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Roquet et al., Sci. Adv. 8, eabq0793 (2022) 16 November 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
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CLIMATOLOGY
Unique thermal expansion properties of water key
to the formation of sea ice on Earth
Fabien Roquet1*, David Ferreira2, Romain Caneill1, Daniel Schlesinger3†, Gurvan Madec4
The formation of sea ice in polar regions is possible because a salinity gradient or halocline keeps the water col-
umn stable despite intense cooling. Here, we demonstrate that a unique water property is central to the mainte-
nance of the polar halocline, namely, that the thermal expansion coefficient (TEC) of seawater increases by one
order of magnitude between polar and tropical regions. Using a fully coupled climate model, it is shown that,
even with excess precipitations, sea ice would not form at all if the near-freezing temperature TEC was not well
below its ocean average value. The leading order dependence of the TEC on temperature is essential to the coex-
istence of the mid/low-latitude thermally stratified and the high-latitude sea ice–covered oceans that character-
ize our planet. A key implication is that nonlinearities of water properties have a first-order impact on the global
climate of Earth and possibly exoplanets.
INTRODUCTION
Most of what makes the water molecule H2O so unique can be traced
back to its structure with the V-shaped arrangement of hydrogen
atoms around the oxygen atom and its electronic structure with two
lone pairs giving rise to a strong polarity (1). Because of its polarity,
a water molecule can form hydrogen bonds with neighboring mol-
ecules, adding cohesion within the liquid and making the heat ca-
pacity, the latent heat of fusion and of evaporation, or the surface
tension of liquid water all exceptionally large. These properties ex-
plain why water is so central to the climate system on Earth (2).
As the hydrogen and oxygen atoms form a 104.5° angle, almost equal
to the 109.5° angle found in a regular tetrahedron (3), water mole-
cules can form open crystal structures where each water molecule is
at the center of a tetrahedron formed by the neighboring molecules.
This is precisely why liquid water is denser than ice near the freez-
ing point.
This is also the reason why the thermal expansion coefficient
(TEC) of seawater drops considerably near the freezing point. Here,
we will show that the strong dependence of the TEC on temperature has
a profound and generally overlooked influence on the formation of sea
ice on Earth, on the general organization of the upper ocean strati-
fication, and on vertical exchanges between the surface and deep
layers of the ocean.
The TEC of liquid water
The TEC measures the relative variation of density caused by a unit
change of temperature
= − 1
─
∂
─
∂
∣
S,p
(1)
where is the mass density, is the conservative temperature, S is the
absolute salinity, and p is the pressure. Note that the exact definition
of TEC varies depending on the standard used to define the tem-
perature or salinity properties. Here, we use the thermodynamic
equation of seawater TEOS-10 standard (4); however, we stress
that our results are independent of the standard used.
In a simple liquid (e.g., liquid argon or nitrogen) (5,6), the TEC
is most commonly positive, i.e., its density monotonously decreases
when temperature increases. However, pure liquid water has the rare
property that, at standard pressure, it does not reach the maximum
density at the freezing point but at a temperature of 4°C. This means
that the TEC for liquid water is negative at temperatures below 4°C.
The implications of this negative TEC are well known for the
stratification of the so-called dimictic lakes (7,8). In these lakes, the
bottom is filled with the densest 4°C water year long and isolated
from surface waters both in winter and in summer. Note, however, that
very deep lakes may have a bottom temperature substantially lower
than 4°C as the temperature of maximum density decreases with pres-
sure, effectively limiting the depth of full overturn (9). The 4°C max-
imum density property enables the formation of ice at the surface,
as only a surface layer of limited depth needs to be cooled down to
drive freezing. It is much harder to freeze entirely the lake over win-
tertime, thus providing a safe habitat for species living in the lake.
