We present a new model for understanding ice cliff dynamics within a debris-covered glacier ablation zone. This simple energy-balance model incorporates a moving frame of reference, made necessary by the melt of the surrounding debris-covered ice. In so doing, this also formalises how different types of field measurements can be utilised and compared. Our predictions include showing: ice cliffs can endogenously select their own slope angles; that there should be an indifference between illuminated north- and south-facing ice cliff slopes; that ice cliffs grow steeper with thicker debris layers; that ice cliffs cannot stably exist below a certain critical debris thickness and that some modelling of ice cliffs (when not incorporating the moving frame) may incorrectly estimate ice mass losses. All of our results are produced using parametrisations from Baltoro Glacier, Karakoram.

Knowledge of snow and firn-density change is needed to use elevation-change measurements to estimate glacier mass change. Additionally, firn-density evolution on glaciers is closely connected to meltwater percolation, refreezing and runoff, which are key processes for glacier mass balance and hydrology. Since 2016, the U.S. Geological Survey Benchmark Glacier Project has recovered firn cores from a site on Wolverine Glacier in Alaska's Kenai Mountains. We use annual horizons in repeat cores to track firn densification and meltwater retention over seasonal and interannual timescales, and we use density measurements to quantify how the firn air content (FAC) changes through time. The results suggest the firn is densifying due primarily to compaction rather than refreezing. Liquid-water retention in the firn is transient, likely due to gravity-fed drainage and irreducible-water-content decreases that accompany decreasing porosity. We show that the uncertainty (±60 kg m−3) in the commonly used volume-to-mass conversion factor of 850 kg m−3 is an underestimation when glacier-wide FAC variability exceeds 12% of the glacier-averaged height change. Our results demonstrate how direct measurements of firn properties on mountain glaciers can be used to better quantify the uncertainty in geodetic volume-to-mass conversions.

Empirical glacier mass-balance models are commonly used in assessments of glacier and runoff evolution. Recent satellite-borne geodetic mass-balance observations of global coverage facilitate large-scale model calibration that previously relied on sparse in situ observations of glacier mass change. Geodetic observations constitute temporally aggregated mass-balance signals with significant uncertainty, raising questions about the role of observations with different temporal resolutions and uncertainties in constraining model parameters. We employ a Bayesian approach and demonstrate the sensitivity of parameter values to commonly used mass-balance observations of seasonal, annual and decadal resolution with uncertainties characteristic to in situ and satellite-borne observations. For glaciers along a continentality gradient in Norway, the use of annual mass balances results in around 20% lower magnitude of modelled ablation and accumulation (1960–2020), compared to employing seasonal balances. Decadal mass balance also underestimates magnitudes of ablation and accumulation, but parameter values are strongly influenced by the prior distribution. The datasets yield similar estimates of annual mass balance with different margins of uncertainty. Decadal observations are afflicted with considerable uncertainty in mass-balance sensitivity due to high parameter uncertainty. Our results highlight the importance of seasonal observations when model applications require accurate magnitudes of ablation, e.g. to estimate meltwater runoff.

In Southeast Greenland, summer melt and high winter snowfall rates give rise to firn aquifers: vast stores of meltwater buried beneath the ice-sheet surface. Previous detailed studies of a single Greenland firn aquifer site suggest that the water drains into crevasses, but this is not known at a regional scale. We develop and use a tool in Ghub, an online gateway of shared datasets, tools and supercomputing resources for glaciology, to identify crevasses from elevation data collected by NASA's Airborne Topographic Mapper across 29000 km2 of Southeast Greenland. We find crevasses within 3 km of the previously mapped downglacier boundary of the firn aquifer at 20 of 25 flightline crossings. Our data suggest that crevasses widen until they reach the downglacier boundary of the firn aquifer, implying that crevasses collect firn-aquifer water, but we did not find this trend with statistical significance. The median crevasse width, 27 meters, implies an aspect ratio consistent with the crevasses reaching the bed. Our results support the idea that most water in Southeast Greenland firn aquifers drains through crevasses. Less common fates are discharge at the ice-sheet surface (3 of 25 sites) and refreezing at the aquifer bottom (1 of 25 sites).

