An approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depth-independent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.

Stakes at 2 km intervals were installed in January 1997 and remeasured in February 1998, January 1999, January 2005 and during the 2007/08 austral summer along a 1248 km traverse route from Zhongshan station to Dome A, East Antarctica. Based on topographical parameters, meteorological features and the records of ∼650 stakes and six stake arrays, the route is divided into five zones. We find that the snow accumulation rate decreases with increasing altitude as one progresses inland, except in the zone 800–1128 km from the coast, where the average annual accumulation rate is higher than in the zone 524–800 km from the coast. The Dome A zone (1128–1248 km) has the lowest accumulation rate (35 kg m−2 a−1, 2005–08) due to having the highest elevation and being furthest from the coast. The surface mass balance in the region 202–1128 km from the coast exhibits no temporal change from 1999–2005 to 2005–08, but there is a change in the accumulation distribution. The zone from 202 to 524 km shows a decrease in surface mass balance from 84 kg m−2 a−1 in 1999–2005 to 67 kg m−2 a−1 in 2005–08, while the zone between 800 and 1128 km shows an increase from 67 kg m−2 a−1 in 1999–2005 to 75 kg m−2 a−1 in 2005–08.

We investigate the performance of five glacier melt models over a multi-decadal period in order to assess their ability to model future glacier response. The models range from a simple degree-day model, based solely on air temperature, to more-sophisticated models, including the full shortwave radiation balance. In addition to the empirical models, the performance of a physically based energy-balance (EB) model is examined. The melt models are coupled to an accumulation and a surface evolution model and applied in a distributed manner to Rhonegletscher, Switzerland, over the period 1929–2012 at hourly resolution. For calibration, seasonal mass-balance measurements (2006–12) are used. Decadal ice volume changes for six periods in the years 1929–2012 serve for model validation. Over the period 2006–12, there are almost no differences in performance between the models, except for EB, which is less consistent with observations, likely due to lack of meteorological in situ data. However, simulations over the long term (1929–2012) reveal that models which include a separate term for shortwave radiation agree best with the observed ice volume changes, indicating that their melt relationships are robust in time and thus suitable for long-term modelling, in contrast to more empirical approaches that are oversensitive to temperature fluctuations.

An investigation was made to estimate the variance, measurement errors and sampling error in currently accepted practices for manual snow density measurement carried out as part of snow profile observations using the available variety of density cutters. A field experiment in dry snow conditions was conducted using a randomized block design to account for layer spatial variability. Cutter types included a 500 cm3 aluminium tube, 200 and 100 cm3 stainless-steel box types, 200 cm3 stainless-steel wedge types and a 100 cm3 stainless-steel tube. Without accounting for variation due to weighing devices, the range of values for ‘accepted practice’ determined in this study included variation within individual cutters of 0.8–6.2%, variation between cutters of 3–12%, variation between cutter means and layer means of 2–7%, and under-sampling errors of 0–2%. The results of a statistical analysis suggest that snow density measurements taken using various density cutters are significantly different from each other. Without adjustment for under-sampling, and given that the mean of all measurements is the accepted true value of the layer density, variation exclusively between cutter types provides ‘accepted practice’ measurements that are within 11% of the true density.

