From 2017 to 2020, three significant calving events took place on Pine Island Glacier, West Antarctica. Ice-shelf velocities changed over this period and the calving events have been suggested as possible drivers. However, satellite observations also show significant changes in the areal extent of fracture zones, especially in the marginal areas responsible for providing lateral support to the ice shelf. Here, we conduct a model study to identify and quantify drivers of recent ice-flow changes of the Pine Island Ice Shelf. In agreement with recent studies, we find that the calving events caused significant velocity changes over the ice shelf. However, calving alone cannot explain observed velocity changes. Changes in the structural rigidity, i.e. ice damage, further significantly impacted ice flow. We suggest that ice damage evolution of the ice-shelf margins may have influenced recent calving events, and these two processes are linked.

The Wilkes Subglacial Basin in East Antarctica contains ice equivalent to 3–4 m of global mean sea level rise and is primarily drained by Cook Glacier. Of concern is that recent observations (since the 1970s) show an acceleration in ice speed over the grounding line of both the Eastern and Western portions of Cook Glacier. Here, we use a numerical ice-flow model (Úa) to simulate the instantaneous effects of observed changes at the terminus of Cook Glacier in order to understand the link between these changes and recently observed ice acceleration. Simulations suggest that the acceleration of Cook West was caused by a retreat in calving-front position in the 1970s, potentially enhanced by grounding-line retreat, while acceleration of Cook East was likely caused by ice-shelf thinning and grounding-line retreat in the mid-1990s. Moreover, we show that the instantaneous ice discharge at Cook East would increase by up to 85% if the whole ice shelf is removed and it ungrounds from a pinning point; and that the discharge at Cook West could increase by ~300% if its grounding line retreated by 10 km.

Ice shelves restrain flow from the Greenland and Antarctic ice sheets. Climate-ocean warming could force thinning or collapse of floating ice shelves and subsequently accelerate flow, increase ice discharge and raise global mean sea levels. Petermann Glacier (PG), northwest Greenland, recently lost large sections of its ice shelf, but its response to total ice shelf loss in the future remains uncertain. Here, we use the ice flow model Úa to assess the sensitivity of PG to changes in ice shelf extent, and to estimate the resultant loss of grounded ice and contribution to sea level rise. Our results have shown that under several scenarios of ice shelf thinning and retreat, removal of the shelf will not contribute substantially to global mean sea level (<1 mm). We hypothesize that grounded ice loss was limited by the stabilization of the grounding line at a topographic high ~12 km inland of its current grounding line position. Further inland, the likelihood of a narrow fjord that slopes seawards suggests that PG is likely to remain insensitive to terminus changes in the near future.

Drag at the bed and along the lateral margins are the primary forces resisting flow in outlet glaciers. Simultaneously inferring these parameters is challenging since basal drag and ice viscosity are coupled in the momentum balance, which governs ice flow. We test the ability of adjoint-based inverse methods to infer the slipperiness coefficient in a power-law sliding law and the flow-rate parameter in the constitutive relation for ice using a regularization scheme that includes coefficients weighted by surface strain rates. Using synthetic data with spatial variations in basal drag and ice rheology comparable to those in West Antarctic Ice Streams, we show that this approach allows for more accurate inferences. We apply this method to Bindschadler and MacAyeal Ice Streams in West Antarctica. Our results show relatively soft ice in the shear margins and spatially varying basal drag, with an increase in drag with distance upstream of the grounding line punctuated by localized areas of relatively high drag. We interpret soft ice to reflect a combination of heating through viscous dissipation and changes in the crystalline structure. These results suggest that adjoint-based inverse methods can provide inferences of basal drag and ice rheology when regularization is informed by strain rates.

Ice rheology governs how glaciers flow and respond to environmental change. The rheology of glacier ice evolves in response to a variety of mechanisms, including damage, heating, melting and the development of crystalline fabric. The relative contributions of these rheological mechanisms are not well understood. Using remotely sensed data and physical models, we decouple the influence of each of the aforementioned mechanisms along the margins of Rutford Ice Stream, a laterally confined outlet glacier in West Antarctica. We show that fabric is an important control on ice rheology in the shear margins, with an inferred softening effect consistent with a single-maximum fabric. Fabric evolves to steady state near the onset of streaming flow, and ice progressively softens downstream almost exclusively due to shear heating. The rate of heating is sensitive to local shear strain rates, which respond to local changes in bed topography as ice is squeezed through the basal trough. The impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback – wherein faster ice flow leads to higher rates of shear heating, further softening the ice – is a fundamental control on glacier dynamics.

Satellite observations of gravity anomalies, ice-surface elevation and glacier velocity show significant increases in net grounded-ice-mass loss over the past decade along the Bellingshausen Sea sector (BSS), West Antarctica, in areas where warm (>1°C) sea water floods the continental shelf. These observations provide compelling but indirect evidence that mass losses are driven primarily by reduced buttressing from the floating ice shelves caused by ocean-driven ice-shelf thinning. Here, we combine recent observations of ice velocity, thickness and thickness changes with an ice flow model to study the instantaneous dynamic response of BSS outlet glaciers to observed ice-shelf thinning, alone. Our model results show that multiple BSS outlet glaciers respond instantaneously to observed ice-shelf thinning, particularly in areas where ice shelves ground at discrete points. Increases in modeled and observed dynamic mass losses, however, account for ~5% of the mass loss rates estimated from gravity anomalies and changes in ice-surface elevation, suggesting that variations in surface mass balance may be key to understanding recent BSS mass loss. Our approach isolates the impact of ice-shelf thinning on glacier flow and shows that if ice-shelf thinning continues at or above current rates, total BSS mass loss will increase in the next decade.

