The ice discharge from the grounded parts of marine ice sheets into the ocean is modulated by their floating extensions – ice shelves. The ice-shelf impact on the grounded ice is typically described as ‘backpressure’ or ‘buttressing’. Theoretical analyses of their effects have been restricted to one horizontal dimension. This study revisits the concepts of ‘backpressure’ introduced by Thomas (1977) and ‘buttressing’ numbers and ratios introduced by Gudmundsson (2013) and extends their theoretical analysis to two horizontal dimensions. Using the integral form of the momentum-balance formulation suitable for fast-flowing ice streams and ice shelves, our analysis provides a natural definition for the total backpressure force exerted by an ice shelf to the grounded ice upstream of its grounding line. The results of numerical analyses suggest that ice shelves whose second principal stress component is compressional over larger areas may provide more buttressing compared to ice shelves with smaller areas of compressional stresses or to ice shelves with both principal stresses being tensile.

The ongoing deceleration of Whillans Ice Stream, West Antarctica, provides an opportunity to investigate the co-evolution of ice-shelf pinning points and ice-stream flux variability. Here, we construct and analyze a 20-year multi-mission satellite altimetry record of dynamic ice surface-elevation change (dh/dt) in the grounded region encompassing lower Whillans Ice Stream and Crary Ice Rise, a major pinning point of Ross Ice Shelf. We developed a new method for generating multi-mission time series that reduces spatial bias and implemented this method with altimetry data from the Ice, Cloud, and land Elevation Satellite (ICESat; 2003–09), CryoSat-2 (2010–present), and ICESat-2 (2018–present) altimetry missions. We then used the dh/dt time series to identify persistent patterns of surface-elevation change and evaluate regional mass balance. Our results suggest a persistent anomalous reduction in ice thickness and effective backstress in the peninsula connecting Whillans Ice Plain to Crary Ice Rise. The multi-decadal observational record of pinning-point mass redistribution and grounding zone retreat presented in this study highlights the on-going reorganization of the southern Ross Ice Shelf embayment buttressing regime in response to ice-stream deceleration.

The observed retreat of the grounding line of the present-day ice sheets and the simulated grounding-line retreat of ice sheets under changing climate conditions are often interpreted as indications of marine ice-sheet instability (MISI), driven by a positive feedback between the ice discharge and conditions at the grounding line. However, the arguments that support this feedback are valid only for steady-state conditions. Here, we assess how unconfined marine ice sheets may behave if atmospheric conditions and basal conditions evolve with time. We find that the behavior of grounding lines can exhibit a range from unstoppable advance and retreat to irregular oscillation irrespective of the stability of the corresponding steady-state configurations obtained with time-invariant conditions. Our results show that numerical simulations with a parameterization of the ice flux through the grounding line used in large-scale ice-sheet models produce markedly different results from simulations without the parameterization. Our analysis demonstrates that the grounding-line migration can be driven by the temporal variability in the atmospheric and basal conditions and not by MISI, which assumes unchanging conditions. Instead, the grounding-line advance or retreat is determined by interactions between ice flow, basal processes and environmental conditions throughout the length of a marine ice sheet in addition to the circumstances at its grounding line.

Upernavik Isstrøm, the largest contributor to sea-level rise in northwest Greenland, has experienced complex and contrasting ice-flow-speed changes across its five outlets over the last two decades. In this study, we present a detailed remote-sensing analysis of the ice dynamics at Upernavik's outlets from 2000 to 2021 to evaluate the details of these changes. Previous research suggested that the presence or absence of floating ice tongues strongly influences Upernavik's ice dynamics. We use several lines of evidence to document the presence of floating ice tongues, and find that, while several outlets experienced ice-tongue formation and/or loss during the study period, these changes do not explain observed fluctuations in ice-flow velocity. Further exploration of ice-dynamic forcings using a flowline model suggests that changes in basal slipperiness near the terminus have a strong impact on upstream ice dynamics and can explain the velocity variations. Our results suggest that speed fluctuations at Upernavik's outlets may be seasonally and interannually controlled by bed conditions near the terminus, and highlight the need for further research on the influence of basal conditions on complex tidewater glacier dynamics.

