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Earth Syst. Dynam., 11, 953–976, 2020
https://doi.org/10.5194/esd-11-953-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
Semi-equilibrated global sea-level change
projections for the next 10 000 years
Jonas Van Breedam1, Heiko Goelzer1,a, and Philippe Huybrechts1
1Earth System Science and Departement Geografie,
Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
anow at: NORCE Norwegian Research Centre, Bjerknes Centre for Climate Research, Bergen, Norway
Correspondence: Jonas Van Breedam (jonas.van.breedam@vub.be)
Received: 16 April 2020 – Discussion started: 22 April 2020
Accepted: 6 August 2020 – Published: 6 November 2020
Abstract. The emphasis for informing policy makers on future sea-level rise has been on projections by the
end of the 21st century. However, due to the long lifetime of atmospheric CO2, the thermal inertia of the climate
system and the slow equilibration of the ice sheets, global sea level will continue to rise on a multi-millennial
timescale even when anthropogenic CO2emissions cease completely during the coming decades to centuries.
Here we present global sea-level change projections due to the melting of land ice combined with steric sea
effects during the next 10 000 years calculated in a fully interactive way with the Earth system model of interme-
diate complexity LOVECLIMv1.3. The greenhouse forcing is based on the Extended Concentration Pathways
defined until 2300 CE with no carbon dioxide emissions thereafter, equivalent to a cumulative CO2release of
between 460 and 5300 GtC. We performed one additional experiment for the highest-forcing scenario with the
inclusion of a methane emission feedback where methane is slowly released due to a strong increase in surface
and oceanic temperatures. After 10 000 years, the sea-level change rate drops below 0.05 m per century and a
semi-equilibrated state is reached. The Greenland ice sheet is found to nearly disappear for all forcing scenarios.
The Antarctic ice sheet contributes only about 1.6 m to sea level for the lowest forcing scenario with a lim-
ited retreat of the grounding line in West Antarctica. For the higher-forcing scenarios, the marine basins of the
East Antarctic Ice Sheet also become ice free, resulting in a sea-level rise of up to 27 m. The global mean sea-
level change after 10 000 years ranges from 9.2 to more than 37 m. For the highest-forcing scenario, the model
uncertainty does not exclude the complete melting of the Antarctic ice sheet during the next 10 000 years.
1 Introduction
Modern sea-level rise started at the end of the 1800s and
has accelerated over the course of the 20th century (Church
and White, 2011; Hay et al., 2015) with an unprecedented
rate over the observational era during the first part of the
21st century (Watson et al., 2015). The rate of sea-level rise
was 2.5 times faster during the last decade than during most
of the 20th century (Oppenheimer et al., 2019). So far, the
horizon for most global mean sea-level change projections
has been the end of the 21st century (Jackson and Jevrejeva,
2016; Kopp et al., 2017; Goelzer et al., 2020b; Seroussi et al.,
2020). Sea-level change projections beyond 2300 are scarce
(Clark et al., 2016). However, due to the long lifetime of car-
bon dioxide in the atmosphere (Archer et al., 2009b) and the
thermal inertia of the climate system (Solomon et al., 2009;
Gillett et al., 2011; Goelzer et al., 2012), sea level is expected
to continue to rise on a multi-centennial to multi-millennial
timescale. Moreover, the large ice sheets themselves have
a very long response time to any perturbations (Golledge,
2020) with the longest response time exceeding several mil-
lennia for changes in the surface mass balance and ice dis-
charge in Antarctica (Alley and Whillans, 1984; Mengel et
al., 2016).
Several feedbacks in the climate system reinforce an initial
perturbation and on a multi-millennial timescale, a climate-
warming–methane feedback might initiate. The increase in
Published by Copernicus Publications on behalf of the European Geosciences Union.
954 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
polar temperatures slowly releases methane from permafrost
regions and accelerates climate change on a centennial
timescale (Schuur et al., 2015). It is believed that a warm-
ing ocean could potentially also release a massive amount of
methane from methane clathrates, somewhat similar to what
is thought to have happened at the Palaeocene–Eocene Ther-
mal Maximum (PETM; Zeebe and Zachos, 2013). This event
took place at about 56 Ma and was characterized by a rapid
global temperature rise of more than 5 ◦C in addition to a
strong background warming, probably caused by the mas-
sive release of methane from clathrate hydrates (Dickens,
2011). These methane hydrates were released due to ther-
modynamic changes in the sediments where the hydrates are
stored and this might happen again under long-term future
climate warming (Dean et al., 2018).
On a multi-millennial timescale, changes in land ice vol-
ume (mass contribution) together with ocean density changes
from thermal expansion (thermosteric contribution) and ha-
line contraction (halosteric contribution) are the main com-
ponents contributing to global sea-level change (Miller et al.,
2005). The mass contribution comes from melting or grow-
ing of the Antarctic ice sheet, the Greenland ice sheet, and
glaciers and ice caps. The steric contribution is the expan-
sion of ocean water when it gets warmer and less saline or,
conversely, the contraction when water is cooling and gets
saltier (Feistel, 2010). The magnitude of thermal expansion
depends on the climatic temperature forcing and on the rate
of oceanic heat uptake. Because of the large mass and slow
turnover time of the deep ocean, the oceanic heat content
(and hence thermal expansion) will continue to rise in the
ocean for multiple centuries, even when surface warming has
halted. Haline contraction – or the expansion of ocean water
due to freshening – is a smaller, though not negligible com-
ponent of steric sea-level change.
Physically based models have been used to study the dif-
ferent components contributing to global sea level on a multi-
millennial timescale. For example, long-term ice sheet evo-
lution and resulting sea-level change projections have been
made for the next few millennia for the Greenland ice sheet
(Charbit et al., 2008; Robinson et al., 2012; Applegate et al.,
2015), the Antarctic ice sheet (Huybrechts, 1993; Golledge
et al., 2015; Pollard et al., 2015; Winkelmann et al., 2015;
DeConto and Pollard, 2016), or both (Vizcaíno et al. 2008;
Huybrechts et al., 2011). Among those studies, few had a
full coupling between the ice sheet, the ocean, and the at-
mospheric component (Charbit et al., 2008; Vizcaíno et al.,
2008; Huybrechts et al., 2011). One study used a full cou-
pling only between the ice sheets and the atmosphere (Robin-
son et al., 2012), while most other studies (Huybrechts, 1993;
Applegate et al., 2015; Golledge et al., 2015; Pollard et al.,
2015; Winkelmann et al., 2015; DeConto and Pollard, 2016)
used ice sheet models that were one-way forced without the
inclusion of freshwater forcing of the ocean or the albedo–
temperature feedback.
Existing long-term sea-level change projections including
both the changes in land ice volume and the steric compo-
nents extend for the next 2000 years (Levermann et al., 2013)
or 10 000 years (Clark et al., 2016). However, these stud-
ies did not take the full coupling between the ice sheets, the
ocean, and the atmosphere into account, which becomes im-
portant when the ice sheets lose large volumes of freshwa-
ter. Goelzer et al. (2012) studied the committed sea-level rise
at the end of 3000 CE with a coupled model approach for a
range of idealized CO2scenarios. So far, the study of semi-
equilibrated sea-level changes including all components of
future sea-level change with the incorporation of feedbacks
between the climate components has not been performed
because of the high computational cost. The trade-off be-
tween model complexity and model interactions on a multi-
millennial timescale adopted here consists of the use of the
Earth system model of intermediate complexity LOVECLIM
with a lower resolution but with full coupling.
In this study, we project the global mean sea-level changes
for the next 10 000 years in a fully interactive way between
all major components in the climate system. The duration of
the simulations allows the climate system to reach a semi-
equilibrated state, a long time after the cessation of anthro-
pogenic greenhouse gas emissions. The greenhouse gas forc-
ing follows the Extended Concentration Pathway (ECP) sce-
narios (Meinshausen et al., 2011) to span the likely range in
emission uncertainties with the inclusion of a methane emis-
sion feedback in a warming climate.
