The response of ice to applied stress on ice-sheet flow timescales is commonly described by a non-linear incompressible viscous fluid, for which the deviatoric stress has a quadratic relation in the strain rate with two response coefficient functions depending on two principal strain-rate invariants I2 and I3. Commonly, a coaxial (linear) relation between the deviatoric stress and strain rate, with dependence on one strain-rate invariant I2 in a stress formulation, equivalently dependence on one deviatoric stress invariant in a strain-rate formulation, is adopted. Glen's uni-axial stress experiments determined such a coaxial law for a strain-rate formulation. The criterion for both uni-axial and shear data to determine the same relation is determined. Here, we apply Steinemann's uni-axial stress and torsion data to determine the two stress response coefficients in a quadratic relation with dependence on a single invariant I2. There is a non-negligible quadratic term for some ranges of I2; that is, a coaxial relation with dependence on one invariant is not valid. The data does not, however, rule out a coaxial relation with dependence on two invariants.

Most glaciers on the Tibetan Plateau have experienced continuous mass losses in response to global warming. However, the seasonal dynamics of glaciers on the southeastern Tibetan Plateau have rarely been reported in terms of glacier surface elevation and velocity. This paper presents a first attempt to explore the seasonal dynamics of the debris-covered Dagongba Glacier within the southeastern Tibetan Plateau. We use the multitemporal unoccupied aerial vehicle images collected over the lower ablation zone on 8 June and 17 October 2018, and 13 May 2019, and then perform an analysis concerning climatic fluctuations. The results reveal that the mean surface elevation decrease of the Dagongba Glacier during the warm season ($2.81\pm 0.44$ m) was remarkably higher than the cold season ($0.72\pm 0.45$ m). Particularly notable glacier surface elevation changes were found around supraglacial lakes and ice cliffs where ice ablation rates were $\sim$3 times higher than the average. In addition, a larger longitudinal decline of glacier surface velocity was observed in the warm season than that in the cold season. In terms of further comparative analysis, the Dagongba Glacier experienced a decrease in surface velocity between 1982–83 and 2018–19, with a decrease in the warm season possibly twice as large as that in the cold season.

This paper introduces the Instructed Glacier Model (IGM) – a model that simulates ice dynamics, mass balance and its coupling to predict the evolution of glaciers, icefields or ice sheets. The novelty of IGM is that it models the ice flow by a Convolutional Neural Network, which is trained from data generated with hybrid SIA + SSA or Stokes ice flow models. By doing so, the most computationally demanding model component is substituted by a cheap emulator. Once trained with representative data, we demonstrate that IGM permits to model mountain glaciers up to 1000 × faster than Stokes ones on Central Processing Units (CPU) with fidelity levels above 90% in terms of ice flow solutions leading to nearly identical transient thickness evolution. Switching to the GPU often permits additional significant speed-ups, especially when emulating Stokes dynamics or/and modelling at high spatial resolution. IGM is an open-source Python code which deals with two-dimensional (2-D) gridded input and output data. Together with a companion library of trained ice flow emulators, IGM permits user-friendly, highly efficient and mechanically state-of-the-art glacier and icefields simulations.

Subglacial hydrology modulates basal motion but remains poorly constrained, particularly for soft-bedded Greenlandic outlet glaciers. Here, we report detailed measurements of the response of subglacial water pressure to the connection and drainage of adjacent water-filled boreholes drilled through kilometre-thick ice on Sermeq Kujalleq (Store Glacier). These measurements provide evidence for gap opening at the ice-sediment interface, Darcian flow through the sediment layer, and the forcing of water pressure in hydraulically-isolated cavities by stress transfer. We observed a small pressure drop followed by a large pressure rise in response to the connection of an adjacent borehole, consistent with the propagation of a flexural wave within the ice and underlying deformable sediment. We interpret the delayed pressure rise as evidence of no pre-existing conduit and the progressive decrease in hydraulic transmissivity as the closure of a narrow (< 1.5 mm) gap opened at the ice-sediment interface, and a reversion to Darcian flow through the sediment layer with a hydraulic conductivity of ≤ 10−6 m s−1. We suggest that gap opening at the ice-sediment interface deserves further attention as it will occur naturally in response to the rapid pressurisation of water at the bed.

Brash ice forms in harbours and ship channels from frequent ship passages and the resulting freezing–breaking cycles create a unique ice formation. The brash ice accumulation over the winter season is a result of meteorological, thermodynamical and mechanical processes. A reliable brash ice growth model is an important asset when determining navigation routes through ice conditions and when establishing port ice management solutions. This review aims to describe the brash ice development and its modelling as well as the key parameters that influence the brash ice growth and its estimation. This paper summarises the brash ice growth models and the fundamental theories of level ice growth upon which these models are based, and outlines the main knowledge gaps. The results highlight the importance of porosity and piece size distribution and their effect on the consolidation process. The inclusion of the brash ice lateral movement and the side ridge formation would improve the accuracy of forecast models. Furthermore, the findings of the study identify the effect of omitting meteorological parameters such as snow and radiation, from the brash ice growth models. Their contribution to the level ice thickness suggests a significant influence on the brash ice consolidation process.

