Figure 5: Large Ensemble model analyses of future Antarctic contributions to GMSL. a, RCP ensembles to 2500. b, RCP ensembles to 2100. Changes in GMSL are shown relative to 2000, although the simulations begin in 1950. Ensemble members use combinations of model parameters (Methods) filtered according to their ability to satisfy two geologic criteria: a Pliocene target of 10–20 m GMSL and a LIG target of 3.6–7.4 m. c and d are the same as a and b, but use a lower Pliocene GMSL target of 5–15 m. Solid lines are ensemble means, and the shaded areas show the standard deviation (1σ) of the ensemble members. The 1σ ranges represent the model’s parametric uncertainty, while the alternate Pliocene targets (a and b versus c and d) illustrate the uncertainty related to poorly constrained Pliocene sea-level targets. Mean values and 1σ uncertainties at 2500 and 2100 are shown.
Long-term commitment to elevated sea level
Ocean warming alone may be limited in its potential to trigger massive, widespread ice loss, but the multi-millennial thermal response time of the ocean47 will have a profound influence on the ice sheet’s recovery. In simulations run 5,000 years into the future, we conservatively assume no ocean warming beyond 2300 and simply maintain those ocean temperatures while the atmosphere cools assuming different scenarios of CO2 drawdown beginning in 2500 (Methods). For RCP8.5 and natural CO2 drawdown, GMSL continues to rise until 3500 with a peak of about 20 m, after which the warm ocean inhibits the re-advance of grounding lines into deep marine basins for thousands of years (Extended Data Fig. 7). Even in the moderate RCP4.5 scenario with rapidly declining CO2 after 2500, WAIS is unable to recover until the global ocean cools, implying a multi-millennial commitment to several metres of sea-level rise despite human-engineered CO2 drawdown.
Given uncertainties in model initial conditions, simplified hybrid ice dynamics, parameterized sub-ice melt, calving, structural ice-margin failure, and the ancient sea-level estimates used in our Large Ensemble analysis, the rates of ice loss simulated here should not be viewed as actual predictions, but rather as possible envelopes of behaviour (Fig. 5) that include processes not previously considered at the continental scale. These are among the first continental-scale simulations with model physics constrained by ancient sea-level estimates, simultaneously accounting for high-resolution atmosphere–ice sheet coupling and ocean model temperatures.
However, several important processes are lacking and should be included in future work. In particular, the model lacks two-way coupling between the ice sheet and the ocean. This is especially relevant for RCP8.5, in which >1 Sv of freshwater and icebergs would be supplied to the Southern Ocean during peak retreat (Extended Data Fig. 8). Rapid calving and ice-margin collapse also implies ice mélange in restricted embayments that could provide buttressing and a negative feedback on retreat. The loss of ice mass would also have a strong effect on relative sea level at the margin owing to gravitational and solid-earth deformation effects48, which could affect MISI and MICI dynamics because of their strong dependency on bathymetry. Future simulations should include coupling with Earth models that account for these processes. Improved ancient sea-level estimates are also needed to further constrain model physics and to reduce uncertainties in future RCP scenarios (Fig. 5).
Despite these limitations, our new model physics are shown to be capable of simulating two very different ancient sea-level events: the LIG, driven primarily by ocean warming and MISI dynamics, and the warmer Pliocene, in which surface meltwater and MICI dynamics are also important. When applied to future scenarios with high greenhouse gas emissions, our palaeo-filtered model ensembles show the potential for Antarctica to contribute >1 m of GMSL rise by the end of this century, and >15 m metres of GMSL rise in the next 500 years. In RCP8.5, the projected onset of major ice-sheet retreat occurs sooner (about 2050), and is substantially faster (>4 cm yr−1 after 2100) and higher (Figs 4 and 5) than implied by other recent studies44,45,49. These differences are mainly due to our addition of model physics linking surface meltwater and ice dynamics via hydrofracturing of buttressing ice shelves and structural failure of marine-terminating ice cliffs. In addition, we use (1) freely evolving grounding-line dynamics that preclude the need for empirically calibrated retreat rates49, (2) highly resolved atmosphere and ocean model components rather than intermediate-complexity climate models45 or simplified climate forcing44, and (3) calibration based on major retreat during warm palaeoclimates rather than recent minor retreat driven by localized ocean forcing.
As in these prior studies, we also find that ocean-driven melt is an important driver of grounding-line retreat where warm water is in contact with ice shelves, but in scenarios with high greenhouse gas emissions we find that atmospheric warming soon overtakes the ocean as the dominant driver of Antarctic ice loss. Surface meltwater may lead to the ultimate demise of the major buttressing ice shelves (Supplementary Videos 8 and 9) and extensive grounding-line retreat, but it is the long thermal memory of the ocean that will inhibit the recovery of marine-based ice for thousands of years after greenhouse gas emissions are curtailed.
Methods
Ice sheet–ice shelf model
We use an established ice-sheet model, with hybrid ice dynamics following the formulation described in ref. 27, and an internal condition on ice velocity at the grounding line15 that captures MISI (Fig. 2a–c) by accounting for migrating grounding lines and the buttressing effects of ice shelves with pinning points and side shear. Bedrock deformation under changing ice loads is modelled as an elastic lithospheric plate above local isostatic relaxation. A grid resolution of 10 km is used for all simulations, the finest resolution computationally feasible for long-term continental simulations. The model includes newly added treatments of hydrofracturing and ice cliff failure (Fig. 2d–f) described in ref. 25 and extended here. Basal sliding coefficients are determined by an inverse method51, iteratively matching ice-surface elevations to observations until a quasi-equilibrium is reached. In this case, inverted sliding coefficients are derived from a modern (preindustrial) surface climatology, using the same RCM used in our Pliocene, LIG, and future simulations.
In addition to the Pliocene and LIG targets highlighted here, the ice sheet–ice shelf model has been shown capable of simulating: (1) the modern ice sheet, including grounding-line positions, ice thicknesses, velocities, ice streams, and ice shelves (Fig. 1b), (2) the Last Glacial Maximum (LGM) extent27, (3) the timing of post-LGM retreat18, and (4) the ability of the ice sheet to regrow to its modern extent following retreat25.
Calving and hydrofracturing
Calving depends on the combined penetration depths of surface and basal crevasses, relative to total ice thickness23,26,52,53. Crevasse depths are parameterized according to the divergence of the ice velocity field52, with an additional contribution depending on the logarithm of ice speed that crudely represents the accumulated strain history (ice damage) along a flow path25. Rapid calving is imposed as ice thickness falls below 200 m for unconfined embayments. The 200-m criterion is decreased in confined embayments according to 200 × max[0, min[1, (α − 40)/20]], where α is the ‘arc to open ocean’ (in degrees), crudely representing the effects of ice mélange in narrow seaways. The unconfined onset thickness of 200 m was increased from its value of 150 m in ref. 25 in order to improve modern Ross and Weddell Sea calving-front locations. A similar dependence on α is imposed for oceanic sub-ice-shelf melt rates, as described below.
Surface crevasses are additionally deepened (hydrofractured) as they fill with liquid water, which is assumed to depend on the grid-scale runoff of surface melt and rainfall available after refreezing23,53. The crevasse-depth dependence on surface runoff plus rainfall rate R (in metres per year) has been modified slightly for low R values. The R used in equation (B.6) of ref. 25 is changed to:
0 for R < 1.5 m yr^{-1}
4*1.5*(R-1.5) for 1.5 m yr^{-1} < R < 3 m yr^{-1}
R^2 for R > 3 m yr^{-1} (as before)


Calving and hydrofracturing
Calving depends on the combined penetration depths of surface and basal crevasses, relative to total ice thickness23,26,52,53. Crevasse depths are parameterized according to the divergence of the ice velocity field52, with an additional contribution depending on the logarithm of ice speed that crudely represents the accumulated strain history (ice damage) along a flow path25. Rapid calving is imposed as ice thickness falls below 200 m for unconfined embayments. The 200-m criterion is decreased in confined embayments according to 200 × max[0, min[1, (α − 40)/20]], where α is the ‘arc to open ocean’ (in degrees), crudely representing the effects of ice mélange in narrow seaways. The unconfined onset thickness of 200 m was increased from its value of 150 m in ref. 25 in order to improve modern Ross and Weddell Sea calving-front locations. A similar dependence on α is imposed for oceanic sub-ice-shelf melt rates, as described below.
Surface crevasses are additionally deepened (hydrofractured) as they fill with liquid water, which is assumed to depend on the grid-scale runoff of surface melt and rainfall available after refreezing23,53. The crevasse-depth dependence on surface runoff plus rainfall rate R (in metres per year) has been modified slightly for low R values. The R used in equation (B.6) of ref. 25 is changed to:
0 for R < 1.5 m yr^{-1}
4*1.5*(R-1.5) for 1.5 m yr^{-1} < R < 3 m yr^{-1}
R^2 for R > 3 m yr^{-1} (as before)
This supposes that minimal hydrofracturing occurs for relatively small R values. The linear segment between 1.5 m yr−1and 3 m yr−1 intersects the R2 parabola as a tangent at R = 3. This modification prevents small amounts of recession in some East Antarctic basins for modern conditions, where small amounts of summer melt and rainfall occur.
