Mass-balance measurements of Icelandic glaciers are sparse through the 20th century. However, the large archive of stereo images available allows estimates of glacier-wide mass balance ($\dot{B}$) in decadal time steps since 1945. Combined with climate records, they provide further insight into glacier–climate relationship. This study presents a workflow to process aerial photographs (1945–1995), spy satellite imagery (1977–1980) and modern satellite stereo images (since 2000) using photogrammetric techniques and robust statistics in a highly automated, open-source pipeline to retrieve seasonally corrected, decadal glacier-wide geodetic mass balances. In our test area, Eyjafjallajökull (S-Iceland, ~70 km2), we obtain a mass balance of $<![CDATA[ $ \dot{\curr B}_{\curr 1945}^{\curr 2014} \curr = -0.27 \pm 0.03\,{\rm \curr m\ w}{\rm. \curr e}{\rm.} {\rm \curr a}^{{\rm \ndash \curr 1}}$, with a maximum and minimum of $\dot{\curr B}_{\curr 1984}^{\curr 1989} \curr = 0.77 \curr \pm 0.19\,{\rm \curr m\ \curr w}{\rm\curr . e}{\rm\curr .} {\rm\curr a}^{{\rm\curr \ndash 1}}$ and $\dot{\curr B}_{\curr 1994}^{\curr 1998}\curr = -1.94 \curr \pm 0.34\,{\rm \curr m\ w}{\rm\curr . e}{\rm\curr .} {\rm \curr a}^{{\rm\curr \ndash 1}}$, respectively, attributed to climatic forcing, and $\dot{\curr B}_{\curr 2009}^{\curr 2010} \curr = -3.39{\rm \;} \curr \pm {\rm \;} \curr 0.43\,{\rm \curr m\ w}{\rm\curr . e}{\rm\curr .} {\rm\curr a}^{{\rm\curr \ndash 1}}$, mostly caused by the April 2010 eruption. The reference-surface mass balances correlate with summer temperature and winter precipitation, and linear regression accounts for 80% of the mass-balance variability, yielding a static sensitivity of mass balance to summer temperature and winter precipitation of − 2.1 ± 0.4 m w.e.a–1K–1 and 0.5 ± 0.3 m w.e.a–1 (10%)–1, respectively. This study serves as a template that can be used to estimate the mass-balance changes and glaciers' response to climate.

Mountain glaciers and ice sheets often host marginal and subglacial lakes that are hydraulically connected through subglacial drainage systems. These lakes exhibit complex dynamics that have been the subject of models for decades. Here we introduce and analyze a model for the evolution of glacial lakes connected by subglacial channels. Subglacial channel equations are supplied with effective pressure boundary conditions that are determined by a simple lake model. While the model can describe an arbitrary number of lakes, we solve it numerically with a finite element method for the case of two connected lakes. We examine the effect of relative lake size and spacing on the oscillations. Complex oscillations in the downstream lake are driven by discharge out of the upstream lake. These include multi-peaked and anti-phase filling–draining events. Similar filling–draining cycles have been observed on the Kennicott Glacier in Alaska and at the confluence of the Whillans and Mercer ice streams in West Antarctica. We further construct a simplified ordinary differential equation model that displays the same qualitative behavior as the full, spatially-dependent model. We analyze this model using dynamical systems theory to explain the appearance of filling–draining cycles as the meltwater supply varies.

Experimental data from creep tests on polycrystalline ice samples highlight not only the non-Newtonian behavior of ice but also suggest a critical dependence of the various rheological parameters upon the applied hydrostatic pressure. We propose a new modeling framework, based on implicit theories of continuum mechanics, that generalizes two well-known constitutive models by taking into account the effect of the pressure in the description of ice in creep. To ascertain the validity of the proposed models, we fit the physical parameters with experimental data for the elongational flow of ice samples. The results show good agreement with the experimental creep curves. In particular, the proposed generalized models reproduce the increase of the creep rate due to the presence of hydrostatic pressure.

