Spatial biases in oxygen-based Phanerozoic seawater temperature reconstructions

Abstract

Stable oxygen isotopes (δ18O) are routinely used to reconstruct sea-surface temperatures (SSTs) in the geological past, with mineral δ18O values reflecting a combination of the temperature and oxygen isotope composition of seawater (δ18Osw). Temporal variation of mean-ocean δ18Osw is usually accounted for following estimates of land-ice volume. Spatial variations in δ18Osw, however, are often neglected or corrected using calibrations derived from the present-day or recent past. Geochemical methods for constraining δ18Osw and isotope-enabled general circulation model (GCM) simulations are still technically challenging. This lack of constraints on ancient δ18Osw is a substantial source of uncertainty for SST reconstructions. Here we use the co-variation of δ18Osw and seawater salinity, together with GCM simulations of ocean salinity, to propose estimations of spatial variability in δ18Osw over the Phanerozoic. Sensitivity tests of the δ18Osw-salinity relationship and climate model, and comparison with results of isotope-enabled GCMs, suggest that our calculations are robust at first order. We show that continental configuration exerts a primary control on δ18Osw spatial variability. Complex ocean basin geometries in periods younger than 66 Ma lead to strong inter-basinal contrasts in δ18Osw. Latitudinal SST gradients may be steeper than previously suggested during most of the Mesozoic and Cenozoic. This work has limitations, with δ18Osw-salinity relationships being less reliable in both low-latitude epicontinental settings and high-latitude regions of deep-water formation. Whilst our calculations are limited use in correcting δ18O measurements for local δ18Osw, they identify the time slices and paleogeographical regions that should be prioritized for future work using isotope-enabled GCMs.

Full text

Spatial biases in oxygen-based Phanerozoic seawater
temperature reconstructions
Alexandre POHL
a,*
, Thomas W. WONG HEARING
b
, Arnaud BRAYARD
a
,
Ethan GROSSMAN
c
, Michael M. JOACHIMSKI
d
, Guillaume LE HIR
e
, Thomas LETULLE
f,g
,
Daniel J. LUNT
h
, Mathieu MARTINEZ
i
, Emmanuelle PUCEAT
a
, Guillaume SUAN
g
,
Paul VALDES
h
, Yannick DONNADIEU
j
a
Biog´
eosciences UMR 6282, Universit´
e Bourgogne Europe, CNRS, F-21000 Dijon, France
b
School of Geography, Geology and the Environment, University of Leicester, Leicester LE1 7RH, UK
c
Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843, USA
d
GeoZentrum Nordbayern, Friedrich-Alexander Universit¨
at Erlangen-Nürnberg (FAU), Schlossgarten 5, 91054 Erlangen, Germany
e
Universit´
e de Paris, Institut de physique du globe de Paris, CNRS, F-75005 Paris, France
f
Department of Geosciences, University of Padua, Padua, Italy
g
Univ Lyon, UCBL, ENSL, UJM, CNRS, LGL-TPE, F-69622, Villeurbanne, France
h
School of Geographical Sciences, University of Bristol, Bristol BS8 1SS, UK
i
Univ Rennes, CNRS, G´
eosciences Rennes - UMR 6118, F-35000 Rennes, France
j
Aix-Marseille Universit´
e, CNRS, IRD, INRAE, Coll`
ege de France, CEREGE, Aix-en-Provence, France
ARTICLE INFO
Editor: Dr Tristan Horner
Keywords:
Stable oxygen isotopes
Salinity effect
Seawater temperature
Paleoclimate
General circulation model
Phanerozoic
ABSTRACT
Stable oxygen isotopes (δ
18
O) are routinely used to reconstruct sea-surface temperatures (SSTs) in the geological
past, with mineral δ
18
O values reecting a combination of the temperature and oxygen isotope composition of
seawater (δ
18
O
sw
). Temporal variation of mean-ocean δ
18
O
sw
is usually accounted for following estimates of
land-ice volume. Spatial variations in δ
18
O
sw
, however, are often neglected or corrected using calibrations
derived from the present-day or recent past. Geochemical methods for constraining δ
18
O
sw
and isotope-enabled
general circulation model (GCM) simulations are still technically challenging. This lack of constraints on ancient
δ
18
O
sw
is a substantial source of uncertainty for SST reconstructions. Here we use the co-variation of δ
18
O
sw
and
seawater salinity, together with GCM simulations of ocean salinity, to propose estimations of spatial variability in
δ
18
O
sw
over the Phanerozoic. Sensitivity tests of the δ
18
O
sw
-salinity relationship and climate model, and com-
parison with results of isotope-enabled GCMs, suggest that our calculations are robust at rst order. We show that
continental conguration exerts a primary control on δ
18
O
sw
spatial variability. Complex ocean basin geometries
in periods younger than 66 Ma lead to strong inter-basinal contrasts in δ
18
O
sw
. Latitudinal SST gradients may be
steeper than previously suggested during most of the Mesozoic and Cenozoic. This work has limitations, with
δ
18
O
sw
-salinity relationships being less reliable in both low-latitude epicontinental settings and high-latitude
regions of deep-water formation. Whilst our calculations are limited use in correcting δ
18
O measurements for
local δ
18
O
sw
, they identify the time slices and paleogeographical regions that should be prioritized for future
work using isotope-enabled GCMs.
1. Introduction
Our understanding of ocean temperatures throughout the Phanero-
zoic is primarily derived from stable oxygen isotope (δ
18
O)-based tem-
perature reconstructions (Gaskell et al., 2022; Grossman and
Joachimski, 2022; Judd et al., 2024, 2022; Scotese et al., 2021; Veizer
and Prokoph, 2015). Stable oxygen isotope data acquired on carbonate
or phosphate biominerals represent half of the entries in a recent
Phanerozoic-scale compilation of sea-surface temperature (SST) proxy
data and constitute the only proxy extending from the Cambrian to
Modern (Judd et al., 2024, 2022). SST reconstructions are pivotal for our
understanding of the evolution of Earth’s climate, which in turn is
* Corresponding author.
E-mail address: alexandre.pohl@cnrs.fr (A. POHL).
Contents lists available at ScienceDirect
Earth and Planetary Science Letters
journal homepage: www.elsevier.com/locate/epsl
https://doi.org/10.1016/j.epsl.2025.119418
Received 26 September 2024; Received in revised form 30 April 2025; Accepted 4 May 2025
Earth Planet. Sci. Lett. 663 (2025) 119418
Available online 9 May 2025
0012-821X/© 2025 Université Bourgogne Europe, CNRS, Biogéosciences UMR 6282, 21000 Dijon, France. Published by Elsevier B.V. This is an open access article
under the CC BY-NC license ( http://creativecommons.org/licenses/by-nc/4.0/ ).