Structural failure of ice cliffs
To account for structural ice-cliff failure26,54 (MICI in Fig. 2), a wastage rate of ice W is applied locally to the grid cell adjacent to tidewater grounding lines with no floating ice, if the required stresses at the exposed cliff face exceed the yield strength of ice. This condition depends on the subaerial cliff height at the interpolated grounding line relative to the maximum ice thickness that can be supported, modified locally to account for any meltwater-enhanced crevasse penetration (hydrofracturing), and any reductions in crevassing caused by backstress. For dry crevassing at an ice margin with no hydrofracturing and no buttressing (backstress), the maximum exposed cliff height is 100 m, assuming an ice yield strength of 1 MPa25,26. The formulation of W results in a steep ramp in wastage rates of 0–3 km yr−1, where exposed ice cliffs ramp from 80 m to 100 m. The maximum wastage rate of 3 km yr−1 used as our default is conservatively chosen, based on recent observations of the Jakobshavn Isbrae Glacier (up to ~12 km yr−1) and the Crane Glacier (~5 km yr−1) following the loss of their ice-buttressing shelves55,56,57.
Other modifications to ice-sheet model physics
The model is modified from ref. 25 to include a more physically based parameterization of the vertical flow of surface mobile liquid water (runoff and rainfall) through moulins and other fracture systems towards the base22,58, which affects the vertical temperature profiles within the ice sheet. Vertical sub-grid-scale columns of liquid water are assumed to exist, through which the water freely drains while exchanging heat by conduction with the surrounding ambient ice that cools and can freeze some or all of the liquid water within the ice interior.
We use uniform parameter values everywhere: we set the fractional area of sub-grid columns to overall area to be 0.1, and the horizontal scale of drainage elements to be 10 m (R in ref. 22, used in the calculations of conductive heat exchange with ambient ice). The fractional area includes both large moulins and any downward movement of liquid water in crevasses or cracks of all scales, which would be prevalent in the future melting scenarios investigated here. Offline sensitivity tests show low sensitivity of our model behaviour to these values, but further investigation is warranted.
For reasonable numerical behaviour, the horizontal heat exchange needs to be part of the time-implicit vertical diffusive heat solution for ambient ice temperature in the main model. To avoid an iterative procedure in cases where all liquid water is frozen before reaching the bed, a time-explicit calculation of the water penetration is made first, and one of the following measures is applied in the time-implicit ice-temperature step: (1) the conductive heat exchange coefficient at all levels is reduced by a constant factor for the column, so that the liquid penetrates to the lowest layer but no further; and (2) the conductive coefficient is set to zero below the depth of furthest penetration. Both methods give very similar results in idealized single-column tests; method (1) was used for all runs here. In cases with greater surface liquid flux, there is no reduction of coefficients and some water reaches the base.
A minor bug fix is corrected in the calculation of vertical velocities within the ice (w′ in ref. 27), which previously did not account for the removal of ice at the base due to oceanic melting. This only affects advection of temperature in ice shelves, and has negligible effects on results.
Ice-sheet initial conditions
Ice-sheet initial conditions and basal sliding coefficients are provided by a 100-kyr inverse simulation following the methodology in ref. 51, using mass-balance forcing provided by a bias-corrected RCM climatology and modern observed ocean temperatures (described below). In the inverse procedure, basal sliding coefficients under modern grounded ice are adjusted iteratively to reduce the misfit with observed ice thickness, with grounding-line positions fixed to observed locations. The LIG simulation using ‘glacial’ initial conditions (Fig. 3) uses the same basal sliding coefficients (along with a relatively slippery value for modern ocean beds), but initialized from a previous simulation of the LGM with a prescribed, cold glacial climate representing conditions at ~20 kyr ago. The total ice volume in the modern and glacial ice sheets is 26.55 × 106 km3 and 32.30 × 106 km3, respectively, equivalent to bedrock-compensated GMSL values of 56.80 m and 62.28 m.
Atmospheric coupling
Atmospheric climatologies providing surface mass-balance inputs to the ice model are provided by decadal averages of meteorological fields from the RegCM3 RCM59, adapted to Antarctica with a polar stereographic grid and small modifications of model physics for polar regions. The RCM uses a 40-km grid, over a generous domain spanning Antarctica and surrounding oceans, nested within the GENESIS v3 Global Climate Model60,61. The GCM and RCM share the same radiation code62 and orbitally dependent calculations of shortwave insolation, important for the Pliocene and LIG palaeoclimate simulations.
Anomaly methods are used to correct a small <2 °C Antarctic cold bias in the RCM:
T = T_{exp} + T_{obs} - T_{ctl}
P = P_{exp} * P_{obs} / P_{ctl}
where T is monthly surface air temperature and P is monthly precipitation. Subscripts ‘exp’, ‘obs’ and ‘ctl’ refer to model experiment, observed modern climatology, and model modern control, respectively. A modern (1950) RCM simulation is used for the model modern control, and the ALBMAP data set [63] is used for observed modern climatology.
In the climatic correction for the difference between the ice-model surface elevation and the interpolated elevation in the climate model or observational data set27, precipitation is now corrected as well as temperature. As before, air temperature T (in degrees Celsius) is shifted by ΔT = γΔz, where γ = −0.008 °C m−1 is the lapse rate (that is, the decrease in atmospheric temperature with respect to altitude) and Δz is the elevation difference. Now, precipitation P is multiplied by a Clausius–Clapeyron-like factor:
P * 2^{∆T/10}


Atmospheric coupling
Atmospheric climatologies providing surface mass-balance inputs to the ice model are provided by decadal averages of meteorological fields from the RegCM3 RCM59, adapted to Antarctica with a polar stereographic grid and small modifications of model physics for polar regions. The RCM uses a 40-km grid, over a generous domain spanning Antarctica and surrounding oceans, nested within the GENESIS v3 Global Climate Model60,61. The GCM and RCM share the same radiation code62 and orbitally dependent calculations of shortwave insolation, important for the Pliocene and LIG palaeoclimate simulations.
Anomaly methods are used to correct a small <2 °C Antarctic cold bias in the RCM:
T = T_{exp} + T_{obs} - T_{ctl}
P = P_{exp} * P_{obs} / P_{ctl}
where T is monthly surface air temperature and P is monthly precipitation. Subscripts ‘exp’, ‘obs’ and ‘ctl’ refer to model experiment, observed modern climatology, and model modern control, respectively. A modern (1950) RCM simulation is used for the model modern control, and the ALBMAP data set [63] is used for observed modern climatology.
In the climatic correction for the difference between the ice-model surface elevation and the interpolated elevation in the climate model or observational data set27, precipitation is now corrected as well as temperature. As before, air temperature T (in degrees Celsius) is shifted by ΔT = γΔz, where γ = −0.008 °C m−1 is the lapse rate (that is, the decrease in atmospheric temperature with respect to altitude) and Δz is the elevation difference. Now, precipitation P is multiplied by a Clausius–Clapeyron-like factor:
P * 2^{∆T/10}
Rates of surface snowfall and rainfall are now consistently multiplied by a factor ρw/ρi ≈ 1.1, where ρw and ρi are the densities of liquid water and of ice respectively. This consistently converts between the units of most climate models and climatological databases (metres of liquid water equivalent per year) and the ice-model surface budget terms (metres of ice equivalent per year).
Oceanic sub-ice shelf and calving-face melt rates
Direct coupling of high-resolution ocean models and ice sheets remains challenging. For present-day simulations we use a parameterization of sub-ice shelf melt rates, similar to that used by other model groups64. The parameterization27 links oceanic melt rates to the nearest observed (or modelled) ocean temperatures:
OM = (KTρwCw/ρiLf) abs(To - Tf) (To - Tf)
where To is ocean temperature interpolated from the nearest point in an observational (or ocean model) gridded data set, Tf is the local freezing-point temperature at the depth of the ice base, and Cw is the specific heat of ocean water. The transfer factor KT = 15.77 m yr−1 °C−1 results in a combined coefficient (KTρwCw/ρiLf) of 0.224 m yr−1 °C−2. The depth dependence on Tf produces higher melt rates at the grounding line, as observed, and the dependence on T0 − Tf is quadratic65. Although spatially coarse observational data sets and standard GCM ocean models fail to capture detailed ocean current systems below ice-shelf cavities, this approach (Extended Data Fig. 6e and f) is preferable to the ad hoc prescription of single temperatures and transfer coefficients along individual sectors of the Antarctic margin as in ref. 27.
The effects of confined geography on ocean currents are represented by reducing basal melting depending on the total arc to open ocean α, representing the concavity of the coastline25. The melt rate computed from ocean temperatures as above is multiplied by the factor: max[0, min[1, alpha - 20) / 20]]
This effect, combined with the reduction of thin-ice calving with a similar dependence on α described above, allows ice to expand into interior basins during cool-climate recovery after major retreats of marine-based ice, as presumably occurred many times in West Antarctica over the last several million years66.
Melting of vertical ice surfaces in direct contact with ocean water is derived from the oceanic melt rate (OM) of surrounding grid cells, but is increased by a scaling factor of 10, producing more realistic calving front positions and in better agreement with hydrographic melt rate observations and detailed modelling67. Present-day sub-ice shelf and calving-face melt rates described here use the 1° resolution World Ocean Atlas32,68 temperatures at 400-m depth, interpolated to the time-evolving ice model grid and propagated under ice-shelf surfaces using contiguous neighbour iteration to provide To. The depth of 400 m represents typical observed levels of Circum-Antarctic Deep Water, a main source of warm-water incursions into the Amundsen Sea Embayment today69.
Pliocene simulation
Our default Pliocene simulation uses the same nested GCM–RCM climatology used in a prior study25, with 400 p.p.m.v. CO2 and a generic warm austral summer orbit28 (Extended Data Fig. 1). Ocean temperatures are increased uniformly by 2 °C everywhere in the Southern Ocean. The resulting Antarctic contribution of 11.3 m GMSL implies >15 m GMSL rise if an additional ~5 m contribution from Greenland70 and the steric effects of a warm Pliocene ocean are also considered. This result is ~6 m less than in ref. 25, reflecting a reduction in the sensitivity of the model with the changes described above.
