The simulations analysed in this study were carried out using the IPSL-CM6A-LR model . IPSL-CM6A-LR is a global climate model (GCM) developed at the Institut Pierre-Simon Laplace (IPSL). It includes three main components: the atmosphere (the general circulation model developed at the Laboratoire de Météorologie Dynamique, LMDZ; ), the ocean and sea ice (Nucleus for European Modelling of the Ocean, NEMO; ) and the land surface (Organising Carbon and Hydrology In Dynamic Ecosystems, ORCHIDEE; ).

The horizontal resolution of the atmospheric model is 144×143 points in longitude and latitude corresponding to a resolution of 2.5∘×1.3∘. There are 79 vertical levels reaching 1.5 Pa at the top of the atmosphere. However, we use global fields interpolated on the 19 standard pressure levels defined for CMIP6 . The ocean model has a resolution of 1∘×1∘ and 75 vertical layers. It includes a representation of sea ice (the Louvain-La-Neuve sea ice model, LIM, ) and geochemistry (the Pelagic Interactions Scheme for Carbon and Ecosystem Studies, PISCES, ). The vegetation model ORCHIDEE uses fractions of 15 different plant functional types. Over ice-free areas, a three-layer explicit snow model is also implemented, whereas over ice sheets and glaciers, the snowpack is represented as a one-layer scheme. Finally, the ORCHIDEE model also includes a carbon cycle representation, which implies that, even though vegetation types are prescribed in each grid box, the seasonal evolution of the leaf area index is computed. The horizontal resolution of ORCHIDEE is the same as that for the atmospheric component.

In this study, we use two simulations run as part of the contribution of the fourth phase of Paleoclimate Modelling Intercomparison Project (PMIP4, ) of the sixth phase of the Coupled Model Intercomparison Project (CMIP6) . The piControl experiment for 1850 CE, described in , is considered our reference simulation and is cited as PI hereafter. The lig127k experiment, hereafter the Last Interglacial (LIG) experiment, is a time-slice experiment corresponding to the 127 ka conditions following the PMIP4 protocol . As mentioned above, atmospheric CO2 and other greenhouse gas (GHG) concentrations are close to their PI values and do not represent the main driver of the LIG climate. The LIG GHG concentrations are provided by Antarctic ice cores (, for CO2; , for CH4; and , for NO2) aligned with the Antarctic Ice Core Chronology 2012 (AICC2012) . The Earth's astronomical parameters are prescribed following . In all simulations, the vernal equinox is fixed to 21 March at noon. Other boundary conditions such as palaeogeography, ice sheet geometry or aerosols are the same as those in the PI simulation (for more details, see ). Forcings and boundary conditions of both simulations are summarised in Table .

The LIG simulation was initialised as the mid-Holocene one . The initial state is the year 1850 (1 January) of the CMIP6 reference pre-industrial simulation with the same model version . The model was first run for 350 years. This initial step constitutes the spin-up period, during which the model reaches a statistical equilibrium under the Last Interglacial forcing. From this spin-up phase, the reference PMIP4-CMIP6 lig127k simulation has been run for 550 years. High-frequency outputs have also been saved over the last 50 years of the simulation for the analyses of extreme events and to provide the boundary conditions for future regional simulations. This reference simulation is called CMIP6.PMIP.IPSL.IPSL-CM6A-LR.lig127k.r1i1p1f1 in the ESGF database.

Because of the combined effects of eccentricity and precession changes, the length of seasons relative to the insolation forcing is different between the LIG and the PI periods. However, both simulations use a fixed present-day calendar to compute online monthly averages, which is aligned with our current definition of seasons in terms of number of days for each month. As a consequence, this adds artificial biases in the analysis due to phase lag in the seasonal cycle, especially in boreal autumn . To prevent such so-called “palaeo-calendar effects”, we have adjusted the LIG monthly outputs with the PaleoCalAdjust algorithm .

The present-day climate simulated by the IPSL-CM6A-LR model has been evaluated in . Compared to the IPSL-CM5 model versions, significant improvements have been made for the turbulence, convection and cloud parameterisations . The adjustment of the subgrid-scale orography parameters has helped to correct a systematic bias in the representation of the Arctic sea ice . On an annual basis, this results in a general reduction of temperature biases from IPSL-CM5A-LR to IPSL-CM6A-LR versions . In the high latitudes of the Northern Hemisphere, the cold bias in surface air temperature has been considerably reduced over the North Atlantic Ocean, as well as the warm bias over northern Canada. However, surface air temperatures are still too low over the Greenland ice sheet, and a warm bias is also simulated in winter over the Arctic. The latter is associated with an underestimation of sea ice extent also found in summer. Despite these biases, the sea ice cover simulated with IPSL-CM6A-LR is in better agreement with satellite data compared to previous model versions.

