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.

Most of the central Himalayan glaciers have surface debris layers of variable thickness, which greatly affect the ablation rate. An attempt has been made to relate debris-cover thickness to glacier surface melting. Thirty stakes were used to calculate ablation for debris-covered and clean ice of Dokriani Glacier (7 km2) from 2009/10 to 2012/13. Our study revealed significant altitude-wise difference in the rate of clean and debris-covered ice melting. We found a high correlation (R2 = 0.92) between mean annual clean-ice ablation and altitude, and a very low correlation (R2 = 0.14) between debris-covered ice melting and altitude. Debris-covered ice ablation varies with variation in debris thickness from 1 to 40 cm; ablation was maximum under debris thicknesses of 1–6 cm and minimum under 40 cm. Even a small debris-cover thickness (1–2 cm) reduces ice melting as compared to that of clean ice on an annual basis. Overall, debris-covered ice ablation during the study period was observed to be 37% less than clean-ice ablation. Strong downwasting was also observed in the Dokriani Glacier ablation area, with average annual ablation of 1.82 m w.e. a–1 in a similar period. Our study suggests that a thinning glacier rapidly becomes debris-covered over the ablation area, reducing the rate of ice loss.

Very large volumes of ice break off regularly from Taconnaz hanging glacier, French Alps. During winter, when the snow mantle is unstable, these collapses can trigger very large avalanches that represent a serious threat to inhabited areas below. Photogrammetric measurements have been performed over 1 year to assess the volume and frequency of the largest collapses. Major collapses occur when the glacier reaches a critical geometry. After a major ice collapse, the glacier is in a minimal position and subsequently recharges over 6 months to reach the maximum position again. This critical geometry is a necessary but not sufficient condition for further large collapses. Large collapses do not systematically occur in the maximum position, as ice is often removed by disintegration into small ice blocks. For two major collapses, the volume of ice breaking off has been assessed at ~275 000 m3. Photogrammetric measurements were used to determine an ice flux of 820 000 m3 a–1 through the studied ice stream, in agreement with an assessment based on ice-flow modeling. This ice flux estimation was used to determine the average ice volumes breaking off over surveyed periods.

Glaciar Perito Moreno (GPM) and Glaciar Ameghino (GA), Southern Patagonia Icefield, are in contact in the accumulation area, but have shown contrasting frontal variations in the past few decades. To investigate recent changes of the two glaciers and processes controlling the different responses to similar climate conditions, we measured surface elevation change from 2000 to 2008 and terminus positions from 1999 to 2012 using several types of satellite data. GPM shows no significant changes in terminus position and 0.4 ± 0.3 m a–1 thickening over the period, whereas GA retreated 55 ± 2 m a–1 and thinned 2.6 ± 0.3 m a–1. Mass-balance measurements over the period 1999/2000 show that accumulation at GPM was ten times greater than that at GA, but ablation was only three times greater. The mass-balance–altitude profile is similar for the two glaciers; differences in the mass-balance distribution are caused by differences in the accumulation–area ratio (AAR). Our results suggest that the AAR and the calving flux exert strong control on the evolution of glaciers in the region.

Basal pressure has been recorded at the Svartisen Subglacial Laboratory, northern Norway, for 20 years, and is measured by load cells installed at the ice–rock interface under ~200m of glacier ice. Synchronous pressure variations between load cells are investigated as evidence of stress redistribution and hydrological bed connectivity. A running Pearson correlation is used to study the temporal variation in the response of several sensors. By studying the nature of this correlation as well as the correlation between sensor pairs, it is possible to investigate the evolution of the degree of synchronous response, and to some extent basal connectivity, at the glacier bed. Persistent seasonal variations associated with the melt season are observed throughout the measurement period, indicating dependence on surface hydrological forcing. Overlying this pattern, specific years with longer periods of positive and negative correlation of pressure between sensors are presented to show contrasting interannual variability in basal pressure. An anticorrelated connectivity is associated with a local increase in the rate of daily subglacial discharge, and is caused by load transfer or passive cavity opening. Stable weather appears to enhance connectivity of the sensors, which is attributed to the development of a persistent drainage system and stress redistribution.

