Accurate estimates of past global mean surface temperature (GMST) help to
contextualise future climate change and are required to estimate the
sensitivity of the climate system to

Under high growth and low mitigation scenarios, atmospheric carbon dioxide
(

Sea surface temperature (SST) and land air temperature (LAT) proxies
indicate that the latest Paleocene and early Eocene were characterised by
global mean surface temperatures (GMSTs) much warmer than those of today
(Cramwinckel et al., 2018; Farnsworth et al., 2019; Hansen et al., 2013;
Zhu et al., 2019; Caballero and Huber, 2013). Having a robust quantitative
estimate of the magnitude of warming at these times relative to modern is
useful for two primary reasons: (1) it allows us to contextualise future
climate change predictions by comparing the magnitude of future
anthropogenic warming with the magnitude of past natural warming; (2) combined with knowledge of the climate forcing, it allows us to estimate
climate sensitivity, a key metric for understanding how the climate system
responds to

Published GMST estimates during the early Paleogene (57 to 48 Ma).
Dots represent average values. The horizontal limits on the individual dots
represent the reported error, and

Previous studies that have determined GMST for the early Eocene (EE), EECO, PETM, or latest Paleocene (LP); n/a indicates that no error bars were reported in the original publications.

Here we calculate GMST estimates within a consistent experimental framework
for the target intervals outlined by DeepMIP: (i) the Early Eocene Climatic
Optimum (EECO; 53.3 to 49.1 Ma), (ii) the Paleocene–Eocene Thermal Maximum
(PETM; ca. 56 Ma), and (iii) the latest Paleocene (LP; ca. 57–56 Ma). We use
six different methods to obtain new GMST estimates for these three time
intervals by employing previously compiled SST and LAT estimates (Hollis et
al., 2019) as well as bottom water temperature (BWT) estimates (Dunkley Jones et
al., 2013; Cramer et al., 2009; Sexton et al., 2011; Littler et al.,
2014; Laurentano et al., 2015; Westerhold et al., 2018; Barnet et al.,
2019). We also undertake a suite of additional sensitivity studies to
explore the influence of particular proxies on each GMST estimate. We then
compile GMST estimates from all six methods to generate a “combined” GMST
estimate for each time slice and use these, with existing estimates of

Three different input datasets are used to calculate GMST: (1) dataset

Dataset

Four methods (

Baseline and optional subsampling experiments applied to

Method

Here, the anomalies of individual proxy temperature data points with respect
to modern values at the corresponding paleolocation are first calculated.
The time period used is between 1979 and 2018, and we used a climatology of
the full ERA-Interim period (Dee et al., 2011). The calculation involves
binning into low, middle, and high latitudes (30

Various sanity checks have been performed to determine if the method is
likely to produce useful results for a given sampling distribution and what
corrections should be applied to optimise it. For example, if the modern
temperature field is sampled using a geographic sampling distribution for a
given time interval, what would the reconstructed modern temperature be?
Sampling the modern global annual average surface temperature field in the
reanalysis product ERA-5 yields a mean value of 15.1

Alongside modern observations, we can also use paleoclimate model results to
characterise how well the existing paleogeographic sampling network will
impact results (Fig. 2). Here we utilise two CESM1 simulations, as
described in Cramwinckel et al. (2018; EO3 and EO4). The two cases are
chosen to minimise the magnitude of the correction to GMST, and the final
result is not sensitive to the choice of reference simulation between these
two (Supplement). For each interval, the difference between
reconstructed global temperatures and the true paleoclimate model mean is

An illustration of method

We note that the magnitude of the global correction could be sensitive to
different models and/or boundary conditions. To explore this further, we
performed the same analysis using Community Earth System Model version 1.2
(CESM1.2) at

GMST estimates are calculated using the method described in Farnsworth et al. (2019), in which a transfer function is used to calculate global mean
temperature from local proxy temperatures. The transfer function is
generated from a pair of early Eocene climate model simulations carried out
at two