The situation is fundamentally different for the oceans, because
salt substantially modifies the physical properties of water. Dissolv-
ing salt in water increases the TEC of the solution at the same time as
it lowers its freezing point (Fig.1B). The structure of the water sol-
vent in NaCl aqueous solutions is known to be modified in a similar
way to that of water under enhanced pressure (10). Increasing salinity
by 1 gkg−1 induces a similar rise in the TEC value as a 100-dbar pres-
sure increase (Fig.1A). Negative TEC values are found only for sa-
linities below 25 gkg−1, making it extremely rare to encounter except
near cold estuaries. Thus, the mechanism promoting the formation
of ice in freshwater lakes does not operate in the ocean. However,
sea ice is forming on large areas of the polar ocean, and this study
explores whether this could be related to patterns of TEC variations
in the upper ocean.
Stratification control in the ocean
Polar regions are generally associated with excess precipitation over
evaporation, freshening the upper ocean and forming a permanent
halocline (11,12). In turn, the permanent halocline limits thermally
1Department of Marine Sciences, University of Gothenburg, 40530 Gothenburg,
Sweden. 2Department of Meteorology, University of Reading, Reading RG66ET, UK.
3Department of Environmental Science and Bolin Centre for Climate Research,
Stockholm University, 106 91 Stockholm, Sweden. 4LOCEAN, Sorbonne Universités,
UPMC, Paris, France.
*Corresponding author. Email: fabien.roquet@gu.se
†Present address: Environment and Health Administration, SLB-analys, Stockholm
104 20, Sweden.
Copyright © 2022
The Authors, some
rights reserved;
exclusive licensee
American Association
for the Advancement
of Science. No claim to
original U.S. Government
Works. Distributed
under a Creative
Commons Attribution
NonCommercial
License 4.0 (CC BY-NC).
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driven deep convection, thus promoting the formation of sea ice in
polar regions. It has long been noted that sea ice formation occurs
only in the presence of a halocline (13). It would seem natural to
assume that the freshwater forcing alone explains why polar regions
are stratified in salinity. However, the argument is somewhat in-
complete and does not explain why the intense cooling is generally
not able to wipe out the polar halocline.
The stratification is commonly quantified by the squared buoyancy
frequency, N 2 = − g
z
/ , where is the potential density, g is the
gravity acceleration, and the subscript z indicates the vertical deriv-
ative (14). The buoyancy frequency can be decomposed into the sum
of temperature and salinity contributions
N 2 = N
2 + N
S
2 (2)
with N
2 = g z and N
S
2 = − g S z . Here, = (∂/∂S)∣, p/ defines
the saline contraction coefficient, analogous to the TEC in Eq. 1
for salt.
Carmack (13) proposed to distinguish between the alpha ocean,
where the upper ocean thermal stratification is stable ( N
2 > 0 ), and
the beta ocean, where the haline stratification is stable ( N
S
2 > 0 ). To
avoid the ambiguity of this definition in regions where both ther-
mal and haline stratifications are stable, we will define three regimes
using the stratification control index (SCI) defined as SCI = ( N
2 −
N
S
2 ) / N 2 : The alpha ocean is found where SCI > 1 immediately be-
low the mixed layer, the beta ocean is where SCI < −1, while regions
where −1 < SCI < 1 will be referred to as the transition zone. Alpha
regions are associated with a thermocline, while beta regions feature
a halocline. In the transition zone, both temperature and salinity
contribute positively to the stratification.
Note that most of the ocean is either alpha or beta with a sharp
transition, meaning that temperature and salinity stratifications are
most often compensating each other (Fig.2). For this reason, a large
fraction of the global ocean is subject to double diffusion, either salt
fingering (alpha) or diffusive (beta) (15), contributing to interior mix-
ing. Figure2C shows that the transition between the two regimes is
generally found in the mid-latitudes, at a mean latitude of 50°N in
both the Northern and Southern Hemispheres, although it can reach
up to 80°N in the Nordic Seas. Note that an alternative definition
for the separation between the three regimes has also been proposed
on the basis of a statistical criterion (16).
The large TEC variations at the surface are dominated by changes
in sea surface temperature (Fig.2A). In the global ocean, the TEC
varies from 0.3 × 10−4 °C−1 near the freezing temperature (≤0 ° C) to
3.5 × 10−4 °C−1 in tropical waters. In contrast, the saline contraction
coefficient varies by less than 10% in the ocean and can be consid-
ered constant to a good approximation. The temperature depen-
dence of the TEC also induces the cabbeling or “densification upon
mixing” effect in frontal regions (17,18). Note, however, that cab-
beling is not a central focus of this work, as will be discussed more
thoroughly in the last section.