Heated needle probes provide the most convenient method to measure snow thermal conductivity. Recent studies have suggested that this method underestimates snow thermal conductivity; however the reasons for this discrepancy have not been elucidated. We show that it originates from the fact that, while the theory behind the method assumes that the measurements reach a logarithmic regime, this regime is not reached within the standard measurement procedure. Using the needle probe without this logarithmic regime leads to thermal conductivity underestimations of tens of percents. Moreover, we show that the poor thermal contact between the probe and the snow due to insertion damages results in a further underestimation. Thus, we encourage the use of fixed needle probes, set up before the snow season and buried under snowfalls, rather than hand-inserted probes. Finally, we propose a method to correct the measurements performed with such fixed needle probes buried in snow. This correction is based on a lookup table, derived specifically for the Hukseflux TP02 needle probe model, frequently used in snow studies. Comparison between corrected measurements and independent estimations of snow thermal conductivity obtained with numerical simulations shows an overall improvement of the needle probe values after application of the correction.

To understand snow structure and snowmelt timing, information about flows of liquid water within the snowpack is essential. Models can make predictions using explicit representations of physical processes, or through parameterization, but it is difficult to verify simulations. In situ observations generally measure bulk quantities. Where internal snowpack measurements are made, they tend to be destructive and unsuitable for continuous monitoring. Here, we present a novel method for in situ monitoring of water flow in seasonal snow using the electrical self-potential (SP) geophysical method. A prototype geophysical array was installed at Col de Porte (France) in October 2018. Snow hydrological and meteorological observations were also collected. Results for two periods of hydrological interest during winter 2018–19 (a marked period of diurnal melting and refreezing, and a rain-on-snow event) show that the electrical SP method is sensitive to internal water flow. Water flow was detected by SP signals before it was measured in conventional snowmelt lysimeters at the base of the snowpack. This initial feasibility study shows the utility of the SP method as a non-destructive snow sensor. Future development should include combining SP measurements with a high-resolution snow physics model to improve prediction of melt timing.

The earliest airborne geophysical campaigns over Antarctica and Greenland in the 1960s and 1970s collected ice penetrating radar data on 35 mm optical film. Early subglacial topographic and englacial stratigraphic analyses of these data were foundational to the field of radioglaciology. Recent efforts to digitize and release these data have resulted in geometric and ice-thickness analysis that constrain subsurface change over multiple decades but stop short of radiometric interpretation. The primary challenge for radiometric analysis is the poorly-characterized compression applied to Z-scope records and the sparse sampling of A-scope records. Here, we demonstrate the information richness and radiometric interpretability of Z-scope records. Z-scope pixels have uncalibrated fast-time, slow-time, and intensity scales. We develop approaches for mapping each of these scales to physical units (microseconds, seconds, and signal to noise ratio). We then demonstrate the application of this calibration and analysis approach to a flight in the interior of East Antarctica with subglacial lakes and to a reflight of an East Antarctic ice shelf that was observed by both archival and modern radar. These results demonstrate the potential use of Z-scope signals to extend the baseline of radiometric observations of the subsurface by decades.

Glacier slip is usually described using steady-state sliding laws that relate drag, slip velocity and effective pressure, but where subglacial conditions vary rapidly transient effects may influence slip dynamics. Here we use results from a set of laboratory experiments to examine the transient response of glacier slip over a hard bed to velocity perturbations. The drag and cavity evolution from lab experiments are used to parameterize a rate-and-state drag model that is applied to observations of surface velocity and ice-bed separation from the Greenland ice sheet. The drag model successfully predicts observed lags between changes in ice-bed separation and sliding speed. These lags result from the time (or displacement) required for cavities to evolve from one steady-state condition to another. In comparing drag estimates resulting from applying rate-and-state and steady-state slip laws to transient data, we find the peaks in drag are out of phase. This suggests that in locations where subglacial conditions vary on timescales shorter than those needed for cavity adjustment transient slip processes control basal drag.

Mountain glaciers have response times that govern retreat due to anthropogenic climate change. We use geometric attributes to estimate individual response times for 383 glaciers in the Cascade mountain range of Washington State, USA. Approximately 90% of estimated response times are between 10 and 60 years, with many large glaciers on the short end of this distribution. A simple model of glacier dynamics shows that this range of response times entails consequential differences in recent and ongoing glacier changes: glaciers with decadal response times have nearly kept pace with anthropogenic warming, but those with multi-decadal response times are far from equilibrium, and their additional committed retreat stands well beyond natural variability. These differences have implications for changes in glacier runoff. A simple calculation highlights that transient peaks in area-integrated melt, either at the onset of forcing or due to variations in forcing, depend on the glacier's response time and degree of disequilibrium. We conclude that differences in individual response times should be considered when assessing the state of a population of glaciers and modeling their future response. These differences in response can arise simply from a range of different glacier geometries, and the same basic principles can be expected in other regions as well.

