Estimate of climate sensitivity from carbonate microfossils dated near the Eocene-Oligocene global cooling

Climate sensitivity is a crucial parameter in global temperature modelling. An estimate is made at the time 33.4 Ma using published high-resolution deep-sea temperature proxy obtained from foraminiferal δ 18 O records from DSDP site 744, combined with published data for atmospheric partial pressure of CO 2 ( p CO 2 ) from carbonate micro- 5 fossils, where δ 11 B provides a proxy for p CO 2 . The p CO 2 data shows a p CO 2 decrease accompanying the major cooling event of about 4 ◦ C from greenhouse conditions to icecap conditions following the Eocene-Oligocene boundary (33.7 My). During the cooling p CO 2 fell from 1150 to 770 ppmv. The cooling event was followed by a rapid and huge increase in p CO 2 back to 1130 ppmv in the space of 50 000 yr. The large p CO 2 in- 10 crease was accompanied by a small deep-ocean temperature increase estimated as 0.59 ± 0.063 ◦ C. Climate sensitivity estimated from the latter is 1.1 ± 0.4 ◦ C (66 % conﬁdence) compared with the IPCC central value of 3 ◦ C. The post Eocene-Oligocene transition (33.4 Ma) value of 1.1 ◦ C obtained here is lower than those published from Holocene and Pleistocene glaciation-related temperature data (800 Kya to present) but 15 is of similar order to sensitivity estimates published from satellite observations of tropo-spheric and sea-surface temperature variations. The value of 1.1 ◦ C is grossly di ﬀ erent from estimates up to 9 ◦ C published from paleo-temperature studies of Pliocene (3 to 4 Mya) age sediments. The range of apparent climate sensitivity values available from paleo-temperature data suggests that either feedback mechanisms vary widely 20 for the di ﬀ erent measurement conditions, or additional factors beyond currently used feedbacks are a ﬀ ecting global temperature-CO 2 relationships. ﬀ for ﬀ erent ﬀ

fossils, where δ 11 B provides a proxy for pCO 2 . The pCO 2 data shows a pCO 2 decrease accompanying the major cooling event of about 4 • C from greenhouse conditions to icecap conditions following the Eocene-Oligocene boundary (33.7 My). During the cooling pCO 2 fell from 1150 to 770 ppmv. The cooling event was followed by a rapid and huge increase in pCO 2 back to 1130 ppmv in the space of 50 000 yr. The large pCO 2 in-10 crease was accompanied by a small deep-ocean temperature increase estimated as 0.59 ± 0.063 • C. Climate sensitivity estimated from the latter is 1.1 ± 0.4 • C (66 % confidence) compared with the IPCC central value of 3 • C. The post Eocene-Oligocene transition (33.4 Ma) value of 1.1 • C obtained here is lower than those published from Holocene and Pleistocene glaciation-related temperature data (800 Kya to present) but 15 is of similar order to sensitivity estimates published from satellite observations of tropospheric and sea-surface temperature variations. The value of 1.1 • C is grossly different from estimates up to 9 • C published from paleo-temperature studies of Pliocene (3 to 4 Mya) age sediments. The range of apparent climate sensitivity values available from paleo-temperature data suggests that either feedback mechanisms vary widely 20 for the different measurement conditions, or additional factors beyond currently used feedbacks are affecting global temperature-CO 2 relationships.

Introduction
Estimation of climate sensitivity to greenhouse gas concentration from the geological past is a useful tool which assists in the assessment of the risks of future climate 25 change associated with current anthropogenic emissions of greenhouse gases. For 4924 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | geological records the available data is largely restricted to CO 2 since other greenhouse gases are not embedded in the geological record with sufficient clarity. The task of separating influences of tectonic change (affecting mountain building and oceanic pathways) is increasingly difficult as one searches for suitable data sets further back in time. That separation is easier when a change in atmospheric CO 2 concentration 5 can be shown to occur in a (geologically) short period of time since this gives opportunity to observe the impulse response of temperature change associated with a rapid atmospheric CO 2 change. A coincidence of paleo-temperature and CO 2 variations in the geological record does not necessarily prove cause and effect, and unquestionably the relationship will be multifactorial, however any observed relationship does provide 10 some bounds on possible models for the relationship. In this paper we consider an event in the early Oligocene (from 33.2 to 33.5 Ma) following the Eocene-Oligocene transition (EOT) where a high resolution deep ocean temperature record is combined with estimates of atmospheric CO 2 to give such an impulse response. before, during and after the temperature change associated with the CO 2 pulse shown in Fig. 4 Using the relationship between isotopic partition between carbonate and water, as a function of temperature T water , as established by Shackleton (1974) and approximated by Duplessey (2002), which gives for the deep ocean at hole 744 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | assuming constant polar ice volume and consequent constant δ 18 O water . Variations in δ 18 O water are known to account for in excess of 50 % of δ 18 O CO 3 in variation in deep Pleistocene glaciations (de Boer, 2010) and are estimated to account for 30 % of the δ 18 O CO 3 change across the EOT (ZQS). For the small variations in temperature and ice volume associated with the pCO 2 pulse post EOT, the 30 % figure can be considered 5 an upper limit. If the 30 % figure were to be applied, then the ∆T water estimate in Eq. (2) reduces by a factor 0.7. The relationship between deep-ocean temperature and mean global temperature is not documented in Oligocene geological records but guidance from sediment and icecore records from Pleistocene glaciation gives a guide. While tectonic changes and 10 associated gross ocean current changes are expected to influence such relationships over geologic time, the fact that the separation of the South America and Antarctica land masses had occurred prior to the post-EOT time under discussion is important. The opening up of the ocean permitting a circum-polar ocean current, and the geologically very short duration of the time under discussion, mean that the likelihood of where S 1 is in the range 1.0 to 0.7 (ice volume correction), and S 2 is in the range 1.0 to 1.5 (ratio of deep ocean to global temperature variation for inter-glacial times).

