G laciers and ice caps outside the Greenland and Antarctic ice sheets ('glaciers' in the following) are changing rapidly in response to climate change 1 . Although they only contain a fraction of the worldwide ice volume 2 , the consequences of their mass loss are widespread and of global significance: glacier changes affect global trends in freshwater availability 3,4 , have dominated cryospheric contributions to recent sea level changes 5,6 and are anticipated to affect regional water resources over the twenty-first century 7,8 . Clearly, projections of such impacts require an estimate of the ice volume stored within present-day glaciers, and for regionalto local-scale projections the ice thickness distribution can also be essential 9,10 . Recent studies showed that even small features in the bedrock topography can cause decadal-scale variations in both ice dynamics response 11 and subglacial water discharge 12 .Despite far-reaching implications, knowledge of the ice thickness distributions of the world's glaciers is remarkably limited. The Glacier Thickness Database (GlaThiDa), which centralizes ice thickness measurements outside the two ice sheets, presently contains information for only about 1,000 out of the 215,000 glaciers worldwide 13 . This is despite important advances in the instrumentation used to measure ice thickness 14,15 , with airborne platforms now capable of operating in mountainous environments as well 16 .Owing to the lack of direct measurements, relations between glacier area and ice volume 17 have traditionally been used to estimate global glacier volumes 18-21 . For individual glaciers, instead, a suite of methods that infer the spatial ice thickness distribution from surface characteristics have been proposed [22][23][24][25][26][27] . Such methods use topographical information-typically extracted from digital elevation models (DEMs)-to estimate the distribution of the glacier's surface mass balance and, hence, its mass turnover. Knowledge of the ice thickness distribution of the world's glaciers is a fundamental prerequisite for a range of studies.Projections of future glacier change, estimates of the available freshwater resources or assessments of potential sea-level rise all need glacier ice thickness to be accurately constrained. Previous estimates of global glacier volumes are mostly based on scaling relations between glacier area and volume, and only one study provides global-scale information on the ice thickness distribution of individual glaciers. Here we use an ensemble of up to five models to provide a consensus estimate for the ice thickness distribution of all the about 215,000 glaciers outside the Greenland and Antarctic ice sheets. The models use principles of ice flow dynamics to invert for ice thickness from surface characteristics. We find a total volume of 158 ± 41 × 10 3 km 3 , which is equivalent to 0.32 ± 0.08 m of sea-level change when the fraction of ice located below present-day sea level (roughly 15%) is subtracted. Our results indicate that High Mountain Asia ...

International audienceThe floating ice shelves along the seaboard of the Antarctic ice sheet restrain the outflow of upstream grounded ice. Removal of these ice shelves, as shown by past ice-shelf recession and break-up, accelerates the outflow, which adds to sea-level rise. A key question in predicting future outflow is to quantify the extent of calving that might precondition other dynamic consequences and lead to loss of ice-shelf restraint. Here we delineate frontal areas that we label as ‘passive shelf ice’ and that can be removed without major dynamic implications, with contrasting results across the continent. The ice shelves in the Amundsen and Bellingshausen seas have limited or almost no ‘passive’ portion, which implies that further retreat of current ice-shelf fronts will yield important dynamic consequences. This region is particularly vulnerable as ice shelves have been thinning at high rates for two decades and as upstream grounded ice rests on a backward sloping bed, a precondition to marine ice-sheet instability. In contrast to these ice shelves, Larsen C Ice Shelf, in the Weddell Sea, exhibits a large ‘passive’ frontal area, suggesting that the imminent calving of a vast tabular iceberg8 will be unlikely to instantly produce much dynamic change

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.

Abstract. Knowledge of the ice thickness distribution of glaciers and ice caps is an important prerequisite for many glaciological and hydrological investigations. A wealth of approaches has recently been presented for inferring ice thickness from characteristics of the surface. With the Ice Thickness Models Intercomparison eXperiment (ITMIX) we performed the first coordinated assessment quantifying individual model performance. A set of 17 different models showed that individual ice thickness estimates can differ considerably – locally by a spread comparable to the observed thickness. Averaging the results of multiple models, however, significantly improved the results: on average over the 21 considered test cases, comparison against direct ice thickness measurements revealed deviations on the order of 10 ± 24 % of the mean ice thickness (1σ estimate). Models relying on multiple data sets – such as surface ice velocity fields, surface mass balance, or rates of ice thickness change – showed high sensitivity to input data quality. Together with the requirement of being able to handle large regions in an automated fashion, the capacity of better accounting for uncertainties in the input data will be a key for an improved next generation of ice thickness estimation approaches.

