A perspective on model-data surface temperature comparison at the Last Glacial Maximum

Quaternary Science Reviews 107 (2015) 1e10

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Invited review

A perspective on model-data surface temperature comparison at the Last Glacial Maximum J.D. Annan*, 1, J.C. Hargreaves 1 RIGC/JAMSTEC, Yokohama, 236-0001, Japan

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 November 2013 Received in revised form 24 September 2014 Accepted 26 September 2014 Available online

We review progress in model and proxy-based reconstruction of the surface temperature field of the Last Glacial Maximum. Both approaches have converged towards a climate state substantially colder than the present day, with the temperature anomaly field showing strong polar amplification and land-sea contrast. The magnitudes of the large-scale changes are increasingly well-constrained, with a recent model-data synthesis generating a value of 4  C, which suggests a moderate equilibrium climate sensitivity of about 2.5  C. However, significant areas of uncertainty remain, particularly in the tropical sea surface temperature change. At finer sub-continental spatial scales, there is limited agreement between models and data regarding the patterns of change. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Last Glacial Maximum Climate model Proxy reconstruction

1. Introduction The Last Glacial Maximum (LGM, 19e23 ka BP (Mix et al., 2001)) represents the most recent interval when the global climate was remarkably different to the present, and therefore it provides us with both a compelling opportunity, and also a challenge, in understanding the climate system. One fundamental challenge has been to address the “100,000 year problem” (that is, the large quasi-periodic change in global climate that is evident at the 100,000 year time scale, despite the absence of any major external forcing at that time scale), which has been a key question in understanding the behaviour of the Earth's climate system ever since the development of Milankovitch Theory (Hays et al., 1976). However, transient simulations over such long duration are generally beyond the reach of state of the art climate models, and therefore one common modelling approach has been to simulate “snapshots”, such as the LGM interval, when the climate system can be considered in quasi-equilibrium over the millennial time scale. Simulating the climate of the LGM climate also has value beyond contributing to our understanding of the ice age cycles. The same models can be used for paleoclimate simulations as are used for running projections of future climate change, and the changes in climate at the LGM are comparable in magnitude d although

* Corresponding author. E-mail address: [email protected] (J.D. Annan). 1 Now at: blueskiesresearch.org.uk. http://dx.doi.org/10.1016/j.quascirev.2014.09.019 0277-3791/© 2014 Elsevier Ltd. All rights reserved.

opposite in direction d to changes that are expected over the coming century. Therefore paleoclimate simulations, when assessed against proxy data which are reasonably plentiful in that time interval, are potentially a powerful tool for assessing the performance of climate models. Additionally, the persistence of a cold near-equilibrium climate state over thousands of years has meant that this interval has also been frequently used for estimation of the equilibrium climate sensitivity, that is, the warming caused by a radiative forcing equivalent to a doubling of the atmospheric concentration of CO2, although (as we discuss in Section 3.3) this approach is not without its limitations. We firstly present a chronological overview of the progress made in both modelling and proxy-based reconstruction of the surface temperature changes at the LGM. Then, we consider in more depth some of the major areas of debate, before summing up with conclusions and prospects for future research. 2. Historical review 2.1. CLIMAP The “Climate: Long range Investigation, Mapping, and Prediction” (CLIMAP) project (CLIMAP Project Members, 1976) compiled proxy data for the time interval 18±2 ka BP, this being the estimated date of the LGM according to the carbon-14 dating methods of the time. This analysis focussed primarily on a sea surface temperature (SST) reconstruction based on planktonic assemblages in sediment cores. According to this analysis, the mean SST cooling in August was estimated to be 2.3  C, and there were even substantial areas

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where warming was indicated, especially in the Pacific low latitudes. The CLIMAP analysis was subsequently updated (CLIMAP Project Members, 1981, 1984) and maps of the final reconstructions for February and August are shown in Figs. 1 and 2 respectively. These data suggest a modest cooling of only 0.8  C on average across the tropics (there meaning 20 S e 20 N). The temperature in the tropical ocean has remained a subject of much debate, and we discuss this in more detail in Section 3.2. Using these data combined with evidence from ice cores, Hoffert and Covey (1992) estimated the global annual mean surface air temperature anomaly at the LGM to be 3±6  C.