2 Model description and initialization
High-resolution general circulation models (GCMs) are the
best tools to project climate changes until the end of the cen-
tury or a few hundred years after that, but they are computa-
tionally too expensive to make millennial to multi-millennial
projections. Earth system models of intermediate complex-
ity (EMICs) have a lower resolution and therefore allow
for longer simulations such as simulating the climate over
the last millennium (Eby et al., 2013) or exploring climate–
carbon-cycle feedbacks during the next 1000 years (Zickfeld
et al., 2013). With recent progress in computational power,
it is expected that Earth system models with a higher spa-
tial resolution will be able to simulate the climate over the
last millennium (Jungclaus et al., 2017). Here we make use
of the EMIC LOVECLIMv1.3 (Goosse et al., 2010) for the
projections of global sea-level change on a multi-millennial
timescale. LOVECLIM is one of the few EMICs (together
with CLIMBER and UVic; Eby et al., 2013) with an ice sheet
component (AGISM) that is fully coupled to the other com-
ponents of the climate system (ECBilt for the atmosphere;
CLIO for the ocean and sea ice; VECODE for the terres-
trial biosphere), allowing for multi-millennial projections of
sea-level change. ECBilt is a quasi-geostrophic atmospheric
model with truncation T21, corresponding to a resolution
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J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 955
in longitude and latitude of approximately 5.625◦and three
vertical levels (Opsteegh et al., 1998). The surface air tem-
perature in the coarse-resolution atmospheric component is
extrapolated from higher levels based on reference profiles
from NCEP-NCAR reanalysis (Kalnay et al., 1996). The sur-
face wind in LOVECLIM is calculated as a fraction (0.8) of
the surface wind speed at the 800 hPa level (Goosse et al.,
2010). CLIO is a global free surface ocean GCM coupled to
a thermodynamic sea-ice model, with a resolution of 3◦in
longitude and latitude and 20 unevenly spaced vertical levels
(Goosse and Fichefet, 1999). AGISM, the ice sheet model
component consists of 3-D thermomechanically coupled ice
sheet models for the Greenland ice sheet and the Antarctic
ice sheet (Huybrechts and de Wolde, 1999). The ice sheet
models include an isostasy model that consists of an elas-
tic lithosphere on top of a viscous asthenosphere to simulate
bedrock elevation changes in response to ice sheet changes.
They are run at a resolution of 10 km for the Greenland ice
sheet and 20 km for the Antarctic ice sheet. The relatively
coarse resolution is necessary to allow for long integrations.
The global glacier melt algorithm is based on the model of
Raper and Braithwaite (2006) that considers a total sea-level
equivalent (SLE) of 0.241 m (mountain glaciers contain 41 %
of this estimate, while the ice caps are responsible for the
other 59 % of sea-level rise, SLR, potential). This is at the
lower end of the range of total recent estimates of ice vol-
ume (0.24–0.40 m SLE) stored in all ∼215 000 glaciers on
Earth (Farinotti et al., 2019), partly explained by the fact
that the glacier model excludes glaciers in the periphery of
the Greenland and Antarctic ice sheets. The steric sea-level
change component is calculated based on regional changes
in ocean temperature and salinity. The ocean carbon cycle
is not activated and greenhouse gas concentrations are pre-
scribed (see Sect. 3 and Appendix A).
The model has been used previously for ice sheet and cli-
mate change projections for periods in the past (Loutre et al.,
2014; Goelzer et al. 2016a, b) and the future (Huybrechts et
al., 2011; Goelzer et al., 2012). The version used here differs
from LOVECLIMv1.3 for the Antarctic ice sheet component
by including surface ablation on the ice shelves, an impor-
tant process under future atmospheric warming. A tundra
warming feedback is also included for retreating ice sheets
by making a distinction between snow/ice albedo and tundra
albedo. The snow/ice albedo is replaced by tundra albedo
(with a lower albedo) once the ice sheet margin is retreat-
ing on land. In order to better represent the climate forc-
ing for the ice sheet models, temperature and precipitation
anomalies are applied to the average over a reference pe-
riod (1970–2000) to eliminate the climatic model bias for
the present day. The surface mass balance is calculated using
the positive degree day (PDD) method for both ice sheets.
The melt is parameterized based on the yearly sum of daily
average temperatures above 0◦C to determine the melt po-
tential. The melt potential is used to melt snow or ice, with
different conversion factors (degree day factors) for snow and
ice. The rain limit determines whether precipitation falls as
snow or as rain. An increase in precipitation will add mass
to the ice sheet surface as long as temperatures are lower
than the rain limit (1 ◦C in our simulations). Retention and
refreezing of meltwater in the snowpack are also included.
The PDD model has the advantage that it is calculated on
the high-resolution grid of the ice sheet model in comparison
to an energy balance model from a coarse-resolution climate
model. The Antarctic ice sheet model uses the shallow ice ap-
proximation (SIA) for grounded ice and the shallow shelf ap-
proximation (SSA) for the ice shelves coupled across a one-
grid-cell-wide transition zone. Basal melting is calculated as
a function of the mean oceanic heat input into the ice shelf
cavities. Sea-level changes resulting from the melting of the
marine-based parts of the Antarctic ice sheet are corrected
for bedrock elevation changes (Goelzer et al., 2020a). The
Greenland ice sheet model is identical to previous versions
of the model employed within the LOVECLIM framework
(Goelzer et al., 2012, 2016a, b). Both ice sheet models have
recently participated in the ISMIP6 initiative (Goelzer et al.,
2020b; Seroussi et al., 2020).
Since many physical parameters in a climate model are
uncertain, LOVECLIM is used to explore the climate re-
sponse for a large combination of climate model parameter
sets (Loutre et al., 2011). Here we have evaluated four dif-
ferent model parameter sets by testing the sea-level contri-
bution for the period 1900–2300 CE. The four model param-
eter sets (P11, P22, P32a, P32b; see Table S3 in the Sup-
plement) differ in their sensitivity to the applied greenhouse
forcing (P32b and P32a >P22 >P11) and freshwater forc-
ing in the North Atlantic (P32a, P32b, and P22 >P11). All
climate model parameter sets yield climate simulations in
agreement with observations over the past 500 years (Loutre
et al., 2011). Model parameter set P22 is chosen for the multi-
millennial integrations because of its mid-range contribution
to sea level at 2100 CE and 2300 CE in comparison with re-
cent studies (Pörtner et al., 2019; Calov et al., 2018; Bulthuis
et al., 2019; Tables S1–S2 and Fig. S1 in the Supplement) and
its agreement in polar temperature forcing at the end of the
21st century. The mean annual temperature anomalies over
the ice sheets for 2070–2100 relative to 1970–2005 (+4.6◦C
over Greenland and +3.8◦C over Antarctica for Represen-
tative Concentration Pathway 8.5, RCP8.5) correspond well
with the mid- to upper ranges of Atmosphere–Ocean Gen-
eral Circulation Model (AOGCM) projections over the polar
regions (Fettweis et al., 2013; Barthel et al., 2020). With an
equilibrium climate sensitivity of 2.3 ◦C, the model param-
eter set is at the lower end of IPCC AR5 estimates (likely
range of 1.5–4.5 ◦C) due to a cold bias in the tropics.
The Greenland ice sheet and Antarctic ice sheet are spun-
up from stand-alone experiments forced with reconstructed
temperature forcing above the ice sheet following ice core
records for respectively two and four glacial–interglacial cy-
cles to carry their long-term ice sheet history (Huybrechts et
al., 2011; Goelzer et al., 2012). A quasi-equilibrium experi-
https://doi.org/10.5194/esd-11-953-2020 Earth Syst. Dynam., 11, 953–976, 2020
956 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
Figure 1. The Greenland ice sheet and the Antarctic ice sheet ge-
ometry after the spin-up procedure at 2000 CE.
ment is run with the aim of getting a climate in equilibrium
at 1500 CE with the ice sheet forcing. The ice sheet mod-
els in this experiment evolve very slowly for a fixed climate
forcing. The climate model on the other hand is subject to
changes in the ice sheet models (changes in freshwater flux,
albedo, and height changes) and equilibrates to these bound-
ary conditions. At the end of the quasi-equilibrium run (af-
ter 2500 years when the temperature and ice sheet volume
changes become negligible), a steady state is reached. A con-
trol experiment with constant pre-industrial greenhouse gas
forcing showed that the drift in climate and ice sheet com-
ponents is negligible. The climate information present at the
end of the quasi-equilibrium experiment is used as input for
the initialization of the fully coupled experiments starting at
1500 CE.
The fully coupled model is run from 1500 to 2000 CE.
LOVECLIM is forced during this historical period with
known greenhouse gas concentrations, total solar irradiance,
and volcanic forcing. Now, all components of LOVECLIM
interact dynamically and are run as an ensemble of five mem-
bers. The ensemble members are identical except for small
perturbations in the initial boundary conditions of the atmo-
spheric component. Next, the ensemble runs are iterated with
an updated reference state for the ice sheet models to de-
termine whether there is convergence for the climatic infor-
mation (e.g. Greenland and Antarctic temperature forcing,
oceanic heat content, and meridional overturning circulation
variability). The experiment performing best at representing
the climate over the last 500 years is chosen as input for
the long-term future projections. The Greenland and Antarc-
tic ice sheet geometry at the start of the future projections
(2000 CE) is shown in Fig. 1.
