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The flow of glaciers and ice sheets is largely influenced by friction at the ice‐bed interface that can trigger rapid changes in glacier motion ranging from seasonal velocity variations to cyclic surge instabilities or even devastating glacier collapse. This wide range of transient glacier dynamics is currently not captured by models, and its implications for long‐term glacier evolution are uncertain. This highlights the need of developing improved descriptions for processes that occur at the glacier bed. Here, we present a model that describes the evolution of basal friction inspired by a "rate and state" approach, coupled to models of subglacial drainage and glacier flow, and investigate how these couplings affect the dynamics of glaciers. We show that a wide range of sliding behavior results from a feedback loop between subglacial drainage efficiency and friction which depends on the evolution of a frictional state that can be interpreted as the degree of cavitation or till porosity for hard and soft beds, respectively. In our simulations, we find that glaciers are susceptible to surging if they exhibit a transition to velocity weakening friction associated with a poor sensitivity of the drainage capacity to the frictional state. This potential materializes if the local topography and mass balance create the conditions for high water pressure to build up in an area sufficiently large to exceed a critical length. We advocate accounting for feedback loops between friction and drainage as a promising avenue for better understanding dynamical instabilities of glaciers and ice sheets. Plain Language Summary: Glaciers move through a combination of basal sliding and viscous deformation of the ice. Observed velocities range widely from glaciers creeping at a few meters per year, to continuously fast‐flowing ice‐streams at velocities of kilometers per year, all the way to devastating ice avalanches. Some glaciers can alter their velocity in quasi‐periodic intervals, known as surge‐type glaciers. These glaciers can move steadily for decades, then speed up for a short period of time by up to two orders of magnitude or more, before returning to quiescence. In this study, we show that a wide range of glacier behavior can be understood from the interaction between friction and the subglacial drainage system. Glacier surges are possible if the efficiency of the drainage system is not high enough to drain the water that enters and is produced at the glacier base. This allows water pressure to increase over time, which can potentially trigger a frictional instability. Depending on the configuration of the subglacial drainage and how it evolves in response to sliding, glaciers can be stable or surge‐type, in addition to exhibiting several different classes of velocity variations. Key Points: We present a model combining rate and state friction with subglacial hydrology processes that spontaneously generates glacier surgesA wide range of glacier behavior emerges from the model, including periodic and quasi‐periodic glacier surgesSurges arise if the drainage system is unable to sufficiently drain water from the glacier base, triggering a frictional instability [ABSTRACT FROM AUTHOR]

In recent decades, most glaciers have been melting, thinning and retreating globally in response to continuously increasing temperatures. We simulated ice thicknesses and volumes on the east and west slopes of Mt Noijin Kang-Sang, Southern Tibetan Plateau (TP), since the Last Glacial Maximum (LGM), using a glacial flowline model. The simulated average ice thicknesses during the LGM and Lateglacial (LG), Early Holocene, Neoglacial and the Little Ice Age (LIA) periods were 1.4, 1.3, 1.1 and 1.2 times greater than those of modern glaciers in the Gangbu (eastern slope) and western valleys, respectively. In the Gangbu Valley, areas from the LGM-LG to LIA periods were 1.7, 1.5, 1.4 and 1.2 times greater than the modern glacier area, and the volume expansion indexes were 2.2, 1.9, 1.5 and 1.4. In the western valleys, the area expansion indexes were 2.2, 1.9, 1.5 and 1.4 times greater than the modern glacier, and volumes were 5.4, 4.4, 3.4 and 2.9 times greater, respectively. Glaciers in the western valleys retreated more extensively than those on the eastern slopes of Gangbu Valley after the LGM-LG, probably due to the smaller glaciers on the leeward western slopes with lower elevations. Equilibrium-line altitudes dropped ~425 m in Gangbu Valley and ~385 m in the western valleys during the LGM-LG, corresponding to a 3.8-4.1 ℃ temperature decrease in this region, which was consistent with cooling on the central Tibetan Plateau, but lower than cooling at the southeastern edge of the Tibetan Plateau. [ABSTRACT FROM AUTHOR]

Marine-terminating glaciers cover more than one-fourth of the total glacierized area in the Northern Hemisphere outside the Greenland ice sheet. It is therefore crucial to ensure an adequate representation of these glaciers when projecting large-scale glacier mass changes. We investigate how the introduction of marine frontal processes in the modeling chain influences the results of mass change projections, compared to projections neglecting such processes. We find that including frontal processes reduces the projected glacier mass loss, since incorporating frontal ablation in the model's mass-balance calibration results in a decrease in marine-terminating glaciers’ sensitivity to atmospheric temperatures. We also find that retrograde bed slopes lead to increased frontal ablation as the atmosphere warms, while frontal ablation decreases if bed slopes are prograde. These opposing effects have the potential to partly cancel each other when considering large glacier ensembles. Although we do not account for potential future changes in oceanic climate yet, any effect of these would be moderated by around half of today's marine-terminating glaciers becoming land-terminating in the course of the 21st century. While we find a significant influence of ice flow parameters on our results, boundary conditions remain the largest source of uncertainty in our projections.

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.

The Antarctic Peninsula's widespread glacier retreat and ice shelf collapse have been attributed to atmospheric and oceanic warming. Following the initial post-collapse period of retreat, several former tributary glaciers of the Larsen A and B ice shelves have been slowly re-advancing for more than a decade. Here, we use a flowline model of Crane Glacier to gauge the sensitivity of former tributary glaciers to future climate change following this period of long-term dynamic adjustment. The glacier's long-term geometry and speed changes are similar to those of other former Larsen A and B tributaries, suggesting that Crane Glacier is a reasonable representation of regional dynamics. For the unperturbed climate simulations, discharge remains nearly unchanged in 2018–2100, indicating that dynamic readjustment to shelf collapse took ~15 years. Despite large uncertainties in Crane Glacier's past and future climate forcing, a wide range of future climate scenarios leads to a relatively modest range in grounding line discharge (0.8–1.5 Gt a−1) by 2100. Based on the model results for Crane, we infer that although former ice shelf tributaries may readvance following collapse, similar to the tidewater glacier cycle, their dynamic response to future climate perturbations should be less than their response to ice shelf collapse.

