A supraglacial debris layer controls energy transfer to the ice surface and moderates ice ablation on debris-covered glaciers. Measurements of vertical temperature profiles within the debris enables the estimation of thermal diffusivities and sub-debris ablation rates. We have measured the debris-layer temperature profiles at 16 locations on Satopanth Glacier (central Himalaya) during the ablation seasons of 2016 and 2017. Debris temperature profile data are typically analysed using a finite-difference method, assuming that the debris layer is a homogeneous one-dimensional thermal conductor. We introduce three more methods for analysing such data that approximate the debris layer as either a single or a two-layered conductor. We analyse the performance of all four methods using synthetic experiments and by comparing the estimated ablation rates with in situ glaciological observations. Our analysis shows that the temperature measurements obtained at equispaced sensors and analysed with a two-layered model improve the accuracy of the estimated thermal diffusivity and sub-debris ablation rate. The accuracy of the ablation rate estimates is comparable to that of the in situ observations. We argue that measuring the temperature profile is a convenient and reliable method to estimate seasonal to sub-seasonal variations of ablation rates in the thickly debris-covered parts of glaciers.

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.

The retreat rates of Triangular Glacier since 1979 and its mass changes during the period 2014/15–2019/20 indicate the sensitive response of small ice masses on the eastern side of the Antarctic Peninsula to air temperature evolution. This cirque glacier in the northern part of James Ross Island receded rapidly during the period of regional warming in the late 20th century, losing 30.8% of its surface area between 1979 and 2006 (−1.7% a−1). The retreat rate then dropped to −0.3% a−1 following the regional cooling trend, but started to accelerate again (−0.8 to −2.3% a−1) with increasing air temperature since the summer 2014/15. Since the glaciological year 2015/16, Triangular Glacier has experienced enhanced snow melt, wind scour and permanent mass loss with annual mass balance ranging from −0.08 ± 0.35 to −0.56 ± 0.25 m w.e. The largest mass loss was observed in the glaciological year 2019/20, which included the warmest summer of the observation period. The cumulative mass balance of −1.66 ± 0.83 m w.e. over the years 2014/15–2019/20 is consistent with the termination of the positive mass-balance period that occurred in the north-eastern Antarctic Peninsula from 2009/10 to 2014/15.

We present geodetic mass-balance estimates for ten glaciers (22.6 ± 1.1 km2) around Volcán Domuyo between 1962 and 2020 (and 46 glaciers covering 29 ± 1.5 km2 between 1984 and 2020), derived from airborne, ASTER and Pléiades imagery. Overall, we find a slightly negative mass balance (−0.15 ± 0.09 m w.e. a–1) for the entire 1962–2020 time span. A closer inspection of sub-periods reveals, however, an increasingly negative mass balance with time. The Domuyo glaciers shifted from a moderately positive mass balance of +0.28 ± 0.13 m w.e. a–1 between 1962 and 1984, to a strongly negative mass balance of −0.99 ± 0.19 m w.e. a–1 between 2012 and 2020. An increase in summer temperatures and a decrease in winter precipitation during the last four decades are likely drivers of the observed glacier changes. We support this finding by implementing a minimal glacier model, relying solely on monthly precipitation and air temperatures. The mass-balance evolution detected in Volcán Domuyo is consistent with other sites spread across the Central Andes, suggesting rapidly increasing glacier wastage impacts are occurring at a geographically wider scale.

