Plots of the mean summer and winter pre-industrial Arctic sea ice concentrations are shown in Fig. . Across the eight-member ensemble, the multi-model mean annual sea ice extent is 16.17×106 km2 (Table 2), with a winter (FMA) multi-model mean of 20.90×106 km2 and a summer (ASO) multi-model mean of 10.98×106 km2. The individual models' annual means range from 12.27×106 km2 (IPSLCM5A) to 19.85×106 km2 (MIROC4m) (Table ), and monthly multi-model means range from a minimum of 10.01×106 km2 (September) to a maximum of 21.24×106 km2 (March, Fig. ). The lowest individual monthly extent is 7.00×106 km2 (HadCM3, September), with the highest monthly extent produced by MRI-CGCM (March), measuring 27.01×106 km2 (Fig. ).

Figure  reveals the differences in the annual sea ice extent cycles across the ensemble. The sea ice extent amplitudes of NorESM-L and IPSLCM5A are 6.39 and 7.36×106 km2 respectively (Table ). These are the only models in the ensemble with seasonal amplitudes below 10×106 km2. Other models in the ensemble show a much larger seasonal cycle, in particular GISS-E2-R, MIROC4m, and MRI-CGCM, which have sea ice extent amplitudes of 14.03, 14.05, and 15.91×106 km2 respectively (Table 2). The ensemble mean sea ice extent amplitude is 11.18×106 km2.

North of 80∘ N, the multi-model mean annual thickness is 2.97 m, with a winter multi-model mean of 3.29 m and a summer multi-model mean of 2.52 m. Across the ensemble, the annual mean thickness varies from 2.27 m (HadCM3) to 3.81 m (CCSM4). The winter thicknesses range from 2.56 m (NorESM-L) to 4.01 m (CCSM4), with summer between 1.27 m (GISS-E2-R) and 3.60 m (CCSM4). Plots of mean winter and summer pre-industrial Arctic sea ice thicknesses are shown in Fig. .

RMSDs and SPCs for mean annual Arctic sea ice thickness (for ice-covered areas north of 60∘ N) are shown in Fig . MIROC4m has the highest SPC with the ensemble mean (0.93), despite the thickest ice in its simulation being located north of eastern Siberia, opposite the region of thickest ice in many of the models (see Fig. ). It also has the lowest RMSD (0.55 m), marginally lower than COSMOS (0.56 m). MRI-CGCM displays the lowest SPC with the ensemble mean (0.76) and the highest RMSD (1.33 m). The lowest SPC between two models is 0.51 (HadCM3 and MRI-CGCM), which have a RMSD of 1.83 m, the highest of the ensemble. HadCM3 has a thickness spatial pattern which appears by eye very different to other PlioMIP models, with the thickest ice in a wedge bounded approximately by the 70∘ N latitude line and 120∘ W and 150∘ E (see Fig. ). However, it has a greater SPC with the ensemble mean than GISS-E2-R or MRI-CGCM, and the RMSD between the ensemble mean thickness and HadCM3 is lower than GISS-E2-R or MRI-CGCM when compared to the ensemble mean (Fig. ).

In agreement with enhanced greenhouse forcing each model in the ensemble simulates a smaller sea ice extent in the mid-Pliocene simulation in comparison to the pre-industrial (Figs. , ). The multi-model mean annual extent for the mid-Pliocene simulations is 10.84×106 km2, a reduction of 5.33×106 km2 (33.0 %) in comparison to the respective multi-model mean of the pre-industrial simulations. Annual means in the ensemble range from 7.60×106 km2 (NorESM-L), to 15.84×106 km2 (MRI-CGCM) (Table ).

The lowest multi-model monthly mean extent is 3.15×106 km2 (September), and the highest is 16.59×106 km2 (March). In comparison to the pre-industrial simulation, the lowest multi-model monthly mean extent is reduced by 6.86×106 km2 (69 %). The reduction for the highest monthly multi-model mean is 4.65×106 km2 (22 %). The relative change in the lowest extent is therefore over 3 times greater than the relative change in the highest extent.

MRI-CGCM, CCSM4, and MIROC4m simulate the highest maximum mid-Pliocene sea ice extents in the ensemble. Both CCSM4 and MRI-CGCM also provide the highest two minimum extents, but MIROC4m is one of the four models that simulates an ice-free Arctic summer. As a result, the sea ice extent amplitude in MIROC4m in the mid-Pliocene simulations is ≈ 64 % greater than the pre-industrial simulation extent amplitude (Table ). The ensemble mean extent amplitude of the mid-Pliocene simulations is ≈ 20 % greater than the pre-industrial ensemble mean amplitude.

