Introduction
The response of the Antarctic ice sheets (AIS) to predicted future oceanic
and atmospheric warming will dictate the magnitude of global sea level
changes for millennia, yet the sensitivity of the AIS system is unclear,
leading to a wide range of sea-level predictions for coming centuries
.
Simulations of future scenarios such as these are most credible when
constrained by observations of past changes. Here we simulate the AIS during
a warmer period of the geological past for which geological and
paleoenvironmental data exist with which to verify simulations. Warm periods of the
Pliocene (2.58–5.33 Ma) are considered some of the most appropriate
analogues for future environmental conditions ,
especially the early to mid-Pliocene (4–5 Ma), when atmospheric CO2
concentrations were in the range 365–415 ppm , similar
to present day. Globally averaged surface temperatures during Pliocene
interglacials were 2 to > 3 ∘C warmer than present
, comparable to warmings anticipated by 2100 under
mid-range emissions scenarios of the Intergovernmental Panel on Climate
Change Fifth Assessment Report . Far-field sea-level
records imply a collapse of the West Antarctic Ice Sheet (WAIS) together with
partial loss of marine-based ice from the East Antarctic Ice Sheet (EAIS) at
this time . Geological records from
close to the East Antarctic coast suggest that a portion of this sea-level
contribution may have originated from the Wilkes Subglacial Basin (WSB), when
the ice sheet margin is thought to have migrated hundreds of kilometres
inland .
Given the large scale of these inferred ice-sheet reconfigurations during
warm periods of the Pliocene, it may be inferred that Antarctica's
marine-based ice sheets may be vulnerable to thresholds beyond which an
abrupt change in state occurs see. If such thresholds exist, and were crossed during
Pliocene glacial–interglacial transitions, simulations of ice-sheet
evolution during this period may be able to provide insights into processes
that could be relevant under future warmer climate scenarios. To investigate
the sensitivity of Antarctica to climate–ice-sheet thresholds under warmer
climates, we first run global and regional climate models to simulate changes
in Antarctic oceanic and atmospheric temperatures under an orbital
configuration representative of an interglacial in the early Pliocene at
4.23 Ma, when austral insolation reached a maximum, and atmospheric CO2
concentration was around 400 ppm (Figs. and ). We
focus on this period, rather than the commonly investigated “PRISM”
interval of the mid-Pliocene , as the higher
insolation and atmospheric CO2 concentration at this earlier time may have
resulted in a warmer climate and a smaller ice sheet than the later period,
which may help reconcile far-field sea-level records for the period. Outputs
from these climate simulations are then used as inputs to ice-sheet model
experiments that use the Parallel Ice Sheet Model, a fully coupled
ice-sheet–ice-shelf model . These
simulations allow us to quantify the continental-scale changes that take
place under the prescribed climatology, and the consequent contribution to
sea level from the AIS. Although the peak climatic conditions we simulate
with the regional-scale climate model (RCM) most likely only persisted for 1–2 kyr, we run our simulations
for 10 kyr in order to quantify how the perturbed ice sheet might evolve if
such warm conditions were maintained. Although this does not realistically
reflect climatic forcings associated with orbital cyclicities, and implies
that our sea-level estimates may be upper bounds for the prescribed climates,
it is nonetheless a useful approach for the study of “unforced” ice-sheet
oscillations, or “tipping points” . In the final part of
our study, therefore, we use our long-term ice-sheet simulations to
investigate whether evidence for tipping points can be seen, and if so, the
mechanisms that give rise to them.
Orbital components and net January insolation at 80∘ S for
the period 3.5–5 Ma. Top panel shows insolation for the interglacial in
which peak Pliocene values occur (grey shading). The insolation peak occurs
at 4.23 Ma. Data from .
Air temperature, precipitation, and sea surface temperature used for
our simulations. Top row: the “control” (CTRL) scenario, employing gridded
data from observations and modelling of present-day conditions
. Middle row: present-day conditions as simulated by the
RCM. Bottom row: Pliocene conditions at 4.23 Ma as
simulated by the RCM.
Methods
Climate and ocean inputs
We use spatially distributed air temperature, precipitation, and sea-surface
temperatures from an established RCM coupled
with the GENESIS version 3.0 global climate model (GCM)
. The GCM parameterizes fluxes
between the land surface boundary and the free atmosphere and includes
detailed representations of snow and land ice. Outputs from the GENESIS model
have been validated against observed polar climates and ice-sheet mass
balance , and are therefore considered reliable
for studies such as ours. Our RCM is RegCM3, which takes
time-dependent lateral boundary conditions from the GCM. It simulates
atmospheric dynamics, radiative transfer, and precipitation, and includes a
representation of the open ocean . RCM simulations at
40 km resolution are initialized from coarser-resolution (T31) GCM outputs.
We simulate the climate during a peak-insolation interglacial at 4.23 Ma
based on an orbital configuration representative of that period
(Fig. ), together with a greenhouse gas concentration of 400 ppm.
Although previous work has suggested that the relative role of insolation and
CO2 in driving warmer climates varies through time, and that high
insolation in one hemisphere may not necessarily lead to elevated temperatures
at the same latitudes , palaeoenvironmental proxies for
this period are consistent with this being an interval of peak warmth (see
“Palaeoenvironmental proxies” below) and fundamentally the ice-sheet
responds only to the integrated warming anomaly, not insolation or radiative
forcing in isolation.
