The geodetic mass balance of a glacier corresponds to glacier-wide volume changes, converted to mass changes using density assumptions. It is typically calculated by differencing multi-temporal digital elevation models. In this study, we show how the annual geodetic mass balance of a glacier can be derived from uncrewed aerial vehicle (UAV) data. The presented workflow is applied to two small- to medium-sized glaciers in the Kyrgyz Tien Shan (Central Asia): Bordu glacier and Sary-Tor glacier. The obtained geodetic mass balance is compared with the glaciological mass balance derived from a network of ablation stakes and snow pits. A previously calibrated mass-balance model is used to correct for the difference in acquisition dates. The results show that the determined geodetic mass balance matches closely with the glaciological mass balance. Besides, for both glaciers the geodetic mass balance does not seem to be particularly sensitive to the assumptions regarding volume-to-mass conversion. Therefore, our results demonstrate that UAVs can serve as a valuable instrument to quantify the annual geodetic mass balance and to validate the glaciological mass balance. The conventional glaciological mass-balance estimation often relies on interpolation and extrapolation methods, whereas UAVs offer the potential for direct data acquisition over the entire glacier surface.

Glaciers in the Tien Shan mountains contribute considerably to the fresh water used for irrigation, households and energy supply in the dry lowland areas of Kyrgyzstan and its neighbouring countries. To date, reconstructions of the current ice volume and ice thickness distribution remain scarce, and accurate data are largely lacking at the local scale. Here, we present a detailed ice thickness distribution of Ashu-Tor, Bordu, Golubin and Kara-Batkak glaciers derived from radio-echo sounding measurements and modelling. All the ice thickness measurements are used to calibrate three individual models to estimate the ice thickness in inaccessible areas. A cross-validation between modelled and measured ice thickness for a subset of the data is performed to attribute a weight to every model and to assemble a final composite ice thickness distribution for every glacier. Results reveal the thickest ice on Ashu-Tor glacier with values up to 201 ± 12 m. The ice thickness measurements and distributions are also compared with estimates composed without the use of in situ data. These estimates approach the total ice volume well, but local ice thicknesses vary substantially.

In this study we analyse a 15-year long time series of surface mass-balance (SMB) measurements performed between 2001 and 2016 in the ablation zone of the Morteratsch glacier complex (Engadine, Switzerland). For a better understanding of the SMB variability and its causes, multiple linear regressions analyses are performed with temperature and precipitation series from nearby meteorological stations. Up to 85% of the observed SMB variance can be explained by the mean May–June–July temperature and the total precipitation from October to March. A new method is presented where the contribution of each month's individual temperature and precipitation to the SMB can be examined in a total sample of 224 (16.8 million) combinations. More than 90% of the observed SMB can be explained with particular combinations, in which the May–June–July temperature is the most recurrent, followed by October temperature. The role of precipitation is less pronounced, but autumn, winter and spring precipitation are always more important than summer precipitation. Our results indicate that the length of the ice ablation season is of larger importance than its intensity to explain year-to-year variations. The widely used June–July–August temperature index may not always be the best option to describe SMB variability through statistical correlation.

The temporal and spatial variability of the annual accumulation rate and the mass budgets of five sub-basins of the Lambert Glacier-Amery Ice Shelf system (LAS), East Antarctica, at high elevations are assessed using a variety of datasets derived from field measurements and modeling. The annual temporal variations of the accumulation rate for four cores from the west and east sides of the LAS are around ±34%. Decadal fluctuation of the accumulation from the DT001 firn core drops to ±10%, and the 30 year fluctuation to ±5%, which is assumed to contain the information about the regional and long-term trend in accumulation. The 15-point running mean of the annual accumulation rate derived from stake measurements can remove most of the high-frequency spatial variation so as to better represent the local accumulation. Model simulations show that the spatial variability of erosion/ deposition of snow by the wind has a noticeable impact on the surface mass balance at the higher parts of the LAS. Mass-budget estimates at high-elevation sub-basins of the LAS suggest drainage 9 has a negative imbalance of −0.7 ± 0.4 Gta-1, Lambert and Mellor Glaciers have a positive imbalance of 3.9 ± 2.1 and 2.1 ±2.4 Gta-1 respectively, and Fisher Glacier and drainage 11 are approximately in balance. The higher-elevation region as a whole has a positive mass imbalance of 4.4 ± 6.3 Gta-1, which is consistent with the most recent radar altimetry assessment that shows an overall thickening over this region.