To better constrain meltwater transport and ice viscosity in temperate glaciers, particularly in ice stream shear margins, we use a custom permeameter to study the untested model relationship between the permeability of temperate ice and its liquid water content. The permeability of lab-made ice of two mean grain diameters (1.8 and 4.2 mm) is measured, and water content is controlled with the ice salinity and measured calorimetrically. Fluorescein dye is added to through-flowing, chilled water to highlight flow pathways through the ice after experiments. As predicted by a simple model, permeability increases with approximately the square of the water content and by about three orders of magnitude across water contents of 0.1–4.4%. However, permeability values are less than those of the model by average factors of 2.6 and 4.1 for the finer and coarser ice, respectively. This discrepancy is likely due to tortuous, truncated or air-clogged veins. The order-of-magnitude agreement between measured and modeled values may indicate that reduced permeability from these factors is nearly compensated by preferential flow in oversized veins that are isolated or arborescent. Both kinds of preferred flow pathways are observed but the latter only in fine-grained ice at water contents > 2%.

Spatial variability in bed topography, characterized as bed roughness, impacts ice-sheet flow and organization and can be used to infer subglacial conditions and processes, yet is difficult to quantify due to sparse observations. Paleo-subglacial beds of formerly expanded glaciers found across the Antarctic continental shelf are well preserved, have relatively limited post-glacial sediment cover and contain glacial landforms that can be resolved at sub-meter vertical scales. We analyze high-resolution bathymetry offshore of Pine Island and Thwaites glaciers in the Amundsen Sea to explore spatial variability of bed roughness where streamlined subglacial landforms allow for the determination of ice-flow direction. We quantify bed roughness using std dev. and Fast Fourier Transform methods, each employed at local (100 km) and regional (101–2 km) scales and in along- and across-flow orientations to determine roughness expressions across spatial scales. We find that the magnitude of roughness is impacted by the parameters selected – which are often not sufficiently reported in studies – to quantify roughness. Important spatial patterns can be discerned from high-resolution bathymetry, highlighting both its usefulness in identifying patterns of streaming ice flow and underscores the need for a standardized way of characterizing topographic variability.

Ice streams are regions of rapid ice sheet flow characterised by a high degree of sliding over a deforming bed. The shallow shelf approximation (SSA) provides a convenient way to obtain closed-form approximations of the velocity and flux in a rapidly sliding ice stream when the basal drag is much less than the driving stress. However, the validity of the SSA approximation breaks down when the magnitude of the basal drag increases. Here we find a more accurate expression for the velocity and flux in this transitional regime before vertical deformation fully dominates, in agreement with numerical results. The closed-form expressions we derive can be incorporated into wider modelling efforts to yield a better characterisation of ice stream dynamics, and inform the use of the SSA in large-scale simulations.

Investigations of the time-dependent behavior of marine ice sheets and their sensitivity to basal conditions require numerical models because existing theoretical analyses focus only on steady-state configurations primarily with a power-law basal shear stress. Numerical results indicate that the choice of the sliding law strongly affects ice-sheet dynamic behavior. Although observed or simulated grounding-line retreat is typically interpreted as an indication of marine ice sheet instability introduced by Weertman (1974), this (in)stability is a characteristic of the ice sheet's steady states – not time-variant behavior. To bridge the gap between theoretical and numerical results, we develop a framework to investigate grounding line dynamics with generalized basal and lateral stresses (i.e. the functional dependencies are not specified). Motivated by observations of internal variability of the Southern Ocean conditions we explore the grounding-line response to stochastic variability. We find that adding stochastic variability to submarine melt rates that produced stable steady-state configurations leads to intermittently advancing and retreating grounding lines. They can also retreat in an unstoppable manner on time-scales significantly longer than the stochastic correlation time-scales. These results suggest that at any given time of their evolution, the transient behavior of marine ice sheets cannot be described in terms of ‘stable’ or ‘unstable’.

