CPClimate of the PastCPClim. Past1814-9332Copernicus GmbHGöttingen, Germany10.5194/cp-11-1801-2015On the state dependency of the equilibrium climate sensitivity during the last 5 million yearsKöhlerP.peter.koehler@awi.dehttps://orcid.org/0000-0003-0904-8484de BoerB.https://orcid.org/0000-0002-3696-6654von der HeydtA. S.https://orcid.org/0000-0002-5557-3282StapL. B.https://orcid.org/0000-0002-2108-3533van de WalR. S. W.Alfred-Wegener-Institut Helmholtz-Zentrum für Polar-und Meeresforschung (AWI), P.O. Box 12 01 61, 27515 Bremerhaven, GermanyDepartment of Earth Sciences, Faculty of Geosciences, Utrecht University, Budapestlaan 4, 3584 CD Utrecht, the NetherlandsInstitute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlandsnow at: School of Earth and Environment, University of Leeds, Leeds, UKP. Köhler (peter.koehler@awi.de)21December20151112180118232June201510July201512October20151December2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://cp.copernicus.org/articles/11/1801/2015/cp-11-1801-2015.htmlThe full text article is available as a PDF file from https://cp.copernicus.org/articles/11/1801/2015/cp-11-1801-2015.pdf
It is still an open question how equilibrium warming in response to
increasing radiative forcing – the specific equilibrium climate
sensitivity S – depends on background climate. We here present
palaeodata-based evidence on the state dependency of S, by using
CO2 proxy data together with a 3-D
ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years
(Myr). We find that the land ice albedo forcing depends
non-linearly on the background climate, while any non-linearity of
CO2 radiative forcing depends on the CO2 data set
used. This non-linearity has not, so far, been accounted for in similar approaches due to previously more simplistic approximations, in which land ice albedo
radiative forcing was a linear function of sea level
change. The latitudinal dependency of ice-sheet area changes is important for the non-linearity between land ice albedo and
sea level. In our
set-up, in which the radiative forcing of CO2 and of the
land ice albedo (LI) is combined, we find a state dependence in the
calculated specific equilibrium climate sensitivity, S[CO2,LI], for most of the Pleistocene (last
2.1 Myr). During Pleistocene intermediate glaciated climates
and interglacial periods, S[CO2,LI] is on average
∼45% larger than during Pleistocene full glacial
conditions. In the Pliocene part of our analysis
(2.6–5 MyrBP) the CO2 data uncertainties prevent
a well-supported calculation for S[CO2,LI], but
our analysis suggests that during times without a large land ice area
in the Northern Hemisphere (e.g. before 2.82 MyrBP), the
specific equilibrium climate sensitivity, S[CO2,LI],
was smaller than during interglacials of the Pleistocene. We thus find
support for a previously proposed state change in the climate system
with the widespread appearance of northern hemispheric ice sheets. This
study points for the first time to a so far overlooked non-linearity
in the land ice albedo radiative forcing, which is important for
similar palaeodata-based approaches to calculate climate
sensitivity. However, the implications of this study for a suggested
warming under CO2 doubling are not yet entirely clear since
the details of necessary corrections for other slow feedbacks are not fully known and the uncertainties that exist in the ice-sheet
simulations and global temperature reconstructions are large.
Introduction
One measure to describe the potential anthropogenic impact on climate
is the equilibrium global annual mean surface air temperature rise
caused by the radiative forcing of a doubling of atmospheric
CO2 concentration. While this quantity, called equilibrium
climate sensitivity (ECS), can be calculated from climate models
e.g., it is also important for model validation to
make estimates based on palaeodata. This is especially relevant since
some important feedbacks of the climate system are not incorporated
into all models. For example, when coupling a climate model interactively
to a model of stratospheric chemistry, including ozone, the calculated
transient warming on a 100-year timescale differs by 20 %
from results without such an interactive coupling
.
Both approaches, model-based and data-based
, still span a wide range for
ECS, e.g. of 1.9–4.4 K (90 % confidence interval) in the
most recent simulations compiled in the IPCC assessment report
or 2.2–4.8 K (68 % probability)
in a palaeodata compilation covering examples from the last 65 million
years . Reducing the uncertainty in ECS is
challenging, but some understanding of model-based differences now
emerges .
The ultimate cause for orbital-scale climate change is latitudinal
and seasonal variation in the incoming solar radiations
, which are then
amplified by various feedbacks in the climate system
.
So far, seasonality in incoming solar radiation is not resolved in our approach.
A major restriction of any geological-data-based estimate of climate
sensitivity is that there was no period in Earth's history during
which the atmospheric CO2 concentration and global temperature
changed as rapidly as today. Therefore, in all these data-based approaches
(including our study here), ECS defined as global equilibrium temperature
rise in response to a doubling of atmospheric CO2 can only be
roughly estimated. Such data-based studies are nevertheless important
to find any specific pattern of how global temperature changed with respect to a given variation in the radiative forcing.
Our approach focuses on the
contribution of various climate feedbacks to the reconstructed global temperature changes
. When using palaeodata to calculate climate
sensitivity, one has to correct for slow feedbacks, whose impacts on
climate are incorporated into the temperature reconstructions. Slow
feedbacks are of interest in a more distant future
but are not yet considered in climate
simulations using fully coupled climate models underlying the fifth
assessment report of the IPCC .
More generally,
from palaeodata the specific equilibrium climate sensitivity,
S[X], is calculated, which is, in line with the proposed nomenclature of
, the ratio of the equilibrium global (g)
surface temperature change (ΔTg) over the specific
radiative forcing (ΔR) of the processes X; hence S[X]=ΔTg⋅ΔR[X]-1. In this concept “slow
feedbacks” are treated the same as the radiative forcing for practical reasons. The division into “forcing” and
“feedback” is based on the timescale of the
process. found that a century is a well-justified timescale that might distinguish fast feedbacks from slow
forcings. All relevant processes that are not considered in the
forcing term X will nevertheless impact on climate change as feedbacks and are contained in the calculated climate sensitivity.
This has to be kept in mind for comparing model-based and data-based
approaches, and it makes their comparison difficult, since in model-based
results only those processes implemented in the model have an impact
on calculated temperature change.
In practical terms, the palaeodata that are typically available for
the calculation of S are the radiative forcing of CO2 and
surface albedo changes caused by land ice (LI) sheets. Thus,
S[CO2,LI] can be calculated containing the
radiative forcing of two processes, which are most important on glacial–interglacial timescales of the late Pleistocene
. The whole approach, therefore, relies on the
simplification that the climate response of the CO2 radiative
forcing and the surface albedo radiative forcing are similar. We are
aware that such a simplification might not be possible for every
radiative forcing, since showed that the per
unit radiative forcing of well-mixed greenhouse gases
(e.g. CO2 or CH4) leads to a different climate
response than that of aerosols or ozone. However, we are not aware
that a difference in the response has been shown for radiative forcing
from surface albedo changes (ΔR[LI]) and CO2
(ΔR[CO2]). Hence we combine them linearly.
Both model-based e.g. and
palaeodata-based approaches have already
indicated that S varies for different background climates; see also a recent review of on the limits of linear models to constrain climate sensitivity.
The majority of simulation studies shows a rise in climate sensitivity for
a warmer background climate. One of the exceptions, based on analysis
for mainly colder than present climates , found the opposite (a rise in climate sensitivity for colder climate) with
various versions of the Community Climate System Model (CCSM), which points to disagreements that still exist between models. However, , using
the same model, found rising climate sensitivity for warmer climates, as did the majority of studies.
The state-dependent character of S based on palaeodata was only
recently investigated more systematically in
. It was found that the strength of some of
the fast feedbacks depends on the background climate state. This is in
agreement with other model-based approaches, which proposed
a state dependency of water vapour or clouds
. Distinguishing
different climate regimes in palaeodata covering the last
800 000 years (0.8 Myr), the time for which ice core
records exist, revealed a ∼36 % larger
S[CO2,LI] for “warm” background climates when
compared to “cold” climates. However, a limitation in this analysis
was that average “warmer” climates were still colder than in the present
day and interglacial periods were largely undersampled. A recent
investigation found that
S[CO2,LI] for the late Pleistocene and the
Plio–Pleistocene transition similarly suggest that no
state dependency in the specific equilibrium climate sensitivity is
observed in their proxy data.
Here, we consider changes in S[CO2,LI] over the
last 5 Myr. We go beyond previous studies in various ways. First, we
increase the amount and spread of the underlying data, which
offers the possibility to calculate S[CO2,LI]
based on palaeodata covering the Pleistocene and most of the
Pliocene. The latter is the comparatively warm epoch between ∼2.6 and
5.3 MyrBP that has been suggested as a palaeoanalogue for the
future . Second, we calculate the radiative
forcing of the land ice albedo from a detailed spatial analysis of
simulated land ice distribution obtained with 3-D ice-sheet models. Our
approach therefore enhances the embedded complexity of the underlying physical climate
system with respect to previous studies. Third, polar amplification was previously
assumed to be constant over time e.g..
However, climate models
indicate that during the Pliocene, when less ice was present on the
Northern Hemisphere, the temperature perturbations were more uniformly
spread over all latitudes. We incorporate this changing polar
amplification into our global temperature record. Fourth, we explicitly
analyse for the first time whether the relationship between
temperature change and radiative forcing is better described by
a linear or a non-linear function. If the applied statistics inform us
that the ΔTg–ΔR relationship contains
a non-linearity, then the specific equilibrium climate sensitivity is
state-dependent. Any knowledge on a state dependency of S is
important for the interpretation of palaeodata and for the projection
of long-term future climate change.