Thwaites Glacier, the second largest ice stream in West Antarctica, drains an area of 166 500 ± 2000 km2 which accumulates 55 ± 5 Gt a−1 (or 60 ± 6 km3 ice a−1) into the Amundsen Sea, unrestrained by an ice shelf. Using interferometric synthetic-aperture radar (InSAR) data collected by the European Remote-sensing Satellites (ERS-1 and -2) in 1996, an output flux of 71 ±7 Gt a−1 (or 77 ± 8 km3 ice a−1) is estimated at the grounding line, where ice thickness is deduced from hydrostatic equilibrium. A similar flux, 70 ± 7 Gt a−1 (or 76 ± 8 km3 ice a−1), is obtained at a gate located 20 km upstream, where ice thickness was measured in 1978 by ice-sounding radar. Total accumulation in between the two gates is 1.6 Gt a−1, or 1.8 km3 ice a−1. Ice discharge therefore exceeds mass accumulation by 30 ± 15%, and Thwaites Glacier must be thinning and retreating at present. The InSAR data show that the glacier floating ice tongue exerts no back pressure on the inland ice, calves into tabular icebergs along a significant fraction of its grounding line, and has a grounding-line thickness which exceeds a prior-calculated limit for stability. Glacier thinning is confirmed at the coast by the detection of a 1.4 ± 0.2 km retreat of its grounding line between 1992 and 1996 with InSAR, which implies 3.2 ± 0.6 m ice a−1 thinning at the glacier center and less near the sides. These results complement the decimeter-scale annual surface lowering observed with satellite radar altimetry several hundred km inland of the grounding line. The magnitude of ice thinning estimated at the coast, however, rules out temporal changes in accumulation as the explanation for surface lowering. Ice thinning must be due to changes in ice flow.

We present a comprehensive new inventory of surge-type glaciers on the Novaya Zemlya archipelago, using high-resolution (up to 4 m) satellite imagery from 1976/77 (Hexagon), 1989 (Landsat TM), 2001 (Landsat ETM+) and 2006 (ASTER). A total of 692 glaciers and their forelands were observed for glaciological and geomorphological criteria indicative of glacier surging (e.g. looped moraines, heavy surface crevassing, surface potholes, thrust-block moraines, concertina eskers). This enabled the identification of 32 potential surge-type glaciers (compared with four previously identified) representing 4.6% of the total but 18% by glacier area. We assess the characteristics of surge-type glaciers. Surge-type glaciers are statistically different from non-surge-type glaciers in terms of their area, length, surface slope, minimum elevation, mid-range elevation and terminus type. They are typically long (median length 18.5 km), large (median area 106.8 km2) outlet glaciers, with relatively low overall surface slopes (median slope 1.7°) and tend to terminate in water (marine or lacustrine). They are predominantly directed towards and located in the more maritime western region of the Russian Arctic, and we suggest that surge occurrence might be related to large and complex catchment areas that receive increased delivery of precipitation from the Barents Sea.

Recent work has shown that surface-to-bed drainage systems re-form annually on parts of the Greenland ice sheet and some High Arctic glaciers, leading to speed-up events soon after the onset of summer melt. Surface observations and geophysical data indicate that such systems form by hydrologically driven fracture propagation (herein referred to as ‘hydrofracturing’), although little is known about their characteristics. Using speleological techniques, we have explored and surveyed englacial drainage systems formed by hydrofracturing in glaciers in Svalbard, Nepal and Alaska. In Hansbreen, Svalbard, vertical shafts were followed through ∼60 m of cold ice and ∼10 m of temperate basal ice to a subglacial conduit. Deep hydrofracturing occurred at this site due to a combination of extensional ice flow and abundant surface meltwater at a glacier confluence. The englacial drainage systems in Khumbu Glacier, Nepal, and Matanuska Glacier, Alaska, USA, formed in areas of longitudinal compression and transverse extension and consist of vertical slots that plunge down-glacier at angles of 55° or less. The occurrence of englacial drainages initiated by hydrofracturing in diverse glaciological regimes suggests that it is a very widespread process, and that surface-to-bed drainage can occur wherever high meltwater supply coincides with ice subjected to sufficiently large tensile stresses.

We have determined the in situ electric field attenuation length Lα (defined as the length over which the signal amplitude diminishes by a factor 1/e) for radio-frequency signals broadcast vertically through South Polar ice and reflected off the underlying bed. Conservatively assuming a bedrock field reflectivity for f = 380 MHz, and T = –50°C; the errors incorporate uncertainties in R. This value is consistent with previous estimates that the radiofrequency attenuation length exceeds the attenuation length at optical frequencies by an order of magnitude.

