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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).

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 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 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.