Methods
We calculate the radiative forcing of CO2 and land ice albedo,
ΔR[CO2,LI], by applying the same energy
balance model as used before for the late Pleistocene
. This approach uses CO2 data from ice
cores as well as from proxies from three different labs
published for the last 5 Myr and calculates changes in surface albedo
from zonally averaged changes in land ice area. The latter are here
based on results from 3-D ice-sheet model simulations
that deconvolved the benthic δ18O
stack LR04 into its temperature and sea
level (ice volume) component. The time series of global temperature
change, ΔTg, over the last 5 Myr used here is also
based on this deconvolution. The reconstructed records of ice volume
and temperature changes are therefore mutually consistent.
A state dependency in S[CO2,LI] is then supported by the
data if a non-linear function (higher-order polynomial) gives a statistically
better fit to the scattered data of ΔTg versus ΔR[CO2,LI] than a linear fit.
Ice-sheet models, changes in surface albedo, and radiative forcing, ΔR[LI]
Using an inverse modelling approach and the 3-D ice-sheet model
ANICE , the benthic δ18O stack LR04
is deconvolved in deep-ocean temperature,
ice-volume-based sea-level variations, and a representation of the four main
ice sheets in Antarctica, Greenland, Eurasia, and North America. The
spatial resolution (grid cell size) for the Antarctic, Eurasian, and
North American ice sheets is 40km× 40km,
while Greenland is simulated by cells of
20km× 20km.
In the vertical dimension, velocities and temperature are calculated for 15
layers. In ANICE, shallow ice and shallow shelf approximations are used. With
respect to the full Stokes 3-D description that completely describes the
temporal and spatial evolution of an ice body, some higher-order stress terms
are therefore neglected in ANICE in order to allow for long transient runs. A
detailed description of the model is found in .
Radiative forcing of land ice sheets averaged for latitudinal bands
of 5∘. Panel (a): annual mean insolation at the top of the
atmosphere, ITOA, based on orbital variations
. Panel (b): fraction of each
latitudinal band of 5∘ covered by land ice as simulated by the 3-D
ice-sheet model ANICE . Panel (c): calculated
radiative forcing of land ice sheets, ΔR[LI], normalized to
global-scale impact.
This approach combines palaeodata and mass conservation for
δ18O with physical knowledge on ice-sheet growth and
decay. It therefore includes a realistic estimate of both volume and
surface area of the major ice sheets. The calculated change in
deep-ocean temperature is in this ice-sheet-centred approach connected
with temperature anomalies over land in the Northern Hemisphere (NH)
high-latitude band (40–85∘N, ΔTNH),
in which the Greenland, Eurasian, and North American ice sheets
grow. Temporal resolution of all simulation results from the 3-D
ice-sheet models is 2 kyr.
From these results, published previously , the
latitudinal distribution of land ice area in
latitudinal bands i of 5∘ (ΔALI(i)) is calculated
(Fig. b), which leads to changes in the
land-ice-sheet-based radiative forcing, ΔR[LI], with
respect to preindustrial times.
ΔR[LI](i) for every latitudinal band (Fig. c) is
calculated from local surface insolation (IS(i)), changes in ice-sheet area (ΔALI(i)), and surface albedo anomalies (Δα), normalized to a global impact (by division by the Earth's surface area AEarth, ΔR[LI](i)=-IS(i)×ΔALI(i)×(Δα)/AEarth) and integrated thereafter.
For the calculation of IS(i), the annual mean insolation at the top of the
atmosphere (TOA) at each latitude, ITOA(i), (Fig. a) is reduced by absorption a and reflection αA within the atmopshere (IS(i)=ITOA(i)×(1-(αA+a))). The values of the parameters a=0.2 and αA=0.212 are here held constant at their present values derived in .
This approach to calculate ΔR[LI] is based on surface albedo anomalies (Δα), implying that
latitudes that are always ice-free contribute nothing to ΔR[LI]. It is assumed that ice sheets cover land when
growing; thus, local surface albedo α rises as assumed previously
from 0.2 to 0.75. For calculating
ITOA(i) (Fig. a), which varies due to orbital
configurations , we use a solar
constant of 1360.8 Wm-2, the mean of more than
10 years of daily satellite data since early 2003 as published
by the SORCE (Solar Radiation and Climate Experiment) project (http://lasp.colorado.edu/home/sorce)
. Changes in solar energy output are not
considered but are – based on present knowledge – smaller than 1 Wm-2 during the last 10 kyr, and,
following our earlier approach , presumably
smaller than 0.2 %.
For validation of the ANICE ice-sheet model, we compare the spatially and
temporally variable results in ΔR[LI] obtained for
Termination I (the last 20kyr) with those based on the land
ice sheet distribution of .
This paper describes an approach called ICE-5G, in which data on sea level
change, which include the contribution from glacial isostatic adjustment, are
used to obtain a physically consistent picture that also considers
viscoelastic modelling of the mantle of Earth in order to derive how the land
ice sheet distribution during the last deglaciation might have looked like.
For this comparison the ICE-5G data are treated similarly to those from
ANICE,
e.g. only data every 2kyr are considered and averaged on
latitudinal bands of 5∘. The spatial distribution of land
ice in the most recent version of ICE-6G are
similar to ICE-5G, and therefore no significant difference to ICE-6G
is expected and the comparison to that version is omitted.
Calculating global surface temperature change, ΔTg. Panel (a): polar amplification factor,
fpa, the ratio between Northern Hemisphere (NH) land temperature
change, ΔTNH, and global temperature change, ΔTg, as a function of time based on values for LGM (blue square)
and mid-Pliocene warm period (mPWP) (red circle) derived from the model
intercomparison projects (MIPs) PMIP3–CMIP5 and
PlioMIP , respectively. In our standard application,
ΔTg1 (black line), fpa is calculated as
a linear function depending on northern hemispheric temperature change,
ΔTNH (insert), inter- and extrapolated between these two
PMIP3 and PlioMIP-based values. Alternatively (ΔTg2, orange
line), fpa varies as a step function with high values for the
Pleistocene (periods with Northern Hemisphere land ice sheets) and low values
for the Pliocene (periods mainly without NH land ice sheets) with the step
between both values occurring at 2.82MyrBP, when our results
indicate large changes in NH land ice. In ΔTg3 (blue line),
fpa varied freely to meet ΔTg reconstructed for
LGM by PMIP3 (-4.6K) and for the mPWP by PlioMIP
(+2.7K). See methods for further details. Panel (b): NH
temperature change, ΔTNH, as deconvolved from the benthic
δ18O stack LR04 by applying a 3-D
ice-sheet model in an inverse mode . Uncertainty in
ΔTNH (grey) is the 1σ error calculated from eight
different model realizations . Panel (c): global
surface temperature change, ΔTg, as used here based on
ΔTg=ΔTNH⋅fpa-1.
Results for ΔTg based on all three approaches for
fpa are given (same colour code as in subfigure a).
Symbols show ΔTg±1σ as derived within PlioMIP
(mPWP, red circle) and PMIP3–CMIP5 (LGM, blue
square). Red vertical lines mark the time period of the mPWP.
Global temperature change, ΔTg
In the ANICE model the temperature anomaly of the deep ocean
(deconvolved from the benthic δ18O stack) is coupled to the NH
temperature change, ΔTNH, by a fixed ratio that has been
derived in a series of transient climate runs. A more extensive analysis of
this parameterization is presented in .
We calculate global surface temperature change, ΔTg,
from these ANICE-based NH temperature anomalies, ΔTNH, using a polar
amplification factor, fpa, which itself depends on
climate (Fig. ).
The value of the polar amplification factor, fpa, was constrained for certain times from simulation results of the Paleoclimate Modelling Intercomparison Project Phase 3 (PMIP3), the Coupled Model Intercomparison Project Phase 5 (CMIP5), and the Pliocene Model Intercomparison Project (PlioMIP). For the Last Glacial Maximum (LGM, about 20 kyr BP),
fpa was determined from PMIP3–CMIP5 to be around 2.7±0.3; for the mid-Pliocene Warm Period (mPWP, about 3.2 Myr BP), fpa was determined to be around 1.6±0.1 based on PlioMIP results . In our standard
set-up (calculating ΔTg1), we linearly inter- and
extrapolate fpa as function of ΔTNH
based on these two anchor values for all background climates found
during the last 5 Myr (insert in Fig. a). Climate models
already suggest that polar amplification is not constant, but how it
is changing over time is not entirely clear . We therefore calculate an alternative global
temperature change, ΔTg2, in which we assume polar
amplification, fpa, to be a step function, with
fpa=1.6 (the mPWP value) taken for times with extensive
northern hemispheric land ice (according to our results before
2.82 MyrBP) and with fpa=2.7 (the LGM value)
thereafter. This choice is motivated by investigations with a coupled
ice-sheet–climate model, from which northern hemispheric land ice was
identified to be the main controlling factor for the polar
amplification .
At the LGM, ΔTg was, based on the eight PMIP3 models
contributing to this estimate in fpa, -4.6±0.8K, so slight colder but showing considerable overlap with the most
recent LGM estimate of ΔTg=-4.0± 0.8K. If we take into consideration
that the MARGO (Multiproxy Approach for the Reconstruction of the Glacial Ocean surface) sea surface temperature (SST) data underlying this LGM temperature estimate
are potentially biased towards tropical
SSTs that are too warm , the PMIP3 results are a good
representation of LGM climate.