LIG simulations
The LIG spans a ~20-kyr interval with greenhouse-gas atmospheric mixing ratios comparable to the pre-industrial Holocene9. Opportunities for Antarctic ice-sheet retreat within this interval include a peak in the duration of Antarctic summers coeval with a boreal summer insolation maximum at 128 kyr ago, and an Antarctic summer insolation maxima one half-precession cycle later at 116 kyr ago (Extended Data Fig. 2). We target these two orbital time slices because they contrast radiatively long and weak (128 kyr ago) versus short and intense Antarctic summers (116 kyr ago), both of which have been postulated to be important drivers of ice volume on glacial–interglacial timescales71.
LIG simulations that include climate–ice sheet feedback asynchronously couple the GCM–RCM and the ice-sheet model. In this case, the nested RCM land (ice) surface boundary conditions are updated at the end of the initial retreat at ice model-year 5000 and the ice-sheet model is rerun using the updated climatology. This improves the representation of ice-climate feedbacks via albedo, ocean surface conditions (sea surface temperatures and sea ice), and dynamical effects of the changing topography on the atmosphere. We find that explicitly including climate–ice feedbacks improves model performance, relative to simple lapse-rate adjustments.
LIG simulations (Extended Data Table 1; Extended Data Fig. 3d, e) apply anomaly-corrected RCM mass-balance forcing at each LIG time slice, using the appropriate greenhouse gas9,72 and orbital values73 in the nested GCM–RCM. Ocean temperatures are provided by the World Ocean Atlas data set32, with incremental warming of 1–5 °C applied uniformly over the Southern Ocean grid domain.
To allow the RCM atmosphere to respond to a warmer Southern Ocean in addition to applying elevated ocean temperatures to the ice model, we increase the southward ocean-heat convergence in the nested GCM–RCM using the methodology described in ref. 28, effectively warming the Southern Ocean sea surface temperatures by ~2 °C and reducing sea-ice extent. Accounting for the effect of a warmer Southern Ocean on the overlying atmosphere produces more LIG ice-sheet retreat for a given ocean warming, improving our model–data fit. With this technique, only 3 °C of assumed sub-surface ocean warming is required to produce >6 m GMSL rise from Antarctica at either LIG orbital time slice, reinforcing the notion of a dominant oceanic control on LIG ice-sheet retreat.


LIG simulations that include climate–ice sheet feedback asynchronously couple the GCM–RCM and the ice-sheet model. In this case, the nested RCM land (ice) surface boundary conditions are updated at the end of the initial retreat at ice model-year 5000 and the ice-sheet model is rerun using the updated climatology. This improves the representation of ice-climate feedbacks via albedo, ocean surface conditions (sea surface temperatures and sea ice), and dynamical effects of the changing topography on the atmosphere. We find that explicitly including climate–ice feedbacks improves model performance, relative to simple lapse-rate adjustments.
LIG simulations (Extended Data Table 1; Extended Data Fig. 3d, e) apply anomaly-corrected RCM mass-balance forcing at each LIG time slice, using the appropriate greenhouse gas9,72 and orbital values73 in the nested GCM–RCM. Ocean temperatures are provided by the World Ocean Atlas data set32, with incremental warming of 1–5 °C applied uniformly over the Southern Ocean grid domain.
To allow the RCM atmosphere to respond to a warmer Southern Ocean in addition to applying elevated ocean temperatures to the ice model, we increase the southward ocean-heat convergence in the nested GCM–RCM using the methodology described in ref. 28, effectively warming the Southern Ocean sea surface temperatures by ~2 °C and reducing sea-ice extent. Accounting for the effect of a warmer Southern Ocean on the overlying atmosphere produces more LIG ice-sheet retreat for a given ocean warming, improving our model–data fit. With this technique, only 3 °C of assumed sub-surface ocean warming is required to produce >6 m GMSL rise from Antarctica at either LIG orbital time slice, reinforcing the notion of a dominant oceanic control on LIG ice-sheet retreat.
The two time-continuous LIG simulations using prescribed climatologies (Fig. 3) use bias-corrected, present-day RCM climatologies with a uniform, time-evolving perturbation derived from the average of Antarctic ice-core climatologies compiled in ref. 29. Southern Ocean temperatures are treated similarly, with World Ocean Atlas temperatures32 increased according to the average of circum-Antarctic LIG anomalies29. Only records from marine drill-cores poleward of 45° S are used in the averages, but we note that there is considerable uncertainty in the proxy sea surface temperature estimates (>2 °C)29. This approach also assumes that the proxy sea surface temperatures reflect changes at sub-surface depths (~400 m), which is uncertain. The resulting anomalies are applied to the ice sheet model at 130 kyr ago, 125 kyr ago, 120 kyr ago, and 115 kyr ago and the ice-sheet model is run continuously from 130 kyr ago to 115 kyr ago. The pairs of air and ocean temperature perturbations applied at each 5-kyr LIG timestep are 1.97° and 1.70°, 1.41° and 1.51°, 0.83° and 1.09°, −1.57° and 0.31°, respectively.
The time-continuous LIG simulations are initialized from either a present-day initial ice state (Fig. 1b), or from a prior Last Glacial Maximum simulation with 5.76 × 106 km3 more ice than today. The latter initial condition may better represent the ice sheet at the onset of the LIG and leads to a greater potential sea-level rise owing to the deeper bed conditions early in the deglaciation, which enhances the bathymetrically sensitive MISI dynamics.
The proxy-forced LIG simulation clearly supports a maximum Antarctic contribution to GMSL early in the interglacial period (Fig. 3). However, we note that owing to the demonstrated influence of Southern Ocean temperature on the timing of retreat and the uncertain magnitude and chronology of our imposed forcing29, these results cannot definitively rule out maximum Antarctic retreat at the end of the LIG, as has also been proposed4,74
Future simulations
Because of the new ice-model physics that directly involve the atmosphere via meltwater enhancement of crevassing and calving, highly resolved atmospheric climatologies are needed at spatial resolutions beyond those of most GCMs. However, multi-century RCM simulations are computationally infeasible. To accommodate the need for long but high-resolution climatologies, the nested GCM–RCM is run to equilibrium with 1 × PAL, 2 × PAL, 4 × PAL and 8 × PAL CO2. In the ice-sheet simulations, CO2 follows the extended RCP greenhouse gas emissions36 to the year 2500, and the climate at any time is the average of the two appropriate surrounding RCM solutions, weighted according to the logarithm of the concentration of CO2. The RCM climatologies follow total equivalent CO2, which accounts for all radiatively active trace gases in the RCP timeseries. In RCP8.5, equivalent CO2 forcing exceeds 8 × PAL after 2175, but it is conservatively limited here to a maximum of 8 × PAL (Fig. 4a). A 10-yr lag is imposed in the RCM climatologies to reflect the average offset between sea surface temperatures and surface air temperatures in the equilibrated RCM (with equilibrated sea surface temperatures from the parent GCM) and the transient response of the real ocean’s mixed layer.
Ocean temperatures in the RCP scenarios are provided by high-resolution (0.5° atmosphere and 1° ocean) NCAR CCSM437 ocean model output, following the RCP2.6, RCP4.5, and RCP8.5 greenhouse gas emissions scenarios run to 2300. Ocean temperatures beyond the limit of the CCSM4 simulations at 2300 are conservatively maintained at their 2300 values. As with the World Ocean Atlas, water temperatures at 400-m depth (between ocean model z-levels 30 and 31) are used in the parameterization of oceanic sub-ice melt (oceanic melt rate) described above. The CCSM4 underestimates the wind-driven warming of Antarctic Shelf Bottom Water41 in the Amundsen and Bellingshausen seas associated with recent increases in melt rates and grounding-line retreats20,42,43. To account for this, additional warming is added to the Amundsen and Bellingshausen sectors of the continental margin. We find the addition of 3 °C to the CCSM4 ocean temperatures increases melt rates to 25–30 m yr−1 (Extended Data Fig. 5f). While still less than observed, this substantially improves grounding-line positions in the Amundsen Sea (Pine Island Glacier in particular) from 1950 to 2015. When applied to RCP4.5 and RCP8.5, the ocean-bias correction accelerates twenty-first-century WAIS retreat (Fig. 4d, g, h) but is found to have little effect beyond 2100 (Extended Data Table 1).
Extended RCP greenhouse gas scenarios36 are available up to 2500, beyond which we assume two different scenarios: (1) natural decay of CO275,76 and no further anthropogenic emissions, or (2) engineered, fast drawdown towards pre-industrial levels with an e-folding time of 100 years. These choices are not intended to be definitive, but serve to illustrate the ice-sheet response to a wide range of possible long-term future forcings.


Ocean temperatures in the RCP scenarios are provided by high-resolution (0.5° atmosphere and 1° ocean) NCAR CCSM437 ocean model output, following the RCP2.6, RCP4.5, and RCP8.5 greenhouse gas emissions scenarios run to 2300. Ocean temperatures beyond the limit of the CCSM4 simulations at 2300 are conservatively maintained at their 2300 values. As with the World Ocean Atlas, water temperatures at 400-m depth (between ocean model z-levels 30 and 31) are used in the parameterization of oceanic sub-ice melt (oceanic melt rate) described above. The CCSM4 underestimates the wind-driven warming of Antarctic Shelf Bottom Water41 in the Amundsen and Bellingshausen seas associated with recent increases in melt rates and grounding-line retreats20,42,43. To account for this, additional warming is added to the Amundsen and Bellingshausen sectors of the continental margin. We find the addition of 3 °C to the CCSM4 ocean temperatures increases melt rates to 25–30 m yr−1 (Extended Data Fig. 5f). While still less than observed, this substantially improves grounding-line positions in the Amundsen Sea (Pine Island Glacier in particular) from 1950 to 2015. When applied to RCP4.5 and RCP8.5, the ocean-bias correction accelerates twenty-first-century WAIS retreat (Fig. 4d, g, h) but is found to have little effect beyond 2100 (Extended Data Table 1).