Temperature and precipitation fields from the Pliocene RCM simulation are
used as inputs to the ice-sheet model by calculating the anomalies from a
present-day RCM simulation and then adding these to the present-day
temperature and precipitation fields used in model initialization and spinup
(Figs. –). This approach is preferable to one that
uses the RCM fields directly, since the RCM does not simulate the present-day
state precisely, when compared to observational data (Fig. ).
Since the climate model also uses an ice-sheet topography in which WAIS is
already removed, we use a standard lapse rate of 8 K km-1 to adjust
the simulated temperatures based on the elevation difference from our
present-day ice geometry. Despite this adjustment, however, it is possible
that the air temperatures in these areas may be anomalously warm as a result
of ocean–atmosphere heat exchange that would not occur if the removed ice
were present in the RCM simulation. This may have an influence of the retreat
rate of West Antarctica in our simulations, but since our focus lies mainly
on the behaviour of the East Antarctic ice sheet we do not expect this issue to
affect our findings. We do not apply any lapse rate adjustment to
precipitation values on the basis that precipitation rates are likely to be
controlled largely by synoptic patterns (which are captured by the RCM)
rather than by a simple elevation-dependent cooling of the near-surface
atmosphere. Since the RCM uses an ice-sheet geometry in which WAIS is absent
it gives us a sea-surface temperature field for areas of our domain where
grounded ice currently persists. However, these ocean temperatures are only
used to calculate basal melt beneath ice shelves, not at the bed of grounded
ice, and so do not affect the ice sheet unless the modelled grounding line
retreats. For areas of grounded ice where we do not have RCM-derived ocean
temperatures we prescribe a uniform value of 271.2 K, essentially the
sea-water freezing point. This avoids potential errors that could be
introduced by interpolating ocean fields landward, but we recognize that
using a single, low, value rather than an interpolation may lead to
underestimated basal melt in subglacial basins during ice-sheet retreat. Our
offline, one-way climate–ice-sheet model coupling is less satisfactory than
a two-way coupling, but is computationally easier and allows first-order
ice-sheet responses to climate perturbations to be investigated. However, we
acknowledge that a fully coupled setup might give more accurate ice-sheet
and climate simulations.
Palaeoenvironmental proxies
Local records of palaeo-temperature around the Antarctic continent are
relatively sparse, yet those that exist, and can be
chronologically constrained with some certainty, offer a means by which
climate model simulations can be evaluated. We compiled marine
paleoenvironmental data from several circum-Antarctic locations that include
drill cores from the western Ross Sea (CIROS-2, DVDP-10, AND-2A), Prydz Bay
(ODP 1165), Kerguelen Plateau (ODP 751A), Wilkes Land (IODP U1361), and northwestern Antarctic Peninsula (ODP 1096) and geological outcrop at the Prydz
Bay coast (Fig. ). Data were obtained from stratigraphic intervals
that span 4.5 to 4.0 Ma (C3n.1r to lowermost C2Ar) which is characterized by
relatively depleted values (< 3.2 ‰) in the benthic
δ18O stack (i.e. relatively warm glacials
and interglacials; MIS CN1 and CN5 are two of the warmest interglacials in
the early Pliocene). Sea water temperature estimates through this interval
are based on a range of proxies including biological analogues and
geochemical data that are described in detail below and which are summarized
in Table .
Inferred high southern latitude winter, summer, and mean annual
sea-surface temperatures from a range of proxy techniques compared to model
predictions. Winter temperatures assume sea ice close to the coast but not in
open water. Summer temperatures (and thus Tmean also) are minima,
and could be higher. Absolute sea-surface temperature predictions from the
RCM shown for each site in italics. Although the considerable uncertainties
associated with temperature inferences from palaeoecological proxies make
precise comparisons impossible, the data generally indicate an underestimate
of mean annual sea-surface temperatures in the RCM that averages
approximately 1 ∘C.
Site
Long
Lat
Winter
Summer
Tmean
Reference
(likely)
(min.)
(min.)
AND-1B
167.083333
-77.888889
-1.8
5
1.6
,
–2.22
3.03
–0.22
CIROS-2
163.533333
-77.683333
-1.8
5
1.6
,
–1.96
3.29
0.07
DVDP-10
163.511667
-77.578612
-1.8
5
1.6
,
–1.96
3.29
0.08
ODP-1165
67.218733
-64.379583
3
5
4
,
–0.02
7.19
3.54
IODP-U1361
143.886653
-64.409547
3
5
4
–0.43
6.24
2.87
ODP-1096
-76.96376
-67.56681
-1.8
5
1.6
–1.87
4.80
1.26
Vestfold Hills
78.132
-68.631111
-1.8
5
1.6
–0.99
6.00
2.37
(a) Air temperature anomaly for 4.23 Ma from regional
climate modelling, adjusted for surface elevation differences between the RCM
input orography and the present-day elevations used to initialize the
ice-sheet model. Contours show 2.5 ∘C increments. Biases used in
certain simulations are additional to the warming values shown here.
(b) As (a) but showing sea-surface temperature anomaly.