For both choices of fpa (varying linearly as a function of
ΔTNH or as step function over time), the global temperature
change at the LGM
obtained in our reconstruction is ΔTg=-5.7±0.6K, so slightly colder than other approaches but
overlapping with the PMIP3-based results within the uncertainties.
The global temperature changes obtained with both approaches to fpa are very similar and mainly differ for some glacial
periods in the late Pliocene and some interglacial periods in the
Pleistocene (Fig. c). Results from the eight models
(CCSM4, CNRM-CM5, FGOALS-g2, GISS-E2-R, IPSL-CM5A-LR, MIROC-ESM,
MPI-ESM-P, MRI-CGCM3) which contributed the relevant results to the
PMIP3–CMIP5 database until mid-January 2014 were analysed, averaging
uploaded results over the last available 30 years. Warming within the
mPWP based on PlioMIP was +2.7±1.2K, overlapping with
our calculated global surface temperature change within the
uncertainties (Fig. c). The models contributing to
PlioMIP, experiment 2 (coupled atmosphere–ocean models), are CCSM4,
COSMOS, GISS-E2-R, HadCM3, IPSL-CM5A, MIROC4m, MRI-CGCM2.3, and
NorESM-L.
As a third alternative (ΔTg3), we constrain the global
temperature changes by the values from PMIP3 for the LGM
(-4.6K) and from PlioMIP for the mPWP (+2.7K)
and vary fpa freely. In this case, fpa rises to
∼3.3 during glacial maxima of the Pleistocene and to ∼1.0
during the Pliocene. Our approach based on the ΔTNH
reconstruction is not able to meet all four constraints given by
PMIP3 and PlioMIP (ΔTg, fpa for both the LGM
and the mPWP) at the same time. This mainly illustrates that the
approach used in , although coherently solving for
temperature and ice volume underestimates polar temperature change
prior to the onset of the NH glacial inception, since it only
calculates ice volume and deep-water temperature change from benthic
δ18O.
Throughout the following, our analysis is based on the temperature time
series ΔTg1. However, we repeat our analysis with
the alternative temperature time series to investigate the robustness
of our approach to the selected time series. As can been seen in the
results our main conclusions and functional dependencies are
independent from the choice of ΔTg and are also
supported if based on either ΔTg2 or ΔTg3 (see Sect. 3.2).
The modelled surface–air temperature change, ΔTNH,
has already been compared with three independent
proxy-based records of sea surface temperature (SST) change in the
North Atlantic , the equatorial Pacific
, and the Southern Ocean
which cover at least the last 3.5Myr. The main features of
the simulated temperature change and the data-based SST reconstruction
agree: the overall cooling trend from about 3.5 to 1Myr ago
is found in the simulation results and in all SST records and so is the
strong glacial–interglacial (100kyr) variability
thereafter.
Radiative forcing of CO2, ΔR[CO2]
Several labs have developed different proxy-based approaches to reconstruct
atmospheric CO2 for times before 0.8Myr, for which no CO2 data from ice cores exist yet. Since we are interested in how CO2 might have
changed over the last 5 Myr, and in its relationship to global climate, we only consider longer time series for our analysis. Thus, some
approaches, e.g. based on stomata, with only a few data points during
the last 5Myr are not considered
see. The considered CO2 data are, in
detail, as follows (Fig. ):
CO2 data. Panel (a): CO2 data from ice
cores based on the stack of consisting of data from
Law Dome, EPICA Dome C, West Antarctic Ice Sheet Divide, Siple Dome, Talos
Dome, EPICA Dronning Maud Land, and Vostok (resampled to time steps of
2kyr) and based on either δ11B
() or alkenones
() from the three labs, Hönisch,
Foster, and Pagani. Panel (b): zoom-in on the time period covered by
ice core data (last 0.8Myr.)
Ice core CO2 data were compiled by
into a stacked ice core CO2 record
covering the last 0.8Myr, including a revision of the
CO2 data from the lowest part of the EPICA Dome C ice
core. Originally, the stack as published
contained 1723 data points before the year 1750 CE, the beginning of the
industrialization, but it was here resampled to the 2 kyr time
step of the ice-sheet simulation results by averaging available data
points and reducing the sample size to n=394. The stack contains
data from the ice cores at Law Dome
(; 0–2 kyrBP), EPICA Dome C
(; 2–11 kyrBP, 104–155 kyrBP,
393–806 kyrBP), West Antarctic Ice Sheet Divide
(; 11–22 kyrBP), Siple Dome
(; 22–40 kyrBP), Talos Dome
(; 40–60 kyrBP), EPICA
Dronning Maud Land (; 60–104 kyrBP), and Vostok
(; 155–393 kyrBP).
CO2 based on δ11B isotopes measured
on planktonic shells of G. sacculifer from the Hönisch lab
(n=52) is obtained from ODP668B located in the
eastern equatorial Atlantic. The data go back to 2.1MyrBP and agree favourably with the ice core
CO2 during the last 0.8Myr.
CO2 data from the Foster lab are available for the last 3.3 Myr (n=105),
obtained via δ11B from ODP site 999 in the Caribbean
Sea. CO2 purely based on G. ruberδ11B was reconstructed for the last glacial cycle
and for about 0.8Myr during the
Plio–Pleistocene transition . We take both
these data sets, using identical calibration as plotted previously
. The overlap of the data with the ice core
CO2 is reasonable, with a tendency to overestimate the
maximum anomalies in CO2 (by more than +50ppmv
during warm previous interglacials and by -25ppmv during
the LGM; Fig. b).
CO2 reconstructions based on alkenone from the
Pagani lab (n=153) cover the
whole 5Myr and are derived from different marine sediment
cores. Site 925 is contained in both publications, although with
different uncertainties. From site 925 we use the extended and most
recent CO2 data of containing 50 data
points over the last 5Myr, 18 points more than initially
published. Data from the sites 806, 925, and 1012 are different from the
ice core CO2 reference during the last 0.8 Myr by +50 to
+100ppmv, while data from site 882 have no overlapping data
points with the ice cores. It is not straightforward to correct these
CO2 data from the Pagani lab that are different from the ice core
CO2. Therefore, we refrain from applying
any corrections but keep these offsets in mind for our interpretation.
Other CO2 data based on B/Ca are not
considered here, since critical issues concerning their calibration have
been raised . A second
δ11B-based record of the Hönisch lab
from G. sacculifer obtained from ODP
site 999 is not used for further analysis because
δ11B was measured on other samples than those proxies that are necessary to determine the related climate state
(e.g. δ18O). Thus, a clear identification of whether glacial or
interglacial conditions were prevailing for individual data points was
difficult. Furthermore, these calculated CO2 values
have very high uncertainties: 1σ is 3
times larger than in the original Hönisch lab data set
. These CO2 data of
disagree with the most recent data from the Foster lab
, especially before the onset of northern
hemispheric glaciation around 2.8Myr ago. Another
CO2 time series form the Foster lab , based
on a mixture of both alkenones and δ11B approaches
covering the last 5Myr, is not considered here, since the
applied size correction for the alkenone producers was subsequently
been shown to be incorrect .
Radiative forcing based on CO2 is calculated using ΔR[CO2]=5.35Wm-2⋅ln(CO2/CO2,0), with CO2,0=278ppmv being the preindustrial reference value
.
How to calculate the specific equilibrium climate sensitivity, S[CO2,LI]
The specific equilibrium climate sensitivity for a forcing X is
defined as S[X]=ΔTg⋅ΔR[X]-1. In
an analysis of S[X] when calculated for every point in time for
the last 0.8 Myr based on ice core data,
revealed the range of possible values, which fluctuated widely, not
following a simple functionality even when analysed as moving
averages. This study also clarified that S[X] based on small
disturbances in ΔTg or ΔR[X] is due to
dating uncertainties prone to unrealistically high or low values. Only when
data are analysed in a scatter plot does a non-linear functionality between
ΔTg and ΔR[X], and therefore
a state dependency of S[X], emerge as a signal out of the noisy
data .
Here, ΔTg is approximated as a function of ΔR[X] by fitting a non-linear function (a polynomial up to the
third order, y(x)=a+bx+cx2+dx3) to the scattered data of ΔTg vs. ΔR[X]. The individual contribution of
land ice albedo and CO2 to a state dependency of
S[CO2,LI] can be investigated by analysing both
S[CO2] and S[CO2,LI]. If the best fit
follows a linear function, e.g. for state-independent behaviour of
S[X], its values might be determined from the slope of the
regression line in the ΔTg–ΔR[X] space. However, note that here a necessary condition for the
calculation of S[X] over the whole range of ΔR[X], but
not for the analysis of any state dependency, is that any fitting
function crosses the origin with ΔR[CO2,LI]=0Wm-2 and ΔTg=0K, implying
for the fitting parameters that a=0. This is also in line with the
general concept that without any change in the external forcing, no
change in global mean temperature should appear. Since the data sets
have apparent offsets from the origin, we first investigate which order
of the polynomial best fits the data by allowing parameter a to vary
from 0.
For the calculation of mean values of S[CO2,LI], we
then analyse the S[CO2,LI]-ΔR[CO2,LI] space in a second step, where
S[CO2,LI]=ΔTg⋅ΔR[CO2,LI]-1 is first calculated individually for
every data point and then stacked for different background conditions
(described by ΔR[CO2,LI]). In doing so, we
circumvent the problem which appeared in the ΔTg–ΔR[X] space that the regression function needs to meet the
origin. Some of the individual values of
S[CO2,LI] are still unrealistically high or low;
therefore, values in S[CO2,LI] outside the
plausible range of 0–3 KW-1m2 are rejected from
further analysis.