Extended RCP greenhouse gas scenarios36 are available up to 2500, beyond which we assume two different scenarios: (1) natural decay of CO275,76 and no further anthropogenic emissions, or (2) engineered, fast drawdown towards pre-industrial levels with an e-folding time of 100 years. These choices are not intended to be definitive, but serve to illustrate the ice-sheet response to a wide range of possible long-term future forcings.
Future high-resolution ocean-model output is not available on multi-millennial timescales. In our long (5,000-year) future simulations (Extended Data Fig. 7), CCSM4 ocean temperatures at 400 m depth are assumed to remain at their 2300 values for thousands of years beyond 2300 (until 7000). This assumption is based on the thermal inertia of the deep ocean (thousands of years)47, its longwave radiative feedback on atmospheric temperatures77, and its relative isolation from surface variations. The response of the intermediate and deep ocean to atmospheric and surface-ocean warming before 2300 is heavily lagged in time, and consequently deep-ocean temperatures would continue to rise long after CO2 levels and surface temperatures began to decline after 250077. However, at some point several thousand years later, intermediate- and deep-ocean waters would start to cool if CO2 levels decay as in Extended Data Fig. 7. The trajectory of these temperatures would vary spatially and depend on details of the ocean circulation. To our knowledge, the state of the ocean as it recovers from a greenhouse gas perturbation over these timescales is largely unknown, as relevant coupled atmosphere–ocean global climate model simulations at the resolution and duration appropriate to our ice model have not been run. Consequently, our assumption of constant 400-m ocean temperatures after 2300, although likely to be conservative beyond 2500, may be questionable for the latter parts of the simulations assuming fast, engineered CO2 drawdown. However, assuming the slow, natural pace of CO2 recovery76, atmospheric concentrations would remain above twice the current level of carbon dioxide (2 × CO2) for thousands of years in the RCP8.5 scenario (Extended Data Fig. 7). Assuming a global temperature sensitivity of ~3 °C per doubling of CO2, our ocean temperatures applied to the long RCP8.5 scenario are probably conservative over the duration of the simulation.
Geologically constrained Large Ensemble analysis of future ice-sheet retreat
To quantify model uncertainty due to poorly known parameter values, ensembles of future RCP scenarios are performed with varying model parameters affecting sub-ice oceanic melt rates, meltwater-enhanced calving (hydrofracturing) and marine-terminating ice cliff failure. Ensemble members use the high-resolution atmospheric and ocean forcing described in the main text and above. Alternative ensembles are run both with and without the bias correction of CCSM4 ocean temperatures in the Amundsen and Bellingshausen Seas. The three parameters and four values used for each are as follows.
OCFAC is the coefficient in the parameterization of sub-ice-shelf oceanic melt, which is proportional to the square of the difference between nearby ocean water temperature at 400-m depth, and the pressure-melting point of ice. It corresponds to K in equation (17) of ref. 27. The relationship between proximal ocean conditions and melting at the base of floating ice shelves remains a challenging topic of ongoing research78, and a simple parameterization64 is used here. Ensemble values of OCFAC are 0.1, 1, 3 and 10 times the default value of 0.224 m yr−2 °C−2.
CREVLIQ is the coefficient in the parameterization of hydrofracturing due to surface liquid. It replaces the constant 100 in equation (B.6) of ref. 25, and is the additional crevasse depth due to surface melt plus rainfall rate, with a quadratic dependence. This crudely represents the complex relationship between surface water and crevasse propagation, and basic model sensitivity is shown in supplementary figure 7b of ref. 25. Values of CREVLIQ are 0 m, 50 m, 100 m and 150 m per (m yr−1)−2.
VCLIF is the maximum rate of horizontal wastage due to ice-cliff structural failure. It replaces the default value of 3,000 (3 km yr−1) in equation (A.4) of ref. 25. Its magnitude is based on observed retreat rates of modern large ice cliffs, and basic model sensitivity is shown in supplementary figure 7a of ref. 25. Values of VCLIF are 0 km yr−1, 1 km yr−1, 3 km yr−1 and 5 km yr−1.
Medium-range, default values of OCFAC, CREVLIQ, and VCLIF used in our nominal Pliocene (Extended Data Fig. 1), LIG (Fig. 3), and Future (Fig. 4) simulations are OCFAC = 1 (corresponding to 0.224 m yr−2 °C−2), CREVLIQ = 100 m per (m yr−1)−2, and VCLIF = 3 km yr−1, respectively.
Simulations for the Pliocene and LIG scenarios are run with all possible combinations of these parameter values, that is, 64 (=43) runs (Extended Data Table 2). Each run is subject to a pass/fail test that its equivalent GMSL rise falls within the observed ranges for the LIG (3.6–7.4 m) and the Pliocene (10–20 m). The filtered subset of parameter combinations that pass (15 out of 64) are then used in an ensemble of future RCP scenarios. An additional ensemble calculation is performed using the same LIG criteria, but a lower accepted range for Pliocene sea-level rise (5–15 m), to reflect the large uncertainty in Pliocene sea-level reconstructions1 (29 out of 64 passed this test). The mean and 1σ range of each ensemble are shown for the three RCP scenarios in Fig. 5, providing both an envelope of possible outcomes and an estimate of the model’s parametric uncertainty. Two alternative sets of future RCP ensembles are run with the ocean-temperature bias correction in the Amundsen and Bellingshausen seas shown in Extended Data Fig. 5. This increases Antarctica’s GMSL contribution by ~9 cm over the next century in both RCP8.5 and RCP8.5, but has almost no effect on longer timescales (Extended Data Tables 1, 2). In the RCP2.6 ensemble calibrated against the higher >10 m Pliocene sea-level targets, the ocean-bias correction increases both the ensemble-mean and 1σ standard deviation to 16 ± 16 cm in 2100 and 62 ± 76 cm in 2500 (Extended Data Table 1). The increased variance is caused by three simulations in the RCP2.6 ensemble set, in which the stability of the Thwaites Glacier grounding line is exceeded and the WAIS retreats into the deep interior. Although the ensemble members with bias-corrected ocean temperatures are generally more consistent with observations of recent retreat in the Amundsen–Bellingshausen sector, the validity of the bias correction in the long-term future is unknown.


Simulations for the Pliocene and LIG scenarios are run with all possible combinations of these parameter values, that is, 64 (=43) runs (Extended Data Table 2). Each run is subject to a pass/fail test that its equivalent GMSL rise falls within the observed ranges for the LIG (3.6–7.4 m) and the Pliocene (10–20 m). The filtered subset of parameter combinations that pass (15 out of 64) are then used in an ensemble of future RCP scenarios. An additional ensemble calculation is performed using the same LIG criteria, but a lower accepted range for Pliocene sea-level rise (5–15 m), to reflect the large uncertainty in Pliocene sea-level reconstructions1 (29 out of 64 passed this test). The mean and 1σ range of each ensemble are shown for the three RCP scenarios in Fig. 5, providing both an envelope of possible outcomes and an estimate of the model’s parametric uncertainty. Two alternative sets of future RCP ensembles are run with the ocean-temperature bias correction in the Amundsen and Bellingshausen seas shown in Extended Data Fig. 5. This increases Antarctica’s GMSL contribution by ~9 cm over the next century in both RCP8.5 and RCP8.5, but has almost no effect on longer timescales (Extended Data Tables 1, 2). In the RCP2.6 ensemble calibrated against the higher >10 m Pliocene sea-level targets, the ocean-bias correction increases both the ensemble-mean and 1σ standard deviation to 16 ± 16 cm in 2100 and 62 ± 76 cm in 2500 (Extended Data Table 1). The increased variance is caused by three simulations in the RCP2.6 ensemble set, in which the stability of the Thwaites Glacier grounding line is exceeded and the WAIS retreats into the deep interior. Although the ensemble members with bias-corrected ocean temperatures are generally more consistent with observations of recent retreat in the Amundsen–Bellingshausen sector, the validity of the bias correction in the long-term future is unknown.
Extended data figures and tables
Extended Data Figure 1: Warm mid-Pliocene climate and ice-sheet simulation. a, January (warmest monthly mean) difference in 2-m (surface) air temperature simulated by the RCM relative to a preindustrial control simulation with 280 p.p.m.v. CO2 and present-day orbit. The temperature difference is lapse-rate-corrected to account for the change in ice-sheet geometry and surface elevations. The Pliocene simulation uses 400 p.p.m.v. CO2, a warm austral summer orbit, and assumes a retreated WAIS to represent maximum Pliocene warm conditions. b, The Pliocene ice-sheet is shown after 5,000 model years, driven by the RCM climate in a, and assuming 2 °C ocean warming relative to a modern ocean climatology32. In the model formulation used here, maximum Pliocene ice-sheet retreat with default model parameters is equivalent to 11.26 m GMSL, about 6 m less than in ref. 25.
Extended Data Figure 2: LIG greenhouse gases, orbital parameters, and RCM climates. a, Greenhouse gas concentrations9,72 converted to radiative forcing shows the LIG interval (light red bar) and the best opportunity for ice-sheet retreat. b, Summer insulation at 70° latitude in both hemispheres73 (red, south; blue, north) and summer duration at 70° S (black)79 shown over the last 150 kyr, and the two orbital time slices (vertical dashed black lines at 128 kyr ago and 116 kyr ago). c, Table showing the greenhouse gas atmospheric mixing ratios (CO2 in parts per million by volume; CH4 and N2O in parts per billion by volume) and orbital parameters (eccentricity, obliquity, precession) used in the GCM–RCM at the LIG time slices (dashed lines 1 and 2 in a and b), respectively. d–f, January (warmest monthly mean) differences in 2-m surface air temperature relative to a preindustrial control simulation at 128 kyr ago (d), 116 kyr ago (e), and the present-day (2015) (f). Simulated austral summer temperatures at 116 kyr ago (e) with relatively high-intensity summer insolation is warmer than the long-duration summer orbit at 128 kyr ago (d), but unlike the Pliocene (Extended Data Fig. 1a), neither LIG climatology is as warm as the present day, producing little to no rain or surface melt on ice-shelf surfaces.