Contours show 0.25 ∘C increments. Locations of profile shown in Fig.
also shown (red line), as well as the locations (red squares) of
the palaeo-environmental proxy data in Table .
Surface water temperatures from biological proxies are derived from diatom,
silicoflagellate, and calcareous nannofossil data. Diatom assemblages within
the target “warm” interval at all of the drill sites contain, and are often
dominated by, open ocean species Thalassionema nitzschioides and
Shionodiscus tetraoestrupii . Modern descendants of T. nitzschiodes and
S. tetraoestrupii are restricted to areas north of the Polar Front
where surface water temperatures are greater than 3.5 and 5.5 ∘C
respectively . Numbers of
Azpeitia spp. also increase within the early Pliocene section at
IODP Site U1361 and reach a maximum abundance of
13 %. Today Azpeitia tabularis is considered cold-tolerant in
Southern Ocean waters but species abundance increases as water temperatures
increase and generally exceeds 10 % near the modern subtropical front
, which suggests that early Pliocene summer sea
surface temperatures at Site U1361 were as high as 10 ∘C.
Importantly, sea-ice-associated diatom taxa are either rare to absent at most
of the drill sites or indicate much reduced sea
ice coverage . Overall, the diatom
assemblages indicate that surface water temperatures at locations south of
60∘ in the early Pliocene were similar to those in modern
sub-Antarctic regions and that the circum-Antarctic ocean was sea-ice-free
throughout most or all of the annual cycle.
Relatively warm early Pliocene surface water temperatures implied by the
diatom assemblages are supported by silicoflagellate data. In the modern
marine environment the silicoflagellate genus Distephanus is
dominant south of the Antarctic polar front and the genus Dictyocha
is rare or absent. The ratio of these genera in ancient sediment samples can
be used to infer past ocean temperature. Dictyocha abundance at Ocean
Drilling Program Site 1165 increases between 4.3 and 4.4 Ma, which suggests
that mean annual SST increased to approximately 4 ∘C during this
interval . A correlative interval in ODP Sites
748 and 751 contains a similar warming signal .
Although temperature reconstructions based on geochemical proxies are rare,
TEX86L-derived SST estimates of 5 ± 4 ∘C were
obtained from diatomite that was deposited between 4.5 and 4.2 Ma at the
AND-1B drill site . These data support the temperature
reconstructions based on biological proxies and indicate that summer surface
water temperatures in the western Ross Sea were 5 to 6 ∘C warmer
than today. Furthermore, sedimentary facies indicate increased sediment input
during interglacials Motif 2b of.
This is interpreted as representing a warmer glacial regime (compared to the
late Pliocene) with more sediment-laden meltwater emanating from the margins
of the EAIS and discharging into the Ross Sea.
Other evidence for warmth in the early Pliocene comes from fossil
invertebrates and a unique assemblage of vertebrates preserved in the Sørsdal Formation, which crops out at Marine Plain in the Vestfold Hills
(Fig. ). The formation comprises up to 7.2 m of friable diatomaceous
siltstone and sandstone with dark limestone lenses .
The age of the deposit is not well constrained, but diatom data suggest it
was deposited between 4.4 and 2.74 Ma, and most likely at the earlier end of
this range, possible 4.2 to 4.1 Ma . Cetacean
fossils include a species of dolphin, a beaked whale, and baleen whale
. These noncryophilic species
indicate that waters were ice-free during summer .
The Sørsdal Formation also contains the scallop Austrochlamys anderssoni. This and similar species of thick-shelled costate scallop
thrived in Antarctic waters during interglacial episodes throughout the
Neogene but disappeared during the late Pliocene . Modern
descendants of these thick-walled species do not live further south than
sub-Antarctic regions where surface water temperatures are warmer than
5.5 ∘C. Diatoms in the formation also indicate an annual range in
SST from -1.8 to 5.0 ∘C () and
the absence of coccoliths indicates that summer SSTs were likely no higher
than 5 ∘C ().
In summary, the evidence listed above indicates that summertime surface water
temperatures in the early Pliocene were at least as high as 4–5 ∘C
during the warmest interglacial periods, and were likely warmer at
64∘ S (IODP site U1361). Evidence for minimal sea ice suggests that
while winter water temperatures may have approached -1.8 ∘C,
summers were sea-ice-free. Based on these data we infer that early Pliocene
surface water temperatures in the oceans adjacent to Antarctica's continental
ice sheets must have been higher than -1.8 ∘C in the winter and at
least 5 ∘C in the summer – a mean annual temperature that was
approximately 3 ∘C warmer than today. Table compares
these proxy-based interpretations with values simulated by our climate model
experiments.
The ice-sheet model
Our ice-sheet simulations use the Parallel Ice Sheet Model (PISM) version
0.6.3, an open-source, three-dimensional, thermodynamic, coupled
ice-sheet–ice-shelf model. Both the model and our implementation of it are
described in detail elsewhere , so only a summary is given here. In brief, the model
combines equations of the shallow-ice and shallow-shelf approximations (SIA
and SSA respectively) for grounded ice, and uses the SSA for floating ice
. Superposing the SIA and SSA velocity solutions
allows basal sliding to be simulated according to the “dragging shelf”
approach , and enables a consistent treatment of
stress regime across the grounded to floating ice transition
. Ice streams develop naturally as a consequence
of plastic failure of saturated basal till , depending on
the thermal regime and volume of water at the ice-sheet bed. Because we
employ a large number of simulations in our study, we adopt a relatively
coarse model grid of 20 km. Mesh dependence of results can be an important
issue under certain circumstances , but in
previous work we have shown that this is not the case in our simulations
. Furthermore, the principal aim of our
experiments is to identify differences between scenarios, rather than to
define absolute ice geometries, and for this purpose we believe our approach
is both suitable and robust.
