We present continuous estimates of snow and firn density, layer depth and accumulation from a multi-channel, multi-offset, ground-penetrating radar traverse. Our method uses the electromagnetic velocity, estimated from waveform travel-times measured at common-midpoints between sources and receivers. Previously, common-midpoint radar experiments on ice sheets have been limited to point observations. We completed radar velocity analysis in the upper ~2 m to estimate the surface and average snow density of the Greenland Ice Sheet. We parameterized the Herron and Langway (1980) firn density and age model using the radar-derived snow density, radar-derived surface mass balance (2015–2017) and reanalysis-derived temperature data. We applied structure-oriented filtering to the radar image along constant age horizons and increased the depth at which horizons could be reliably interpreted. We reconstructed the historical instantaneous surface mass balance, which we averaged into annual and multidecadal products along a 78 km traverse for the period 1984–2017. We found good agreement between our physically constrained parameterization and a firn core collected from the dry snow accumulation zone, and gained insights into the spatial correlation of surface snow density.

Marine ice accretes at the base of ice shelves, often infilling open structural weaknesses and increasing ice-shelf stability. However, the timing and location of marine ice formation remain poorly understood. This study determines marine ice source water composition and origin by examining marine ice crystal morphology, water isotope and solute chemistry in ice samples collected from the southern McMurdo Ice Shelf (SMIS), Antarctica. The measured co-isotopic record together with the output of a freezing model for frazil crystals indicate a spatio-temporally varying water source of sea water and relatively fresher water, such as melted meteoric or marine ice. This is in agreement with the occurrence of primarily banded and granular ice crystal facies typical for frazil ice crystals that nucleate in a supercooled mixture of water masses. We propose that marine ice exposed at the surface of SMIS, which experiences summer melt, is routed to the ice-shelf base via the tide crack. Here frazil crystals nucleate in a double diffusion mechanism of heat and salt between two water masses at their salinity-dependent freezing point. Recycling of previously formed marine ice facilitates ice-shelf self-sustenance in a warming climate.

The energy-line method results from the graphical representation of the energy law as applied in hydraulics. It makes it easier to understand the entire process of the movement of an avalanche from where it breaks away to where it is deposited. The technique, the energy lines, and the average slope of avalanches, as well as the theoretical energy lines of the one-coefficient and two-coefficient models of avalanche dynamics, are described. The method is explained by means of an example.

Layering affects the air flow through snow caused by surface pressure variations. The horizontal and total fluxes are high in hoar layers but the pressure perturbations and vertical components of the flow do not penetrate as deeply as in homogeneous snow. That is because the layers “pipe” the flow horizontally toward the area of low pressure. An ice layer at the surface reduces the total flow everywhere. The flow decreases as ice-layer thickness increases and, in general, flow changes with permeability. However, the magnitude of the effect is proportionately weaker when the ice layers are further from the surface. The residence time is reduced when hoar layers are present due to shorter flow paths, reduced penetration into the deeper snow and higher speeds.

Radio-echo soundings were collected on Black Rapids Glacier, Alaska, USA, from mid-May to mid-July 1993 to investigate spring speed-up and summer slowdown including high-speed events associated with three lake drainages. Temporal changes in echo power from all depths were highly correlated, indicating a strong effect from varying amounts of near-surface water. Evaluation of bed reflectivity was corrected for this effect based on the time variation of spatially stable patterns of internal scattering identified using principal component analysis. Hourly time series collected at two fixed locations over the deepest part of two valley cross sections showed no detectable change in bed reflection power (<5%) or phase (<0.05 rad). Reoccupation of fixed locations toward the margins at several-day intervals revealed changes in bed power reflectivity up to 50%, but with no definable relation to lake drainages. Theoretical analyses indicate that changes in reflectivity of <5% from a rock bed constrain basal water thickness changes to centimeter scale or less. Conductive basal till degrades the constraint to decimeter scale or more. Changes in bed reflectivity of 50% indicate probable absence of thick conductive till at such locations, and that the changes were caused by centimeter to decimeter changes in equivalent water thickness.