Jakobshavn Isbræ, a tidewater glacier that produces some of Greenland's largest icebergs and highest speeds, reached record-high flow rates in 2012 (Joughin and others, 2014). We use terrestrial radar interferometric observations from August 2012 to characterize the events that led to record-high flow. We find that the highest speeds occurred in response to a small calving retreat, while several larger calving events produced negligible changes in glacier speed. This non-linear response to calving events suggests the terminus was close to flotation and therefore highly sensitive to terminus position. Our observations indicate that a glacier's response to calving is a consequence of two competing feedbacks: (1) an increase in strain rates that leads to dynamic thinning and faster flow, thereby promoting destabilization, and (2) an increase in flow rates that advects thick ice toward the terminus and promotes restabilization. The competition between these feedbacks depends on temporal and spatial variations in the glacier's proximity to flotation. This study highlights the importance of dynamic thinning and advective processes on tidewater glacier stability, and further suggests the latter may be limiting the current retreat due to the thick ice that occupies Jakobshavn Isbræ’s retrograde bed.

Donjek Glacier has an unusually short and regular surge cycle, with eight surges identified since 1935 from aerial photographs and satellite imagery with a ~12 year repeat interval and ~2 year active phase. Recent surges occurred during a period of long-term negative mass balance and cumulative terminus retreat of 2.5 km since 1874. In contrast to previous work, we find that the constriction where the valley narrows and bedrock lithology changes, 21 km from the terminus, represents the upper limit of surging, with negligible surface speed or elevation change up-glacier from this location. This positions the entire surge-type portion of the glacier in the ablation zone. The constriction geometry does not act as the dynamic balance line, which we consistently find at 8 km from the glacier terminus. During the 2012–2014 surge event, the average lowering rate in the lowest 21 km of the glacier was 9.6 m a−1, while during quiescence it was 1.0 m a−1. Due to reservoir zone refilling, the ablation zone has a positive geodetic balance in years immediately following a surge event. An active surge phase can result in a strongly negative geodetic mass balance over the surge-type portion of the glacier.

Spectral reflectance of natural snow samples representing various stratigraphies was investigated in a controlled dark laboratory environment. Mean and Std dev. of band specific reflectance values were determined for several satellite sensor bands utilized in remote sensing of snow. The reflectance values for dry, moist, wet and wet and littered snow for different instruments varied between 0.63–0.97 in the visible and near-infrared bands at an incoming light zenith angle of θ = 55°. The results indicate that in MODIS band 4 (545–565 nm), essential to snow mapping, the reflectance of snow drops by 9% when dry snow changes to wet snow and by a further 10% when typical forest litter inclusions exist on the wet snow surface. A separate investigation of individual snow types revealed that they can be grouped either as dry or wet snow based on their spectral behavior. However, some snow types were located between these two distinct groups, such as snow with near-surface melt-freeze crusts, and could not be clearly distinguished. The reflectance statistics collected and analyzed here can be directly used to refine accuracy characterization and parametrization of snow mapping algorithms, such as the SCAmod method, used for the mapping of snow cover area.

Snow properties relevant to the fracture processes involved in dry-snow slab avalanche release include weak layer specific fracture energy, slab elastic modulus and density. Various techniques exist to determine these snow mechanical properties, but it is presently unclear how values determined with different methods compare. In the laboratory, the 3-D microstructure of cm-sized snow samples is reconstructed by micro-computed tomography (μCT) so that density and elastic modulus can be computed. In the field, fracture energy and modulus are estimated based on particle tracking velocimetry (PTV) of the displacement field observed during propagation saw tests. Snow stratigraphy is measured with the snow micro-penetrometer (SMP) in either, field or laboratory. We compared SMP-derived properties to corresponding μCT- and PTV-derived values. Values of snow density related well to μCT results and so were SMP-derived elastic moduli related to PTV-derived values. By taking into account snow anisotropy a good relation between SMP- and μCT-derived moduli resulted suggesting the SMP-derived modulus characterizes the components of the modulus perpendicular to the axis of penetration. SMP- and PTV-derived values of fracture energy were correlated. The SMP can provide a bridge between scales and techniques, yet further improvements in signal interpretation are still needed.