crucial for investigating the co-evolution of marine biodiversity and the
physical environment (Ontiveros et al., 2023; Trotter et al., 2008).
However, major uncertainties persist in the reconstruction of ocean
temperatures during the Phanerozoic, as testied by the range in pub-
lished estimates across the Phanerozoic (Grossman and Joachimski,
2022; their Fig. 5).
Several factors contribute to the uncertainty in δ
18
O-based SST re-
constructions. Early meteoric diagenesis can distort or reset primary
environmental isotopic signatures, particularly by shifting δ
18
O towards
lighter values. Although the potential impact of early diagenesis can
never be fully excluded, consideration of several visual, textural,
elemental, and isotopic indicators can be used to screen out samples that
are most likely to be diagenetically altered (Brand et al., 2011; Wheeley
et al., 2012). Additional limitations in δ
18
O-based temperature re-
constructions arise from uncertainties linked to kinetic effects (Davies
et al., 2023; Huyghe et al., 2022), uncertainties inherent in the oxygen
isotope fractionation equations (Da¨
eron and Gray, 2023; Letulle et al.,
2023; Puc´
eat et al., 2010), or differences in analytical methods (Wheeley
et al., 2012).
There is also a lack of consensus regarding the long-term evolution of
the δ
18
O
sw
value of the global ocean. There is a long-term trend towards
more negative δ
18
O in values in fossils and microfossils towards more
ancient periods during the Phanerozoic. The secular trend is interpreted
either as reecting very warm ocean temperatures (possibly 50 ◦C at low
latitudes) in the early Paleozoic balanced by a near-constant mean-
ocean δ
18
O
sw
value (Grossman and Joachimski, 2022), or reecting a
modern-like range of SST balanced by a changing δ
18
O
sw
value for the
global ocean (Isson and Rauzi, 2024; Veizer and Prokoph, 2015). The
constant global-δ
18
O
sw
hypothesis is supported by clumped-isotope ev-
idence detecting no signicant change in δ
18
O
sw
over the past 500
million years (Bergmann et al., 2018; Henkes et al., 2018); the evolving
δ
18
O
sw
hypothesis is supported by temperature estimates based on the
actualistic interpretation of climatic zones reconstructed based on lith-
ological indicators of the climate (Scotese et al., 2021) and pairwise
comparisons of δ
18
O measurements from multiple mineral systems with
different temperature sensitivities (Galili et al., 2019; Isson and Rauzi,
2024; Keller et al., 2019; Shields and Veizer, 2002).
Sampling bias is also a problem when interpreting δ
18
O-based sea-
temperature reconstructions. Jones and Eichenseer (2021) demon-
strated that temporal variability in spatial sampling bias makes it dif-
cult to infer changes in global temperatures from available proxy data.
They showed that uneven spatial sampling distorts our vision of changes
in global ocean temperature across the Phanerozoic.
Finally, the lack of constraints on regional variations in δ
18
O
sw
can
generate major uncertainties in δ
18
O-based temperature re-
constructions, especially in epicontinental settings that represent most
of the Phanerozoic δ
18
O database. The impact of the local δ
18
O
sw
composition is often neglected or approximated using calibrations
established in the modern (O’Brien et al., 2017; Zachos et al., 1994) or
recent geological past (Grossman and Joachimski, 2022; Roberts et al.,
2011). Whilst δ
18
O
sw
can be determined using carbonate clumped
isotope analyses, these analyses cannot currently be performed at scale
and remain vulnerable to uncertainties related to reordering at burial
temperatures, especially in the case of early Paleozoic samples
(Finnegan et al., 2011; Henkes et al., 2018). To a lesser extent, vital
effects may also inuence clumped isotope temperature and thus δ
18
O
sw
determinations (Davies et al., 2023; Huyghe et al., 2022). Alternatively,
regional variations in δ
18
O
sw
can be simulated using isotope-enabled
GCMs (Gaskell et al., 2022; Zhou et al., 2008). This approach is prom-
ising and has proven useful in accounting for local δ
18
O
sw
variations in
δ
18
O-based temperature calculations, for instance by Gaskell et al.
(2022) who reconstructed SST evolution over the last 95 million years.
The main limitation (beyond uncertainties in model boundary condi-
tions) is the computational cost that isotope-enabled simulations
represent, which also renders their paleoclimatic application at scale
very challenging. For instance, Gaskell et al. (2022) interpolated
between isotope-enabled simulations conducted at several pCO
2
levels
for only two paleogeographical congurations (Eocene, 55 million years
ago [Ma] and Miocene, 15 Ma) when working across the last 95 million
years. Similarly, Valdes et al. (2021) calculated that 18 wall-clock
months would be required to run a fully-equilibrated deep-time
climate simulation using the isotope-enabled version of HadCM3.
Isotope-enabled GCM simulations are limited to only a few intervals in
the geological past (e.g., key Cenozoic time slices including the Last
Glacial Maximum, Miocene, and Eocene, and rare Mesozoic and Paleo-
zoic time slices; Gaskell and Hull, 2023; Macarewich et al., 2021; Zhou
et al., 2008). These technical limitations leave the impact of local δ
18
O
sw
on Phanerozoic paleo-temperature reconstructions mostly
unconstrained.
Here we use an alternative approach to investigate the magnitude of
δ
18
O
sw
variations in space and time during the entire Phanerozoic using
salinity, a variable that is commonly calculated in GCM simulations. We
make use of the co-variation of seawater salinity and δ
18
O
sw
to estimate
spatial and temporal δ
18
O
sw
patterns over the last 541 million years.
Salinity and oxygen isotopic composition co-vary in surface seawater
because they are controlled by similar processes (Railsback et al., 1989;
Tiwari et al., 2013). Evaporation both increases seawater salinity and
concentrates the heavier isotope (
18
O) in seawater, while isotopically
light freshwater input directly from atmospheric precipitation or from
continental runoff reduces seawater salinity and enriches seawater in
16
O. Recognition of this ‘salinity effect’ permitted the development of
δ
18
O
sw
-salinity relationships by which local δ
18
O
sw
can be estimated if
local salinity is known (LeGrande and Schmidt, 2006; Railsback et al.,
1989). Global expressions for δ
18
O
sw
-salinity relationships do not pre-
cisely capture spatial variations in δ
18
O
sw
because the relationship is
controlled by both oceanic basin geometry and latitude through varia-
tions in oceanic circulation (Zhu et al., 2020) and the regional hydro-
logical cycle (LeGrande and Schmidt, 2006; Tiwari et al., 2013). Zhu
et al. (2020) notably demonstrated that changes in the sites of
deep-water formation have a very signicant impact on upper-ocean
δ
18
O
sw
. Intensied convection brings
18
O-enriched subsurface water
upwards, which can then mix with sea-surface water masses and be
advected to lower latitudes through gyre circulations. Nevertheless,
δ
18
O
sw
-salinity relationships provide a practical method for estimating
local δ
18
O
sw
using results of GCMs that are not isotope-enabled.
This approach allows us to provide a rst-order quantication of the
inuence of local δ
18
O
sw
on SST reconstructions throughout the Phan-
erozoic. Our results demonstrate that continental conguration exerts a
major control on large-scale δ
18
O
sw
spatial patterns and allow us to
identify which geological intervals and geographical regions are most
vulnerable to SST reconstruction biases.
2. Methods
Here, we use the salinity elds from 109 stage-level Phanerozoic
climate simulations conducted using the coupled ocean-atmosphere
Hadley Centre general circulation model HadCM3. These simulations
are largely similar to those of Valdes et al. (2021) but have undergone a
number of developments permitting to better simulate latitudinal tem-
perature gradients (Judd et al., 2024; Supplementary Text). We translate
simulated salinity into local δ
18
O
sw
following the δ
18
O
sw
-salinity rela-
tionship established by Railsback et al. (1989; Supplementary Fig. S1).
This provides an estimate of δ
18
O
sw
for each ocean model grid cell over
the Phanerozoic. To illustrate the impact of these spatial and temporal
δ
18
O
sw
patterns on deep-time SST reconstructions, we then calculate a
‘SST interpretation bias’ outlined below that would arise from esti-
mating SST using a globally-uniform δ
18
O
sw
rather than the calculated
local δ
18
O
sw
. All δ
18
O values are given relative to Vienna standard mean
ocean water (VSMOW).
For every model ocean grid cell, we rst translate the SST simulated
in HadCM3 and the salinity-derived local δ
18
O
sw
value into a biogenic
phosphate δ
18
O value (δ
18
O
phosphate
) using the oxygen fractionation
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
2

