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A model of the four main outlet glaciers that drain the Greenland Ice Sheet predicts that they will contribute 19 to 30 millimetres to sea-level rise by 2200 in a mid-range future warming scenario, and 29 to 49 millimetres in a more extreme scenario. Greenland's role in sea-level rise revisited Recent dramatic acceleration of ice loss from the Greenland Ice Sheet has raised concerns about the possibility of runaway ice loss and consequent sea-level rise. Now Faezeh Nick and colleagues simulate the dynamics of ice movement for four of Greenland's largest outlet glaciers to 2200 using a model that takes account of the complicated dynamics that operate at the ice–ocean interface, such as calving and submarine melting. They find that in spite of several bursts of retreat, the current rate of acceleration of ice loss is unlikely to continue. This suggests that the contribution of the Greenland Ice Sheet to sea-level rise is likely to be considerably less than the upper limit of previous estimates. Over the past decade, ice loss from the Greenland Ice Sheet increased as a result of both increased surface melting and ice discharge to the ocean 1 , 2 . The latter is controlled by the acceleration of ice flow and subsequent thinning of fast-flowing marine-terminating outlet glaciers 3 . Quantifying the future dynamic contribution of such glaciers to sea-level rise (SLR) remains a major challenge because outlet glacier dynamics are poorly understood 4 . Here we present a glacier flow model that includes a fully dynamic treatment of marine termini. We use this model to simulate behaviour of four major marine-terminating outlet glaciers, which collectively drain about 22 per cent of the Greenland Ice Sheet. Using atmospheric and oceanic forcing from a mid-range future warming scenario that predicts warming by 2.8 degrees Celsius by 2100, we project a contribution of 19 to 30 millimetres to SLR from these glaciers by 2200. This contribution is largely (80 per cent) dynamic in origin and is caused by several episodic retreats past overdeepenings in outlet glacier troughs. After initial increases, however, dynamic losses from these four outlets remain relatively constant and contribute to SLR individually at rates of about 0.01 to 0.06 millimetres per year. These rates correspond to ice fluxes that are less than twice those of the late 1990s, well below previous upper bounds 5 . For a more extreme future warming scenario (warming by 4.5 degrees Celsius by 2100), the projected losses increase by more than 50 per cent, producing a cumulative SLR of 29 to 49 millimetres by 2200.

Marine sediment records from the Oligocene and Miocene reveal clear 400,000-year climate cycles related to variations in orbital eccentricity. These cycles are also observed in the Plio-Pleistocene records of the global carbon cycle. However, they are absent from the Late Pleistocene ice-age record over the past 1.5 million years. Here we present a simulation of global ice volume over the past 5 million years with a coupled system of four three-dimensional ice-sheet models. Our simulation shows that the 400,000-year long eccentricity cycles of Antarctica vary coherently with δ 13 C data during the Pleistocene, suggesting that they drove the long-term carbon cycle changes throughout the past 35 million years. The 400,000-year response of Antarctica was eventually suppressed by the dominant 100,000-year glacial cycles of the large ice sheets in the Northern Hemisphere. The precise contributions of solar forcing, the carbon cycle and glaciation to the pacing of global climate remains unresolved. Using four 3D ice-sheet models, de Boer et al. show that Antarctic ice volume and carbon-cycle dynamics varied coherently during the Pleistocene, as has been observed in the Miocene.

The accurate quantification of uncertainties in regional sea-level projections is essential for guiding policy makers. As climate models do not currently simulate total sea level, these uncertainties must be quantified through summation of uncertainties in individual sea-level components. This summation depends on the correlation between the components, which has previously been prescribed or derived from each individual component's dependence on global mean surface temperature. In this study, we quantify, for the first time, regional correlations between sea-level components based on regional climate change projections. We compute regional sea-level projections consistent with climate projections from an ensemble of 14 Earth System Models. From the multi-model spread, we estimate the uncertainty in the regional climate's response to greenhouse forcing. To quantify the total uncertainty, we add the uncertainty in the response of sea-level components to this regional climate change. This approach reveals how regional climate processes impose correlations between sea-level components, affecting the total uncertainty. One example is an anti-correlation between North Atlantic sterodynamic change and Antarctic dynamic mass loss, suggesting a teleconnection established by the large-scale ocean circulation. We find that prescribed correlations, applied in the fifth assessment report of the Intergovernmental Panel on Climate Change, lead to a global overestimation in the uncertainty in regional sea-level projections on the order of 20%. Regionally, this overestimation exceeds 100%. We conclude that accurate uncertainty estimates of regional sea-level change must be based on projections of regional climate change and cannot be derived from global indicators such as global mean surface temperature.