3 Scenario description
Six different forcing scenarios are constructed to span a
large range of future greenhouse gas forcing. The main dif-
ference between the different scenarios is the atmospheric
carbon dioxide forcing. Four of the CO2forcing scenarios
are extensions of the ECP scenarios (Meinshausen et al.,
2011) and will be introduced here as Multi-Millennial Con-
centration Pathways (MMCPs) with the same designation
as the RCP scenarios (MMCP2.6, MMCP4.5, MMCP6.0,
and MMCP8.5). The scenarios range from a peak in the
CO2concentration of 443 ppmv in 2053 CE with temporar-
ily negative emissions thereafter (MMCP2.6) to a peak of
1962 ppmv in 2250 CE (MMCP8.5). Estimates of the total
recoverable carbon (oil, gas, lignite, and coal) reserves (the
total exploitable carbon) and resources (total carbon mass
stored on earth, including the non-exploitable carbon) are
disputed, ranging from <1500 GtC reserves and 4000 GtC
resources (Hasselmann et al., 2003) up to 2900 GtC reserves
and 11 000 GtC resources (McGlade and Ekins, 2015). In this
study, the MMCP scenarios (extended ECP scenarios with
zero emissions after 2300 CE) are equivalent to a total cumu-
lative emission ranging from less than 200 GtC for scenario
MMCP2.6 to more than 5000 GtC for scenario MMCP8.5
relative to the year 2000 CE (see Appendix A: Table A3).
This is comparable to the study from Clark et al. (2016)
with an emission pulse of 1280–5120 GtC but well below the
study from Winkelmann et al. (2015), which assumes a total
carbon release of up to 10 000 GtC.
Two additional scenarios are constructed because of
the large difference in emissions between MMCP6.0 and
MMCP8.5 and to allow for an upper-end scenario that
exceeds MMCP8.5 because of a methane emission feed-
back. The first one assumes that CO2concentrations fol-
low ECP8.5 but emissions will cease completely by the
year 2150 CE. This scenario is referred to as MMCP-break
and is an intermediate forcing scenario between MMCP6.0
and MMCP 8.5. The second additional scenario (MMCP-
feedback) is similar to MMCP8.5 up to 2250 CE but assumes
that methane emissions increase as a feedback to the warm-
ing climate (Table A3). The size of the methane reservoir is
a major unknown and estimates range from 500–3000 GtC
(Piñero et al., 2013) to 5000–20 000 GtC (Dickens, 2011).
Ruppel and Kessler (2017) made an extensive review to es-
timate the size of the methane hydrate reservoir and finds a
converging value of around 2000 GtC. MMCP-feedback as-
sumes a moderate methane release from methane hydrates
of 600 GtC by adding constantly CO2after 2250 CE (from
the peak concentration onwards) until the end of the simula-
tions (equivalent to a release of 6.15 GtC per 100 years), in
accordance with the experiments of Archer et al. (2009a). It
is thought that methane hydrate dissolution caused a strong
increase in atmospheric CO2levels with a possible total re-
lease of >5000 GtC during the PETM (Dickens, 2011). This
release would have been caused by an initial warming trig-
ger and might have lasted for more than 100 kyr (Zeebe and
Lourens, 2019). Therefore, our estimate of the strength of
the methane emission feedback is in the same order of mag-
nitude as the methane emission rate during the PETM (5 GtC
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J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 957
Figure 2. (a) Atmospheric CO2concentration scenario from 1500 CE to 12 000CE for the six different forcing scenarios. (b) Global mean
temperature change for the historical period 1500–2000 CE and the future projections, (c) Greenland mean temperature change, and (d)
Antarctic mean temperature change for the six forcing scenarios. All temperature projections are shown as an anomaly to a reference period
1970–2000.
per 100 years). Also, it is thought that it takes a long time
(>10 000 years) before a significant part of the sediment
has warmed in response to the ocean bottom temperature in-
crease (Zeebe, 2013), supporting our conservative methane
release in comparison to the size of the methane reservoir. At
least 50 % of the methane released from the hydrates would
be anaerobically oxidized inside the seafloor, and an addi-
tional part is converted into CO2in the water column by
aerobic oxidation (Treude et al., 2003). In our experiments,
it is assumed that the methane released from methane hy-
drates is completely oxidized into CO2when it reaches the
atmosphere. Note that this approach neglects the short-term
warming effect of methane when it is released. Also, in our
RCP-based scenarios, we do not include a case where car-
bon dioxide removal (CDR) technologies become so efficient
that CO2levels might drop below present-day levels in the
next decades, even though scenario MMCP2.6 includes the
use of CDR technologies to achieve negative emissions after
2050 CE.
The carbon dioxide concentrations follow the ECP scenar-
ios until 2300 CE with zero emissions thereafter (Fig. 2a).
Impulse response functions are used to construct the falloff of
carbon dioxide concentrations (Appendix A). Carbon cycle
models show that a perturbation of CO2can remain in the at-
mosphere for tens of thousand of years (Archer et al., 2009b;
Lord et al., 2016). After a perturbation, atmospheric carbon is
taken up by the land biosphere (∼100 years), ocean invasion
(10–1000 years), CaCO3weathering (1000–10 000 years),
and silicate weathering (10 000–1 000000 years) to eventu-
ally restore the initial concentrations (Ciais et al., 2013). The
more carbon is emitted, the slower the uptake of carbon diox-
ide in the ocean due to the reduction in buffering capac-
ity (Archer et al., 2009b). The constructed carbon dioxide
concentrations for the next 10 000 years take these effects
into account in a schematic way and are shown in Fig. 2a.
Methane (average lifetime of 9 years) and nitrous oxide (av-
erage lifetime of 131 years) concentrations are kept con-
stant at their concentration in 2300 CE (Meinshausen et al.,
2011) because the natural emission rate is high and the nat-
ural emission rate is expected to increase in a warming cli-
mate (Kirschke et al., 2013; Griffis et al., 2017). Methane and
nitrous oxide and other greenhouse gases follow the trajec-
tory until 2300 CE as presented in Meinshausen et al. (2011)
and either decrease to zero when the trend is declining and
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958 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
the lifetime of the gases is short (chlorofluorocarbons, CCl4,
and CH3CCl3) or stay constant over the next 10 000 years
when the overall trend is unclear (hydrofluorocarbons and
hydrochlorofluorocarbons).
The orbital parameter variations and insolation changes
are accounted for. However, the insolation differences in
the polar regions are rather small (summer insolation will
slightly increase in the Northern Hemisphere and decrease
in the Southern Hemisphere compared to the present day)
on account of a low eccentricity (eccentricity will decrease
further from the present-day value of 0.0167 to 0.0116 at
12 000 CE), and therefore its influence on the radiative forc-
ing is limited. The future solar cycles are unknown and there-
fore the last 11-year solar cycle is repeated for the next
10 000 years.
4 Climate response and global sea-level budget of
individual terms
The following section shows the climate response to the
greenhouse gas forcing and insolation variations. Next, the
sea-level changes resulting from mass changes of the Green-
land ice sheet (GrIS), the Antarctic ice sheet (AIS), glaciers
and ice caps, and the steric contribution to sea-level are
shown. The relative importance of each contribution to global
mean sea level (GMSL) following a specific scenario is dis-
cussed. Additionally, the interactions between the Greenland
ice sheet and the Atlantic Meridional Overturning Circula-
tion (AMOC) and the Antarctic ice sheet and Antarctic Bot-
tom Water (AABW) are addressed. Finally, the uncertainty
in GMSL rise is assessed for the extreme forcing scenar-
ios MMCP2.6 and MMCP-feedback using different climatic
model parameters.
4.1 Climate response
Global mean surface air temperature (SAT) is projected to
increase between 1.7 and 5 ◦C following the strong increase
in greenhouse gas forcing (Fig. 2b). In the polar regions, the
reduction in sea-ice area and its large effect on absorption
of heat through the ocean surface albedo leads to an ampli-
fied response to the climatic forcing. Moreover, the height–
mass-balance feedback and the albedo–temperature feedback
cause the GrIS mean annual SAT to rise even further as ice
is melting. This is most obvious for the mean annual SAT
anomaly using scenarios MMCP2.6 to MMCP-break where
the SAT increased strongly when the GrIS melted an equiv-
alent of around 2 m of sea level (Fig. 2c). The increase in
Antarctic mean temperature over the next 10 000 years shows
a very large spread between the different scenarios. This is
partly caused by a decreasing sea-ice area trend and its in-
fluence on the albedo, where the retreat will be larger for
the high-forcing scenarios (Fig. 3). The simulated SAT for
the Greenland and Antarctic region are provided at 2000 CE,
3000 CE, and 12 000 CE (Figs. S2, S3 and S4). The influence
Figure 3. Mean sea-ice area evolution in the Southern Ocean for
the six different forcing scenarios.