We compare European remote-sensing satellite (ERS) synthetic aperture radar interferograms with artificial interferograms constructed using output of a finite-element ice-shelf flow model to study the dynamics of Filchner-Ronne Ice Shelf (FRIS), Antaretica, near Hemmen Ice Rise (HIR) where the iceberg-calving front intersects Berkner Island. We find that the model must account for rifts, mechanically competent sea ice which fills rifts, and ice softening in coastal boundary layers in order to agree with the ice-deformation pattern implied by observed interferograms. Analysis of the stress field in the model experiment that best matches the observed interferograms suggests that: (1) HIR introduces weakness into the ice shelf through the generation of large-scale rifts, and (2) the melange of sea ice and ice-shelf fragments that fills the rifts stabilizes the shelf front by providing mechanical coupling between the fractured shelf front and the adjacent coast. The rift-filling melange could melt more easily than the surrounding ice shelf and thus could represent a vulnerability of the FRIS to climate warming.

Deforming till and low-pressure water channels are observed to coexist subglacially, but till also is observed to creep rapidly into low-pressure subglacial regions. A simple model shows that these observations are not contradictory. Creep of a thin till to a low-pressure region can occur from a narrow zone only, and will lead to isolation of channels from till farther away.

Annual balances of eight alpine glaciers were slightly negative for 1961–90 and highly negative for 1991–2018. We explain this by changes in positive degree-day sums and summer temperatures extrapolated to the median altitudes of the glaciers. We test a new way of calculating degree-day sums that performs better than the traditional method which used daily mean temperatures. Annual degree-day sums are highly correlated with May–September temperatures as suggested in 1866 by Karl von Sonklar. We find moderate correlations between annual balances and degree-day sums, and with May–September temperatures. Calculated degree-day factors for the eight glaciers cover the reported range for snow and ice ablation, while the temperature sensitivity of annual balance is from −0.4 to −1.0 m w.e. for a +1°C temperature change. We accurately predict mean balances for 1991–2018 using May–September temperatures in regression models calibrated for 1961–90. May–September temperatures in the Alps have already increased ~+3°C since 1880 and, if temperatures continue to rise, these glaciers will shrink rapidly. As annual balances are already negative for present-day temperatures, these glaciers will not be ‘safe’ under the further temperature increase permitted by the Paris Agreement.

To gain new insight into the mechanisms of basal motion, we have demonstrated the feasibility of an active seismic technique to measure temporal changes in basal conditions on sub-hourly time-scales. One region of the bed of Black Rapids Glacier, Alaska, U.S.A., was monitored for a period of 45 days using seismic reflections. The majority of these reflections were nearly identical. However, three significant anomalies were recorded several days apart. These corresponded with the englacial drainage of two ice-marginal lakes and one supraglacial pothole, each up-glacier of the study site, as well as dramatic increases in basal motion. Two of these seismic anomalies revealed identical changes over 1 km2 of the bed despite the fact that their drainage events occurred at different locations. Further, these two seismic anomalies were followed by records identical to the non-anomalous state, showing that the seismic changes were reversible. In one of these events, two records taken 36 min apart revealed that the transition between the anomalous and normal states occurred completely within this short interval.

Borehole instrument records from a cirque glacier with an overdeepened bed are examined to assess the validity of widely held glacial hydrological assumptions. At this glacier, hydraulic-potential calculations suggest water below overburden pressure will flow into the overdeepening, where the steepness of the riegel causes water to pool in the basin and increase in pressure. Our subglacial water pressure data also show high consistent pressures in the overdeepening and the presence of an active, variable-pressure drainage system towards the margin of the cirque. Therefore, we find that although uniform hydraulic-potential calculations are not directly applicable, they can still be useful for interpretation of the subglacial hydrological system. We also examine supercooling assumptions under different pressure and temperature regimes for water flowing over a riegel, driven using our borehole records of subglacial water temperatures that are consistently above the pressure-melting point during the late melt season. Our results show that even a slight increase in basal temperatures relative to the local pressure-melting point is sufficient to prevent a reduction in basal hydraulic conductivity as a result of supercooling freeze-on.

The glacier system covering Europe's highest mountain, Elbrus, has exhibited an accelerated retreat since 1980. Some studies have related this retreat to a significant summer temperature increasing trend. Relief- and aspect-related parameters for the glacierized area have an important impact on glacier changes. In this paper, the changes in glacier area are identified, quantified and correlated with relief parameters for the period 1985–2007. Spatial analysis was performed using the GLAM-CD (Glacier Mapper – Change Detector) algorithm. The input data for this algorithm were Landsat 5 images, the Aster Global Digital Elevation and the glacier outlines from the GLIMS project (Global Land Ice Measurements from Space). Regression analyses between glacier area losses and relief-related parameters indicate a significant positive relation with the altitude and a significant negative relation with the glacier surface area. In this context, we used a correlated component regression to model these relations. The model explains >50% of the total variation.