The long-term warming on the Antarctic Peninsula in the second half of the 20th century prompted rapid retreat of glaciers on the peninsula and surrounding islands. Retreat accelerated until the beginning of the new millennium when the regional warming trend significantly decreased. The response of glaciers to the change in temperature trend has been observed around the northern part of the Antarctic Peninsula but the timing of the shift from the surface lowering to mass gain remains unclear. Using historical aerial photographs, DEMs and satellite altimeter data from ICESat, we estimate areal and surface elevation changes of two small ice caps in the northern part of James Ross Island over the last 39 years. The glacierized area on Lachman Crags decreased from 4.337 ± 0.037 to 3.581 ± 0.014 km2 (−17.4%) between 1979 and 2006 and then increased to 3.597 ± 0.047 km2 (0.4%) until 2016. Surface lowering observed on ice caps after 1979 continued at least until 2008 as indicated by the ICESat data. The change from the lowering trend to increase in glacier surface elevation probably occurred after the ablation season 2008/09, which ranks among the warmest summers in the north-eastern Antarctic Peninsula since the mid-20th century.

We use the full-Stokes model Elmer/Ice to investigate the present dynamics of Bowdoin Glacier, a marine-terminating outlet glacier in northwestern Greenland. Short-term speed variations of the glacier were observed, correlating with air temperature and precipitation, and with the semi-diurnal ocean tides. We use a control inverse method to determine the distribution of basal friction. This reveals that most of the glacier area is characterized by near-plug-flow conditions, while some sticky spots are also identified. We then conduct experiments to test the sensitivity of the glacier flow to basal lubrication and tidal forcing at the calving front. Reduction of the basal drag by 10–40% produces speed-ups that agree approximately with the observed range of speed-ups that result from warm weather and precipitation events. In agreement with the observations, tidal forcing and surface speed near the calving front are found to be in anti-phase (high tide corresponds to low speed, and vice versa). However, the amplitude of the semi-diurnal variability is underpredicted by a factor ~ 3, which is likely related to either inaccuracies in the surface and bedrock topographies or mechanical weakening due to crevassing.

Glaciological ablation is computed from point-scale data at a few ablation stakes that are usually regressed as a function of elevation and averaged over the area-elevation distribution of a glacier. This method is contingent on a tight control of elevation on local ablation. However, in debris-covered glaciers, systematic and random spatial variations of debris thickness modify the ablation rates. We propose and test a method to compute sub-debris ablation where stake data are interpolated as a function of debris-thickness alone and averaged over the debris-thickness distribution at different parts of the glacier. We apply this method on Satopanth Glacier located in Central Himalaya utilising ~1000 ablation measurements obtained from a network of up to 56 stakes during 2015–2017. The estimated mean sub-debris ablation ranges between 1.5±0.2 to 1.7±0.3 cm d−1. We show that the debris-thickness-dependent regression describes the spatial variability of the sub-debris ablation better than the elevation dependent regression. The uncertainties in ablation estimates due to the corresponding uncertainties in the measurement of ablation and debris-thickness distribution, and those due to interpolation procedures are estimated using Monte Carlo methods. Possible biases due to a finite number of stakes used are also investigated.

Light-absorbing impurities (LAIs, e.g. black carbon (BC), organic carbon (OC), mineral dust (MD)) deposited on snow cover reduce albedo and accelerate its melting. Northern Xinjiang (NX) is an arid and semi-arid inland region, where snowmelt leads to frequent floods that have been a serious threat to local ecological security. There is still a lack of quantitative assessments of the effects of LAIs on snowmelt in the region. This study investigates spatial variations of LAIs in snow and its effect on snow albedo, radiative forcing (RF) and snowmelt across NX. Results showed that concentrations of BC, OC (only water-insoluble OC), MD ranged from 32 to 8841 ng g−1, 77 to 8568 ng g−1 and 0.46 to 236 µg g−1, respectively. Weather Research and Forecasting Chemistry model suggested that residential emission was the largest source of BC. Snow, Ice, and Aerosol Radiative modelling showed that the average contribution of BC and MD to snow albedo reduction was 17 and 3%, respectively. RF caused by BC significantly exceeded RF caused by MD. In different scenarios, changes in snow cover duration (SCD) caused by BC and MD decreased by 1.36 ± 0.61 to 6.12 ± 3.38 d. Compared with MD, BC was the main dominant factor in reducing snow albedo and SCD across NX.