Figure 4. Summer insolation at 70◦N (June) and 70◦S (Decem-
ber) from 130 kyr ago at the onset of the last interglacial to the next
50 kyr. The period of our study is highlighted with vertical red lines.
of the orbital parameter changes results in an increased forc-
ing above the GrIS and a decreased forcing above the AIS
during the next 10 000 years compared to the present day
(Fig. 4). Snow accumulation is projected to increase for all
forcing scenarios due to the increase in atmospheric water
vapour, whereas the increase in accumulation will be larger
for the strongest warming scenarios (up to 16 % for scenario
MMCP-feedback over the Antarctic continent). Freshwater
fluxes from the Greenland and Antarctic ice sheets lead to
temporarily reduced temperatures and a delayed peak warm-
ing over the ice sheets.
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J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 959
4.2 The steric component
The steric component of GMSL change shows an increase
following global mean temperature perturbations with the
longer response time for the higher-forcing scenarios. Steric
sea level rises rapidly before showing a period of stabiliza-
tion for all scenarios. Except for scenarios MMCP2.6 and
MMCP4.5, this period is followed by another more grad-
ual increase in sea-level rise during the second half of the
simulations (Fig. 5). This is most pronounced for scenar-
ios MMCP6.0 and MMCP-break, where the steric contribu-
tion to GMSL rise reaches 0.3 and 0.4 m respectively be-
tween 7000 CE and 12 000CE. Oceanic temperatures have
already equilibrated to the forcing, and at 12 000 CE, deep
ocean temperatures are slightly lower than temperatures at
7000 CE, following the slow decrease in global mean tem-
perature anomalies (Fig. 6). Therefore, we attribute the sea-
level rise during the second half of the simulations to the
continued freshwater release from the Antarctic ice sheet. On
the other hand, the steric contribution to GMSL slightly de-
creases for scenarios MMCP2.6 and MMCP4.5 after a peak
at 3000 CE. Freshwater fluxes are still high due to a slow
melting of the GrIS, suggesting that the lower increase in
global mean temperatures decreases the response time. At
the end of the simulations, the total range of the steric com-
ponent to GMSL change is between 0.4 (MMCP2.6) and 3 m
(MMCP-feedback).
4.3 The Greenland ice sheet and the AMOC
The GrIS volume changes because of an imbalance between
the surface mass balance (SMB), i.e. the difference between
accumulation and ablation, and iceberg calving at the ice
sheet margin. Surface runoff is projected to increase for all
the forcing scenarios, though the magnitude differs signif-
icantly. After 4000 years, surface runoff exceeds accumu-
lation and the surface mass balance becomes negative even
for the lowest forcing scenario (Fig. 7c). In scenario MMCP-
feedback, this might happen already at the end of the 21st
century (Fig. 7d). When looking at all the mass balance com-
ponents, one can see that the relative importance of iceberg
calving decreases when the ice sheet retreats on land. The
large amounts of meltwater result in a total freshwater flux
anomaly of 0.03 to 0.05 Sv for the three higher-forcing sce-
narios and are sustained for 1000 to 1500 years (Fig. 8a). The
AMOC almost completely shuts down for the two highest-
forcing scenarios (Fig. 9). This results in a local cooling
south of the GrIS and a delayed peak warming above the
Greenland ice sheet (most pronounced for MMCP-feedback;
Fig. 2c), pointing to the importance of simulations with a
coupled ocean–atmosphere–ice-sheet model. The AMOC re-
covers again after the ice sheet has melted entirely and even
becomes stronger for the higher-forcing scenarios (Fig. 10).
4.4 The Antarctic ice sheet and AABW
The Antarctic continent is very cold, and there is almost no
surface melt over the grounded ice at present. There is a very
distinct response of the AIS to a low or a high forcing in
terms of mass loss. Looking at the two extremes, ice dis-
charge at the grounding line is projected to increase slightly
for scenario MMCP2.6, similar to previous suggestions that
increased ice discharge is a response to increased accumula-
tion (Winkelmann et al., 2012). The ice shelves thin for 1700
years because of atmospheric warming, while basal melting
rates below the ice shelves remain low with a mean value
of 0.3 m yr−1over all the ice shelves. The ice shelves lose
two-thirds of their volume, but they recover again to reach
their initial volume after 5000 years when surface ablation
becomes negligible. In scenario MMCP-feedback, even the
large ice shelves around Antarctica disappear nearly com-
pletely after 300 years as a combination of atmospheric
warming (and subsequent surface ablation) and a quadru-
pling in ice shelf basal melt rates. Ice discharge across the
grounding line is projected to increase for about 500 years
and drops below present-day values after 1700 years when
the West Antarctic Ice Sheet has collapsed and the East
Antarctic Ice Sheet starts to retreat land inwards. The in-
crease in surface runoff is even stronger and exceeds accu-
mulation at the end of the first millennium for about 3000
years, after which surface runoff and ice discharge along the
grounding line stabilize and account each for about half of
the mass loss (Fig. 11d). The freshwater input in the South-
ern Ocean increases with 0.14 Sv for the highest-forcing sce-
nario and remains elevated until the end of the simulations
with an anomaly of 0.07 Sv due to continued ice sheet melt-
ing and increased runoff over land (Fig. 8b). As a conse-
quence of the freshwater release into the Southern Ocean, the
strength of AABW declines with 23 % for MMCP2.6 and up
to 77 % for MMCP-feedback during the next 500 years due
to rapid ice sheet melting (Fig. 9b). These freshwater fluxes
from the AIS lead to reduced oceanic warming in the vicinity
of Antarctica and relatively low basal melt rates in our exper-
iments (mean basal melt rates of 0.5–1.1 m yr−1for scenario
MMCP-feedback during the coming centuries). Mean SAT
anomalies above the Antarctic ice sheet reach a maximum
between 5000 and 6000 CE when the ice sheet retreats on
land and the albedo–temperature feedback sets in (Fig. 2d).
The mass balance components stabilize during the second
half of the simulations with iceberg calving and ablation both
accounting for half of the mass loss, a situation comparable
to the Greenland ice sheet today.
There is a very large difference in ice sheet geometry of
the AIS after 10 000 years for the lowest- and highest-forcing
scenario. In scenario MMCP2.6, the grounding line retreats
mostly in the Weddell Sea and the Ross Sea basin, with al-
most no retreat for the East Antarctic Ice Sheet (Fig. 11a).
For the high emission pathway, the West Antarctic Ice Sheet
collapses and grounding line retreat initiates in the Wilkes
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960 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
Figure 5. The contribution of the different components to GMSL rise during the next 10 000 years for each of the forcing scenarios. The ice
sheet geometry of Greenland and Antarctica is shown at the end of the simulations.
subglacial basin (Fig. 11b). Due to isostatic rebound of
the Earth’s crust, more land is exposed above sea level at
12 000 CE compared to the situation at 7000CE and the ice
sheet margin becomes land-based for most of East Antarc-
tica as has been proposed for warm intervals during the mid-
Miocene (Gasson et al., 2016; Frigola et al., 2018).
4.5 Glaciers and ice caps
Glaciers and ice caps have a decadal to century timescale
response and are vulnerable to small perturbations in the
climate forcing. For the highest-forcing scenarios MMCP-
break, MMCP8.5, and MMCP-feedback, the glaciers and ice
caps melt away entirely in the coming 1000 to 2000 years.
Under scenario MMCP2.6 it takes up to 3000 years before
the glaciers and ice caps lose most of their ice volume. On
the multi-millennial timescale, the differences in the glaciers’
and ice caps’ contribution to sea-level change are very small
compared to the other components with total contributions
between 0.23 and 0.24 m for any of the forcing scenarios.
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J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 961
Figure 6. Ocean temperature anomaly across the Atlantic ocean using scenario MMCP2.6 at 2100 CE (a), 2300 CE (b), 7000 CE, and (c),
12 000 CE (d) and using scenario MMCP-feedback at 2100 CE (e), 2300 CE (f), 7000 CE (g), and 12 000CE (h).