Numerical glacier and ice-sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or smaller, these models usually require time steps shorter than climate-coupling time scales because they update ice thickness after each velocity solution. High-resolution performance is degraded by the stability restrictions of such explicit time-stepping. This short note, which considers the shallow ice approximation and Stokes models as stress-balance end members, clarifies the scaling of numerical model performance by quantifying simulation cost per model year in terms of mesh resolution and the number of degrees of freedom. The performance of current-generation explicit time-stepping models is assessed, and then compared to the prospective performance of implicit schemes. The main results highlight the key roles played by the algorithmic scaling of stress-balance solvers and coupled, implicit-step solvers.

In this study, we investigate the differences between two transient, three-dimensional, thermomechanically coupled ice-sheet models, namely, a first-order approximation model (FOM) and a ‘full’ Stokes ice-sheet model (FSM) under the same numerical framework. For all numerical experiments, we take the FSM outputs as the reference values and calculate the mean relative errors in the velocity and temperature fields for the FOM over 100 years. Four different boundary conditions (ice slope, geothermal heat flux, basal topography and basal sliding) are tested, and by changing these parameters, we verify the thermomechanical behavior of the FOM and discover that the velocity and temperature biases of the FOM generally increase with increases in the ice slope, geothermal heat flux, undulation amplitude of the ice base, and with the existence of basal sliding. In addition, the model difference between the FOM and FSM may accumulate over time, and the spatial distribution patterns of the relative velocity and temperature errors are in good agreement.

Marine-terminating glaciers cover more than one-fourth of the total glacierized area in the Northern Hemisphere outside the Greenland ice sheet. It is therefore crucial to ensure an adequate representation of these glaciers when projecting large-scale glacier mass changes. We investigate how the introduction of marine frontal processes in the modeling chain influences the results of mass change projections, compared to projections neglecting such processes. We find that including frontal processes reduces the projected glacier mass loss, since incorporating frontal ablation in the model's mass-balance calibration results in a decrease in marine-terminating glaciers' sensitivity to atmospheric temperatures. We also find that retrograde bed slopes lead to increased frontal ablation as the atmosphere warms, while frontal ablation decreases if bed slopes are prograde. These opposing effects have the potential to partly cancel each other when considering large glacier ensembles. Although we do not account for potential future changes in oceanic climate yet, any effect of these would be moderated by around half of today's marine-terminating glaciers becoming land-terminating in the course of the 21st century. While we find a significant influence of ice flow parameters on our results, boundary conditions remain the largest source of uncertainty in our projections. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Antarctic Peninsula's widespread glacier retreat and ice shelf collapse have been attributed to atmospheric and oceanic warming. Following the initial post-collapse period of retreat, several former tributary glaciers of the Larsen A and B ice shelves have been slowly re-advancing for more than a decade. Here, we use a flowline model of Crane Glacier to gauge the sensitivity of former tributary glaciers to future climate change following this period of long-term dynamic adjustment. The glacier's long-term geometry and speed changes are similar to those of other former Larsen A and B tributaries, suggesting that Crane Glacier is a reasonable representation of regional dynamics. For the unperturbed climate simulations, discharge remains nearly unchanged in 2018–2100, indicating that dynamic readjustment to shelf collapse took ~15 years. Despite large uncertainties in Crane Glacier's past and future climate forcing, a wide range of future climate scenarios leads to a relatively modest range in grounding line discharge (0.8–1.5 Gt a−1) by 2100. Based on the model results for Crane, we infer that although former ice shelf tributaries may readvance following collapse, similar to the tidewater glacier cycle, their dynamic response to future climate perturbations should be less than their response to ice shelf collapse. [ABSTRACT FROM AUTHOR]

We revise and evaluate frontal ablation fluxes obtained by the Open Global Glacier Model (OGGM) for Greenland's tidewater peripheral glaciers de-coupled from the ice sheet. By making use of new region-wide ice thickness and solid ice discharge data, we re-evaluate model performance and suggest future research directions to improve the ice thickness estimation of glacier models. OGGM is unable to predict individual tidewater glacier dynamics well if it has to rely only on surface mass balance estimates and the assumption of a closed budget to constrain the calving parameterization. Velocity observations are essential to constrain the model and estimate the dynamic mass loss of Greenland's tidewater peripheral glaciers. [ABSTRACT FROM AUTHOR]

We perform Bayesian inference of the parameters of a time-dependent model of ice flow and calving at Helheim Glacier, East Greenland. We find that, while a time-independent calving parameterization can recover the mean observed terminus position, such a model is unable to recover sub-annual variability, even when forced with seasonally varying climate. To address this, we develop a simple stochastic model relating surface runoff rates and calving threshold. Again inferring model parameters from observations, we find that this parameterization is able to reproduce observations with respect to both mean position and characteristic temporal variability. This result demonstrates the importance of considering potential sub-annual controls on calving rates in numerical models, which may include variable undercutting rates or surface runoff-dependent surface crevasse propagation.

A combination of 10Be surface-exposure dating of glacially transported boulders and glacially polished bedrock, and numerical modeling of the ∼600 km2 Late Pleistocene icefield complex in the northern Medicine Bow Mountains of Wyoming, USA, constrains the timing and climate forcing of the local last glacial maximum (LLGM) and the subsequent deglaciation in the range. The chronology reported here indicates initial recession of the ∼100 km2 Libby Creek glacier on the east side of the complex from its terminal moraine at 20.7 ± 2.8 ka, followed by length reduction of 38% by 18.0 ± 0.8 ka and 75% by 14.7 ± 0.4 ka. By 14.2 ± 0.3 ka, the icefield had nearly completely disappeared although there is evidence of two subsequent standstills or minor readvances at ∼11.5 ± 0.5 ka and ∼10.5 ± 0.3 ka. Results of numerical glacier-modeling experiments suggest that the LLGM was associated with temperatures 6.0 °C colder than present with an uncertainty of about ±1.7 °C, assuming no change from modern precipitation. If precipitation differed at the LLGM, over a range from half to twice modern, the temperature depression necessary to sustain the icefield complex could have been as much as 8.0 ± 1.7 °C or as little as 3.1 ± 1.7 °C respectively. As most available proxies and climate-model output suggest mildly decreased precipitation at the LLGM, a temperature depression of somewhat more than 6.0 °C is the most likely scenario. Model experiments further suggest that nearly complete deglaciation by 14.2 ± 0.3 ka involved only a ∼1.7 °C rise from LLGM temperature, assuming no change in precipitation. The sensitivity of the icefield complex to such limited warming reflects its plateau-like hypsometry, which makes it particularly sensitive to changing equilibrium-line altitude. While the precise chronology of deglaciation remains open to interpretation, most of the ice loss preceded the North Atlantic Bølling-Allerød interval (∼14.7–12.9 ka), suggesting that global atmospheric CO2 and rising summer insolation were the dominant forcings of ice retreat.