Daugaard Jensen Gletscher, Greenland, is a large tidewater glacier terminating in the northwest corner of the Scoresby Sund fjords. We present a time series of surface flow speeds spanning 1985–2010 based on feature tracking of satellite images. The time series confirms that flow speeds remained stable and reveals a persistent summer acceleration of up to 10% over the lower 10 km of the glacier. The front of the 6 km floating tongue fluctuates by little more than the average size of calved icebergs, ~1 km. While we are unable to detect any imbalance between ice discharge and surface mass balance within our error estimates, observations suggest that the region is losing mass and experiencing decreases in surface elevation. We conclude that as flow speeds and surface mass balance have remained steady since 1985, the shift from balance to imbalance, leading to elevation decrease, must have occurred prior to this date. As for other stable Greenland tidewater glaciers, the seasonal melt cycle is the dominant influence on flow velocity variation but, if the apparent current thinning rates continue, there is potential for the grounding line to retreat, for calving rates to increase and for the glacier to accelerate.

We present results from a greenhouse warming experiment obtained from an atmosphere–ocean–sea-ice general circulation model that is interactively coupled with a three-dimensional model of the Greenland ice sheet. the experiment covers the period 1970–2099 and is driven by the mid-range Intergovernmental Panel on Climate Change SRESB2 scenario. the Greenland model is a thermomechanical high-resolution (20 km) model coupled with a viscoelastic bedrock model. the melt-and-runoff model is based on the positive degree-day method and includes meltwater retention in the snowpack and the formation of superimposed ice. the atmospheric–oceanic general circulation model (AOGCM) is a coarse-resolution model without flux correction based on the Laboratoire de Météorologie Dynamique (Paris) LMD 5.3 atmospheric model coupled with a primitive-equation, free-surface oceanic component incorporating sea ice (coupled large-scale ice–ocean (CLIO)). By 2100, average Greenland annual temperature is found to rise by about 4.5˚C and mean precipitation by about 35%. the total fresh-water flux approximately doubles over this period due to increased runoff from the ice sheet and the ice-free land, but the calving rate is found to decrease by 25%. the ice sheet shrinks equivalent to 4 cm of sea-level rise. the contribution from the background evolution is not more than 5% of the total predicted sea-level rise. We did not find significant changes in the patterns of climate change over the North Atlantic region compared with a climate-change run without Greenland fresh-water feedback.

We used remote-sensing and in situ measurements of surface accumulation rate, ice surface velocity, thickness and elevation to evaluate the mass budgets of grounded ice-flow regimes that form the Lambert Glacier–Amery Ice Shelf system. Three distinct drainage regimes are considered: the western and eastern margins of the ice shelf, and the southern grounding line at the major outlet glacier confluence, which can be identified with drainage zones 9, 11 and 10 respectively of Giovinetto and Zwally (2000). Our findings show the entire grounded portion of the basin is approximately in balance, with a mass budget of –4.2±9.8 Gt a–1. Drainages 9, 10 and 11 are within balance to the level of our measurement uncertainty, with mass budgets of –2.5±2.8 Gt a–1, –2.6±7.8 Gt a–1 and 0.9±2.3 Gt a–1, respectively. The region upstream of the Australian Lambert Glacier basin (LGB) traverse has a net mass budget of 4.4±6.3 Gt a–1, while the downstream region has –8.9±9.9 Gt a–1. These results indicate that glacier drainages 9, 10 and 11, upstream and downstream of the Australian LGB traverse, are in balance to within our measurement error.

Due to the lack of measurements of ice velocity, mass balance, glacier geometry and other baseline data, model-based studies of glacial systems in the Nepal Himalaya are very limited. Here a numerical ice-flow model has been developed for glacier AX010 in order to study its relation to local climate and investigate the possible causes of its general retreat since the end of the Little Ice Age. First, an attempt is made to simulate the historical front variations, considering each climatic parameter separately. Good agreement between the observations and model projections can be obtained under the assumption that variations in glacier front position are a response to changes in temperature alone. The same assumption is made about future changes to explore the 21st-century evolution of the glacier. Under a no-change scenario, the glacier will retreat by another ∽600m by AD 2100, whereas it is projected to vanish completely during this century for all trends with a temperature rise larger than +2.5˚C by AD 2100 with respect to the 1980–99 mean. With constant precipitation at the 1980–99 mean, the model predicts that the glacier will cease to exist at AD 2083, 2056 or 2049 if the temperature rises linearly by 3˚C, 4.5˚C or 6˚C respectively by the end of this century. With an additional range of precipitation changes between –30% and +30%, the life expectancy of glacier AX010 varies by 18, 6 and 2 years for the respective temperature rises. Thus the role of precipitation becomes minimal for the higher trends of temperature rise.