Measurements of short-interval variations in glacier surface velocity, which contribute to our understanding of ice motion mechanisms, remain scarce on the Tibetan Plateau. Here we present sub-hourly measurements of glacier surface motion variations at the terminus region of Laohugou No. 12 Glacier. Field observations were collected over 4 d in July 2015 from terrestrial radar interferometry. The observed glacier displacement time series are generally in agreement with the results measured by differential GPS and highlight that glacier surface velocity is characterized by clear diurnal fluctuations in the study period. During day-time hours, glacier flow speeds were higher than 3.0 mm h−1, whereas they were below 1.0 mm h−1 during night-time hours. The large diurnal fluctuations of glacier surface velocity indicate that variations in basal slip are the dominant motion mechanism. Moreover, a positive correlation (R = 0.82, P < 0.001) between air temperature and glacier surface velocity suggests that glacier motion variations are probably affected by changes in air temperature during the ablation season.

Climate variability can complicate efforts to interpret any long-term glacier mass-balance trends due to anthropogenic warming. Here we examine the impact of climate variability on the seasonal mass-balance records of 14 glaciers throughout Norway, Sweden and Svalbard using dynamical adjustment, a statistical method that removes orthogonal patterns of variability shared between each mass-balance record and sea-level pressure or sea-surface temperature predictor fields. For each glacier, the two leading predictor patterns explain 27–81% of the winter mass-balance variability and 24–69% of the summer mass-balance variability. The spatial and temporal structure of these patterns indicates that accumulation variability for all of the glaciers is strongly related to the North Atlantic Oscillation (NAO), with the Atlantic Multidecadal Oscillation (AMO) also modulating accumulation variability for the northernmost glaciers. Given this result, predicting glacier change in the region may depend on NAO and AMO predictability. In the raw mass-balance records, the glaciers throughout southern Norway have significantly negative summer trends, whereas the glaciers located closer to the Arctic have negative winter trends. Removing the effects of climate variability suggests it can bias trends in mass-balance records that span a few decades, but its effects on most of the longer-term mass-balance trends are minimal.

To obtain information on changes in glacier mass balance in the central Nyainqentanglha Range, a comprehensive study was carried out based on digital-elevation models derived from the 1968 topographic maps, the Shuttle Radar Topography Mission DEM (2000) and TerraSAR-X/TanDEM-X (2013). Glacier area changes between 1968 and 2016 were derived from topographic maps and Landsat OLI images. This showed the area contained 715 glaciers, with an area of 1713.42 ± 51.82 km2, in 2016. Ice cover has been shrinking by 0.68 ± 0.05% a−1 since 1968. The glacier area covered by debris accounted for 11.9% of the total and decreased in the SE–NW directions. Using digital elevation model differencing and differential synthetic aperture radar interferometry, a significant mass loss of 0.46 ± 0.10 m w.e. a−1 has been recorded since 1968; mass losses accelerated from 0.42 ± 0.20 m w.e. a−1 to 0.60 ± 0.20 m w.e. a−1 between 1968–2000 and 2000–2013, with thinning noticeably greater on the debris-covered ice than the clean ice. Surface-elevation changes can be influenced by ice cliffs, as well as debris cover and land- or lake-terminating glaciers. Changes showed spatial and temporal heterogeneity and a substantial correlation with climate warming and decreased precipitation.

Basal ice of glaciers and ice sheets frequently contains a well-developed stratification of distinct, semi-continuous, alternating layers of debris-poor and debris-rich ice. Here, the nature and distribution of shear within stratified basal ice are assessed through the anisotropy of magnetic susceptibility (AMS) of samples collected from Matanuska Glacier, Alaska. Generally, the AMS reveals consistent moderate-to-strong fabrics reflecting simple shear in the direction of ice flow; however, AMS is also dependent upon debris content and morphology. While sample anisotropy is statistically similar throughout the sampled section, debris-rich basal ice composed of semi-continuous mm-scale layers (the stratified facies) possesses well-defined triaxial to oblate fabrics reflecting shear in the direction of ice flow, whereas debris-poor ice containing mm-scale star-shaped silt aggregates (the suspended facies) possesses nearly isotropic fabrics. Thus, deformation within the stratified basal ice appears concentrated in debris-rich layers, likely the result of decreased crystal size and greater availability of unfrozen water associated with high debris content. These results suggest that variations in debris-content over small spatial scales influence ice rheology and deformation in the basal zone.

