During the Eocene, the Earth remained in the “greenhouse” state, which had persisted since the early Cretaceous, with polar air temperatures remaining above 0 ∘C for most of the year (Wing and Greenwood, 1993), no permanent polar ice caps, reduced Equator–pole temperature gradients and lower ocean–land temperature contrasts, inferred from fossil and isotope indicators of temperature and environmental conditions. Climate modellers have experienced difficulty in simulating Cretaceous and Palaeogene “equable climates” (Sloan and Barron, 1990; Wing and Greenwood, 1993) with sufficient warming at high latitudes, without overheating the tropics, although Huber and Caballero (2011), hereafter HC11, have demonstrated that with sufficiently high levels of CO2 (as a proxy for all forms of radiative forcing), climate models can generate global air temperature distributions in broad agreement with the proxy temperature measurements.

The onset of the PETM, at approximately 55.9 Ma (Westerhold et al., 2009), is recognised as the boundary between the Palaeocene and Eocene epochs (Aubry et al., 2007), and is characterised by a large CIE, indicating large GHG emissions, accompanied by a sudden rise in global temperature (Kennett and Stott, 1991), extensive extinction and origination of nanoplankton (Gibbs et al., 2006) and widespread ocean anoxia (Dickson et al., 2012). There is some evidence from analysis and modelling of the timing and duration of variations in δ13C and δ18O observed in nanoplankton fossils that some of the GHG emissions were initially in the form of CH4 (Dickens, 2011; Lunt et al., 2011; Thomas et al., 2002), which is rapidly oxidised in the atmosphere to CO2. The PETM is also marked by enhanced precipitation and continental weathering (Carmichael et al., 2016; Chen et al., 2016; Penman, 2016), rapid and sustained surface ocean acidification (Penman et al., 2014; Zachos et al., 2005), and shares many features of the global-scale oceanic anoxic events of the Cretaceous and Jurassic periods (Jenkyns, 2010); see McInerney and Wing (2011) for a review of PETM research.

The duration of the onset phase of the PETM is uncertain. Cui et al. (2011) have suggested that the peak rate of addition of CO2 to the atmosphere was much lower than the present-day rate of anthropogenic GHG emissions, but this is disputed by Sluijs et al. (2012). Zeebe et al. (2016) have estimated that the initial release of carbon at the onset of the PETM lasted at least 4 kyr, at a rate which was little more than 1/10 of the present rate of anthropogenic emissions, so the Earth may already be in a “no-analogue” state, with anthropogenic climate change likely to exceed that of the PETM. However rapid the onset, the greenhouse conditions of the early Eocene, and particularly the PETM, provide an opportunity to apply lessons from the past, with a view to improving predictions of the future (Lunt et al., 2013).

The arrangement of the continents and oceans in the early Eocene was broadly similar to that of the present, with the Earth's land mass divided into the same major continents and with most of the land mass in the Northern Hemisphere. India had not yet collided with the Eurasian continent, and the closure of the Tethys Ocean was not yet complete. Such tectonic movements may have effected some changes to the climate system. In particular, the configuration of ocean gateways strongly influences modes of ocean circulation and hence affects energy transport throughout the climate system (Lunt et al., 2016; Sijp et al., 2014).

PLASIM-GENIE (Holden et al., 2016) is an intermediate complexity atmosphere–ocean global circulation model (AOGCM). We apply the model at a spectral T21 atmospheric resolution, which corresponds to a triangular truncation applied at wave number 21 and a horizontal resolution of 5.625∘, with 10 layers, and a matching ocean grid with 32 depth levels. We apply the calibrated parameter set of Holden et al. (2016). The component modules are as follows.

“Plasim” (Fraedrich, 2012) is built around the 3-D primitive equation atmosphere model PUMA (Fraedrich et al., 2005). The radiation scheme considers two wavelength bands in the short wave and uses the broad band emissivity method for long wave. Fractional cloud cover is diagnosed. Other parameterised processes include large-scale precipitation, cumulus and shallow convection, dry convection and boundary layer heat fluxes.

“Goldstein” is a 3-D frictional-geostrophic ocean model (Edwards and Marsh, 2005; Marsh et al., 2011), dynamically similar to classical GCMs, except that it neglects momentum advection and acceleration. Barotropic flow around the four continental islands (Fig. 1) is derived from linear constraints that arise from integrating the depth-averaged momentum equations.