Numerical glacier and ice-sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or smaller, these models usually require time steps shorter than climate-coupling time scales because they update ice thickness after each velocity solution. High-resolution performance is degraded by the stability restrictions of such explicit time-stepping. This short note, which considers the shallow ice approximation and Stokes models as stress-balance end members, clarifies the scaling of numerical model performance by quantifying simulation cost per model year in terms of mesh resolution and the number of degrees of freedom. The performance of current-generation explicit time-stepping models is assessed, and then compared to the prospective performance of implicit schemes. The main results highlight the key roles played by the algorithmic scaling of stress-balance solvers and coupled, implicit-step solvers. [ABSTRACT FROM AUTHOR]

This study aims to quantify the contribution of anthropogenic forcings on the retreat of the Argentière Glacier (European Alps). The glacier evolution is simulated over 1850–2014 following retrospective scenarios produced with the IPSL‐CM6‐LR climate model, with and without natural and anthropogenic forcings. The scenarios used to force an ice flow model are statistically downscaled, preserving the long‐term trends and the physical consistency between precipitation and temperature. Since the late 19th century, the regional aerosol cooling has partially counteracted the greenhouse gas‐induced warming, delaying the time of emergence of the anthropogenic signal. The anthropogenic signal emerged from natural variability in 1979 for temperature and surface melting, and in 2008 for the glacier mass, whereas its snout position in 2014 remains compatible with natural variability. From the total mass loss between 1850 and 2014, 66% [21%–111%] is attributed to anthropogenic activities. Plain Language Summary: This work aims to quantify the anthropogenic impact on the Argentière Glacier with respect to changes related to climate natural variability. We use a detection‐attribution approach to produce retrospective ensemble simulations of the climate and the glaciers, with and without greenhouse gasses and aerosol forcings over 1850–2014. The time of emergence of the anthropogenic signal, that is, the date when it becomes statistically distinguishable from climate natural variability, occurs in 1979 for temperature in the Argentière location, with warming reaching 1.35°C in 2014 relative to 1850. The emergence of the anthropogenic signal occurs later for the glacier changes: the snout position is still compatible with natural variability in 2014, whereas for the glacier mass change, it occurred in 2008, ∼30 years after that of the temperature. In 2014, 66% [21%–111%] of the total mass loss since 1850 can be attributed to anthropogenic activities, a result that is dependent on the natural variability estimated from the climate model used in this study. The combination of increasing concentration of greenhouse gasses and decreasing aerosols in the atmosphere led to an acceleration of the glacier retreat over the last 3 decades. Key Points: Glacier simulations forced with climate model outputs are used to explore natural and anthropogenic imprints on Argentière GlacierStatistical downscaling needs to preserve the trends and the physical relationship between temperature and precipitationThe anthropogenic imprint on Argentière Glacier mass emerged in 2008, 30 years after the emergence of the temperature signal [ABSTRACT FROM AUTHOR]

In this study, we investigate the differences between two transient, three-dimensional, thermomechanically coupled ice-sheet models, namely, a first-order approximation model (FOM) and a 'full' Stokes ice-sheet model (FSM) under the same numerical framework. For all numerical experiments, we take the FSM outputs as the reference values and calculate the mean relative errors in the velocity and temperature fields for the FOM over 100 years. Four different boundary conditions (ice slope, geothermal heat flux, basal topography and basal sliding) are tested, and by changing these parameters, we verify the thermomechanical behavior of the FOM and discover that the velocity and temperature biases of the FOM generally increase with increases in the ice slope, geothermal heat flux, undulation amplitude of the ice base, and with the existence of basal sliding. In addition, the model difference between the FOM and FSM may accumulate over time, and the spatial distribution patterns of the relative velocity and temperature errors are in good agreement. [ABSTRACT FROM AUTHOR]

Increased surface melt in the percolation zone of the Greenland ice sheet causes significant changes in the firn structure, directly affecting the amount and timing of meltwater runoff. Here we force an energy-balance model with automatic weather stations data at two sites in the percolation zone of southwest Greenland ($2040$ and 2360 m a.s.l.) between spring $2017$ and fall $2019$. Extensive model validation and sensitivity analysis reveal that the skin layer formulation used to compute the surface temperature by closing the energy balance leads to a consistent overestimation of melt by more than a factor of two or three depending on the site. In contrast, model results match the observations well when the model is forced by observed surface temperatures; however, unexplained residuals in the energy balance occur. The sensible and ground heat flux differ markedly in the two simulations accounting largely for the difference in modeled melt amounts. This indicates that the energy available for melt is highly sensitive to small changes in surface temperature. Thus, regional climate models that also use the skin layer formulation may have a bias in surface temperature and melt energy in the percolation zone of the ice sheet.

Data assimilation in high-order ice flow modeling is a challenging and computationally costly task, yet crucial to find ice thickness and ice flow parameter distributions that are consistent with ice flow mechanics and mass balance while best matching observations. Failing to find these distributions that are required as initial conditions leads to a disequilibrium between mass balance and ice flow, resulting in nonphysical transient effects in the prognostic model. Here we tackle this problem by inverting an emulator of the Stokes ice flow model based on deep learning. By substituting the ice flow equations using a convolutional neural network emulator, we simplify, make more robust and dramatically speed up the solving of the underlying optimization problem thanks to automatic differentiation, stochastic gradient methods and implementation of graphics processing unit (GPU). We demonstrate this process by simultaneously inferring the ice thickness distribution, ice flow parametrization and ice surface of ten of the largest glaciers in Switzerland. As a result, we obtain a high degree of assimilation while guaranteeing an equilibrium between mass-balance and ice flow mechanics. The code runs very efficiently (optimizing one large-size glacier at 100 m takes < 1 min on a laptop) while it is open-source and publicly available.