2.2. Early model runs The forerunners of today's state of the art climate models were general circulation models of the atmosphere (AGCM) (eg Manabe et al., 1965). It was not long until those models were being used to make predictions of temperature change caused by increasing CO2 in the atmosphere (Manabe, 1968). One of the first global simulations of the LGM using such a model was performed by Williams et al. (1974), who assembled land and ocean boundary conditions from a variety of sources, and investigated the resulting equatorwards shift in storm tracks. Gates (1976) used CLIMAP boundary conditions for the land and ocean, and obtained a global mean surface air temperature (SAT) cooling of 4.9  C for the month of July. In perhaps the first attempt to directly link the LGM state to the equilibrium climate sensitivity, Hansen et al. (1984) simulated the LGM using CLIMAP boundary conditions and an AGCM, obtaining a global mean cooling of 3.6  C, and from this (and other analysis) generated an estimate for the equilibrium climate sensitivity of 2.5e5  C. Manabe and Broccoli (1985) took this idea a step further and tested two versions of an AGCM coupled to a simple slab ocean model. The two models, which had substantially different equilibrium climate sensitivities (2.3  C and 4  C respectively), also exhibited significantly different responses to the LGM boundary conditions. However, uncertainties in the LGM data prevented the authors from making any confident statement regarding which model (and therefore, sensitivity) was closer to reality. Webb et al.

(1997) subsequently pointed to the importance of horizontal heat transport, which Manabe and Broccoli (1985) had excluded, in enhancing cooling, particularly in the tropics.

2.3. The PMIP(1) era The Paleoclimate Modeling Intercomparison Project (PMIP, hereafter PMIP1) grew from a 1991 NATO Advanced Workshop, with the general goal of increasing cooperation and coordination in model-data comparisons for paleoclimate research. For the first phase of the project, the aim was to “evaluate models under paleoclimate conditions and improve our understanding of past climates” (Joussaume and Taylor, 2000). Experimental protocols were developed for modelling the mid-Holocene (6 ka BP) and the LGM, which by then had been re-calibrated to 21 ka BP. For the LGM, two options were included: using either an atmosphere-only general circulation model (AGCM) forced by SSTs from CLIMAP, or an atmospheric model coupled to a slab ocean (ASGCM). For the latter, the model calculates the SSTs prognostically, with the spatiotemporal pattern of the annual cycle of atmosphere-ocean heat flux calculated according to a modern “control” simulation with fixed (observed) SSTs. This standard approach relies on the assumption that the true heat flux (and therefore ocean heat transport) does not change significantly between these climate states. The continental ice sheets for these simulations were defined by Peltier (1994). The total number of groups participating in PMIP1 was 18, although there was no obligation for each group to complete all of the prescribed integrations. In total, 18 LGM simulations were completed, consisting of 9 AGCMs and 9 ASGCMs from 11 modelling groups. All models produced a significant cooling for the LGM climate. Globally, annual mean temperature changes for the AGCMs were all about 4  C (Joussaume and Taylor, 2000) and those for the ASGCMs varied between 1.8 and 5.4  C (Pinot et al., 1999). The cooling was found to be stronger in the Northern hemisphere especially over and near the land ice sheets, and also stronger over land than ocean. Since the AGCMs were forced by the CLIMAP SST field, the surface temperatures in the different models here were tightly

Fig. 1. The CLIMAP February sea surface temperature reconstruction, together with MARGO data points for the JanuaryeFebruaryeMarch season.

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Fig. 2. The CLIMAP August sea surface temperature reconstruction, together with MARGO data points for the JulyeAugusteSeptember season.