We present seismic and radar data from the onset region of Rutford Ice Stream, West Antarctica, which show the form and internal structure of a variety of bed forms beneath an active ice stream. The ice flow in the area of our survey accelerates from 72 to >200 m a–1, the ice is 2200–3200 m thick, and the bed of the ice stream lies up to 2000 m below present sea level. We have imaged the internal structure of the bed forms with seismic reflection techniques and also observed radar reflections from below the bed in some circumstances. We observed a transverse moraine 2 km wide and 1.5 km long beneath the slower-flowing part of the ice stream, which we interpret to be composed of unconsolidated sediment undergoing active deformation near the ice–sediment interface. We observed drumlins of classical form with elongation ratios of between 1:1.5 and 1:4.0 where the surface flow speed exceeded 95 m a–1. The conformity of the internal structure of the bed forms with the ice base suggests that the bed forms are active depositional features in congruence with the observation of a contemporary drumlin-forming episode in the distal part of the same ice stream. These observations provide the first direct evidence of the association between ice-stream flow speed and bed-form shape.

In this paper, a higher-order numerical flowline model is presented which is numerically stable and fast and can cope with very small horizontal grid sizes (<10 m). The model is compared with the results from Blatter and others (1998) on Haut Glacier d’Arolla, Switzerland, and with the European Ice-Sheet Modelling Initiative benchmarks (Huybrechts and others, 1996). Results demonstrate that the significant difference between calculated basal-drag and driving-stress profiles in a fixed geometry disappears when the glacier profile is allowed to react to the surface mass-balance conditions and reaches a steady state. Dynamic experiments show that the mass transfer in higher-order models occurs at a different speed in the accumulation and ablation areas and that the front position is more sensitive to migration compared to the shallow-ice approximation.

The ApRES (autonomous phase-sensitive radio-echo sounder) instrument is a robust, lightweight and relatively inexpensive radar that has been designed to allow long-term, unattended monitoring of ice-shelf and ice-sheet thinning. We describe the instrument and demonstrate its capabilities and limitations by presenting results from three trial campaigns conducted in different Antarctic settings. Two campaigns were ice sheet-based – Pine Island Glacier and Dome C – and one was conducted on the Ross Ice Shelf. The ice-shelf site demonstrates the ability of the instrument to collect a time series of basal melt rates; the two grounded ice applications show the potential to recover profiles of vertical strain rate and also demonstrate some of the limitations of the present system.

Water flowing in tubular channels inside a glacier produces frictional heat, which causes melting of the ice walls. However the channels also have a tendency to close under the overburden pressure. Using the equilibrium equation that at every cross-section as much ice is melted as flows in, differential equations are given for steady flow in horizontal, inclined and vertical channels at variable depth and for variable discharge, ice properties and channel roughness. It is shown that the pressure decreases with increasing discharge, which proves that water must flow in main arteries. The same argument is used to show that certain glacier lakes above long flat valley glaciers must form in times of low discharge and empty when the discharge is high, i.e. when the water head in the subglacial drainage system drops below the lake level. Under the conditions of the model an ice mass of uniform thickness does not float, i.e. there is no water layer at the bottom, when the bed is inclined in the down-hill direction, but it can float on a horizontal bed if the exponent n of the law for the ice creep is small. It is further shown that basal streams (bottom conduits) and lateral streams at the hydraulic grade line (gradient conduits) can coexist. Time-dependent flow, local topography, ice motion, and sediment load are not accounted for in the theory, although they may strongly influence the actual course of the water. Computations have been carried out for the Gornergletscher where the bed topography is known and where some data are available on subglacial water pressure.