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962 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
Figure 7. (a) Greenland ice sheet configuration at 3000 CE, 7000 CE, and 12 000CE using scenario MMCP2.6 and (b) MMCP-feedback.
Main mass balance components explaining the change in ice sheet geometry for scenarios MMCP2.6 (c) and MMCP-feedback (d). Note that
the land–sea mask has not changed due to the change in GMSL but only due to isostatic changes.
5 Global mean sea-level change
Total GMSL changes in our experiments range between
9.2 and 37.4 m at the end of the 10 000 year experiments
(Fig. 12a). Moreover, the rates of GMSL rise vary substan-
tially between the different scenarios and over time. We in-
vestigate the relation between cumulative CO2emissions and
GMSL change, somewhat similar to the notion of a rela-
tionship between global warming and cumulative CO2emis-
sions by a certain time, expressed as the transient climate re-
sponse to cumulative carbon emissions (TCRE; Matthews et
al., 2018) or the multi-millennial climate response to cumula-
tive carbon emissions (MCRE; Frölicher and Paynter, 2015).
In Fig. 12b, the realized GMSL rise after each 1000 years
is shown as a function of the total cumulative CO2emission
after 2000 CE for each experiment.
In the case of total cumulative CO2emission exceeding
2000 GtC, GMSL change rates are highest during the first
2 millennia. However, when cumulative CO2emissions stay
below 200 GtC (MMCP2.6), the peak rates in GMSL change
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J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 963
Figure 8. Freshwater flux anomalies with respect to 1970–2000
from (a) the Greenland ice sheet and (b) the Antarctic ice sheet
for the six different forcing scenarios.
occur only 4000 to 8000 years from now due to slow melt-
ing of the GrIS and ensuing feedbacks. A total sea-level rise
of 9.2 m is achieved after 10 000 years, even though CO2
emissions already ceased before the mid-21st century. For
the other experiments, the rate of sea-level change decreases
with time. All experiments approach a semi equilibrium after
10 000 years (Fig. 12a). The rate of global sea-level change is
then still positive for all simulations, albeit reduced to about
0.05 m per century for the experiment with the largest cu-
mulative CO2emission (MMCP-feedback). This reflects the
long equilibration time for the ice sheets and the ocean within
the coupled climate system to adapt to temperature changes.
In our simulations, Greenland is the largest contributor to
GMSL rise up to a cumulative CO2emission of 2000 GtC.
The grounding line of the West Antarctic Ice Sheet (WAIS)
retreats several 100 km inland using scenario MMCP2.6 and
MMCP4.5. The WAIS disintegrates completely for cumu-
lative CO2emissions around 2000 GtC, but East Antarctica
Figure 9. Mean annual strength of the North Atlantic Deepwater
(NADW) (a) and the Antarctic Bottom Water (AABW) (b) forma-
tion from 2000 CE to 12 000CE. AABW is defined as the maximum
of the global meridional overturning streamfunction in the bottom
cell and NADW as the maximum of the meridional overturning cir-
culation in the Greenland, Iceland, and Norwegian seas.
still remains mostly unaffected. For higher cumulative emis-
sions, marine-based parts of East Antarctica start to disinte-
grate and Antarctica becomes the largest source for GMSL
rise.
The total sea-level rise at 12 000 CE includes the (nearly)
entire melt of the Greenland ice sheet as well as glaciers and
ice caps. The spread is largest for the Antarctic contribution
taken over all scenarios, ranging from 1.6 to 27 m (corre-
sponding to ∼200 to ∼5000 GtC cumulative CO2emissions
after 2000 CE). The steric contribution ranges between 0.4
and 3 m. Table 1 gives an overview of the sea-level contribu-
tion and the relative share to GMSL of each component for
all forcing scenarios.
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964 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
Table 1. Sea-level contribution from the different components contributing to GMSL change for scenarios MMCP2.6, MMCP4.5, MMCP6.0,
MMCP-break, MMCP8.5, and MMCP-feedback, shown in metres and as a percentage of GMSL change.
Antarctic Greenland Steric Glaciers and GMSL
ice sheet ice sheet component ice caps rise
MMCP2.6 1.6 m (17.4 %) 7.0 m (76.1 %) 0.4 m (4.3 %) 0.23 m (2.5 %) 9.2 m
MMCP4.5 1.9 m (18.8 %) 7.3 m (72.3 %) 0.7 m (6.9 %) 0.23 m (2.3 %) 10.1 m
MMCP6.0 6.6 m (42.9 %) 7.3 m (47.4 %) 1.3 m (8.4 %) 0.24 m (1.6 %) 15.4 m
MMCP-break 12.0 m (54.8 %) 7.4 m (33.8 %) 2.3 m (10.5 %) 0.24 m (1.1 %) 21.9 m
MMCP8.5 19.7 m (65.4 %) 7.4 m (24.6 %) 2.8 m (9.3 %) 0.24 m (0.8 %) 30.1 m
MMCP-feedback 26.8 m (71.7 %) 7.4 m (19.8 %) 3.0 m (8.0 %) 0.24 m (0.6 %) 37.4 m
6 Global mean sea-level change uncertainty
The uncertainty in the future sea-level change projections, re-
lated to the climatic parameters in LOVECLIM, is evaluated
by running the coupled model for three different climatic pa-
rameter combinations (P32a, P22, and P11). As explained
in the model description, the main difference is denoted by
the first digit and represents a measure of the model climate
sensitivity (CS) where the CS is largest for P32a and low-
est for P11 (more information on the parameter differences
can be found in the Supplement). There is limited model un-
certainty in GMSL change during the next 10 000 years for
the lowest-forcing scenario MMCP2.6. GMSL rise ranges
between 7.5 m for parameter set P11 to 9.2 m for parameter
set P22. For scenario MMCP-feedback, the range in GMSL
rise is very large going from about 19.9 m for parameter set
P11 to 77.0 m for parameter set P32a (Fig. 13). The maxi-
mum sea-level rise consists of a contribution of 63m from
the AIS, 7.3 m from the GrIS, 5.8 m from the steric compo-
nent, and 0.24 m from glaciers and ice caps. Note that the
contribution of 63 m from the AIS is more than the estimate
of 58 m SLE stored in the AIS volume (Fretwell et al., 2013)
due to the inclusion of bedrock elevation changes after iso-
static unloading and its influence on sea-level rise (Goelzer
et al., 2020a).
The large uncertainty that arises using scenario MMCP-
feedback comes mainly from the AIS. Especially the accel-
eration in GMSL using parameter set P32a is remarkable,
where the fastest rates in sea-level rise occur around 7000
years from now. In this experiment, a very strong albedo–
temperature feedback initiates once a significant part of the
ice sheet retreats on land. The ice melts at a rate of 30 m SLE
in 1500 years. This freshwater input is even larger than melt-
water pulse 1A around 14.6 ka BP, where the global meltwa-
ter input is estimated to have been between 14 and 25 m in
400–500 years (Cronin, 2012), albeit in a situation where ini-
tially 3 times more ice volume was present.
7 Long-term sea-level rise in the light of the
geological record
An interesting test for our sea-level change projections can be
provided by the geological record of sea-level high stands as
a function of the reconstructed atmospheric carbon dioxide
concentration. Estimates of paleo sea-level variations range
from a lowstand of −120 m for CO2concentrations around
180 ppmv during glacial intervals of the Quaternary to a
highstand of +65 m for CO2concentrations up to 1200 ppmv
during the Eocene (Alley et al., 2005; Foster and Rohling,
2013). Such data suggest a linear sigmoidal behaviour for
(semi)-equilibrated periods in the past, where sea-level high
stands change abruptly for deviations in the greenhouse gas
forcing from the pre-industrial period due to the build-up of
the large Northern Hemisphere ice sheets during glacial peri-
ods and the total melting of the Greenland and Antarctic ice
sheets for a high-CO2greenhouse world during the Eocene
(Fig. 14). Assuming that our climate (and sea-level change)
components are nearly equilibrated after 10 000 years, we
compare our GMSL changes with the geological archive
(Foster and Rohling, 2013). For this comparison, it is im-
portant to realize that the timescale of carbon input in the
atmosphere may be a critical parameter as the peak atmo-
spheric CO2concentration shows a strong dependence on the
emission pathway. However, simulations with biogeochem-
ical models show that the mean atmospheric CO2concen-
tration over multiple kiloyears is mostly independent of the
duration of carbon release (Zeebe and Zachos, 2013). More-
over, on a multi-centennial timescale, global mean temper-
ature perturbations converge to a single value, suggesting a
pathway independence of cumulative emissions (Zickfeld et
al., 2012; Rogelj et al., 2016). We therefore opt to average
the CO2concentration over the next 10 000 years, suggesting
that the mean concentration represents the multi-millennial
temperature change at best.