Extended Data Figure 3: Effect of Southern Ocean warming on Antarctic surface air temperatures and the ice sheet at 128 kyr ago. a–c, January (warmest monthly mean) differences in 2-m surface air temperature at 128 kyr ago, relative to a preindustrial control simulation (top row). GHG, greenhouse gas; SST, sea surface temperature. d, e, Ice-sheet thickness (m) after 5,000 model years, driven by the corresponding climate in a–c. a and d, Without climate–ice sheet coupling (present-day ice extent and surface ocean temperatures in the RCM), and prescribed 5 °C sub-surface ocean warming felt only by the ice sheet. b and e, With asynchronous coupling between the RCM atmosphere and ice sheet, and prescribed 5 °C sub-surface ocean warming felt only by the ice sheet. c and f, With asynchronous coupling between the RCM atmosphere and ice sheet, prescribed 3 °C sub-surface ocean warming felt by the ice sheet, and ~2 °C surface ocean warming felt by the RCM atmosphere. c shows the locations of East Antarctic ice cores (EDC, EPICA Dome C; V, Vostock; DF, Dome F; EDML, EPICA Dronning Maud Land) indicating warming early in the interglacial29 and previously attributed to WAIS retreat80; this warming is similar to that simulated in c from a combination of ice-sheet retreat and warmer Southern Ocean temperatures, supporting the notion that the timing of LIG retreat was largely driven by far-field ocean influences, rather than local astronomical forcing.
Extended Data Figure 4: RCM climates used in future, time-continuous RCP scenarios and evolving ice-surface melt rates linked to hydrofracturing model physics. a–d, January surface (2-m) air temperatures simulated by the RCM at the present-day (2015) (a), twice the present level of carbon dioxide, 2 × CO2 (b), 4 × CO2 (c), and 8 × CO2 (d) with the retreating ice sheet. The colour scale is the same in all panels. Yellow to red colours indicate temperatures above freezing with the potential for summer rain, and surface meltwater production. e–h, Evolving ice-surface meltwater production (in metres per year) in the time-evolving RCP8.5 ice-sheet simulations, driven by a time-continuous RCM climatology (Methods) following the RCP8.5 greenhouse gas time series (Fig. 4a). Black lines show the positions of grounding lines and ice-shelf calving fronts at discrete time intervals—e, 2050; f, 2100; g, 2150; and h, 2500—with superposed meltwater production rates.
Extended Data Figure 5: NCAR CCSM4 ocean temperatures and oceanic sub-ice-shelf melt rates. a, RCP2.6 ocean warming at 400-m depth, shown as the difference of decadal averages from 1950–1960 to 2290–2300. b, Same as a but for RCP4.5. c, Same as a but for RCP8.5. d, CCSM4 RCP8.5 ocean warming from 1950–1960 to 2010–2020 showing little to no warming in the Amundsen and Bellingshausen seas. The red line shows the area of imposed, additional ocean warming. e, f, Oceanic melt rates at 2015 calculated by the ice-sheet model from interpolated CCSM4 temperatures (e), and with +3 °C adjustment in the Amundsen and Bellingshausen seas (f), corresponding to the area within the red line in d.


Extended Data Figure 4: RCM climates used in future, time-continuous RCP scenarios and evolving ice-surface melt rates linked to hydrofracturing model physics. a–d, January surface (2-m) air temperatures simulated by the RCM at the present-day (2015) (a), twice the present level of carbon dioxide, 2 × CO2 (b), 4 × CO2 (c), and 8 × CO2 (d) with the retreating ice sheet. The colour scale is the same in all panels. Yellow to red colours indicate temperatures above freezing with the potential for summer rain, and surface meltwater production. e–h, Evolving ice-surface meltwater production (in metres per year) in the time-evolving RCP8.5 ice-sheet simulations, driven by a time-continuous RCM climatology (Methods) following the RCP8.5 greenhouse gas time series (Fig. 4a). Black lines show the positions of grounding lines and ice-shelf calving fronts at discrete time intervals—e, 2050; f, 2100; g, 2150; and h, 2500—with superposed meltwater production rates.
Extended Data Figure 5: NCAR CCSM4 ocean temperatures and oceanic sub-ice-shelf melt rates. a, RCP2.6 ocean warming at 400-m depth, shown as the difference of decadal averages from 1950–1960 to 2290–2300. b, Same as a but for RCP4.5. c, Same as a but for RCP8.5. d, CCSM4 RCP8.5 ocean warming from 1950–1960 to 2010–2020 showing little to no warming in the Amundsen and Bellingshausen seas. The red line shows the area of imposed, additional ocean warming. e, f, Oceanic melt rates at 2015 calculated by the ice-sheet model from interpolated CCSM4 temperatures (e), and with +3 °C adjustment in the Amundsen and Bellingshausen seas (f), corresponding to the area within the red line in d.
Extended Data Figure 6: Effect of future ocean warming only. a, Antarctic contribution to future GMSL rise in long, 5,000-yr ice-sheet simulations driven by sub-surface ocean warming simulated by CCSM4, following RCP8.5 (black line), with a +3 °C adjustment in the Amundsen and Bellingshausen seas (blue line; see Extended Data Fig. 5) and a warmer +5 °C adjustment (red line). Atmospheric temperatures and precipitation are maintained at their present values. b–d, Ice-sheet thickness at model-year 5,000, driven by sub-surface ocean forcing from CCSM4 (b) and from CCSM4 with a +3 °C (c) or +5 °C (d) adjustment in the Amundsen and Bellingshausen seas. Note the near-complete loss of ice shelves, but modest grounding-line retreat in b, the retreat of Pine Island Glacier in c, and the near-complete collapse of WAIS once a stability threshold in the Thwaites Glacier grounding line is reached in d.
Extended Data Figure 7: The long-term future of the ice sheet and GMSL over the next 5,000 years following RCP8.5 and RCP4.5. a, Equivalent CO2 forcing following RCP8.5 until the year 2500, and then assuming zero emissions after 2500 and allowing a natural relaxation of greenhouse gas levels (red) or assuming a fast, engineered drawdown (blue) with an e-folding timescale of 100 years. b. Antarctic contribution to GMSL over the next 5,000 years, following the greenhouse gas scenarios in a. c, The same as a, except showing long-term RCP4.5 greenhouse gas forcing. d, The same as b, except following the RCP4.5 scenarios in c. The insets in b and d show the ice sheet (and remaining sea-level rise) after 5,000 model years in RCP8.5 and RCP4.5, respectively, assuming fast CO2 drawdown (blue lines), highlighting the multi-millennial commitment to a loss of marine-based Antarctic ice, even in the moderate RCP4.5 scenario. Note the different y-axes in RCP8.5 versus RCP4.5.
Extended Data Figure 8: Freshwater input to the Southern Ocean. Total freshwater and iceberg flux from 1950 to 2500, following the future RCP scenarios shown in Fig. 4b. Freshwater input calculations include contributions from ice loss above and below sea level and exceed 1 Sv in RCP8.5.
Extended Data Table 1: Summary of Antarctic contributions to GMSL during the Pliocene, LIG, future centuries, and future millennia. Antarctic contributions to GMSL for the Pliocene and LIG simulations (rows 1–9) with +2 °C ocean warming in the Pliocene and incrementally imposed ocean warming in the LIG simulations. Values shown represent ice retreat at the end of quasi-equilibrated 5000-yr simulations. Time-continuous LIG simulations forced by proxy-based atmosphere and ocean climatologies (rows 10–12) list maximum GMSL contributions occurring early in the LIG (Fig. 3a). The remaining rows list Antarctic contributions to GMSL at specific times (years as shown) in time-dependent future simulations. Ensemble means and standard deviations (1σ) of the RCP ensemble members listed in Extended Data Table 2 are also shown. Future GMSL contributions are shown relative to 2000.
Extended Data Table 2: Ensemble simulations of Pliocene, LIG, and future Antarctic contributions to GMSL. Varying combinations of three model parameters (first column) correspond to OCFAC, CREVLIQ and VCLIF, respectively (see Methods). The resulting GMSL contributions of each ensemble member driven by Pliocene and LIG climatologies are shown in the second and third columns. Combinations of model parameters satisfying Pliocene and LIG sea-level targets are assigned a Large Ensemble number (LE#) in the fourth column. Default model parameter values (LE# 12) and resulting Pliocene and LIG GMSL rise are in bold type. Four future ensembles using alternative sets of the palaeo-filtered Large Ensemble members and following RCP2.5, RCP4.5 and RCP8.5 emissions scenarios are shown at right. The top two ensembles use 29 combinations of parameter values that satisfy LIG sea-level targets and a range of Pliocene sea-level targets between 5 m and 15 m. The bottom two ensembles use a more restricted set of 15 parameter combinations that satisfy a higher Pliocene target range >10 m. Future RCP ensembles at left correspond to the GMSL time series in Fig. 5. The two ensemble sets at far right include the ocean-temperature bias correction described in the text, Fig. 4 and Extended Data Fig. 5. Antarctic GMSL contributions for each ensemble member are shown at 2100 and 2500. Ensemble means and 1σ standard deviations are also shown. GMSL contributions in future ensembles are relative to 2000.