The scattered data of S[CO2,LI] as a function of
ΔR[CO2,LI] are then compiled in
a probability density function (PDF), in which we also consider the
given uncertainties of the individual data points. For the calculation
of the PDFs, we distinguish between a few different climate states,
when supported by the data. For the time being, the data coverage is
too sparse and uncertainties are too large to calculate any
state-dependent values of S[CO2,LI] in greater
detail.
The fitting routines use the method of general
linear least squares. Here, a function χ2=∑in(yi-y(x))2σy2 is minimized, which calculates the sum of
squares of the offsets of the fit from the n data points normalized
by the average variance σy2. Since established numerical
methods for calculating a non-linear fit through data cannot consider
uncertainties in x, we base our regression analysis on a Monte Carlo
approach. Data points are randomly picked from the Gaussian
distribution described by the given 1σ standard deviation of
each data point in both directions x (ΔR[X]) and y
(ΔTg). We generated 5000 of these data sets,
calculated their individual non-linear fits, and further analysed
results based on averages of the regression parameters. The
Monte Carlo approach converges if the number of replicates exceeds
1000, e.g. variations in the mean of the parameters are at least 1
order of magnitude smaller than the uncertainties connected with the
averaging of the results. We used the χ2 of the fitting routines
in F tests to investigate whether a higher-order polynomial would
describe the scattered data in the ΔTg–ΔR[X] parameter space better than a lower-order polynomial, and we use
the higher-order polynomial only if it significantly better describes
the data at the 1% level (p value of F test: p≤0.01).
Uncertainty estimates
As previously described in detail , standard
error propagation is used to calculate uncertainties in ΔT and
ΔR. For ΔR[LI], changes in surface albedo are
assumed to have a 1σ uncertainty of 0.1. Simulated changes in
land ice area have a relative uncertainty of 10%
in the various simulation scenarios performed in . The
different approaches in reconstructing CO2 all have different
uncertainties, as plotted in Fig. . Ice core CO2
has a 1σ uncertainty of 2ppmv, while those based on
other proxies have individual errors connected with the data points
that are of the order of 20–50 ppmv. Radiative forcing based
on CO2, ΔR[CO2]=5.35Wm-2⋅ln(CO2/CO2,0), has in addition to the
uncertainty in CO2 itself also another 10 %
1σ uncertainty . The
uncertainty in the incoming insolation is restricted to variations in the solar constant known to be of the order of
0.2%. Annual mean global surface temperature, ΔTg, is solely based on the polar amplification factor, fpa, and ΔTNH. Uncertainty in ΔTNH is estimated based on eight different model
realizations of the deconvolution of benthic δ18O into
sea level and temperature . Based on the analysis
of the PMIP3 and PlioMIP results, the polar amplification factor
fpa=ΔTNH⋅ΔTg-1
has a relative uncertainty of 10% (see Fig. a).
These uncertainties used in an error propagation lead to the
σΔTg, σΔR[CO2],
and σΔR[CO2,LI] of the individual
data points and are used to constrain the Monte Carlo statistics. The
stated uncertainties of the parameters of the polynomials fitting the
scattered ΔT–ΔR data given in Table
and used to plot and calculate S[CO2,LI] are
derived from averaging results of the Monte Carlo approach. Note that
higher-order polynomials give more constrains on the parameters and
therefore lead to smaller uncertainties.
ResultsIndividual radiative forcing contributions from land ice albedo and CO2
We calculate a resulting radiative forcing of CO2, ΔR[CO2], that spans a range of -2.8Wm-2 to +2.5Wm-2 when compared to the forcing of preindustrial
conditions, e.g. when ΔR[CO2]=0Wm-2 (Fig. b). The uncertainty in ΔR[CO2]
depends on the proxy. It is about 10% in ice cores, and
generally less than 0.5Wm-2 for other proxies, with the
exception of some individual points from the Pagani lab with
uncertainties of around 1Wm-2.
Changes in temperature and radiative forcing over the last
5Myr. Panel (a): global mean surface temperature change,
ΔTg, calculated with the polar amplification factor,
fpa, being a linear function of the Northern Hemisphere land
temperature change, ΔTNH. Marked are the mid-Pliocene warm
period (mPWP) (red horizontal bar), global warming calculated within PlioMIP
(red circle), and global cooling during the LGM derived from PMIP3 and CMIP5
(blue square). Panel (b): changes in radiative forcing based on
atmospheric CO2 (ΔR[CO2]). CO2 data are
from ice cores and based on δ11B
(Hönisch lab , Foster lab ) and on alkenones (Pagani lab ). Panel (c) shows radiative forcing of land ice,
ΔR[LI], and, for comparison, global annual mean insolation
changes due to orbital variation, ΔR[orbit]. Panel
(d): the sum of the radiative forcing changes due to CO2 and
land ice sheets (ΔR[CO2,LI]) whenever CO2
data allow its calculation. Uncertainties show 1σ.
In contrast to these rather uncertain and patchy results, the ice-sheet
simulations lead to a continuous time series of surface albedo changes
and ΔR[LI] ranging between -4Wm-2
during the ice ages of the late Pleistocene and +1Wm-2
during the interglacials of the Pliocene (Fig. c). During
warmer than preindustrial climate, ΔR[LI] is thus
rather small and between 4.2 and 3.0Myr ago only slightly
higher than ΔR[orbit], the radiative forcing due to
global annual mean insolation changes caused by variations in the
orbital parameters of the solar system
(Fig. c).
Reconstructed ΔR[LI] for the last 20kyr
agrees reasonably well with an alternative based on the ICE-5G ice-sheet reconstruction of
(Fig. ). Changes in land ice fraction in the
northern high latitudes around 15kyr ago are more abrupt around
70∘N in ICE-5G than in ANICE (Fig. b,
e). The northward retreat of the southern edge of the NH ice sheets
happens later in ICE-5G than in ANICE. In combination, both effects
lead to only small differences in the spatial and temporal
distribution of the radiative forcing, ΔR[LI], when
based on either ANICE or ICE-5G (Fig. c and f).
Comparing the calculation of radiative forcing of land ice sheets
for the last 20kyr for two different ice-sheet set-ups. Left: the
3-D ice-sheet model ANICE used in this study ; right:
calculation based on 1∘×1∘ model output from ICE-5G
, results for radiative forcing of land ice sheets,
ΔR[LI], then based on similar aggregation to latitudinal
bands of 5∘ as for ANICE. Panels (a, d): annual mean
insolation at the top of the atmosphere, ITOA, based on orbital
variations . Panels (b, e): fraction
of each latitudinal bands of 5∘ covered by land ice as simulated by
the 3-D ice-sheet models. Panels (c, f): calculated radiative
forcing of land ice sheets, ΔR[LI], normalized to
global-scale impact.
The ice-albedo forcing, ΔR[LI], has a non-linear
relationship to sea level change (Fig. a), which is
caused by the use of sophisticated 3-D ice-sheet models. Hence,
other approaches which approximate ΔR[LI] directly
from sea level or
from simpler 1-D ice-sheet models or calculate ΔR[LI]
from global land ice area changes without considering latitudinal
dependency lack an
important non-linearity of the climate system. This non-linearity in
the ΔR[LI] sea level relationship is also weakly
contained in results based on ICE-5G for Termination I
(Fig. a). However, when plotting identical time
steps of Termination I from results based on ANICE, the non-linearity
is not yet persistent. This implies that a larger pool of results
from various different climates needs to be averaged in order to obtain
a statistically robust functional relationship between ΔR[LI] and sea level (as done in this study).
Details on land ice albedo forcing (ΔR[LI]). Panel
(a): scatter plot of sea level change against
land ice albedo forcing (this study), ΔR[LI], based on the
3-D ice-sheet model ANICE. Data are approximated with a third-order
non-linear fit. For comparison, a fit based on sea level change as applied in
other applications is
shown as dashed line. Furthermore, for Termination I (T-I), results based on
ANICE and on ICE-5G are compared. Panels
(b, c): relationship between global surface temperature change,
ΔTg, and land ice albedo forcing, ΔR[LI],
for different set-ups. Results plotted over the whole last 5Myr
(one data point every 2kyr). Panel (b): standard set-up
with ΔTg=ΔTg1=ΔTNH⋅fpa-1 using a polar amplification, fpa, that varies
linearly as a function of ΔTNH. ΔR[LI] as
based on 3-D ice-sheet models as calculated in this study (see
Fig. c). Panel (c): set-up with a constant
fpa=2.7 as applied previously in .
ΔR[LI] is based on 1-D ice-sheet model results and is
calculated from sea level change with 0.0308Wm-2 per metre of
sea level change. Underlying 1-D ice-sheet model results of ΔTNH and sea level have been published previously
and used elsewhere .
The combined forcing, ΔR[CO2,LI], can only be
obtained for the data points for which CO2 data exist
(Fig. d). The combined forcing ranges from -6 to
-7Wm-2 during the LGM to, in
general, positive values during the Pliocene with a maximum of
+3Wm-2. Between 5.0 and 2.7Myr ago (most of
the Pliocene), the ice-sheet area and ΔR[LI], apart from two exceptions around
3.3Myr and after 2.8Myr ago
(Fig. c), are smaller than today suggesting warmer temperatures
throughout. Proxy data suggest that CO2 and ΔR[CO2] were mostly higher in the Pliocene than during
preindustrial times.