A comparison between the global distributions of the TEC and
SCI in the upper ocean indicates that beta regions correspond to
relatively small TEC (Fig.2). In this study, we investigate whether this
correspondence is fortuitous or whether the decrease in TEC at low
temperature is a key condition for the existence of beta regions in
the ocean. This question cannot be addressed experimentally, as the
equation of state (EOS) of seawater cannot be changed. The situation
is, in this respect, analogous to the question of how a given bathy-
metric configuration constrains the observed circulation, which can
only be investigated through theory and numerical simulations.
Forced ocean simulations (i.e., with imposed conditions at the
surface boundary) have been performed in previous studies (19,20),
which showed a large sensitivity of the global stratification distribu-
tion to changes in the TEC value, especially changes near the freezing
point. However, the impact on sea ice was not realistic because
forced simulations do not include atmospheric feedbacks. To avoid
these unrealistic constraints, we use a fully coupled ocean–atmosphere–
sea ice model with a simplified geometry (see Materials and Methods
for details on the model configuration and sensitivity experiments).
The nonlinear EOS implemented in the model will be replaced by a
series of linear EOS with different TEC constant values, allowing us to
investigate the sensitivity of the global climate to this water property.
RESULTS
The most marked changes observed when switching from a nonlin-
ear to a linear EOS (at approximately constant global mean TEC) are
A
B
Fig. 1. Variation of the TEC with respect to temperature, salinity, and depth. (A) TEC
function of temperature and depth for fresh water, i.e., at salinity S = 0 g kg−1.
Here, depth is taken proportional to pressure (1 m ≃ 1 dbar). (B) Variation of the
TEC with respect to temperature and salinity at atmospheric pressure p = 0 dbar.
The typical salinity range of seawater is indicated with light solid contours. The TEC
decreases quasi-linearly with respect to temperature, pressure, and salinity. In both
panels, the dashed line indicates the freezing point, while the solid line indicates
where the TEC changes sign.
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found in polar regions. While the control simulation Ctrl simulates
a large ice pack in the Southern Hemisphere south of 60°S, the sim-
ulation Lin2.0 with a constant TEC value of 2.0 × 10−4 °C−1 is com-
pletely sea ice free (Fig.3A; see also fig. S3). The sensitivity runs with
linear EOS exhibit an abrupt regime transition between ice-free cli-
mates for large TEC and ice-covered poles for low TEC. The critical
TEC value allowing the presence of sea ice is near 1.2 × 10−4 °C−1. A
constant value of about 0.8 × 10−4 °C−1 is required to produce the
sea ice area found in Ctrl.
The surface and atmospheric responses to variations in TEC can
be explained to a large extent by the changes in sea ice cover. A
wider sea ice cover increases the planetary albedo, either directly or
through changes in cloud cover, which not only tends to reduce the
solar radiation absorbed at the surface (21) but also insulates the
ocean from the atmosphere, allowing colder and drier conditions
to develop in winter (22). The mean surface temperature increases
rapidly (by about 2.5°C) with the disappearance of sea ice to stabi-
lize just above 24°C in ice-free climates (Fig.3B, blue).
Surface ocean forcings (fig. S5) are weakly affected by changes in
TEC, with two notable exceptions. First, in polar regions and in the
presence of sea ice, the strong divergence of fresh water from within
the ice pack to its edge (due to equatorward spreading of ice) desta-
bilizes the stratification and drives the formation of high-salinity
bottom waters. In ice-free climates, the freshwater flux (due to net
precipitation) stabilizes the stratification, but it is overcome by the
destabilizing effect of the intense surface cooling that produces
more widespread deep convection. Second, the surface heat flux is
substantially modified in the mid-latitudes for the low-TEC run
Lin0.5, reflecting fundamental differences in the structure of the over-
turning circulation with shallower overturning cells shifted equa-
torward (fig. S4). Changes in the Northern polar regions are less
marked, probably because Ctrl had very little sea ice there to start
with so surface fluxes are less likely to be modified.