Whether there were more extensive glaciations during the Marine Isotope Stage (MIS) 3 relative to MIS 2 across the Tian Shan in Central Asia is intensely debated because of the uncertainty in chronological data and fully understanding the driving mechanisms. To help resolve the ongoing debate, we assess the climate sensitivity of the glaciers and reconstruct the extent of glaciation during MIS 2 and 3 across the Tian Shan, using a glacier-resolving (250 × 250 m) ice sheet model asynchronously coupled with a global climate model. Our results demonstrate that the equilibrium-line altitude (ELA) over the Tian Shan decreases by ∼180 m for every 1 °C cooling under a modern precipitation regime, but precipitation reduction greatly lowers the sensitivity of the glaciers to temperature decrease (e.g., the effect of 2 °C cooling is broadly offset by a 50% decrease in precipitation). Under the modeled colder/drier-than-present climate, the model predicts an ELA depression (∆ELA) of ∼75 m (162 m) over the Tian Shan during MIS 3 interstadials (stadials). The extent of MIS 3 glaciation is much smaller than that during MIS 2 (i.e., ∆ELA = ∼726 m). The more extensive glaciation during MIS 2 is largely attributed to the enhanced summer cooling. Furthermore, through a site-to-site model-data comparison, we find that the closest match between the modeled glacier margin and the locations of the glacial deposits previously argued to be MIS 3 is generally achieved under MIS 2 climatic conditions. These results suggest more extensive glacier advances over the Tian Shan during MIS 2 than MIS 3 on a regional scale, although MIS 3 glaciation may still occur in individual glacier catchments. This pattern suggests general synchronicity with the timing of maximum Northern Hemisphere ice sheets during the last glacial, which should be further tested in a multimodel framework in the future.

Tidewater glaciers have been observed to experience instantaneous, stepwise increases in velocity during iceberg-calving events due to a loss of resistive stresses. These changes in stress can potentially impact tidewater glacier stability by promoting additional calving and affecting the viscous delivery of ice to the terminus. Using flow models and perturbation theory, we demonstrate that calving events and subsequent terminus readvance produce quasi-periodic, sawtooth oscillations in stress that originate at the terminus and propagate upstream. The stress perturbations travel at speeds much greater than the glacier velocities and, for laterally resisted glaciers, rapidly decay within a few ice thickness of the terminus. Consequently, because terminus fluctuations due to individual calving events tend to be much higher frequency than climate variations, individual calving events have little direct impact on the viscous delivery of ice to the terminus. This suggests that the primary mechanism by which calving events can trigger instability is by causing fluctuations in stress that weaken the ice and lead to additional calving and sustained terminus retreat. Our results further demonstrate a stronger response to calving events in simulations that include the full stress tensor, highlighting the importance of accounting for higher order stresses when developing calving parameterizations.

Upernavik Isstrøm, a marine glacier undergoing rapid retreat, is simulated by forcing a numerical model with ocean-driven melt. A review of processes driving retreat led us to hypothesize that a glacier undergoing rapid retreat may be less sensitive to perturbations in the balance of forces than a glacier that is undergoing moderate changes or a glacier in steady state. Numerical experiments suggest this is not the case, and that a system in rapid retreat is as sensitive to basal traction perturbations as a system that is near to steady state. This result is important when considering other glacier systems experiencing marine-forced retreat. While the ice–ocean interface is of primary importance, additional perturbations from meltwater-forced decoupling of the glacier from its bed continue to feature in glacier dynamics.

Iceberg calving, the process where icebergs detach from glaciers, remains poorly understood. Moreover, few parameterizations of the calving process can easily be integrated into numerical models to accurately capture observations, resulting in large uncertainties in projected sea level rise. Recent efforts have focused on estimating crevasse depths assuming tensile failure occurs when crevasses fully penetrate the glacier thickness. However, these approaches often ignore the role of advecting crevasses on calculations of crevasse depth. Here, we examine a more general crevasse depth calving model that includes crevasse advection. We apply this model to idealized prograde and retrograde bed geometries as well as a prograde geometry with a sill. Neglecting crevasse advection results in steady glacier advance and ice tongue formation for all ice temperatures, sliding law coefficients and constant slope bed geometries considered. In contrast, crevasse advection suppresses ice tongue formation and increases calving rates, leading to glacier retreat. Furthermore, crevasse advection allows a grounded calving front to stabilize on top of sills. These results suggest that crevasse advection can radically alter calving rates and hint that future parameterizations of fracture and failure need to more carefully consider the lifecycle of crevasses and the role this plays in the calving process.

We revise and evaluate frontal ablation fluxes obtained by the Open Global Glacier Model (OGGM) for Greenland's tidewater peripheral glaciers de-coupled from the ice sheet. By making use of new region-wide ice thickness and solid ice discharge data, we re-evaluate model performance and suggest future research directions to improve the ice thickness estimation of glacier models. OGGM is unable to predict individual tidewater glacier dynamics well if it has to rely only on surface mass balance estimates and the assumption of a closed budget to constrain the calving parameterization. Velocity observations are essential to constrain the model and estimate the dynamic mass loss of Greenland's tidewater peripheral glaciers.

We perform Bayesian inference of the parameters of a time-dependent model of ice flow and calving at Helheim Glacier, East Greenland. We find that, while a time-independent calving parameterization can recover the mean observed terminus position, such a model is unable to recover sub-annual variability, even when forced with seasonally varying climate. To address this, we develop a simple stochastic model relating surface runoff rates and calving threshold. Again inferring model parameters from observations, we find that this parameterization is able to reproduce observations with respect to both mean position and characteristic temporal variability. This result demonstrates the importance of considering potential sub-annual controls on calving rates in numerical models, which may include variable undercutting rates or surface runoff-dependent surface crevasse propagation. [ABSTRACT FROM AUTHOR]

Abstract This study aims to quantify the contribution of anthropogenic forcings on the retreat of the Argentière Glacier (European Alps). The glacier evolution is simulated over 1850–2014 following retrospective scenarios produced with the IPSL‐CM6‐LR climate model, with and without natural and anthropogenic forcings. The scenarios used to force an ice flow model are statistically downscaled, preserving the long‐term trends and the physical consistency between precipitation and temperature. Since the late 19th century, the regional aerosol cooling has partially counteracted the greenhouse gas‐induced warming, delaying the time of emergence of the anthropogenic signal. The anthropogenic signal emerged from natural variability in 1979 for temperature and surface melting, and in 2008 for the glacier mass, whereas its snout position in 2014 remains compatible with natural variability. From the total mass loss between 1850 and 2014, 66% [21%–111%] is attributed to anthropogenic activities.

