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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.

Changes in both global and regional mean sea level, and changes in the magnitude of extreme flood heights, are the result of a combination of several distinct contributions most, but not all, of which are associated with climate change. These contributions include effects in the solid earth, gravity field, changes in ocean mass due to ice loss from ice sheets and glaciers, thermal expansion, alterations in ocean circulation driven by climate change and changing freshwater fluxes, and the intensity of storm surges. Due to the diverse range of models required to simulate these systems, the contributions to sea-level change have usually been discussed in isolation rather than in one self-consistent assessment. Focusing on the coastline of northwest Europe, we consider all the processes mentioned above and their relative impact on 21st century regional mean sea levels and the 50-year return flood height. As far as possible our projections of change are derived from process-based models forced by the A1B emissions scenario to provide a self-consistent comparison of the contributions. We address uncertainty by considering both a mid-range and an illustrative high-end combination of the different components. For our mid-range ice loss scenario we find that thermal expansion of seawater is the dominant contributor to change in northwest European sea level by 2100. However, the projected contribution to extreme sea level, due to changes in storminess alone, is in some places significant and comparable to the global mean contribution of thermal expansion. For example, under the A1B emissions scenario, by 2100, change in storminess contributes around 15 cm to the increase in projected height of the 50-year storm surge on the west coast of the Jutland Peninsula, compared with a contribution of around 22 cm due to thermal expansion and a total of 58 cm from all of the contributions we consider. An illustrative combination of our high-end projections suggests increases in the 50-year return level of 86 cm at Sheerness, 95 cm at Roscoff, 106 cm at Esbjerg, and 67cm at Bergen. The notable regional differences between these locations arise primarily from differences in the rates of vertical land movement and changes in storminess.

Climate change has the potential to influence global mean sea level through a number of processes including (but not limited to) thermal expansion of the oceans and enhanced land ice melt. In addition to their contribution to global mean sea level change, these two processes (among others) lead to local departures from the global mean sea level change, through a number of mechanisms including the effect on spatial variations in the change of water density and transport, usually termed dynamic sea level changes. In this study, we focus on the component of dynamic sea level change that might be given by additional freshwater inflow to the ocean under scenarios of 21st-century land-based ice melt. We present regional patterns of dynamic sea level change given by a global-coupled atmosphere–ocean climate model forced by spatially and temporally varying projected ice-melt fluxes from three sources: the Antarctic ice sheet, the Greenland Ice Sheet and small glaciers and ice caps. The largest ice melt flux we consider is equivalent to almost 0.7 m of global mean sea level rise over the 21st century. The temporal evolution of the dynamic sea level changes, in the presence of considerable variations in the ice melt flux, is also analysed. We find that the dynamic sea level change associated with the ice melt is small, with the largest changes occurring in the North Atlantic amounting to 3 cm above the global mean rise. Furthermore, the dynamic sea level change associated with the ice melt is similar regardless of whether the simulated ice fluxes are applied to a simulation with fixed CO2 or under a business-as-usual greenhouse gas warming scenario of increasing CO2.

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.

We apply a new parameterisation of the Greenland ice sheet (GrIS) feedback between surface mass balance (SMB: the sum of surface accumulation and surface ablation) and surface elevation in the MAR regional climate model (Edwards et al., 2014) to projections of future climate change using five ice sheet models (ISMs). The MAR (Modèle Atmosphérique Régional: Fettweis, 2007) climate projections are for 2000–2199, forced by the ECHAM5 and HadCM3 global climate models (GCMs) under the SRES A1B emissions scenario. The additional sea level contribution due to the SMB–elevation feedback averaged over five ISM projections for ECHAM5 and three for HadCM3 is 4.3% (best estimate; 95% credibility interval 1.8–6.9%) at 2100, and 9.6% (best estimate; 95% credibility interval 3.6–16.0%) at 2200. In all results the elevation feedback is significantly positive, amplifying the GrIS sea level contribution relative to the MAR projections in which the ice sheet topography is fixed: the lower bounds of our 95% credibility intervals (CIs) for sea level contributions are larger than the "no feedback" case for all ISMs and GCMs. Our method is novel in sea level projections because we propagate three types of modelling uncertainty – GCM and ISM structural uncertainties, and elevation feedback parameterisation uncertainty – along the causal chain, from SRES scenario to sea level, within a coherent experimental design and statistical framework. The relative contributions to uncertainty depend on the timescale of interest. At 2100, the GCM uncertainty is largest, but by 2200 both the ISM and parameterisation uncertainties are larger. We also perform a perturbed parameter ensemble with one ISM to estimate the shape of the projected sea level probability distribution; our results indicate that the probability density is slightly skewed towards higher sea level contributions.

We present a new parameterisation that relates surface mass balance (SMB: the sum of surface accumulation and surface ablation) to changes in surface elevation of the Greenland ice sheet (GrIS) for the MAR (Modèle Atmosphérique Régional: Fettweis, 2007) regional climate model. The motivation is to dynamically adjust SMB as the GrIS evolves, allowing us to force ice sheet models with SMB simulated by MAR while incorporating the SMB–elevation feedback, without the substantial technical challenges of coupling ice sheet and climate models. This also allows us to assess the effect of elevation feedback uncertainty on the GrIS contribution to sea level, using multiple global climate and ice sheet models, without the need for additional, expensive MAR simulations. We estimate this relationship separately below and above the equilibrium line altitude (ELA, separating negative and positive SMB) and for regions north and south of 77° N, from a set of MAR simulations in which we alter the ice sheet surface elevation. These give four "SMB lapse rates", gradients that relate SMB changes to elevation changes. We assess uncertainties within a Bayesian framework, estimating probability distributions for each gradient from which we present best estimates and credibility intervals (CI) that bound 95% of the probability. Below the ELA our gradient estimates are mostly positive, because SMB usually increases with elevation: 0.56 (95% CI: −0.22 to 1.33) kg m−3 a−1 for the north, and 1.91 (1.03 to 2.61) kg m−3 a−1 for the south. Above the ELA, the gradients are much smaller in magnitude: 0.09 (−0.03 to 0.23) kg m−3 a−1 in the north, and 0.07 (−0.07 to 0.59) kg m−3 a−1 in the south, because SMB can either increase or decrease in response to increased elevation. Our statistically founded approach allows us to make probabilistic assessments for the effect of elevation feedback uncertainty on sea level projections (Edwards et al., 2014).

Four high-resolution regional climate models (RCMs) have been set up for the area of Greenland, with the aim of providing future projections of Greenland ice sheet surface mass balance (SMB), and its contribution to sea level rise, with greater accuracy than is possible from coarser-resolution general circulation models (GCMs). This is the first time an intercomparison has been carried out of RCM results for Greenland climate and SMB. Output from RCM simulations for the recent past with the four RCMs is evaluated against available observations. The evaluation highlights the importance of using a detailed snow physics scheme, especially regarding the representations of albedo and meltwater refreezing. Simulations with three of the RCMs for the 21st century using SRES scenario A1B from two GCMs produce trends of between −5.5 and −1.1 Gt yr−2 in SMB (equivalent to +0.015 and +0.003 mm sea level equivalent yr−2), with trends of smaller magnitude for scenario E1, in which emissions are mitigated. Results from one of the RCMs whose present-day simulation is most realistic indicate that an annual mean near-surface air temperature increase over Greenland of ~ 2°C would be required for the mass loss to increase such that it exceeds accumulation, thereby causing the SMB to become negative, which has been suggested as a threshold beyond which the ice sheet would eventually be eliminated.