equation of Puc´
eat et al. (2010). We then use this hypothetical
δ
18
O
phosphate
value to reconstruct a new SST value assuming a globally
uniform value of δ
18
O
sw
(i.e. neglecting local δ
18
O
sw
effects). The dif-
ference between the δ
18
O
phosphate
-recalculated SST and the
model-simulated SST for each grid cell constitutes the ‘SST interpreta-
tion bias’ and represents the potential impact of unknown spatial δ
18
O
sw
patterns on proxy-derived paleoclimate reconstructions.
Consider an oxygen isotope fractionation equation between water
and biogenic minerals of the form:
SST =a(δ18Omineral −δ18 Osw)+b (1)
where SST is the calculated sea-surface temperature, a and b are
equation-specic constants, δ
18
O
mineral
is the measured fossil mineral
δ
18
O value, and δ
18
O
sw
is the seawater δ
18
O value. The SST interpreta-
tion bias for each model grid cell can be expressed as:
SST interpretation bias =a(δ18 Osw-model −δ18Osw-hyp )(2)
where δ
18
O
sw-model
is the local δ
18
O
sw
calculated from the GCM salinity,
and δ
18
O
sw-hyp
is the globally-uniform δ
18
O
sw
hypothetical value. Eq. (2)
demonstrates that the calculated SST interpretation bias only depends
on the gradient of the oxygen isotope fractionation equation and GCM
salinity, and not on the model SST.
We use the phosphate oxygen isotope temperature equation of
Puc´
eat et al. (2010), which has a gradient, a, of –4.22 ◦C/‰ to illustrate
the SST interpretation bias. The narrow range of temperature sensitiv-
ities (approximately –4 to –5 ◦C/‰) of oxygen isotope fractionation
equations at marine temperatures means that using other fractionation
equations would give similar results (Bemis et al., 1998; Grossman,
2012). Da¨
eron and Gray (2023) further demonstrated that taxonomic
differences in foraminiferal (calcite) oxygen isotope temperature equa-
tions produce absolute offsets in reconstructed temperatures without
affecting the temperature sensitivity (gradient) of the equations, which
remains indistinguishable from that of inorganic calcite.
For our main calculations we use the δ
18
O
sw
-salinity relationship of
Railsback et al. (1989; Supplementary Fig. S1), which has the advantage
of incorporating δ
18
O
sw
-salinity trends from multiple present-day ocean
basins with a wide range of salinity values into simple generalized re-
lationships. These general relationships can be adapted to represent
ancient conditions by modifying a few key parameters. The δ
18
O
sw
-sa-
linity relationship of Railsback et al. (1989) can be simplied to the
general form:
δ18Osw =δ18 O0+
α
(S−S0)(3)
where δ
18
O
sw
is the local value of seawater, δ
18
O
0
and S
0
are the global
ocean average δ
18
O and salinity, respectively, S is the local seawater
salinity value, and
α
is a regionally-dependent constant, which also
varies with the global climatic state (see below). Global-ocean δ
18
O
(δ
18
O
0
in Eqn. (3)) was varied during the Phanerozoic to account for
variations in land-ice volumes following Grossman and Joachimski
(2022) but was not otherwise detrended (Supplementary Fig. S2). The
value of
α
is determined by whether regional salinity (S) is above or
below the global average (S
0
) to account for rst-order impacts of
changing hydrological and thermal regimes as a function of latitude
(Railsback et al., 1989). We followed Railsback et al. (1989) in using
α
=
0.35 ‰/ppt for regions where salinity exceeds the global average, and
α
=21.0/S
0
or
α
=8.0/S
0
where salinity is below the global average
respectively for icehouse and greenhouse climates (
α
=m
e
for S >S
0
and
α
=Δ
fw
/S
0
for S <S
0
in the equations on p. 587 of Railsback et al.,
1989). In these calculations, we dened icehouse periods during the
Phanerozoic based on the compilation of Cather et al. (2009). These time
slices are characterized by global-ocean δ
18
O >–1.08 ‰ in Grossman
and Joachimski (2022; Supplementary Fig. S2). A value
α
=8.0/S
0
,
reecting more equable climates than the late Cenozoic icehouse state,
leads to more
18
O-enriched low-salinity waters than the value
α
=
21.0/S
0
used for icehouse climates.
We evaluated the sensitivity of our calculations to different models of
the δ
18
O
sw
-salinity relationship (Gaskell et al., 2022; Tiwari et al., 2013;
Supplementary Fig. S1). We also calculated the SST interpretation bias
after correcting δ
18
O
phosphate
for latitude using the formula proposed for
the present-day southern Pacic and Atlantic oceans by Zachos et al.
(1994), as this correction is widely used in paleoclimate studies (e.g.,
O’Brien et al., 2017):
δ18Osw (‰,VSMOW) = 0.576 +0.041L−0.0017L2+0.0000135L3(4)
where L is the paleolatitude.
We further evaluated the impact that the choice of climate model had
on our results by repeating our calculations for two time slices with
contrasting continental congurations (Late Ordovician, 445 Ma and
Late Cretaceous, 95 Ma) using two additional GCMs with different levels
of complexity: IPSL-CM5A2 (Laugi´
e et al., 2021) and FOAM v1.5 (Pohl
et al., 2014) (Supplementary Text).
3. Results and discussion
3.1. Validating the approach in the modern
The δ
18
O
sw
-salinity relationship of Railsback et al. (1989) applied to
our 0 Ma HadCM3 simulation reasonably captures rst-order spatial
patterns in present-day sea-surface δ
18
O
sw
but produces substantial de-
viations in terms of absolute values (Fig. 1). Global-mean calculated
sea-surface δ
18
O
sw
is offset by –0.41 ‰ compared with the gridded
dataset of LeGrande and Schmidt (2006). This negative bias is relatively
uniform in space, with the exception of particularly strong negative
biases observed at equatorial latitudes in southeastern Asia and along
the western coasts of Africa and central America. The Mediterranean Sea
and Russian Arctic are characterized by strong, positive deviations
relative to the dataset of LeGrande and Schmidt (2006).
Regional model-data mismatches, both positive and negative, largely
arise from anomalies in sea-surface salinity (Supplementary Fig. S3).
These regional anomalies, however, do not escalate into any clear sys-
tematic bias in the simulated latitudinal SSS gradient (Supplementary
Fig. S3c).
Model-data mismatch may further reect uncertainties in the grid-
ded dataset of LeGrande and Schmidt (2006), who reconstructed mod-
ern δ
18
O
sw
using sparse data by means of regional δ
18
O
sw
-salinity
relationships. Data coverage is particularly poor in some regions of
maximum model-data mismatches, at equatorial latitudes in south-
eastern Asia and along the western coast of Africa.
The use of a global δ
18
O
sw
-salinity relationship, rather than basin-
specic equations, also comes with its own biases. Although evalu-
ating the skill of published δ
18
O
sw
-salinity relationships is beyond the
scope on this work, we illustrate the impact of the δ
18
O
sw
-salinity rela-
tionship on the bias in calculated δ
18
O
sw
by repeating our calculations
using the δ
18
O
sw
-salinity relationship of Gaskell et al. (2022; their sup-
plementary eqn. 6) (Supplementary Fig. S4).
Using the equation of Gaskell et al. (2022) overall improves
model-data agreement. The global-mean calculated sea-surface δ
18
O
sw
offset is reduced (from –0.41 ‰) to –0.20 ‰. Spatial patterns of biases in
δ
18
O
sw
more closely track sea-surface salinity anomalies. The same
regional biases are found at equatorial latitudes in southeastern Asia and
along the western coasts of Africa and central America, and in the
Mediterranean Sea and Russian Arctic. This model-data comparison
shows that global δ
18
O
sw
-salinity relationships permit calculating
rst-order spatial patterns in δ
18
O
sw
based on salinity elds simulated
using a global GCM. Calculated spatial patterns are particularly robust in
open-ocean settings, whereas coastal regions at equatorial and polar
latitudes, and enclosed basins, are often associated with larger errors
arising from local biases in simulated sea-surface salinity.
Therefore, the δ
18
O
sw
-salinity relationship of Gaskell et al. (2022)
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
3