Results from 15 years of work on glacier-bed mapping by radio-echo soundings on Finsteraar-, Lauteraar- and Unteraargletscher, Switzerland, are summarized, and a new and greatly improved map of the ice-thickness distribution presented. In contrast to the tongue of Unteraargletscher, its two main tributaries, Lauteraar and Finsteraar, are both deep and narrow, and ice-thickness determination depends on the detection of more than just the primary reflection. Migrating the data led to considerably improved bed determination. Wherever possible, additional information on ice thicknesses gained from numerous hot-water drillings to the glacier bed is used as an independent verification of the results of the radar measurements, and a fair agreement is found.

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.

Over a two-year period, continuous measurements of temporal changes in tilt, conducted with a string of tilt meters in a borehole on Unteraargletscher, Bernese Alps, Switzerland, have been used to estimate the basal-motion component. This estimation is based on a comparison of the measurements with synthetic tilt curves, computed using a parameterization of a simplified flow field. The best agreement is found for a ratio of basal motion to forward motion due to ice deformation (slip ratio) equal to about 1.2. Measured tilt curves exhibit a number of different transient features. While an overall increase in tilt angle is observed at every tilt-meter location, two of the sensors recorded anomalous tilt behaviour. These anomalies are characterized by sudden and drastic variations in tilt. A particularly intriguing example of such short-term tilt variations was recorded with a tilt meter positioned 40 m above the bed during the 1997 summer melt season.

The amplitude ratio between surface and bedrock topography has been predicted to depend strongly on the ratio of deformational velocity to mean basal sliding velocity. Observations made prior to and during a surge of Tungnaárjökull, Vatnajökull ice cap, Iceland, allow this prediction to be tested. During the surge, the ratio of internal deformational velocity and basal sliding (slip ratio) changed from about unity to a few hundred. The amplitude ratio changed from about 0.1 to about 0.7. This increase in amplitude ratio is in good overall agreement with predictions based on an analytical perturbation analysis for a linearly viscous medium which includes the effects of horizontal deviatoric stresses on glacier flow. An increase in amplitude ratio of this magnitude is not predicted by a similarly linearized analysis that employs the commonly used shallow-ice approximation. The strong increase in transfer amplitude observed in the surge of Tungnaárjökull is a clear illustration of the effects of horizontal stress transmission on glacier flow reported here for the first time.

The effects of spatial and temporal variations in basal lubrication on the englacial strain rate and surface velocity distribution are investigated with a numerical ice-flow model. General aspects of the solutions are compared to measurements made on Lauteraargletscher, Switzerland, in 2001, that showed diurnal fluctuations in both surface velocity and englacial vertical strain. We find that spatial gradients in basal lubrication can set up variations in the deviatoric stress field that increases with distance to the bed and has a maximum value near the glacier surface. This stress field produces a significant strain rate near the surface. The temporal evolution of a slippery zone is identified as a possible cause of the observed diurnal variations in the vertical strain rate. Although general aspects of the measurements can be explained in this way, the calculated vertical strain rates are too small, suggesting that the modeled effective viscosity values using Glen’s flow law are too large near the surface.

Short-term variations in horizontal and vertical surface motion were studied with high temporal resolution during the ablation season in Lauteraargletscher, Bernese Alps, Switzerland. Horizontal surface flow speed oscillated diurnally, showing a correlation with the water level in a borehole. Flow speed increased as a function of the water level, with an asymptote at the ice overburden level. This observation implied that the flow variations were principally controlled by the local water pressure which enhanced basal motions. Detailed examination of the diurnal variations, however, showed that the speed was larger when the pressure was increasing than when it was decreasing. Greater speed with increasing pressure was interpreted by subglacial water-cavity opening and/or longitudinal stress coupling with the upper reaches of the glacier. Upward surface movements were observed when the glacier flow speed increased. Simultaneous measurement of internal vertical strain in a borehole showed that the uplift had two different sources: vertical straining of ice and volume increase of subglacial water cavities. The vertical surface movement was largely affected by the vertical strain, and the uplift events could not be simply attributed to cavity opening.

The determination of basal properties on ice streams from surface data is formulated as a Bayesian statistical inference problem. The theory is applied to a flowline on Rutford Ice Stream, West Antarctica. Estimates of bed topography and basal slipperiness are updated using measurements of surface topography and the horizontal and vertical components of the surface velocity. The surface topography is allowed to vary within measurement errors. We calculate the transient evolution of the surface until rates of surface elevation change are within limits given by measurements. For our final estimation of basal properties, modelled rates of elevation change are in full agreement with estimates of surface elevation changes. Results are discarded from a section of the flowline where the distribution of surface residuals is not consistent with error estimates. Apart from a general increase in basal slipperiness toward the grounding line, we find no evidence for any spatial variations in basal slipperiness. In particular, we find that short-scale variability (<10 × ice thickness) in surface topography and surface velocities can be reproduced by the model by variations in basal topography only. Assuming steady-state conditions, an almost perfect agreement is found between modelled and measured surface geometry, suggesting that Rutford Ice Stream is currently close to a steady state.