The theoretical basis of subglacial channel dynamics can be traced back to the work of Röthlisberger (1972) and Nye (1953). Röthlisberger (1972) considered the channels’ behaviour to be governed by a mix between water friction melting back the channel walls and the viscous closure of the surrounding ice; Nye (1953) derived a viscous closure rate for the ice. While their modelling is evidently well constructed, two aspects of their work have gone undeveloped. The first is the consideration of a finite glacier depth within the viscous closure law, instead of the assumption of an infinite glacier depth. The second is the allowance of a region of open channel flow, so that a channel’s water may transition from a region of closed channel flow to one where the water is exposed to the atmosphere. This paper helps close these two gaps, showing how Nye’s equation for the rate of ice closure can be modified, and how the point of transition between closed and open channel flow may be determined.

A two-dimensional surface mass-balance model is coupled to a three-dimensional higher-order ice flow model to assess the imbalance between climate and glacier geometry for the Morteratsch (Engadine, Switzerland) glacier complex. The climate–geometry imbalance has never been larger than at present, indicating that the temperature increase is faster than the geometry is able to adapt to. We derive response times from transient and steady-state geometries and find that the volume response time is correlated to the magnitude of the mass-balance forcing. It varies between 22 and 43 years, while the length response time is between 47 and 55 years. Subsequently, the modelled response times are compared with different analytical methods from the literature. The effect of a climatic perturbation on the response time, which produces a spatially distributed mass-balance forcing, is also examined. We investigate the effect of glacier size on the response time and project that the response time will decrease in the future due to a surface steepening. Finally, volume–area scaling methods with different parameters are tested and an alternative method is proposed that takes into account the surface slope. The effect of a transient state on the method is also evaluated.

Mass changes of polar ice sheets have an important societal impact, because they affect global sea level. Estimating the current mass budget of ice sheets is equivalent to determining the balance between surface mass gain through precipitation and outflow across the grounding line. For the Antarctic ice sheet, grounding line outflow is governed by oceanic processes and outlet glacier dynamics. In this study, we compute the mass budget of major outlet glaciers in the eastern Dronning Maud Land sector of the Antarctic ice sheet using the input/output method. Input is given by recent surface accumulation estimates (SMB) of the whole drainage basin. The outflow at the grounding line is determined from the radar data of a recent airborne survey and satellite-based velocities using a flow model of combined plug flow and simple shear. This approach is an improvement on previous studies, as the ice thickness is measured, rather than being estimated from hydrostatic equilibrium. In line with the general thickening of the ice sheet over this sector, we estimate the regional mass balance in this area at 3.15 ± 8.23 Gt a−1 according to the most recent SMB model results.

Internal layers in polar ice sheets have been mapped in many areas using information from radio-echo sounding surveys. The layers contain imprints of past accumulation patterns and ice flow and can potentially provide estimates of past accumulation rates. In this study, average accumulation rates for the past 14.7 ka in north and central Greenland are recovered from the mapped depth of one pronounced isochrone using a simple ice flow model, accounting for both vertical and horizontal flow combined with formal inversion techniques. Using this method, upstream variations in the accumulation and flow are taken into account when inferring the accumulation rates from the deep layer. This resulted in larger spatial variations in the inferred accumulation rates compared to approaches using a one-dimensional ice flow model. The largest differences were found in areas of significant horizontal flow. The inferred accumulation rates agree with Holocene estimates from ice cores in the interior of the ice sheet. Across the central ice divide, the inferred accumulation pattern shows a pronounced gradient in accumulation rates, similar to the present-day pattern, suggesting that the large-scale pattern in the interior of central northern Greenland has been consistent throughout the past 14.7 ka.

This study evaluates sensitivities of glacier mass balance and runoff to both annual and monthly perturbations in air temperature and precipitation at four highly glacierized catchments: Engabreen in northern Norway and Ålfotbreen, Nigardsbreen and Storbreen, which are aligned along a west–east profile in southern Norway. The glacier mass-balance sensitivities to changes in annual air temperature range from 1.74 m w.e. K−1 for Ålfotbreen to 0.55 m w.e. K−1 for Storbreen, the most maritime and the most continental glaciers in this study, respectively. The runoff sensitivities of all catchments are 20–25% per degree temperature change and 6–18% for a 30% precipitation change. A seasonality of the sensitivities becomes apparent. With increasing continentality, the sensitivity of mass balance and runoff to temperature perturbations during summer increases, and the sensitivity of annual runoff to both temperature and precipitation perturbations is constricted towards changes during the ablation period. Comparing sensitivities in northern and southern Norway, as well as the variability across southern Norway, reveals that continentality influences sensitivities more than latitude does.