Close inspection at zonal-mean temperature and salinity sec-
tions (Fig.4) highlights the major impact that the value of TEC has
on the ocean structure. For sufficiently high TEC values (2 × 10−4 to
3.5 × 10−4 °C−1), the stratification in subtropical regions compares
well with that of Ctrl (and the real ocean), with the characteristic
W-shaped thermocline extending down to a similar depth of about
500m. In the southern polar region, however, deep convection
A
C D
B
Fig. 2. Stratification control and surface TEC in the ocean. (A) Surface distribution of the TEC, showing a notable correlation with sea surface temperature.
(B) Zonal-mean TEC showing an order of magnitude of var. (C) SCI (see core text for the definition). Blue, stratification dominated by salinity (beta regions); red, domi-
nated by temperature (alpha regions). (D) Zonal-mean SCI. All figures are based on the Estimating the Circulation and Climate of the Ocean (ECCO) state estimate, version
4, release 4 (66). For each year, the SCI was computed on the layer found between 10 and 30 m below the mixed layer for the month of deepest mixed layer. The SCI
distribution is obtained by averaging over the 21 years available in ECCO.
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becomes more vigorous at high TEC, and the stratification there
nearly vanishes (Fig.4, middle for Lin2.0). As a result, the southern
polar surface becomes warmer/saltier and the bottom becomes
cooler/fresher than in runs without convection. The spread of cold/
fresh southern water masses results in lower bottom temperature
globally (Fig.3B, red) and a cooler global ocean, associated with a
stronger deep overturning cell (fig. S4).
In contrast, at a low-TEC run (Lin0.5in Fig.4,CandF), deeper
but weakly stratified thermoclines develop in both polar and sub-
tropical regions. The abyssal ocean is filled with a warm water mass
(10°C bottom temperature; Fig.3B). This, as well as the absence of
a subsurface salinity maximum in the subtropics, indicates the pres-
ence of salinity-driven convection in the subtropics. Overall, this
run has weaker and less connected overturning cells, producing
an essentially unventilated bottom ocean (fig. S4). The temperature
contrast between surface and deep waters in the Southern Ocean is
as large as 13°C, which is only possible due to the strong stabilizing
effect of vertical salinity gradients.
The global mean sea surface salinity increases nearly linearly with
the TEC (∼1 g kg−1 for a unit 10−4 °C−1 of TEC; see Fig.3C, blue).
This is balanced by a freshening of the bottom ocean with increas-
ing TEC, so as to satisfy global salt conservation in the ocean. The
overall pattern of change is one of increasing contrast between the
top and bottom of the ocean in both temperature and salinity
(Fig.3B). These temperature and salinity changes have opposite ef-
fects on the stabilization of the global stratification. As the tempera-
ture effect dominates (both the vertical temperature contrast and
the impact of temperature on density increase with TEC), the top-
to-bottom mean stratification strengthens for increasing values of
TEC (Fig.5).
The effect of the TEC on the stratification can be quantified by
the SCI, which becomes systematically larger for higher values of
TEC. In ice-free states, the thermal stratification N
T
2 is everywhere
positive, indicating an inability to maintain cold waters near the
surface while a salinity inversion ( N
S
2 < 0 , also seen in Ctrl) de-
velops in the tropics and subtropics (corresponding to SCI > 1;
Fig.5C). In contrast, the low-TEC states have a marked tempera-
ture inversion in polar regions, as in Ctrl (see Fig.4), but no salinity
inversion in the subtropics, contrary to all the other simulations.
The beta region (SCI < −1) in the low-TEC climates extends far into
the subtropics up to 25° latitude, while the high-TEC climates do
not exhibit beta regions at all.
It appears that the SCI in Ctrl closely matches at each latitude
that the SCI value obtained in linear EOS simulations with the cor-
responding surface TEC. At high latitude where the TEC is low in
Ctrl, the stratification resembles that of Lin0.5, while at low latitude,
it resembles that of Lin2.0. This indicates that the TEC provides a
strong constraint on the type of stratification that a particular loca-
tion may experience. That is, the existence of distinct alpha and beta
regions is primarily a consequence of the temperature dependence
of the TEC of seawater.
