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The land ice contribution to global mean sea level rise has not yet been predicted1 using ice sheet and glacier models for the latest set of socio-economic scenarios, nor using coordinated exploration of uncertainties arising from the various computer models involved. Two recent international projects generated a large suite of projections using multiple models2-8, but primarily used previous-generation scenarios9 and climate models10, and could not fully explore known uncertainties. Here we estimate probability distributions for these projections under the new scenarios11,12 using statistical emulation of the ice sheet and glacier models. We find that limiting global warming to 1.5 degrees Celsius would halve the land ice contribution to twenty-first-century sea level rise, relative to current emissions pledges. The median decreases from 25 to 13 centimetres sea level equivalent (SLE) by 2100, with glaciers responsible for half the sea level contribution. The projected Antarctic contribution does not show a clear response to the emissions scenario, owing to uncertainties in the competing processes of increasing ice loss and snowfall accumulation in a warming climate. However, under risk-averse (pessimistic) assumptions, Antarctic ice loss could be five times higher, increasing the median land ice contribution to 42 centimetres SLE under current policies and pledges, with the 95th percentile projection exceeding half a metre even under 1.5 degrees Celsius warming. This would severely limit the possibility of mitigating future coastal flooding. Given this large range (between 13 centimetres SLE using the main projections under 1.5 degrees Celsius warming and 42 centimetres SLE using risk-averse projections under current pledges), adaptation planning for twenty-first-century sea level rise must account for a factor-of-three uncertainty in the land ice contribution until climate policies and the Antarctic response are further constrained.

Global sea level provides an important indicator of the state of the warming climate, but changes in regional sea level are most relevant for coastal communities around the world. With improvements to the sea-level observing system, the knowledge of regional sea-level change has advanced dramatically in recent years. Satellite measurements coupled with in situ observations have allowed for comprehensive study and improved understanding of the diverse set of drivers that lead to variations in sea level in space and time. Despite the advances, gaps in the understanding of contemporary sea-level change remain and inhibit the ability to predict how the relevant processes may lead to future change. These gaps arise in part due to the complexity of the linkages between the drivers of sea-level change. Here we review the individual processes which lead to sea-level change and then describe how they combine and vary regionally. The intent of the paper is to provide an overview of the current state of understanding of the processes that cause regional sea-level change and to identify and discuss limitations and uncertainty in our understanding of these processes. Areas where the lack of understanding or gaps in knowledge inhibit the ability to provide the needed information for comprehensive planning efforts are of particular focus. Finally, a goal of this paper is to highlight the role of the expanded sea-level observation network-particularly as related to satellite observations-in the improved scientific understanding of the contributors to regional sea-level change.

Earlier large-scale Greenland ice sheet sea-level projections (e.g., those run during the ice2sea and SeaRISE initiatives) have shown that ice sheet initial conditions have a large effect on the projections and give rise to important uncertainties. The goal of the initMIP-Greenland intercomparison exercise is to compare, evaluate and improve the initialisation techniques used in the ice sheet modelling community and to estimate the associated uncertainties in modelled mass changes. initMIP-Greenland is the first in a series of ice sheet model intercomparison activities within ISMIP6 (the Ice Sheet Model Intercomparison Project for CMIP6), which is the primary activity within the Coupled Model Intercomparison Project - phase 6 (CMIP6) focusing on the ice sheets. Two experiments for the large-scale Greenland ice sheet have been designed to allow intercomparison between participating models of 1) the initial present-day state of the ice sheet and 2) the response in two idealised forward experiments. The forward experiments serve to evaluate the initialisation in terms of model drift (forward run without additional forcing) and in response to a large perturbation (prescribed surface mass balance anomaly), and should not be interpreted as sea-level projections. We present and discuss results that highlight the diversity of data sets, boundary conditions and initialisation techniques used in the community to generate initial states of the Greenland ice sheet. We find good agreement across the ensemble for the dynamic response to surface mass balance changes in areas where the simulated ice sheets overlap, but differences arising from the initial size of the ice sheet. The model drift in the control experiment is reduced for models that participated in earlier intercomparison exercises.