For Yanamarey Glacier in Cordillera Blanca, Peru, mostly situated between about 5000 and 4600 m, maps of the surface topography at a scale of 1: 5000 obtained by terrestrial triangulation for 1973, 1982 and 1988 and by aerial photogrammetry for 1948 and 1962 are compared with the glacier boundaries from a 1939 map and an undated maximum extent inferred from moraine morphology. The glacier length decreased from the maximum, 2800 m to 1600 m in 1948. and to 1250 m in 1988, with an accompanying decrease in area from 17 × 105 to 10 × 105 and thence to 8 × 105 m2. The shrinkage of ice volume was 35 × 106 m3 from the maximum to 1948. and 29 × 106 m3 from 1948 to 1988. compared to a total remaining ice volume of about 25 × 106 m3 in 1988. This quantitative assessment of mass-loss rates creates the observational basis for sensitivity studies of the climatic forcing.

The performance of a thermal ice-drill having a smooth, solid, impervious frontal surface, termed a “solid-nose hotpoint”, is determined by the velocities, pressures, and temperatures in the thin layer of warm melt water between the hotpoint and the ice. The efficiency, the speed of penetration, the temperature of the frontal surface, and the distribution of pressure on it can be calculated from the equations of non-turbulent fluid flow. For hotpoints whose frontal surfaces are isothermal and axially symmetric, these quantities are functions of the total input of power Q of the weight W on the hotpoint, of the radius a and “shape factor” S of the frontal surface, and of the pertinent physical properties of water and ice. The calculation shows that with increasing “performance number” the efficiency E decreases and the surface temperature θ0 increases. Thus, for example, E = 1·00 and θ0 = 0°C. when N = 0.0 E = 0·76 and θ0 = 48°C when N = 1.4; and E = 0·60 and θ0 = 103°C. when N = 3.0. The coefficient Λ is a constant equal to . The shape factor S is a dimensionless number between 0 and 1 that varies according to the shape of the frontal surface, greater values of S being associated with blunter profiles (thus S = 1.0 for a plane frontal surface perpendicular to the axis). For coring hotpoints the same numerical results are obtained, but the performance number is given by

where 2ϖia is the inside diameter of the hotpoint.

Increasing ice flux from glaciers retreating over deepening (retrograde) bed topography has been implicated in the recent acceleration of mass loss from the Greenland and Antarctic ice sheets. We show in observations that some glaciers have remained at peaks in bed topography without retreating despite enduring significant changes in climate. Observations also indicate that some glaciers which persist at bed peaks undergo sudden retreat years or decades after the onset of local ocean or atmospheric warming. Using model simulations, we show that persistence of a glacier at a bed peak is caused by ice slowing as it flows up a reverse-sloping bed to the peak. Persistence at bed peaks may lead to two very different future behaviors for a glacier: one where it persists at a bed peak indefinitely, and another where it retreats from the bed peak after potentially long delays following climate forcing. However, it is nearly impossible to distinguish which of these two future behaviors will occur from current observations. We conclude that inferring glacier stability from observations of persistence obscures our true commitment to future sea-level rise under climate change. We recommend that further research is needed on seemingly stable glaciers to determine their likely future.

Spatial variations in the debris-bearing basal ice layer exposed at the ice-sheet margin in West Greenland reflect the geography of basal melting and ice flow around large obstacles close to the margin. This paper demonstrates the character of the basal ice layer, which comprises fine material incorporated in an interior, subglacial environment and coarser material entrained in an ice-marginal environment. We develop an empirical model of ice flow close to a lobate margin of the ice sheet in which ice convergence and divergence, and limited subglacial melting affect the character and distribution of the basal ice at the margin. There is a tendency for the convergence and divergence to thicken the basal layer in lobate areas and to thin it in inter-lobate areas. Under certain circumstances, basal melting may remove much of the layer from beneath the snouts of larger lobes, thus causing the basal layer to be thickest in an intermediate location.