Mass loss in sea-level equivalent metres from the simulated Pliocene
Antarctic ice sheet after 10 kyr, using environmental conditions from the
regional climate model and augmented with a range of air and ocean
temperature bias corrections. Numbers in parentheses represent duplicate
experiments in which a more aggressive grounding-line scheme is employed (see
“Methods”).
Sea-surface temperature bias
0
1
2
Air
0
4 (4.6)
6 (8.7)
7.9 (12.2)
temp.
1
5.6 (6.2)
7.7 (9.4)
8.8 (13)
bias
2
7.7 (8.4)
9.1 (10.9)
10.3 (14.1)
Grounding-line migration is a key component of Antarctic ice-sheet
simulations, and is a much-debated modelling challenge. By default we adopt
here a novel grounding-line scheme that uses a sub-grid interpolation method
to more accurately track migrations . In this
scheme we allow the sub-grid interpolation of driving stress at the bed, and
the calculation of one-sided derivatives to better characterize the ice-sheet–shelf junction. We run duplicate experiments both with and without an
additional interpolation scheme that allows basal melt rates to be smoothly
propagated across the grounding line from the first floating cell upglacier
to the last grounded cell .
This mechanism tends to accelerate grounding-line retreat, leading to rapid
mass loss in the initial centuries of the experiments, and greater long-term
(near-equilibrium) sea-level-equivalent mass loss from the simulated ice
sheets (Table ). It is conceptually supported by geophysical studies
of modern-day grounding lines that infer an “estuarine”-type environment at
ice-stream grounding zones , and although less
catastrophic than the cliff-collapse mechanism used in other models
the approach is consistent
with recent grounding-line process analyses .
Basal melt beneath ice shelves (and at the grounding line) is calculated from
a three-equation model that uses temperature, salinity, and pressure to
determine the freezing point in the boundary layer . Depending on whether there is melt, freeze-on, or
neither, a different approximation of the temperature at the ice-shelf base
is used. Outputs from RegCM3 do not include subsurface ocean temperatures,
and furthermore, PISM is currently set up to read in just a single ocean
temperature field. Consequently we are not able to investigate how vertical
differences in ocean warming may impact the ice sheet. Our model does,
however, allow the pressure effects of deeper bathymetry to be accounted for,
giving rise to enhanced basal melt near grounding lines and less melt in
central and outer sectors of the shelf
seeFig. S5.
Surface mass balance depends on monthly climatological data and a positive
degree-day model that tracks snow thickness and allows for melting of snow
and ice at 3 and 8 mm ∘C-1 day-1 respectively. We incorporate a white noise signal
(normally distributed, mean zero random temperature increment) into the
calculation of daily temperature variations. The standard deviation of daily
temperature variability is set at 2 ∘C, somewhat lower than the
commonly employed value of 5 ∘C, on the basis that the latter has a
tendency to overestimate melt . Surface
temperatures are adjusted for elevation according to an altitudinal lapse
rate of -8 K km-1, and a refreezing coefficient of 0.6 is used to
mimic meltwater capture within the snowpack.
Experimental methods
There are two approaches to dealing with ice model parameter uncertainty in
the kind of study we present here. One approach undertakes thousands of
low-resolution experiments (a large ensemble) with incremental changes in
each of several key parameters, such as flow enhancement factors. The results
are then subsequently analysed with respect to observational constraints to
establish which ensemble members are consistent with the data. We do not
adopt this kind of approach. Instead we follow a more targeted methodology in
which model parameter choice is incrementally refined through an iterative
procedure in which we constrain our model to fit the present-day ice-sheet
geometry and surface velocity field. To achieve a good fit we adjust ice flow
parameters based on expert judgement, not in an unguided manner as is done
with ensemble approaches. We start with an initial 20-year smoothing run that
uses only the shallow-ice approximation to derive velocities. This removes
spurious surface irregularities. Secondly, we implement a 150 000-year run in
which the ice-sheet geometry is held fixed but where internal thermal fields
are allowed to evolve. The third phase uses a 25 000-year simulation in which
full model physics are employed and the ice sheet is allowed to evolve on all
boundaries – that is, it is entirely unconstrained. Through carefully guided
parameter iteration our procedure results in a spun-up, thermally and
dynamically equilibrated ice-sheet simulation that is the best fit to
observational constraints that is possible by tuning available model
parameters . Thus although
parameter uncertainty can be a large source of error under certain
circumstances see, we argue that our approach
significantly reduces this uncertainty prior to our undertaking the
prognostic experimentation. All experiments start from the same spun-up
present-day ice-sheet simulation.