The coupled model also tends to underestimate deep water formation in the North Atlantic and associated overturning circulation. In the Northern Hemisphere, the northward heat transport is more intense compared to previous model versions but remains weaker than that deduced from the few available direct observations. As the warm Atlantic and Pacific waters entering the Arctic Basin affect the position of the sea ice front, they may be partly responsible for temperature and sea ice biases mentioned above.

To evaluate the ability of IPSL-CM6A-LR to simulate the Last Interglacial climate, we compare the simulated surface temperature changes with the new data synthesis provided by . We use temperature reconstructions representing annual or summer surface conditions (Fig. ).

Marine proxies generally display more heterogeneous LIG–PI changes than model outputs. In summer, the IPSL-CM6A-LR model simulates the surface warming well, but it does not reproduce local cooling in the Labrador and Norwegian seas. This mismatch appears to be a general feature across CMIP5 and CMIP6 models. This has been attributed to uncertainties or simplifications in the specified boundary conditions. Indeed, the PMIP4-CMIP6 protocol consists of setting the ice sheets to their modern configuration and neglects the freshwater inputs to the North Atlantic from ice melting in the LIG simulation. These have been shown to be responsible for local heterogeneities in simulations of the Last Interglacial climate : these freshwater fluxes modulate the strength of the AMOC and thus the inflow of warm Atlantic waters in the Arctic Ocean. Moreover, comparison with sedimentary data suggests that the IPSL-CM6A-LR model simulates too much sea ice in the Labrador Sea . With a larger sea ice cover in this region, air–sea heat exchange is reduced, which also influences the AMOC intensity .

The IPSL-CM6A-LR model and terrestrial data generally agree on the sign of the near-surface temperature anomaly. They often differ on its magnitude, but the amplitude of the reconstructed temperature anomalies is not always consistent for sites close to each other (at the scale of the model's spatial resolution), as is the case in the North Atlantic Ocean in summer. The model does not capture the strong annual warming recorded in the North Greenland Eemian Ice Drilling (NEEM) ice core .

By analysing the reasons for Arctic climate change in our simulations, our aim is also to contribute to understand the mechanisms of these climatic changes and how their representation could be improved to obtain better agreement with the reconstructions. In this study, we consider that the model–data agreement is sufficient to investigate the processes contributing to the Last Interglacial Arctic warming.

The energy budget framework has been developed to identify key dynamical processes contributing to the Arctic amplification from observations and reanalyses or climate models . We estimate the coupled atmosphere–ocean–land–sea ice energy budget of the Arctic during the LIG and the PI periods based on the work of and .

The seasonal cycle of this energy budget computed from model outputs is averaged over the last 200 years of the simulations to smooth out the interannual and decadal variability. We quantify the heat transfer between the surface and the atmosphere, the oceanic and atmospheric heat transport and the heat storage terms over the Arctic region defined as the area between 60 and 90∘ N. A schematic representation of the different contributions involved in the energy budget is displayed in Fig. . All terms are expressed in W m-2.

We consider the energy content of an atmospheric column from the surface to the top (AHC, Eq. ). It can be expressed as the sum of internal (CpaT), kinetic (Ek), latent (Leq) and potential (ϕs) energies. The time derivative of the atmospheric heat content yields the atmospheric heat storage (AHS, Eqs.  and ) which varies with the radiative flux at the top of the atmosphere (FTOA), surface heat flux (FSFC) and the heat transport (AHT). 1AHC=1g∫0psCpaT+Ek+Leq+ϕsdp2AHS=∂∂t1g∫0psCpaT+Ek+Leq+ϕsdp3AHS=FTOA-FSFC+AHT g is the gravitational acceleration (9.81 m s-2), Cpa is the specific heat of the atmosphere at constant pressure (1005.7 J  K-1 kg-1), T is the temperature (in Kelvin), Ek is the kinetic energy computed as u2+v22 (in m2 s-2), Le is the latent heat of evaporation (2.501×106 J kg-1), q is the specific humidity (in kg kg-1, ϕs is the surface geopotential (in m2 s-2), p is the pressure (in Pa), and ps is the surface pressure (in Pa).