Tasman Glacier, a temperate maritime glacier in the New Zealand Southern Alps, is rapidly receding. Climate warming is resulting in lengthening of the ablation season, meaning crevasses in the accumulation area are becoming exposed at the surface for longer. We combine measurements of air temperature and wind speed from inside crevasses with surface meteorological data, finding that during summer, in-crevasse air temperature is frequently positive, and can at times exceed surface air temperature. Greatest warming occurred in the widest crevasses during clear-sky conditions, but full depth warming of crevasses also occurred at night. Net shortwave radiation contributes to heating of air in the upper regions of crevasses, but turbulent sensible heat transfer was responsible for driving warm air deeper into crevasses. Crevasses orientated to maximise radiation retrieval, and running parallel to wind flow, have the greatest potential for warming and heat storage. We hypothesise a positive feedback loop in the surface energy-balance system, where crevasses entrain and trap heat, which enhances melting, that in turn enlarges the crevasses, enabling greater heat storage and further melting. Energy-balance models that treat accumulation areas of alpine glaciers as homogeneous surfaces will therefore underestimate snow melt and overestimate mass balance.

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.

Glacier surficial melt rates are commonly modelled using surface energy balance (SEB) models, with outputs applied to extend point-based mass-balance measurements to regional scales, assess water resource availability, examine supraglacial hydrology and to investigate the relationship between surface melt and ice dynamics. We present an improved SEB model that addresses the primary limitations of existing models by: (1) deriving high-resolution (30 m) surface albedo from Landsat 8 imagery, (2) calculating shadows cast onto the glacier surface by high-relief topography to model incident shortwave radiation, (3) developing an algorithm to map debris sufficiently thick to insulate the glacier surface and (4) presenting a formulation of the SEB model coupled to a subsurface heat conduction model. We drive the model with 6 years of in situ meteorological data from Kaskawulsh Glacier and Nàłùdäy (Lowell) Glacier in the St. Elias Mountains, Yukon, Canada, and validate outputs against in situ measurements. Modelled seasonal melt agrees with observations within 9% across a range of elevations on both glaciers in years with high-quality in situ observations. We recommend applying the model to investigate the impacts of surface melt for individual glaciers when sufficient input data are available.

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

The Arctic sea-ice cover has undergone a significant decline in recent decades. The melt season is starting earlier, ice is thinner and seasonal ice dominates. Here we examine the effects of these changes on the solar heat input to the upper ocean in ice-covered Arctic waters from 1985 to 2014. Satellite observations of ice concentration, onset dates of melt and freeze-up and ice age, are combined with ice thicknesses from the PIOMAS model and incident solar irradiance from reanalysis products to calculate the contributions of open ocean and ice to the solar heat input in the upper ocean. Of the total, 86% of the area has positive trends for solar heat input to the ocean through leads due to decreases in ice concentration. Only 62% of the area shows positive trends of solar heat input to the ocean explicitly through the ice. Positive trends are due to thinning ice, while negative trends occur in regions where the ice-free season has lengthened. The annual total solar heat input to the ocean exhibits positive trends in 82% of the area. The spatial pattern of the cumulative annual total solar heat input is similar to the pattern of solar heat input directly to leads.