Bolivian glaciers are an essential source of fresh water for the Altiplano, and any changes they may undergo in the near future due to ongoing climate change are of particular concern. Glaciar Zongo, Bolivia, located near the administrative capital La Paz, has been extensively monitored by the GLACIOCLIM observatory in the last two decades. Here we model the glacier dynamics using the 3-D full-Stokes model Elmer/Ice. The model was calibrated and validated over a recent period (1997–2010) using four independent datasets: available observations of surface velocities and surface mass balance were used for calibration, and changes in surface elevation and retreat of the glacier front were used for validation. Over the validation period, model outputs are in good agreement with observations (differences less than a small percentage). The future surface mass balance is assumed to depend on the equilibrium-line altitude (ELA) and temperature changes through the sensitivity of ELA to temperature. The model was then forced for the 21st century using temperature changes projected by nine Coupled Model Intercomparison Project phase 5 (CMIP5) models. Here we give results for three different representative concentration pathways (RCPs). The intermediate scenario RCP6.0 led to 69 ± 7% volume loss by 2100, while the two extreme scenarios, RCP2.6 and RCP8.5, led to 40 ± 7% and 89 ± 4% loss of volume, respectively.

Englacial and basal temperature data for the Greenland ice sheet (GrIS) are sparse and mostly limited to deep interior sites and ice streams, providing an incomplete representation of the thermal state of ice within the ablation zone. Here we present 11 temperature profiles at five sites along a 34 km east–west transect of West Greenland. These profiles depict ice temperatures along a flowline and local temperature variations between closely spaced boreholes. A temperate basal layer is present in all profiles, increasing in thickness in the flow direction, where it expands from ∼3% of ice height furthest inland to 100% at the margin. Temperate thickness growth is inconsistent with modeled heat contributions from strain heating, heat conduction, and vertical extension of the temperate layer. We suggest that basal crevassing, facilitated by water pressures at or near ice overburden pressure, is responsible for the large temperate ice thicknesses observed. High-temperature kinks at 51–85 m depth are likely remnants from the thermal influence of partially water-filled crevasses up ice sheet. Steep horizontal temperature gradients between closely grouped boreholes suggest the recent thermal influence of a moulin. These profiles demonstrate the ability of meltwater to rapidly alter ice temperatures at all depths within the ablation zone.

We revisit the input–output mass budget of the high-elevation region of the Greenland ice sheet evaluated by the Program for Arctic Regional Climate Assessment (PARCA). Our revised reference period (1961–90) mass balance of 54±48 Gt a–1 is substantially greater than the 0±21 Gt a–1 assessed by PARCA, but consistent with a recent, fully independent, input–output estimate of high-elevation mass balance (41±61 Gt a–1). Together these estimates infer a reference period high-elevation specific mass balance of 4.8±5.4 cm w.e. a–1. The probability density function (PDF) associated with this combined input–output estimate infers an 81% likelihood of high-elevation specific mass balance being positive (>0 cm w.e. a–1) during the reference period, and a 70% likelihood that specific balance was >2 cm w.e. a–1. Given that reference period accumulation is characteristic of centurial and millennial means, and that in situ mass-balance observations exhibit a dependence on surface slope rather than surface mass balance, we suggest that millennial-scale ice dynamics are the primary driver of subtle reference period high-elevation mass gain. Failure to acknowledge subtle reference period dynamic mass gain can result in underestimating recent dynamic mass loss by ~17%, and recent total Greenland mass loss by ~7%.

The flow of Glacier d’Argentière, French Alps, has been extensively studied by glaciologists for >100 years, but high-temporal- and high-spatial-resolution monitoring of its dynamics has rarely been carried out. In this paper, the terminal part of the main glacier was selected to undertake such a survey. The 2 month experiment (September–November 2013) included remote sensing to map the velocity field of the whole area, and a network of in situ measurements to record the ice velocity at the surface as well as at the base of the glacier with high precision and at high temporal resolution. These monitoring methods are combined to produce a comprehensive and reliable picture of the ice flow. Basal and surface in situ measurements are used to precisely monitor the temporal variability of the ice flow at a section of the glacier where crevassed areas and non-cracked ice coexist. The achieved results are an innovative and efficient tool to investigate the acceleration/deceleration pattern heterogeneities in ice flow that occur after heavy rainfall.