The surface flux (FSFC, Eq. ) can be broken down into downwelling shortwave radiation (SWdnSFC), upwelling shortwave radiation (SWupSFC), downwelling longwave radiation (LWdnSFC), upwelling longwave radiation (LWupSFC), latent heat flux (flat) and sensible heat flux (fsens). 4FSFC=SWdnSFC-SWupSFC+LWdnSFC-LWupSFC+flat+fsens Finally, the energy flux at the top of the atmosphere (FTOA) is equal to the difference between upwelling and downwelling radiative fluxes: 5FTOA=SWdnTOA-SWupTOA-LWupTOA. As for the atmosphere, the energy content of the ocean (OHC, Eq. ) is integrated from the surface to the bottom of the oceanic column (Eqs.  and ). 6OHC=ρwCpw∫0zTconsdz 7OHS=ρwCpw∂∂t∫0zTconsdz 8OHS=FSFC×foce-FBOT×fice+OHT foce is the ocean area fraction, fice is the sea ice area fraction, ρw is the seawater density (1035 kg m-3), Cpw is the specific heat of the ocean at constant pressure (J K-1 kg-1), Tcons is the seawater conservative temperature (in Kelvin), and z is the depth (in m). We use the seawater conservative temperature because it better represents the oceanic heat content than the seawater potential temperature . In Eqs. () and (), we use a monthly time step to derive the atmosphere and ocean heat content, respectively.

The sea ice bottom heat flux (FBOT) represents the heat exchange between the ocean and sea ice. It is defined as the difference between the ocean heat flux (FOCE) and the conductive heat flux (FCOND) at the bottom of the sea ice cover (Eq. ). 9FBOT=FOCE-FCOND The sea ice heat content results primarily from heat exchange with the atmosphere and the ocean. The heat flux derived from the sea ice transport (IHT) from regions of ice formation to regions of ice melt is included in the calculation of the sea ice heat storage (IHS, Eq. ). 10IHS=FSFC×fice+FBOT×fice+IHT For terrestrial regions, the energy budget variations are only due to changes in FSFC over the continents. Lateral heat transport divergences are small and can be ignored . Thus, the storage term is equal to the air–land heat exchange.

We choose the same sign convention for all fluxes; i.e. positive fluxes point downward. They act to warm the surface when they are positive except for FBOT, which cools the sea ice when positive.

Ocean, atmosphere and sea ice transport is computed as the residual of the surface heat fluxes, the bottom heat flux and the heat storage term. From Eqs. (), () and (), we can write 11AHT=AHS+FSFC-FTOA12OHT=OHS-FSFC×foce+FBOT13IHT=IHS-FSFC×fice-FBOT. These equations give coherent zonally averaged profiles for the PI simulation with a zero northward atmospheric and oceanic heat transport at the North Pole (Fig. ). To validate this approach, we also compared the mean annual OHT computed as a residual with the OHT computed online by the model (AHT and IHT are not stored in the CMIP6 database). The difference between both methods is around 0.005 PW for the Arctic region, which represents less than 2 % of the model average.

The annual value of storage terms should be zero in the ideal case of an equilibrium climate. This is not the case for both simulations. The PI AHS and OHS are lower than the current observed energy imbalance of 0.5 W m-2 in terms of absolute value . However, the LIG AHS and more specifically the LIG OHS are far above this reference value since they are, respectively, equal to 0.5 and 1.1 W m-2. This “energy excess” may arise from assumptions made for the energy budget computation or from an ocean drift in the LIG simulation. Nevertheless, Fig.  shows that the SST and ocean heat content drifts are small over the last 200 years of the simulations.

We also estimate the energy provided by snowfall (ESF, Eq. ) as defined by : 14ESF=Lf(Tp)Psnow, where Lf(Tp) is the latent heat of fusion (-0.3337×106 J kg-1) and Psnow is the snowfall rate (in kg m-2 s-1).

We obtain an annual snowfall contribution to the atmospheric heat budget of 2.95 W m-2 for the PI period and of 2.66 W m-2 for the LIG period. The LIG–PI anomaly is very small compared to the anomaly of the other fluxes. Thus, we have decided to neglect the snowfall contribution in the rest of this study.

Change in insolation between the LIG and the PI periods leads to an annual Arctic near-surface air temperature anomaly of 0.9 ∘C. This value is in the range of the PMIP4 multi-model mean of 0.82±1.20 ∘C . Furthermore, the IPSL-CM6A-LR model simulates cooler mean annual near-surface air temperatures than the maximum reconstructed value of 2∘ . Indeed, despite the 127 ka period being near the peak warmth, it does not correspond to the warmest period of the Last Interglacial. Moreover, this mismatch can also be partly amplified by the use of prescribed ice sheets and vegetation, which results in ignoring the ice sheet–climate and vegetation–climate feedback .