constrained over the open ocean and could only vary over the land surface (and above sea ice). Further syntheses of proxy data over land, such as tropical land temperatures (Farrera et al., 1999) pollen and plant macro fossil spectra for Europe (Peyron et al., 1998; Tarasov et al., 1999) enabled a more detailed analysis of model performance here. A major conclusion from PMIP1 (confirming an earlier suggestion made by Hansen et al. (1984) and evidence from newer proxy analyses such as Guilderson et al. (1994)) was that forcing the climate with CLIMAP SSTs resulted in land surface temperatures that were generally too warm, inconsistent with evidence from the proxy data that was available for the tropical land surface. On the other hand, the less directly constrained ASGCM results generated a wider range of results, which was considered to be more consistent with the data (Pinot et al., 1999; Joussaume and Taylor, 2000).
, Newer alkenone data from the TEMPUS dataset (Rosell-Mele 1998) also challenged the mild tropical SST estimates from CLIMAP. It is worth remarking that these assessments were based on a comparison of regional averages from the models to sparse pointwise observations of proxy data, with fewer than 5 data points in 5 of the 8 regions inspected (Pinot et al., 1999). Thus, the robustness of the conclusions is not assured. There were further common differences between the ASGCM results and CLIMAP/AGCM results: in the ASGCM simulations, the tropics were cooler and CLIMAP's warm pool in the tropical Pacific was not evident; there was also a greater inter-hemispheric difference in temperature response. Over much of Eurasia both the AGCMs and ASGCMs were found to be broadly consistent with available data (Joussaume and Taylor, 2000; Kageyama et al., 2001). The exception was Western Europe where both types of models failed to produce sufficient cooling in winter, resulting in an underestimate of the meridional temperature gradient between Europe and Africa. Outstanding issues identified in PMIP1 were the influence of vegetation, not just in terms of albedo and evapotranspiration, but also in affecting the amount of dust in the atmosphere, which was now thought to be a potentially large forcing on the climate (Harrison, 2000). In addition, EMIC simulations with coupled ocean models pointed to the possibility of substantial changes in ocean circulation (Ganopolski et al., 1998; Weaver et al., 1998), which

might violate the underlying assumption of fixed ocean heat transport made in ASGCM simulations. 2.4. Coupled model runs and PMIP2 By the turn of the century, fully coupled atmosphere-ocean models (AOGCMs) were increasingly widespread. Some researchers were starting to run LGM simulations with these models, and had found that changes in ocean circulation had resulted in some significant regional effects (Kitoh et al., 2001; Hewitt et al., 2003). Thus, PMIP2 invited participation by fully coupled atmosphere-ocean models, some of which also included dynamic vegetation (AOVGCM). For models without dynamic vegetation, the pre-industrial control vegetation field was used for the LGM. The experimental protocol for the LGM was updated from the previous PMIP experiments, but the changes were generally minor. The ice sheet was updated to ICE-5G (Peltier, 2004), CO2lowered by 15 ppme185 ppm, and for the first time appropriate CH4 and NO trace gas concentrations were defined (Braconnot et al., 2007a). The effect of dust forcing was not included in the protocol, although there were estimates that this had been quite significant, at around 1 W m 2 in the global mean with substantial regional variability (Mahowald et al., 1999). AOGCMs intrinsically require a longer time to reach climatological equilibrium than AGCMs or ASGCMs due to the slow time scale of the deep ocean. The spin-up time for the PMIP2 LGM simulation was not prescribed, however, and computational costs may have prevented some models from achieving their equilibrium state. The main results from PMIP2 for the LGM temperature field was a narrowing of the ensemble spread compared to the ASGCMs of PMIP phase 1, and a general improvement in consistency with data. The model outputs were observed to have similar spatial patterns, albeit with different magnitudes of changes (Braconnot et al., 2007a). By this time, there had also been many developments in proxy analysis and synthesis. Widespread dissatisfaction over the CLIMAP reconstructions motivated the EPILOG project (Mix et al., 2001) to establish a plan for updating it, and GLAMAP (Sarnthein et al., 2003) focussed particularly on the glacial Atlantic, where ocean core data were most plentiful and uncertainty over possible