We construct initial conditions for an ice flow model of the Greenland ice sheet (GrIS). GrIS has been losing mass at an increasing rate over the past two decades, and a significant proportion of this loss is due to dynamic thinning of narrow outlet glaciers. We solve an inverse problem to estimate poorly known basal and englacial parameters given observed geometry and surface velocities. A weighted cost function, resolved to 4 km in the interior of the ice sheet and 1 km in regions of fast-flowing ice at the margin, is minimized to find two-dimensional fields for a stiffness factor, which is a coefficient of the effective viscosity, and basal traction coefficient. Using these fields, we run the model under present-day climate to damp large-amplitude, short-wavelength fluctuations in the flux divergence. The time-dependent model uses an adaptive mesh with resolution ranging from 8 km of the base grid to 500 m in areas of fast-flowing ice to capture the behaviour of the main outlet glaciers. The ice discharge calculated from the initial conditions for GrIS and individual glaciers compares well with values calculated from observations.

We present new glacier mass-balance field data from Glaciar Bahía del Diablo, Vega Island, northeastern Antarctic Peninsula. The results provided here represent glacier mass-balance data over a 10 year period (2001–11) obtained by the glaciological and geodetic methods relying on field measurements. Glacier surface digital elevation models (DEMs) were obtained in 2001 and 2011 from a kinematic GPS field survey with high horizontal and vertical accuracies. In situ mass-balance data were collected from yearly stake measurements. The results attained by the two methods agree, which may be considered a measure of their accuracy. A cumulative mass change of –1.90 ± 0.31 m w.e. over the 10 year period was obtained from the annual mass-balance field surveys. The total mass change derived from DEM differencing was –2.16 ± 0.23 m w.e.

The supply of glacier water to La Paz city, Bolivia, between 1963 and 2006 was assessed at annual and seasonal timescales based on the mass-balance quantification of 70 glaciers located within the drainage basins of La Paz. Glaciers contributed ∼15% of water resources at an annual scale (14% in the wet season, 27% in the dry season). Uncertainties in our estimation are related to the assumed constant precipitation (∼0.5% for ice-free areas and up to 6.5% for glaciated areas), the constant runoff coefficient (∼1%), the surface areas of the glaciers and catchments (∼5%) and the mean mass-balance uncertainty of the 21 glaciers used to obtain the mass balance of the 70 glaciers (12% of the total discharge). Despite the loss of 50% of the glacierized area during the study period, runoff at La Paz did not change significantly, showing that increase in ice melt rates compensated for reduction in the surface area of the glaciers. In the future, assuming complete disappearance of the glaciers and no change in precipitation, runoff should diminish by ∼12% at an annual scale, 9% during the wet season and 24% during the dry season.

While measurements of ice-sheet surface elevation change are increasingly used to assess mass change, the processes that control the elevation fluctuations not related to ice-flow dynamics (e.g. firn compaction and accumulation) remain difficult to measure. Here we use radar data from the Thwaites Glacier (West Antarctica) catchment to measure the rate of thickness change between horizons of constant age over different time intervals: 2009–10, 2010–11 and 2009–11. The average compaction rate to ~25 m depth is 0.33 m a−1, with largest compaction rates near the surface. Our measurements indicate that the accumulation rate controls much of the spatio-temporal variations in the compaction rate while the role of temperature is unclear due to a lack of measurements. Based on a semi-empirical, steady-state densification model, we find that surveying older firn horizons minimizes the potential bias resulting from the variable depth of the constant age horizon. Our results suggest that the spatio-temporal variations in the firn compaction rate are an important consideration when converting surface elevation change to ice mass change. Compaction rates varied by up to 0.12 m a−1 over distances <6 km and were on average >20% larger during the 2010–11 interval than during 2009–10.

The thickness and density of the Antarctic firn layer vary considerably in time and space, thereby contributing to ice-sheet volume and mass changes. Distinguishing between these mass and volume changes is important for ice-sheet mass-balance studies. Evolution of firn layer depth and density is often modeled, because direct measurements are scarce. Here we directly compare modeled firn compaction rates with observed rates obtained from repeat-track airborne radar data over a 2 year interval (2009–11) in West Antarctica. Spatially, the observed compaction rates exhibit significant variability, but when averaged to scales comparable to the model resolution (20–50 km), the measurements and model results qualitatively agree. A colder and drier period preceding the 2009 survey led to lower compaction rates during the 2009–10 interval, when compared to 2010–11, which is partly captured by the firn model. Spatially, higher compaction rates are observed and modeled in warmer regions with higher accumulation.