Antarctic tabular icebergs are important active components of the ice–ocean system. To investigate the relevance of inherent ice dynamics to iceberg evolution, we developed a numerical model based on the fundamental equations of ice-shelf flow and heat transfer, forced by environmental parameters of the ice–ocean–atmosphere system. Model experiments with idealized icebergs of constant density show that the strain thinning rate for a typical iceberg with a thickness of 250 m and a temperature of −15°C is about 1 m a−1. Sensitivity studies for different scenarios of environmental conditions confirmed the reliability of our model. A 5 year simulation of the evolution of iceberg A-38B yielded a mean decrease in thickness from 220 m to 106.3 m, 95% of which was caused by basal melting, 1% by surface melting and 4% by strain thinning. We found iceberg spreading decelerating by about 75%, and ice temperatures being strongly affected by progressive erosion of the relatively warm basal layers and warming in the uppermost part. According to the model results, basal melting is the primary cause of change of iceberg geometry during drift, whereas strain thinning is only relevant in cold areas where basal melting is low.

By using a simple parameterized model of thermomechanically coupled flow in cold ice sheets, together with a physically based sliding law which includes a description of basal drainage, we show that relationships between ice flux and ice thickness can realistically be multi-valued, and hence that hydraulically induced surges can occur. We term this mechanism hydraulic run-away, as it relies on the positive feed-back between sliding velocity and basal melt production. For this feedback to operate, it is essential that water pressure increases with water storage. This is consistent with various recent ideas concerning drainage, under ice sheets, be it through a system of canals, a distnbuted film or a subglacial aquifer. For confined flows, such as valley glaciers (e.g. Trapridge Glacier) or topographically constrained ice streams (e.g. Hudson Strait in the Laurentide ice sheet), which are underlain by sufficiently deformable sediment, we can expect thermally regulated surges to occur, while in a laterally unconfined drainage basin (such as that which flows into the Ross Ice Shelf), we might expect ice streams to develop.

We present a two-dimensional, coupled, mesoscale atmosphere–sea-ice model, and apply it to simulate the air–ice interaction during warm-air advection. The model was run into a steady state under various conditions with respect to the season, cloud cover and wind speed. The spatial and temporal evolution of the thermodynamics of the ice, snow and the atmospheric boundary layer (ABL) were investigated. The development of the stably stratified ABL downwind of the ice edge depended above all on the wind speed and cloud cover. If the turbulent heat flux from air to snow was large enough to compensate the radiative cooling of the surface, a downward conductive heat flux was generated in the upper ice and snow layers. The stronger was the surface heating (strong wind, overcast skies) and the shorter its duration (on a scale down to a few hours), the wider was the region where this downward flux occurred. From the point of view of ABL modelling, the interactive coupling between air and ice was most important when the wind was strong, while from the point of view of ice thermodynamic modelling the coupling was most important when the wind was weak.

Ground-penetrating radar (GPR) surveys at a center frequency of 500 MHz were used to determine winter (2007/08) and net annual (2005–07) snow water equivalent (SWE) patterns across the upper parts of Belcher Glacier, Devon Ice Cap, Nunavut, Canada. The GPR measurements were validated against snow depths determined from avalanche probe measurements, and converted to SWE values using densities measured with a down-borehole neutron density probe and in shallow snow pits. Distinct internal reflection horizons (IRHs) in the GPR record were formed during warm summers in 2007 and 2005, and a large rain event in summer 2006 which caused ice to accumulate above the 2005 melt surface. Elevation provides the dominant control on winter SWE distribution across the basin, with surface topography (e.g. gullies) also being locally important. Based on the location where IRHs intersected the ice-cap surface, the basin-wide firn line occurred at an altitude of 1260–1300 m over the period 2005–08. Net mass balance across the accumulation area of Belcher Glacier averaged 0.24 m w.e. a−1 over the period 2005–07, mainly dependent on altitude. This is a little higher than most previous estimates for the period since the 1960s, although the differences lie within error limits.

Band ogives are a striking and enigmatic feature of Mer de Glace glacier flow. The surface mass balances (SMBs) of these ogives have been thoroughly investigated over a period of 12 years. We find similar cumulative SMBs over this period, ranging between −64.1 and −66.2 m w.e., on the dark and light ogives even though the dark ogive albedo is ~40% lower than that of the light ogives. We, therefore, looked for another process that could compensate for the large difference of absorbed short-wave radiation between dark and light ogives. Based on in situ roughness measurements, our numerical modeling experiments demonstrate that a significant difference in turbulent flux over the dark and light ogives due to different surface roughnesses could compensate for the difference in radiative forcing. Our results discard theories for the genesis of band ogives that are based on the assumption of a strong ice ablation contrast between dark and light ogives. More generally, our study demonstrates that future roughness changes are as important to analyze as the radiative impacts of a potential increase of aerosols or debris at the surface of glaciers.