“Goldsteinseaice” (Edwards and Marsh, 2005) solves for the fraction of the ocean surface covered by ice within a grid cell and for the average sea-ice height. A diagnostic equation is solved for the ice surface temperature. Growth or decay of sea ice depends on the net heat flux into the ice (Hibler III, 1979; Semtner Jr., 1976). Sea-ice dynamics are represented by diffusion and advection by surface currents.

“Ents” (Williamson et al., 2006) models vegetative and soil carbon densities, assuming a single plant functional type. Photosynthesis depends upon temperature (with a double-peaked response representing boreal and tropical forest), atmospheric CO2 concentration and soil moisture availability. Self-shading is parameterised. Land surface albedo, moisture bucket capacity and surface roughness are parameterised in terms of the simulated carbon pool densities.

The computational efficiency of PLASIM-GENIE is achieved mainly through low spatial resolution (∼ 5∘) and, relative- to high-complexity Earth system models, simplifying assumptions in physical processes. These include, for instance, simplified parameterisations of radiative transport and convection in the atmosphere, the neglect of momentum transport in the ocean and the representation of all vegetation as a single plant functional type. Climate sensitivity, the response of the climate to a doubling of atmospheric CO2 concentration, including feedbacks, is an emergent property of the model.

Comparison of the forcing parameters applied in the ensemble with the model output fields can be more efficiently achieved by reducing the dimensionality of the model output while retaining information on key components of the climate system.

Analysis of the model results has focused on variation in surface air temperature and precipitation in both winter and summer in each hemisphere, although it should be noted that our experiment has not been designed such that mean values in our ensemble output represent direct estimates of the Eocene climate mean. In the left column of Fig. 2, median temperatures at each grid cell for the full ensemble are plotted for DJF (Fig. 2a) and for JJA (Fig. 2c), with the standard deviations plotted in the right column column (Fig. 2b and d).

Ranges of median temperatures over land are greater than over the oceans, but TPTD is smaller in both seasons and both hemispheres than simulated in the modern world (see Fig. 2, Holden et al., 2016). It is apparent from the standard deviation field that the tropical–polar temperature difference varies substantially across the ensemble, particularly in northern winter. The temperature distributions are similar to those of the 2240 ppm CO2 simulation of HC11, regarded as their “mid-to-late Eocene” analogue (they consider elevated CO2 as a proxy for all radiative forcing, including uncertain climate sensitivity). The principal difference is in high northern latitude winter temperatures; the Arctic ocean remains above freezing in HC11. We note that the Arctic winter median air temperature is below freezing over both land and sea in the PLASIM-GENIE ensemble (see Fig. 3), and the Arctic does not remain ice free throughout the year in any of the 50 simulations in our study. Tropical temperatures in excess of 35 ∘C were simulated in some cases, as in HC11, which they regarded as their “most troubling result”, although they note observational data are currently insufficient to rule this out. Finally, we note that multi-model ensembles have found significant inter-model differences including, for instance, a 9 ∘C spread in global average temperature under the same CO2 forcing (Lunt et al., 2012). Quantification of model-related uncertainty is beyond the scope of the present study.

Full ensemble distributions of mean latitudinal distributions of annual mean sea surface temperature (SST), with mean latitudinal distributions of maritime and continental surface air temperature in both DJF and JJA, are plotted in Fig. 3, together with ensemble medians and 5 and 95 % percentiles of global annual mean SST and maritime surface air temperature in both DJF and JJA. The greater range of temperatures below rather than above median values reflects our use of a uniform range of CO2 forcing values and the logarithmic response of temperature to increasing CO2 concentration. There is substantial variation of mean temperature across the ensemble, around 20∘ over land, but the temperature offset varies little with latitude outside of polar regions where snow and ice greatly reduce winter temperatures in the colder simulations. The variation in TPTD across the ensemble thus appears to be essentially driven by the strength of snow and ice albedo feedbacks.