The surface air temperature anomaly displays substantial seasonal (Fig. ) and spatial variations (Fig. ). During the LIG, winter (DJF) and spring (MAM) seasons are about 0.1 ∘C colder compared to the PI period. Most of this cooling takes place over continents (Fig. a, b). Conversely, over the Arctic Ocean, the surface air temperature anomaly is positive, especially in areas where sea ice concentration decreases (Fig. a, b, e and f). This difference between land and ocean is explained by the larger effective heat capacity of the ocean resulting in a greater amount of energy absorbed and stored by the ocean. However, it should be noted that even if the seasonal averages of the surface air temperature anomalies is similar in winter and spring when averaged over the whole Arctic region, the magnitude of the anomalies is locally higher in winter.

Summer (JJA) and autumn (SON) are warmer during the LIG than during the PI period over both the ocean and the continents. The behaviour of the climatic fields is very different for both seasons. While the maximum warming occurs in summer over continental areas, over the oceanic regions, the largest temperature anomalies are found in autumn. There are also differences in the magnitude of summer and autumn warmings. The temperature anomaly is expected to be especially large in summer when the insolation anomaly is the largest. Indeed, it reaches +3.1 ∘C on average over the Arctic region, but the autumn value is even larger and reaches +4.2 ∘C (Figs.  and c, d).

Surface air temperature anomalies are also associated with variations of snow cover and Arctic sea ice. The strong warming occurring during summer and autumn results in a large retreat of the Arctic sea ice cover that persists during the rest of the year south of Svalbard and in the Barents Sea (Fig. e–h). On the other hand, the snow cover does not appear to respond to the temperature rise in summer (Fig. i–l). The snow cover anomaly is generally very low because the PI snow cover is relatively small during summertime. However, in autumn, the snow cover anomaly is strongly negative. The cooling in DJF and MAM reduces the effects of polar amplification in summer and autumn. Despite the slight decrease in temperature in DJF and MAM, sea ice does not fully recover after its strong decline during the summer and autumn seasons. As a result, compared to the PI simulation, the sea ice area decreases by 0.5×106 km2 in DJF and by 0.3×106 km2 in MAM.

Figure  displays a time lag of 4 months between the maximum of insolation (in June) and the surface air temperature (in October) anomalies. This lag has already been observed in previous studies investigating the future polar amplification . It suggests the existence of processes limiting the summer warming and/or feedback inducing a strong warming in autumn despite the decrease in insolation anomaly. In the following, we investigate the origin of this time lag. To achieve this, we analyse the respective roles of the atmosphere, ocean, sea ice and continental surfaces in summer (Sect. ) and in autumn (Sect. ).

In summer, the positive anomaly of near-surface air temperature reaches 3.1 ∘C over the Arctic and it is associated with a large retreat of the sea ice area of 1.9 million km2 (see Sect. ). As previously mentioned, this warming corresponds to a strong insolation anomaly in the high latitudes of the Northern Hemisphere. It affects the entire atmospheric column with a maximum air temperature anomaly between 600 and 300 hPa reaching more than 5 ∘C (Fig. a). At the top of the atmosphere, downwelling shortwave radiation (SWdnTOA) increases by more than 25 W m-2 on average compared to PI (Fig. ). This energy excess is uniformly distributed between 60 and 90∘ N. Since solar forcing only depends on latitude, it is similar over land and ocean. However, only 25 % of this energy excess is absorbed by the ocean and 50 % by the continents.

Despite a small insolation anomaly (Fig. ), the strongest surface warming occurs in autumn (Fig. d). Figure  shows that the warming does not extend over the entire atmospheric column as in summer but is confined in the lower layers of the atmosphere below 800 hPa.

In autumn, the LIG insolation is similar to the PI one (Fig. ). As a consequence, the shortwave radiation anomalies (SWdnTOA, SWdnSFC and SWupSFC) do not much contribute to the total energy budget anomaly compared to summer (Fig.  compared to Fig. ). By contrast, longwave radiation anomalies play a crucial role in the autumn warming. Larger longwave fluxes are also emitted into the atmosphere because open ocean waters are warmer than the cold sea ice surface. The LWupSFC anomaly is 11 W m-2 on average (Fig. ) and peaks at more than 40 W m-2 over the East Siberian and the Kara seas (Fig. d). Similarly to the summer months, the LWdnSFC anomaly is stronger than the LWupSFC anomaly resulting in a positive longwave radiative budget. The increase in specific humidity over the ocean (Fig. ) is likely related to the large retreat of sea ice cover and associated evaporation (Figs. h and f). In response to increasing humidity in the atmosphere (Fig. ), the Arctic cloud cover expands (Fig. c), leading to a positive cloud feedback over the Arctic Ocean (Fig. b). This longwave cloud radiative effect (LW CRE, computed in a similar way to the SW CRE) favours the autumn warming by trapping outgoing LW radiation in the atmosphere .