The principal assumption of this approach is that global temperatures scale
linearly with local temperatures and that a climate model can represent
this scaling correctly (see below). The resulting GMST estimate is therefore
independent of the climate sensitivity of the model but dependent on the
modelled spatial distribution of temperature. For a single given proxy
location with a local temperature estimate (

An illustration of method

Inferred global mean temperature (

Recent work has demonstrated that CESM1.2 and GFDL model simulations offer a
major improvement over earlier models (Zhu et al., 2019; Lunt et al., 2020).
As such, we also calculated GMST using CESM1.2 (

For

Predicted surface warming by Gaussian process regression using

A heteroscedastic noise model is used to weight the influence of individual
proxy data by their associated uncertainty; i.e. the model will better fit
reconstructions with a smaller reported error. Proxy uncertainties are taken
from Hollis et al. (2019). Standard deviations for TEX

The Gaussian process approach provides probabilistic predictions of temperature values, i.e. uncertainty estimates of the predicted field. The uncertainty reported for an individual GMST estimate is calculated via random sampling. We generate 10 000 surfaces from a multivariate normal distribution based on the predicted mean and full covariance matrix and calculate the GMST for each sample. Uncertainty of the mean estimate is then defined as the standard deviation of the 10 000 random samples. Regional model uncertainty (expressed as standard deviation fields) is typically highest in areas with sparse data coverage (e.g. the Pacific Ocean and Southern Hemisphere landmasses; Fig. S2). The lower uncertainty for the latest Paleocene relative to the PETM and EECO is related to the smaller reported uncertainties in the proxy dataset rather than enhanced data coverage. The large spread in reconstructed terrestrial temperatures for North America during the PETM and EECO (Fig. S2) propagates through into relatively large uncertainties in the GMST estimates for these intervals.

For

For each data point, we account for three types of uncertainty (i.e. temperature, elevation, latitude). For temperature, we assume a skew-normal
probability distribution based on the stated 90 % confidence intervals.
Where uncertainty estimates are not given, we assume a (symmetric) normal
distribution with a 90 % confidence interval of

Dataset

For

Dataset

For

Probability distributions for each time interval were computed as follows.
In the case of the tropical SST data, 1000 subsamples were taken, following
which a random normally distributed error was added to each data point in
the DeepMIP compilation, including both calibration uncertainty and variance
in the data where multiple reconstructions are available for a given site
and time interval. Mean tropical SST was calculated for each of these
subsamples. To provide a BWT dataset of the same size as the subsampled
tropical SST data, 1000 normally distributed values were calculated for each
time interval based on the mean

The following section discusses our baseline GMST estimates calculated on
the mantle-based reference frame only. During the latest Paleocene and PETM,
GMST estimates derived from

Individual GMST estimates for the latest Paleocene (LP), PETM, and EECO.
Reported GMST estimates utilise baseline experiments except

GMST estimates during the

GMST estimates for the latest Paleocene, PETM, and EECO, calculated using

GMST estimates for the latest Paleocene, PETM, and EECO, calculated using

To explore the importance of the proxies themselves for

The removal of TEX

The input of brGDGTs from archives other than mineral soils or peat can bias
LAT estimates towards lower values (Inglis et al., 2017; Hollis et al.,
2019), and the exclusion of MBT(')

The removal of

To derive a combined estimate of GMST during the latest Paleocene, PETM, and
EECO, we employ a probabilistic approach, using Monte Carlo resampling with
full propagation of errors. Our combined estimate employs GMST estimates
from each baseline experiment (except

Probability density function of combined GMST during the DeepMIP intervals with full propagation of errors. GMST estimates are calculated on the mantle-based reference frame.

Combined GMST estimates (66 % and 90 % confidence intervals) during the (i) latest Paleocene (LP), (ii) PETM, and (iii) EECO.