Arctic ice shelves have declined over the past several decades, one of many indications of a rapidly changing cryosphere. Here we use a collection of off-nadir Landsat 8 images, a 1978 digital orthophotograph and photogrammetrically derived DEM, satellite altimetry and other data to examine the causes of an Arctic ice-shelf retreat in northernmost Greenland, the Hunt Fjord Ice Shelf (HFIS). HFIS has several distinct provenance regions comprised of glacier-derived ice and corrugated multi-decadal fast ice, with varying ice thicknesses (5–64 m). Available imagery shows little change in HFIS between 1978 and 2012, after which several midsummer calving events occurred (2012, 2016 and 2019) that reduced the HFIS by 42.5 km2 (~56%). Shelf area losses began as the number of surface melt days on the adjacent ice sheet more than doubled relative to the 1980s. Recent calving events also occurred during open-water periods at the ice-shelf front. Prior to mid-2012, there were no calving events during similar open-water periods. HFIS tributary glaciers have thinned by 3–20 m near their grounding zones, and may have accelerated since the 1980s, likely due to increased basal melting from contact with warm Atlantic Water.

Glacier motion responds dynamically to changing meltwater inputs, but the multi-decadal response of basal sliding to climate remains poorly constrained due to its sensitivity across multiple timescales. Observational records of glacier motion provide critical benchmarks to decode processes influencing glacier dynamics, but multi-decadal records that precede satellite observation and modern warming are rare. Here we present a record of motion in the ablation zone of Saskatchewan Glacier that spans seven decades. We combine in situ and remote-sensing observations to inform a first-order glacier flow model used to estimate the relative contributions of sliding and internal deformation on dynamics. We find a significant increase in basal sliding rates between melt-seasons in the 1950s and those in the 1990s and 2010s and explore three process-based explanations for this anomalous behavior: (i) the glacier surface steepened over seven decades, maintaining flow-driving stresses despite sustained thinning; (ii) the formation of a proglacial lake after 1955 may support elevated basal water pressures; and (iii) subglacial topography may cause dynamic responses specific to Saskatchewan Glacier. Although further constraints are necessary to ascertain which processes are of greatest importance for Saskatchewan Glacier's dynamic evolution, this record provides a benchmark for studies of multi-decadal glacier dynamics.

We present spatially distributed seasonal and annual surface mass balances of Wolverine Glacier, Alaska, from 2016 to 2020. Our approach accounts for the effects of ice emergence and firn compaction on surface elevation changes to resolve the spatial patterns in mass balance at 10 m scale. We present and compare three methods for estimating emergence velocities. Firn compaction was constrained by optimizing a firn model to fit three firn cores. Distributed mass balances showed good agreement with mass-balance stakes (RMSE = 0.67 m w.e., r = 0.99, n = 41) and ground-penetrating radar surveys (RMSE = 0.36 m w.e., r = 0.85, n = 9024). Fundamental differences in the distributions of seasonal balances highlight the importance of disparate physical processes, with anomalously high ablation rates observed in icefalls. Winter balances were found to be positively skewed when controlling for elevation, while summer and annual balances were negatively skewed. We show that only a small percent of the glacier surface represents ideal locations for mass-balance stake placement. Importantly, no suitable areas are found near the terminus or in elevation bands dominated by icefalls. These findings offer explanations for the often-needed geodetic calibrations of glaciological time series.

Glacial ripping involves glaciotectonic disintegration of rock hills and extensive removal of rock at the ice-sheet bed, triggered by hydraulic jacking caused by fluctuating water pressures. Evidence from eastern Sweden shows that glacial ripping caused significant subglacial erosion during the final deglaciation of the Fennoscandian ice sheet, distinct from abrasion and plucking (quarrying). Here we analyse the ice drag forces exerted onto rock obstacles at the base of an ice sheet, and the resisting forces of such rock obstacles: glaciotectonic disintegration requires that ice drag forces exceed the resisting forces of the rock obstacle. We consider rock obstacles of different sizes, shapes and fracture patterns, informed by natural examples from eastern Sweden. Our analysis shows that limited overpressure events, unfavourable fracture patterns, low-transmissivity fractures, slow ice and streamlined rock hamper rock hill disintegration. Conversely, under fast ice flow and fluctuating water pressures, disintegration is possible if the rock hill contains subhorizontal, transmissive fractures. Rock steps on previously smooth, abraded surfaces, caused by hydraulic jacking, also enhance drag forces and can cause disintegration of a rock hill. Glacial ripping is a physically plausible erosion mechanism, under realistic glaciological conditions prevalent near ice margins.