outperforms that of Railsback et al. (1989) for the present-day, icehouse,
climate. However, the δ
18
O
sw
-salinity relationship of Railsback et al.
(1989) is adaptable to a greenhouse climate state (Supplementary
Fig. S1), unlike that of Gaskell et al. (2022). This climate state adapt-
ability is important for developing a scheme that can be applied
consistently across the Phanerozoic, which was predominantly charac-
terized by greenhouse climates (Judd et al., 2024). Therefore, we use the
equation of Railsback et al. (1989) in our baseline calculations, but we
also show key results using the equation of Gaskell et al. (2022) for
comparison.
3.2. Spatial patterns in SST interpretation bias
Estimating SST using a globally-uniform δ
18
O
sw
rather than the
calculated local δ
18
O
sw
generally underestimates SST at low latitudes
and overestimates SST at higher latitudes (Fig. 2; Supplementary
Fig. S5). This is because evaporation tends to exceed precipitation at low
latitudes, leading to higher salinity and hence heavier δ
18
O
sw
values
(Railsback et al., 1989), while the opposite applies to the mid- and polar
latitudes (Supplementary Figs. S6–S7).
The longitudinal variation of the bias is generally stronger in more
recent, Cenozoic time slices (<66 Ma) because of the development of
more complex ocean basin geometries which exert a strong impact on
ocean salinity. The ocean basin effect is exemplied by the stronger SST
interpretation bias simulated in the Atlantic Ocean compared to the
Pacic Ocean at 52 Ma, 26 Ma and to a lesser extent at 0 Ma (Fig. 2a–c).
The δ
18
O
sw
-salinity relationship of Gaskell et al. (2022) produces very
similar spatial patterns but stronger contrasts in calculated δ
18
O
sw
(Supplementary Fig. S8).
We simulate large deviations from the general latitudinal pattern in
all time slices in coastal areas. SST is overestimated near river mouths
due to the massive input of low-salinity and light-δ
18
O water. This
freshwater effect is particularly strong in the vicinity of the intertropical
convergence zone due to the strong precipitation rates – in line with
isotope-enabled simulations (Macarewich et al., 2021; Zhu et al., 2020).
This can be seen at equatorial δ
18
O sampling locations at, for example,
425 Ma (around Baltica), and 301 Ma and 252 Ma on the western coast
of the equatorial landmasses (Fig. 2).
Fig. 1. Biases in calculated sea-surface δ
18
O
sw
using the δ
18
O
sw
-salinity relationship ofRailsback et al. (1989). (a) Present-day δ
18
O
sw
(LeGrande and Schmidt,
2006), regridded to the HadCM resolution using a bi-linear interpolation. (b) δ
18
O
sw
calculated using the 0 Ma HadCM3 simulation, the δ
18
O
sw
-salinity relationship of
Railsback et al. (1989) and a globally-averaged oceanic δ
18
O
sw
of 0 ‰. (c) Difference between δ
18
O
sw
values calculated using the 0 Ma HadCM3 simulation and (i.e.,
minus) present-day δ
18
O
sw
values of LeGrande and Schmidt (2006). (d) Cross-plot of δ
18
O
sw
values calculated using the 0 Ma HadCM3 simulation and the present-day
δ
18
O
sw
values of LeGrande and Schmidt (2006). The red line represents the 1:1 line that would reect perfect model-data agreement. (e) As per panel (d) but shown
for a narrower δ
18
O
sw
range extending from –4 ‰ to 4 ‰. In panels (a)–(c), emerged landmasses are outlined and shaded white; Robinson projections with latitude
shown every 30◦.
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
4

Fig. 3 illustrates the impact of estimating SST using the latitude-
based δ
18
O
sw
correction of Zachos et al. (1994; Eqn. (4)), instead of a
globally-uniform δ
18
O
sw
value as per Fig. 2. Although more reliable
latitudinal corrections have been proposed over the years (see Gaskell
et al., 2022; Grossman and Joachimski, 2022; Roberts et al., 2011), the
formula of Zachos et al. (1994) is still very often used in paleoclimate
studies (e.g., O’Brien et al., 2017). This approximation, derived from
recent ocean values from the southern hemisphere Atlantic and Pacic
oceans (Zachos et al., 1994; their p. 362), over-corrects low-latitude
δ
18
O
sw
according to our method (Supplementary Fig. S9) and, as a
result, produces a positive SST interpretation bias over most of the
global ocean (Fig. 3). For this reason, this correction will not be used
hereafter.
3.3. Validating results using geological data and sensitivity testing
Important uncertainties are associated with simulated sea-surface
salinity (SSS) values, impacting our calculations of δ
18
O
sw
, especially
in coastal regions. Model SSSs near continental masses are largely
dependent on the watersheds imposed as boundary condition in the
GCM simulations, which are difcult to reconstruct due to large un-
certainties in deep-time land topography. Riverine runoff comprises the
input of freshwater, with zero salinity, to coastal ocean grid points.
Overestimating runoff, for example due to the inappropriate positioning
of an important river mouth in the model, will inappropriately reduce
local SSS. This SSS underestimation translates into an underestimation
of δ
18
O
sw
following the δ
18
O
sw
-salinity relationship equations
(Supplementary Fig. S1), ultimately resulting in a more positive SST
interpretation bias (Eqn. (2)). Applying this locally anomalous positive
SST interpretation bias as a correction factor in a δ
18
O-temperature
calculation will lead to over-correction for local δ
18
O
sw
and therefore an
excessively cold SST interpretation (see discussion in Section 3.5).
Nevertheless, some SSS spatial patterns are expected on grounds of
physical climatology. This is the case for the very saline Paleo-Tethys
Ocean during the Late Permian and Early Triassic (Fig. 2k; Supple-
mentary Fig. S6k). Numerical simulations showed that oceanic
connection between the Paleo-Tethys and the Panthalassa oceans was
limited by the geometry of the Paleo-Tethys basin and regional ba-
thymetry, making it a relatively restricted oceanic basin at tropical
latitudes (Wu et al., 2024). Some SSS patterns are further supported by
geological evidence. For instance, Mutterlose et al. (2012) interpreted
the offset between their Hauterivian to early Barremian TEX
86
and δ
18
O
data as reecting SSS values being 3 psu (practical salinity units) higher
than global average in northwest Europe. This aligns with the values
reaching ca. 37.3 psu (+2.5 psu compared with the model global
average) in our GCM simulations (Fig. 2f; Supplementary Fig. S6f).
Similarly, remnant Early Cretaceous North Atlantic seawater is charac-
terized by high salinity values (up to twice the modern global average;
Sanford et al., 2013), supporting the high model SSS values (up to 45
psu) in the North Atlantic at 149 Ma (Fig. 2g; Supplementary Fig. S6g).
During the Permian-Triassic transition, interbedded uvial and tidal
deposits and important terrigenous inputs show that the equatorial
northwestern American basin was characterized by important riverine
uxes (e.g., Blakey and Ranney, 2008), a feature that is also consistent
Fig. 2. Effect of estimating SST using a globally-uniform δ
18
O
sw
rather than the calculated local δ
18
O
sw
. SST over- / under- estimation (positive and negative
values respectively) arising from neglecting spatial δ
18
O
sw
variations when converting δ
18
O
phosphate
measurements to SST. Calculations were conducted using the
HadCM3 climatic simulations, the δ
18
O
sw
-salinity relationship of Railsback et al. (1989) and the temperature-δ
18
O
phosphate
relationship of Puc´
eat et al. (2010). For
each time slice, locations of StabisoDB data (Grossman and Joachimski, 2022) are shown with circle markers, the color of which represents the SST bias calculated in
the closest oceanic model grid point. Emerged landmasses are outlined and shaded white. Robinson projections with latitude shown every 30◦. For readability, only a
subset of the 109 stage-level HadCM3 simulations is represented here (every ca. 25 Myrs), although the full series of HadCM3 simulations is used elsewhere. See
Supplementary Fig. S5 for zonal averages.
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
5

