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We produce projections of global mean sea-level rise to 2500 for low and medium emissions scenarios (Shared Socioeconomic Pathways SSP1-2.6 and SSP2-4.5), based on extending and combining model ensemble data from current literature. We find that emissions have a large effect on sea-level rise on these long timescales, with a difference of 0.95 m at 2300 and 1.40 m at 2500 between the medians for the two scenarios. The largest and most uncertain component is the Antarctic ice sheet, projected to contribute median and 5-95% intervals of 0.86 [0.40, 1.57] m by 2500 under SSP1-2.6 and 1.44 [0.68, 2.71] m under SSP2-4.5. We discuss how the simple statistical extensions used here could be replaced with more physically-based methods for more robust predictions. We show that, despite their uncertainties, current multi-centennial projections combined into multi-study projections as presented here can be used to avoid future ‘lock-ins’ in terms of risk and adaptation needs to sea-level rise.

<p>The Antarctic ice sheet has the potential to be a major contributor to future global sea level rise, but this has been difficult to predict, in part due to the combination of expected ice mass loss and snowfall accumulation. A great deal of uncertainty arises from the large variation of atmospheric and oceanic changes across climate models, and sensitivity to ocean changes across ice sheet models, but these uncertainties cannot be fully sampled because the models are too computationally expensive.</p><p>Here we make projections of Antarctica’s contribution to global sea level rise based on the simulations of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6). Using a Gaussian process emulator, a statistical approximation of expensive computer models, we estimate probability distributions by sampling uncertainties in future climate and ice sheet sensitivity to ocean warming far more thoroughly than the original ISMIP6 ensemble could. We find a sea level contribution of 4 cm (5<sup>th</sup>-95th percentile range -5 to 14 cm) sea level equivalent by 2100 under current emissions policies, increasing to 21 cm (5<sup>th</sup>-95th percentile range 7 to 43 cm) if we use the subset of climate models, ice sheet models and ice sheet/ocean sensitivity values that lead to the highest sea level contributions.</p><p>We then compare the output from this emulator to a linear mixed model emulator, which  incorporates a random effect to represent the variation arising from different ice sheet models. We do this for all three Antarctic regions (West and East Antarctica, and the Peninsula) under two greenhouse emissions scenarios (SSP1-26 and SSP5-85). Both methods produce similar probability distributions of sea level contribution in 2100, demonstrating that differences in statistical models are not dominating the results.</p>

<div> <div> <div> <p>Better understanding changes in the cryosphere is key to predicting future global sea level rise, as is being done in the PROTECT project (https://protect-slr.eu). There are large uncertainties around how these changes will present over the next few centuries, with the Antarctic ice sheet being the component with the most varied predictions of potential mass change; statistical methods are required in order to quantify this uncertainty and estimate more robust projections.</p> <p>We present here results from a multivariate Gaussian process emulator (Rougier, 2008; Rougier et al., 2009) of an ensemble of ice sheet and glacier models. We build projec- tions of contributions to global sea level rise over several centuries from the Antarctic and Greenland ice sheets, and the world’s glaciers, emulating them individually in order to better understand the biases and internal variability each model contains. Our use of an outer-product emulator allows us to model multi-variate output, resulting in projections over several centuries rather than a single year at a time. We predict changes for differ- ent Shared Socioeconomic Pathways (SSPs) to show how different emissions scenarios will affect land ice contributions to sea level rise, and demonstrate the differing sensitivity to parameters and forcings of the ensemble of models used.</p> <p>References</p> <p>Rougier, J. (2008). Efficient emulators for multivariate deterministic functions. Journal of Computational and Graphical Statistics, 17(4):827–843.</p> <p>Rougier, J., Guillas, S., Maute, A., and Richmond, A. D. (2009). Expert knowledge and multivariate emulation: The thermosphere–ionosphere electrodynamics general circula- tion model (tie-gcm). Technometrics, 51(4):414–424.</p> </div> </div> </div>

<p>Understanding the effect warming has on ice sheets is vital for accurate projections of climate change. A better understanding of how the Antarctic ice sheets have changed size and shape in the past would allow us to improve our predictions of how they may adapt in the future; this is of particular relevance in predicting future global sea level changes. This research makes use of previous reconstructions of the ice sheets, ice core data and Bayesian methods to create a model of the Antarctic ice sheet at the Last Glacial Maximum (LGM). We do this by finding the relationship between the ice sheet shape and water isotope values. </p><p>We developed a prior model which describes the variation between a set of ice sheet reconstructions at the LGM. A set of ice sheet shapes formed using this model was determined by a consultation with experts and run through the general circulation model HadCM3, providing us with paired data sets of ice sheet shapes and water isotope estimates. The relationship between ice sheet shape and water isotopes is explored using a Gaussian process emulator of HadCM3, building a statistical distribution describing the shape of the ice sheets given the isotope values outputted by the climate model. We then use MCMC to sample from the posterior distribution of the ice sheet shape and attempt to find a shape that creates isotopic values matching as closely as possible to the observations collected from ice cores. This allows us to quantify the uncertainty in the shape and incorporate expert beliefs about the Antarctic ice sheet during this time period. Our results suggests that there may have been a thicker West Antarctic ice sheet at the LGM than previously estimated.</p>