Stratification below the sea ice
Our numerical experiments indicate the existence of a threshold in
TEC above which sea ice cannot be sustained. The threshold value
is between 1 × 10−4 and 1.5 × 10−4 °C−1 with a nonlinear transition,
as a centennial oscillation between two unstable states is observed in
Lin1.25 (see fig. S2). The quantitative prediction for the threshold
value is likely model dependent and should be taken with caution.
We argue, however, that the existence of such a threshold is expected
and can be rationalized using the theoretical model of Martinson
(23) for the stratification below sea ice.
The model considers a steady-state upper ocean and expresses
the conservation of mass, salt, and heat. A central element is that,
in the presence of sea ice, the surface layer is at the freezing point,
which is the minimum possible temperature of seawater. This im-
plies that the vertical gradient of temperature below sea ice is neces-
sarily negative, ∂z ≤ 0.
To ensure static stability and a steady state, the total stratifica-
tion N2 must be positive, implying that the salinity stratification N
S
2
must be positive and large enough to compensate the temperature
inversion or (see Eq. 2)
∂ z S ≤ ∂ z ≤ 0 (3)
In the case of a freshwater lake (∂zS = 0), where < 0, the stabil-
ity condition (Eq. 3) is satisfied unconditionally (recall, ∂z ≤ 0). In
the saltwater ocean, however, the TEC is everywhere positive, so
that N
2 ≤ 0 under the sea ice. There, the stratification must be sa-
linity controlled, with ∂zS ≤ 0 (fresh water on top). This introduces
an upper limit on the magnitude of the (negative) temperature gra-
dient that can be maintained, which depends not only on the salin-
ity gradient but also strongly on the TEC value.
0123
(10
–4
K
–1
)
0
10
20
30
40
10
6
km
2
A Global sea ice area
0123
20
22
24
26
2
4
6
8
10
12
B Temperature
0123
33
34
35
36
34
34.
2
34.
4
34.
6
34.
8
35
C Salinity
(10
–4
K
–1
) (10
–4
K
–1
)
Fig. 3. Climate model sensitivity to different prescribed TECs. (A) Sea ice area, (B) sea surface temperature (0 to 40 m, blue) and bottom temperature (3000 to 4000 m,
red), and (C) sea surface salinity (blue) and bottom salinity (red). Bottom values are averaged over the lowest kilometer (3000 to 4000 m), while surface values are averaged
over the top 40 m. The horizontal lines denote the corresponding values in Ctrl.
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A critical value for the TEC can be obtained in the limit where
the stratification would vanish
≤ c =
∂ z S
─
∂ z (4)
In a steady state, the gradient of salinity must be primarily con-
trolled by the net rate of precipitation, which acts to stabilize the
stratification. The surface cooling, which weakens the stability, may
occur not only by air-sea/ice-sea interaction but also as a result of
the ice melting needed to close the ice mass budget. Conservation of
salt, mass, and heat requires compensating diffusive fluxes at the
base of the mixed layer. Using simplified ice mass, heat, and salt
budgets and assuming identical diffusivities for temperature and
salinity, one finds an expression for the critical TEC c (see the Sup-
plementary Materials for detailed derivations)
c = S 0 w c p P
─
Q + 0 L i AP . (5)
where P is the net precipitation (defined as precipitation minus
evaporation plus river runoff), Q is the net surface heat flux, and A
is the sea ice fraction (see table S1 for definitions of constants). A
stable state with sea ice can only be maintained for a TEC value
smaller than c. In polar regions where precipitation dominates
evaporation (P > 0) and the ocean loses heat to the ice/atmosphere
(Q > 0), c is positive. Equation 5 shows that, as expected, larger
heat loss reduces c and the range of stability. The role of net precip-
itation P is more complex, appearing both in the numerator and
denominator of Eq. 5. Larger precipitation stabilizes the water col-
umn by lowering the surface salinity, which permits a larger c
(numerator). Simultaneously, larger precipitation over ice must be
balanced by melting at the ice base and hence larger latent heat loss,
which reinforces the destabilizing effect of Q (denominator).