Not all of the models, however, show this trend. Table  lists the seasonal extent amplitudes for each model's PlioMIP simulation, in addition to the mean annual sea ice extent. Three of the eight models (CCSM4, IPSLCM5A, and MRI-CGCM) simulate mid-Pliocene sea ice extent amplitudes which are smaller than the pre-industrial extent amplitudes. For CCSM4 and IPSLCM5A, the differences in extent amplitude between pre-industrial and mid-Pliocene are less than 106 km2, and represent changes of 4.1 and 6.1 % respectively, so there is no substantial change in the annual cycles of both simulations by CCSM4 and IPSLCM5A. The increase in MRI-CGCM on the other hand is larger (2.22×106 km2, or 13.9 %).

In four of the eight models (COSMOS, GISS-E2-R, MIROC4m and NorESM-L) the mid-Pliocene Arctic Ocean is ice-free at some time during the summer (August–September, Fig. ). In contrast to this, CCSM4 and MRI-CGCM simulate minimum sea ice extents of 8.90×106 km2 and 8.26×106 km2 respectively, which both exceed the pre-industrial minimum of HadCM3 (7.00×106 km2), with the CCSM4 minimum also exceeding the NorESM-L pre-industrial minimum (8.34×106 km2). This indicates the large spread in the representation of sea ice extent in the models.

For those models that simulate summer sea ice in the mid-Pliocene, the summer sea ice conditions vary strongly. Summer sea ice in HadCM3 is confined to the Arctic Basin, with concentrations that do not exceed 60 %, and very low concentrations along all ice edges. The summer sea ice margin in MRI-CGCM, on the other hand, extends almost to the southern tip of Greenland, and a large proportion of the sea ice cover is characterised by concentrations greater than 90 % (Fig. ).

Four of the five models with larger mid-Pliocene extent amplitudes simulated ice-free conditions for part of the summer in the mid-Pliocene. The increase in extent amplitude ranges from a 9.4 % increase in COSMOS to a 101.3 % increase in NorESM-L. It might be expected that simulating a seasonally ice-free mid-Pliocene Arctic would lead to a decrease in extent amplitude, as the minimum extent has decreased as low as possible; however, this is not the case. As Fig.  shows, the four models with seasonally ice-free mid-Pliocene simulations have the thinnest pre-industrial summer ice, which disappears in the mid-Pliocene summer, whereas much of the winter sea ice has simply thinned, so there is less of a reduction in extent.

Plots of the mean summer and winter mid-Pliocene Arctic sea ice thicknesses are shown in Fig. . The multi-model mean annual sea ice thickness is 1.30 m, which, compared to the pre-industrial simulations, is a reduction of 1.7 m (56 %). Across the ensemble, the annual mean thicknesses range from 0.44 m (NorESM-L) to 2.56 m (MRI-CGCM). The multi-model winter mean thickness is 1.77 m, 1.5 m (46 %) less than the pre-industrial, whereas the summer multi-model mean thickness drops by 1.8 m (71 %) to 0.74 m. Similar to the sea ice extent, the summer sea ice thickness shows a greater relative decline with respect to pre-industrial than during the winter, although the contrast is not as stark for the thickness. The individual model winter sea ice thicknesses range from 0.79 m (NorESM-L) to 2.78 m (MRI-CGCM), with the summer sea ice thicknesses between 0.3 m (NorESM-L) and 2.24 m (MRI-CGCM).

SPCs and RMSDs between the pre-industrial and mid-Pliocene simulations are shown in Fig. . All but five of the mid-Pliocene RMSDs are lower than the equivalent RMSD for the pre-industrial simulations. This trend is not seen in the SPCs, where just over half (19 out of 36) of the mid-Pliocene correlations are higher than the corresponding pre-industrial correlation. These results show that the differences in thicknesses between the models are lower in the mid-Pliocene simulations, but the differences between thickness patterns are comparable. Lower overall RMSDs are likely to be at least part in due to the increase in the area of ice-free ocean, and lower mean thicknesses in the mid-Pliocene simulations compared to the pre-industrial.