We make an assumption regarding the state of the AIS prior to the
interglacial at 4.23 Ma based on geological evidence that indicates ice
extent greater than present during early Pliocene glacial episodes
, implying that the AIS retreated through a
present-day configuration during interglacial transitions. However, since the
initial condition of the ice sheet is not known, our assumption of a
present-day configuration may be erroneous. However, differences in initial
geometry would most likely affect the rate at which new equilibria to the
imposed climatologies occurred, rather than the geometries of those steady
states. Consequently we consider our equilibrium simulations to be
representative of the likely long-term Antarctic response to the prescribed
orbital and greenhouse gas configuration. We use outputs from the RCM
(described above) to define anomalies to our present-day climate grids
. Simulations are run for
10 kyr, which is long enough for most simulations to approach a steady state
(see “Results” below). We first model ice-sheet evolution using climate
fields simulated by the RCM, using both implementations of the sub-grid
grounding-line scheme described above. Then we explore the threshold response
of the EAIS by running additional experiments with uniform increments of 1
and 2 ∘C added to the air and sea-surface temperature fields, which
address both a known cold bias in the RCM as well as mismatches between RCM
and proxy-based temperature reconstructions. By bracketing a range of
temperatures we are also able to investigate more easily the existence and
sensitivity of the AIS to climate–ice-sheet thresholds. To isolate the
effects of the imposed climatic perturbations most clearly we keep sea level
at its modern level, rather than the +10 to +30 m thought likely for the
Pliocene . We
note, however, that in separate experiments not shown here the response of
the ice sheet appears to be unaffected by sea level changes of these
magnitudes. We run duplicates of all experiments using the two variants of
the sub-grid grounding-line scheme described above.
Tipping point analysis
The aim of this technique is to analyse time series data (in our case ice mass
evolution) to find early warning signs of impending tipping points. Such
events are characterized by a non-linear response to an underlying forcing,
based on the phenomenon of “critical slowing down”, and relies on the
gradual shallowing and widening of the state-space of the system (also known
as the “basin of attraction”) . This “slowing down” can be mathematically detected
by looking at the pattern of fluctuations in the short-term trends of the
data before the threshold is passed . This change in
shape of the state-space allows the system to travel further from its point
of equilibrium , whereupon the system takes
increasingly longer to recover from small perturbations
, which can be detected as an increase in the lag-1
autocorrelation and variance of the time series . A change in
skewness may also be interpreted as a precursor to tipping
.
This tipping point analysis technique has been applied to a range of climate
and palaeoclimate data using both natural archives and model outputs
. Importantly, the early warning signs, or precursors, are
only expected in the presence of two or more quasi-stationary states,
separated by an unstable equilibrium, and are not expected in the case of
tipping induced by stochastic fluctuations only, so their identification
tends to imply a real threshold change. The method only analyses data preceding the
tipping point. These data are detrended using a Gaussian kernel smoothing
filter over a suitable bandwidth, so that long-term trends are removed
without overfitting the data. The resulting residuals are then measured for
autocorrelation at lag-1 and variance over sliding windows of two different
sizes. The Kendall tau rank correlation coefficient is
used to provide a quantitative measure of the trend; this metric varies
between +1 and -1, where higher values indicate a greater concordance of
pairs and a stronger increasing trend. Importantly, it is the presence of a
parallel increasing trend in both autocorrelation and variance, rather than
the absolute values of the indicators, that indicates critical slowing down
.
For the purposes of this study we make an important distinction between a
tipping point and a threshold, which are sometimes used synonymously. We
define a tipping point as a transient feature, whereas a threshold is
non-temporal. During the evolution of an ice sheet under a constant forcing
it may be that a point is reached in which the trajectory of evolution
changes, i.e. the system “tips” into a new state of behaviour. By
analysing the time series data from a constant forcing experiment, tipping
point analysis is able to not only show where genuine system instabilities
occur, but also to provide information on the timescale over which this
instability evolves. This is what the final part of our study investigates.
However, this point of change, under a steady forcing, is not the same as the
identification of a single temperature at which the ice sheet may be stable
or unstable in a given area and over a discrete period of time. Consequently
it is not possible from our tipping point analysis to provide information on
a threshold, as the two phenomena are simply different entities. A detailed
explanation of tipping points in Earth systems can be found in
, whereas threshold temperatures for individual Antarctic
ice-sheet catchments have been quantified in .
Results
Histogram representation on the anomaly data shown in Fig. . Biases used in certain simulations are additional to the warming
values shown here. Note the very long tail that skews the mean value of modelled land surface warming,
indicating that the modal value might be most representative of the continent as a whole. Sea-surface
temperature anomalies are also higher in the open ocean than those of a subset representing ocean areas where present-day ice shelves exist.
For the first of our experiments, we run our RCM to simulate the early
Pliocene climate at 4.23 Ma. The model yields spatially variable annual air
and sea-surface temperature changes whose means are approximately 5 and
2 ∘C above present respectively, for presently ice-covered areas of
Antarctica (Figs. and ). The advantage of using a known
period of the past such as this, rather than a forward projection, is that we
can use empirical data to evaluate our modelled climate fields and to
constrain our ice-sheet simulations. Proxy data suggest that our simulated
climate may be 1–2 ∘C cooler than actually occurred
(Table ); thus, we run duplicate simulations allowing for
additional warming of 1 and 2 ∘C in both the atmosphere and ocean.
