate and refreeze, has to be filled in with refrozen meltwater first, before hydrofracturing can occur at all. Here we build upon this notion of firn air depletion as a precursor of ice-shelf collapse, by using a firn model to show that pore space was depleted in the firn layer on former ice shelves, which enabled their collapse due to hydrofracturing. Two climate scenario runs with the same model indicate that during the 21st century most Antarctic Peninsula ice shelves, and some minor ice shelves elsewhere, are more likely to become susceptible to collapse following firn air depletion. If warming continues into the 22nd century, similar depletion will become widespread on ice shelves around East Antarctica. Our model further suggests that a projected increase in snowfall will protect the Ross and Filchner–Ronne Ice Shelves from hydrofracturing in the coming two centuries.

We use a simple numerical model to test whether surface water influx to the bed of the interior Greenland ice sheet has the potential to cause significant subglacial channel growth similar to that observed near the ice-sheet margin and at alpine glaciers. We examine the effects on channel growth from (1) rapid supraglacial lake drainage events and (2) sustained water input into moulins. By assuming that all drainage occurs through subglacial channels and by prescribing favorable pressure conditions at the domain inlet, the model can provide upper bounds on channel growth. Our results indicate that R-channels do not grow significantly within the limited period of high pressure associated with lake drainage events. Subsequent channel growth only occurs with sustained pressures above overburden. Rapid closure of channels at low pressures suggests channels in the interior are unlikely to draw significant quantities of water from nearby distributed networks. These results indicate that other drainage mechanisms such as turbulent sheets or linked-cavity networks are likely to be of greater importance for interior subglacial drainage than the growth of channels.

We study the relation between glacier hypsometry and sensitivity of mass-balance rate to changes in equilibrium-line altitude (ELA) to assess whether hypsometry can reliably be used to estimate the sensitivity of unmeasured glaciers to changes in ELA. We express the sensitivity of mass-balance rate to ELA, dḂ/ dELA, as a function of accumulation–area ratio (AAR), its derivative against altitude, dAAR/dELA, and mass-balance functions of ELA. We then apply the concept to 139 glaciers in the Southern Patagonia Icefield for which we derive hypsometry and AAR, and analyze the influence of hypsometry on their mass-balance rate sensitivity. We confirm that glaciers where the bulk of area is located above (below) the ELA are the least (most) sensitive. Glaciers with unimodal hypsometric curves where the peak of area fraction is around the present ELA, and glaciers with bi-or multimodal area distributions, with the ELA located approximately between the bulges, have intermediate sensitivities. We conclude that hypsometry can be used as a first-order estimator of mass-balance rate sensitivity to ELA change.

We study the presence and effect of subglacial water on the motion of inland ice in western Dronning Maud Land, Antarctica. A full-Stokes model including three routing schemes for a thin film of subglacial water and a modification of a Weertman-type sliding relation, to account for higher sliding velocities under wet basal conditions, were used to perform 200 ka spin-up simulations on a 2.5 km grid. Subsequent 30 ka simulations with wet and dry basal conditions were analysed for the effects of sliding on the thermal regime and velocities. The occurrence of the major ice streams in this area is mainly controlled by the ice and bedrock geometry. Smaller glaciers only appear as pronounced individual glaciers when subglacial water is taken into account. The thermal regime is affected by creep instabilities produced by an ice rheology including a microscopic water content, leading to cyclic behaviour on millennial timescales of the ice flow and occurrence of temperate ice at the base.

Calving activity at the termini of tidewater glaciers produces a wide range of iceberg sizes at irregular intervals. We present calving-event data obtained from continuous observations of the termini of two tidewater glaciers on Svalbard, and show that the distributions of event sizes and inter-event intervals can be reproduced by a simple calving model, focusing on the mutual interplay between calving and the destabilization of the glacier terminus. The event-size distributions of both the field and the model data extend over several orders of magnitude and resemble power laws. The distributions of inter-event intervals are broad, but have a less pronounced tail. In the model, the width of the size distribution increases with the calving susceptibility of the glacier terminus, a parameter measuring the effect of calving on the stress in the local neighborhood of the calving region. Inter-event interval distributions, in contrast, are insensitive to the calving susceptibility. Above a critical susceptibility, small perturbations of the glacier result in ongoing self-sustained calving activity. The model suggests that the shape of the event-size distribution of a glacier is informative about its proximity to this transition point. Observations of rapid glacier retreats can be explained by supercritical self-sustained calving.