As simulations of 21st-century climate start to include components with longer timescales, such as ice sheets, the initial conditions for those components will become critical to the forecast. This paper describes an algorithm for specifying the initial state of an ice-sheet model, given spatially continuous observations of the surface elevation, the velocity at the surface and the thickness of the ice. The algorithm can be viewed as an inverse procedure to solve for the viscosity or the basal drag coefficient. It applies to incompressible Stokes flow over an impenetrable boundary, and is based upon techniques used in electric impedance tomography; in particular, the minimization of a type of cost function proposed by Kohn and Vogelius. The algorithm can be implemented numerically using only the forward solution of the Stokes equations, with no need to develop a separate adjoint model. The only requirement placed upon the numerical Stokes solver is that boundary conditions of Dirichlet, Neumann and Robin types can be implemented. As an illustrative example, the algorithm is applied to shear flow down an impenetrable inclined plane. A fully three-dimensional test case using a commercially available solver for the Stokes equations is also presented.

Observations of surface elevation (s) and horizontal velocity components (u and v) are inverted to infer the topography (b) and lubrication (c) at the bed of an ice stream, based on a linearized perturbation theory of the transmission of flow disturbances through the ice thickness. Synthetic data are used to illustrate non-uniqueness in the inversion, but also demonstrate that effects of b and c can be separated when s, u and v are specified, even with added noise to simulate measurement errors. We have analyzed prominent short-horizontal-scale (∼2 km) features in topography and velocity pattern in a local 64 km by 32 km area of the surface of Ice Stream E,West Antarctica. Our preferred interpretation of bed conditions beneath the most prominent features on the surface identifies a deep trough in the basal topography with low lubrication in the base of the trough.

During a motion event on Unteraargletscher, Bernese Alps, Switzerland, in spring 1996, surface velocities were measured up to eight times a day at four different locations along the central flowline using global positioning system equipment. In addition, accumulated vertical strains over the uppermost 50 and 100 m were measured at a location where the total ice thickness is 260 m. The motion event was accompanied by high horizontal and vertical strain rates as compared to annual mean values. A reversal in strain regime was observed, with horizontal strain rates changing to extension while vertical strain rates became compressive. This strain-rate reversal coincided, within the temporal resolution of the data, with a maximum in vertical ice displacement at the surface.Within a day, variations in vertical strain from 0.04 a−1 to −0.06 a−1 were observed over the uppermost 100 m. Vertical stretching is estimated to have contributed to at least 20% of the anomalous vertical ice movement at the surface. There were significant differences between measured longitudinal strain, averaged over a distance corresponding to a few ice thicknesses, and measured vertical strain. In spring 1997 a similar, but more detailed, set of measurements was collected at the same measuring site, and vertical strain rates were found to vary non-uniformly with depth, with the largest values closest to the surface.

Tidal flexure in ice shelf grounding zones has been used extensively in the past to determine grounding line position and ice properties. Although the rheology of ice is viscoelastic at tidal loading frequencies, most modelling studies have assumed some form of linear elastic beam approximation to match observed flexure profiles. Here we use density, radar and DInSAR measurements in combination with full-Stokes viscoelastic modelling to investigate a range of additional controls on the flexure of the Southern McMurdo Ice Shelf. We find that inclusion of observed basal crevasses and density dependent ice stiffness can greatly alter the flexure profile and yet fitting a simple elastic beam model to that profile will still produce an excellent fit. Estimates of the effective Young's modulus derived by fitting flexure profiles are shown to vary by over 200% depending on whether these factors are included, even when the local thickness is well constrained. Conversely, estimates of the grounding line position are relatively insensitive to these considerations for the case of a steep bed slope in our study region. By fitting tidal amplitudes only, and ignoring phase information, elastic beam theory can provide a good fit to observations in a wide variety of situations. This should, however, not be taken as an indication that the underlying rheological assumptions are correct.

A glacier-wide ice-thickness distribution and bedrock topography is presented for Starbuck Glacier, Antarctic Peninsula. The results are based on 90 km of ground-based radio-echo sounding lines collected during the 2012/13 field season. Cross-validation with ice-thickness measurements provided by NASA's IceBridge project reveals excellent agreement. Glacier-wide estimates are derived using a model that calculates distributed ice thickness, calibrated with the radio-echo soundings. Additional constraints are obtained from in situ ice flow-speed measurements and the surface topography. The results indicate a reverse-sloped bed extending from a riegel occurring ~ 5 km upstream of the current grounding line. The deepest parts of the glacier are as much as 500 m below sea level. The calculated total volume of 80.7 ± 7.2 km3 corresponds to an average ice thickness of 312 ± 30 m.