Study region: Qiyi Glacier in the Qilian Mountains, northeast Tibetan Plateau. Study focus: Future glacier changes are critical to the sustainable use of regional water resources and the survival and development of the densely populated Tibetan Plateau and surrounding regions. A distributed energy-mass balance model is applied to simulate the historical and future mass balance and ice volume of Qiyi Glacier from 1980 to 2100. The aims of this study are to illuminate the spatial and temporal patterns of mass balance and energy balance, to forecast future changes of this glacier under different scenarios of CMIP6, and to identify the timing of peak ice loss. New hydrological insights for the region: Compared to the historical reconstruction, future projections show that ablation will increase, and accumulation will decrease due to less snowfall and increased net shortwave radiation that is induced by lower albedos. The average mass balance increases by a factor of 1.08, 1.67 and 2.68 under the SSP1-2.6, SSP2-4.5 and SSP5-8.5 scenarios during 2021–2100, respectively. By the end of the 21st century, Qiyi Glacier ice volume will reduce by 107.61 × 106 m3 (95.3 %) for the SSP1-2.6 scenario, and 112.12 × 106 m3 (99.3 %) for the SSP2-4.5 scenario, and will disappear entirely by 2082 for the SSP5-8.5 scenario. In all scenarios, the glacier mass loss rate will peak around 2030–2045, then decrease in parallel with the decreasing ice volume.

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.

Increased surface melt in the percolation zone of the Greenland ice sheet causes significant changes in the firn structure, directly affecting the amount and timing of meltwater runoff. Here we force an energy-balance model with automatic weather stations data at two sites in the percolation zone of southwest Greenland ($2040$ and 2360 m a.s.l.) between spring $2017$ and fall $2019$. Extensive model validation and sensitivity analysis reveal that the skin layer formulation used to compute the surface temperature by closing the energy balance leads to a consistent overestimation of melt by more than a factor of two or three depending on the site. In contrast, model results match the observations well when the model is forced by observed surface temperatures; however, unexplained residuals in the energy balance occur. The sensible and ground heat flux differ markedly in the two simulations accounting largely for the difference in modeled melt amounts. This indicates that the energy available for melt is highly sensitive to small changes in surface temperature. Thus, regional climate models that also use the skin layer formulation may have a bias in surface temperature and melt energy in the percolation zone of the ice sheet. [ABSTRACT FROM AUTHOR]

Data assimilation in high-order ice flow modeling is a challenging and computationally costly task, yet crucial to find ice thickness and ice flow parameter distributions that are consistent with ice flow mechanics and mass balance while best matching observations. Failing to find these distributions that are required as initial conditions leads to a disequilibrium between mass balance and ice flow, resulting in nonphysical transient effects in the prognostic model. Here we tackle this problem by inverting an emulator of the Stokes ice flow model based on deep learning. By substituting the ice flow equations using a convolutional neural network emulator, we simplify, make more robust and dramatically speed up the solving of the underlying optimization problem thanks to automatic differentiation, stochastic gradient methods and implementation of graphics processing unit (GPU). We demonstrate this process by simultaneously inferring the ice thickness distribution, ice flow parametrization and ice surface of ten of the largest glaciers in Switzerland. As a result, we obtain a high degree of assimilation while guaranteeing an equilibrium between mass-balance and ice flow mechanics. The code runs very efficiently (optimizing one large-size glacier at 100 m takes < 1 min on a laptop) while it is open-source and publicly available. [ABSTRACT FROM AUTHOR]

Tidewater glaciers have been observed to experience instantaneous, stepwise increases in velocity during iceberg-calving events due to a loss of resistive stresses. These changes in stress can potentially impact tidewater glacier stability by promoting additional calving and affecting the viscous delivery of ice to the terminus. Using flow models and perturbation theory, we demonstrate that calving events and subsequent terminus readvance produce quasi-periodic, sawtooth oscillations in stress that originate at the terminus and propagate upstream. The stress perturbations travel at speeds much greater than the glacier velocities and, for laterally resisted glaciers, rapidly decay within a few ice thickness of the terminus. Consequently, because terminus fluctuations due to individual calving events tend to be much higher frequency than climate variations, individual calving events have little direct impact on the viscous delivery of ice to the terminus. This suggests that the primary mechanism by which calving events can trigger instability is by causing fluctuations in stress that weaken the ice and lead to additional calving and sustained terminus retreat. Our results further demonstrate a stronger response to calving events in simulations that include the full stress tensor, highlighting the importance of accounting for higher order stresses when developing calving parameterizations. [ABSTRACT FROM AUTHOR]

For several decades, mathematical models of mountain glaciers and ice sheets have been used to study the dynamics of the cryosphere. In recent years, a new step in glaciological modeling has made possible to recon- struct processes in mountain-glacial systems both regionally and globally. The proposed review analyses rea- sons to use this possibility for global glaciological models, key assumptions and methods, general approaches and differences between individual models. Global glacier modeling is a rapidly developing field. This became possible only after the data on all glaciers of the world appeared in the Randolph Glacier Inventory in 2012. The ice thickness inversion procedures discussed in this review made it possible to calculate the initial volume and geometry of glaciers. Methods of varying complexity were used to regionalize global climate data and cal- culate glacier mass balance. Modeling the dynamics of glaciers required the adaptation of simplified schemes to represent the fluidity of ice (or the flow of ice). To date, only two global glacier models contain ice dynamics calculations based on Glenn's law and the diffusion equation: OGGM and GloGEMflow. Simulation results are subject to uncertainties due to input errors, climate predictions, model approximations, and calibration proce- dures. A new stage in the development of methods opens up opportunities to use a number of new directions in the study of the mechanisms that control the evolution of glaciation, depending on the implementation of a particular climatic scenario. Global glacier models make possible to build glaciological projections, calculate potential changes in the regime of glacial runoff, as well as assess risks and predict the occurrence of dangerous processes caused by changes in glaciation parameters, such as mudflows, landslides, and glacial lake outbursts.