Climate ups and downs The climate has passed through a series of glacials and interglacials over the past million years, but the nature of this cyclicity (in terms of temperature, ice volume and sea level), and the underlying causes, are not well known. Bintanja et al . use a new method to deduce a one-million-year time series of these variables. The reconstructed records are much longer than other methods have provided for any of these variables individually. The most intense glacial stages were 17 °C colder than today, and most of the continental ice was present in North America. Strong cooling in the beginning of glacials was found to precede ice-sheet build-up. These findings may shed light on the causes of ice age cycles. Marine records of sediment oxygen isotope compositions show that the Earth's climate has gone through a succession of glacial and interglacial periods during the past million years. But the interpretation of the oxygen isotope records is complicated because both isotope storage in ice sheets and deep-water temperature affect the recorded isotopic composition 1 , 2 , 3 , 4 , 5 . Separating these two effects would require long records of either sea level or deep-ocean temperature, which are currently not available. Here we use a coupled model of the Northern Hemisphere ice sheets 6 and ocean temperatures, forced to match an oxygen isotope record for the past million years compiled from 57 globally distributed sediment cores, to quantify both contributions simultaneously. We find that the ice-sheet contribution to the variability in oxygen isotope composition varied from ten per cent in the beginning of glacial periods to sixty per cent at glacial maxima, suggesting that strong ocean cooling preceded slow ice-sheet build-up. The model yields mutually consistent time series of continental mean surface temperatures between 40 and 80° N, ice volume and global sea level. We find that during extreme glacial stages, air temperatures were 17 ± 1.8 °C lower than present, with a 120 ± 10 m sea level equivalent of continental ice present.

Sea-level rise magnifies flood hazards, raising the question when adaptation measures need to be taken. Here, we quantify when the recurrence of extreme water level events will double due to projected sea-level rise. Reproducing the most common method based on extreme water levels observed with tide gauges, at least one third of the coastal locations are to expect a doubling of extremes within a decade. However, tide gauges are commonly placed in wave-sheltered harbours where the contribution of waves to water levels is much smaller than at nearby wave-exposed coastlines such as beaches and dikes. In this study, we quantify doubling times at a variety of idealised shorelines based on modelled tides, storm surges and waves. We apply an extreme value analysis that accounts for the joint probability of extreme storm surges and extreme waves. Our results indicate that doubling times at wave-exposed shorelines are longer than those in wave-sheltered harbours, allowing for more time to adapt to magnified flood hazards. The median doubling times of average water levels including parameterised wave set-up are 1.2 to 5 times longer than those of still water levels as observed with tide gauges. For instantaneous water levels including wave run-up, doubling times are an additional 30% to 100% longer. We conclude that tide gauge-based analyses underestimate adaptation times by underestimating the contribution of waves to extreme water levels, and provide a quantitative framework to guide adaptation policy at wave-exposed shorelines.

Ice-dynamical processes constitute a large uncertainty in future projections of sea-level rise caused by anthropogenic climate change. Improving our understanding of these processes requires ice-sheet models that perform well at simulating both past and future ice-sheet evolution. Here, we present version 2.0 of the ice-sheet model IMAU-ICE, which uses the depth-integrated viscosity approximation (DIVA) to solve the stress balance. We evaluate its performance in a range of benchmark experiments, including simple analytical solutions and both schematic and realistic model intercomparison exercises. IMAU-ICE has adopted recent developments in the numerical treatment of englacial stress and sub-shelf melt near the grounding line, which result in good performance in experiments concerning grounding-line migration (MISMIP, MISMIP+) and buttressing (ABUMIP). This makes it a model that is robust, versatile, and user-friendly, which will provide a firm basis for (palaeo-)glaciological research in the coming years.