Increases in ocean temperatures in the Filchner Ronne region of Antarctica are likely to result in increased ice mass loss and sea level rise. We constrain projections of the 21st century sea level contribution of this region using process-based ice-sheet modeling, with model parameters controlling ice dynamics calibrated using observed surface speeds and Markov-chain Monte Carlo sampling. We use climate forcing from Representative Concentration Pathway (RCP) scenarios as well as a set of hypothetical scenarios of deep ocean warming to evaluate the sensitivity of this region to ocean temperatures. Projected changes in regional ice mass correspond to a decrease in global mean sea level of 24±7 mm over 2015–2100 under RCP 2.6 and 28±9 mm under RCP 8.5. Increased regional inland surface accumulation related to higher warming levels in RCP 8.5 leads to more ice above flotation, offsetting increased ice shelf basal melt. The tests involving step changes in ocean temperatures with constant surface forcing show that one degree of ocean warming from present results in an additional +11 mm contribution to sea level by 2100 and 1% of the ice-covered area in the domain becomes ungrounded (23 200 km2). The rate of mass loss with temperature increases at higher temperatures.

The dynamics of the Greenland Ice Sheet are affected by surface meltwater reaching the base of the ice, altering ice contact with the bedrock. Lack of understanding of this evolution hampers the ability to predict the effects of increasing temperatures on the Greenland Ice Sheet mass balance. Here we present a unique high-resolution study of ice velocity response to surface melting based on data from a COSMO-SkyMed satellite campaign over Upernavik Isstrøm (Northwest Greenland) for two months around the end of the 2014 melt season. We show that the velocity variations, due to both short-term (days) and seasonal variations in surface melt rates, are increasing in relative strength farther from the glacier terminus. Furthermore, we observe how ice dynamic response to frontal retreat, reaching several kilometres inland, can obscure the meltwater-induced velocity change close to the terminus. Future studies should consider the flow velocity dependence on the distance to the terminus, and local geometry, to distinguish subglacial hydrologic system changes from frontal processes and local basal conditions.

Ice streams are warmed by shear strain, both vertical shear near the bed and lateral shear at the margins. Warm ice deforms more easily, establishing a positive feedback loop in an ice stream where fast flow leads to warm ice and then to even faster flow. Here, we use radar attenuation measurements to show that the Siple Coast ice streams are colder than previously thought, which we hypothesize is due to along-flow advection of cold ice from upstream. We interpret the attenuation results within the context of previous ice-temperature measurements from nearby sites where hot-water boreholes were drilled. These in-situ temperatures are notably colder than model predictions, both in the ice streams and in an ice-stream shear margin. We then model ice temperature using a 1.5-dimensional numerical model which includes a parameterization for along-flow advection. Compared to analytical solutions, we find depth-averaged temperatures that are colder by 0.7°C in the Bindschadler Ice Stream, 2.7°C in the Kamb Ice Stream and 6.2–8.2°C in the Dragon Shear Margin of Whillans Ice Stream, closer to the borehole measurements at all locations. Modelled cooling corresponds to shear-margin thermal strengthening by 3–3.5 times compared to the warm-ice case, which must be compensated by some other weakening mechanism such as material damage or ice-crystal fabric anisotropy.