Fitting a linear or a non-linear function to the data: 5000 Monte
Carlo-generated realizations of the scattered ΔTg–ΔR[CO2] or ΔTg–ΔR[CO2,LI] were analysed. The data are randomly picked from
the entire Gaussian distribution described by the 1σ of the given
uncertainties in both ΔTg and ΔR[X]. The
parameter values of fitted polynomials are given as mean ±1σ
uncertainty from the different Monte Carlo realizations. Data sets differ in
the underlying ΔTg and CO2 data. ΔTg: either ΔTg or polar amplification,
fpa, are fixed at LGM and mPWP at values from PMIP3 and PlioMIP
with different functionality for fpa (see methods for details).
CO2 data from ice cores and Hönisch, Foster, and Pagani labs.
Data setnχ2FpLr2abcd1st2nd%ΔTg1: based on a fixed polar amplification factor, fpa, at LGM and mPWP, with fpa being a linear function of ΔTNH elsewhere analysing ΔTg vs. ΔR[CO2]Ice cores3942123183960.4<0.001**56-1.28±0.093.67±0.180.89±0.080Hönisch525805453.20.08/53-2.15±0.131.36±0.1200Foster105419938459.4<0.01*42-1.73±0.110.95±0.09-0.19±0.050Pagani153915291090.70.40/3-2.29±0.110.30±0.1100analysing ΔTg vs. ΔR[CO2,LI]Ice coresa3941219117614.3<0.001**72-0.43±0.072.16±0.100.36±0.040.02±0.00Hönisch5232725613.6<0.001**79-1.15±0.141.27±0.120.10±0.020Foster105258925690.80.38/61-1.53±0.050.63±0.0300Pagani153512550402.50.11/45-2.19±0.070.82±0.0400ΔTg2: based on a fixed fpa that steps from its mPWP value to its LGM value at 2.82 Myr BP analysing ΔTg vs. ΔR[CO2]Ice cores3942668241541.0<0.001**56-0.92±0.083.41±0.170.74±0.070Hönisch527256972.00.17/55-1.78±0.121.36±0.1100Foster1054911436912.7<0.001**39-1.47±0.110.09±0.09-0.21±0.050Pagani153972996830.70.40/2-2.08±0.110.27±0.1000analysing ΔTg vs. ΔR[CO2,LI]Ice cores3941874156876.3<0.001**72-0.46±0.061.41±0.050.11±0.010Hönisch523703178.2<0.01*80-0.85±0.131.13±0.110.07±0.020Foster105324331463.10.08/55-1.37±0.080.58±0.0500Pagani153577857042.00.17/43-2.00±0.060.76±0.0400ΔTg3: fixed ΔTg at LGM and mPWP, based on fpa being a linear function of ΔTNH elsewhere analysing ΔTg vs. ΔR[CO2]Ice cores3941788148281.2<0.001**53-1.39±0.083.15±0.160.84±0.070Hönisch524714314.60.04/50-2.10±0.111.09±0.1000Foster105396737934.70.03/30-1.90±0.060.76±0.0600Pagani153966096200.60.43/2-1.99±0.110.30±0.1100analysing ΔTg vs. ΔR[CO2,LI]Ice coresa394103894439.0<0.001**70-0.50±0.072.17±0.100.44±0.040.03±0.00Hönisch5230522218.3<0.001**76-1.26±0.131.13±0.110.10±0.020Foster105277827521.00.33/51-1.44±0.040.56±0.0300Pagani153606358834.60.03/39-1.89±0.070.81±0.0500
n: number of data points in data set.χ2: weighted sum of squares following either a linear fit (first-order) or a non-linear fit (second-order polynomial); for some data sets (labelled: a), there are also second- or third-order polynomials.F: F ratio for F test to determine where the higher-order fit describes the data better than the lower-order fit (first- vs. second-order polynomial or second- vs. third-order polynomial).p: p value of the F test.L: significance level of F test (/: not significant (p>0.01); *: significant at 1 % level (0.001<p≤0.01); **: significant at 0.1 % level (p≤0.001)).r2: correlation coefficient of the fit.a, b, c, d: derived coefficients of fitted polynomial
y(x)=a+bx+cx2+dx3.
Detecting any state dependency in S[CO2,LI]
As explained in detail in Sect. , S[CO2,LI] can be considered state-dependent if the
scattered data of ΔTg against ΔR[CO2,LI] are better described by a non-linear
rather than a linear fit. The plots for the different CO2
approaches reveal proxy-specific results (Fig. ). Ice
core data (r2=0.72) are best described by a third-order
polynomial and the Hönisch data (r2=0.79) by a second-order
polynomial, while for the Foster (r2=0.61) and the Pagani (r2=0.45) data, a second-order fit is not statistically significantly
better than a linear fit (Table ).
Scatter plots of data of global temperature change, ΔTg, against radiative forcing ΔR[X]. ΔTg is calculated with the polar amplification factor,
fpa, being a linear function of ΔTNH. Left
column (a, c, e, g): radiative forcing of CO2 (ΔR[CO2]). Right column (b, d, f, h): radiative forcing
of CO2 and land ice albedo (ΔR[CO2,LI]).
Lines show average best fits (first-, second-, or third-order polynomials) to
5000 Monte Carlo realizations of the data (details in
Table ). Subfigures differ by the CO2 data they are
based on: (a, b) – ice cores ;
(c, d) – δ11B from the Hönisch lab
; (e, f) – δ11B from the
Foster lab ; (g, h) –
alkenones from the Pagani lab . Each row
contains information on the number of data points n; each subfigure shows
the mean uncertainty of the fit by dividing χ2 (the weighted sum of
squares from the regression analysis) by n and the correlation coefficient
r2. Uncertainties show 1σ.
The fit through the Hönisch data agrees more with the fit through
the ice core CO2 data than with the fit through the other
CO2-proxy-based approaches; however, the Hönisch data set only extends 2.1Myr back in time and contains no
CO2 data in the warm Pliocene. Thus, our finding of
a state dependency in climate sensitivity obtained from the ice core
data and covering predominately colder than present periods – for which a first indication was published in
– is extended to the last
2.1Myr. However, we can still not
extrapolate this finding to the warmer than present climates of the
last 5Myr since the ice core and the Hönisch data do not
cover these periods and the Foster and the Pagani data do not suggest
a similar relationship. These findings remain qualitatively the same
if our analyses are based on the alternative global temperature
changes ΔTg2 and ΔTg3
(Table ).
When analysing the contribution from land ice albedo (ΔR[LI]) and CO2 radiative forcing (ΔR[CO2]) separately, we find a similar non-linearity in the
ΔTg–ΔR[CO2] scatter plot only in
the CO2 data from ice cores (Fig. a). The
relationship between temperature and radiative forcing of CO2
is best described by a linear function in the Hönisch and the Pagani
data sets (Fig. c and g, Table ) and in data from the Foster lab even by a second-order polynomial with
inverse slope leading to a decline in S[CO2] for rising
ΔR[CO2] (Fig. e). This inverse
slope obtained for the Foster data between ΔTg and
ΔR[CO2] is the only case in which a detected
non-linearity partly depends on the use of the temperature change time
series, e.g. the relationship is linear when based on ΔTg3 (Table ). Furthermore, this inverse
slope might be caused by the under-representation of data for negative
radiative forcing. However, when data in the ΔTg–ΔR[X] scatter plots are binned in x or
y direction to overcome any uneven distribution of data, no change in
the significance of the non-linearities is observed. The data scatter
is large and regression coefficients between ΔR[CO2] and ΔTg for Foster (r2=0.42)
and Pagani (r2=0.03) are small. This large scatter and weak
quality of the fit in the Pagani data are probably caused by some
difficulties in the alkenone-based proxy, e.g. in the size dependency, and
by variations in the degree of passive vs. active uptake of CO2
by the alkenone-producing coccolithophorids
. Furthermore, already
showed that the relationship of CO2 to temperature change
during the last 20Myr is opposite in sign for
alkenone-based CO2 than for other approaches.
The ice-albedo forcing, ΔR[LI], in our simulation
results based on 3-D ice-sheet models
has a specific relationship to global temperature change. Here
both a step function or a linear change in the polar amplification
factor, fpa, lead to similar results
(Fig. b).
However, when overly simplified approaches to calculate
ΔR[LI] are applied (e.g. based on 1-D ice-sheet
models , related to sea level
, or based on global
land ice area changes without considering their latitudinal changes in
detail ), the
ΔTg–ΔR[LI] relationship is more
linear. The range of ΔR[LI] proposed for the same
range of ΔTg is then reduced by 30 %
(Fig. b and c). ΔR[LI] is
effected by ice-sheet area rather than ice-sheet volume. Three-dimensional ice-sheet
models include this effect better than calculations based on 1-D ice-sheet models or calculations directly from sea level variations. This non-linearity
between ice volume (or sea level) and ice area is supported by data
and theory from the scaling of glaciers . In addition, latitudinal variation in land ice
distribution affects the radiative forcing, ΔR[LI], in
a non-linear way (Fig. ) and thereby likely contributes
to a state dependency in the equilibrium climate sensitivity, S[CO2,LI].