Large-scale positive degree-day based melt parameterizations for the Greenland ice sheet are highly sensitive to their parameters (standard temperature deviation, snow and ice degree-day factors). In this paper, these parameters are simulated with a coupled atmosphere–snow regional climate model for southern Greenland during summer 1991, forced at the lateral boundaries with European Centre for Medium-Range Weather Forecasts re-analyses at a high horizontal resolution of 20 km. the calculated (from net ablation, i.e. melt minus refreezing) snow and ice positive degree-day factors vary considerably over the ice sheet. At low elevations, the modelled snow degree-day factor closely approaches the generally accepted value of 3 mm w.e. d–1 ˚C–1.Higher up the ice sheet, large values up to 15 mm w.e. d– 1 ˚C– 1 are simulated. for ice melt, maximum values of 40 mm w.e. d–1 ˚C– 1 are found. the snow and ice positive degree-day factor distributions peak, respectively, at 3 and 8mm w.e. d–1 ˚C–1. Refreezing is of small importance close to the ice-sheet margin. Higher up the ice sheet, refreezing considerably lowers the amount of net ablation. the monthly simulated 2 m air-temperature standard deviation exhibits a strong seasonal cycle, with the highest (3.0–5.0˚C) values in May and June. July shows the lowest temperature fluctuations, due to the melting of the surface.

We used internal ice layers from a radio-echo sounding profile between the Kohnen and Dome Fuji deep drilling sites to infer the spatio-temporal pattern of accumulation rate in this sector of Dronning Maud Land, East Antarctica. Continuous internal reflection horizons can be traced to about half of the ice thickness and have a maximum age of approximately 72.7 ka BP. To infer palaeo-accumulation rates from the dated layers, we derived the thinning functions from a flow calculation with a high-resolution higher-order model of Dronning Maud Land embedded into a three-dimensional thermomechanical model of the Antarctic ice sheet. The method takes into account complex ice-flow dynamics and advection effects that cannot be dealt with using traditional local approaches. We selected seven time intervals over which we determine the average accumulation rate and average surface temperature at the place and time of origin of the layer particles. Our results show lower accumulation rates along eastern parts of the profile for the late Holocene (0–5 ka BP) than are shown by existing maps, which had no surface control points. During the last glacial period we find a substantially lower accumulation rate than predicted by the usual approach linking palaeo-accumulation rates to the condensation temperature above the surface inversion layer. These findings were used to fine-tune the relation between accumulation rate and temperature.

We have reconstructed the annual balance of Vadret da Morteratsch, Engadine, Switzerland, with a two-dimensional energy-balance model for the period 1865–2005. The model takes into account a parameterization of the surface energy fluxes, an albedo that decreases exponentially with snow depth as well as the shading effect of the surrounding mountains. The model was first calibrated with a 5 year record of annual balance measurements made at 20 different sites on the glacier between 2001 and 2006 using meteorological data from surrounding weather stations as input. To force the model for the period starting in 1865, we employed monthly temperature and precipitation records from nearby valley stations. The model reproduces the observed annual balance reasonably well, except for the lower part during the warmest years. Most crucial to the results is the altitudinal precipitation gradient, but this factor is hard to quantify from the limited precipitation data at high elevations. The simulation shows an almost continuous mass loss since 1865, with short interruptions around 1920, 1935 and 1980. A trend towards a more negative annual balance can be observed since the beginning of the 1980s. The simulated cumulative mass balance for the entire period 1865–2005 was found to be –46mw.e.

Mechanisms that determine time-dependent changes of the marine ice margin in dynamic ice-sheet models are important but poorly understood. Here we derive an empirical formulation for changes in the marine extent when modelling the Northern Hemisphere ice sheets over the last glacial cycle in a three-dimensional thermomechanically coupled ice-sheet model. We assume that the strongest control on changes in marine extent is ice calving, and that the variable most crucial to calving is water depth. The empirical marine-extent relationship is tuned so that the major marine-retreat history of the Laurentide and Eurasian ice sheets is modelled accurately in time and space. We find that this empirical treatment relating marine extent to water depth is sufficient to reproduce the observations, and discuss the implications for the physics of marine margin changes and the dynamics of the Northern Hemisphere ice sheets since the Last Glacial Maximum.