Global glacier models provide a new way for studying glaciers on the regional and global scales. They make it possible to perform predictive experiments - for example, to forecast changes in glaciation and river runoff, and diagnostic ones – to identify regularities in the behavior of glaciers (a response time to climate change) taking account of their characteristics. The characteristics and design of global glacier models were described in the first part of the review (see Postnikova T.N., Rybak O.O. Global glaciological models: a new stage in the development of methods for predicting glacier evolution. Part 1. General approach and model architecture. Led i Sneg. Ice and Snow. 2021, 61 (4): 620–636. [In Russian]. doi: 10.31857/S2076673421040111.). In the second part, we present the methods for setting up of numerical experiments with these models, including model initialization, climate forcing, calibration, and validation procedures. The only way to provide the climate forcing of a glaciological model on a regional or global scale is to use low-resolution reanalysis or output of climate modeling on GCMs or RCMs that needs to use a process of scaling to reproduce the local climate in a complex topography where glaciers are usually located. Calibration of mass balance complements the downscaling of climate forcing for each glacier, and usually it includes parameters responsible for the glacier's response to climate change. Sampling from the Latin hypercube and Bayesian inversion are some of the methods discussed in this connection. In this review we present a comparative description of the selected global glaciological models, the results obtained by both diagnostic and prognostic ones, as well as scale and significance of them. We discuss also ways for further development of global glacier models, in particular the inclusion of 3D-modeling and the moraine (debris cover) block. The difficulties arising in a process of modeling glaciation of a particular mountain region or several regions are noted.

Changes in water pressure at the beds of glaciers greatly modify their sliding rate, affecting rates of ice mass loss and sea level change. However, there is still no agreement about the physics of subglacial sliding or how water affects it. Here, we present a new simplified physical model for the effect of transient subglacial hydrology on basal ice velocity. This model assumes that a fraction of the glacier bed is connected by an active hydrologic system that, when averaged over an appropriate scale, is governed by two parameters with limited spatial variability. The sliding model is reminiscent of Budd's empirical sliding law but with fundamental differences including a dependence on the fractional area of the active hydrologic system. With periodic surface meltwater forcing, the model displays classic diffusion-wave behavior, with a downstream time lag and decay of subglacial water pressure perturbations. Testing the model against Greenland observations suggests that, despite its simplicity, it captures key features of observed proglacial discharges and ice velocities with reasonable physical parameter values. Given these encouraging findings, including this sliding model in predictive ice-sheet models may improve their ability to predict time-evolving velocities and associated sea level change and reduce the related uncertainties.

We present a theoretical framework that integrates the dynamics of glaciers with and without the topographic confinement. This Part 1 paper concerns the former, which may exhibit surge cycles when subjected to thermal switches associated with the bed condition. With the topographic trough setting the glacier width and curbing the lateral drainage of the meltwater, the problem falls under the purview of the undrained plastic bed (UPB) formalism. Employing the UPB, we shall examine the external controls of the glacial behavior and test them against observations. Through our non-dimensionalization scheme, we construct a 2-D regime diagram, which allows a ready prognosis of the glacial properties over the full range of the external conditions, both climate- and size-related. We first discern the boundaries separating the glacial regimes of steady-creep, cyclic-surging and steady-sliding. We then apply the regime diagram to observed glaciers for quantitative comparisons. These include the Svalbard glaciers of both normal and surge types, Northeast Greenland Ice Stream characterized by steady-sliding, and Hudson Strait Ice Stream exhibiting cyclic surges. The quantitative validation of our model containing no free parameters suggests that the thermal switch may unify the dynamics of these diverse glaciers.

To get a better overview of atmosphere-driven mass changes at the 79N Glacier (Nioghalvfjerdsfjorden Glacier), the largest outlet glacier of the northeast Greenland ice stream, the surface mass balance (SMB) is modeled by linking the COupled Snowpack and Ice surface energy and mass-balance model in PYthon (COSIPY) with the output of a regional atmospheric model (Polar WRF) for the years 2014–2018. After a manual model optimization, the model produces reliable results when compared to observations in the region and to values from the literature. High spatial resolution (1 km) simulations reveal strong interannual variability of the SMB. Stronger surface melting increased the ablation and runoff in years with high mass loss (2016 and 2017) whereas in other years (2015 and 2018) melting and refreezing inside the snowpack dominated the mass balance (MB). A cooler regional climate with higher snowfall-driven accumulation, higher albedo and reduced surface melt in the ablation period of 2018 resulted in a positive SMB in 2018, however, the annual total MB remained negative. The results suggest a promising new dataset for gaining more insights into mass-balance processes and their contribution to the acceleration of glacier retreat in northeast Greenland.

For several decades, mathematical models of mountain glaciers and ice sheets have been used to study the dynamics of the cryosphere. In recent years, a new step in glaciological modeling has made possible to recon- struct processes in mountain-glacial systems both regionally and globally. The proposed review analyses rea- sons to use this possibility for global glaciological models, key assumptions and methods, general approaches and differences between individual models. Global glacier modeling is a rapidly developing field. This became possible only after the data on all glaciers of the world appeared in the Randolph Glacier Inventory in 2012. The ice thickness inversion procedures discussed in this review made it possible to calculate the initial volume and geometry of glaciers. Methods of varying complexity were used to regionalize global climate data and cal- culate glacier mass balance. Modeling the dynamics of glaciers required the adaptation of simplified schemes to represent the fluidity of ice (or the flow of ice). To date, only two global glacier models contain ice dynamics calculations based on Glenn's law and the diffusion equation: OGGM and GloGEMflow. Simulation results are subject to uncertainties due to input errors, climate predictions, model approximations, and calibration proce- dures. A new stage in the development of methods opens up opportunities to use a number of new directions in the study of the mechanisms that control the evolution of glaciation, depending on the implementation of a particular climatic scenario. Global glacier models make possible to build glaciological projections, calculate potential changes in the regime of glacial runoff, as well as assess risks and predict the occurrence of dangerous processes caused by changes in glaciation parameters, such as mudflows, landslides, and glacial lake outbursts.