Supplementary information
RCP2.6 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 470 kb)
RCP4.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 522 kb)


Supplementary information
RCP2.6 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 470 kb)
RCP4.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 522 kb)
RCP8.5 ice-sheet thickness (m) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 584 kb)
RCP2.6 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 593 kb)
RCP4.5 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 691 kb)
RCP8.5 oceanic melt rates (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 808 kb)
RCP2.6 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 477 kb)
RCP4.5 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 594 kb)
RCP8.5 surface melt-water production (m a-1) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 778 kb)
RCP8.5 ice-surface speeds (norm of ice-surface velocities (m a-1)) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 918 kb)
Nature Podcast Discussion
Adam Levy: Prediction is very difficult, especially about the future. This saying, attributed to physicist Niels Bohr, is often used to refer to quantum mechanics. But climate scientists know it applies to their research too.
After all, how do you work out what the future holds for the climate when you’ve only got one planet? You’re still learning how it works, and you can’t carry out carefully controlled studies. Well, the typical approach is to build computer models that simulate the relevant laws of physics and can be checked against the real world.
But what if you only have limited data from the real world, and how do you cope with processes that haven’t even happened yet, but might come into play in the future? These are questions that scientists looking at the Antarctic are grappling with. We only have satellite data of Antarctica from the last few decades, so scientists have to work hard to make the most of the information we have.


RCP8.5 ice-surface speeds (norm of ice-surface velocities (m a-1)) from 1950 to 2500 CE: This video shows various aspects of our ice-sheet simulations from 1950 to 2500 CE, following future greenhouse-gas emission scenarios: RCP2.6, RCP4.5, and RCP8.5. Animations show the time-evolution of ice sheet thickness (m), oceanic melt rates (m a-1) driven by NCAR CCSM4 ocean temperatures, and surface melt-water production (m a-1) driven by our atmospheric RCM. Surface ice speeds (m a-1) illustrate the evolution of ice streams during ice-sheet retreat in the RCP8.5 scenario. The simulations in the videos use default model parameters and correspond to the simulations shown in Figure 4. (MOV 918 kb)
Nature Podcast Discussion
Adam Levy: Prediction is very difficult, especially about the future. This saying, attributed to physicist Niels Bohr, is often used to refer to quantum mechanics. But climate scientists know it applies to their research too.
After all, how do you work out what the future holds for the climate when you’ve only got one planet? You’re still learning how it works, and you can’t carry out carefully controlled studies. Well, the typical approach is to build computer models that simulate the relevant laws of physics and can be checked against the real world.
But what if you only have limited data from the real world, and how do you cope with processes that haven’t even happened yet, but might come into play in the future? These are questions that scientists looking at the Antarctic are grappling with. We only have satellite data of Antarctica from the last few decades, so scientists have to work hard to make the most of the information we have.
But understanding what’s going to happen to Antarctica’s ice is vital to understanding how global warming will impact the world.
Robert DeConto: There’s just so much potential sea level rise locked up in Antarctica there. There’s such a vast amount of ice.
Adam Levy: This is Rob DeConto from the University of Massachusetts who reporters in this week’s nature.
He’s been trying to peer into the future by modeling how Antarctica contributes to sea level rise.
Robert DeConto: So even a small fraction of Antarctica being mobilized and going into the ocean is going to have a global impact.
Adam Levy: Because it could have such a big influence. Lots of different groups have tried simulating Antarctica’s future and have come up with a broad range of results.
Here’s Tamsin Edwards of the Open University who published a study a few months ago on future ice loss in the Antarctic.
Tamsin Edwards: I would say it’s the the biggest unknown in future sea level rise.
Adam Levy: But why? What makes it so hard to pin down?
Tamsin Edwards: Pretty much everything about it. All of these different ways in which ice can flow, can crack, can be lost and gained, it makes quite a complicated picture.
Adam Levy: Both Tamsin Edwards and Rob DeConto have used models to try to get to grips with this problem, but they’re somewhat divided about what their models should be based on. Here’s Tamsin again.
Tamsin Edwards: So we kind of assumed that if the model is good at simulating the recent past, it’s more likely to be good at predicting the future.
Adam Levy: But Rob thinks there’s only so much that the last few decades can teach us.
Robert DeConto: In the very recent past, the climate and the oceans have been certainly not as warm as they’re predicted to become in the next century. So we compare the results that we get with geologic records.
Adam Levy: Geologic records that just means records of the climate from the distant past, deduced from things like the erosion of now inland cliffs.
Rob favors using data like these because there’ve been times in the Earth’s past where the climate has looked pretty similar to today’s situation.
Robert DeConto: 125,000 years ago, the world looks a lot like it does today. Similar climate, and yet sea level was between six and nine meters higher.
Adam Levy: So where Tamsin’s model uses direct observations of Antarctica from the last few decades, Rob’s uses our understanding of sea levels from thousands of years ago.
But whatever you are checking your model against, you can never be sure it’ll apply to the future. Says Tamsin
Tamsin Edwards: If you’re calibrating with past data, and that includes paleo climate data as well, because you never find a perfect analog of the future in paleo climate. There are always different things going on, so you have to bear that in mind when you’re thinking about your predictions and be a bit cautious.
Adam Levy: And the same goes for models based on today’s climate. It’s not a done deal that tomorrow will behave like today. And what if Antarctica loses ice in different ways tomorrow than it does today? Rob’s model includes certain processes that we haven’t observed in Antarctica. For example, the possibility that melt water on top of ice could make ice cliffs unstable.
This could cause ice to collapse into the sea much faster than we’re seeing today. Rob says his model is only accurate if he includes these kind of dramatic processes. But it’s not easy to build these processes into a model.
Robert DeConto: I would say that these are just really the first baby steps to try to incorporate processes like these in the models.
Adam Levy: But Tamsin is not convinced that including processes like this, that we’ve not really seen taking place yet, is the best bet.
Tamsin Edwards: We haven’t seen direct evidence of this. I would say that really says we have to put it in the models. Basically at the moment. It’s an exciting time. The jury’s out.
Adam Levy: So whereas Tamsin’s model is limited to the behavior we know to have happened in Antarctica, Rob’s includes processes that may or may not arise in the future.
They’re both trying to make the best use of limited information. And so to the results: According to these different models, how much is the Antarctic going to contribute to sea level rise by 2100? We’ll get to what these numbers mean in a minute, but first his Tamsin’s estimate.
Tamsin Edwards: We came up with the most likely of about 10 centimeters, quite low, and we came up with a prediction that there was only a 1-in-20 chance it would be more than 30 centimeters by the end of the century.
Adam Levy: How about Rob’s model?
Robert DeConto: We’re getting something between 64 centimeters and a little over a meter.
Adam Levy: It’s a huge difference. Yes, the two models used slightly different scenarios of greenhouse gas emissions, and yes, there are plenty of other uncertainties, but the difference is still striking. And Rob’s results could mean, for example, that low lying island nations could have to evacuate sooner than was previously anticipated.
Robert DeConto: You know, I hope we’re wrong.
Adam Levy: Understandable, when Rob’s model also predicts over 10 meters of sea level rise 500 years from now. And remember, Antarctica is just one piece of the sea level rise puzzle added to other sources of sea level rise, like the Greenland ice sheet. Even Tamsin’s estimate could lead to sea level rises of about a meter by the end of the century. A huge challenge for coastal cities around the world.
But such big uncertainties mean that it’s hard for the world to know what to prepare itself for. Rob is hopeful that techniques like his and Tamsin’s could be combined in the future to take advantage of both recent observations and geological records.
Tamsin, on the other hand, thinks that for the time being, it’s good that we have a range of models tackling the problem in different ways.
Tamsin Edwards: We may come up with some super ice sheet model that captures everything perfectly, but it’s a good idea to have different models with different approaches and that they’d be independent and you can compare their results.
Adam Levy: After all, if you can’t compare lots of different Earths, at least you can compare lots of different models.
Podcaster: The details of both those model studies are available at nature.com/nature. You heard from Tamsin Edwards, whose paper came out in Nature in December, and Rob DeConto, whose paper is out this week.


Index


Kuhlbrodt and Gregory (2012)
Title:
Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change
Key Points:
The spread of the OHU efficiency explains half of the spread in total OHU
Most models are biased towards a too weak stratification and a too strong OHU
The Southern Ocean and its stratification dominate global OHU in the models
Corresponding author:
Kuhlbrodt
Keywords:
CMIP5 models, climate change, ocean heat uptake, sea level rise
Citation:
Kuhlbrodt, T., and J. M. Gregory (2012), Ocean heat uptake and its consequences for the magnitude of sea level rise and climate change, Geophys. Res. Lett., 39, L18608, doi:10.1029/2012GL052952
URL:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL052952
Abstract
Under increasing greenhouse gas concentrations, ocean heat uptake moderates the rate of climate change, and thermal expansion makes a substantial contribution to sea level rise. In this paper we quantify the differences in projections among atmosphere-ocean general circulation models of the Coupled Model Intercomparison Project in terms of transient climate response, ocean heat uptake efficiency and expansion efficiency of heat. The CMIP3 and CMIP5 ensembles have statistically indistinguishable distributions in these parameters. The ocean heat uptake efficiency varies by a factor of two across the models, explaining about 50% of the spread in ocean heat uptake in CMIP5 models with CO2 increasing at 1%/year. It correlates with the ocean global-mean vertical profiles both of temperature and of temperature change, and comparison with observations suggests the models may overestimate ocean heat uptake and underestimate surface warming, because their stratification is too weak. The models agree on the location of maxima of shallow ocean heat uptake (above 700 m) in the Southern Ocean and the North Atlantic, and on deep ocean heat uptake (below 2000 m) in areas of the Southern Ocean, in some places amounting to 40% of the top-to-bottom integral in the CMIP3 SRES A1B scenario. The Southern Ocean dominates global ocean heat uptake; consequently the eddy-induced thickness diffusivity parameter, which is particularly influential in the Southern Ocean, correlates with the ocean heat uptake efficiency. The thermal expansion produced by ocean heat uptake is 0.12 m YJ^{-1}, with an uncertainty of about 10% (1 YJ = 10^{24} J).