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changes in ocean circulation are particularly pertinent. A metaanalysis of many newer proxies estimated the LGM SST anomaly in the tropics to be 2.7±0.5  C (Ballantyne et al., 2005), contrasting strongly with the 0.8  C value of CLIMAP. While the PMIP2 simulations were generally not quite this cold, the discrepancy could partially be accounted for by missing dust forcing (and the absence of vegetation changes in the AOGCMs). The new ice sheet was found to be more consistent with proxy data over Siberia (Kageyama et al., 2006). Interestingly, it was primarily a new analysis of the pollen data for Western Europe, rather than model improvements, which resulted in better agreement for December temperatures (Ramstein et al., 2007). The main influences on the temperature field were found to be snow, sea-ice and land-ice in the cooler Northern Hemisphere, while in the southern hemisphere, the decrease in water vapour and carbon dioxide were thought to be the dominant cause of cooling (Braconnot et al., 2007b). The globally-averaged surface air temperature change between the LGM and pre-industrial climate was estimated to be between 4 and 7  C in the IPCC AR4 (Jansen et al., 2007). This was, perhaps surprisingly, the first time such a clear consensus statement on the LGM temperature anomaly had been presented, and was based primarily on the comparison of the PMIP2 models to a range of regional assessments of proxy data. This estimate was further confirmed by calculations in which simpler intermediate complexity climate models were tuned by varying internal parameters of the models in order to fit regional syntheses of data (eg Schneider von Deimling et al., 2006a; Holden et al., 2009), which found best estimates for the global mean temperature anomaly of 5e6  C. Changes in ocean circulation remained a major uncertainty in the climate of the LGM (Weber et al., 2007), and difficulties in adequately spinning up models to equilibrium, together with dependence on initial conditions (Zhang et al., 2013), may continue to make the resolution of this problem particularly challenging. 2.5. Recent data syntheses Two years after the IPCC AR4 was published, the MARGO Project Members (2009) synthesis of LGM SST was published. This data compilation included 6 different types of proxy over the interval 19e23 ka BP, which although having different geographical distributions and variously representing seasonal or annual temperature signals, were collated and harmonised in a common framework, including for the first time an assessment of uncertainty in the resulting estimates (Kucera et al., 2005). The authors emphasised the robustness of the multiproxy approach in identifying spatial signals such as latitudinal gradients across ocean basins, which are not adequately reproduced in models. The mean tropical SST cooling of 1.5±1.2  C was somewhat greater than was the case in the CLIMAP data set, albeit with an overlapping uncertainty range. The seasonal MARGO data points are presented here in Figs. 1 and 2. There are notable disagreements with the CLIMAP reconstructions at the grid point level, such that the correlation coefficients between the data sets are only 0.1e0.2 in each season. This may be considered rather surprising, given that many of the underlying proxy data points are included in both analyses. An earlier version of these data (Kucera et al., 2005) had already been used in previous years. For example, Kageyama et al. (2006) used some of these data to conclude that the pattern of change in the North Atlantic was not well reproduced in the PMIP2 models. Otto-Bliesner et al. (2009) compared PMIP2 and MARGO SSTs in the latitude band 15 Se15 N, concluding that the average temperature change in the models of 1.0e2.4  C was consistent with the MARGO average of 1.7±1  C. However, they also observed that the spatial variation in the data is not reproduced in the models, even up to the

scale of the PacificeAtlantic interbasin variation. Common biases in the control models' ocean dynamics were thought to be partly responsible for the greater spatial homogeneity in the models. Hargreaves et al. (2011) also found the full MARGO data to be consistent on broad scales with the PMIP2 models. An ongoing difficulty with the quantitative evaluation of model simulations under the auspices of PMIP is that the experimental protocols exclude some negative forcings that are believed to be significant (Jansen et al., 2007), potentially biasing the results. A year after MARGO, a complementary synthesis of surface air temperature (SAT) over land from pollen data was published (Bartlein et al., 2011). These two data sets now together provided much better (though still not truly high density) spatial coverage, allowing a much more detailed examination of model performance. Hargreaves et al. (2013) analysed the skill and reliability of the PMIP2 ensemble in the context of the combined SST and SAT dataset. The results indicated that, including the quoted uncertainties on the data, on broad scales the data sets were consistent with the PMIP2 ensemble. The models were also found to have skill at reproducing the broadest spatial scales such as the land-sea contrast and polar amplification, but (in agreement with the analysis of Otto-Bliesner et al. (2009)) on scales below approximately continental there was poor agreement between the models and the data. The reasons for this disagreement are not yet resolved. While there are likely some problems with both model performance and proxy calibration, a further issue may be whether the proxy-derived data are truly representative of the model variable that is being simulated. Examples of this would be information from a core on land that is not representative of an average over a 2 grid box; information on the ocean that is representative of a deeper level in the ocean rather than the surface; or the dispersion of the model numerics causing a two degree grid-box value to actually be more representative of a larger physical scale. Accounting more fully for the additional uncertainty relating to these representation errors, is an important area for research. A comprehensive data set, augmenting both MARGO Project Members (2009) and (Bartlein et al., 2011) with some additional data including ice cores, was presented by Schmittner et al. (2011) who (en route to estimating the climate sensitivity) fitted an intermediate complexity climate model to these data and thereby estimated the global mean temperature change to be only 3  C, matching the CLIMAP-derived value of Hoffert and Covey (1992). However, the quality of the fit of the model to the data was not great, probably due to the simple and overly diffusive atmosphere of the EMIC that they used. In fact this reconstruction only achieved a correlation of 0.53 to the data, and had a substantial bias over land areas. Annan and Hargreaves (2013) presented an alternative reconstruction which used the same data together with the ensemble of PMIP2 models in a multiple linear regression methodology. The improved fit with a correlation of 0.73 to the data (largely due to the stronger spatial contrasts exhibited by these more sophisticated models) resulted in a global mean temperature anomaly at the LGM of 4.0±0.8  C. However, even this reconstruction still shows less spatial heterogeneity than the proxy data, in particular having a somewhat lower contrast between the land and sea, and failing to represent the mild MARGO tropical Pacific data. Both of these reconstructions are highly reliant on climate models to interpolate between data points. While more purely statistical methods have also been used for ocean temperature reconstructions (Sch€ afer-Neth and Paul, 2004), such approaches would require modification to apply to surface air temperatures due to the unobserved ice sheets. In order to better compare with the CLIMAP seasonal results, and also to investigate the possible influence of different components of the recent proxy syntheses, we present new model-data