Sequential removal of one GMST method at a time (jackknife resampling) was
performed to examine the influence of a single method upon the average GMST
estimate. Jackknifing reveals that no single method overly influences
the mean GMST or 66 % confidence intervals during the latest Paleocene,
PETM, or EECO (

During the latest Paleocene, the average GMST estimate is 26.3

Equilibrium climate sensitivity (ECS) can be defined as the equilibrium
change in global near-surface air temperature resulting from a doubling in
atmospheric

Estimates of ECS (66 % and 90 % confidence) during the (i) latest Paleocene (LP), (ii) PETM, and (iii) EECO.

Probability density function of bulk ECS during the latest
Paleocene, PETM, and EECO that explicitly accounts for non-

ECS may be strongly state-dependent, and model simulations indicate a
non-linear increase in ECS at higher temperatures (Caballero and Huber,
2013; Zhu et al., 2019) due to changes in cloud feedbacks (Abbot et al.,
2009; Caballero and Huber, 2010; Arnold et al., 2012; Zhu et al., 2019).
This implies caution when relating geological estimates to modern climate
predictions (e.g. Rohling et al., 2012; Zhu et al., 2020) and it may be more
appropriate to calculate ECS between different time intervals (e.g. latest
Paleocene to PETM; Shaffer et al., 2016). To this end, we also calculate ECS
between the transition from the latest Paleocene to the PETM, assuming that
non-

Using six different methods, we have quantified global mean surface
temperatures (GMSTs) during the latest Paleocene, PETM, and EECO. GMST was
calculated within a coordinated, experimental framework and utilised six
methodologies including three different input datasets. After evaluating the
impact of different proxy datasets upon GMST estimates, we combined all six
methodologies to derive an average GMST value during the latest Paleocene,
PETM, and EECO. We show that the “average” GMST estimate (66 % confidence)
during the latest Paleocene, PETM, and EECO is 26.3

Data can be accessed via the Supplement or from the authors (contact email: gordon.inglis@soton.ac.uk).

The supplement related to this article is available online at:

Authorship of this paper is organised into three tiers according to the contributions of each individual author. GNI (Tier I) organised the structure and writing of the paper, contributed to all sections of the text, and designed the figures. FB, NJB, MJC, DE, GLF, MH, DJL, NS, SS, JET, and RW (Tier II authors) assumed a leading role by contributing the methodologies used in the text. EA, AMdB, TDJ, KE, CJH, DKH, and RDP (Tier III authors) contributed intellectually to the text and figure design.

The authors declare that they have no conflict of interest.

We thank two anonymous reviewers whose thoughtful comments significantly improved the paper. This research was funded by NERC through NE/P01903X/1 and NE/N006828/1, both of which supported Gordon N. Inglis, Daniel J. Lunt, Sebastian Steinig, and Richard D. Pancost. Gordon N. Inglis was also supported by a GCRF Royal Society Dorothy Hodgkin Fellowship. Natalie J. Burls is supported by NSF AGS-1844380 and the Alfred P. Sloan Foundation as a Research Fellow. Fran Bragg, Daniel J. Lunt, and Richard Wilkinson were funded by the EPSRC Past Earth Network (EP/M008363/1). Matthew Huber was funded by NSF OPP 1842059. Tom Dunkley Jones, Kirsty M. Edgar, and Gavin L. Foster were supported by NERC grant NE/P013112/1. Agatha De Boer and David Hutchinson acknowledge support from the Swedish Research Council under project 2016-03912. GFDL numerical simulations were performed using resources provided by the Swedish National Infrastructure for Computing (SNIC) at NSC, Linköping. David Hutchinson was also supported by FORMAS project 2018-01621. The authors also thank Chris Poulsen and Jiang Zhu for assistance with the CESM1.2 model simulations.

This research has been supported by the Natural Environment Research Council (grant nos. NE/P01903X/1 and NE/N006828/1), the National Science Foundation (grant nos. AGS-1844380 and OPP 1842059), the EPSRC Past Earth Network (EP/M008363/1),
NERC (NE/P013112/1),
the Swedish Research Council (grant nos. 2016-03912 and 2018-01621),
and the Royal Society (grant no. DHF

This paper was edited by Yannick Donnadieu and reviewed by two anonymous referees.