Figure 14 shows the GMSL change after 10 000 years as
a function of the mean atmospheric CO2compared with the
geological archive. We compared the best fit of the data ob-
tained in this paper (red line; polynomial with exponent 3)
with the best fit of the geological data (blue line, polynomial
with exponent 2; data from Foster and Rohling, 2013). The
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J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 965
Figure 10. Meridional overturning stream function for the global
ocean at 2000 CE, 3000 CE, and 5000 CE using forcing scenario
MMCP-feedback.
fitted lines compare quite well. There is a somewhat larger
discrepancy for the lowest CO2concentrations, because we
do not include sea-level projections for CO2concentrations
below pre-industrial levels. The geological estimates of sea-
level high stands include data that are affected by the hys-
teresis effect between ice sheet growth and ice sheet decay,
where an ice sheet can either exist or not exist at a certain
CO2level depending on its history (Pollard and DeConto,
2005). In this regard, higher CO2values are needed to melt
ice sheets than to make them grow. Also the effect of a differ-
ent paleotopography might have had an influence on the in-
ception of ice on paleo timescales where the AIS could grow
for higher CO2values during the Oligocene than at present
due to the higher bedrock topography (Paxman et al., 2019).
Both arguments suggest that our curve (red line) is expected
to be below the best estimate of the geological data (blue
line), requiring higher CO2levels to melt the ice sheets on
Earth in the future than during periods in geological history.
8 Discussion
Glaciers and ice caps are the second-largest contributor to
present-day GMSL rise (after the thermosteric component)
and will continue to be a major source of sea-level rise dur-
ing the next century (Huss and Hock, 2015; Hock et al.,
2019; Marzeion et al., 2020). At the end of the 21st cen-
tury, the global glacier volume is projected to decrease by
between 21 % (MMCP2.6) and 24 % (MMCP8.5) of its cur-
rent value. The contribution to GMSL from glaciers and ice
caps melting generally corroborates the findings by Hock
et al. (2019), who found that by the end of the 21st cen-
tury mountain glaciers and ice caps lose between 11 %–25%
(RCP2.6) and 25 %–47 % (RCP8.5) of their volume. For sce-
nario MMCP8.5, our results are below the average estimates
at the end of the 21st century because of the rather low
climate sensitivity in LOVECLIM. At the end of the sim-
ulations, the lower sensitivity of our glacier model to the
high-forcing scenarios is irrelevant, and glaciers and ice caps
will lose 96 %–100 % of their volume for any of the forcing
scenarios. Raper and Braithwaite (2006) and Goelzer et al.
(2012) found that glaciers and ice caps disappear completely
for a global warming of around 4 ◦C by the end of the third
millennium.
The steric sea-level contribution has a sensitivity of be-
tween 0.27 and 0.68 m ◦C−1in our study, where the stronger
forcing scenarios have the higher contribution due to the ad-
ditional effect of haline contraction. Levermann et al. (2013)
identified a similar linear relation between thermal expan-
sion and global mean temperatures of 0.2 to 0.63 m ◦C−1.
Hieronymus (2019) assessed several coupled climate models
that include ocean circulation changes and found an updated
sensitivity of 0.51 to 0.83 m ◦C−1of surface warming. The
higher sensitivity is present in climate models that show an
increase in AMOC strength. However, the AMOC strength
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966 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
Figure 11. (a) Antarctic ice sheet configuration at 7000 CE and 12 000 CE using scenario MMCP2.6 and (b) MMCP-feedback. Only
grounded ice is shown. Main mass balance components (over grounded ice) explaining the change in ice sheet geometry for scenarios
MMCP2.6 (c) and MMCP-feedback (d). GL: grounding line. Note that the land–sea mask has not changed due to the change in GMSL but
only due to isostatic changes.
(temporarily) decreases in our experiments, especially in the
simulations where the GrIS is melting fast. Therefore, the
higher sensitivity reported by Hieronymus (2019) might be
an overestimation in future scenarios where the ice sheets
will melt strongly, due to the neglection of ice-sheet–ocean
interactions.
The largest (scenario-based) uncertainty in future multi-
millennial sea-level rise comes from the polar ice sheets. In
our simulations, the melting of the entire GrIS takes about
10 000 years for a mean SAT anomaly of 2◦C with respect
to 1970–2000 CE. In higher scenarios, the GrIS needs be-
tween 8000 years for MMCP4.5 with a mean SAT anomaly
of 5.1 ◦C and 2000 years for MMCP-feedback with a mean
SAT anomaly of 9.8 ◦C, to disintegrate entirely. Robinson et
al. (2012) found the temperature threshold for melting the
entire Greenland ice sheet to lie between 0.8 and 3.2 ◦C,
with a long decay time for temperatures close to this thresh-
old. Since the temperature anomaly in scenario MMCP2.6 is
close to this threshold, it takes about 10 000 years in our sim-
ulations to melt the entire GrIS. According to Aschwanden et
al. (2019), the GrIS will lose between 72 % and 100 % of its
volume by the end of the next millennium, using an extreme
melt forcing and neglecting the temporary cooling effect of
a reduced AMOC. Other studies found that the GrIS could
disappear in less than 3000 years for a constant CO2forcing
exceeding 1100 ppmv (Alley et al., 2005; Driesschaert et al.,
2007; Huybrechts et al., 2011), in the same range as our sim-
ulations even though the results are not entirely comparable
owing to a different time evolution of the CO2and tempera-
ture forcing.
The AMOC in LOVECLIM exhibits a monostable be-
haviour where the recovery to the initial state starts as soon as
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J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 967
Figure 12. (a) GMSL rise as the sum of the contributions from the
AIS, the GrIS, glaciers and ice caps, and the steric component. The
rate of sea-level rise during each millennium is indicated for the
lowest and highest scenarios. (b) GMSL rise for a given cumulative
CO2emission at the end of each millennium until 12 000 CE.
the meltwater pulse halts. An EMIC intercomparison study
found that seven models show a bistable regime and four
others a monostable regime following a freshwater perturba-
tion in the North Atlantic (Rahmstorf et al., 2005). A monos-
table regime of the AMOC is simulated in most GCMs where
a freshwater pulse leads to a temporary reduction in the
AMOC strength and a recovery when the freshwater pulse
terminates (Liu et al., 2014). However, it is speculated that
a monostable regime might be caused by a negative salin-
ity bias in GCMs (Mecking et al., 2017) and that a bistable
regime would explain the rapid climatic changes during the
deglaciation better (Ganopolski and Rahmstorf, 2001). The
equilibrium response of the ocean suggests that the AMOC
strength will also increase in response to atmospheric warm-
ing, possibly due to a decrease in sea-ice area (Jansen et
al., 2018). Several studies found that the AMOC was also
Figure 13. Global sea-level rise for three different climatic pa-
rameter sets of LOVECLIM using forcing scenario MMCP2.6 and
MMCP-feedback. GMSL change from our preferred parameter set
P22 is given in solid lines.
Figure 14. Semi-equilibrated GMSL change projections at
12 000 CE compared to the geological record of sea-level high
stands (Foster and Rohling, 2013) for a given atmospheric CO2con-
centration. The atmospheric CO2concentrations used for the pro-
jections of GMSL are averaged over the 10000-year simulation.
The horizontal line at 0 m GMSL change represents the present-day
situation. For scenario MMCP2.6 and MMCP-feedback, the GMSL
uncertainty is given by including the experiments with the three dif-
ferent climatic parameter sets. The red line is the best fit for the data
from our study, while the blue line is the best fit for the Foster and
Rohling (2013) data.
stronger during the mid-Pliocene, in the absence of freshwa-
ter feedbacks due to ice sheet melting (Chandan and Peltier,
2017; Chan and Abe-Ouchi, 2020). Our study supports the
increase in the AMOC strength when the freshwater forcing
halts.