The sea-level equivalent ice volume loss from Antarctica in these simulations
ranges from 4 to 14 m (Table ; Fig. ). Assuming a 5 to
7 m contribution from the Greenland ice sheet and
0.5 to 1 m from thermal expansion of the oceans (assuming 1 to 3 ∘C
ocean warming) , all of our simulations are
consistent with a Pliocene sea level highstand range of approximately 10 to
> 20 m reconstructed from proxy records . However, by considering likely air–ocean
temperature relationships , as well as
empirical records of an absent WAIS and a retreated EAIS at this time
, we are able to identify two
scenarios as most plausible. Figure a and b illustrate the modelled
Antarctic ice-sheet geometry that arises under constant forcing with the
Pliocene climate, modified to incorporate a +2 ∘C air temperature
bias and a 0 or 1 ∘C bias in the ocean (see “Methods”). In both
cases we reproduce the smaller-than-present ice geometry, as well as the
pattern of basal ice velocities that would have controlled bedrock erosion
and sediment transport, that are necessary to be consistent with geological
interpretations .
Simulated Antarctic ice-sheet contributions to global mean sea level under a range of RCM-based climatologies,
using two different grounding-line parameterizations. Values from previous studies are also shown (grey bars), as well as global sea-level highstand values inferred from far-field sites.
Basal ice velocities for the simulated early Pliocene ice sheet under environmental conditions
from regional climate model simulations using two different bias adjustments. Fastest-flowing outlets occur in
the subglacial basins and troughs of East Antarctica. These zones correspond to inferred areas of
subglacial erosion during past warm climates .
Red line identifies catchment transect shown in Fig. .
In both of the scenarios shown in Fig. , substantial
grounding-line retreat is evident in the WSB, but the Aurora and Recovery
basins are less affected. To better understand the timescales and rates
involved in retreat in the WSB, we take timeslice ice and bed geometries
along the WSB flowline from the two simulations considered representative of
Pliocene conditions at 4.23 Ma (Fig. a, b). In both scenarios, we
find that margin retreat under constant climate forcing is punctuated by
periods of stability. Figure a illustrates a gradual surface
lowering at the margin of the ice sheet that continues for 2000 years before
flotation and grounding-line retreat ensue. At this point, rapid retreat
takes place across the deepest part of the WSB, and grounded ice is replaced
by a floating ice shelf. Peak retreat rates are sustained for two to three
centuries during this period (Fig. c) before declining. Continued
retreat across the inner portion of the WSB proceeds more slowly, but is
similarly punctuated by alternating episodes of acceleration and relative
stability that continue for 7 to 8 kyr (Fig. c). Under warmer
oceanic conditions (Fig. b) retreat proceeds more quickly, but
initial destabilization from the seaward pinning point still requires
thinning and lowering of the ice-sheet margin, which in this case takes place
over the first 1000 years.
Mechanism and timescale of ice-sheet retreat across Wilkes
Subglacial Basin. (a) Ice-sheet margin initially occupies stable
location pinned on bedrock high, unaffected by marine influence. Gradual
surface lowering from rising air temperatures promotes thinning, flotation,
and subsequent rapid inland retreat of margin. (b) Identical
simulation to (a) but employing a warmer ocean. Coloured lines
denote ice geometries at 200-year intervals. Note also the associated bedrock
uplift following ice retreat. (c) Rate of retreat across the WSB is
non-uniform, despite time-invariant forcings, and is governed primarily by
the location of bedrock pinning points.
Figure illustrates that thresholds clearly exist in areas like the
Wilkes subglacial basin where the topography beneath the ice sheet allows for
rapid retreat after prolonged thinning under a warmer climate destabilizes
the grounded margin. However, in order to robustly assess whether genuine
“tipping points” exist in the Antarctic ice-sheet system it is necessary to
use a statistical treatment of the time series data in which statistical
signatures of instability are sought. To do this we first plot sea-level
equivalent whole-continent ice volume trends (Fig. a, h), using air
and ocean temperature bias corrections as described above. Viewing ice volume
evolution of these six simulations in semi-log space it is evident that the
modelled ice sheets evolve through three distinct phases. First, in all
experiments there is a period of rapid mass loss in which the marine-based
sectors of the WAIS collapse. This phase takes one to three centuries,
depending on the magnitude of the applied forcing. The second phase is
characterized by a slower, but sustained, sea-level contribution from the
EAIS, arising from both dynamic adjustment to the loss of fringing ice
shelves, and from surface lowering resulting from negative mass balance in
coastal areas. It is during this phase that trajectories begin to diverge,
depending on the air temperature forcing applied. Using the unadjusted RCM
air temperatures, the EAIS stabilizes and actually accumulates sufficient
mass from the associated increase in precipitation to offset
domain-integrated losses. In this scenario, the ice sheet effectively removes
water from global oceans and leads to a slight lowering of sea level
(Fig. a, blue line). Perturbing the climate with an additional one
or two degrees of atmospheric warming, however, means that surface melt is no
longer completely offset by increased precipitation, and the sea-level
contribution from the ice sheet continues to increase. The third and final
phase of ice-sheet evolution in our simulations takes place once ice in major
subglacial basins begins to retreat. Interestingly, in terms of ice-sheet
thresholds the key tipping point identified in the Wilkes Subglacial Basin
appears to be triggered in very similar ways by both atmospheric and oceanic
forcing (Fig. ), suggesting that several climate scenarios may
produce equilibrium ice-sheet geometries that are consistent with the
empirical constraints.