Retention of meltwater runoff by percolation and/or refreezing in the snowpack cannot be neglected when studying the surface mass balance of the Greenland ice sheet. In this paper, we make a detailed comparison of several treatments proposed in the literature to account for this process in large-scale mass-balance parameterizations. The melt on the Greenland ice sheet is calculated with a revised degree-day model using updated datasets of surface elevation and precipitation rate on a 5 km grid. Crucial model parameters are recalibrated by comparing mass-balance characteristics with available observations on a regional basis. We discuss the role of meltwater retention in the light of the overall mass balance of the Greenland ice sheet and its sensitivity to climatic change, and display patterns of effective-retention fractions for the various methods. As a main conclusion it appears that overall results are quite similar for the various models, but that meltwater retention has a large spatial variation not described by the simple treatments. Using the most comprehensive retention model, the sensitivity of the runoff is found to be +0.35 mm ˚C–1 of sea-level change per year. We also present a new map of the different zones (facies) that characterize the accumulation area of the Greenland ice sheet, which is useful for interpreting field data and calibrating satellite observations.

Accurate dating in ice sheets is required for a correct interpretation of palaeoclimatic records and for incorporation of material characteristics in the flow law which depend on ice age. In this paper, we make a comparison between a Lagrangian and Eulerian approach to the ice advection problem in numerical ice-sheet models. This comparison is first performed for a schematic two-dimensional ice sheet of Nye–Vialov type with a prescribed stationary velocity field. Severalcases are examined which incorporate basal melting, basal sliding and an undulating bed. A further comparison is made with an analytical solution for the ice divide. Both methods are also applied in a thermomechanical model of the Antarctic ice sheet for steady-state present-day conditions. Our main conclusion is that, for similar discretization parameters, the Lagrangian method produces less error than an Eulerian approach using a second-order upwinding finite-difference scheme, though the difference is small (<1%) for the largest part of the model domain. However, problems with the Lagrangian approach are introduced by the dispersion of tracers, necessitating the use of interpolation procedures that are a main source of additional error. It is also shown that a cubic-spline approximation of Lagrangian trajectories improves accuracy, but such a method is computationally hardly applicable in large-scale ice-sheet models.

We used surface climate fields from high-resolution (~0.5660.56˚) European Centre for Medium-RangeWeather Forecasts (ECMWF) operational analyses (1992–98), together with meteorological and glaciological models of snow accumulation and surface meltwater runoff/retention, to produce novel maps of Greenland ice sheet (GIS) net accumulation, net runoff and surface mass balance (SMB). We compared our runoff maps with similar-scaled runoff (melt minus refreezing) maps based on passive-microwave satellite data. Our gross spatial/temporal patterns of runoff compared well with those from the satellite data, although amounts of modelled runoff are likely too low. Mean accumulation was 0.287 (0.307)ma–1, and mean runoff was 0.128 (0.151)ma–1, averaged across the W. Abdalati (T. L. Mote) GIS mask. Corresponding mean SMB was 0.159 (0.156)ma–1, with considerable interannual variability (standard deviation ~0.11ma–1) primarily due to variations in runoff. Considering best estimates of current iceberg calving, overall the GIS is probably currently losing mass. Our study shows great promise for meaningfully modelling SMB based on forthcoming ``second-generation’’ ECMWF re-analysis (ERA-40) data, and comparing the results with ongoing laser/radarmeasurements of surface elevation. This should help elucidate to what extent surface elevation changes are caused by short-term SMB variations or other factors (e.g. ice dynamics).

This paper presents a new compilation of gridded datasets for three-dimensional modelling of the Antarctic ice sheet. These are for surface elevation, ice thickness, bedrock elevation and accumulation rate as interpolated on a 281 × 281 mesh with 20 km spacing, and encompass all the ice sheet and surrounding continental shelf. Data sources include the Bamber digital-elevation model from ERS-1 radar-altimeter data, a redigitization of available ice-thickness data, the Giovinetto accumulation data, recent ice-thickness data from British and German expeditions as well as accumulation data from German and Norwegian expeditions. In particular, new data were incorporated for the Filchner-Ronne Ice Shelf and for Dronning Maud Land, Antarctica, arising from the EPICA pre-site survey. Special attention was devoted to matching the various data sources carefully, both among themselves and across the grounding line and below the ice shelves, to enable ice-sheet expansion and retreat in dynamic situations. As an application, the balance flow is calculated over the entire ice sheet using a two-dimensional finite-difference scheme and compared with a previous assessment. This brought to light the existence of ice-streaming features extending well inland. A detailed zoom over Dronning Maud Land exhibits the general flow characteristics of interest for locating a future deep-drilling site. As a by-product, an updated value of 26.4 × 106km3 was obtained for the total volume of the ice sheet and ice shelves, or equivalent to 61.1 m of global sea-level rise after removal of the ice sheet and subsequent oceanic invasion and isostatic rebound. The total accumulation over the grounded ice sheet, including the Antarctic Peninsula, is 1924 Gta−1, or between 5 and 20% higher than earlier estimates. Including all the ice shelves, the value is 2344 Gt a−1.