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Fig. 3. New JanuaryeFebruaryeMarch sea surface temperature reconstruction, and equivalent MARGO data points.

syntheses of seasonal climate changes in Figs. 3e6. These reconstructions use the approach of Annan and Hargreaves (2013) to generate spatially complete fields from model-generated output fields which are fitted to (and interpolate between) the available data points. The method is essentially a generalisation of pattern scaling in which multiple linear regression is used to calculate scaling factors which are applied to the modelled anomaly fields in order to optimise the fit of their scaled sum to the data. The reader is referred to Annan and Hargreaves (2013) for further details of this method and demonstrations of its performance. In contrast to that previous application (which focussed on annual means), here we use seasonal data, which is somewhat more prevalent in the southern ocean. For MARGO Project Members (2009), the proxy

reconstructions are presented as 3-month means, and from Bartlein et al. (2011) we have the temperature anomaly of the warmest and coldest month. Equivalent data fields were also obtained from the model outputs. The results are in many respects rather similar to the annual reconstructions of Annan and Hargreaves (2013), showing significant polar amplification and land-sea contrast. On a global mean basis, there is less than a degree between the temperature anomalies for the reconstructions of warmest and coldest months, but this conceals large regional differences such as around Antarctica (Gersonde et al., 2005). The model-based reconstructions again fail to reproduce the mild mid-Pacific warming shown in the data, and a new region of disagreement which emerges from the seasonal

Fig. 4. New JulyeAugusteSeptember sea surface temperature reconstruction, and equivalent MARGO data points.

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Fig. 5. New reconstruction of surface air temperature change of the coldest month with equivalent points from Bartlein et al.

comparison is that the model-based reconstruction also does not represent the increase in maximum temperatures robustly exhibited in the data across Africa. Whether this is a genuine climatic feature that the models fail to represent due to errors in construction or boundary conditions, or perhaps a bias in proxy calibration due to other environmental factors, is unclear. It must be recognised that the method used here is constrained to some extent by model results and other more sophisticated methods might generate superior results. We return to the subject of spatial variability in Section 3.1. While the reconstructions do appear to show some regions of relatively fine spatial structure (such as the small warm patches in the high latitude Pacific region), these are in a region where our reconstruction carries high uncertainty, and

thus seem likely to be artefacts of imperfect interpolation and model biases. 2.6. PMIP3 The third phase of PMIP was organised to co-ordinate with the CMIP5 project (Taylor et al., 2012). The remit of PMIP3 is considerably larger than that of the previous two phases. The LGM and mid-Holocene, the core of the previous phases of PMIP, were now also included within the “Tier 1” set of runs for CMIP5. This was a very constructive step forwards in encouraging wide participation from climate modelling groups, and also ensured that the models used for paleoclimate simulations were identical to those used for

Fig. 6. New surface air temperature change of the warmest month with equivalent points from Bartlein et al.