We have estimated temperature gradients and melt rates at the bottom of the ice streams in West Antarctica. Measured velocities were used to include the effects of horizontal advection and strain heating in the temperature model and to determine shear heating at the bed. Our modeled temperatures agree well with measured temperatures from boreholes in regions of steady flow. We find that ice-stream tributaries and the inland ice account for about 87% of the total melt generated beneath the Ross ice streams and their catchments. Our estimates indicate that the ice plains of Whillans Ice Stream and Ice Stream C (even when active) have large areas subject to basal freezing, confirming earlier estimates that import of water from upstream is necessary to sustain motion. The relatively low melt rates on Whillans Ice Stream are consistent with observations of deceleration over the last few decades and suggest a shutdown may take place in the future, possibly within this century. While there are pockets of basal freezing beneath Ice Streams D and E, there are larger areas of basal melt that produce enough melt to more than offset the freezing, which is consistent with inferences of relatively steady flow for these ice streams over the last millennium.

Glacier area changes on the Tibetan Plateau were studied in different drainage basins based on Landsat satellite images from three epochs: 263 in the mid-1970s, 150 in 1999–2002 and 148 in 2013/14. Three mosaics (M1976, M2001 and M2013) with minimal cloud and snow cover were constructed, and the uncertainty due to each epoch having a finite span was accounted for. Glacier outlines (TPG1976, TPG2001 and TPG2013) were digitized manually with guidance from the SRTM DEM v4.1 and Google Earth imagery. To achieve complete multi-temporal coverage in a reasonable time, only debris-free ice was delineated. Area mapping uncertainty was evaluated at three study sites, Mount Qomolangma (Everest), Mount Naimona'Nyi, Mount Geladandong, where the largest differences between present and earlier measurements were within ~±4%. Area differences with previous inventories ranged from −19.6% (TPG1976 minus the first Chinese Glacier Inventory) to −3.6% and −1.1% (TPG2013 and TPG2001, respectively minus the second Chinese Glacier Inventory), while the difference TPG2001 minus the GAMDAM Glacier Inventory was +10.4%. Glacier area on the plateau decreased from 44 366 ± 2827 km2 (1.7% of the study area) in the 1970s to 42 210 ± 1621 km2 in 2001 and 41 137 ± 1616 km2 in 2013. Shrinkage was faster in external drainage basins of the southeast than in the interior basins of the northwest, from a maximum of −0.43% a−1 (−1.60% a−1 during 1994–2013) in the Mekong catchment down to a minimum of −0.12% a−1 in the Tarim interior drainage.

Using dense networks of three-component seismometers installed in direct contact with the ice, the seismic activity of Gornergletscher, Switzerland, was investigated during the summers of 2004 and 2006, as subglacial water pressures varied drastically. These pressure variations are due to the diurnal cycle of meltwater input as well as the subglacial drainage of Gornersee, a nearby marginal ice-dammed lake. Up to several thousand seismic signals per day were recorded. Whereas most icequakes are due to surface crevasse openings, about 200 events have been reliably located close to the glacier bed. These basal events tend to occur in clusters and have signals with impulsive first arrivals. At the same time, basal water pressures and ice-surface velocities were measured to capture the impact of the lake drainage on the subglacial hydrological system and the ice-flow dynamics. Contrary to our expectations, we did not observe an increase of basal icequake activity as the lake emptied, thereby raising the subglacial water pressures close to the flotation level for several days. In fact, the basal icequakes were usually recorded during the morning hours, when the basal water pressure was either low or decreasing. During the high-pressure period caused by the drainage of the lake, no basal icequakes were observed. Furthermore, GPS measurements showed that the glacier surface was lowering during the basal seismic activity. These observations lead us to conclude that such icequakes are connected to the diurnal variation in glacier sliding across the glacier bed.