Our ensemble distributions of sea and air temperatures are in broad agreement with the values from the Eocene model studies compared by Lunt et al. (2012), hereafter L12, and with the tables of marine and terrestrial proxy data compiled by L12 and HC11, covering the early Eocene, and including some records from the very latest Paleocene but not including the PETM. Our palaeogeography specifically represents the early Eocene, but our range of CO2 and orbital inputs is more representative of the variation in forcing across the whole era. L12 have summarised variations of SST with latitude from their proxy data set, in their Fig. 1, including large error bars representing uncertainty which they attribute to assumptions about seawater chemistry, possible non-analogous behaviour between modern and ancient systems, and uncertainty in calibrations of relationships between proxy data and properties of the palaeoclimate. Our median values of SST are close to the median estimates of SST in L12 at midlatitudes, and well within the uncertainty indicated by error bars at high latitudes.

Median values and standard deviations of precipitation at each grid cell are plotted in Fig. 4. Higher precipitation values and variation are largely confined to the tropics, especially to regions associated with monsoons in the present day: Africa and S. America in DJF, and southeast (S.E.) Asia in JJA.

In Figs. 5 and 6, CO2, obliquity (ε) and precession index (esin⁡ω) are plotted against MAT, northern seasonality, northern winter TPTD and northern summer TPTD (Fig. 5), and southern winter polar OLC, northern winter polar OLC, Asian monsoon index, African monsoon index and the S. American (hereafter referred to as “American”) monsoon index (Fig. 6). Subplots for obliquity and precession index in Figs. 5 and 6 denote the CO2 level on a continuous colour scale. The dominant effect of CO2 on MAT and northern seasonality is apparent in Fig. 5, and it can also be seen that CO2 strongly affects the northern TPTD in the winter, but not in the summer, when the combined influence of obliquity and precession index is discernible, suggesting that temperature proxies with seasonal bias may have a significant orbital imprint. The plot of atmospheric CO2 against northern winter TPTD shows a change in gradient at approximately 1000 ppm CO2 and 32 ∘C. This may be related to the logarithmic dependence of radiative forcing on CO2 concentration, the disappearance of ice above some threshold level and a minimum level of land surface albedo related to maximum vegetation cover. A possible sea-ice-related threshold mechanism influencing both SST and maritime air temperature in high northern latitudes may be observed in Fig. 3, and this is strongly associated with the increase in northern winter TPTD at low CO2 levels. Zeebe et al. (2017) have analysed a high-resolution benthic isotope record covering the late Palaeocene – early Eocene and have concluded that orbitally paced cycles are unlikely to have been driven by high-latitude mechanisms, but our PLASIM-GENIE modelling suggests that while northern TPTD is not orbitally paced in the winter, being controlled by CO2, it is orbitally paced in the summer, by a combination of obliquity and precession.

It can be observed in Fig. 6 that there is strong correlation between CO2 and southern winter polar OLC. The African and Asian monsoon indices are both correlated with the precession index, a well-established feature of Quaternary records (e.g. Cruz et al., 2005). The American monsoon index is fairly strongly correlated with the precession index at high levels of CO2 and negatively correlated with CO2 at low levels of CO2. In each of the other examples, there is no apparent correlation between the simple metric and two of the three forcing factors. We have selected these simple metrics with visible correlations to the forcing parameters for further analysis with the linear modelling and emulation methods. Total effects on the simple metrics have been calculated for each of the forcing parameters, with eccentricity and precession considered separately, rather than combined within the precession index, and are shown in Table 4.

The total effects of CO2 on MAT, northern winter TPTD and southern winter polar OLC, and of precession on both the Asian and African monsoon indices are all very high (> 0.90), and the total effects of obliquity on northern winter polar OLC and northern summer TPTD are both fairly high (> 0.65), providing quantitative confirmation of the correlations visible in Figs. 5 and 6.

Figure 7 shows the relationship between CO2 (plotted on a logarithmic scale) and MAT, with an abrupt change of gradient clearly visible at a CO2 concentration of 1000 ppm. From the two gradients, we derive climate sensitivity values for a doubling of CO2 concentration at CO2 levels below 1000 ppm and at CO2 levels above 1000 ppm, of 4.36 and 2.54 ∘C, respectively. We note that our modelled values of carbon in vegetation in the ENTS module remain low outside of the tropics at low CO2 concentration, but as CO2 concentration increases, land areas at higher latitudes reach maximum values of carbon in vegetation, with all land areas showing no further capacity for increased carbon in vegetation at an atmospheric concentration of ∼ 1000 ppm. The increase in land vegetation cover, with corresponding reduction in albedo, acts as a positive feedback to rising temperature caused by increasing CO2, but this feedback mechanism ceases to operate when all available land is at its maximum vegetation capacity, with a consequent reduction in the climate sensitivity.