An estimate of a pulse of atmospheric pCO 2
We use estimates of atmospheric CO 2 concentration (pCO 2 ) from Pearson et al. (2009, 5 referred to hereafter as PFW) obtained by study of δ 11 B isotopes in upper-ocean planktonic foraminifera preserved in the Kilwa formation of coastal Tanzania. Figure 4 and Table 1 show pCO 2 values computed as an average of two low and two high values of pCO 2 in the PFW data set. Uncertainty of the average values and the difference are computed using 1-sigma uncertainties (being half the 2-sigma uncertainties provided 10 by PFW). Thus we have from a baseline of 774 ppmv. It is obvious that there is some discrepancy in timing between the time segments for 15 the δ 18 O and the pCO 2 data. The relationship between temperature and pCO 2 is in this example is discussed quantitatively by PFW who used results of Merico et al. (2008) to conclude that the pCO 2 increase and decrease following the EOT are consistent with carbon-cycle models, apart from a discrepancy that the models predict the pCO 2 rebound to occur over 500 000 yr whereas the observations indicate the rebound oc-20 curred over 50 000 yr.
For the purposes of this study we take the empirical view that the pCO 2 pulse occurred, and associated with the pulse there was a measureable deep-ocean temperature shift. We therefore use the two parameters to place some limits on climate 4928 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | sensitivity (CS) at the time. The imperfect synchronization of the start of the temperature increase and the start of the pCO 2 rebound adds to uncertainties, but a value for CS near the EOT is a useful addition to paleo-climate records.
This estimate hereafter called CS EOT is also subject to systematic errors associated with the uncertainty of scale-factors S 1 and S 2 noted at Eq. (4).

Significance relative to other recent estimates of climate sensitivity 10
It is reasonable to classify values of CS obtained from paleo-temperature data as being for equilibrium climate sensitivity, incorporating both fast and slow feedbacks, whereas values obtained from satellite or historical meteorological data represent transient climate sensitivity, incorporating fast feedbacks only. Lunt et al. (2010), Rohling et al. (2012) and Hansen and Sato (2012) provide discussions on the differences. 15 CS for a "no-feedback model" can be computed for an earth with atmosphere exhibiting infra-red absorption by CO 2 but no additional feedbacks associated with watervapor, clouds and aerosols. The value is given as about 1 • C (e.g. Lindzen and Choi, 2011) or 1.2 • C (Hansen and Sato, 2012).
The value for CS EOT obtained here is compared in Table 2 with values published 20 from other methodologies. The value obtained is similar to values for a "no-feedback model", and is comparable with CS obtained from satellite data (Douglas and Christy, 2009;Lindzen and Choi, 2011) and is placed at or below the low end of ranges of CS 4929 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | obtained from meteorological data by Annan and Hargreaves (2011), Lewis (2012), andGillett et al. (2012). It is significantly below the ranges given by the IPCC (Solomon et al., 2007) and Forest et al. (2006). Among values obtained for CS from Pleistocene and Holocene paleo-temperature data, CS EOT is at or below the low end obtained by Chylek and Lohmann (2008), Kohler 5 et al. (2010) and Schmittner et al. (2011). It is significantly below values presented by Lea (2004), Rohling et al. (2012) and Hansen and Sato (2012). Values of CS obtained from Pliocene paleo-temperature data (Pagani et al., 2010;Dowsett et al., 2012), shown in Table 2, are much higher than CS EOT by a factor 6 to 8. There is a quite fundamental difference in the nature of the experimental system the event as having a temperature increase of 5 to 9 • C over a few thousand years, accompanied by the release of about 3000 Pg of carbon into the atmosphere, producing a pCO 2 increase from about 1000 ppmv to 1700 ppmv. The large temperature change is a factor 2 to 5 times that which might be predicted using the IPCC CS, and Zeebe et al. (2009) conclude that feedbacks and/or forcings other than atmospheric 20 CO 2 caused a major portion of the PETM warming. The post EOT CO 2 pulse discussed in this paper is likewise very large (about 50 % of the magnitude of the PETM pulse), but is accompanied by a warming only about a factor 0.3 of that expected from the IPCC central value of CS. This suggests the feedbacks and forcings for the two events are very different.

Conclusions
The very wide range of values of CS obtained for CS for different groupings of paleotemperature data, for meteorological data, and for satellite data suggest either a widely varying feedback conditions for the different observational data sets, or the existence of additional factors beyond currently used feedbacks affecting global temperature.