Shadowgraphy was employed to study snow saltation in boundary-layer wind tunnel experiments with fresh, naturally deposited snow. The shadowgraphy method allowed for a temporally and spatially high-resolution investigation of snow particle characteristics within a measurement area of up to 50 mm × 50 mm. Snow particle size and number characteristics, and their variation with height in the saltation layer, were analysed. The following observations and findings were made for the saltation layer: (1) the particle number decreases exponentially with height, (2) the mean particle diameter is fairly constant, with a very slight tendency to decrease with height, (3) the maximum particle diameter decreases linearly with height, and (4) the snow particle size distribution can be adequately described by gamma probability density functions. The shape and scale parameters of the gamma distribution were found to vary systematically, though only slightly, with height over ground and between experiments with different snowpack characteristics.

Our objective is to map dynamic provinces and investigate dynamic changes in Jakobshavn Isbræ, Greenland. We use an approach that combines structural glaciology and remote-sensing data analysis, facilitated by mathematical characterization of generalized spatial surface roughness that provides parameters related to ice dynamics, deformation and interaction of the ice with bed topography. The approach is applied to derive time series of elevation and roughness changes and to attribute changes during rapid retreat. Different dynamic types of fast- and slow-moving ice can be mapped from ICESat Geoscience Laser Altimeter System data (2003–09) and Airborne Topographic Mapper data, using spatial roughness characterization, validated with ASTER and bed-topographic data. Results of comparative analysis of elevation changes and roughness changes of Jakobshavn south ice stream indicate (1) surface lowering of 10–15 m a-1 between 2004 and 2009 and (2) no change in surface roughness and dynamic types. These findings are consistent with a front retreat as part of a fjord-glacier cycle or following warming of fjord water and with climatic warming, but not with an internal dynamic acceleration as a cause of the observed changes during rapid retreat. Relationships to changes in basal water pressure are discussed. All glaciodynamic changes appear to have initiated near the front and propagated up-glacier.

We simulated the Late Weichselian extent and dynamics of the Eurasian ice sheets using the shallow-ice approximation ice-sheet model SICOPOLIS. Our simulated Last Glacial Maximum ice-sheet extents closely resemble geomorphological reconstructions, and areas of modelled fast flow are consistent with the known locations of palaeo-ice streams. Motivated by documented velocity response to increased meltwater inputs on Greenland, we tested the sensitivity of the simulated ice sheet to the surface meltwater effect (SME) through a simple parameterization relating basal sliding to local surface melt rate and ice thickness. Model runs including the SME produce significantly reduced ice volume during deglaciation, with maximum ice surface velocities much greater than in similar runs that neglect the SME. We find that the simple treatment of the SME is not applicable across the whole ice sheet; however, our results highlight the importance of the SME for dynamic response to increased melting. The southwest sector of the Scandinavian ice sheet is most sensitive to the SME, with fast flow in the Baltic ice stream region shutting off by 15 ka BP when the SME is turned on, coincident with a retreat of the ice-margin position into the Gulf of Bothnia.

Radio-echo sounding (RES) is a radar technique widely employed in Antarctica and Greenland to define bedrock topography but, over the last decade, it has also played an important role in subglacial lake exploration and hydrogeological studies at the bedrock/ice interface. In recent studies, bedrock characterization has been improved through analysis of radar power echoes to evaluate the electromagnetic (EM) properties of the interface and allow the distinction between wet and dry interfaces. The RES received signal power depends on ice absorption and bedrock reflectivity, which is closely linked to the specific physical condition of the bedrock. In this paper, an evaluation of EM ice absorption was conducted starting from RES measurements collected over subglacial lakes in Antarctica. The idea was to calculate ice absorption starting from the radar equation in the case of subglacial lakes, where the EM reflectivity value is considered a known constant. These values were compared with those obtained from analysis of ice-core dielectric profiles from EPICA ice-core drilling data. Our analysis reveals that the ice absorption rate calculated from RES measurements has an average value of 7.2 dB km−1, and it appears constant, independent of the subglacial lake depth in different zones of the Dome C area.

This paper provides an introduction to adjoint methods, which are used to find the gradient of an objective function, as required by optimization algorithms. Examples are included, culminating in a data-assimilation problem from glaciology.

Fedchenko glacier is by far the largest glacier in the Pamir, Tajikistan. Owing to early accurate mapping of the glacier it is possible to evaluate glacier changes over eight decades, which is an exceptionally long time period for this remote mountain region. During this time a total volume loss of 5 km3 was observed on the main trunk of the glacier, while the total area changed by only 1.4%. It is observed that the volume loss migrates from the lower parts of the glacier towards the upper ablation zone. The comparatively small change in area is a result of the supraglacial debris cover on the glacier tongue, which decouples the area loss from the volume loss to a considerable degree. The observed velocities of the glacier do not reflect the volume changes up to now because the interannual variability is larger than possible long-term changes so far. The intra-annual velocity distribution in the central ablation zone probably reflects the evolution of the basal drainage system. Based on ice thickness measurements and simple ice-dynamic assumptions, the total volume of Fedchenko glacier is 123.4 ± 8 km3.