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future projections. This enables the paleoclimate results to inform more directly on the realism of the models, and potentially be combined with data to further constrain future climate predictions. Around 15 modelling groups have announced their plans to submit these integrations. However, at the time of writing, the available ensemble is around half this value, similar to that obtained by PMIP2. In terms of the models themselves, the CMIP5/PMIP3 ensemble is expected to contain a greater proportion of models with a coupled carbon cycle. Analysis of the outputs of 7 models by Harrison et al. (2013) concluded that the PMIP3 ensemble is not readily distinguishable from that for PMIP2, having a similar range of results and similar strengths and weaknesses. As before, the signals are compatible with the observations on the broadest scales but there is little agreement between models and data on fine scales. 3. Ongoing debates 3.1. Spatial patterns A consistent theme from the above research is that models successfully simulate the climate of the LGM on the widest scales, not just qualitatively but even to a quantitatively reasonable degree. There is some debate as to whether the polar amplification in the models may be a little too low, at least in some regions (Braconnot et al., 2012) and the land-sea contrast also appears greater in the data (Annan and Hargreaves, 2013; Harrison et al., 2013) d although this may relate in part to biases in some of the proxy interpretations. More concerning perhaps, is that the models fail to represent the patterns of temperature at higher spatial scales. It has long been known that models perform rather worse at higher spatial scales (Grotch and MacCracken, 1991). Various relatively sophisticated methods have been applied to investigate this question, more usually in relation to modern climate (Sakaguchi et al., 2012) (where data are relatively precise) and occasionally the mid-Holocene, where the large-scale externally-forced climate signal is modest (Guiot et al., 1999; Brewer et al., 2007). For the LGM, the relative success at reproducing the large-scale signal is already a significant success, but once these robust features are accounted for, there is relatively little indication that the models can reproduce the finer scales of response. One example from our new seasonal reconstruction presented here is the lack of warmth in Africa, which is shown across a wide area by proxy data. Attempts to represent high resolution features not resolved in current O (100 km) climate models, by statistical (Levavasseur et al., 2011) or dynamical (Strandberg et al., 2011) downscaling, or even by the use of high resolution global modelling (Ballarotta et al., 2013), have not lead to any clear improvements in model-data comparisons. A major caveat here must be that proxy-based reconstructions have substantial uncertainties. On this point, it must be noted that different syntheses of proxy data have generated rather different results, even over scales as large as the tropical Pacific. There is continuing uncertainty over the correct interpretation of some proxies, such as the depth in the ocean that they best represent (Telford et al., 2013) which may impact on biases in estimated temperature anomalies. Such patterns that have been reconstructed, have therefore sometimes turned out to be illusory when proxies have been reinterpreted or updated. Many examples of this can be seen in Figs.1 and 2, where there is little correspondence between the patterns exhibited by the MARGO and CLIMAP data sets, especially in the Pacific. While of course high spatial variability may have existed at the LGM, we can have therefore have little confidence in our ability to reconstruct and understand them at this time. This limited performance at even continental scale must also remain a concern insofar as models are used for this purpose in future projections.

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3.2. The tropical controversy Perhaps the biggest area of debate concerning the LGM climate has been concerning the temperature in the tropical ocean. In the CLIMAP Project Members (1981) assessment, the mean tropical SST was estimated to be only 0.8  C cooler than the modern ocean. However, there had already been considerable debate over this reconstruction, with for example Rind and Peteet (1985) arguing that CLIMAP was implausibly warm in comparison to estimates of snowline depression over land, and found better overall agreement with an additional cooling of about 2  C (changing the global mean cooling from 3.6  C to 5e6  C). Dong and Valdes (1998) also compared computed vs prescribed SSTs, and found that the former resulted in lower tropical SSTs but also less sea ice. Nevertheless, the PMIP experiment used the 1981 CLIMAP reconstruction for the fixed SST simulations using AGCMs. They also found that these simulations failed to match pollen-based estimates of SAT over land, and also that slab ocean models (which simulated greater cooling) were more consistent with both the pollen data and new estimates of ocean SST based on alkenone
, 1998). As a result of data from the TEMPUS dataset (Rosell-Mele this, Houghton et al. (2001, Chapter 8) concluded that “CLIMAP SSTs tend to be relatively too warm in the tropics” (see also Pinot et al. (1999)). PMIP2 simulations, which by this time used for the most part fully coupled AOGCMs, generated similar results, which were in reasonable agreement with the data. Crowley (2000) reviewed the evidence for tropical temperatures in some detail, and concluded that while CLIMAP was indeed probably too mild, the most extreme estimates of cooling were also unrealistic, with the likely value lying in between. Ballantyne et al. (2005) used a Bayesian methodology to combine a wide range of proxies and estimated an SST temperature change for the tropics at the LGM of 2.7±0.5  C. The MARGO Project Members (2009) analysis has reverted to a milder tropical state with a mean cooling of around 1.6  C, which is very much at the lower limit of model simulations (suggesting that the models may be somewhat over-sensitive). But there are still contrasting results arising particularly from Mg/Ca ratios Lea et al. (2000); Linsley et al. (2010), suggesting greater cooling of up to about 3  C, although this may in any case be a somewhat regional result focussing on the west Pacific warm pool. However, it is encouraging to note that, while this discrepancy remains troublesome, the range of reconstructed temperatures is rather lower than was the case previously. Thus, while this range still represents a factor of perhaps up to around 2, this is now comparable in scale to the 2e4.5  C range frequently presented for the equilibrium climate sensitivity. 3.3. Climate sensitivity One major reason for the interest in the climate of the LGM d though certainly not the only one d is the hope that it might also provide insight into the response of the climate to external forcing in the future. This is commonly summarised by the concept of (equilibrium) climate sensitivity, expressed as the long-term change in temperature in response to a doubling of the atmospheric CO2concentration (roughly 3.7 Wm 2). While it is doubtful that the full earth system is ever truly in equilibrium, the atmosphere-ocean system can be considered to be close to this condition over the millennial time scale associated with the LGM state (since a sustained and significant radiative imbalance over this long a time interval would result in major changes in temperature and/or ice volume). The stability of the climate system at that time, together with the reasonably well-known temperature anomaly and radiative forcing, suggests that the LGM may be a