with model results (see Fig. 2k δ
18
O data point on the western coast of
equatorial Pangea; Supplementary Fig. S6k).
Although our approach is based on a global δ
18
O
sw
-salinity rela-
tionship and therefore does not account for regional or temporal vari-
ations, several lines of evidence suggest that our results capture
important features of the spatial biases in δ
18
O data interpretations.
First, spatial patterns and numerical values for our 0 Ma, 26 Ma, and 52
Ma time slices using the latitude-based δ
18
O
sw
correction of Zachos et al.
(1994) (Fig. 3) are in relatively good agreement with the results ob-
tained by Gaskell and Hull (2023; their Fig. 1), using the same
latitude-based δ
18
O
sw
correction, based on isotope-enabled GCM simu-
lations for the modern and Last Glacial Maximum, Miocene, and Eocene,
respectively. The zonally-averaged SST interpretation bias calculated in
our Late Cretaceous simulations also aligns with the values simulated by
Zhou et al. (2008) for the Cenomanian using an isotope-enabled GCM
(Fig. 4c). We tentatively compared δ
18
O
sw
values estimated from car-
bonate clumped isotope values of Phanerozoic fossil material (Supple-
mentary Text and Supplementary Table S1) with model-derived δ
18
O
sw
values (Supplementary Fig. S10), but the limited number of data points
does not permit any statistical assessment. While models and data
sometimes align (for instance in the Central Atlantic during the Early
Cretaceous; Supplementary Fig. S10b), we also note important mis-
matches both between models and data and between adjacent data
points. Some obvious model-data mismatches arise from the represen-
tation of regional paleogeography; this is well illustrated by the lack of
Western Interior Seaway in our Late Cretaceous time slice (Supple-
mentary Fig. S10a). This model-data comparison effort is hence of
limited use to date due to the small number of data points, but will
benet from additional constraints as new data become available.
Second, Fig. 5 shows that our simulated spatial-temporal patterns in
SST interpretation biases stand when alternative δ
18
O
sw
-salinity
relationships are used, including the δ
18
O
sw
-salinity relationship pro-
posed for the Indian and Southern oceans by Tiwari et al. (2013; their
Fig. 4b) and the δ
18
O
sw
-salinity relationship proposed for the modern by
Gaskell et al. (2022).
Third, results obtained using different GCMs share similarities
(Fig. 4). In all three models tested, the primarily latitudinal variation of
SST interpretation biases simulated for the Late Ordovician (Fig. 4a,d,g)
contrasts with the more complex spatial patterns obtained for the Late
Cretaceous (Fig. 4b,e,h), but note that FOAM Late Ordovician results
exhibit stronger longitudinal contrasts in SST interpretation bias than
the other two models (Fig. 4a,d,g). All Late Cretaceous simulations show
a very fresh (low-SSS) Arctic ocean associated with a strongly positive
SST bias of ca. +10 ◦C in IPSL-CM5A2, +20 ◦C in FOAM and providing
the closest match to the results of Zhou et al. (2008) (Fig. 4f) and +25 ◦C
in HadCM3. The magnitude of the SST interpretation bias in the Arctic
seems to be directly related to the degree of isolation of the Arctic Ocean
from the Tethys and Central Atlantic oceans, which varies across models
due to differences in the paleogeographical congurations interpolated
at the different model grid resolutions (Fig. 4b,e,h). Specically,
although the three simulations use the paleogeographies of the PALE-
OMAP project (Scotese and Wright, 2018), the IPSL-CM5A2 simulation
is the only one that includes three straits between the Arctic, Tethys, and
Central Atlantic, with both HadCM3 and FOAM simulations only
including one strait. The stronger mixing of Arctic water masses with the
rest of the ocean in the IPSL-CM5A2 simulation probably contributes to
the smaller contrast in salinity, hence reduced SST interpretation bias in
the Arctic compared to the other two simulations. An SST interpretation
bias of a few tens of degrees is the same order of magnitude of bias (>40
◦C) calculated by Gaskell and Hull (2023) for the 66.5–90◦N latitudinal
band in an Eocene isotope-enabled simulation published by Zhu et al.
(2020).
Fig. 3. Effect of estimating SST using the latitude-based approximation of Zachos et al. (1994) rather than the calculated local δ
18
O
sw
. As per Fig. 2 but
correcting δ
18
O
sw
for latitude using the formula of Zachos et al. (1994) instead of assuming a globally-uniform δ
18
O
sw
. The latitude-based correction of Zachos et al.
(1994) is valid only within 70◦latitude (higher latitudes are left blank).
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
6

Fourth, additional Late Ordovician and Late Cretaceous FOAM sim-
ulations run under a wide range of alternative atmospheric pCO
2
levels
conrm that palaeogeography has a much greater inuence on calcu-
lated SST biases than does global climate state (Fig. 6). These results
imply that the main patterns and values in SST interpretation bias
calculated using the 109 HadCM3 simulations during the Phanerozoic
(Fig. 2) would be little impacted by uncertainties in atmospheric CO
2
concentrations.
3.4. Temporal trends in SST interpretation bias and implications for
proxy data interpretation
In our simulations (Fig. 7a), the time slices and regions that are prone
to the strongest SST interpretation biases are the southern middle to
high latitudes from the Devonian to the Permian, middle to high
northern latitudes (45◦N to 90◦N) from the Triassic to present-day, and
to a lesser extent the southern high latitudes during the Cretaceous and
Neogene. The strongest biases correspond to SST overestimations in
regions of low salinity at higher latitudes.
Fig. 7c shows that mean SSTs are consistently overestimated in the
45◦–60◦latitude band in each hemisphere; this latitudinal window
represents the high-latitude edge of the region for which most δ
18
O
proxy data are available (Fig. 7a; see also Judd et al., 2022). There are
two clear intervals of substantial biases in these latitudinal bands: the
southern hemisphere during the Devonian to Permian, and the northern
hemisphere during the Triassic to present-day, with zonally-averaged
biases of the order of +5 ◦C and +2.5 ◦C, respectively. The strong bia-
ses in these two regions arise from the continental arrangement that
isolates high-latitude oceanic basins and leads to the development of
low-salinity water masses.
To estimate the impact of SST interpretation bias on proxy data in-
terpretations, we evaluated the geographical distribution of the δ
18
O
data available in the StabisoDB database (Grossman and Joachimski,
2022) in Fig. 2 and Fig. 7a. We only used quality-controlled δ
18
O data of
the StabisoDB database, which have been selected from calcite and
aragonite δ
18
O values of samples with metadata documenting preser-
vation of primary isotopic signatures, and removed all incomplete Sta-
bisoDB entries, notably those missing geographic coordinates. In our
selected StabisoDB dataset, no data are available in the region of
strongest bias located at the southern middle to high latitudes during the
Devonian and Carboniferous (Fig. 7a). Despite the strong local de-
viations of δ
18
O
sw
in enclosed oceanic basins of the southern middle to
high latitudes during this period of time, these local deviations are not
expected to impact the interpretation of currently available proxy data
(Fig. 2n–p). Some Permian δ
18
O data points, in contrast, are available at
polar latitudes (Fig. 7a). Although they do not come from the enclosed
Fig. 4. Sensitivity to the global climate model. Effect of estimating SST using a globally-uniform δ
18
O
sw
rather than the calculated local δ
18
O
sw
. Calculations were
conducted using the δ
18
O
sw
-salinity relationship of Railsback et al. (1989) and the temperature-δ
18
O
phosphate
relationship of Puc´
eat et al. (2010), and 3 different
GCMs: (a-c) HadCM3, (d-f) FOAM v1.5 and (g-i) IPSL-CM5A2, for 2 periods of time: the Late Ordovician (left column) and the Late Cretaceous (middle and right
columns). Note that all simulations use paleogeographical reconstructions based on or derived from the paleogeographical reconstructions of Scotese and Wright
(2018). For the Late Cretaceous (Ordovician), the following simulations are used: 97 Ma – 1426 ppm pCO
2
(449 Ma – 782 ppm pCO
2
) for HadCM3, 90 Ma – 1120 ppm
(445 Ma – 2240 ppm) for IPSL-CM5A2, 95 Ma – 1120 ppm (445 Ma – 1960 ppm) for FOAM. Differences in SST interpretation bias arising for each time slice from the
use of different pCO
2
values are expected to be second-order compared to differences arising from the use of different models (see sensitivity test to pCO
2
discussed in
Section 3.3). Panels (c), (f) and (i) show the simulated SST (blue line with envelope; left y-axis), the SST reconstructed assuming a globally-uniform δ
18
O
sw
(orange
line with envelope, left y-axis) and the resulting SST interpretation bias (grey line with envelope, right y-axis). Lines represent zonal means and envelopes extend
from the 10
th
to the 90
th
percentiles. For comparison, the black line represents the Late Cretaceous SST bias calculated by Zhou et al. (2008) using an isotope-enabled
model (right y-axis; to be compared with the gray line). IPSL-CM5A2 elds of temperature and salinity were interpolated from the native model tripolar irregular grid
to a 1◦by 1◦regular grid (using a nearest-neighbor algorithm) before conducting calculations.
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
7