Force-balance calculations on Byrd Glacier, East Antarctica, reveal large spatial variations in the along-flow component of driving stress with corresponding sticky spots that are stationary over time. On the large scale, flow resistance is partitioned between basal (~80%) and lateral (~20%) drag. Ice flow is due mostly to basal sliding and concentrated vertical shear in the basal ice layers, indicating the bed is at or close to the pressure-melting temperature. There is a significant component of driving stress in the across-flow direction resulting in nonzero basal drag in that direction. This is an unrealistic result and we propose that there are spatial variations of bed features resulting in small-scale flow disturbances. The grounding line of Byrd Glacier is located in a region where the bed slopes upward. Nevertheless, despite a 10% increase in ice discharge between December 2005 and February 2007, following drainage of two subglacial lakes in the catchment area, the position of the grounding line has not retreated significantly and the glacier has decelerated since then. During the speed-up event, partitioning of flow resistance did not change, suggesting the increase in velocity was caused by a temporary decrease in basal effective pressure.

Thwaites Glacier, Antarctica, is experiencing rapid change and its mass could, if disgorged into the ocean, lead to ∼1 m of global sea-level rise. Efforts to model flow for Thwaites Glacier are strongly dependent on an accurate model of bed topography. Airborne radar data collected in 2004/05 provide 35 000 line km of bed topography measurements sampled every 20 m along track. At ∼15 km track spacing, this extensive dataset nevertheless misses considerable important detail, particularly: (1) resolution of mesoscale channelized morphology that can guide glacier flow; and (2) resolution of small-scale roughness between the track lines that is critical for determining topographic resistance to flow. Both issues are addressed using a conditional simulation that merges a stochastic realization (an unconditional simulation) with a deterministic surface. A conditional simulation is a non-unique interpolation that reproduces observed statistical behavior without affecting data values. Channels are resolved in the deterministic surface using an interpolation algorithm designed for sinuous channels. Small-scale roughness is resolved using a statistical analysis that accounts for heterogeneity, including an abrupt transition between ‘lowland’ and ‘highland’ morphology. Multiple realizations of the unconditional simulation can be generated to sample the probability space and allow error characterization in flow modeling.

We present a diagnostic glacier flowline model parameterized and constrained by new velocity data from ice-surface GPS installations and speckle tracking of TerraSAR-X satellite images, newly acquired airborne-radar data, and continental gridded datasets of topography and geothermal heat flux, in order to better understand two outlet glaciers of the East Antarctic ice sheet. Our observational data are employed as primary inputs to a modelling procedure that first calculates the basal thermal regime of each glacier, then iterates the basal sliding coefficient and deformation rate parameter until the fit of simulated to observed surface velocities is optimized. We find that the two glaciers have both frozen and thawed areas at their beds, facilitating partial sliding. Glacier flow arises from a balance between sliding and deformation that fluctuates along the length of each glacier, with the amount of sliding typically varying by up to two orders of magnitude but with deformation rates far more constant. Beardmore Glacier is warmer and faster-flowing than Skelton Glacier, but an up-glacier deepening bed at the grounding line, coupled with ice thicknesses close to flotation, lead us to infer a greater vulnerability of Skelton Glacier to grounding-line recession if affected by ocean-forced thinning and concomitant acceleration.

Blue-ice areas (BIAs) cover ~1% of the East Antarctic ice sheet and are visual evidence of persistent ablation. In these regions, more snow is sublimated and/or eroded than is accumulated. The physical processes driving the formation of BIAs are poorly understood. Here we combine a firndensification model with high-resolution (5.5 km) maps of surface mass balance and ice velocity to simulate the build-up and removal of a firn layer along an ice flowline passing Byrd Glacier. A BIA is formed once the complete firn layer is removed. Feedback processes, which enhance blue-ice formation through the difference in surface characteristics of snow and ice, are examined using sensitivity simulations. The presence of blue ice on Byrd Glacier is found to be mainly determined by (1) ice velocity, (2) surface mass balance and (3) the characteristics (thickness, mass) of the firn layer prior to entering the ablation area. With a moderate decrease of the surface mass balance, the location and extent of the simulated BIA on Byrd Glacier is found to be in good qualitative agreement with MODIS optical imagery.