Floating ice shelves that fringe the coast of Antarctica resist the flow of grounded ice into the ocean. One of the key factors governing the amount of flow resistance an ice shelf provides is the rigidity (related to viscosity) of the ice that constitutes it. Ice rigidity is highly heterogeneous and must be calibrated from spatially continuous surface observations assimilated into an ice-flow model. Realistic uncertainties in calibrated rigidity values are needed to quantify uncertainties in ice sheet and sea-level forecasts. Here, we present a physics-informed machine learning framework for inferring the full probability distribution of rigidity values for a given ice shelf, conditioned on ice surface velocity and thickness fields derived from remote-sensing data. We employ variational inference to jointly train neural networks and a variational Gaussian Process to reconstruct surface observations, rigidity values and uncertainties. Applying the framework to synthetic and large ice shelves in Antarctica demonstrates that rigidity is well-constrained where ice deformation is measurable within the noise level of the observations. Further reduction in uncertainties can be achieved by complementing variational inference with conventional inversion methods. Our results demonstrate a path forward for continuously updated calibrations of ice flow parameters from remote-sensing observations.

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.

Understanding the effects of climate on glaciers requires precise estimates of ice volume change over several decades. This is achieved by the geodetic mass balance computed by two means: (1) the digital elevation model (DEM) comparison (SeqDEM) allows measurements over the entire glacier, however the low contrast over glacierized areas is an issue for the DEM generation through the photogrammetric techniques and (2) the profiling method (SePM) is a faster alternative but fails to capture the spatial variability of elevation changes. We present a new framework (SSD) that relies upon the spatial variability of the elevation change to densify a sampling network to optimize the surface-elevation change quantification. Our method was tested in two small glaciers over different periods. We conclude that the SePM overestimates the elevation change by ~20% with a mean difference of ~1.00 m (root mean square error (RMSE) = ~3.00 m) compared with results from the SeqDEM method. A variogram analysis of the elevation changes showed a mean difference of <0.10 m (RMSE = ~2.40 m) with SSD approach. A final assessment on the largest glacier in the French Alps confirms the high potential of our method to compute the geodetic mass balance, without going through the generation of a full-density DEM, but with a similar accuracy than the SeqDEM approach.

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.

The effect of growth velocity υ and solute concentration C on the cellular substructure that develops in NaCl ice is studied in the range 3×10−3 to 10−5 cm s−1 and 1 to 100‰ respectively. The substructure is the result of the formation of a constitutionally super-cooled zone in the liquid ahead of the advancing interface. Unidirectional freezing runs were made by placing a cold plate in contact with the “top” of the solution and using cold-plate temperatures of −20 and −70°C. The growth velocities were determined from a least-squares fit of the growth data to a power series. The average spacings between neighboring substructures a0were measured from photomicrographs of precisely located thin sections. Log-log plots of a0against υ show that the slope n gradually changes as a function of υ. In the run where no convection occurred, n changes from to 1 as υ decreases in agreement with the prediction of Bolling and Tiller. The results of Rohatgi and Adams are also shown to be in good agreement with this prediction. On the other hand when convection occurs, n changes from to approximately o as υ decreases. This is caused by convection reducing the effective value at C at the growing interface. The variation of a0with C is quite complex and shows a minimum in the composition range 9 to 25‰ NaCl.

Borehole-based electrical resistivity surveys have the capacity to enhance our understanding of the structure of englacial drainage pathways in temperate ice. We summarize inter-borehole electrical resistivity tomography (ERT) as currently used in hydrogeological investigations and as adapted for imaging englacial drainage. ERT connections were successfully made for the first time in glacier ice, following artificial mineralization of borehole waters at Haut Glacier d’Arolla, Switzerland. Here, two types of electrical connection were made between boreholes spaced up to 10 m apart and drilled to depths of between 20 and 60 m. Most tests indicated the presence of resistively homogeneous ice with uniform bulk resistivities of ~108 - 109 Ω m. However, ERT was also successfully used to identify and characterize a hydraulically conductive englacial fracture that intersected two boreholes at a depth of ~ 13 m below the glacier surface. The presence of this connecting void was suggested by drilling records and verified by dual borehole-impulse testing. The reconstructed tomogram for these boreholes is characterized by a background ice-resistivity field of ~109 Ω m that is disrupted at a depth of ~13 m by a sharp, sub-horizontal low-resistivity zone (~10 4 Ω m). Inter-borehole ERT, therefore, has the capacity to image both uniform and fractured temperate glacier ice.