Ice streams are sites of ice-sheet drainage and together with other processes, such as calving, have an impact on deglaciation rates and ice-sheet mass balance. Proglacial lake deposits provide records of ice-sheet deglaciation and have the potential to supplement other paleoclimate records. Oneida Lake, northeastern USA, contains a thick proglacial lake sequence that buries evidence of ice streaming and a paleo-calving margin that developed during retreat of the Laurentide Ice Sheet. Previous high-resolution digital elevation models identified the Oneida Ice Stream from glacial landforms northwest of the lake. In this study, we utilize seismic refractions from a multichannel seismic (MCS) reflection dataset to estimate the thickness of glacial deposits using seismic tomography. With this method we constrain the depth to top of Paleozoic strata, especially in areas where the reflection data yielded poor outcomes and validate our reflection data in regions of good coverage. We demonstrate that where long offset seismic data are available, the first-arrival tomography method is useful in studies of formerly glaciated basins. Our study identifies a ~108 m thick sedimentary section and potentially long paleoclimate record in Oneida Lake, and identifies a paleotopographic low that likely encouraged formation of the Oneida Ice Stream.

Results of ice-stream models that treat temperate ice deformation as a two-phase flow are sensitive to the ice permeability. We have constructed and begun using a custom, falling-head permeameter for measuring the permeability of temperate, polycrystalline ice. Chilled water is passed through an ice disk that is kept at the pressure-melting temperature while the rate of head decrease indicates the permeability. Fluorescein dye in the water allows water-vein geometry to be studied using fluorescence microscopy. Water flow over durations of seconds to hours is Darcian, and for grain diameter d increasing from 1.7 to 8.9 mm, average permeability decreases from 2 × 10−12 to 4 × 10−15 m2. In tests with dye on fine (d = 2 mm) and coarse (d = 7 mm) ice, average area-weighted vein radii are nearly equal, 41 and 34 μm, respectively. These average radii, if included in a theory slightly modified from Nye and Frank (1973), yield permeability values within a factor of 2.0 of best-fit values based on regression of the data. Permeability values depend on d−3.4, rather than d−2 as predicted by models if vein radii are considered independent of d. In future experiments, the dependence of permeability on liquid water content will be measured.

In Part 1, we have considered the dynamics of topographically confined glaciers, which may undergo surge cycles when the bed becomes temperate. In this Part 2, we consider the ice discharge over a flatbed, which would self-organize into alternating stream/ridge pairs of wet/frozen beds. The meltwater drainage, no longer curbed by the bed trough, would counter the conductive cooling to render a minimum bed strength at some intermediate width, toward which the stream would evolve over centennial timescale. At this stationary state, the stream width is roughly twice the geometric mean of the stream height and length, which is commensurate with its observed width. Over a flatbed, streams invariably interact, and we deduce that the neighboring ones would exhibit compensating cycles of maximum velocity and stagnation over the centennial timescale. This deduction is consistent with observed time variation of Ross ice streams B and C (ISB/C), which is thus a manifestation of the natural cycle. Moreover, the model uncovers an overlooked mechanism of the ISC stagnation: as ISB widens following its reactivation, it narrows ISC to augment the loss of the meltwater, leading to its stagnation. This stagnation is preceded by ice thickening hence opposite to the thinning-induced surge termination.

This paper examines the effect of basal topography and strength on the grounding-line position, flux and stability of rapidly-sliding ice streams. It does so by supposing that the buoyancy of the ice stream is small, and of the same order as the longitudinal stress gradient. Making this scaling assumption makes the role of the basal gradient and accumulation rate explicit in the lowest order expression for the ice flux at the grounding line and also provides the transcendental equation for the grounding-line position. It also introduces into the stability condition terms in the basal curvature and accumulation-rate gradient. These expressions revert to well-established expressions in circumstances in which the thickness gradient is large at the grounding line, a result which is shown to be the consequence of the non-linearity of the flow. The behaviour of the grounding-line flux is illustrated for a range of bed topographies and strengths. We show that, when bed topography at a horizontal scale of several tens of ice thicknesses is present, the grounding-line flux and stability have more complex dependencies on bed gradient than that associated with the ‘marine ice-sheet instability hypothesis’, and that unstable grounding-line positions can occur on prograde beds as well as stable positions on retrograde beds.