Knowledge of the precipitation contribution to the Antarctic surface mass balance is essential for defining the ice-sheet contribution to sea-level rise. Observations of precipitation are sparse over Antarctica, due to harsh environmental conditions. Precipitation during the summer months (November–December–January) on four expeditions, 2015–16, 2016–17, 2017–18 and 2018–19, in the Terra Nova Bay area, were monitored using a vertically pointing radar, disdrometer, snow gauge, radiosounding and an automatic weather station installed at the Italian Mario Zucchelli Station. The relationship between radar reflectivity and precipitation rate at the site can be estimated using these instruments jointly. The error in calculated precipitation is up to 40%, mostly dependent on reflectivity variability and disdrometer inability to define the real particle fall velocity. Mean derived summer precipitation is ~55 mm water equivalent but with a large variability. During collocated measurements in 2018–19, corrected snow gauge amounts agree with those derived from the relationship, within the estimated errors. European Centre for the Medium-Range Weather Forecasts (ECMWF) and the Antarctic Mesoscale Prediction System (AMPS) analysis and operational outputs are able to forecast the precipitation timing but do not adequately reproduce quantities during the most intense events, with overestimation for ECMWF and underestimation for AMPS.

The retention of meltwater in the accumulation area of the Greenland ice sheet and other Arctic ice masses buffers their contribution to sea level change. However, sustained warming also results in impermeable ice layers or ‘ice slabs’ that seal the underlying pore space. Here, we use a 1-D, physically based, high-resolution model to simulate the surface mass balance (SMB), percolation, refreezing, ice layer formation and runoff from across the high-elevation area of Devon Ice Cap, Canada, from 2001 to 2016. We vary the thickness of the ‘impermeable’ ice layer at which underlying firn becomes inaccessible to meltwater. Thick near-surface ice layers are established by an initial deep percolation, the formation of decimetre ice layers and the infilling of interleaving pore space. The cumulative SMB increases by 48% by varying impermeable layer thickness between 0.01 and 5 m. Within this range we identify narrower range (0.25–1 m) that can simulate both the temporal variability in SMB and the observed near-surface density structure. Across this range, cumulative SMB variation is limited to 6% and 45–49% of mass retention takes place within the annually replenished snowpack. Our results indicate cooler summers after intense mid-2000s warming have led to a partial replenishment of pore space.

Surface mass balance (SMB) is the net input of mass on a glacier's upper surface, composed of snow deposition, melt and erosion processes, and is a major contributor to the overall mass balance. Pine Island Glacier (PIG) in West Antarctica has been dynamically imbalanced since the early 1990s, indicating that discharge of solid ice into the oceans exceeds snow deposition. However, observations of the SMB pattern on the fast flowing regions are scarce, and are potentially affected by the firn's strain history. Here, we present new observations from radar-derived stratigraphy and a relatively dense network of firn cores, collected along a ~900 km traverse of PIG. Between 1986 and 2014, the SMB along the traverse was 0.505 m w.e. a−1 on average with a gradient of higher snow deposition in the South-West compared with the North-East of the catchment. We show that along ~80% of the traverse the strain history amounts to a misestimation of SMB below the nominal uncertainty, but can exceed it by a factor 5 in places, making it a significant correction to the SMB estimate locally. We find that the strain correction changes the basin-wide SMB by ~0.7 Gt a−1 and thus forms a negligible (1%) correction to the glacier's total SMB.

Multiple studies on regional glacier mass balance in the Pamir Mountains have been conducted using the geodetic method, but they were rarely extended to the period before 2000. In this study, we used KH-9 imagery acquired in 1975 to generate the historical DEM for the central Pamir, and then obtained the glacier elevation change by comparing this with the SRTM C-band DEM. The penetration depth of the C-band radar was corrected for different glacier surfaces, i.e. 2.96, 1.68 and 0 m for firn/snow cover, bare ice and debris-covered areas, respectively. The final results suggest that the central Pamir glaciers, overall, experienced a near-zero mass balance of −0.03 ± 0.24 m w.e. a−1 for 1975–99. Due to glacier surge activity, the elevation change patterns of individual glaciers were highly variable, and their mass balances varied from −0.12 ± 0.26 to 0.63 ± 0.20 m w.e. a−1. The mean mass budgets of the surge-type glaciers and non-surge-type glaciers were 0.03 ± 0.14 and −0.05 ± 0.28 m w.e. a−1, respectively. Concurring with previous studies, we conclude that the central Pamir glaciers may have been in a state of approximately balanced mass budget or slight mass deficit from the mid-1970s to the mid-2010s.