The surface air temperature anomaly and the additional heat absorbed by the upper ocean during summer amplify the retreat of the sea ice edge. The autumn months experience the largest sea ice decline with a sea ice area anomaly of -3.5×106 km2 (Fig. h). This reveals large open-water areas which favour heat transfer from ocean to the atmosphere. Figure  indicates that turbulent heat fluxes slightly increase (by 1.9 W m-2 on average over the ocean). However, at the local scale, their contribution is larger (Fig. b and e). In regions where the sea ice loss is the greatest (i.e. along the Siberian and Alaskan coasts and over the Barents and Greenland seas), the sum of sensible and latent heat fluxes reaches more than 20 W m-2 (Fig. h). Over the continental areas, the turbulent heat fluxes anomaly does not seem to have a significant impact on the surface heat budget (Fig. ).

Despite the strong Arctic warming, the atmospheric energy storage (AHS) anomaly is negative, meaning that the atmosphere loses more energy than it does for the PI period. During autumn, the internal energy storage (-4.9 W m-2) and the potential energy storage anomalies (-4.5 W m-2) contribute significantly to the energy loss (Table ). The anomaly of the internal energy storage depends on air temperature fluctuations from one season to the other. As illustrated in Fig. , the air temperature increases from summer to autumn near the surface but peaks in August over the rest of the atmospheric column. The potential energy storage anomaly is also strongly dependent on the temperature in the atmospheric column and follows the same trend as the internal energy storage from summer to autumn.

Moreover, poleward oceanic and atmospheric heat transport weakens (Fig. ). This modulates the warming of the Northern Hemisphere high latitudes and does not contribute to the observed temperature increase.

Processes of the Arctic autumn warming are summarised in Fig. .

In summary, the Arctic region continues to experience the effects of the preceding summer warming through ocean and sea ice feedback during the autumn. Sea ice cover changes allow the ocean to release heat leading to a significant warming of the surface atmospheric layer. As illustrated in Fig. , feedback only operates in the lower atmosphere. first explained such process using a surface heat budget analysis with the LOVECLIM-LLN model, which they called the “summer remnant effect”. This effect modifies the seasonal impact of the astronomical forcing. In the IPSL-CM6A-LR model, it appears during autumn and, to a lesser extent, persists until winter.

Section  and  highlight the key role of Arctic sea ice on the ocean and atmosphere heat balances. In particular, the expansion of sea ice cover determines the amplitude of air–sea exchange through variations of surface albedo and sea ice insulating effect. During the LIG, the sea ice cover is reduced all year round relative to the PI period, reaching a peak of -3.4×106 km2 in autumn (Figs.  and e–h). The sea ice mass decreases too and loses about 0.08 Gt on annual average. To better understand the causes of this decline, we compute the anomalies of the different terms of the mass budget using new diagnostics developed for CMIP6 . These terms are the following: the basal growth, the ice formation in supercooled open water (or frazil), the melting at the top surface and the base of the ice, the ice formation due to the transformation of snow to sea ice, the change in ice mass due to evaporation and sublimation and the ice advection into or outside the Arctic domain. The IPSL-CM6A-LR model outputs do not contain explicit lateral melt. These different processes are represented in Fig.  in summer and autumn for both PI and LIG periods. In summer, the main process responsible for sea ice melt is basal melt during both periods. However, the LIG–PI surface melting anomaly is higher than the LIG–PI basal melting anomaly. Thus, changes in summer sea ice volume are mainly related to changes in incident shortwave radiation rather than changes in ocean–sea ice energy exchange. In autumn, ice melt and growth processes are less strong during the LIG. The large autumn sea ice retreat (Fig. h) is therefore not caused by increasing melt. It is the consequence of the substantial sea ice loss during the previous summer, exacerbated by the poor recovery of sea ice cover in autumn. While show that it is one of the main factors of the mass budget variations, it is worth mentioning that in our study, this process is surprisingly weak (Fig. ).