(a) Sea-level equivalent ice mass loss for ice-sheet
simulations forced by regional climate model outputs allowing for
0–2 ∘C air temperature bias. Inset box identifies region shown in
(b, c). Precursor signatures of tipping points:
(b) increasing autocorrelation (AR1), and (c) increasing
variance (Var). Grey lines show precursors over 1500-year sliding window,
black lines show precursors during the 250-year sliding window immediately
preceding the tipping point. Additional detail shown in Fig. . Mean
annual thinning rate over precursor (d) and response
(e) periods. (f, g) Thinning rate (dHdt) and surface
velocity (Vel.) at locations in the Recovery and Wilkes subglacial basins
(white boxes in d, e). Note the lagged response of peak ice velocity
compared to thinning maxima. Panels (h–n) as (a–g) but
for scenarios with 1 ∘C sea-surface temperature bias.
Using a sliding window to carry out tipping point analyses of these data we
can establish whether or not statistical signatures of instability are
evident during any of these three phases. We analysed six ice-sheet
trajectories that encompass the range of environmental conditions considered
most consistent with RCM simulations and empirical constraints, using air
temperature biases of 0, 1, and 2 ∘C and ocean temperature biases of
0 and 1 ∘C added to the RCM-simulated climatologies. In these six
experiments we found evidence of critical slowing down in three. The loss of
WAIS occurs too quickly in our simulations to determine whether tipping
points for that ice sheet exist or not. However, in the coolest of the six
scenarios, using the unadjusted RCM values, we found evidence for a tipping
point that leads to accelerated growth of the East Antarctic ice sheet
(Fig. a, blue line). The next warmest scenario yields a stable EAIS
(Fig. a, yellow line) with no clear tipping point, and the two
warmest scenarios (Fig. h, yellow and red lines) lead to such rapid
mass loss that no tipping points are detected. In the two intermediate
scenarios (Fig. a, red line; h, blue line), however, two obvious
inflections in mass loss are visible. Focusing on these two scenarios, we
employ sliding analysis windows of two different widths, 250 and 1500 years,
to see if precursor signals indicative of the build-up to a tipping point can
be seen in advance of the actual threshold. Figure b, c, i, j
illustrate the trends in autocorrelation at lag-1 (AR1) and variance (Var)
for the two scenarios, overlain on the corresponding mass loss trajectories.
In all cases, analyses using the 250-year window (black lines) reveal
abruptly increasing AR1 and Var values (early warning signals of critical
slowing down) immediately preceding the tipping point. A change in skewness
is also observed (Fig. ), which suggests that the system may have
reached a region of asymmetry in its basin of attraction. What is surprising,
however, is that even the analyses using the 1500-year sliding window
(Fig. b, c, i, j, grey lines) show evidence of increasing trends
(Kendall tau values shown in Fig. ), suggesting that the system may
be showing signs of instability far in advance of the observed tipping point,
and on a timeframe comparable to the gradual thinning observed in the Wilkes
subglacial basin analysis described above (Fig. ).
Tipping point analyses for two scenarios. Upper row shows results of
analyses of dT +2 ∘C, dSST +0 ∘C, lower row shows dT
+0 ∘C, dSST +1 ∘C. In each panel, top row shows
modelled mass loss curve with inset identifying period used in the tipping
point analysis. The four lower rows each show one key indicator metric
(residuals, autocorrelation, variance, skewness) as described in “Methods”.
Left and right columns show results based on 1500-year (from the solid line;
dashed line shows analysis prior to this window) and 250-year sliding windows
respectively. Note the steeper trends and higher tau values in the shorter
analyses, indicative of a stronger signal over the shorter timeframe. Inset
contour plots display the range of Kendall tau values for different sliding
window lengths (25–50 %) and smoothing bandwidths (5–15 %).
To determine whether the results are sensitive to parameter choices such as
the length of the smoothing bandwidth or sliding window size, we ran repeats
of the analysis with a range of 25 smoothing bandwidths (ranging from 5 to
15 % of the time-series length) and 25 sliding window sizes (ranging from
25 to 50 % of the time-series length). The results are visualized using
contour plots of the Kendall tau values of these repeats; a more homogeneous
colour indicates increased robustness (Fig. ). In order to test the
significance of these results we created a surrogate dataset by randomizing
the original data over 5000 permutations based on the null
hypothesis that the data are generated by a stationary Gaussian linear
stochastic process. This method guarantees the same amplitude distribution as
the original time series, but removes any ordered structure or linear
correlation and makes no assumption about the
statistical distribution of the data. The Kendall tau values for
autocorrelation at lag-1 and variance were computed for each of the surrogate
time series, and the probability of making a type I statistical error (false
positive) for the original data was computed by comparing to the probability
distribution of the surrogate data (Table and Fig. ).