To verify the robustness of our findings with respect to the uncertainties
attached to all data points, we performed an additional sensitivity study by
artificially reducing the uncertainties in ΔTg
(σΔTg) and ΔR[CO2,LI]
(σΔR) by a factor of 2 or 10. For both reduction factors, we
find statistically the same non-linearities in the ΔTg-ΔR[CO2,LI]-scattered data than with
the original uncertainties in all four CO2 data sets (non-linearity
between ΔTg and ΔR[CO2,LI] in the
data sets based on CO2 in ice cores and from the Hönisch lab; a
linear relationship between both variables only exists if based on Foster or Pagani lab CO2 data;
Table ). Our proposed state dependency of
S[CO2,LI] is therefore independent of the assumed
uncertainties. Any calculated value of S[CO2,LI]
nevertheless depends in detail on the assumed uncertainties in the underlying
data.
Sensitivity analyses: (1) investigating the
importance of the uncertainties on the regression results by artificially
reducing both σΔTg and σΔR by a factor of 2
or 10; (2) investigating the importance of the three variables ΔTg, CO2, and ΔR[LI] with respect to
the previous analysis of the ice-core-based CO2 data of
(cited here as vdH2014). Here, all data are
resampled to 2 kyr, while in vdH2014 data are resampled to 100 yrs and
binned in ΔTg before any regression analysis. The
coefficients a, b, c, and d describe the linear or higher-order polynomial
that best fits the data (F test statistics based on 5000 Monte
Carlo-generated realizations of the scattered ΔTg–ΔR[CO2,LI] data). The data are randomly picked from the
entire Gaussian distribution described by the 1σ of the given
uncertainties in both ΔTg and ΔR[CO2,LI]. The parameter values of fitted polynomials are
given as mean ±1σ uncertainty from the different Monte Carlo
realizations. In all scenarios summarized here, ΔTg vs.
ΔR[CO2,LI] with ΔTg=ΔTg1 was investigated.
Data setnχ2FpLr2abcd1st2nd%Sensitivity analysis 1: investigating the importance of the uncertainties Ice coresa, original uncertainties3941219117614.3<0.001**72-0.43±0.072.16±0.100.36±0.040.02±0.00Ice coresa, uncertainties ×1/239432683105210.6<0.001**80-0.36±0.042.23±0.060.41±0.030.03±0.00Ice coresa, uncertainties ×1/10394834897755330.0<0.001**83-0.31±0.012.34±0.010.47±0.010.04±0.00Hönisch, original uncertainties5232725613.6<0.001**79-1.15±0.141.27±0.120.10±0.020Hönisch, uncertainties ×1/25285059820.7<0.001**87-1.01±0.081.37±0.070.10±0.010Hönisch, uncertainties ×1/1052162351071225.3<0.001**89-0.97±0.021.40±0.010.11±0.000Foster, original uncertainties105258925690.80.38/61-1.53±0.050.63±0.0300Foster, uncertainties ×1/2105897289540.20.65/61-1.53±0.030.67±0.0200Foster, uncertainties ×1/101053061053060790.10.93/61-1.53±0.000.69±0.0000Pagani, original uncertainties153512550402.50.11/45-2.19±0.070.82±0.0400Pagani, uncertainties ×1/215315283147955.00.03/56-2.23±0.041.00±0.0300Pagani, uncertainties ×1/101533431343292926.30.01/60-2.24±0.011.07±0.0100Sensitivity analysis 2: investigating the importance of ΔTg, CO2, and ΔR[LI] in the data set from ice cores with respect to vdH2014 Data at 2 kyr intervals (if available) This studya3941219117614.3<0.001**72-0.43±0.072.16±0.100.36±0.040.02±0.00CO2 as in vdH2014a3901283123515.0<0.001**70-0.42±0.062.17±0.100.37±0.040.02±0.00ΔR[LI] as in vdH20143901684137387.7<0.001**67-0.49±0.081.70±0.060.16±0.010ΔTg as in vdH201439074265849.4<0.001**660.13±0.121.13±0.080.08±0.010ΔTg, CO2, ΔR[LI] as in vdH201439078874422.9<0.001**620.25±0.141.12±0.100.07±0.010Data binned in ΔR[CO2,LI] to bins of 0.2 W m2This study31563714.4<0.001**81-0.66±0.371.61±0.260.14±0.040CO2 as in vdH201431604212.00.002*80-0.68±0.361.56±0.250.14±0.040ΔR[LI] as in vdH20142743328.30.008*79-0.41±0.431.75±0.340.16±0.060ΔTg as in vdH20143142355.60.025/73-0.34±0.230.63±0.0800ΔTg, CO2, ΔR[LI] as in vdH20142835322.30.138/74-0.07±0.260.72±0.0900Data binned in ΔTg to bins of 0.2 K This study3220314810.80.003*87-0.20±0.181.70±0.200.14±0.040CO2 as in vdH2014322131609.60.004*85-0.20±0.191.67±0.210.13±0.040ΔR[LI] as in vdH2014321931645.10.031/82-0.39±0.161.08±0.0800ΔTg as in vdH20142440343.70.068/77-0.05±0.250.70±0.0900ΔTg, CO2, ΔR[LI] as in vdH20142442391.60.218/760.23±0.300.80±0.1100
n: number of data points in data set.χ2: weighted sum of squares following either a linear fit (first order) or a non-linear fit (second-order polynomial); for some data sets (labelled: a), there are also second- or third-order polynomials.F: F ratio for F test to determine where the higher-order fit describes the data better than the lower-order fit (first- vs. second-order polynomial or second- vs. third-order polynomial).p: p value of the F test.L: significance level of F test (/: not significant (p>0.01); *:
significant at 1 % level (0.001<p≤0.01);
**: significant at 0.1 % level (p≤0.001)).r2: correlation coefficient of the fit.a, b, c, d: derived coefficients of fitted polynomial
y(x)=a+bx+cx2+dx3.
Since a first detection of any state dependency in
S[CO2,LI] has already been performed for the ice core
CO2 data in , it is of interest to
investigate which of our improvements with respect to this earlier analysis
are most important. We therefore performed a further sensitivity study in
which one or all of the three
times series ΔTg, ΔR[CO2], and ΔR[LI] were identical to the approach of
. However, since in this earlier study all data
have been resampled to 100 yr, we have to preprocess these data sets prior
to Monte Carlo statistics to 2-kyr averages to match the temporal resolution
of the 3-D ice-sheet models used here. In this additional analysis
(Table ), we find that even when all three data sets are
substituted with those used in , we find a
non-linearity in the ΔTg-ΔR[CO2,LI] scatter plot that points to a state dependency
in S[CO2,LI]. However, the r2 is then 10% smaller
than in our results indicating a weaker correlation between temperature
change and radiative forcing, and a second-order polynomial is sufficient to
fit the data, while in our best guess these ice-core-based CO2 data
are best described by a third-order polynomial. If data are binned before
analysis, similarly as in , we find a non-linearity
in the scattered data only for the data sets used in this study or when
CO2 is substituted by the previous time series but not when the
previous versions of ΔR[LI] or ΔTg are used.
In these binned data both our improved time series of ΔTg
and ΔR[LI] are necessary to generate this non-linearity
indicating a state dependency in S[CO2,LI]. The analysis
of both studies are still different in detail (higher-order polynomial versus
piecewise linear regressions), and therefore the absence of any non-linearity
in the binned data when all three time series have been substituted by those
from the previous study are not contradictory to our stated non-linearity.
In model-based approaches the final radiative forcing ΔR including
all feedbacks from an obtained temperature change leads to a different
nomenclature, in which temperature change is the independent variable,
typically plotted on the x axis
e.g.. Our approach differs from those studies
since feedbacks are not contained in ΔR (but in S), which we only
understand as the forcing terms. Therefore, in our study ΔR is the
independent variable that determines the background condition of the climate
system.
Calculating the specific equilibrium climate sensitivity, S[CO2,LI]
The non-linear regression of the ΔTg–ΔR[CO2,LI] scatter plot revealed that both the ice
core CO2 and the Hönisch lab data contain a state dependency
in S[CO2,LI]. As explained in Sect. ,
we analyse the mean and uncertainty in
S[CO2,LI] for both data sets from probability density functions for
different background climate states represented by ΔR[CO2,LI] based on the pointwise results
(Fig. ). For both the Pagani and the Foster data
sets, the slopes of the linear regression lines in ΔTg–ΔR[CO2,LI] might in principle
be used to calculate S[CO2,LI]. However, both data
sets have a rather large offset in the y direction (ΔTg) (y interception is far away from the origin) that
might bias these results. These offsets are nearly identical when
calculations are based on the alternative global temperature changes
ΔTg2 or ΔTg3
(Table ). Note that S[CO2,LI] as
calculated for each data point in Fig. also
contains 20 and 11 outliers in the ice core and the Hönisch data sets,
respectively, that do not fall into the most plausible range of
0.0–3.0 KW-1m2. These outliers are typically
generated when dividing smaller anomalies in ΔTg
and ΔR[CO2,LI] during interglacials, when
already small uncertainties generate a large change in the ratio ΔTg⋅ΔR[CO2,LI]-1 that defined S[CO2,LI].
They are omitted from further analysis.