Iceberg calving, the process where icebergs detach from glaciers, remains poorly understood. Moreover, few parameterizations of the calving process can easily be integrated into numerical models to accurately capture observations, resulting in large uncertainties in projected sea level rise. Recent efforts have focused on estimating crevasse depths assuming tensile failure occurs when crevasses fully penetrate the glacier thickness. However, these approaches often ignore the role of advecting crevasses on calculations of crevasse depth. Here, we examine a more general crevasse depth calving model that includes crevasse advection. We apply this model to idealized prograde and retrograde bed geometries as well as a prograde geometry with a sill. Neglecting crevasse advection results in steady glacier advance and ice tongue formation for all ice temperatures, sliding law coefficients and constant slope bed geometries considered. In contrast, crevasse advection suppresses ice tongue formation and increases calving rates, leading to glacier retreat. Furthermore, crevasse advection allows a grounded calving front to stabilize on top of sills. These results suggest that crevasse advection can radically alter calving rates and hint that future parameterizations of fracture and failure need to more carefully consider the lifecycle of crevasses and the role this plays in the calving process. [ABSTRACT FROM AUTHOR]

Upernavik Isstrøm, a marine glacier undergoing rapid retreat, is simulated by forcing a numerical model with ocean-driven melt. A review of processes driving retreat led us to hypothesize that a glacier undergoing rapid retreat may be less sensitive to perturbations in the balance of forces than a glacier that is undergoing moderate changes or a glacier in steady state. Numerical experiments suggest this is not the case, and that a system in rapid retreat is as sensitive to basal traction perturbations as a system that is near to steady state. This result is important when considering other glacier systems experiencing marine-forced retreat. While the ice–ocean interface is of primary importance, additional perturbations from meltwater-forced decoupling of the glacier from its bed continue to feature in glacier dynamics. [ABSTRACT FROM AUTHOR]

Presently available information on the glacier equilibrium line altitude (ELA) is being collected and examined. The historical course of the world's longest ELA series of 107 years at the Claridenfirn is reviewed together with climatic elements. Further, the changes in ELAs of 70 glaciers the world over are investigated, and a linear plane model for the speed of the ELA shift is proposed as a function of the changing rates of summer temperature and winter mass balance. The four glaciers in Europe, which diverge most from the plane, are investigated in detail. The cause of the divergence is likely due to be the change in solar global radiation. Although a precise quantification of the role of radiation is not possible at this stage for the entire world, the role of solar radiation is investigated for these glaciers. Globally viewed, ten, or 15% of the 70 investigated glaciers, are expected to lose their accumulation areas within the next ten years. Half of all studied glaciers will follow the same fate by the end of this century under the present climatic conditions. If climate change is accelerated, the disappearance of glaciers will occur sooner than presented in this study. [ABSTRACT FROM AUTHOR]

We revise and evaluate frontal ablation fluxes obtained by the Open Global Glacier Model (OGGM) for Greenland's tidewater peripheral glaciers de-coupled from the ice sheet. By making use of new region-wide ice thickness and solid ice discharge data, we re-evaluate model performance and suggest future research directions to improve the ice thickness estimation of glacier models. OGGM is unable to predict individual tidewater glacier dynamics well if it has to rely only on surface mass balance estimates and the assumption of a closed budget to constrain the calving parameterization. Velocity observations are essential to constrain the model and estimate the dynamic mass loss of Greenland's tidewater peripheral glaciers. [ABSTRACT FROM AUTHOR]

Alaska's largest city, Anchorage, depends on Eklutna Glacier meltwater for drinking water and hydropower generation; however, the 29 km2 glacier is rapidly retreating. We used a temperature-index model forced with local weather station data to reconstruct the glacier's mass balance for the period 1985–2019 and quantify the impacts of glacier change on discharge. Model calibration involved a novel combination of in situ, geodetic mass-balance measurements and observed snowlines from satellite imagery. A resulting ensemble of 250 best-fitting model parameters was used to model mass balance and discharge. Eklutna Glacier experienced a significant negative trend (−0.31 m w.e. decade−1) in annual mean surface mass balance (mean: −0.62 ± 0.06 m w.e.). The day of the year when 95% of annual melt occurs was five days later in 2011–19 than in 1985–93, demonstrating a prolongation of melt season (May–September). Modeled mean specific discharge increased at 0.14 m decade−1, indicating peak water, the year when annual discharge reaches a maximum due to glacier retreat, has not been reached. Four of the five highest discharge years occurred since 2000. Increases in discharge quantity and melt season length require water resource managers consider future decreased discharge as the glacier continues to shrink.

The energy and mass balance of mountain glaciers translate into volume changes that play out as area changes over time. From this, together with former moraines during maximum advances, information on past climate conditions and the climatic drivers behind during glacier advances can be obtained. Here, we use the distributed COupled Snowpack and Ice surface energy and mass balance model in PYthon (COSIPY) to simulate the present state of an Italian glacier, named Fürkeleferner, for the mass balance years 2013–2017. Next, we investigate the local climate during the time of the last “Little Ice Age” (LIA) maximum glacier advance using COSIPY together with the LIA glacier outline retrieved from moraine mapping and a digital elevation model (DEM) adapted for the glacier’s geometry at the time of the LIA as a benchmark. Furthermore, the glacier’s sensitivity to future air temperature increase of +1 K and +2 K is investigated using the same model. For all simulations, meteorological data of closely located climate stations are used to force the model. We show the individual monthly contribution of individual energy and mass balance components. Refreezing during the summer months is an important component of the energy and mass balance, on average about 9 % relative to total annual ablation. The results from simulating past climate show a 2.8 times larger glacier area for Fürkeleferner during the LIA than today. This further implies a 2.5 K colder climate, assuming that the amount of precipitation was 10 %–20 % in excess of today’s value. Concerning further temperature increase of 2 K, the glacier would only consist of the ablation area implying sustained mass loss and eventual total mass loss. Even under current climatic conditions, the glacier area would have to decrease to 17 % of its current area to be in a steady state. We discuss the reliability of the results by comparing simulated present mass balance to measured mass balances of neighboring glaciers in the European Alps and with short-term measurements on Fürkeleferner itself. In conclusion, we are able to show how the glacier responds to past and future climate change and determine the climatic drivers behind.