Estimating the future evolution of the Antarctic Ice Sheet (AIS) is critical for improving future sea level rise (SLR) projections. Numerical ice sheet models are invaluable tools for bounding Antarctic vulnerability; yet, few continental-scale projections of century-scale AIS SLR contribution exist, and those that do vary by up to an order of magnitude. This is partly because model projections of future sea level are inherently uncertain and depend largely on the model's boundary conditions and climate forcing, which themselves are unknown due to the uncertainty in the projections of future anthropogenic emissions and subsequent climate response. Here, we aim to improve the understanding of how uncertainties in model forcing and boundary conditions affect ice sheet model simulations. With use of sampling techniques embedded within the Ice Sheet System Model (ISSM) framework, we assess how uncertainties in snow accumulation, ocean-induced melting, ice viscosity, basal friction, bedrock elevation, and the presence of ice shelves impact continental-scale 100-year model simulations of AIS future sea level contribution. Overall, we find that AIS sea level contribution is strongly affected by grounding line retreat, which is driven by the magnitude of ice shelf basal melt rates and by variations in bedrock topography. In addition, we find that over 1.2 m of AIS global mean sea level contribution over the next century is achievable, but not likely, as it is tenable only in response to unrealistically large melt rates and continental ice shelf collapse. Regionally, we find that under our most extreme 100-year warming experiment generalized for the entire ice sheet, the Amundsen Sea sector is the most significant source of model uncertainty (1032 mm 6σ spread) and the region with the largest potential for future sea level contribution (297 mm). In contrast, under a more plausible forcing informed regionally by literature and model sensitivity studies, the Ronne basin has a greater potential for local increases in ice shelf basal melt rates. As a result, under this more likely realization, where warm waters reach the continental shelf under the Ronne ice shelf, it is the Ronne basin, particularly the Evans and Rutford ice streams, that are the greatest contributors to potential SLR (161 mm) and to simulation uncertainty (420 mm 6spread).

Identifying fast and robust numerical solvers is a critical issue that needs to be addressed in order to improve projections of polar ice sheets evolving in a changing climate. This work evaluates the impact of using advanced numerical solvers for transient ice-flow simulations conducted with the JPL-UCI Ice Sheet System Model (ISSM). We identify optimal numerical solvers by testing a broad suite of readily available solvers, ranging from direct sparse solvers to preconditioned iterative methods, on the commonly used Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models benchmark tests. Three types of analyses are considered: mass transport, horizontal stress balance, and incompressibility. The results of the fastest solvers for each analysis type are ranked based on their scalability across mesh size and basal boundary conditions. We find that the fastest iterative solvers are ĝ1/4ĝ€1.5-100 times faster than the default direct solver used in ISSM, with speed-ups improving rapidly with increased mesh resolution. We provide a set of recommendations for users in search of efficient solvers to use for transient ice-flow simulations, enabling higher-resolution meshes and faster turnaround time. The end result will be improved transient simulations for short-term, highly resolved forward projections (10-100 year time scale) and also improved long-term paleo-reconstructions using higher-order representations of stresses in the ice. This analysis will also enable a new generation of comprehensive uncertainty quantification assessments of forward sea-level rise projections, which rely heavily on ensemble or sampling approaches that are inherently expensive.

Abstract. Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model, written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of ISSM. We present a comprehensive approach to 1) carry out type changing through ISSM, hence facilitating operator overloading, 2) bind to external solvers such as MUMPS and GSL-LU and 3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the North-East Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, Central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential of enabling a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected in Greenland and Antarctica, such as surface altimetry, surface velocities, and/or gravity measurements.

The increasing contribution of the Antarctic Ice Sheet to sea level rise is linked to reductions in ice shelf buttressing, driven in large part by basal melting of ice shelves. These ocean-driven buttressing losses are being compounded as ice shelves weaken and fracture. To date, model projections of ice sheet evolution have not accounted for weakening ice shelves. Here we present the first constitutive framework for ice deformation that explicitly includes mechanical weakening, based on observations of the progressive degradation of the remnant Larsen B Ice Shelf from 2000 to 2015. We implement this framework in an ice sheet model and are able to reproduce most of the observed weakening of the ice shelf. In addition to predicting ice shelf weakening and reduced buttressing, this new framework opens the door for improved understanding and predictions of iceberg calving, meltwater routing and hydrofracture, and ice shelf collapse.

Calving is a major mechanism of ice discharge of the Antarctic and Greenland ice sheets, and a change in calving front position affects the entire stress regime of marine terminating glaciers. The representation of calving front dynamics in a 2-D or 3-D ice sheet model remains non-trivial. Here, we present the theoretical and technical framework for a level-set method, an implicit boundary tracking scheme, which we implement into the Ice Sheet System Model (ISSM). This scheme allows us to study the dynamic response of a drainage basin to user-defined calving rates. We apply the method to Jakobshavn Isbræ, a major marine terminating outlet glacier of the West Greenland Ice Sheet. The model robustly reproduces the high sensitivity of the glacier to calving, and we find that enhanced calving triggers significant acceleration of the ice stream. Upstream acceleration is sustained through a combination of mechanisms. However, both lateral stress and ice influx stabilize the ice stream. This study provides new insights into the ongoing changes occurring at Jakobshavn Isbræ and emphasizes that the incorporation of moving boundaries and dynamic lateral effects, not captured in flow-line models, is key for realistic model projections of sea level rise on centennial timescales.

Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM), written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written, but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of the ISSM. We present a comprehensive approach to (1) carry out type changing through the ISSM, hence facilitating operator overloading, (2) bind to external solvers such as MUMPS and GSL-LU, and (3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the northeastern Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential to enable a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected, in Greenland and Antarctica.

The Ice Sheet System Model (ISSM) team, which is funded primarily by NASA (Cryosphere and Modeling, Analysis and Prediction programs), as well as the Jet Propulsion Laboratory, University of California, Irvine, and National Science Foundation's Office of Polar Programs, organized a workshop in collaboration with the Bjerknes Centre for Climate Research (BCCR) at the University of Bergen in Norway, in June 2014.

The Sea-level Response to Ice Sheet Evolution (SeaRISE) effort explores the sensitivity of the current generation of ice sheet models to external forcing to gain insight into the potential future contribution to sea level from the Greenland and Antarctic ice sheets. All participating models simulated the ice sheet response to three types of external forcings: a change in oceanic condition, a warmer atmospheric environment, and enhanced basal lubrication. Here an analysis of the spatial response of the Greenland ice sheet is presented, and the impact of model physics and spin-up on the projections is explored. Although the modeled responses are not always homogeneous, consistent spatial trends emerge from the ensemble analysis, indicating distinct vulnerabilities of the Greenland ice sheet. There are clear response patterns associated with each forcing, and a similar mass loss at the full ice sheet scale will result in different mass losses at the regional scale, as well as distinct thickness changes over the ice sheet. All forcings lead to an increased mass loss for the coming centuries, with increased basal lubrication and warmer ocean conditions affecting mainly outlet glaciers, while the impacts of atmospheric forcings affect the whole ice sheet. Key Points Sensitivity study of Greenland to atmospheric, oceanic and subglacial forcings Each forcing result in a different regional thickness response All forcings lead to an increased mass loss for the coming centuries ©2013. American Geophysical Union. All Rights Reserved.

Atmospheric, oceanic, and subglacial forcing scenarios from the Sea-level Response to Ice Sheet Evolution (SeaRISE) project are applied to six three-dimensional thermomechanical ice-sheet models to assess Antarctic ice sheet sensitivity over a 500 year timescale and to inform future modeling and field studies. Results indicate (i) growth with warming, except within low-latitude basins (where inland thickening is outpaced by marginal thinning); (ii) mass loss with enhanced sliding (with basins dominated by high driving stresses affected more than basins with low-surface-slope streaming ice); and (iii) mass loss with enhanced ice shelf melting (with changes in West Antarctica dominating the signal due to its marine setting and extensive ice shelves; cf. minimal impact in the Terre Adelie, George V, Oates, and Victoria Land region of East Antarctica). Ice loss due to dynamic changes associated with enhanced sliding and/or sub-shelf melting exceeds the gain due to increased precipitation. Furthermore, differences in results between and within basins as well as the controlling impact of sub-shelf melting on ice dynamics highlight the need for improved understanding of basal conditions, grounding-zone processes, ocean-ice interactions, and the numerical representation of all three. Key Points Sensitivity study of Antarctica to atmospheric, oceanic and subglacial forcings Different sectors of Antarctica are vulnerable to the forcings Atmospheric forcing lead to a growth, but dynamic forcing lead to a mass loss ©2013. American Geophysical Union. All Rights Reserved.

Ice flow numerical models are essential for predicting the evolution of ice sheets in a warming climate. Recent research emphasizes the need for higher-order and even full-Stokes flow models, instead of the traditional shallow-ice approximation, whose assumptions are not valid in certain critical areas. These higher-order models are, however, computationally intensive and difficult to use at the continental scale. Here we present a new technique, the Tiling method, to couple ice flow models of varying orders of complexity. The goal of the method is to limit the spatial extent of where higherorder models are applied to reduce the computational cost, while maintaining the model precision. We apply this method on synthetic geometries to demonstrate its practical use. We first use a geometry for which all models yield the same results to check the consistency of the method. Then we apply our method to a geometry for which a full-Stokes model is required in the vicinity of the ice front. Our results show that the hybrid models present significant improvements over mono-model approaches and reduce computational times.