Introduction
Ocean heat uptake moderates the rate of time-dependent climate change. Thermal expansion of sea-water is a consequence of ocean heat uptake and one of the major contributors to global-mean sea level rise [Church et al., 2011]. Our general aim in this paper is to quantify the differences in predictions of the magnitude and distribution of ocean heat uptake, and its consequences for global-mean surface air temperature change and thermal expansion, among atmosphereÐocean general circulation models (which we henceforth refer to simply as “models”, for convenience) used for projections of anthropogenic climate change.
We analyse results from 22 models that participated in the Coupled Model Intercomparison Project Phase 3 (CMIP3), and from the 20 models in the CMIP5 project whose data were available at the time of writing this paper (Spring 2012). See Figure 1 and Table 1 in Text S1 in the auxiliary material, for a list.1 We mainly use the control experiments and experiments with atmospheric CO_2 concentration increasing at 1%/year (details in the auxiliary material).
Ocean Heat Uptake Efficiency and Transient Climate Response
Gregory and Forster [2008] showed that there is an approximately linear relationship between the global mean surface air temperature change ΔTa and the radiative forcing F (due to greenhouse gases etc.): ΔTa = F/ρ, with the climate resistance ρ in W m−2 K−1. This relationship holds well for observations and model simulations of recent decades, and for projections of climate change under a continuously increasing forcing, which is a characteristic of most scenarios considered for the 21st century. The basis of this relationship is that the difference between the radiative forcing and the radiative feedback yields the net heat flux N into the climate system: N = F − ΔTa, and N can be approximated by N ≃ κΔTa. The climate resistance ρ is thus the sum of α, the climate feedback parameter, and κ, which is identified as the ocean heat uptake efficiency because nearly all the added heat is stored in the ocean [e.g., Church et al., 2011].
Following Gregory and Forster [2008], the ocean heat uptake efficiency κ, the climate feedback parameter α and the climate resistance ρwere calculated for CMIP5 by ordinary least squares regression (OLS) of decadal-meanN, F-N and F respectively against ΔTa under the standard idealized scenario of CO2 increasing at 1% per year, giving a forcing F(t) = F2×t/70 which is linear with time t in years, where F2× is obtained from experiments in which CO2 is instantaneously increased and then held constant [Andrews et al., 2012] (Table 1 in Text S1). The transient climate response (TCR) was calculated, following its definition, as ΔTafor the time-mean of years 61–80 in this scenario (Figure 1 and Table 1 in Text S1). The coefficient of variation (ratio of ensemble standard deviation to ensemble mean) of TCR is about 20% in CMIP5.
Figure 1: The ocean heat uptake efficiency κ (blue bars), the climate feedback parameter α (red bars), the transient climate response (crosses) and the expansion efficiency of heat ϵ (circles) for the CMIP3 (numbers) and the CMIP5 (letters) models. The total bar length is the climate resistance ρ = α + κ. The models are arranged in order of κ. See Table 1 in Text S1 in the auxiliary material for an alphabetical list of the models. It can be seen from this diagram that TCR and κ are anticorrelated (the crosses are further left towards the bottom), but there is no relationship between κ and α or ϵ (the red bars and the circles do not show any tendency from top to bottom). For several technical reasons, not all parameters could be calculated for every model.
We see that α obtained by this method agrees closely with α obtained from the CO2step-increase experiments [Andrews et al., 2012]. F2× is not correlated with α or κ. Whereas Gregory and Forster [2008] found α and κto be independent in CMIP3, they have a correlation of 0.56 in CMIP5, significant at the 5% level (one-tailed). This is due principally to the models GFDL-ESM2G and GFDL-ESM2M, which haveα and κ that are both larger than in any other model (except for alpha of MIROC5). Without these models, the correlation is insignificant (0.32). Further investigation of these models is needed to establish whether there is a link between their large α and large κ.
The definition of ρ implies that TCR = F2×/ρ = F2×/(α + κ). Thus, a larger κ gives a smaller TCR (correlation of κand TCR is −0.76). Excluding GFDL-ESM2G and GFDL-ESM2M, so thatκ is uncorrelated with α, we can compute the fraction of the across-model variance of TCR explained byκ by comparing var(F2×/(α + κ)) with var(〈F2×〉/(〈α〉 + κ)), where the angle brackets denote the model mean (see the auxiliary material for further comment on the method). The fraction explained is about 10%.
Boé et al. [2009, 2010] present evidence from CMIP3 suggesting that ocean heat uptake has a much stronger influence than this on surface warming. Their strong relationship, however, depends particularly on a cluster of five models [Boé et al., 2009, Figure 3b]. In the high-latitude Southern Ocean region which was analysed for that figure, three of these models (csiro_mk3_0, giss_e_h and giss_e_r) have an extremely weak ocean temperature stratification. Another model (ncar_pcm1) has the lowest climate sensitivity of any CMIP3 model. We therefore suspect that the correlation could be strong by chance rather than from a common physical behaviour exhibited by these models.


We see that α obtained by this method agrees closely with α obtained from the CO2step-increase experiments [Andrews et al., 2012]. F2× is not correlated with α or κ. Whereas Gregory and Forster [2008] found α and κto be independent in CMIP3, they have a correlation of 0.56 in CMIP5, significant at the 5% level (one-tailed). This is due principally to the models GFDL-ESM2G and GFDL-ESM2M, which haveα and κ that are both larger than in any other model (except for alpha of MIROC5). Without these models, the correlation is insignificant (0.32). Further investigation of these models is needed to establish whether there is a link between their large α and large κ.
The definition of ρ implies that TCR = F2×/ρ = F2×/(α + κ). Thus, a larger κ gives a smaller TCR (correlation of κand TCR is −0.76). Excluding GFDL-ESM2G and GFDL-ESM2M, so thatκ is uncorrelated with α, we can compute the fraction of the across-model variance of TCR explained byκ by comparing var(F2×/(α + κ)) with var(〈F2×〉/(〈α〉 + κ)), where the angle brackets denote the model mean (see the auxiliary material for further comment on the method). The fraction explained is about 10%.
Boé et al. [2009, 2010] present evidence from CMIP3 suggesting that ocean heat uptake has a much stronger influence than this on surface warming. Their strong relationship, however, depends particularly on a cluster of five models [Boé et al., 2009, Figure 3b]. In the high-latitude Southern Ocean region which was analysed for that figure, three of these models (csiro_mk3_0, giss_e_h and giss_e_r) have an extremely weak ocean temperature stratification. Another model (ncar_pcm1) has the lowest climate sensitivity of any CMIP3 model. We therefore suspect that the correlation could be strong by chance rather than from a common physical behaviour exhibited by these models.
The time-integrated heat uptake in the 1%/year CO2 scenario up to year 70 is H2× = ∫070N(t) dt ≃ 35F2×κ/(κ + α) (in W year m−2). Across the CMIP5 1%/year CO2 scenarios, it has a coefficient of variation of about 10%. Using the same CMIP5 models and method as for TCR (see also the auxiliary material), we find that H2× has a correlation of 0.92 with F2×κ/(κ + α), and the fraction of variance of H2× explained by κ is ∼50%. Thus κ influences heat uptake more than it influences surface warming because of its appearance in the numerator of H2×. (In the auxiliary material, we derive a formula for var(H2×) in terms of var(κ) and var(TCR).)
The distributions of κ, α, ρ and TCR are not significantly different for the CMIP3 and CMIP5 ensembles according to Kolmogorov–Smirnov tests. In both ensembles, κ varies by about a factor of 2. Investigating the reasons for this substantial spread motivates the next section.
Vertical Distribution of Temperature and Temperature Change
Ocean heat uptake efficiency depends on how fast the heat can be transported downwards. We put forward the hypothesis that a model with a weak vertical temperature gradient in the control state has a larger capacity for downward heat transport (e.g. because a large diapycnal mixing coefficient erodes the stratification) and therefore should have a larger κ.The hypothesis applies to net global-mean vertical heat transport, comprising diapycnal mixing and other processes.
Figure 2a shows the global-mean vertical temperature profile from the control runs of the CMIP3 and CMIP5 models (the average over the first 20 years that are parallel to the 1%/year CO2 runs) and from observations (WOA05 [Locarnini et al., 2006]), each profile being expressed as a difference from its surface temperature. This confirms that in the top 2000 m most models are less stratified than the real ocean. To elucidate the relationship between κ and the global temperature profiles, we use a simple measure of the vertical temperature gradient, namely the vertical temperature difference Tz between two layers, 0–100 m and 1500–2000 m (similar to Boé et al. [2009]). The relationship of κ to Tz is shown in Figure 3a and is negative, as expected (r = −0.35 with p= 0.07 [one-sided]). HadGEM2-ES (model J) has a very smallκ and is strongly stratified in the uppermost layers, being closer to the observed profile than most other models, particularly in the top 500 m. The κ-Tz relationship therefore suggests that κ tends to be too large in AOGCMs.