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particularly useful interval to constrain the possibility of a very high equilibrium climate sensitivity (Annan and Hargreaves, 2006). Simple calculations in which the global temperature anomaly at the LGM is divided by the total estimated forcing relative to the preindustrial state have long been used to generate estimates of the equilibrium climate sensitivity. These estimates have remained close to 3  C throughout changes in estimates of both components (Hansen and Lacis, 1990; Hoffert and Covey, 1992; Annan and Hargreaves, 2006; Rohling et al., 2012). The most modern estimates for the (negative) forcing of 8 W m 2 (Annan and Hargreaves, 2006; Jansen et al., 2007) and temperature anomaly of 4  C (Annan and Hargreaves, 2013) would suggest a figure of just under 2  C, which is at the lower end of the previous range of values. However, there are substantial uncertainties and perhaps biases associated with this approach. It is not expected that the response of the climate system to large negative and positive forcings will be perfectly linear, even at the global scale. In fact, model simulations show significant (and model-dependent) nonlinearity (Hargreaves et al., 2007). Moreover, the response to different forcings is not linearly additive. Thus, the climatic effect of large ice sheets, when combined with a reduction in greenhouse gas concentrations, is not equal to that of the same forcing when produced by changes in GHGs alone (Yoshimori et al., 2011). Various researchers have attempted to account for these factors by using climate models to simulate the past and future climates (Hansen et al., 1984; Manabe and Broccoli, 1985). Annan et al. (2005); Schneider von Deimling et al. (2006b); Holden et al. (2009) and Schmittner et al. (2011) all used ensembles of models with a range of parameter values. In all cases, a strong response between the LGM cooling and 2  CO2 warming was found across the ensemble, but the relationship itself was considerably model-dependent. When a range of GCMs was examined, the relationship between past and future was much weaker. Crucifix (2006) found no significant relationship at all across a small ensemble of PMIP2 models, but, in a larger ensemble, Hargreaves et al. (2012) did find a significant relationship between tropical SST at the LGM, and climate sensitivity. When constrained with the proxy-based observation of LGM cooling, this implies an equilibrium sensitivity of around 2.5  C with a 90% confidence interval of about 0.5e4  C. However, this result must be considered somewhat provisional, due to the small ensemble size and the previously mentioned uncertainties in forcings and proxy data. 4. Conclusions Running simulations of the LGM serves a useful purpose in assessing the ability of models to represent climate states both qualitatively and, increasingly, quantitatively. However, recent modelling results suggest that the returns on this activity may be diminishing somewhat, as model performance (as evaluated by model-data comparisons) is only changing marginally, and in fact the largest changes appear to have been due to updated proxy data and their analyses. That is not to say that simulating the LGM with climate models is not useful, as it remains one of the strongest methods available for both model validation and evaluating the large-scale response of the climate system to large forcing perturbations. A larger ensemble of climate model simulations would also help to understand and improve the robustness of the results. However, model performance at the finer spatial scale is both unclear and hard to evaluate. The models show limited agreement even amongst themselves, and there is also very limited correlation with the data. Whether this can be improved by model development, or by increased understanding of the processes influencing the proxy record, remains to be seen. One possible avenue for further work might be in increased efforts for forward modelling of proxy record, which could enable a wide range of influences to be