The synthetic-aperture radar-interferometry technique is used to detect the migration of the limit of tidal flexing, or hinge line, of the floating ice longue of Peter-mann Gletscher, a major outlet glacier of north Greenland. The hinge line is detected automatically from differential interferograms using a model-fitting technique based on an elastic-beam theory. The statistical noise of the model fit is less than 3 mm, and the hinge line is mapped with a precision of 30 m. Following automatic registration of multidate image data to a precision of 5m, hinge-line migration is subsequently detected with a precision of 40 m in the horizontal plane across the glacier width. The results show that the hinge line of Petermann Gletscher migrates back and forth with tide by ±70m, in excellent agreement with the migration calculated from ocean tides predicted by a tidal model combined with the glacier surface and basal slope measured by an ice-sounding radar. Superimposed on the short-term hinge-line migration due to tide, we detect a hinge-line retreat of 270 m in 3.87 years which varies across the glacier width by ± 120 m. The retreat suggests glacier thinning at a rate of 78 + 35 cm ice a−1. Coincidentally, an analysis of ice-volume fluxes indicates that the hinge-line ice flux of Petermann Gletscher exceeds its balance flux by 0.88±1km3 ice a−1, which in turn implies glacier thinning at 83+95cm ice a−1 in the glacier lower reaches. Both methods therefore suggest that Petermann Gletscher is currently losing mass to the ocean.

The measurements by seismic sounding of the long profile of the Unteraar Glacier reported by Mercanton and Renaud are compared with theoretical calculations. By taking the valley to be a cylinder of parabolic cross-section a theoretical curve for the surface is deduced which depends on one unknown parameter only, the average shear stress on the bed. If this parameter is given the value 0.77 × 106 dynes/cm.2 the theoretical curve agrees well with the measurements.

‘Extrusion flow’ describes any velocity field where maximum horizontal velocity occurs below the surface. By 1914, viscous flow and basal sliding over rough beds were accepted concepts. Between the world wars, there was little communication between naturalists describing complicated ice sheets, and physicists studying fundamental processes controlling flow. Max Demorest brought concepts from mechanics into glaciology and glacial geology; however, his extrusion flow theory, to explain how ice flowed out of central Greenland, overlooked force imbalance. Rudolf Streiff-Becker found an apparent large imbalance between ice flux discharged through a gate and net accumulation in the upstream catchment at Claridenfirn, Switzerland. Because he underestimated uncertainty in ice depth, he had to propose a strong undercurrent (extrusion flow) to evacuate the excess mass. Reassessment of his assumptions shows that extrusion was actually unnecessary. However, confluence of two lines of evidence for extrusion flow added stature to the concept. In 1952, John Nye showed that free extrusion flow was impossible due to force imbalance. Two forms of extrusion flow survive: capped extrusion flow is possible on local scales where longitudinal stress gradients allow upper ice to move slowly, and rigid- body rotational flow can allow deeper ice to move faster without strain.

When an ice-flow model is constrained by data that exist over only a section of an ice sheet, it is computationally advantageous to limit the model domain to only that section. For example, a limited domain near an ice-core site might cross an ice divide, and have no termini. Accurately calculating ice-sheet evolution in response to spatial and temporal variations in climate and ice flow depends on accurately calculating the transient ice flux crossing the limited-domain boundaries. In the absence of information from outside the limited domain, this is an ill-posed problem. Boundary conditions based only on information from inside the limited domain can produce ice-sheet evolution incompatible with the full ice sheet within which we suppose it to exist. We use impulse-response functions to provide boundary values that are informed by the external ice sheet, without conventionally 'nesting' the limited domain in a full ice-sheet model. Evolution within a limited domain can then be consistent with evolution of boundary conditions is designed for future use in affected the limited domain can be inferred from the full ice sheet. Our treatment of limited-domain an inverse problem in which external changes that data from within the limited domain.

This paper presents a newly derived velocity field of the Brunt Ice Shelf and Stancomb-Wills Ice Tongue in East Antarctica. Velocity is derived using automated feature-tracking techniques on RADARSAT-1 imagery from the 1997 Antarctic Mapping Mission-1 (AMM-1) and 2000 Modified Antarctic Mapping Mission (MAMM). We measure velocities up to 1350 m a−1 at the ice front. Closer investigation of the velocity field and radar images reveals an obvious divergence of contemporary flowlines from relict flow stripes along a portion of Stancomb-Wills Ice Tongue. Analysis of relict flow stripes can reveal glacial events in the past. Assuming relatively steady flow since the event occurred, we utilize the current velocity field to reconstruct former stripe configuration. We believe the flowline deviation points to a change in dynamics that occurred approximately 140 years ago, perhaps due to thinning and an associated shift in grounding-line position. This seems to be supported by historic observations and bottom topography data.

In our comments, we re-evaluate Brugger and others (2018) Lycopodium/Eucalyptus double marker approach, based on the fact that previous evidence already demonstrated that the batch of Eucalyptus tablets used by Brugger and others (2018) is not suitable for quantitative comparisons as they are characterized by inconsistent pollen concentration. We present clear evidence that the Eucalyptus tablets do feature inaccurate pollen concentrations, and are therefore improper for all quantitative comparisons of microfossil extraction methods. Consequently, the results of the quantitative and qualitative assessment of different pollen extraction methods from ice samples compiled by Brugger and others (2018) are highly questionable due to the use of faulty marker tablets.

Experiments have established that the fracture toughness of fresh-water, bubbly ice is not affected by the presence of salt water.