Calculating specific equilibrium climate sensitivity,
S[CO2,LI]. Only data with their mean in
S[CO2,LI] in the range [0,3]KW-1m2
are analysed and plotted. Panel (a): ice-core-based time series of
pointwise calculations of S[CO2,LI] for the last
0.8Myr. Panel (b): same data as in (a) in
a scatter plot of S[CO2,LI] against radiative forcing
ΔR[CO2,LI]. Panel (c): probability density
distribution of ice-core-based S[CO2,LI]. Data from
“cold” periods (ΔR[CO2,LI]<-3.5Wm-2) and “warm” periods (ΔR[CO2,LI]>-3.5Wm-2) are analysed
separately. Labels in (c) denote 16th, 50th, and 84th percentile.
Panels (d, e, f): same as (a, b, c), but for the
Hönisch data over the last 2.1Myr.
S[CO2,LI] based on the ice core and the Hönisch lab
data rarely falls below 0.8KW-1m2
(Fig. ). In both data sets, we distinguish between “cold”
from “warm” conditions using the threshold of ΔR[CO2,LI]=-3.5Wm-2 to make our
results comparable to the piecewise linear analysis of “warm” and
“cold” periods in . For the ice core data
of the last 0.8Myr, the S[CO2,LI] is not
normally distributed but has a long tail towards higher values
(Fig. c). However, this long tail is partially
caused by data points with ΔR[CO2,LI] not
far from 0Wm-2, which are prone to high
uncertainties. Only conditions during “cold” periods, representing
glacial maxima, have a nearly Gaussian distribution in
S[CO2,LI], with a mean value of
1.05-0.21+0.23KW-1m2. For “warm” periods
the PDF is skewed, with S[CO2,LI]=1.56-0.44+0.60KW-1m2. Results based on the
Hönisch data covering the last 2.1 Myr are nearly identical with
S[CO2,LI]=1.07-0.24+0.29KW-1m2 (“cold”) and
S[CO2,LI]=1.51-0.55+0.68KW-1m2 (“warm”). Both data
sets thus consistently suggest that during Pleistocene warm periods, S[CO2,LI] was about ∼45% larger than
during Pleistocene cold periods.
In a piecewise linear regression analysis of data covering the last
0.8 Myr, a state dependency in climate sensitivity was already
detected , including a rise in
S[CO2,LI] from 0.98±0.27KW-1m2 during “cold” periods to 1.34±0.12KW-1m2 during “warm” periods of the late
Pleistocene. To allow a direct comparison with our study, we here cite
results shown in the Supporting Information of in which
the global temperature anomaly was similar to our ΔTg. Some important details, however, of our study and the
previous study differ because (i) the
assumed changes in temperature and land ice albedo are based on
different time series and (ii) we here use CO2 as resampled to
the 2 kyr temporal spacing of the 3-D ice-sheet models while
all data are resampled at 100 years time steps and binned
before analysis in . Note, that we tested
that data binning does not lead to large changes in our results and
conclusions. Nevertheless, the calculated
S[CO2,LI] of the “cold” periods
matches our
glacial values of S[CO2,LI] derived from the ice cores within the uncertainties, but the values for the
“warm” periods are smaller in the previous estimates of
than in our results
(Fig. ). This difference in the “warm” period for
both studies is caused by the revised ΔR[LI], which
mainly leads to differences with respect to previous studies for
intermediate glaciated and interglacial climates.
Probability density function of different approaches to calculate
specific equilibrium climate sensitivity, S[CO2,LI].
Results of this study are based on pointwise analysis of the ice core (last
0.8Myr) and the Hönisch (last 2.1Myr) data for
“cold” periods (ΔR[CO2,LI]<-3.5Wm-2) and “warm” periods (ΔR[CO2,LI]>-3.5Wm-2). In
, a similar split of the ice core data was
performed. We show their results based on similar ΔTg as
obtained here published in the Supporting Information in
. calculated
S[CO2,LI] either for ice core data of the whole last
0.8Myr or based on δ11B for 0.8Myr of
the Pliocene between 2.5–3.3 MyrBP. Vertical lines and labels give
the mean of the different results.
The calculated PDFs of S[CO2,LI]
(Fig. ) based on ice cores or Hönisch lab data are
qualitatively the same if based on the alternative assumptions regarding
polar amplification, which also include a case with a constant polar
amplification during the Pleistocene. The mean values of the PDF of
S[CO2,LI] are then shifted by less than
0.15KW-1m2 for “cold” periods and by less than
0.25KW-1m2 for “warm” periods towards smaller values.
The 5Myr long data sets from the Foster and the Pagani lab
show no indication of state dependency. One might argue that these
5Myr long time series should be split into times when large
ice sheets in the NH were present and when they were absent because their presence
is expected to have an influence on the climate and its sensitivity. According to
our simulation results (Fig. b), large NH
land ice first appeared around 2.82MyrBP, which is also the
time which has been suggested by for the onset
of NH land ice and for which found a pronounced
decline in CO2. Note that the start of northern hemispheric
glaciation in our 3-D ice-sheet simulations was gradual at first and
intensified around 2.7Myr ago (Fig. b), in
agreement with other studies
. We tested the Foster lab
data for any changes in the regression analysis if the data set was
split into two time periods, one with and one without NH ice sheets. We
found significantly different relationships between temperature change
and radiative forcing for most of the Pleistocene than for either an
ice-free NH Pliocene (Foster lab data
2.82–3.3 MyrBP) or all available Pliocene data
(Foster lab data 2.5–3.3 MyrBP)
(Fig. ). For the Pleistocene, ΔTg-ΔR[CO2,LI] data are in
themselves non-linear (thus, S[CO2,LI] is state-dependent), and for the Pliocene the relationship seems to be linear
(thus, S[CO2,LI] seems to be constant) over this period. However, the fit through ΔTg–ΔR[CO2,LI] is of low quality (r2=0.04 for
2.82–3.3 MyrBP and r2=0.23 for
2.5–3.3 MyrBP,) which prevents us from calculating
any quantitive values of S[CO2,LI] based on
these data. Remember, that in all regression analyses we consider the
uncertainties in both x and y direction in all data points by the
application of Monte Carlo statistics, something which also
distinguishes our approach from and
possibly contributes to different results.
Best-guess 3.3Myr scatter plot of global temperature
change, ΔTg, against the radiative forcing of CO2
and land ice albedo (ΔR[CO2,LI]). The Hönisch lab
data for the last 2.1Myr (most of the
Pleistocene) and the Pliocene part of the Foster lab data
– entire data (2.5–3.3 MyrBP) and only
the data for the almost land-ice-free Northern Hemisphere times
(2.82–3.3 MyrBP) – are compiled to illustrate how the functional
dependency between ΔTg and ΔR[CO2,LI] changed as function of background climate
state.
Nevertheless, our data compilation clearly points to a regime shift in
the climate system with different climate sensitivities before and
after 2.82MyrBP. From the available proxy-based
data indicating CO2 around 400ppmv during various times in the Pliocene, together with our simulated global temperature change
of around 2 K and ice-sheet albedo forcing of about
0.5Wm-2 (Fig. ), we can estimate that in
the NH ice-free Pliocene, S[CO2,LI] was around
1KW-1m2, in agreement with
. This estimate is of a similar size as our results
for the full glacial conditions of most of the Pleistocene, but it is smaller than
during intermediate glaciated to interglacial conditions of the late
Pleistocene. A possible reason could be that in the warm Pliocene, the
sea ice albedo feedback might have been weaker or even absent
, but some studies also suggest that processes are missing in
state-of-the-art climate models. A recent study
concluded that at the onset of the
northern hemispheric glaciation, a fundamental change in the interplay
of the carbon cycle and the climate system occurred leading to a switch
from in-phase glacial–interglacial changes in deep-ocean
δ18O and δ13C to antiphase changes. If
true such a change in the carbon cycle–climate system might also
affect climate sensitivity.
A more direct calculation of the specific equilibrium climate sensitivity,
S[CO2,LI], as a function of background climate state that
goes beyond the PDFs provided so far is desirable, but with the available
data and within the given theoretical and methodological framework, it is not
yet possible.
Discussion
recently analysed the ice core CO2
and the new CO2 data from the Foster lab around the end of the
Pliocene separately, finding S[CO2,LI] of 0.91±0.10 and 1.01±0.19KW-1m2, respectively. Both results are nearly indistinguishable within
their uncertainties; thus, concluded that
S[CO2,LI] is not state-dependent, since it did not
change between the Pliocene and Pleistocene. However, since they based the
radiative forcing of land ice albedo (ΔR[LI]) on
a linear function of sea level, they miss an important non-linearity of
the climate system. We find that the large uncertainty in ΔR[CO2] might also be another reason for state independency
in S[CO2,LI] in the Foster lab data set.
S[CO2,LI] based on the ice core analysis of
is slightly smaller than our results based
on the cold periods from the ice core data set
(Fig. ). This indicates that the information which
is relevant to suggest any state dependency in
S[CO2,LI] is mainly contained in data covering
the so-called “warm” climates of the Pleistocene. Thus, especially
the land ice area distribution and ΔR[LI] from
intermediate glaciated states are important here.
However, it should be emphasized that never
attempted to detect any state dependency in S[CO2,LI]
within either the Pleistocene or the Pliocene data sets. In searching for
non-linearities in the scattered data of ΔTg versus ΔR[CO2,LI] by statistical methods, we here go beyond their approach.