Results from the Heinrich Event Intercomparison (HEINO) topic of the Ice-Sheet Model Intercomparison Project (ISMIP) are presented. ISMIP HEINO was designed to explore internal large-scale ice-sheet instabilities in different contemporary ice-sheet models. These instabilities are of interest because they are a possible cause of Heinrich events. A simplified geometry experiment reproduces the main characteristics of the Laurentide ice sheet, including the sedimented region over Hudson Bay and Hudson Strait. The model experiments include a standard run plus seven variations. Nine dynamic/thermodynamic ice-sheet models were investigated; one of these models contains a combination of the shallow-shelf (SSA) and shallow-ice approximation (SIA), while the remaining eight models are of SIA type only. Seven models, including the SIA–SSA model, exhibit oscillatory surges with a period of ∼1000 years for a broad range of parameters, while two models remain in a permanent state of streaming for most parameter settings. In a number of models, the oscillations disappear for high surface temperatures, strong snowfall and small sediment sliding parameters. In turn, low surface temperatures and low snowfall are favourable for the ice-surge cycles. We conclude that further improvement of ice-sheet models is crucial for adequate, robust simulations of cyclic large-scale instabilities.

We use a 3-D higher-order glacier flow model for Vadret da Morteratsch, Engadin, Switzerland, to simulate its strong retreat since the end of the Little Ice Age (LIA) and to project its future disintegration under a warming climate. The flow model, coupled to a 2-D energy-balance model, is initialized with the known maximum glacier extent during the LIA and subsequently forced with mean monthly precipitation and temperature records. To correctly reproduce the observed retreat of the glacier front for the period 1864–2010, additional mass-balance perturbations are required to account for uncertainties in the initial state, the mass-balance model and climate variations not captured by the ambient meteorological records. Changes in glacier volume and area are in good agreement with additional information from historical topographic maps. Under constant 2001–10 climate conditions, a strong retreat and mass loss continue and Vadret da Morteratsch disconnects from its main tributary, Vadret Pers, before 2020. The future glacier evolution is analysed in detail to understand the timing and rate of retreat, and to assess the role of ice dynamics. Assuming a linearly increasing warming of >3°C by 2100, only isolated and largely stagnant ice patches remain at high elevation.

Predictions of marine ice-sheet behaviour require models able to simulate grounding-line migration. We present results of an intercomparison experiment for plan-view marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no buttressing effects from lateral drag). Perturbation experiments specifying spatial variation in basal sliding parameters permitted the evolution of curved grounding lines, generating buttressing effects. The experiments showed regions of compression and extensional flow across the grounding line, thereby invalidating the boundary layer theory. Steady-state grounding-line positions were found to be dependent on the level of physical model approximation. Resolving grounding lines requires inclusion of membrane stresses, a sufficiently small grid size (<500 m), or subgrid interpolation of the grounding line. The latter still requires nominal grid sizes of <5 km. For larger grid spacings, appropriate parameterizations for ice flux may be imposed at the grounding line, but the short-time transient behaviour is then incorrect and different from models that do not incorporate grounding-line parameterizations. The numerical error associated with predicting grounding-line motion can be reduced significantly below the errors associated with parameter ignorance and uncertainties in future scenarios.

We present a series of benchmark experiments designed for testing and comparing numerical ice-sheet models. Following the outcome of two EISMINT workshops organized to intercompare large-scale ice-sheet models currently in operation, model benchmark experiments ate described for ice sheets under fixed and moving margin conditions. These address both steady-state and time-dependent behaviour under schematic boundary conditions and with prescribed physics. A comparison was made of each model’s prediction of basic geophysical variables such as ice thickness, velocity and temperature. Consensus achieved in the model inter-comparison provides reference solutions against which the accuracy and consistency of ice-sheet modelling codes can be assessed.