For a pre-industrial atmospheric CO2 concentration of 280 ppm, the value of MAT indicated by our results for our early Eocene palaeogeography is 14.0 ∘C. Holden et al. (2016) applied an identically configured PLASIM-GENIE to a modern geography, and their results show that with a pre-industrial CO2 concentration, the model climate sensitivity is 3.8 ∘C, and MAT is 12.9 ∘C.

Our results also indicate values of global MAT for double and 4 times the pre-industrial levels of CO2 of 18.5 and 22.5 ∘C, respectively; both these values are within the ranges of results for land near-surface air temperature in the modelling studies compared by L12 and shown in their Fig. 2b.

Figure 8 shows the first three PCs of surface air temperature in DJF and JJA, with the percentages of temperature variation explained by each PC. Each of these plots illustrates the PC scaled by the standard deviation of the PC scores, thereby reflecting the variability across the ensemble. Note the variable scales for each of the subplots. In both DJF and JJA, PC1 explains over 95 % of the variance, with TPTD clearly visible in both hemispheres in DJF but apparent only in the Southern Hemisphere in JJA. OLC is apparent in the plots of PC1 in both DJF and JJA. OLC is discernible in PC2 for DJF temperature, which explains 2.4 % of variance, but less apparent, at least in the Southern Hemisphere, for JJA temperatures, in which PC2 explains 2.6 % of the variance. For temperature in both DJF and JJA, PC3 explains less than 1 % of the variance, with some indication of TPTD and OLC in DJF, but only of weak OLC at high latitudes in JJA. It is worth noting that even though lower-order PCs explain small percentages of global variances, these PCs are generally associated with specific regions where they are comparably important to the first PC.

In their presentation of the SVD method applied in this study, Holden et al. (2015) investigated the effects of orbital parameters on the Earth's climate in the present day but without including CO2 as a forcing parameter in their ensemble, and found that obliquity had a dominant effect on the PC score of annual average surface air temperature. In our study of the Eocene climate, CO2 is strongly correlated with northern seasonality (Fig. 5), and obliquity is weakly correlated with TPTD in JJA (Fig. 5) and with OLC in DJF (Fig. 6). The first three PCs of precipitation in DJF and JJA are shown in Fig. 9. PC1 explains approximately 55 % of the variance in both seasons, with PC2 and PC3 explaining over 20 and over 5 %, respectively, in both seasons. In both PC2 and PC3, areas of high seasonal contrast appear to correspond to areas which experience monsoons in the modern world.

Correlations between the PC scores of temperature and precipitation are provided in Table 5. The first PC scores of temperature, reflecting a global warming signal, are highly correlated with the first PC scores for precipitation, suggesting that these PCs reflect a strengthening of the hydrological cycle in response to warming. Similar considerations reveal connections between lower-order PC scores, though we note that the second (third) component of DJF temperature is associated with the third (second) component of DJF precipitation. In order to address the drivers of these modes, we first consider the correlation coefficients, r, between forcing factors and the PC scores, shown in Table 6. These demonstrate that for each output there is a mode of variability driven by CO2 and another mode driven by precession, suggesting they reflect global warming (and associated hydrological strength) and precessional forcing of the monsoon system.

There is strong correlation (r2 > 0.5) between CO2 and the first PC scores of temperature in DJF and JJA. There are also strong correlations between precession index and the third PC scores for DJF temperature, and between precession index and the second PC scores for JJA temperature.

CO2 is strongly correlated with the first PC scores of precipitation in both DJF and JJA, and there is a strong relationship between precession index and the second PC scores of precipitation in both DJF and JJA. An increase in the second PC scores for JJA precipitation in the Asian monsoon region (Fig. 9) corresponds to a decrease in the second PC scores for JJA temperature (Fig. 8), and as already noted, the second PC scores for both temperature and precipitation in JJA are strongly correlated to the precession index. This temperature reduction during the Asian monsoon was also observed by Holden et al. (2014) and attributed to a reduction in incoming solar radiation associated with increased cloud cover and surface evaporation.