We use ice flow modelling to simulate the englacial stratigraphy of Blåskimen Island, an ice rise in Dronning Maud Land and elucidate the evolution of this data-sparse region. We apply a thermo-mechanically coupled Elmer/Ice model to a profile along flowlines and through the ice-rise summit, where surface mass balance (SMB), flow velocity and ice stratigraphy were recently measured. We conclude that: (i) the ice rise is presently thickening at a rate of 0.5~0.6 m ice equivalent per year (mieq a−1), which is twice an earlier estimate using the field data and the input–output method; (ii) present thickening started 20–40 years in the past, before which the ice rise was in a steady state; (iii) SMB contrast between the upwind and downwind slopes was stronger than the present value by ~23% (or 0.15 mieq a−1) prior to ~1100 years ago. Since then, this contrast has been decreasing overall. We surmise that these SMB changes are likely a result of synoptic-scale atmospheric changes, rather than local atmospheric changes controlled by local ice topography. Our technique effectively assimilates geophysical data, avoiding the complexity of ice flow beneath the ice divide. Thus, it could be applied to other ice rises to elucidate the recent glacial retreat.

We simulate the ice dynamics of the San Rafael Glacier (SRG) in the Northern Patagonia Icefield (46.7°S, 73.5°W), using glacier geometry obtained by airborne gravity measurements. The full-Stokes ice flow model (Elmer/Ice) is initialized using an inverse method to infer the basal friction coefficient from a satellite-derived surface velocity mosaic. The high surface velocities (7.6 km a−1) near the glacier front are explained by low basal shear stresses (<25 kPa). The modelling results suggest that 98% of the surface velocities are due to basal sliding in the fast-flowing glacier tongue (>1 km a−1). We force the model using different surface mass-balance scenarios taken or adapted from previous studies and geodetic elevation changes between 2000 and 2012. Our results suggest that previous estimates of average surface mass balance over the entire glacier (Ḃ) were likely too high, mainly due to an overestimation in the accumulation area. We propose that most of SRG imbalance is due to the large ice discharge (−0.83 ± 0.08 Gt a−1) and a slightly positive Ḃ (0.08 ± 0.06 Gt a−1). The committed mass-loss estimate over the next century is −0.34 ± 0.03 Gt a−1. This study demonstrates that surface mass-balance estimates and glacier wastage projections can be improved using a physically based ice flow model.

The climatic condition that prevails at a glacier equilibrium line altitude (ELA) is often parameterized in terms of summer air temperature (T) and annual precipitation (P). This simple parameterization was initially proposed by Hans W:son Ahlmann. The physical background of the relationship between P and T on the equilibrium line, however, has been left unexplained since Ahlmann first questioned the mathematical form of the relationship. This relationship can be explained when the thermal and hydrological processes of the ELA formation are investigated. The present authors studied the energy exchange processes that prevail on the ELA during the melt season. The inclusion of solar radiation brings Ahlmann's hypothesis closer to energy balance, and improves his P/T diagram. By comparing the observed fluxes from the polar through the mid-latitude to the equatorial glaciers, it was found that these glaciers in different climatic regions share important similarities at the ELA. Further, it was found that the classic P/T curve originally proposed by Ahlmann in the early 20th century is a concise expression of the conservation principle of energy and mass at the ELA of glaciers, and takes the form of a polynomial of the fourth order.

