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Predicting the climate for the future and how it will impact ice sheet evolution requires coupling ice sheet models with climate models. However, before we attempt to develop a realistic coupled setup, we propose, in this study, to first analyse the impact of a model simulated climate on an ice sheet. We undertake this exercise for a set of regional and global climate models. Modelled near surface air temperature and precipitation are provided as upper boundary conditions to the GRISLI (GRenoble Ice Shelf and Land Ice model) hybrid ice sheet model (ISM) in its Greenland configuration. After 20 kyrs of simulation, the resulting ice sheets highlight the differences between the climate models. While modelled ice sheet sizes are generally comparable to the observed one, there are considerable deviations among the ice sheets on regional scales. These deviations can be explained by biases in temperature and precipitation near the coast. This is especially true in the case of global models. But the deviations between the climate models are also due to the differences in the atmospheric general circulation. To account for these differences in the context of coupling ice sheet models with climate models, we conclude that appropriate downscaling methods will be needed. In some cases, systematic corrections of the climatic variables at the interface may be required to obtain realistic results for the Greenland ice sheet (GIS).

We present 17 velocity records derived from in situ stand-alone single-frequency Global Positioning System (GPS) receivers placed on eight marine-terminating ice sheet outlet glaciers in South, West and North Greenland, covering varying parts of the period summer 2009 to summer 2012. Common to all the observed glacier velocity records is a pronounced seasonal variation, with an early melt season maximum generally followed by a rapid mid-melt season deceleration. The GPS-derived velocities are compared to velocities derived from radar satellite imagery over six of the glaciers to illustrate the potential of the GPS data for validation purposes. Three different velocity map products are evaluated, based on ALOS/PALSAR data, TerraSAR-X/Tandem-X data and an aggregate winter TerraSAR-X data set. The velocity maps derived from TerraSAR-X/Tandem-X data have a mean difference of 1.5% compared to the mean GPS velocity over the corresponding period, while velocity maps derived from ALOS/PALSAR data have a mean difference of 9.7%. The velocity maps derived from the aggregate winter TerraSAR-X data set have a mean difference of 9.5% to the corresponding GPS velocities. The data are available from the GEUS repository at doi:10.5280/GEUS000001.

We measure the potential of an observational data set to constrain a set of inputs to a complex and computationally expensive computer model. We use each member in turn of an ensemble of output from a computationally expensive model, corresponding to an observable part of a modelled system, as a proxy for an observational data set. We argue that, given some assumptions, our ability to constrain uncertain parameter inputs to a model using its own output as data, provides a maximum bound for our ability to constrain the model inputs using observations of the real system. The ensemble provides a set of known parameter input and model output pairs, which we use to build a computationally efficient statistical proxy for the full computer model, termed an emulator. We use the emulator to find and rule out "implausible" values for the inputs of held-out ensemble members, given the computer model output. As we know the true values of the inputs for the ensemble, we can compare our constraint of the model inputs with the true value of the input for any ensemble member. Measures of the quality of constraint have the potential to inform strategy for data collection campaigns, before any real-world data is collected, as well as acting as an effective sensitivity analysis. We use an ensemble of the ice sheet model Glimmer to demonstrate our measures of quality of constraint. The ensemble has 250 model runs with 5 uncertain input parameters, and an output variable representing the pattern of the thickness of ice over Greenland. We have an observation of historical ice sheet thickness that directly matches the output variable, and offers an opportunity to constrain the model. We show that different ways of summarising our output variable (ice volume, ice surface area and maximum ice thickness) offer different potential constraints on individual input parameters. We show that combining the observational data gives increased power to constrain the model. We investigate the impact of uncertainty in observations or in model biases on our measures, showing that even a modest uncertainty can seriously degrade the potential of the observational data to constrain the model.

The basal topography is largely unknown beneath most glaciers and ice caps, and many attempts have been made to estimate a thickness field from other more accessible information at the surface. Here, we present a two-step reconstruction approach for ice thickness that solves mass conservation over single or several connected drainage basins. The approach is applied to a variety of test geometries with abundant thickness measurements including marine- and land-terminating glaciers as well as a 2400 km2 ice cap on Svalbard. The input requirements are kept to a minimum for the first step. In this step, a geometrically controlled, non-local flux solution is converted into thickness values relying on the shallow ice approximation (SIA). In a second step, the thickness field is updated along fast-flowing glacier trunks on the basis of velocity observations. Both steps account for available thickness measurements. Each thickness field is presented together with an error-estimate map based on a formal propagation of input uncertainties. These error estimates point out that the thickness field is least constrained near ice divides or in other stagnant areas. Withholding a share of the thickness measurements, error estimates tend to overestimate mismatch values in a median sense. We also have to accept an aggregate uncertainty of at least 25 % in the reconstructed thickness field for glaciers with very sparse or no observations. For Vestfonna ice cap (VIC), a previous ice volume estimate based on the same measurement record as used here has to be corrected upward by 22 %. We also find that a 13 % area fraction of the ice cap is in fact grounded below sea level. The former 5 % estimate from a direct measurement interpolation exceeds an aggregate maximum range of 6–23 % as inferred from the error estimates here.

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.