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.

The geometry and thermal structure of western Greenland ice sheet are known to have undergone relatively substantial change over the Holocene. Evolution of the frozen and melted fractions of the bed associated with the ice-sheet retreat over this time frame remains unclear. We address this question using a thermo-mechanically coupled flowline model to simulate a 11 ka period of ice-sheet retreat in west central Greenland. Results indicate an episode of ~100 km of terminus retreat corresponded to ~16 km of upstream frozen/melted basal boundary migration. The majority of migration of the frozen area is associated with the enhancement of the frictional and strain heating fields, which are accentuated toward the retreating ice margin. The thermally active bedrock layer acts as a heat sink, tending to slow contraction of frozen-bed conditions. Since the bedrock heat flux in our region is relatively low compared to other regions of the ice sheet, the frozen region is relatively greater and therefore more susceptible to marginward changes in the frictional and strain heating fields. Migration of melted regions thus depends on both geometric changes and the antecedent thermal state of the bedrock and ice, both of which vary considerably around the ice sheet.

Firn is the pervasive surface material across Antarctica, and its structures reflect its formation and history in response to environmental perturbations. In addition to the role of firn in thermally isolating underlying glacial ice, it defines near-surface elastic and density structure and strongly influences high-frequency (> 5 Hz) seismic phenomena observed near the surface. We investigate high-frequency seismic data collected with an array of seismographs deployed on the West Antarctic Ice Sheet (WAIS) near WAIS Divide camp in January 2019. Cross-correlations of anthropogenic noise originating from the approximately 5 km-distant camp were constructed using a 1 km-diameter circular array of 22 seismographs. We distinguish three Rayleigh (elastic surface) wave modes at frequencies up to 50 Hz that exhibit systematic spatially varying particle motion characteristics. The horizontal-to-vertical ratio for the second mode shows a spatial pattern of peak frequencies that matches particle motion transitions for both the fundamental and second Rayleigh modes. This pattern is further evident in the appearance of narrow band spectral peaks. We find that shallow lateral structural variations are consistent with these observations, and model spectral peaks as Rayleigh wave amplifications within similarly scaled shallow basin-like structures delineated by the strong velocity and density gradients typical of Antarctic firn.

During the past 20 years, multi-channel radar emerged as a key tool for deciphering an ice sheet's internal architecture. To assign ages to radar reflections and connect them over large areas in the ice sheet, the layer genesis has to be understood on a microphysical scale. Synthetic radar trace modelling based on the dielectric profile of ice cores allows for the assignation of observed physical properties’ variations on the decimetre scale to radar reflectors extending from the coring site to a regional or even whole-ice-sheet scale. In this paper we rely on the available dielectric profiling data of the northern Greenland deep ice cores: NGRIP, NEEM and EGRIP. The three records are well suited for assigning an age model to the stratigraphic radar-mapped layers, and linking up the reflector properties to observations in the cores. Our modelling results show that the internal reflections are mainly due to conductivity changes. Furthermore, we deduce fabric characteristics at the EGRIP drill site from two-way-travel-time differences of along and across-flow polarized radarwave reflections of selected horizons (below 980 m). These indicate in deeper parts of the ice column an across-flow concentrated c-axis fabric.

Marine-terminating glaciers lose mass through melting and iceberg calving, and we find that meltwater drainage systems influence calving timing at Helheim Glacier, a tidewater glacier in East Greenland. Meltwater feeds a buoyant subglacial discharge plume at the terminus of Helheim Glacier, which rises along the glacial front and surfaces through the mélange. Here, we use high-resolution satellite and time-lapse imagery to observe the surface expression of this meltwater plume and how plume timing and location compare with that of calving and supraglacial meltwater pooling from 2011 to 2019. The plume consistently appeared at the central terminus even as the glacier advanced and retreated, fed by a well-established channelized drainage system with connections to supraglacial water. All full-thickness calving episodes, both tabular and non-tabular, were separated from the surfacing plume by either time or by space. We hypothesize that variability in subglacial hydrology and basal coupling drive this inverse relationship between subglacial discharge plumes and full-thickness calving. Surfacing plumes likely indicate a low-pressure subglacial drainage system and grounded terminus, while full-thickness calving occurrence reflects a terminus at or close to flotation. Our records of plume appearance and full-thickness calving therefore represent proxies for the grounding state of Helheim Glacier through time.

Ice flow models typically assume that ice is incompressible, a reasonable assumption because ice density changes are indeed small and have a correspondingly small effect on the overall mass balance of glaciers and ice sheets. Given the immense volume of the ice sheets, however, even relatively small changes may influence global mean sea level to a degree that severely impacts humanity (Hauer and others, 2020). Here, we quantify the role of gravitational compression and thermal contraction in estimating ice sheet mass.