basins on the western side of Pangea (e.g., South America), but from the
Neo-Tethys and Panthalassa (e.g., from Australia), they are subject to
strong interpretation biases (Fig. 2k–m). Proxy data from the Late
Jurassic onwards are also susceptible to SST interpretation biases in the
northern middle to high latitudes (Figs. 2a-i, 7a).
SST interpretation biases for specic proxy data locations show that
SST values above ca. 45◦latitude are systematically overestimated,
while the sign of the SST biases is variable at lower latitudes (Figs. 2, 7b;
Supplementary Fig. S5). At low latitudes, SSTs are generally
underestimated except near the coast at river mouths. The impact of
continental runoff is very visible during the Silurian, Carboniferous, and
Permian (Fig. 7b), when δ
18
O data mostly come from shallow seas,
which in our GCM simulations are under the inuence of strong riverine
freshwater input (Fig. 2m–o,r).
The middle latitudes represent a transitional domain between the
low latitudes, characterized by an overall SST underestimation, and the
higher latitudes, characterized by a strong positive SST interpretation
bias that increases rapidly with increasing latitude. Geological periods
Fig. 5. Sensitivity to the δ
18
O
sw
-salinity relationship. Zonally-averaged effect of estimating SST using a globally-uniform δ
18
O
sw
rather than the calculated local
δ
18
O
sw
. Calculations were conducted using the HadCM3 climatic simulations, the temperature-δ
18
O
phosphate
relationship of Puc´
eat et al. (2010) and (a) the
δ
18
O
sw
-salinity relationship of Railsback et al. (1989), as per Fig. 2; (b) the δ
18
O
sw
-salinity relationship proposed for the Indian and Southern oceans by Tiwari et al.
(2013); and (c) the δ
18
O
sw
-salinity relationship proposed for the modern by Gaskell et al. (2022). Ꞓ: Cambrian; O: Ordovician; S: Silurian; D: Devonian; C:
Carboniferous; P: Permian; T: Triassic; J: Jurassic; K: Cretaceous; P: Paleogene; N: Neogene.
Fig. 6. Sensitivity to the global climatic state. Effect of estimating SST using a globally-uniform δ
18
O
sw
rather than the calculated local δ
18
O
sw
. Calculations were
conducted using the δ
18
O
sw
-salinity relationship of Railsback et al. (1989) and the temperature-δ
18
O
phosphate
relationship of Puc´
eat et al. (2010), and the FOAM model
run at various atmospheric pCO
2
levels (see atmospheric CO
2
concentrations expressed in ppm in the legend) for two time slices: (a) the Late Ordovician and (b) the
Late Cretaceous. Lines represent zonal means and envelopes extend from the 10
th
to the 90
th
percentiles at each model latitude.
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
8

for which proxy data are available in the 30◦–60◦latitudinal band may
thus be characterized by strong distortions of their reconstructed lat-
itudinal SST gradients. Specically, an SST underestimation at the low
latitudes, combined with an overestimation at the higher latitudes (>45
◦), may articially atten latitudinal SST gradients. As previously noted
by Zhou et al. (2008), this result is interesting since it may contribute to
reconciling proxy data with numerical climate models that have been
routinely considered to overestimate the steepness of latitudinal SST
gradients during greenhouse periods. Based on StabisoDB data, we es-
timate that this phenomenon may impact our understanding of lat-
itudinal SST gradients during the Jurassic and Cretaceous (Figs. 2, 7a,b).
3.5. Re-examining the phanerozoic low-latitude SST curve using local
δ
18
O
sw
In an attempt to quantify the impact of correcting proxy data for local
δ
18
O
sw
on long-term SST reconstructions, we revisit in Fig. 8 the recent
Phanerozoic tropical SST reconstruction of Grossman and Joachimski
(2022). The latter is based on a subset of quality-controlled δ
18
O
carbonate
and δ
18
O
phosphate
data covering the last 500 million years. The black line
in Fig. 8 shows the SSTs calculated as per the original publication: global
δ
18
O
sw
was varied through time to account for changing land-ice vol-
umes (Supplementary Fig. S2) and local δ
18
O
sw
was corrected for lati-
tude using two different equations representative of either greenhouse
or icehouse periods (Grossman and Joachimski, 2022, their eqn. (4) and
5; Roberts et al., 2011). Small differences from the originally published
curve (Grossman and Joachimski, 2022; their Fig. 4E) are due to the use
of a different smoothing algorithm. In addition, data points that were
not correctly rotated back to their paleo-positions were ignored. The
blue line shows the Phanerozoic tropical SST record calculated using the
same methods except that, instead of taking a latitude-based δ
18
O
sw
correction as in the original paper, we extracted for each StabisoDB
entry the δ
18
O
sw
value simulated at the closest oceanic grid points in the
closest of the 109 HadCM3 simulations (see Fig. 7a,b). The offset be-
tween the black and blue lines therefore represents the impact of
salinity-corrected local δ
18
O
sw
versus a latitude-based δ
18
O
sw
correction
derived from modern oceans or the recent geological past. Here we
follow the original publication by not detrending for long-term δ
18
O
changes, which is a broader topic beyond the scope of this study.
Although the long-term temperature trends calculated with and
without accounting for local δ
18
O
sw
are mostly similar, we nd impor-
tant deviations on shorter time scales (<10 million years) during spe-
cic time intervals. Taken at face value, our results suggest that the well-
known early Paleozoic cooling (Trotter et al., 2008), instead of reaching
an acme during the latest Ordovician, may have continued for another
20 million years and culminated during the latest Silurian (but see dis-
cussion below). Our results also suggest that the warming documented
during the latest Carboniferous, around 300 million years ago, may
instead be a sampling artefact with proxy data reecting low-latitude
cooling (see discussion below). Finally, our revised estimates suggest
that the background climate during the middle Permian was cooler than
previously reported, making the late Permian warming even stronger
relative to the earlier part of the Permian. The scarcity of δ
18
O data in
younger time slices in our StabisoDB dataset, which arises in part from
the loss of data points during the calculation of their paleo-positions,
does not permit interpreting temporal trends from the Triassic
Fig. 7. Temporal trends in simulated SST interpretation bias. (a) Zonally-averaged effect of estimating SST using a globally-uniform δ
18
O
sw
rather than the
calculated local δ
18
O
sw
(as per Fig. 5a), with paleo-latitudes of StabisoDB data (Grossman and Joachimski, 2022) superimposed as circle markers. (b) As per panel (a)
but at StabisoDB locations only. (c) Effect of estimating SST using a globally-uniform δ
18
O
sw
rather than the calculated local δ
18
O
sw
averaged over the northern
(orange line) and southern (blue line) mid- to polar latitudes (45 to 60 ◦N). All calculations were conducted using the HadCM3 climatic simulations, the δ
18
O
sw
--
salinity relationship of Railsback et al. (1989) and the temperature-δ
18
O
phosphate
relationship of Puc´
eat et al. (2010). Ꞓ: Cambrian; O: Ordovician; S: Silurian; D:
Devonian; C: Carboniferous; P: Permian; T: Triassic; J: Jurassic; K: Cretaceous; P: Paleogene; N: Neogene.
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
9