Glaciers are commonly conceptualized as bodies composed of snow and ice. Yet, many glaciers contain a substantial amount of rock, especially those abutting steep mountains. Mountain slopes erode, depositing rocks on glaciers below. This loose rock (or debris) is buried in glaciers and melts out lower down creating a debris cover. Debris cover reduces ice melt, which changes the shape and movement of glaciers. Glacier movement, specifically basal sliding, efficiently sculpts landscapes. To date, we know little about the impacts of surface debris on conditions below glaciers. To help remedy this, we run numerical model simulations which show that debris‐covered glaciers erode slower than glaciers unaffected by debris. Reduced melt under surface debris lowers sliding speeds and causes sediment to accumulate at the bed, potentially establishing conditions for surging. The influence of surface debris cover on the subglacial environment may hold substantial implications for alpine sediment storage and landscape evolution. Plain Language Summary: Glaciers are imagined as bodies composed entirely of snow and ice. But many glaciers, especially those in steep mountains contain a substantial amount of rock as well. Rocks are deposited on glaciers from steep mountain slopes above them. This loose rock (or debris), buried by snow, can completely cover glaciers' lower reaches as it melts out of the ice. Debris reduces melt, which changes the glacier shape and in turn how glaciers move down valley. To test how debris‐covered glaciers erode and sculpt landscapes we use numerical models. Our simulations show that debris‐covered glaciers erode landscapes at lower rates than glaciers unaffected by debris. The reduced amount of melt from debris cover causes glaciers to slide slower and causes sediment to accumulate under debris‐covered ice, shielding bedrock from erosion. The tendency for debris‐covered glaciers to build sediment layers at their bed may lead to the rapid speed up and advancement of glaciers, also known as surges. The influence of surface debris cover on the subglacial environment may hold substantial implications for alpine sediment storage and landscape evolution. Key Points: Erosion is reduced under debris‐covered ice because of compounding effects between reduced surface melt and the subglacial environmentTill accumulates under debris‐covered ice because surface melt is suppressed by surface debris coverDebris cover on glaciers promotes subglacial fluvial conditions that can store sediment in alpine environments, altering erosional patterns [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study shows the dramatic but probable future evolution of Mexico's largest glacier. Mass and energy balances of this glacier have been previously studied, as well as reconstructions of its evolution up to the present time. In this work, for the first time, the real evolution of the glacier is compared with the first years of models of its future evolution. Two dynamic models of glacier thickness evolution have been developed based on a network of stakes and ground penetrating radar complemented by geometrical characterizations of the glacier bed shape. Calculated mean annual mass balance leads the equilibrium line altitude to be increasingly higher and even higher than that of the mountain summit. Two models that complement each other to describe the how and when of the different states and stages in which the glacier front retracts, the thickness decreases causing the separation of the glacier to finally disappear in the middle of the 21st century. This study provides the first view of a glacier that is about to disappear in Mexico, where the cryosphere represents the best climate proxy for future scenarios of related ecosystems, water availability. [Display omitted] • When will the glaciers disappear from mexico. • How much ice is left on the citlaltepetl, mexico. • What happens to the biggest glacier in mexico. • Is it possible to know the future evolution of a glacier. [ABSTRACT FROM AUTHOR]

Changes in water pressure at the beds of glaciers greatly modify their sliding rate, affecting rates of ice mass loss and sea level change. However, there is still no agreement about the physics of subglacial sliding or how water affects it. Here, we present a new simplified physical model for the effect of transient subglacial hydrology on basal ice velocity. This model assumes that a fraction of the glacier bed is connected by an active hydrologic system that, when averaged over an appropriate scale, is governed by two parameters with limited spatial variability. The sliding model is reminiscent of Budd's empirical sliding law but with fundamental differences including a dependence on the fractional area of the active hydrologic system. With periodic surface meltwater forcing, the model displays classic diffusion-wave behavior, with a downstream time lag and decay of subglacial water pressure perturbations. Testing the model against Greenland observations suggests that, despite its simplicity, it captures key features of observed proglacial discharges and ice velocities with reasonable physical parameter values. Given these encouraging findings, including this sliding model in predictive ice-sheet models may improve their ability to predict time-evolving velocities and associated sea level change and reduce the related uncertainties. [ABSTRACT FROM AUTHOR]

Several global datasets of glacier thickness exist, but the number of observations from western Canada are sparse and spatially biased. To supplement these limited observations, we measured ice thickness with ice penetrating radar on five glaciers in the Columbia Mountains, Canada. Our radar surveys, when combined with previous surveys for two glaciers in the Rocky Mountains, total 182 km of transects that represent 34 672 point measurements of ice thickness. Our measurements are, on average, 38% thicker than previous surface inversion model estimates of glacier thickness. Using our measurements within a cross-validation scheme, we model ice thickness with the Open Global Glacier Model (OGGM) driven with recent observations of surface mass balance and glacier elevation. We calibrated OGGM ice thickness by optimizing the ice creep parameter in the model. The optimized OGGM yields an ice volume for Columbia Basin of 122.5 ± 22.4 km3 for the year 2000, which is 23% greater than the range of previous estimates. At current rates of glacier mass loss for this region, glaciers would disappear from the basin in about 65–80 years. Disappearance of these glaciers will negatively affect the basin's surface hydrology, freshwater availability and aquatic ecosystems.

Glacier ice thickness is crucial to quantifying water resources in mountain regions, and is an essential input for ice-flow models. Using a surface velocity inversion method, we combine ice thickness measurements with detailed surface elevation and velocity data, and derive ice thickness and volume estimates for the Monte Tronador glaciers, North Patagonian Andes. We test the dependence of the inversion model on surface slope by resampling glacier slopes using variable smoothing filter sizes of 16–720 m. While total glacier volumes do not differ considerably, ice thickness estimates show higher variability depending on filter size. Smaller (larger) smoothing scales give thinner (thicker) ice and higher (lower) noise in ice thickness distribution. A filter size of 300 m, equivalent to four times the mean ice thickness, produces a noise-free thickness distribution with an accuracy of 35 m. We estimate the volume of the Monte Tronador glaciers at 4.8 ± 2 km3 with a mean ice thickness of 75 m. Comparison of our results with earlier regional and global assessments shows that the quality of glacier inventories is a significant source of discrepancy. We show that including surface slope as an input parameter increases the accuracy of ice thickness distribution estimates.

The representation of iceberg calving in numerical models is a key source of uncertainty in century-scale sea-level rise projections. Parameters central to model representations of calving, including the tensile strength of glacier ice, remain poorly constrained. Grain-size and sample-size dependence make it difficult to reconcile laboratory and in situ estimates of ice tensile strength. Further, assumptions of various numerical models obscure comparison of the ‘strength’ parameter with a physically observable value. Here, we address the problem of fracture during calving using an analogous natural laboratory: a viscoelastic analysis of observed surface deformation and associated stresses in the 2015 collapse of eastern Skaftá cauldron, Vatnajökull ice cap, Iceland. We find that the ice within the cauldron could have experienced instantaneous elastic stress on the order of several MPa. We observe surface crevasses at the cauldron edges and center, but find that large areas of ice remain intact despite high stress. Our findings suggest a tensile strength of glacier ice on the order of 1 MPa, consistent with laboratory estimates but exceeding previous glacier-specific estimates.