For realistic values of the parameters (table S1), a critical value of
c ≈ 0.9 × 10−4 °C−1 is obtained. Despite strong simplifications, this
estimate is consistent with the TEC values where the transition to
an ice-free climate occurs in the coupled model (Fig.3). The fact
that the critical TEC value is well below the global mean TEC value
confirms that the conditions to form sea ice in the open ocean could
not be met in the current Earth climate if the TEC value was not
dropping at low temperature. Furthermore, it demonstrates that
this water property, through (Eq. 5), imposes a constraint on the
Earth’s climate state.
AB C
DE F
Fig. 4. Global modifications of the mean thermohaline stratification for different prescribed TECs. Zonally averaged sections of temperature (top) and salinity
(bottom): (A to D) Ctrl, (B to E) Lin2.0, and (C to F) Lin0.5. Dashed orange lines in the top left corner denote the zonally reentrant section above the seal and south of the
continents. Blue squares indicate the sea ice extent.
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DISCUSSION
Here, we have shown that the temperature dependence of the TEC
is key to favoring the formation of a beta ocean (stratified by salini-
ty) and largely controls the sea ice extent using a range of coupled
ocean-atmosphere simulations. It was further shown that, even if a
net freshwater flux in polar regions is necessary to form a halocline,
it is not enough to maintain the beta stratification stable in the
presence of intense surface cooling except maybe in geographically
limited cold estuarine regions. Sea ice formation has long been
noted to require beta ocean conditions to occur away from shallow
areas (13,24). The idea that a reduction of the TEC in the cold high
latitudes could promote sea ice formation was even suggested
(13,20,25), and it is demonstrated here.
The transition from alpha to beta stratification is not caused by
cabbeling, contrary to previous suggestions (13). Cabbeling, also
known as densification upon mixing, generates a convergence
across the frontal boundaries as isopycnal mixing in the interior
acts to densify seawater (26,27). Rates of cabbeling depend on how
fast the TEC varies with temperature; however, they also require a
combination of eddy stirring and molecular diffusion to generate
the convergence. That cabbeling may increase the abruptness of the
transition from alpha to beta cannot be entirely discarded here; how-
ever, our results based on linear EOS simulations (thus entirely free
of cabbeling by construct) show that cabbeling is not necessary for
the existence of these transitions (Fig.5).
This is consistent with recent numerical experiments showing
that the transition zone in polar regions is set by an inversion of the
mean surface buoyancy flux, linked to the drop in polar TEC value
at low temperature (28) rather than cabbeling. This temperature de-
pendence of the TEC should also imply a weaker and more indirect
role of the wind forcing on the position of fronts than previously
hypothesized (29). The position of the transition zone can, however,
be influenced by changes in the strength of the halocline, which can
be driven by hydrological changes (30), ice shelf melting (31), or
wind anomalies (32). This points toward a subtle, nonlinear inter-
play between heat and freshwater surface fluxes in controlling the
meridional structure of the upper ocean stratification.
The idea that the TEC might have a global influence on the cli-
mate is, of course, not entirely new although not always explicitly
acknowledged. Experiments using global atmosphere/ocean general
circulation models can be found in the literature, where the global
mean salinity (33,34) or the global mean temperature (35) of the sim-
ulated ocean is artificially modified, indirectly modifying the ther-
mohaline range of water masses and, consequently, the way the TEC
varies with temperature. Our simulations show that increased TEC
values in the polar region, as may be found in warmer climates, are
associated with colder and fresher deep water properties (Fig.3).
The ventilation is expected to be stronger in warm climates than in
cold climates, as the polar halocline necessitates temperature near
the freezing point to be maintained (36). This, in turn, may induce
an anticorrelation between the global mean temperature and the
carbon storage in the deep ocean, further amplifying climate changes.
This mechanism has been suggested to explain the transition to the
Pleistocene cycle of ice ages, 2.7 million years ago (37). This may
also explain why salinity forcing seems to dominate during the Last
Glacial Maximum, simply because it was in a colder state (38).