Comparing data-based estimates of S[CO2,LI]
directly with climate model results e.g. is not
straightforward, and it is not done in the following because in climate
models only those processes considered explicitly as forcing will have
an impact on calculated temperature change, while the data-based
temperature reconstruction contains the effect of all processes
. Furthermore, in climate
simulation results have been discussed to understand which processes
and mechanisms were responsible for the spatially very heterogeneous
changes observed during the last 5 Myr, e.g. the increase in the
polar amplification factor over time. Since the results of
were unable to explain all observations, it was
concluded that a combination of different dynamical feedbacks is underestimated in the climate models. We are not able to generate
spatially explicit results. However, from our analysis we could
conclude that the equilibrium climate sensitivity represented by
S[CO2,LI] was a function of background climate
state and probably changed dramatically between conditions with and
without Northern Hemisphere land ice.
The contribution of greenhouse gas radiative forcing and of seasonally and
latitudinally variable incoming solar radiation to the simulated global
temperature anomalies of the last eight interglacials have been analysed
individually before . It was found that the greenhouse gas
forcing was the main driver of the simulated temperature change with the
incoming solar radiation amplifying or dampening its signal for all but one
interglacial (Marine Isotope Stage (MIS) 7), with two interglacials (MIS 1
and MIS 19) having variations close to zero. Furthermore, they calculated the
ECS (temperature rise for a doubling of CO2) for the different
interglacial background conditions and found ECS to decrease with increasing
background temperature. A calculation of climate sensitivity for individual
points in time has been performed before but has been
rejected due to large uncertainties, mainly during interglacials since in the
definition of S, one then needs to calculate the ratio of two small numbers
in ΔTg and ΔR[CO2,LI], which has
typically a low signal-to-noise ratio. At first glance, this might seem
contrary to our finding of a larger climate sensitivity during late
Pleistocene interglacials when compared to late Pleistocene full glacial
conditions. However, as mentioned already in the previous paragraph, the
comparison of (palaeo)data-based calculations of S with ECS calculated from
climate models is not directly possible. Furthermore, in our approach we
include changes in land ice sheet (albedo forcing or ΔR[LI]), while kept ice sheets at present state.
When investigating S[CO2,LI] over the whole range of
climate states (from full glacial conditions to a warm Pliocene with a
(nearly) ice-free Northern Hemisphere resulting in a variable forcing term
ΔR[LI]), we therefore probe a completely different climate
regime, which is not directly comparable with results obtained from
simulations of interglacials only.
There exist some intrinsic uncertainties in our approach based on the
underlying data sets, which are not included in the Monte Carlo
statistic. For example, the global temperature anomaly in the LGM
still disagrees in various approaches , and Pliocene sea level and ice-sheet
dynamics are still a matter of debate . Taking
these issues into account might lead to changes in our quantitative
estimates but not necessarily to a revision of our main finding of
state dependency in S[CO2,LI]. In the light of the existing
uncertainties, our findings must be supported by other modelling approaches to come to firm
conclusions. Furthermore, our assumption that we can estimate
equilibrium climate sensitivity from palaeodata implicitly assumes
that these data represent predominately equilibrium climate
states. This might be a simplification, but since filtering out data
points in which temperature changed abruptly led to similar results
, it should only have a minor effect on the
conclusions.
To calculate in detail the effect of climate change on temperature, it
would be important to also include other forcing agents,
e.g. CH4, N2O, or aerosols. For the Pliocene, strong
chemistry–climate feedbacks have been proposed , suggesting high ozone and aerosol levels and potentially high
CH4 values. This implies that the relationship of CO2
to other forcing agents might have been different for the cold climates of
the late Pleistocene than for the warm climates of the
Pliocene. Therefore, assumptions on the influence of other slow
feedbacks based on data of the late Pleistocene
cannot be extrapolated to the Pliocene. Hence, we restrict our
analysis of the Pliocene data to S[CO2,LI] and
again emphasize that an estimate of climate sensitivity for the present day, Sa, from our palaeo sensitivity
is not straightforward, especially for these data.
For the Pleistocene data we might roughly approximate the implications
of our findings for equilibrium temperature changes under CO2
doubling, or ECS, by considering the so far neglected feedbacks
(CH4, N2O, aerosols, or vegetation). However, we are
aware that this is a simplification, since it was already shown that
the per unit radiative forcing climate effect of well-mixed greenhouse
gases and aerosols differs . In palaeodata of
the last 0.8Myr, the equilibrium climate sensitivity
considering all feedbacks was only about two thirds of
S[CO2,LI]. A CO2
doubling would then lead to an equilibrium rise in global temperature
of, on average, 2.5 K (68 % probability range:
2.0–3.5 K) or to, on average, 3.7K (68%
probability range: 2.5–5.5 K) during Pleistocene full glacial
climates (“cold”) or Pleistocene “warm” climates (intermediate
glaciated to interglacial conditions), respectively. Both average
values of ECS are well within the range proposed by palaeodata and
models so far , but we especially
emphasize the potential existence of a long tail of
S[CO2,LI] towards higher values. Such estimates
of ECS are very
uncertain due to the different effect of various forcings and are not yet possible for Pliocene climate states (see
above). These long-term temperature change estimates for a doubling of
CO2 are mainly of interest for model validation. To be
applicable to the not so distant future, these equilibrium estimates
need to be corrected for oceanic heat uptake to calculate any
transient temperature response . Whether climate
in the future is more comparable to the climate states of interglacials of
the late Pleistocene or to the warm Pliocene is difficult to say,
although this has, according to our results, major implications for
the expected equilibrium temperature rise.
The Greenland ice sheet might completely
disappear in the long-term for the projected future
greenhouse gas emissions, but it might reduce its ice volume in the next 2000 years by
less than 50%.
Another study suggests that the Greenland ice sheet
might also disappear in the long run for atmospheric CO2
concentrations between 200 and 300 pmmv.
These studies suggest that for the coming millennia, the
Earth might still contain a significant amount of northern hemispheric land
ice, and thus the climate and the proposed climate sensitivity
S[CO2,LI] will probably be more comparable to
the interglacials of the late Pleistocene. In the more distant future, the Northern Hemisphere may become free of land ice and its climate and climate sensitivity more comparable to the warm Pliocene.
When compared to the two most recent contributions to this topic
,
our study goes beyond them by
four improvements that have been laid out in detail in the introduction. The
most important of these improvements is the systematical detection of state
dependency in S[CO2,LI] using Monte Carlo statistics.
However, we have been able to extend the finding of state dependency in
S[CO2,LI] from the ice core data of the last
800kyr to the last 2.1Myr. Furthermore, the
improvements in the underlying time series of ΔR[LI] have
been important to obtain a data set in which the state dependency
S[CO2,LI] can be detected. The role of the ΔTg time series seems at first glance to be of similar importance
to that of ΔR[LI]. However, state dependency in
S[CO2,LI] was also obtained for the alternative
temperature time series ΔTg2 or ΔTg3, and
therefore a detailed knowledge of ΔTg is of minor
importance for our overall conclusions.
Conclusions
In conclusion, we find that the specific equilibrium climate
sensitivity based on radiative forcing of CO2 and land ice
albedo, S[CO2,LI], is state-dependent if
CO2 data from ice cores or from the Hönisch lab, based on
δ11B, are analysed. The state dependency arises from
the non-linear relationship between changes in radiative forcing of
land ice albedo, ΔR[LI], and changes in global
temperature. Previous studies were not able to detect such
a state dependency because land ice albedo forcing was not based on
results from 3-D ice-sheet models, which contain much of this
non-linearity. So far, the state dependency of
S[CO2,LI] based on ice core CO2, which
was derived from predominately glacial conditions of the late
Pleistocene, can be extrapolated to the last 2.1Myr. During
intermediate glaciated and interglacial periods of most of the
Pleistocene, S[CO2,LI] was, on average, about
∼45% higher (mean: 1.54KW-1m2;
68% probability range: 1.0–2.2 KW-1m2) than
during full glacial conditions of the Pleistocene (mean
1.06KW-1m2; 68% probability range:
0.8–1.4 KW-1m2).
Before 2.1MyrBP the published CO2 data are too sparse,
depend on the applied methodology, and have uncertainties that are too large
to come to a statistically well-supported conclusion on the
value of S[CO2,LI]. The data available so far
suggest that the appearance of northern hemispheric land ice sheets
changed the climate system and accordingly influenced climate
sensitivity. In the Pliocene, S[CO2,LI] was
therefore probably smaller than during the interglacials of the
Pleistocene.
Acknowledgements
PMIP3 model output was derived from the LGM scenarios of CMIP5;
PlioMIP model output was taken from uploaded published results of its large-scale
features . We acknowledge the World Climate
Research Programme's Working Group on Coupled Modelling, which is
responsible for CMIP. For CMIP, the US Department of Energy's Program
for Climate Model Diagnosis and Intercomparison provides coordinating
support and led the development of software infrastructure in partnership
with the Global Organization for Earth System Science Portals. We
thank the climate modelling groups from which we received the PMIP3 and PlioMIP results as available in mid-January 2014 and as listed in the
“Methods” section of this paper for producing and making available their
model output. We also thank G. Foster for providing CO2 data
and comments on our manuscript, B. Hönisch for insights into the
measurements of the Bartoli data set, and G. Knorr and J. Bijma for
helpful comments. Financial support for B. de Boer was partially
provided through the NWO-VICI grant of L. J. Lourens. L. Stap
was funded by NWO-ALW. This paper contributes to the program of the
Netherlands Earth System Science Centre (NESSC), financially supported
by the Ministry of Education, Culture and Science (OCW). Data sets of
ΔTg and ΔR[LI] are available
from the PANGAEA database at http://dx.doi.org/10.1594/PANGAEA.855449.Edited by: U. Mikolajewicz
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