Figure 2: (a) Globally averaged temperature profiles for the control runs of the CMIP3 and CMIP5 models shown as difference from surface temperature, with observations for comparison (dash-dotted; WOA05 [Locarnini et al., 2006]). NorESM1-M is an outlier in that it is unusually weakly stratified in the top 200 m, giving a largeκ, but very strongly stratified in the 500 m or so below, giving a large Tz. Another outlier is giss_e_r with an extremely weak stratification. (b) Change of the temperature profiles in the 1%/year CO2 runs, divided by the vertical integral between 0 m and 2000 m. Units are dimensionless (“DL”). (c) Change of the temperature profiles in the CMIP3 models during the observational record [Levitus et al., 2012] (“Lev12”), scaled as in Figure 2b. Shown is the difference of a 20-year average (2000 to 2019) from the SRES A1B runs minus a 20-year average from 20C3M (1945–1964). Two models (red, orange) overestimate surface warming because of their too small total heat uptake. To some extent, a few models capture the surface intensification (“SFI” [light green]: bccr_bcm2_0, gfdl_cm2_0, gfdl_cm2_1, miub_echo_g, mri_cgcm2_3_2a) seen in the observations (dash-dotted). Also note the shallow subsurface maximum warming in observations, but not in models, for which we have no explanation.
Figure 3: The ocean heat uptake efficiency κ [W m−2 K−1] against (a) the globally averaged vertical temperature difference Tz in the control runs, (b) its change ΔTz in the 1%/year CO2runs, scaled with the total warming, and (c) the quasi-Stokes diffusivity parameterκGM for those CMIP3 models where it is a constant. The black lines are regression lines. The CMIP3 models have red numbers while the CMIP5 models have black letters (see Table 1 in Text S1 for key). Blue crosses on the horizontal axis denote the values of Tz from WOA05 and of ΔTz from Levitus et al. [2012].
The change of the global vertical temperature profile averaged over the years 61–80 of the 1%/year CO2 runs is shown in Figure 2b. The profiles were scaled with (i.e., divided by) their vertical integral between 0 m and 2000 m in order to compare their shapes rather than the total warming. The amount of warming in the top 100 m, as compared to the deeper layers, varies considerably across the models. As Figure 3b shows, the variation of κ across models is strongly related to ΔTz, defined as the change of (the scaled) Tz in the 1%/year CO2 runs. The correlation (r = −0.66) is significant at the 99% level (p < 0.01). If ΔTz is large, then the temperature increase at the surface is larger than at depth, indicating that most heat has been taken up at the surface. This goes along with a small κ. Conversely, models that distribute the additional heat further down have a smaller ΔTz and a larger κ.
The κ-Tz relationship suggests most models will probably transport heat too deeply. Consistent with this, Figure 2c shows that the observed warming over recent decades [Levitus et al., 2012] is more strongly surface-intensified than in the CMIP3 simulations of the same period.
Geographical Distribution of Ocean Heat Uptake


Figure 3: The ocean heat uptake efficiency κ [W m−2 K−1] against (a) the globally averaged vertical temperature difference Tz in the control runs, (b) its change ΔTz in the 1%/year CO2runs, scaled with the total warming, and (c) the quasi-Stokes diffusivity parameterκGM for those CMIP3 models where it is a constant. The black lines are regression lines. The CMIP3 models have red numbers while the CMIP5 models have black letters (see Table 1 in Text S1 for key). Blue crosses on the horizontal axis denote the values of Tz from WOA05 and of ΔTz from Levitus et al. [2012].
The change of the global vertical temperature profile averaged over the years 61–80 of the 1%/year CO2 runs is shown in Figure 2b. The profiles were scaled with (i.e., divided by) their vertical integral between 0 m and 2000 m in order to compare their shapes rather than the total warming. The amount of warming in the top 100 m, as compared to the deeper layers, varies considerably across the models. As Figure 3b shows, the variation of κ across models is strongly related to ΔTz, defined as the change of (the scaled) Tz in the 1%/year CO2 runs. The correlation (r = −0.66) is significant at the 99% level (p < 0.01). If ΔTz is large, then the temperature increase at the surface is larger than at depth, indicating that most heat has been taken up at the surface. This goes along with a small κ. Conversely, models that distribute the additional heat further down have a smaller ΔTz and a larger κ.
The κ-Tz relationship suggests most models will probably transport heat too deeply. Consistent with this, Figure 2c shows that the observed warming over recent decades [Levitus et al., 2012] is more strongly surface-intensified than in the CMIP3 simulations of the same period.
Geographical Distribution of Ocean Heat Uptake
The projected ocean heat uptake (OHU, i.e., the increase in ocean heat content) in model simulations with an increasing CO2 content has a distinct regional structure. We analyse this for the CMIP3 SRES A1B scenario, for which we have the largest number of models available. For comparison, the same analysis for the 1% CO2 runs of CMIP3 and CMIP5 can be found in the auxiliary material. They show generally less heat uptake because ∫F dt is smaller, but the geographical features are similar.
The ensemble-mean top-to-bottom integrated OHU is shown inFigure 4a. It was calculated as the difference between the 20-year averages 2080–2099 and 1980–1999. It is largest in the Southern Ocean, in a band around 40°S, with maxima in the Argentine Basin and south of Africa. This leads to a clear signal in steric sea level rise [cf.Pardaens et al., 2011, Figure 2], which is predominantly thermosteric in the Southern Ocean. The models agree on these features (R > 1, thin black contours), and they are also visible in the top 700 m alone (Figure 4b), which accounts for up to 50% of the heat uptake in the full depth.
Figure 4: Vertically integrated ocean heat uptake (colour shading; in GJ m−2) in the ensemble average of the SRES A1B scenario of 17 CMIP3 models for (a) the total water column, (b) the upper 700 m and (c) below 2000 m. Thick black line: zonal total in 1015 J m−1 (scale in the upper left corner), with ±1 standard deviation (dotted). Note the different scales in Figure 4c. Black contours show the ratio R of ensemble mean and ensemble standard deviation (solid: R > 1, thick solid: R = 1, dashed: R < 1). For Figures 4a and 4b, R> 1 in most areas indicating agreement across models. An exception are the deep-water formation regions in the Southern Ocean and the North Atlantic. In Figure 4c the models mainly show OHU in the Southern Ocean.
OHU below 2000 m is substantial in several large areas of the Southern Ocean (Figure 4c), including the Argentine basin and the area west of the Drake Passage, where there are maxima of top-to-bottom OHU. The pattern bears resemblance to observations [Purkey and Johnson, 2010]. In these areas, the deep OHU can amount to up to 40% of the total. In the deep-water formation areas in the Southern Ocean and in the North Atlantic the ensemble mean OHU displays minima above 700 m. The models show a large spread in these areas (R < 1).
The zonal total heat uptake (thick black line in the left hand side of the panel, dotted: one standard deviation) confirms that the global maximum of OHU per degree latitude is in the mid-latitude Southern Ocean [Stouffer et al., 2006]. Therefore, the stratification in that region could have a particularly large influence on κ.In the large majority of the models, the Southern Ocean stratification is strongly influenced by the parameterization of the eddy-induced tracer transports. Consistent with this, we find that the quasi-Stokes diffusivity parameterκGM(often called the eddy-induced thickness diffusivity) has a significant influence onκ (Figure 3c). When κGM is small, the isopycnal layers are steep, leading to a strong horizontal density gradient [Kuhlbrodt et al., 2012, Figure 1c] but a weak stratification and thus a large κ.
Expansion Efficiency of Heat
The expansion efficiency of heat [Russell et al., 2000], as a property of a model in m YJ^{−1} (1 YJ ≡ 1024 J), is defined as ϵ = hx/H, where hx is the global mean sea level rise due to thermal expansion and Hthe global-integral OHU. We calculateϵ by OLS regression of hx against H, using results from 1%/year CO2 and all available 21st-century scenarios.
In all models, there is an excellent scenario-independent linear relationship, butϵ varies across models (Figure 1 and Table 1 in Text S1) because the thermal expansivity of sea water (1/ρ) ∂ρ/∂T increases with pressure and temperature. Therefore, the magnitude of thermal expansion depends on the latitudes and depths at which the heat is actually stored; this pattern depends on the model, but not on the scenario for a given model.
The ranges of ϵ in the CMIP3 and CMIP5 ensembles are similar: 0.12 ± 0.01 m YJ−1 in CMIP3 and 0.11 ± 0.01 m YJ−1 in CMIP5. This is consistent with the observational estimates for 0 m to 2000 m, 1955–2010 [Levitus et al., 2012], from which we infer ϵ = 0.12 ± 0.01 m YJ−1. The observational estimates by Church et al. [2011] for 1972–2008 for the full ocean depth indicate ϵ = 0.15 ± 0.03 m YJ−1, which is slightly higher but not significantly different. We did not find any correlation of ϵ with κ, Tz or ΔTz, although such relationships would be plausible. It might well be that the stratification in the individual regions which are particularly important to OHU (section 4) influences ϵmore than global-mean properties do.
Concluding Remarks
Our analysis of CMIP3 and CMIP5 model results indicates that model spread in ocean vertical heat transport processes is responsible for a substantial part of the spread in predictions of global-mean ocean heat uptake (about 50% in the CMIP5 1%CO2/year experiments), and for some of the spread in predictions of surface warming. Since most AOGCMs have weaker global-mean stratification than observed, it is possible that they generally overestimate ocean heat uptake and underestimate surface warming [Forest et al., 2008]. The ocean heat uptake in CMIP5 1%CO2/year experiments has a spread of about 10%, and there is also a spread of about 10% in the expansion efficiency of heat ϵ, due to the different spatial distribution of the warming in the models. These factors contribute roughly equally to the spread of thermal expansion projection in response to CO2. Comparison, analysis and evaluation of model processes of ocean interior heat transport is essential to make progress in reducing uncertainties in projections of the magnitude and distribution of ocean heat uptake and the consequent sea-level rise.