The large sensitivity of the global ocean structure and sea ice for-
mation to the TEC highlighted here has strong implications for how
the ocean may respond to a climate change. If the position of the
polar transition zone is controlled by the value of the TEC, itself
mostly a function of the sea surface temperature, migrations of the
transition zone between alpha and beta regions should be largely
driven by the surface heat fluxes. This appears consistent with the
current “atlantification” of the Eurasian Arctic basin, caused by a
warming of the Atlantic inflows and producing a northward migra-
tion of the transition zone and a concurrent shrinking of the sea ice
extent (39). On the other hand, the idea of an increased ventilation
in a warmer climate (35,36) somewhat contradicts the common in-
ference that global warming may induce a slowdown and even pos-
sibly a collapse of the Atlantic Meridional Overturning Circulation
(40). The competing effects of freshening and warming in shifting
the stratification control, particularly in the Nordic Seas (41,42),
need to be better understood to predict how polar climate changes
affect the ventilation and overturning rates.
Our simulation with a uniform TEC corresponding to the present-
day global ocean value ( = 2.0 × 10−4 °C−1) is warmer than the
A
B
Fig. 5. Relative contributions of temperature and salinity on the stratification con-
trolled by the TEC. (A) Zonally averaged haline ( N
S
2 ) and thermal ( N
2 ) buoyancy fre-
quencies averaged from the surface to bottom, shown for the control run and the
three sensitivity experiments. (B) SCI computed using vertically and zonally averaged
buoyancy frequencies. The mean SCI of Ctrl compares well with that of Lin0.5 in
polar regions, especially in the southern ice-covered domain, but is closer to th at of
Lin2.0 and Lin3.5 in subtropical regions. These variations in SCI are consistent
with changes in surface TEC in Ctrl related to sea surface temperature changes.
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control simulation by about 2°C and is totally ice free. Depending
on estimates of the climate sensitivity (43), a decrease in atmo-
spheric CO2 by a factor of about 2 to 5 would be necessary to form
sea ice with this uniform TEC (see the Supplementary Materials).
All things equal (concentration of CO2 and other greenhouse gas,
solar constant, continental distribution, etc.), the unique variation
of the water TEC greatly facilitates the growth of sea ice, with a cas-
cading impact on global climate conditions. For example, by affect-
ing the stratification and rates of transport of essential nutrients
such as phosphate, variations of seawater’s TEC constrain the ocean
productivity (with feedbacks on the global carbon cycle), making it
potentially relevant to habitability conditions in the presence of an
ocean (44). These exoplanets that have attracted a lot of attention as
salty (e.g., the presence of nutrient) oceans, in addition to being a
favorable medium to harbor life, can significantly moderate climate
response to changing astronomical parameters and therefore widen
the habitable zone (45).
Our study highlights that estimates of habitable zone should
avoid simplified linear EOS with constant TEC (34,46). As shown
by our simulations, neglecting the unique thermal expansion prop-
erties of seawater may significantly overestimate the global mean
temperature and therefore underestimate the possibilities of a de-
scent into global glaciation with potential relevance to the transition
toward and from snowball states (47,48). Also, salinity of oceans
may vary markedly over time (49) and between planets (50), affect-
ing the thermal sensitivity of the global ocean. Exploration of the
full range of salinity and their climate impact will require to account
for the full nonlinearity of the seawater EOS.
MATERIALS AND METHODS
Description of the climate model
Simulations are carried out with the MIT General Circulation Mod-
el (51), which solves for the three-dimensional circulation of atmo-
sphere and ocean and includes sea ice and land surface processes.
The atmospheric physics is of “intermediate” complexity based on
SPEEDY (52) at low vertical resolution (further details in the Sup-
plementary Materials). The configuration comprises two land-barrier
masses defining a narrow Atlantic-like basin and a wide Pacific-like
basin connecting to an unblocked Southern Ocean. Despite its sim-
plified geometry, the configurations include many of the essential
dynamics that shape Earth’s climate system (e.g., hydrological cycle
and storm tracks) (53). It also captures two key asymmetries: an asym-
metry between the two northern basins with the absence of deep
water formation in the Pacific Ocean (54) and a north-south
asymmetry between wind-driven gyres in the north and a vigorous
Southern Ocean circumpolar current.