Regional assessments of ice elevation change provide insight into the processes controlling an ice sheet's geometric response to climate forcing. In Southwest Greenland's land terminating sector (SWLTS), it is presumed that ice surface elevation changes result solely from changing surface mass balance (SMB). Here we test this assumption by developing a multi-decadal (1985–2017) record of elevation change from digital elevation models (DEMs) and comparing it to regional climate model output and available records of ice speed. The SWLTS thinned by >12 m on average over the full 32-year period, but the change was highly variable in time and space. Thinning was amplified in the central region of the SWLTS, relative to the north and south. During 1985–2007, the north and south regions demonstrated net thickening while the central region thinned. Regional differences in elevation change are inconsistent with SMB anomalies, indicating that enhanced ice flow in the north and south contributed to thickening during this early time interval. While clear validation in the south is prevented by incomplete velocity data, historical surface speeds in the north were elevated. These findings support the interpretation that changing ice flow can influence ice surface elevation in the slow-moving SWLTS.

Remotely sensed land surface temperature (LST) data, such as the Moderate Resolution Imaging Spectroradiometer (MODIS) LST thermal infrared products, are useful for monitoring surface processes on the Greenland Ice Sheet in remote areas but must be validated to ensure accuracy. Using data from the Programme for Monitoring the Greenland Ice Sheet (PROMICE), we conducted a MODIS LST validation (MOD/MYD11 C6 swath level product) using radiometric in-situ skin temperature records from 2014 to 2017 over 17 PROMICE sites mostly in the ice sheet's ablation zone. There is a significant cold bias in MODIS LST when compared to PROMICE skin temperature, particularly when PROMICE records temperatures below 0°C (mean bias: 2.4 ± 0.01°C mean ± standard error, RMSE = 3.2°C). Multiple linear regression analysis reveals the difference between MODIS LST and PROMICE skin temperature is larger at lower temperatures, lower latent heat fluxes and higher specific humidity. Our results confirm the presence of a progressive cold bias in the MODIS LST that should be considered in use of this product, and we identify and corroborate areas for ongoing algorithm development.

We assess the evolution of glaciological structures during the 2003–05 surge in the Paulabreen glacier system, Svalbard. Glaciological structures on the glacier surface were mapped using aerial photographs captured in the early stages of the surge (2003) and 5 years after surge termination (2011). Three-dimensional measurements of glaciological structures were collected at the tidewater front in 2013. These datasets document the physical changes during (1) the late quiescent phase; (2) the early phase of the surge as the surge front propagated down Skobreen and advanced into Paulabreen and (3) the final stages of the surge following the surge front reaching the glacier terminus. Crevasse patterns and clusters of arcuate shear planes record zones of compressive and extensional flow associated with the downglacier progression of the surge front. The transfer of surging ice from Skobreen into Paulabreen caused lateral displacement of the medial moraines to the northeast. At the ice front, this movement tilted glaciological structures in the same direction. Structures at the southwest margin record strike–slip faulting and the elevation of debris into the ice in a zone of compression and transpression. We summarise these observations in a schematic reconstruction of structural evolution during the surge.