The long-accepted theory to explain why snow is slippery postulates self-lubrication: frictional heat from sliding melts and thereby lubricates the contacting snow grains. We recently published micro-scale interface observations that contradicted this explanation: contacting snow grains abraded and did not melt under a polyethylene slider, despite low friction values. Here we provide additional observational and theoretical evidence that abrasion can govern snow kinetic friction. We obtained coordinated infrared, visible-light and scanning-electron micrographs that confirm that the evolving shapes observed during our tribometer tests are contacting snow grains polished by abrasion, and that the wear particles can sinter together and fill the adjacent pore spaces. Furthermore, dry-contact abrasive wear reasonably predicts the evolution of snow-slider contact area, and sliding-heat-source theory confirms that contact temperatures would not reach 0°C during our tribometer tests. Importantly, published measurements of interface temperatures also indicate that melting did not occur during field tests on sleds and skis. Although prevailing theory anticipates a transition from dry to lubricated contact along a slider, we suggest that dry-contact abrasion and heat flow can prevent this transition from occurring for snow-friction scenarios of practical interest.

We determined ice velocities for the Academy of Sciences Ice Cap, Severnaya Zemlya, Russian Arctic, during November 2016–November 2017, by feature-tracking 54 pairs of Sentinel-1 synthetic-aperture radar images. Seasonal velocity variations with amplitudes up to 10% of the yearly-averaged velocity were observed. Shorter-term (<15 d) intra-annual velocity variations had average and maximum deviations from the annual mean of up to 16 and 32%, respectively. This indicates the errors that could be incurred if ice discharge values determined from a single pair of images were extrapolated to the whole year. Average ice discharge for 2016–2017 was 1.93 ± 0.12 Gt a−1. The difference from an estimate of ~ 1.4 Gt a−1 for 2003–2009 was attributed to the initiation of ice stream flow in Basin BC. The total geodetic mass balance over 2012–2016 was − 1.72 ± 0.67 Gt a−1 (− 0.31 ± 0.12 m w.e. a−1). The climatic mass balance was not significantly different from zero, at 0.21 ± 0.68 Gt a−1 (0.04 ± 0.12 m w.e. a−1), and has remained near zero at decadal-scale for the last four decades. Therefore, the total mass balance has been controlled largely by variations in ice discharge, whose long-term changes do not appear to have responded to environmental changes but to the intrinsic characteristics of the ice cap governing tidewater glacier dynamics.

This work combines very detailed measurements from terrestrial laser scanner (TLS), ground-based interferometry radar (GB-SAR) and ground-penetrating radar (GPR) to diagnose current conditions and to analyse the recent evolution of the Monte Perdido Glacier in the Spanish Pyrenees from 2011 to 2017. Thus, this is currently one of the best monitored small glacier (<0.5 km2) worldwide. The evolution of the glacier surface was surveyed with a TLS evidencing an important decline of 6.1 ± 0.3 m on average, with ice losses mainly concentrated over 3 years (2012, 2015 and 2017). Ice loss is unevenly distributed throughout the study period, with 10–15 m thinning in some areas while unchanged areas in others. GB-SAR revealed that areas with higher ice losses are those that are currently with no or very low ice motion. In contrast, sectors located beneath the areas with less ice loss are those that still exhibit noticeable ice movement (average 2–4.5 cm d─1 in summer, and annual movement of 9.98 ma─1 from ablation stakes data). GPR informed that ice thickness was generally <30 m, though locally 30–50 m. Glacier thinning is still accelerating and will lead to extinction of the glacier over the next 50 years.

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.

Previous studies reported that Good Friday Glacier had been actively surging in the 1950–60s, 1990s and again in 2000–15. Based on observations of terminus position change from air photos and satellite imagery, we fill the gaps between previous studies and conclude that the glacier has been advancing continuously since 1959. Ice surface velocities extracted from optical and synthetic aperture radar satellite images show higher flow rates than on most other marine-terminating glaciers in the region. This behaviour contrasts with the regional trend of glacier retreat over this period. Possible explanations involve a delayed response to positive mass-balance conditions of the Little Ice Age, or a dynamic instability. There is, however, insufficient evidence to attribute this behaviour to classical glacier surging as suggested in previous studies. Based on present-day ice velocity and glacier geometry patterns in the terminus region, we reconstruct the evolution of ice motion throughout the advance, and suggest that what has previously been interpreted as a surge, may instead have been a localised response to small-scale perturbations in bedrock topography.