West Antarctic climate and surface mass balance (SMB) records are sparse. To fill this gap, regional atmospheric climate modelling is useful, providing that such models are employed at sufficiently high horizontal resolution and coupled with a snow model. Here we present the results of a high-resolution (5.5 km) regional atmospheric climate model (RACMO2) simulation of coastal West Antarctica for the period 1979–2015. We evaluate the results with available in situ weather observations, remote-sensing estimates of surface melt, and SMB estimates derived from radar and firn cores. Moreover, results are compared with those from a lower-resolution version, to assess the added value of the resolution. The high-resolution model resolves small-scale climate variability invoked by topography, such as the relatively warm conditions over ice-shelf grounding zones, and local wind speed accelerations. Surface melt and SMB are well reproduced by RACMO2. This dataset will prove useful for picking ice core locations, converting elevation changes to mass changes, for driving ocean, ice-sheet and coupled models, and for attributing changes in the West Antarctic Ice Sheet and shelves to changes in atmospheric forcing.

This sensitivity study applies the offline Canadian Land Surface Scheme (CLASS) version 3.6 to simulate snowpack evolution in idealized topography using observations at Likely, British Columbia, Canada over 1 July 2008 to 30 June 2009. A strategy for a subgrid-scale snow (SSS) parameterization is developed to incorporate two key features: ten elevation bands at 100 m intervals to capture air temperature lapse rates, and five slope angles on four aspects to resolve solar radiation impacts on the evolution of snow depth and SWE. Simulations reveal strong elevational dependencies of snow depth and SWE when adjusting temperatures using a moist adiabatic lapse rate with elevation, with 26% peak SWE differences between that at the average elevation versus the mean of the remainder of the elevation bands. Differences in peak SWE on north- and south-facing slopes increase from 3.0 mm at 10° slope to 17.9 mm at 50° slope. When applied to elevation, slope and aspect combinations derived from a high-resolution digital elevation model, elevation dominates the control of peak SWE values. Inclusion of the range of SSS effects into a regional climate model will improve snowpack and hydrological simulations of western North America's snow-dominated, mountainous watersheds.

We study the response of firn to a stepwise surface temperature change, using a firn model that includes meltwater hydrology and is driven by an idealized surface climate. We find that adjustment of dry firn (i.e. without surface melt) to surface warming takes longer than a subsequent cooling to the original, colder climate, mainly because firn compacts faster at higher firn temperatures. In contrast, wet firn adjusts faster to a surface warming than to a cooling. Increased meltwater percolation enhances the downward transport of latent heat, whereas there is no such mechanism that can enhance the downward transport of a cooling signal. Thus, wastage of firn after surface warming is faster than its regeneration if the warming were reversed. Furthermore, the response of wet firn to temperature change exhibits a complex relation between accumulation rate and the steady-state deep-firn temperature. For high accumulation rates, the deep-firn temperature is higher because latent heat release upon refreezing is isolated by winter snow. As a result, the response of wet firn to a temperature change varies strongly with accumulation rate. In general, the magnitude and the rate of density change is larger in wet firn than in dry firn.

Combinations of various numerical models and datasets with diverse observation characteristics have been used to assess the mass evolution of ice sheets. As a consequence, a wide range of estimates have been produced using markedly different methodologies, data, approximation methods and model assumptions. Current attempts to reconcile these estimates using simple combination methods are unsatisfactory, as common sources of errors across different methodologies may not be accurately quantified (e.g. systematic biases in models). Here we provide a general approach which deals with this issue by considering all data sources simultaneously, and, crucially, by reducing the dependence on numerical models. The methodology is based on exploiting the different space–time characteristics of the relevant ice-sheet processes, and using statistical smoothing methods to establish the causes of the observed change. In omitting direct dependence on numerical models, the methodology provides a novel means for assessing glacio-isostatic adjustment and climate models alike, using remote-sensing datasets. This is particularly advantageous in Antarctica, where in situ measurements are difficult to obtain. We illustrate the methodology by using it to infer Antarctica’s mass trend from 2003 to 2009 and produce surface mass-balance anomaly estimates to validate the RACMO2.1 regional climate model.