onwards with condence.
The GCM and δ
18
O
sw
-salinity relationships are factors that may
strongly impact reconstructed temporal trends. Interestingly, however,
very similar results are obtained when using the δ
18
O
sw
-salinity rela-
tionship of Gaskell et al. (2022) (Supplementary Fig. S11). The lack of
alternative Phanerozoic-scale series of GCM simulations providing ac-
cess to sea-surface salinity prevents us from quantifying the
model-dependence of reconstructed long-term SST trends. Although
large-scale spatial patterns in SST interpretation bias share important
similarities amongst three models tested on two different time slices, we
also note regional deviations (Fig. 4). The middle latitudes constitute a
critical transition between the contrasting hydrological regimes of the
low and high latitudes, characterized by a steep gradient in SST inter-
pretation bias. This may render the interpretation of SSTs during periods
for which oxygen isotope data are found at these latitudes – Jurassic and
younger (Fig. 7) – particularly vulnerable to model choice.
Although the δ
18
O
sw
-salinity-SST calculation approach can be
reasonably applied through most of the Phanerozoic, the late Carbon-
iferous is a notable aberration during which this method produces
strongly negative SSTs (Fig. 8). This is impossible to reconcile with
available constraints on the range of variations in Phanerozoic low-
latitude SSTs reconstructed using independent approaches based on
different proxies (Finnegan et al., 2011; Isson and Rauzi, 2024; O’Brien
et al., 2017; Scotese et al., 2021). Clumped isotope temperatures for
fossils from the aragonite-bearing Boggy Formation in Oklahoma (305
Ma) yield an average temperature of 24.9 ±1.1 ◦C (mean ±1 SE; Came
et al., 2007), similar to clumped isotope temperatures for the older
fossils from the Russian Platform (27.0 ±3.0 ◦C; Henkes et al., 2018).
Other evidence is the presence of widespread late Carboniferous tropical
carbonate platforms with abundant warm-water faunas (Kiessling et al.,
2003).
In their recent climatic reconstruction obtained by statistically
combining proxy data with a large ensemble of HadCM3 simulations,
Judd et al. (2024) proposed very small deviations from the SST values of
Grossman and Joachimski (2022) during the Carboniferous (their sup-
plementary g. S20). This contrasts with the very strong, unrealistic
cooling reconstructed in this study (Fig. 8). The difference arises, at least
in part, from the fact that Judd et al. (2024) used an alternative
approach to calculate past δ
18
O
sw
based on paleoclimate simulations.
Instead of using a single δ
18
O
sw
-salinity relationship, they calculated
δ
18
O
sw
in ancient times by deriving δ
18
O
sw
from analog oceanographic
settings found in the present day, based on sea-surface salinity,
sea-surface temperature, precipitation, latitude and distance to the
coast. This approach, which is largely anchored in the present day and
may seem less mechanistic than the one proposed by Railsback et al.
(1989), provides more reasonable results in the Carboniferous. This
probably reects the better skill of the approach employed by Judd et al.
(2024) in capturing δ
18
O
sw
values in specic oceanographic contexts
like low-latitude epicontinental seas and restricted basins where salinity
values simulated in climate models and δ
18
O
sw
-salinity relationships are
poorly reliable (see discussion below).
The underestimation of low-latitude SSTs during the late Carbonif-
erous reects in part inaccurate sea-surface salinity values simulated in
the GCM. Specically, sea-surface salinity drops below 20 psu in the
restricted equatorial basin on the western side of Pangea at 301 Ma,
where most StabisoDB data points are found, as a result of continental
runoff in the intertropical convergence zone and poor connection of the
basin with the global ocean at the model resolution (Fig. 2m; Supple-
mentary Fig. S6m). Seawater salinity values below 20 psu are unlikely
considering that δ
18
O was measured on conodonts and brachiopods that
are considered to be intolerant of large changes in salinity. In the
modern ocean, such seawater salinity values in open-ocean settings are
Fig. 8. Model-informed Phanerozoic SST reconstruction. (a) Low-latitude (–30:30 ◦N) SST reconstruction derived from the quality-controlled δ
18
O
carbonate
(cross
markers) and δ
18
O
phosphate
(square markers) data of the StabisoDB database as per the original calculations of Grossman and Joachimski (2022) (black markers and
line) vs. using for each data point the δ
18
O
sw
value averaged over the closest oceanic grid point and immediately adjacent grid points in the closest of the 109
Phanerozoic HadCM3 time slices considered (blue markers and line). (b) Difference induced by using the δ
18
O
sw
value averaged over the closest oceanic grid point
and immediately adjacent grid points in the closest of the 109 Phanerozoic time slices considered, instead of the original calculations of Grossman and Joachimski
(2022) (i.e., blue minus black lines of panel (a)). Calculations were conducted using the HadCM3 climatic simulations, the δ
18
O
sw
-salinity relationship of Railsback
et al. (1989), the temperature-δ
18
O
phosphate
relationship of Puc´
eat et al. (2010) and the temperature-δ
18
O
carbonate
relationship of Kim and O’Neil (1997). Ꞓ: Cambrian;
O: Ordovician; S: Silurian; D: Devonian; C: Carboniferous; P: Permian; T: Triassic; J: Jurassic; K: Cretaceous; P: Paleogene; N: Neogene.
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
10