The barrier to the west of the small basin (analogous to the
American continent) is extended with a submarine ridge between
2000 and 4000m in depth. This allows a northward propagation
of bottom water produced in the south and a more realistic repre-
sentation of the bottom meridional cell than in previous reported
simulations (54). Furthermore, a maximum sea ice concentration of
90% is set in the model, and an ice thickness diffusion is applied to
prevent the formation of ice caps that completely insulate the ocean
from the atmosphere and ensure a more realistic production of bot-
tom waters in ice-covered areas.
In its reference configuration, the coupled model uses the stan-
dard EOS-80 for salty water, with potential temperature and practical
salinity as prognostic variables (4). However, following recent rec-
ommendations (55), we will nonetheless interpret them as conser-
vative temperature (a quantity proportional to potential enthalpy
with units of temperature) and absolute salinity (the grams of solute
per kilogram of seawater), respectively. Note that quantitative dis-
crepancies between thermodynamic standards are small (<1%) and
are not susceptible to modify the conclusions here.
Design of the sensitivity experiments
To test the sensitivity of the climate to the TEC value, we implement
a linear EOS approximation
model = 0 (1 − 0 + 0 S) (6)
where 0, 0, and 0 are uniform globally. Having a linear EOS en-
ables us to investigate the effect of the TEC value at different lati-
tudes while keeping the analysis simple. We chose not to include a
nonlinear term in the EOS, despite their potential impact on the
global water mass distribution through cabbeling or thermobaricity
effects (19), to better isolate the local impact of the TEC value on the
surface buoyancy forcings and on the upper stratification.
We carry out the following experiments, which only differ by
their EOS:
1) Ctrl: Control simulation with the nonlinear EOS-80; spin up
of 9 thousand years (ka).
2) Lin2.0: Simulation with the linear EOS with 0 = 2.0 × 10−4 °C−1.
The simulation is initialized from the end state of Ctrl and then
run for 7 ka.
3) Lin0.5, Lin1.0, Lin1.25 and Lin1.5, and Lin3.5: Simulations with
linear EOS with 0 = 0.5, 1.0, 1.25, 1.5, and 3.5in units of 10−4 °C−1,
respectively. These simulations are branched off from the end state
of Lin2.0 and run for a minimum of 5 ka.
Note that the globally averaged TEC values in Ctrl (nonlinear
EOS) and Lin2.0 (linear EOS) are very similar. The haline contrac-
tion coefficient is set to the constant 0 = 7.8 × 10−4(g/kg)−1. The
time series of the sea surface temperature and sea ice area are shown
in figs. S1 and S2. Illustrations below use the past 50 years of each
simulation.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at https://science.org/doi/10.1126/
sciadv.abq0793
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Acknowledgments
Funding: No funding was required for this work. Author contributions: F.R. initiated the
project. D.F. performed numerical runs and helped with their analysis. R.C. carried out analysis
of the Estimating the Circulation and Climate of the Ocean (ECCO) product. D.S. contributed with
his expertise in chemical physics of water. G.M. provided important inputs in interpreting the
results. F.R. wrote the initial draft. All authors contributed to the final manus cript. Competing
interests: The authors declare that they have no competing interests. Data and materials
availability: All data needed to evaluate the conclusions in the paper are present in the paper
and/or the Supplementary Materials. Model data supporting the results reported here are
openly available from the University of Reading Research Data Archive at https://doi.
org/10.17864/1947.000394.
Submitted 16 March 2022
Accepted 23 September 2022
Published 16 November 2022
10.1126/sciadv.abq0793
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Unique thermal expansion properties of water key to the formation of sea ice on
Earth
Fabien RoquetDavid FerreiraRomain CaneillDaniel SchlesingerGurvan Madec
Sci. Adv., 8 (46), eabq0793. • DOI: 10.1126/sciadv.abq0793
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