Medial moraines form striking dark stripes that widen non-linearly, steepen laterally and increase in relief down-glacier from the equilibrium line. Coalescence of these low-ablation-rate features can feed back strongly on the mass balance of a glacier snout. Ablation-dominated medial moraines originate from debris delivered to glacier margins, producing a debris-rich septum between tributary streams of ice below their confluence. Emergence of this ice below the equilibrium line delivers debris to the glacier surface, which then moves down local slopes of evolving morainal topography. A quantitative description of moraine evolution requires specification of the debris concentration field within the glacier, treatment of the melt-rate dependence on debris thickness, and characterization of processes that transport debris once it emerges onto the ice surface. Debris concentration at glacier tributary junctions scales with the erosion rates and the lengths of the tributary-valley walls, and inversely with the tributary ice speeds. Melt rate is damped exponentially by debris, with a ∼10 cm decay scale. Debris flux across the glacier surface scales with the product of debris thickness and local slope. Analytical and numerical results show that medial moraines should develop cross-glacier profiles with parabolic crests and linear slopes, and should widen with age and hence distance down-glacier. Debris should be both thin and uniform over the moraine. Observed faster-than-linear growth of moraine widths with distance reflects the increasing ablation rate down-glacier. Increase in medial moraine cover reduces the local average ablation rate, allowing the glacier to extend further down-valley than meteorology alone would suggest. This feedback is especially effective when moraines merge.

Supraglacial ponds on Tasman Glacier, New Zealand, initiated the development of the large Tasman Lake during the 1980s and still play an important role for ice loss and further terminus disintegration. Limnological and glaciological measurements between 2001 and 2003 reveal distinct differences between ponds. The hydraulic connection of a pond to the englacial water level exerts a key control on whether the pond contributes to longer-term terminus disintegration. In the earlier stages of pond development, ice loss occurs predominantly in the horizontal dimension by subaerial melt. Subaqueous calving at later stages plays a major role for ice loss. During the capture of a pond by the lake, substantial limnological changes lead to changes in relative significance and rates of ice loss processes, the most important being the change from melting to predominantly calving. As a result, ice loss accelerated from around 11 m a−1 of melt under partial debris cover to a retreat by calving and melting of 34 m a−1. Ice loss at the ponds accounted for only 10% of the surface loss in the lower terminus area, but is likely to increase in the future with enlargement and coalescence of ponds.

Basal slip accounts for a large part of the flow of ice streams draining ice from Antarctica and Greenland into the ocean. Therefore, an appropriate representation of basal slip in ice flow models is a prerequisite for accurate sea level rise projections. Various friction laws have been proposed to describe basal slip in models. Here, we compare the influence on grounding line (GL) dynamics of four friction laws: the traditional Weertman law and three effective pressure-dependent laws, namely the Schoof, Tsai and Budd laws. It turns out that, even when they are tuned to a common initial reference state, the Weertman, Budd and Schoof laws lead to thoroughly different steady-state positions, although the Schoof and Tsai laws lead to much the same result. In particular, under certain circumstances, it is possible to obtain a steady GL located on a reverse slope area using the Weertman law. Furthermore, the predicted transient evolution of the GL as well as the projected contributions to sea level rise over a 100-year time horizon vary significantly depending on the friction law. We conclude on the importance of choosing an appropriate law for reliable sea level rise projections and emphasise the need for a coupling between ice flow models and physically based subglacial hydrological models.

Englacial cave systems were mapped using speleological techniques in three debris-covered glaciers in the Khumbu Himal, Nepal. Detailed three-dimensional mapping of the cave systems and observations of relationships with structures in the surrounding ice show conduits formed by a mechanism directly analogous to speleogenesis in limestone karst. The highest, oldest parts of all passages developed along debris-filled crevasse traces with hydraulic conductivity in the range 10–4 to 10–5ms–1. Conduits form when these hydraulically efficient pathways bridge between areas with different hydraulic potential. They then evolve by grading (through head-ward migration of nick points and vertical incision) to local base level, often the surface of supraglacial lakes. Most supraglacial lakes on Himalayan glaciers are perched above the elevation of the terminal stream, and exist for a few years before draining through englacial conduits. As a result, near-surface drainage evolution is frequently interrupted by base-level fall, and conduits may record multiple phases of incision. Conduits commonly migrate laterally during incision, undermining higher levels of the ice and encouraging collapse. Voids can be created by fluvial processes and collapse of crevassed ice. The oft-noted resemblance of the surface morphology of debris-covered glaciers to karst landscapes thus extends to the subsurface, and karst hydrology provides a framework for understanding englacial drainage.