Antarctic Ice Sheet elevation changes, which are used to estimate changes in the mass of the interior regions, are caused by variations in the depth of the firn layer. We quantified the effects of temperature and accumulation variability on firn layer thickness by simulating the 1980-2004 Antarctic firn depth variability. For most of Antarctica, the magnitudes of firn depth changes were comparable to those of observed ice sheet elevation changes. The current satellite observational period (~15 years) is too short to neglect these fluctuations in firn depth when computing recent ice sheet mass changes. The amount of surface lowering in the Amundsen Sea Embayment revealed by satellite radar altimetry (1995-2003) was increased by including firn depth fluctuations, while a large area of the East Antarctic Ice Sheet slowly grew as a result of increased accumulation.

Purpose of Review This paper reviews the recent literature on numerical modelling of the dynamics of the Greenland ice sheet with the goal of providing an overview of advancements and to highlight important directions of future research. In particular, the review is focused on large-scale modelling of the ice sheet, including future projections, model parameterisations, paleo applications and coupling with models of other components of the Earth system. Recent Findings Data assimilation techniques have been used to improve the reliability of model simulations of the Greenland ice sheet dynamics, including more accurate initial states, more comprehensive use of remote sensing as well as paleo observations and inclusion of additional physical processes. Summary Modellers now leverage the increasing number of high-resolution satellite and air-borne data products to initialise ice sheet models for centennial time-scale simulations, needed for policy relevant sea-level projections. Modelling long-term past and future ice sheet evolution, which requires simplified but adequate representations of the interactions with the other components of the Earth system, has seen a steady improvement. Important developments are underway to include ice sheets in climate models that may lead to routine simulation of the fully coupled Greenland ice sheet–climate system in the coming years.

Improving our confidence in future projections of sea-level rise requires models that can simulate ice-sheet evolution both in the future and in the geological past. A physically accurate treatment of large changes in ice-sheet geometry requires a proper treatment of processes near the margin, like grounding line dynamics, which in turn requires a high spatial resolution in that specific region, so that small-scale topographical features are resolved. This leads to a demand for computationally efficient models, where such a high resolution can be feasibly applied in simulations of 105–107 years in duration. Here, we present and evaluate a new ice-sheet model that solves the hybrid SIA–SSA approximation of the stress balance, including a heuristic rule for the grounding-line flux. This is done on a dynamic adaptive mesh which is adapted to the modelled ice-sheet geometry during a simulation. Mesh resolution can be configured to be fine only at specified areas, such as the calving front or the grounding line, as well as specified point locations such as ice-core drill sites. This strongly reduces the number of grid points where the equations need to be solved, increasing the computational efficiency. A high resolution allows the model to resolve small geometrical features, such as outlet glaciers and sub-shelf pinning points, which can significantly affect large-scale ice-sheet dynamics. We show that the model reproduces the analytical solutions or model intercomparison benchmarks for a number of schematic ice-sheet configurations, indicating that the numerical approach is valid. Because of the unstructured triangular mesh, the number of vertices increases less rapidly with resolution than in a square-grid model, greatly reducing the required computation time for high resolutions. A simulation of all four continental ice sheets during an entire 120 kyr glacial cycle, with a 4 km resolution near the grounding line, is expected to take 100–200 wall clock hours on a 16-core system (1600–3200 core hours), implying that this model can be feasibly used for high-resolution palaeo-ice-sheet simulations.

Sea-level science has seen many recent developments in observations and modelling of the different contributions and the total mean sea-level change. In this overview, we discuss (1) the evolution of the Intergovernmental Panel on Climate Change (IPCC) projections, (2) how the projections compare to observations and (3) the outlook for further improving projections. We start by discussing how the model projections of 21st century sea-level change have changed from the IPCC AR5 report (2013) to SROCC (2019) and AR6 (2021), highlighting similarities and differences in the methodologies and comparing the global mean and regional projections. This shows that there is good agreement in the median values, but also highlights some differences. In addition, we discuss how the different reports included high-end projections. We then show how the AR5 projections (from 2007 onwards) compare against the observations and find that they are highly consistent with each other. Finally, we discuss how to further improve sea-level projections using high-resolution ocean modelling and recent vertical land motion estimates.