Calculated significance statistics for two precursor metrics of tipping points. Kendall tau and p values
are shown for autocorrelation (“AR1”) and variance (“Var”) trends over 250 (“short”) and 1500 (“long”) sliding windows, for two
scenarios in which distinct inflections occur in their mass loss time series. See Fig. for more information.
Kendall tau
p value
Scenario 3 short
AR1
0.805
< 0.05
Var
0.626
< 0.12
Scenario 3 long
AR1
0.588
< 0.15
Var
0.584
< 0.15
Scenario 4 short
AR1
0.771
< 0.05
Var
0.911
< 0.01
Scenario 4 long
AR1
0.656
< 0.1
Var
0.721
< 0.06
Histograms showing Kendall tau correlation coefficients for
surrogate time series, generated from the two scenarios for which the
existence of tipping points was investigated. Values relate to
autocorrelation (blue lines) and variance (red lines) scores shown in
Table . Dashed lines mark 90 and 95 % confidence intervals.
To understand the glaciological changes taking place as these thresholds are
crossed, we divided the analysis time periods into “precursor” and
“response” episodes, and calculated mean thinning rates across the ice
sheet (Fig. d, e, k, l). There are clear indicators of ice-sheet
thinning in the major subglacial basins of East Antarctica, but when velocity
and thinning rate data are extracted from two of the most dynamic areas there
appears to be no clear distinction between the two episodes – in one
scenario thinning and acceleration seem to occur during both the precursor
and the response phases, whereas in the other scenario dynamic thinning takes
place only during the response phase (Fig. f, g, m, n). What is
clear, however, is that wherever ice-sheet thinning is observed, it is
associated with an acceleration of ice flow at the same location. In our
examples the lag between peak thinning rates and maximum velocities ranges
from 200 to 1200 years.
Discussion
Far-field records of Pliocene sea-level changes are sparse, and their
interpretation is complicated by glacio-isostatic effects and dynamic
topography . Various techniques
used to define an envelope of the likely Pliocene sea-level highstand
imply a GMSL
contribution from the EAIS, but the uncertainties involved are sufficiently
great that the sea-level contribution from East Antarctica remains hard to
quantify, even though some loss from this ice sheet seems likely
. Novel isotope-enabled climate and ice-sheet
modelling has allowed the likely GMSL contribution from Antarctica to be
constrained to 3–12 m during the warmest parts of the mid-Pliocene, with an
absolute maximum of 13 m , which requires at least
some loss of ice from East Antarctica. The 4.23 Ma interglacial in our study
was likely warmer than mid-Pliocene interglacials, however, suggesting
mid-Pliocene sea-level estimates
should be treated as minima in our comparison. Warmer air temperatures during
all Pliocene interglacials most likely led to increased precipitation in East
Antarctica, thickening the ice-sheet interior .
Consequently, any sea-level-equivalent mass loss from the EAIS must have been
over and above these mass gains, perhaps supporting geologically based
inferences of large-scale ice-sheet margin retreat in areas such as the
Wilkes Subglacial Basin .
Our study set out to shed further light on this period of uncertainty by
investigating the sensitivity of the Antarctic ice sheet to climate-related
thresholds, with a particular focus on a peak-warmth interglacial of the
early Pliocene period at 4.23 Ma. To establish the likely climatic
conditions of this time we use global and regional climate models, but lean
heavily on empirical biogeochemical proxy data to validate these simulations.
Because there are considerable uncertainties in both the modelled and
proxy-inferred temperatures, we defined an envelope of air and ocean
temperatures and ran a small ensemble of ice-sheet simulations to capture the
range of possible responses. We find that, under the applied climate
conditions, the Antarctic ice sheet contributed 8.6 ± 2.8 m to global
mean sea level in the early Pliocene, consistent with some recent studies of
the mid-Pliocene but higher than
, and lower than
, .
The reduction in AIS volume that we simulate arose from a loss of
marine-based portions of WAIS, and an inland migration of the EAIS grounding
line into the Wilkes subglacial basin. Lesser retreat occurred in the eastern
Weddell Sea, in the Amery Basin, and at the margins of the Aurora subglacial
basin. In our simulations it appears that the significant retreat in the WSB
arises as a consequence of prolonged surface lowering due to atmospheric
warming and increasing surface melt, which after 1000 to 2000 years allows
flotation of the present-day ice margin and retreat from the primary pinning
point that currently maintains stability of this sector. An increase in
surface melting at this time is consistent with facies of this age in the
Ross Sea that record increased deposition of terrigenous sediment
. Subsequent retreat proceeds rapidly into the
inland-deepening basin, but is punctuated by periods of slower retreat where
bedrock highs allow temporary stabilization of the ice margin.
The delayed atmospheric warming control on ice-sheet behaviour that occurs in
the WSB is also mirrored at the continental scale. Our whole-continent ice
volume trajectories show that, over multi-millennial timescales, the
magnitude of atmospheric warming is critical in determining whether or not
ice-sheet mass loss exhibits tipping points (i.e. non-linear behaviour). We
find the clearest evidence of tipping under climate scenarios that are
moderate, rather than extreme. This is because of the sensitive interplay
between the climate forcing that drives retreat and the topographic restraint
afforded by pinning points that aid stability. This balance is overwhelmed
under extremely warm climates and ice-sheet retreat proceeds rapidly and
linearly.