considered. However, the additional complexity of these models will itself introduce uncertainties and require calibration. The disagreement over tropical temperatures continues to hinder our ability to use the LGM to robustly evaluate the response of climate models to radiative forcing. However, it should be acknowledged that the range of disagreement is now substantially lower than in previous decades. There is increasing interest in the use of paleoclimate data and model simulations to learn about future climate changes (Schmidt et al., 2014), and the Last Glacial Maximum is one of the most powerful intervals in this respect. For this enterprise, a larger ensemble of model simulations would be very helpful in improving confidence in the robustness of the results. Acknowledgements We are particularly grateful to Masa Kageyama and Jean-Yves Peterschmitt for their help with the CLIMAP data, and two reviewers for their helpful comments. This work was supported by the Sousei project of MEXT, Japan. We acknowledge all those involved in producing the PMIP and CMIP multi-model ensembles and also those involved in paleoclimatic data syntheses, without which this work would not exist. We acknowledge the World Climate Research Programmes Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output. For CMIP the US Department of Energys Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. References Annan, J.D., Hargreaves, J.C., 2006. Using multiple observationally-based constraints to estimate climate sensitivity. Geophys. Res. Lett. 33, L06704. Annan, J.D., Hargreaves, J.C., 2013. A new global reconstruction of temperature changes at the Last Glacial maximum. Clim. Past 9 (1), 367e376. http:// dx.doi.org/10.5194/cp-9-367-2013. http://www.clim-past.net/9/367/2013/. Annan, J.D., Hargreaves, J.C., Ohgaito, R., Abe-Ouchi, A., Emori, S., 2005. Efficiently constraining climate sensitivity with paleoclimate simulations. Sci. Online Lett. Atmos. 1, 181e184. Ballantyne, A.P., Lavine, M., Crowley, T.J., Liu, J., Baker, P.B., 2005. Meta-analysis of tropical surface temperatures during the Last Glacial Maximum. Geophys. Res. Lett. 32, L05712. http://dx.doi.org/10.1029/2004GL021217. €o €s, K., 2013. Last Glacial Ballarotta, M., Brodeau, L., Brandefelt, J., Lundberg, P., Do Maximum world ocean simulations at eddy-permitting and coarse resolutions: do eddies contribute to a better consistency between models and palaeoproxies? Clim. Past 9 (6), 2669e2686. http://dx.doi.org/10.5194/cp-9-26692013. http://www.clim-past.net/9/2669/2013/. Bartlein, P.J., Harrison, S.P., Brewer, S., Connor, S., Davis, B.A.S., Gajewski, K., Guiot, J., Harrison-Prentice, T.I., Henderson, A., Peyron, O., Prentice, I.C., Scholze, M., Seppa€ a, H., Shuman, B., Sugita, S., Thompson, R.S., Viau, A.E., Williams, J., Wu, H., 2011. Pollen-based continental climate reconstructions at 6 and 21 ka: a global synthesis. Clim. Dyn. 37 (3), 775e802. Braconnot, P., et al., 2007a. Results of PMIP2 coupled simulations of the midHolocene and Last Glacial Maximum, Part 1: experiments and large-scale features. Clim. Past 3 (2), 261e277. Braconnot, P., et al., 2007b. Results of PMIP2 coupled simulations of the MidHolocene and Last Glacial MaximumePart 2: feedbacks with emphasis on the location of the ITCZ and mid-and high latitudes heat budget. Clim. Past 3 (2), 279e296. Braconnot, Pascale, Harrison, Sandy P., Kageyama, Masa, Bartlein, Patrick J., MassonDelmotte, Valerie, Abe-Ouchi, Ayako, Otto-Bliesner, Bette, Zhao, Yan, 2012. Evaluation of climate models using palaeoclimatic data. Nat. Clim. Change 2 (6), 417e424. Brewer, S., Guiot, J., Torre, F., et al., 2007. Mid-Holocene climate change in Europe: a data-model comparison. Clim. Past 3 (3), 499e512. CLIMAP Project Members, 1976. The surface of the ice-age earth. Science 191 (4232), 1131e1137. CLIMAP Project Members, 1981. Seasonal Reconstruction of the Earth's Surface at the Last Glacial Maximum. CLIMAP Project Members, 1984. The Last Interglacial ocean. Quat. Res. 21 (2), 123e224.

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