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The marine-based WAIS is considered the most vulnera-
ble part of the AIS and collapses for cumulative CO2emis-
sion exceeding ∼1100 GtC. The Wilkes subglacial basin in
East Antarctica becomes ice-free in scenarios MMCP-break,
MMCP8.5, and MMCP-feedback. The Aurora Basin also
loses its ice cover for scenario MMCP-feedback. The ice
sheet respectively contributes 12, 19.6, and 27m to sea level
following scenarios MMCP-break, MMCP8.5, and MMCP-
feedback (Fig. 5). Our numbers for MMCP8.5 are compara-
ble to the study by Golledge et al. (2015), equally based on
an extension of the ECP8.5 scenario with constant forcing
after 2300 CE. They found that AIS retreat over the Wilkes
and Aurora basins would contribute up to 11.4 m to GMSL
after 5000 years and 15.7 m after 50 000 years. In the simula-
tions of Winkelmann et al. (2015), the grounding line retreats
significantly along the WAIS for a cumulative emission of
1000 GtC, while in East Antarctica the retreat is most rapid
for the Wilkes and Aurora subglacial basins and initiates for a
cumulative CO2emission of 2500 GtC. Considering a cumu-
lative CO2emission of 10 000GtC, Winkelmann et al. (2015)
even found that the Antarctic ice sheet could nearly disappear
entirely. However, that is an extreme scenario at the upper
end of potential carbon reserves and resources available for
combustion, which we did not consider in the present paper.
Even though the resolution of the ice sheet models and
the climate model is relatively coarse, especially to simu-
late the retreat along the outlet glaciers in Greenland and the
grounding line retreat in the most sensitive Antarctic regions
such as Thwaites or Pine Island glaciers in West Antarc-
tica, we have confidence that the model is performing quite
well to simulate the ice sheet response on the millennial
timescale. Marine-terminating glaciers along the Greenland
ice sheet will retreat in the coming decades and the SMB
will dominate the Greenland mass loss. The Antarctic ice
sheet model run at 20 km resolution is too coarse to simu-
late fast-flowing glaciers in great detail, and the omission of
sub-grid scale mechanisms makes the model less sensitive
in the short term to basal melting (Levermann et al., 2020,
Seroussi et al., 2020). However, the grounding line retreats
on land in Antarctica for most scenarios and also here, the
influence of SMB processes becomes more important. Be-
cause of the rather low contribution of the AIS to sea-level
by 2300 CE for scenario MMCP2.6 and the lower sensitivity
to grounding line retreat compared to other ice sheet models
(Levermann et al., 2020), we assume that our lowest sea-level
change value is a conservative estimate.
It should be noted that our ice sheet models do not include
hydrofracturing. Hydrofracturing may significantly speed up
Antarctic ice sheet decay as achieved by the marine ice cliff
instability (MICI) mechanism (Pollard et al., 2015). DeConto
and Pollard (2016) find Antarctic ice sheet volume losses
equivalent to a freshwater input into the surrounding ocean
in excess of 1 Sv, much larger than the peak freshwater input
in our simulations of 0.15 Sv. However, the MICI is contro-
versial for its large contribution to sea level already at the end
of the 21st century (e.g. Edwards et al., 2019).
Clark et al. (2016) found the AIS to be the largest contrib-
utor to sea-level rise after 10 000 years for all of the scenar-
ios they considered. Moreover, it is suggested that the sen-
sitivity of GMSL change to atmospheric CO2decreases for
higher cumulative CO2emissions with a logarithmic relation
between both. For the first 2 millennia, our results show a
similar behaviour, but at the end of the 10 000-year simula-
tions, GMSL increased more for the higher-emission scenar-
ios, and a stronger non-linear relationship between GMSL
and cumulative CO2emissions was established. Part of the
discrepancy can be explained by the difference between sce-
nario MMCP8.5 and MMCP-feedback. Both scenarios as-
sume the same peak CO2values, but the latter adds more car-
bon to the atmosphere after 10 000 years due to the methane
emission feedback. Another difference with our experiments
is that we include the albedo–temperature feedback, which
gains importance once the Antarctic ice sheet retreats inland.
Oppositely to previous modelling studies investigating the
Antarctic ice sheet evolution on a multi-millennial timescale
(Winkelmann et al., 2015; DeConto and Pollard, 2016; Clark
et al., 2016), we include the two-way feedbacks between the
ice sheets, the atmosphere, and the ocean. Large amounts
of freshwater – due to the melting of the ice shelves and
grounded ice from Antarctica – enter the Southern Ocean and
impact on Antarctic Bottom Water (AABW) and sea-ice for-
mation (Swingedouw et al., 2008; Goelzer et al., 2016a, b).
On the other hand, freshwater fluxes from melting the GrIS
strongly reduce the North Atlantic Deepwater (NADW) for-
mation and weaken the AMOC. The interhemispheric see–
saw effect is understood as weakening NADW formation,
leading to a reduced transport of cold water to the Antarc-
tic leading to a warming of the Antarctic continent (Stocker,
1998). However, in our future warming simulations, the AIS
is also melting and freshwater fluxes act as a negative feed-
back by limiting the ocean temperature increase locally. The
observed limited warming in our simulations is supported
by a study from Swingedouw et al. (2009), who found re-
gional cooling of up to 10 ◦C following a freshwater release
of 1 Sv in the Southern Ocean. In contrast, other studies sug-
gest an increase in sea-ice area due to large freshwater pulses
(Swingedouw et al., 2008; Goelzer et al., 2016b) where the
ocean stratification increases beneath the ocean surface lead-
ing ultimately to ice shelf melting at depth (Golledge et al.,
2014). This positive feedback is not observed in our simula-
tions, where the sea-ice area (and volume) declines strongly
in all our experiments and almost all sea ice disappears for
the three highest-forcing scenarios at the end of the first mil-
lennium (Fig. 3).
Earth Syst. Dynam., 11, 953–976, 2020 https://doi.org/10.5194/esd-11-953-2020
J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 969
9 Conclusions
In this paper we have assessed multi-millennial sea-level
change projections having fully interactive ice sheet com-
ponents as obtained within the Earth system model of in-
termediate complexity LOVECLIM. Global mean sea level
is shown to continuously rise during the next 10 000 years
for all scenarios considered. These build further on IPCC
RCP/ECP scenarios with emission pathways ranging from
temporarily negative emissions to burning ∼5000 GtC with
the addition of a methane emission feedback. Using the
RCP-based scenarios, our sea-level change projections are
found to be irreversible on a 10 000-year timescale, even
for the lowest-forcing scenario based on extending scenario
RCP2.6/ECP2.6 with zero emissions.
The interactive nature of our model study on the multi-
millennial timescale is important to simulate most climatic
feedbacks in an accurate way. Ice-sheet–ocean interactions
result in temporarily large perturbations in the ocean cir-
culation with freshwater fluxes from the GrIS leading to a
strongly reduced AMOC strength and local cooling. Apart
from the local cooling effect and its influence on atmospheric
temperatures in the vicinity of the Greenland ice sheet, our
findings suggest that the reduced AMOC also lowers the
contribution from the steric component to GMSL. Fresh-
water fluxes from the AIS lead to reduced oceanic warm-
ing in the vicinity of Antarctica and relatively low basal
melt rates. Ice-sheet–atmosphere interactions on a multi-
millennial timescale are important to take into account be-
cause of the SMB–elevation feedback that sets in when the
ice sheet starts to melt and the surface elevation decreases.
The strong albedo–temperature feedback initiates when the
ice sheets retreat on land, where temperatures increase due
to an increase in the tundra-like surface type (in addition to
the effect of a reduced sea-ice area). As a consequence, sur-
face melting accelerates once a critical area of land becomes
ice-free.
It is found that the Greenland ice sheet will melt entirely
over the next 10 000 years, but the rate of sea-level rise is de-
termined by the forcing scenario. Oppositely, the fate of the
Antarctic ice sheet is largely dependent on the future green-
house gas forcing scenario considered. For the lowest forc-
ing scenario, there is only a limited retreat of the grounding
line in West Antarctica and the East Antarctic Ice Sheet re-
mains mostly unaffected, resulting in a limited sea-level con-
tribution of 1.6 m. For the highest-forcing scenarios, the West
Antarctic Ice Sheet is found to collapse entirely and there is
significant marginal ice sheet retreat along the East Antarctic
Ice Sheet with a total volume loss of around 27 m SLE. The
steric sea-level change component continues to contribute to
sea-level rise as long as there is a freshwater influx, even
though the bulk of the oceanic heat increase takes place in
the first centuries after the steep rise in temperatures. It is the
only component contributing to sea level that reaches a peak
during the coming millennia and decreases slowly towards
the end of the simulations (only for the two lowest scenarios)
following a slight global cooling trend after a few thousand
years. Glaciers and ice caps are the smallest component in
the sea-level budget and disappear relatively fast during the
coming centuries.