The relationships between the forcing parameters (with precession expressed as both sinω and cosω) and the simple metrics, and between the forcing parameters and the PC scores of 2-D fields, derived through linear modelling, include first- and second-order terms of forcing factors, together with products of forcing factors. In all cases, most of the main effects are confined to the first-order terms, and in no case does eccentricity have a significant effect independently of either of the precession terms. All significant effects of the precession terms are accompanied by a small effect of eccentricity.

In Fig. 10, we plot the main effects of the forcing parameters on the first three PCs of temperature and precipitation for DJF. Figure 11 shows the main effects of the forcing parameters on the first three PCs of temperature and precipitation plotted for JJA.

In both seasons, PC1 for temperature and precipitation can be almost entirely explained by CO2, reinforcing the earlier conclusion that these describe a connected mode, global warming with associated effects on the hydrological cycle. The main effects also suggest connections between the modes of variability of temperature and precipitation in lower-order components. In both seasons, and apparent in both variables, there is a mode that is driven by precession; we interpret this as a monsoon signal, given precessional forcing and spatial patterns of rainfall that are characteristic of modern monsoons (Figs. 8 and 9). In JJA, this is the second component of both variables. The mode is associated with precipitation variability of ∼ 2.5 mm day-1 and temperature variability of ∼ 3 ∘C, with increased precipitation associated with a surface air cooling (note the negative correlation in Table 3, so that positive change in one field is associated with negative change in the other). In both cases, the local magnitude of variability is comparable to that driven by CO2. In DJF, the precessional signal is again apparent in the second mode of precipitation but the third mode of temperature. This mode is notable in that it drives changes in simulated precipitation over east Africa (5 mm day-1) that exceed CO2-driven variability. The remaining modes are more complex and may not represent a clear mode of variability that can be straightforwardly attributed. For instance, the third-order mode of JJA temperature is driven by an interaction between CO2 and obliquity, but in precipitation can be explained by a combination of precession and CO2.

All of the terms in the linear models derived from the forcing factors and the three monsoon indices are shown in Table 7. The Asian and African models are dominated by precession terms, roughly equally distributed between first-order sin(ω) and the cross product of e and sin(ω), with |sin⁡(ω)| being approximately 5 and 8 times larger than |cos⁡(ω)| for the Asian and African models, respectively. The American model identifies significant influence of CO2, in both the negative first-order and positive second-order terms, with a similar magnitude of influence from combined precession terms, and with |sin⁡(ω)| being approximately 3 times larger than |cos⁡(ω)|. All of the models have small contributions from first or second order, or cross products of ε, and from those terms of e, in addition to significant contributions from esin⁡(ω). The terms in the models clearly reflect the relationships between the three monsoon indices and the two forcing factors, CO2 and esin⁡(ω), shown in Fig. 6.

We apply these linear models as emulators to estimate values of monsoon indices corresponding to the full range of precession (ω), with eccentricity fixed at its high limit of 0.06, low and high values of CO2 (300 and 3000 ppm), and low and high values of obliquity (22.0 and 24.5∘). Precession index (esin⁡ω) and emulated values of the Asian, African and American monsoon indices for all four combinations of high and low CO2 and obliquity are plotted in Figs. 12, 13 and 14, respectively. The elliptical form of each of the plots is controlled by model terms which include cos(ω) and identify seasonal processes in the development of the monsoons. Running each of the emulators with all of the terms in cos(ω) excluded, generates points on a straight line between each apex of the ellipses generated by the full emulator. In each of the 12 plots in Figs. 12–14, ω increases anticlockwise from a value of 0∘ in the centre of the lower arc of the ellipse (with perihelion at the March equinox), through a value of 180∘ in the centre of the upper arc (with perihelion at the September equinox). Relationships between the precession index and the monsoon indices which are visually suggested in Fig. 6 are shown with clear structure in Figs. 12, 13 and 14. In each of the monsoon areas, the highest levels of precipitation occur when perihelion coincides with the summer solstice, in June for the Asian monsoon in the Northern Hemisphere and in December for the African and American monsoons in the Southern Hemisphere. For the Asian and African monsoons, precipitation is increased by high CO2, particularly when perihelion is at the summer solstice, but for the American monsoon, high CO2 decreases precipitation. The plots of the emulated African and American monsoons (Figs. 13 and 14) show the lowest and highest degrees of non-stationarity, respectively, due to the relative magnitude of the cos(ω) terms in the linear models.