ABSTRACT. Physically based projections of the Greenland ice sheet contribution to future sea-level change are subject to uncertainties of the atmospheric and oceanic climatic forcing and to the formulations within the ice flow model itself. Here a higher-order, three-dimensional thermomechanical ice flow model is used, initialized to the present-day geometry. The forcing comes from a high-resolution regional climate model and from a flowline model applied to four individual marine-terminated glaciers, and results are subsequently extended to the entire ice sheet. The experiments span the next 200 years and consider climate scenario SRES A1B. The surface mass-balance (SMB) scheme is taken either from a regional climate model or from a positive-degree-day (PDD) model using temperature and precipitation anomalies from the underlying climate models. Our model results show that outlet glacier dynamics only account for 6-18% of the sea-level contribution after 200 years, confirming earlier findings that stress the dominant effect of SMB changes. Furthermore, interaction between SMB and ice discharge limits the importance of outlet glacier dynamics with increasing atmospheric forcing. Forcing from the regional climate model produces a 14-31% higher sea-level contribution compared to a PDD model run with the same parameters as for IPCC AR4.

Abstract. Continuing global warming will have a strong impact on the Greenland ice sheet in the coming centuries. During the last decade (2000–2010), both increased melt-water runoff and enhanced ice discharge from calving glaciers have contributed 0.6 ± 0.1 mm yr−1 to global sea-level rise, with a relative contribution of 60 and 40% respectively. Here we use a higher-order ice flow model, spun up to present day, to simulate future ice volume changes driven by both atmospheric and oceanic temperature changes. For these projections, the flow model accounts for runoff-induced basal lubrication and ocean warming-induced discharge increase at the marine margins. For a suite of 10 atmosphere and ocean general circulation models and four representative concentration pathway scenarios, the projected sea-level rise between 2000 and 2100 lies in the range of +1.4 to +16.6 cm. For two low emission scenarios, the projections are conducted up to 2300. Ice loss rates are found to abate for the most favourable scenario where the warming peaks in this century, allowing the ice sheet to maintain a geometry close to the present-day state. For the other moderate scenario, loss rates remain at a constant level over 300 years. In any scenario, volume loss is predominantly caused by increased surface melting as the contribution from enhanced ice discharge decreases over time and is self-limited by thinning and retreat of the marine margin, reducing the ice–ocean contact area. As confirmed by other studies, we find that the effect of enhanced basal lubrication on the volume evolution is negligible on centennial timescales. Our projections show that the observed rates of volume change over the last decades cannot simply be extrapolated over the 21st century on account of a different balance of processes causing ice loss over time. Our results also indicate that the largest source of uncertainty arises from the surface mass balance and the underlying climate change projections, not from ice dynamics.

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We have reconstructed the ice thickness distribution of the Morteratsch glacier complex, Switzerland, and used this to simulate its flow with a higher-order 3-D model. Ice thickness was measured along transects with a ground-penetrating radar and further extended over the entire glacier using the plastic flow assumption and a distance-weighted interpolation technique. We find a maximum ice thickness of 350 ±52.5 m for the central trunk of Vadret da Morteratsch, resulting from a bedrock overdeepening. The average thickness of the glacier complex is 72.2 ±18.0 m, which corresponds to a total ice volume of 1.14 ± 0.28 km3. The flow of the glacier is modelled by tuning the rate factor and the sliding parameters taking into account higher-order terms in the force balance. The observed velocities can be reproduced closely (root-mean-square error of 15.0 m a-1, R2 = 0.93) by adopting a sliding factor of 12 x 10–16 m7 N–3 a-1 and a rate factor of 1.6 x 10-16 Pa-3 a-1 . In this setting, ice deformation accounts for 70% of the surface velocity and basal sliding for the remaining 30%. The modelled velocity field reaches values up to 125 ma-1, but also indicates an almost stagnant front and confluence area, which are crucial for understanding the ongoing glacier retreat.