Several large submerged ice masses are described from along western McMurdo Sound, Antarctica. The most important discovery is that Cape Chocolate and the adjacent island that form Salmon Bay are large, grounded ice masses mounted with morainal sediment. Both features are probably remnants of a past expansion of the Ross Ice Shelf. As such, their strata and potential temporal markers may help to unravel the glacial geological chronology of McMurdo Sound. The island was connected to Cape Chocolate during the early British Antarctic expeditions and split away between 1908 and 1956. Large sections of the Ross Ice Shelf have broken out along western McMurdo Sound several times since 1908. Ice walls grounded in shallow water were only observed near large receding ice masses. The location of these walls also corresponds to the recent calving pattern of the Ross Ice Shelf.

While hot-water drilling is a well-established technique used to access the subsurface of ice masses, drilling into high-elevation (≳ 4000 m a.s.l.) debris-covered glaciers faces specific challenges. First, restricted transport capacity limits individual equipment items to a volume and mass that can be slung by small helicopters. Second, low atmospheric oxygen and pressure reduces the effectiveness of combustion, limiting a system's ability to pump and heat water. Third, thick supraglacial debris, which is both highly uneven and unstable, inhibits direct access to the ice surface, hinders the manoeuvring of equipment and limits secure sites for equipment placement. Fourth, englacial debris can slow the drilling rate such that continued drilling becomes impracticable and/or boreholes deviate substantially from vertical. Because of these challenges, field-based englacial and subglacial data required to calibrate numerical models of high-elevation debris-covered glaciers are scarce or absent. Here, we summarise our experiences of hot-water drilling over two field seasons (2017–2018) at the debris-covered Khumbu Glacier, Nepal, where we melted 27 boreholes up to 192 m length, at elevations between 4900 and 5200 m a.s.l. We describe the drilling equipment and operation, evaluate the effectiveness of our approach and suggest equipment and methodological adaptations for future use.

The geographical distribution of firn temperature, annual accumulation rate as well as deuterium and oxygen-18 content in the firn were determined along an east-west transect through central Greenland. This study is based on isotopic and chemical analyses of shallow firn cores at 18 sites along the EGIG line and high-precision firn-temperature measurements m 17 steam-drilled boreholes along the eastern part of the transect. The firn temperatures at 15 m depth range from -31.6°C at Dome GRIP (3230 m a.s.l.) to -11.4°C at Caecilia Nunatak (eastern ice margin at 1600 m a.sl.) and -18°C at T05 (near the western ice margin at 1900 m a.s.l.). The temperature/altitude gradient changes from -0.7°C (100 m)−1 in the ice divide region to -1.1 °C (100 m)−1 in the eastern part of the dry-snow zone. The temperature/latitude gradient in the central part of the EGIG line is -0.7° C lat−1 The average annual accumulation decreases significantly from the west (~47 cm a−1 water equivalent at T05) towards the ice divide (20–25 cm a−1 water equivalent from T99 to T43). Accumulation rates are constantly low east of the ice divide (−23–17 cm a−1 water equivalent), thus dividing central Greenland into two climatologically different regions. The average δ18O and δD values along the whole EGIG line reflect the well-known temperature-dependence for Greenland very well (e.g. ∂18O/∂Tm = 0.69%ₒ °C–1 Different regression lines for the western and eastern part, however, should be applied. Unlike the mean annual temperature, the isotopic minimum along the EGIG line lies east of the ice divide. This geographical distribution supports the choice of different water-vapour trajectories in central Greenland for the west and for the east. Significant parts of the water precipitated over the western slope are attributed to cyclonic systems entering Greenland from the west. The deuterium excess shows no significant geographical trend but a uniform seasonal variation at all sites along the EGIG line, suggesting equal contributions from vapour-source areas of the water precipitated over central Greenland.

High-resolution maps of the glacier bed are developed through a pseudo-three-dimensional migration of a dense array of radio-echo sounding profiles. Resolution of three-dimensional maps of subglacial surfaces is determined by the radio-echo sounding wavelength, data sparing in the field, and migration. Based on synthetic radio-echo sounding profile experiments, the maximum resolution of the final map cannot exceed one half-wavelength. A methodology of field and processing techniques is outlined to develop a maximum-resolution map of the glacier bed. The field and processing techniques are used to develop a map of the glacier bed below part of Worthington Glacier, a temperate valley glacier in south-central Alaska. The field techniques and the processing steps used on the glacier result in a map of 20 m x 20 m resolution.

Sediment-laden icebergs are rarely sighted in Antarctic waters. However, during the recent Deep Freeze 79-USCGC Glacier expedition to the George V Coast and the south-western Ross Sea, nine sediment-laden icebergs and several pieces of pack ice with surficial sediment layers were observed. These observations include basal debris zones, debris slumped on to glaciers and floating ice, and englacial debris believed to have been incorporated along shear zones.

Sediment samples collected from icebergs were texturally and mineralogically variable. Some were unsorted mixtures consisting of a wide variety of angular minerals and rock fragments; others consisted primarily of slate clasts, quartz sand, and rock flour.