only found near high-latitude river mouths in the Arctic (Reagan et al.,
2024).
The underestimation of low-latitude SSTs also arises from limitations
in the δ
18
O
sw
-salinity relationship in low-salinity, low-latitude settings.
In contrast with the middle to high latitudes where precipitation and
hence continental runoff waters are strongly
18
O-depleted (with δ
18
O
values as low as –20 ‰), water that runs off to the ocean in low-latitude
settings is generally characterized by higher (sometimes even positive)
δ
18
O values (Nan et al., 2019). The higher δ
18
O values are due to the
combined contributions of less
18
O-depleted precipitation and down-
stream evaporative enrichment in watersheds extending over arid areas.
This induces a local decoupling of salinity and δ
18
O
sw
. For instance,
surface waters of the present-day Nile river are characterized by mean
δ
18
O values of +0.8 ‰ and +3.9 ‰ during the wet and dry seasons,
respectively (Cockerton et al., 2013). Today, low δ
18
O
sw
values at the
low latitudes arise in the specic case of
18
O-depleted runoff (e.g., <–8
‰ VSMOW) in regions with high-altitude runoff such as the Pacic coast
of Panama (Tao et al., 2013).
Similarly, sea-level curves and clumped isotopes show that land-ice
volumes reached a maximum during the latest Ordovician (Hirnan-
tian) and decreased afterwards (Finnegan et al., 2011). Although a very
similar climatic trend was reconstructed during the Silurian by Judd
et al. (2024), featuring a double-peak cooling centered on 30 ◦C tropical
SST (their supplementary g. S20), aforementioned geological evidence
suggests that the drop in Silurian SSTs below Late Ordovician values
calculated in our revised SST estimates is unlikely. The same sources of
error as for the latest Carboniferous probably apply in the case of the
Silurian. We further note that, while the geological record of Silurian
glaciations is not sufcient to quantify temporal changes in land-ice
volumes (Loydell, 2007), the persistence of substantial land ice during
the Silurian, by increasing global-ocean δ
18
O
sw
above the land-ice-free
value of –1.08 ‰ used in Fig. 8 (see Supplementary Fig. S2), may be
enough to raise Silurian reconstructed SSTs by a few degrees (Puc´
eat
et al., 2010; Eqn. (1)) to Late Ordovician levels.
Fig. 8 demonstrates the overall limitation of our approach in
reconstructing δ
18
O
sw
in low-latitude shallow shelves, due to difculties
in accurately simulating sea-surface salinity in these settings in GCMs
combined with the potential decoupling of salinity and δ
18
O
sw
that
limits the applicability of global δ
18
O
sw
-salinity relationships. While
these biases apply to all our time slices, their expression becomes
prominent during the latest Carboniferous when most StabisoDB data
come from such low-latitude, epicontinental settings under the inuence
of continental runoff. Our δ
18
O
sw
-salinity relationship may also inac-
curately capture the contribution of upwelling systems to shallow-water
δ
18
O
sw
on the western coast of low-latitude continents, while previous
isotope-enabled simulations proved that this mechanism signicantly
inuences the δ
18
O
sw
composition in epicontinental seas (Macarewich
et al., 2021).
Our results illustrate well the inuence of continental runoff on
many δ
18
O data available in the geological record, which largely come
from epicontinental settings especially in pre-Mesozoic time intervals.
Previous work demonstrated that today SSTs in these environments are
warmer and more seasonal than open-ocean values from the same lati-
tudes, and deviate from the zonal average due to oceanic gyre circula-
tion (Judd et al., 2020). Our analysis demonstrates that, while regional
δ
18
O
sw
values largely impact paleo-SST reconstructions, δ
18
O
sw
in
epicontinental settings is extremely challenging to constrain, inviting
further caution when calculating SSTs based on these coastal data
sources. Results also suggest that the large spatial variability in δ
18
O
sw
in
epicontinental settings may be an important source of scatter in SST
reconstructions deriving from oxygen isotope measurements conducted
during the same period of time but at different paleogeographical lo-
cations (see Supplementary Fig. S7).
Future work with clumped isotopes (Letulle et al., 2022) and
isotope-enabled GCMs may help provide better estimates of δ
18
O
sw
for
the calculation of SSTs, although models would also face several of the
issues raised above, notably the difculty to represent coastal environ-
ments and the impact of downstream evaporative
18
O enrichment.
4. Concluding remarks
We use the well-documented co-variation of δ
18
O
sw
and ocean
salinity, together with GCM simulations, to calculate changes in δ
18
O
sw
and their implications for δ
18
O-derived SST reconstructions over the last
541 million years. We demonstrate a rst-order impact of continental
conguration on δ
18
O
sw
and hence potential biases in SST re-
constructions during the Phanerozoic, with the global climatic state
having a much smaller impact on this bias. Although our calculations are
based on a number of assumptions, large-scale spatial patterns are
instructive. Our results for several Cenozoic time intervals and the Late
Cretaceous, in particular, are supported by isotope-enabled GCM ex-
periments, and our Late Cretaceous results are relatively robust to
alternative climate models and δ
18
O
sw
-salinity relationship equations.
Our study identies the oceanic regions and time intervals that are
prone to the strongest δ
18
O
sw
-induced SST reconstruction biases, which
should constitute a priority for future work using isotope-enabled GCMs.
Among the main features of our results, we note that latitudinal SST
gradients since the Jurassic may have been signicantly under-
estimated, especially in the northern hemisphere (Fig. 2). Biases in SST
gradients could have strong regional imprints, such as over Europe
during the Early Cretaceous (Fig. 2f) when SSTs may have been under-
estimated at 30◦N and overestimated at 45–60◦N, articially attening
the northern hemisphere reconstructed SST gradient. We also note that
regional SSTs may have been signicantly underestimated in the Paleo-
Tethys during the Permian and in the European Tethys during the
Triassic (Fig. 2i,k). These regional SST interpretation biases, combined
with the clustering of available SST proxy data in these same regions,
may have led to an overall underestimation of temperatures in the
geological past. Warmer background temperatures may have constituted
a further challenge for marine organisms facing global climate warming
during the Permian-Triassic and end-Triassic mass extinctions
(Joachimski et al., 2012; Penn et al., 2018; Sun et al., 2012).
However, our approach fails to accurately calculate δ
18
O
sw
values in
low-latitude epicontinental seas under the inuence of strong conti-
nental runoff. Global δ
18
O
sw
-salinity relationships do not permit
capturing the complex mechanisms controlling δ
18
O
sw
in these specic
hydrographic contexts. In line with previous work that quantied some
biases associated with inferring SSTs based on epicontinental-sea data
(Judd et al., 2020), our results further invite to remain cautious when
dealing with SST proxy data coming from low-latitude shallow-water
environments that are strongly inuenced by continental runoff.
This type of approach to reconstruct large-scale δ
18
O
sw
spatial pat-
terns during the Phanerozoic based on GCMs (see also Judd et al., 2024)
probably represents one of the best options until geochemical analyses
permitting to disentangle changes in temperature and δ
18
O
sw
can be
readily produced (Finnegan et al., 2011; Henkes et al., 2018; Isson and
Rauzi, 2024; Letulle et al., 2022), or increased computational power
makes isotope-enabled simulations more widely available.
Data availability
HadCM3 simulation data are available online (instructions to
download: https://www.paleo.bristol.ac.uk/ummodel/scripts/papers
/Using_BRIDGE_webpages.pdf). The Late Cretaceous IPSL simulation is
available from Laugi´
e et al. (2021). All other climatic elds used in this
paper, together with other les required to reproduce the calculations
and gures, are hosted on Zenodo (https://zenodo.org/records
/13836450). All les are also available on GitHub (https://github.
com/alexpohl/d18O_phanero); this is the recommended mode of ac-
cess as it will contain any updates and clarications. δ
18
O
sw
values
calculated using HadCM3 simulations for all Phanerozoic time slices,
stored in the form of NetCDF les, are also hosted on Zenodo (https:
A. POHL et al.
Earth and Planetary Science Letters 663 (2025) 119418
11

//zenodo.org/records/15240528).
CRediT authorship contribution statement
Alexandre POHL: Writing – review & editing, Writing – original
draft, Visualization, Validation, Software, Resources, Project adminis-
tration, Methodology, Investigation, Funding acquisition, Formal anal-
ysis, Data curation, Conceptualization. Thomas W. WONG HEARING:
Writing – review & editing, Visualization, Validation, Resources,
Methodology, Conceptualization. Arnaud BRAYARD: Writing – review
& editing, Validation, Resources. Ethan GROSSMAN: Writing – review
& editing, Validation, Resources, Investigation, Data curation. Michael
M. JOACHIMSKI: Writing – review & editing, Validation, Resources,
Methodology, Data curation. Guillaume LE HIR: Writing – review &
editing, Resources. Thomas LETULLE: Writing – review & editing,
Validation, Resources, Methodology, Formal analysis, Data curation.
Daniel J. LUNT: Writing – review & editing, Validation, Resources.
Mathieu MARTINEZ: Writing – review & editing, Validation, Re-
sources. Emmanuelle PUCEAT: Writing – review & editing, Validation,
Resources. Guillaume SUAN: Writing – review & editing, Validation,
Resources, Methodology. Paul VALDES: Writing – review & editing,
Validation, Resources. Yannick DONNADIEU: Writing – review &
editing, Validation, Resources, Methodology.
Declaration of competing interest
The authors have no competing interests to declare.
Acknowledgements
This is a contribution to UNESCO project IGCP 735 "Rocks and the
Rise of Ordovician Life" (Rocks n’ ROL). AP acknowledges the support of
the French Agence Nationale de la Recherche (ANR) under references
ANR-22-CE01–0003 (project ECO-BOOST) and ANR-23-CE01–0003
(project CYCLO-SED). AP and MM acknowledge the support of the
programme TelluS of the Institut National des Sciences de l’Univers, CNRS
(project WAOW). AP and TWWH thank the Leverhulme Trust for sup-
porting the project ‘Earth System dynamics at the dawn of the animal-
rich biosphere’ (RPG-2022–233). CM5A2 simulations used in this
work have been performed on the HPC resources of the CEA-TGCC using
computing hours provided by GENCI under allocations A0130102212
and A0150102212. Calculations were performed using HPC resources
from DNUM CCUB (Centre de Calcul de l’Universit´
e de Bourgogne). The
authors thank Daniel E. Gaskell and an anonymous reviewer for
constructive comments that signicantly improved the manuscript, and
Tristan J. Horner for editorial handling.
Supplementary materials
Supplementary material associated with this article can be found, in
the online version, at doi:10.1016/j.epsl.2025.119418.
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