We have identified the existence of a threshold in total cu-
mulative CO2emissions for which GMSL is dominated by
the melting of the Greenland ice sheet or the Antarctic ice
sheet. In our simulations, GMSL rise is dominated by the
melting of the Greenland ice sheet for a total cumulative CO2
emission of up to 1100 GtC (after 2000 CE). Under these sce-
narios, GMSL is found to quasi stabilize between 9.2 and
15 m above current levels. For the higher-emission scenar-
ios, the AIS contribution exceeds the GrIS contribution after
1000 years due to grounding line retreat and surface melting
in East Antarctica, and total GMSL rise after 10 000 years
ranges between 22 and 37.4 m. Near the end of the simula-
tions, the rate of sea-level change decreases to values below
0.05 m per century for all forcing scenarios and sea-level ap-
proaches a semi-equilibrated state.
https://doi.org/10.5194/esd-11-953-2020 Earth Syst. Dynam., 11, 953–976, 2020
970 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
Appendix A: Construction of the carbon dioxide
concentration scenarios
We assume that an impulse response function (IRF) repre-
sents the time-dependent abundance of a gas after an addi-
tional emission pulse (Joos et al., 2013; Maier-Reimer and
Hasselmann, 1987). After the peak concentration, the CO2
concentration decreases exponentially reaching a short-term
equilibrium COequis
2(after 1000 years) and a long-term equi-
librium COequil
2(after 10 000 years) based on Eqs. (1) and (2)
(Solomon et al., 2009). The time constants used for the two
exponentials do not have a process-based meaning but are
fitting parameters to best represent the wide range of IRFs
present in the literature. The peak airborne fraction (AFpeak),
the short-term stabilization level COequis
2, and the long-term
stabilization level COequil
2(∗can be replaced by l and s in
Eq. 2) represent the different theoretical neutralization pro-
cesses.
CO2(t)=COequil
2+hCOpeak
2−COequis
2e−λst
+COequil
2−COequis
2e−λlti,(A1)
where COequis
2is equilibrium CO2concentration after
1000 years, COequil
2is equilibrium CO2concentration after
10 000 years, COpeak
2is peak CO2concentration, λsis short-
term decay rate, λlis long-term decay rate, and tis time (be-
tween peak concentration and 12 000 CE).
COequi∗
2=AFequi∗
AFpeak COpeak
2−CO0
2+CO0
2,(A2)
where CO0
2=280 ppmv, AFequi∗is equilibrium airborne
fraction, and AFpeak is peak airborne fraction.
The instantaneous or peak airborne fraction (AFpeak) is the
atmospheric CO2peak concentration as a percentage of the
total released CO2(Archer and Brovkin, 2008). AFequi mea-
sures the fraction of emitted CO2that remains in the atmo-
sphere after 1000 years (AFequis) and 10 000 years (AFequil)
respectively. The main principle is that the more CO2is emit-
ted in the atmosphere, the lower the capacity of the ocean
to buffer the excess of carbon due to the limited size of the
ocean (Archer et al., 2009a). Dissolved carbon in the ocean
consists of bicarbonate (HCO−
3) and carbonate ions (CO2−
3).
The latter buffers the ocean against CO2invasion but is
less abundant than bicarbonate. Depletion of the bicarbonate
ions starts with increasing atmospheric CO2concentrations.
As a consequence, the buffering capacity of the ocean de-
creases with higher-CO2atmospheric injections (Archer and
Brovkin, 2008).
The airborne fractions are chosen in accordance with the
values present in the literature (Table A1) and extrapolated
for the scenarios that do not correspond to the CO2emission
pulses (Table A2). The peak airborne fraction after a pulse
injection of CO2is 100 % and therefore not completely com-
parable with the more gradual injections as assumed by the
MMCP scenarios. Therefore, these peak airborne fractions
are scaled to the peak airborne fractions for a slower injec-
tion of CO2where the peak atmospheric CO2value is be-
tween 50 % and 70% of the real atmospheric CO2emissions
(Archer and Brovkin, 2008).
Earth Syst. Dynam., 11, 953–976, 2020 https://doi.org/10.5194/esd-11-953-2020
J. Van Breedam et al.: Semi-equilibrated global sea-level change projections 971
Table A1. Estimates of CO2airborne fractions available in the literature 1000 and 10 000 years after a pulse of CO2into the atmosphere.
Reference CO2emission pulse (GtC) AF (1000 years) AF (10 000 years)
Archer and Brovkin 1000 29 % 14 %
(2008) 5000 57 % 26 %
Archer et al. (2009a) 1000 24 %–31% 10 %–21 %
5000 32 %–62 % 14 %–32 %
Eby et al. (2009) 1000 30 % 17 %
5000 60 % 30 %
Joos et al. (2013) 100 10 %–21% /
100 (+350) 20 %–30 % /
5000 30 %–60 % /
Table A2. Average equilibrium airborne fractions for total emissions of around 500 to 5000GtC according to the values given in Table A1.
The equilibrium airborne fraction for 2000 GtC is extrapolated from the average equilibrium airborne fraction for the 1000 GtC and 5000 GtC
scenarios. The instantaneous airborne fraction is the airborne fraction reached after 1 year (AFpeak). Airborne fractions after 1000 and 10 000
years are given. The columns highlighted in bold give the fractions of atmospheric CO2still present 1000 and 10 000 years after the peak
concentration. The numbers in the first column denote the cumulative emissions CO2emissions with respect to pre-industrial levels.
AFpeak AFequisAFequis
AFpeak AFequilAFequil
AFpeak
(1000 years) (10 000 years)
461 GtC – MMCP2.6 (low) 50 % 25 % 50 % 12 % 24 %
1361 GtC – MMCP4.5 (moderate) 55 % 28 % 51 % 15 % 27 %
2234 GtC – MMCP6.0 (moderate) 60 % 33 % 55 % 18 % 30 %
3393 GtC – MMCP-break (high) 65 % 40 % 62 % 22 % 34 %
5288 GtC – MMCP8.5 (high) 70 % 47 % 67 % 25 % 36 %
5888 GtC – MMCP-feedback (high) 70 % 55 % 78 % 33 % 47 %
Table A3. Different CO2scenarios used in the simulations with their time of peak concentration, the values for the peak concentration,
the mean concentration over the next 10 000 years, and the equivalent total emissions (calculated as in Meinshausen et al., 2011). The total
cumulative emissions are an approximation for the RCP scenarios (the numbers give the total fossil fuel cumulative CO2emissions expressed
in gigatonnes of Carbon for the period 2000–2300 CE). These numbers are on top of the cumulative CO2emissions before 2000 CE given in
brackets (about 270 GtC; Ciais et al., 2013).
Scenario Time of peak Peak concentration Mean concentration Cumulative
concentration (ppmv) (ppmv) emissions (GtC)
MMCP2.6 2053 443 305 191 (+270)
MMCP4.5 2130 543 358 1091 (+270)
MMCP6.0 2150 752 431 1964 (+270)
MMCP-break 2150 1429 674 3723 (+270)
MMCP8.5 2250 1962 918 5018 (+270)
MMCP-feedback 2250 1962 1088 5618 (+270)
https://doi.org/10.5194/esd-11-953-2020 Earth Syst. Dynam., 11, 953–976, 2020
972 J. Van Breedam et al.: Semi-equilibrated global sea-level change projections
Code and data availability. The LOVECLIM v1.3 model code
can be downloaded from https://www.elic.ucl.ac.be/modx/index.
php?id=289 (last access: 6 October 2020) (ELIC members, 2020).
Model output data are available upon author request.
Supplement. The supplement related to this article is available
online at: https://doi.org/10.5194/esd-11-953-2020-supplement.
Author contributions. PH, HG, and JVB designed the experi-
ments and JVB carried them out. HG and PH developed the model
code. JVB prepared the paper with contributions from all co-
authors.
Competing interests. The authors declare that they have no con-
flict of interest.
Acknowledgements. We would like to thank two anonymous re-
viewers and Paolo Scussolini for their detailed comments and useful
feedback.
Pierre Regnier and Pierre Friedlingstein are acknowledged for
their discussions on the applied impulse response function and the
use of the constructed carbon dioxide scenarios. We acknowledge
support through the Belgian Federal Science Policy Office within
its Research Programme on Science for a Sustainable Develop-
ment under contract SD/CS/06A (iCLIPS) and the Belgian National
Agency for Radioactive Waste and enriched Fissile Material (ON-
DRAF/NIRAS).
Financial support. This research has been supported by the Bel-
gian Federal Science Policy Office (grant no. SD/CS/06A).
Review statement. This paper was edited by Zhenghui Xie and
reviewed by Paolo Scussolini and two anonymous referees.
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