Global glacier mass balance decreased rapidly over the last two decades, exceeding mass loss from the Greenland and Antarctic Ice Sheets. In Greenland, peripheral glaciers and ice caps (GICs) cover only ~5% of Greenland's area but contributed ~20% of the island's ice mass loss between 2000 and 2018. Although Greenland GIC mass loss due to surface meltwater runoff has been estimated using atmospheric models, mass lost to changes in ice discharge into oceans (i.e., dynamic mass loss) remains unquantified. We use the flux gate method to estimate discharge from Greenland's 585 marine-terminating peripheral glaciers between 1985 and 2018, and compute dynamic mass loss as the discharge anomaly relative to the 1985–98 period. Greenland GICs discharged between 2.94 ± 0.23 and 4.03 ± 0.23 Gt a−1 from 1985 to 1998, depending on the gap-filling method, and abruptly increased to 5.10 ± 0.21 Gt a−1 from 1999 to 2018. The resultant ~1–2 Gt a−1 dynamic mass loss was driven by synchronous widespread acceleration around Greenland. The mass loss came predominantly from the southeast region, which contains 39% of the glaciers. Although changes in discharge over time were small relative to surface mass-balance changes, our speed and discharge time series suggest these glaciers may quickly accelerate in response to changes in climate.

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.

Establishing an accurate chronology is crucial for interpretation of ice core-based climatic records. While high snow accumulation rates characterise coastal Antarctica, thus enabling recovery of highly resolved climatic records, summertime melting at such low-elevation sites offers challenges in establishing a reliable chronological framework through traditional approaches using the seasonality of stable water isotope and ionic proxy records. Here, we assess visual stratigraphy (VS) obtained from line-scan images as a proxy for annual layer counting in firn section (top 50 m) of the IND-36/B9 ice core (dated 1919–2016 CE) from the Djupranen Ice Rise in central Dronning Maud Land, East Antarctica. We also used these images to obtain melt history for the site and found that traditional thickness-based quantification of melt proportion results in significant overestimations. Since density has dominant control on VS profile over the firn section, we first used circulant single-spectrum analysis to remove the secular trend and then we extracted the seasonal VS signals attributed to dust and sea-salt inclusions. We find that melt layers do not significantly alter the VS records if masked during pre-processing. The age–depth model based on the reconstructed VS profile revealed an excellent match with identified time-markers within an uncertainty of ±2 years.

The marginal areas of the Greenland ice sheet develop streams and lakes each summer, documenting that surface runoff of meltwater is a major component of ice-sheet mass balance. Here we map the slush limit, a proxy for the extent of surface runoff, using daily MODIS data for the years 2000–2021. We develop an automated algorithm capable of detecting daily slush limits, provided sufficient image quality. The algorithm is applied to the ice sheet's western flank (61.7 $^{\circ }$N to 76.5 $^{\circ }$N). We find significant increasing trends in maximum slush limits until the year 2012, but not thereafter. We show that the slush limit typically rises quickly early in the ablation season but stabilizes before melting ceases. The data provide evidence that upward migration of surface runoff in summer 2012 stopped early at the upper margin of the ice slabs. These thick and continuous ice layers are located close to the surface, in the firn, and impede percolation of melt into deeper pore space. Had the ice slabs extended higher, the summer 2012 provided sufficient energy to raise the slush limit by another $\sim$300 m in elevation.

A recent study (Millan and others, 2022a, Nature Geoscience 15(2), 124–129) claims that ice volume contained in all glaciers outside the ice sheets and its potential contribution to sea level is 20% less than previously estimated. However, the apparent decrease is largely due to differences in choice of domain, as the study excludes 80% of the glacier area in the Antarctic periphery that was included in previous global glacier volume estimates. The issue highlights the difficulty in separating glaciers from the ice-sheet proper, especially in Antarctica, and the need for both the glacier and ice-sheet communities to develop standards and protocols to avoid double-counting in global ice volume and mass-change assessments and projections. Process-based inversion models have replaced earlier scaling methods, but large uncertainties in global glacier volume estimation remain due to the ill-posed nature of the inversion problem and poorly constrained parameters emphasizing the need for more direct ice thickness observations.

The shallow ice approximation for glaciers and ice sheets is a degenerate model in which the ice surface slope at the margin may be infinite. This result is due to the neglect of the otherwise small longitudinal stress terms. Here we derive a corrected approximation for the basal shear stress, and show that the resulting model provides an explanation for the observed finite slope margins.