Ice stream discharge responds to a balance between gravity, basal friction and lateral drag. Appreciable viscous heating occurs in shear margins between ice streams and adjacent slow-moving ice ridges, altering the temperature-dependent viscosity distribution that connects lateral drag to marginal strain rates and ice stream velocity. Warmer ice deforms more easily and accommodates faster flow, whereas cold ice supplied from ice ridges drives advective cooling that counteracts viscous heating. Here, we present a two-dimensional (three velocity component), steady-state model designed to explore the thermal controls on ice stream shear margins. We validate our treatment through comparison with observed velocities for Bindschadler Ice Stream and verify that calculated temperatures are consistent with results from previous studies. Sweeping through a parameter range that encompasses conditions representative of ice streams in Antarctica, we show that modeled steady-state velocity has a modest response to different choices in forcing up until temperate zones develop in the shear margins. When temperate zones are present, velocity is much more sensitive to changes in forcing. We identify key scalings for the emergence of temperate conditions in our idealized treatment that can be used to identify where thermo-mechanical feedbacks influence the evolution of the ice sheet.

Three holes were drilled to the bed of Rutford Ice Stream, through ice up to 2154 m thick, to investigate the basal processes and conditions associated with fast ice flow and the glacial history of the West Antarctic Ice Sheet. A narrative of the drilling, measuring and sampling activities, as well as some preliminary results and initial interpretations of subglacial conditions, is given. These were the deepest subglacial access holes ever drilled using the hot-water drilling method. Samples of bed and englacial sediments were recovered, and a number of instruments were installed in the ice column and the bed. The ice–bed interface was found to be unfrozen, with an existing, well-developed subglacial hydrological system at high pressure, within ~1% of the ice overburden. The bed itself comprises soft, water-saturated sediments, consistent with previous geophysical interpretations. Englacial sediment quantity varies significantly between two locations ~2 km apart, and possibly over even shorter (~20 m) distances. Difficulties and unusual observations encountered while connecting to the subglacial hydrological system in one hole possibly resulted from the presence of a large clast embedded in the bottom of the ice.

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.

Computing predictions of future sea level that include well-defined uncertainty bounds requires models that are capable of robustly simulating the evolution of ice sheets and glaciers. Ice flow behaviour is known to be sensitive to the location and geometry of dynamic ice boundaries such as the grounding line (GRL), terminus position and ice surface elevation, so that any such model should track these interfaces with a high degree of accuracy. To address this challenge, we implement a numerical approach that uses the level-set method (LSM) that accurately models the evolution of the ice–air and ice–water interface as well as capturing topological changes in ice-sheet geometry. This approach is evaluated by comparing simulations of grounded and marine-terminating ice sheets to various analytical and numerical benchmark solutions. A particular advantage of the LSM is its ability to explicitly track the moving margin and GRL while using a fixed grid finite-difference scheme. Our results demonstrate that the LSM is an accurate and robust approach for tracking the ice surface interface and terminus for advancing and retreating ice sheets, including the transient marine ice-sheet interface and GRL positions.

Streaming ice accounts for a major fraction of global ice flux, yet we cannot yet fully explain the dominant controls on its kinematics. In this contribution, we use an anisotropic full-Stokes thermomechanical flow solver to characterize how mechanical anisotropy and temperature distribution affect ice flux. For the ice stream and glacier geometries we explored, we found that the ice flux increases 1–3% per °C temperature increase in the margin. Glaciers and ice streams with crystallographic fabric oriented approximately normal to the shear plane increase by comparable amounts: an otherwise isotropic ice stream containing a concentrated transverse single maximum fabric in the margin flows 15% faster than the reference case. Fabric and temperature variations independently impact ice flux, with slightly nonlinear interactions. We find that realistic variations in temperature and crystallographic fabric both affect ice flux to similar degrees, with the exact effect a function of the local fabric and temperature distributions. Given this sensitivity, direct field-based measurements and models incorporating additional factors, such as water content and temporal evolution, are essential for explaining and predicting streaming ice dynamics.