GISS-E2-R has the highest SPC with the ensemble mean (0.90), with NorESM-L the lowest (0.60). NorESM-L has correlations of less than 0.5 with two models, CCSM4 (0.49) and MRI-CGCM (0.27). As with the pre-industrial results, MRI-CGCM has the highest RMSD compared to the ensemble of all the simulations (1.05 m), and the RMSD of 1.46 m between MRI-CGCM and NorESM-L is the highest between any two models. The highest SPC between two models is 0.97, between COSMOS and MIROC4m, which also have the lowest RMSD, at 0.11 m.

Figure  also shows RMSDs and SPCs between each model's pre-industrial and mid-Pliocene runs. All but two models have SPCs exceeding 0.9 between the thicknesses of both simulations, with the exceptions being GISS-E2-R (0.81) and NorESM-L (0.56). The SPC between the ensemble means is 0.79.

The sea ice components of each model differ in resolution, representation of sea ice dynamics and thermodynamics, and formulation of various parameterisations, such as sea ice albedo. The key details of each model's sea ice component are summarised in Table . The models CCSM4 and NorESM-L use the same sea ice component, based on CICE4 , although NorESM-L has a coarser model grid in the atmosphere than CCSM4, and furthermore employs a completely different ocean component (Table ).

The sea ice dynamics of the ensemble members can be categorised into three groups. First, CCSM4, NorESM-L, and MIROC4m, which all use the elastic–viscous–plastic (EVP) rheology of . Second, COSMOS, GISS-E2-R, and IPSLCM5A, which are based on viscous–plastic (VP) rheologies . Third, HadCM3 and MRI-CGCM, which do not consider any type of sea ice rheology, the sea ice following simple free-drift dynamics . In PlioMIP, there does not appear to be any link between the type of dynamics of the sea ice components and the simulated sea ice extents – MRI-CGCM and MIROC4m produce the two highest annual means for pre-industrial whilst having very different sea ice dynamics. The three models that produce the lowest pre-industrial extents, i.e. NorESM-L, IPSLCM5A, and HadCM3, employ different rheologies – EVP, VP, and no rheology respectively.

Most of the models use a leads parameterisation in their sea ice thermodynamics component, with only CCSM4 and NorESM-L employing explicit melt pond schemes. The models HadCM3 and COSMOS both use the leads parameterisation based on . The models HadCM3, MIROC4m and MRI-CGCM all utilise the “zero-layer” model developed by . Similarly to the considered sea ice dynamics, there is no clear influence of the thermodynamics schemes used in the models on the simulated pre-industrial sea ice extent.

The simulation of Arctic sea ice by means of GCMs has been demonstrated to be very sensitive to the parameterisation of sea ice albedo. This has been observed in the case of variations in albedo in different models , and adjusting the parameterisation in one specific model . show that clear-sky albedo is the dominant factor in high-latitude warming in the PlioMIP ensemble. The four models that display the highest warming effect from the clear-sky albedo are those four models that simulate an ice-free mid-Pliocene summer (COSMOS, GISS-E2-R, MIROC4m, and NorESM-L). The NorESM-L shows the largest warming due to clear-sky albedo; CCSM4, on the other hand, shows the smallest clear-sky albedo effect. Both NorESM-L and CCSM4 use the same sea ice component, based on CICE4 . This sea ice model employs a shortwave radiative transfer scheme to internally simulate the sea ice albedo and thus produce a more physically based parameterisation .

However, it appears that the performance of this albedo scheme is very sensitive to differences in other components of the climate models: NorESM-L (which shows a large contribution of clear-sky albedo) uses the same atmosphere component as CCSM4 (low contribution of clear-sky albedo), albeit at a lower resolution version in the PlioMIP experiment, but it employs a different ocean component that also has a lower resolution than the ocean component used in CCSM4. The contrast in the contribution of clear-sky albedo to high-latitude warming between NorESM-L and CCSM4 is reflected in the large difference in their simulations of summer mid-Pliocene sea ice. One cause is certainly the nature of the sea ice–albedo feedback mechanism . Reduced albedo at high latitudes can be both a cause of and a result of a reduced sea ice extent. Models with parameterisations with a lower sea ice albedo minimum therefore have a greater potential to amplify the warming that originates from other sources in simulations of the mid-Pliocene, such as greenhouse gas emissivity. The low sea ice albedo assumed in NorESM-L is a likely explanation for the low sea ice extents it simulates (Figs. , ), both in mid-Pliocene and pre-industrial simulations.

Clear-sky albedo has the highest contribution to high-latitude warming in NorESM-L, with the second highest being in MIROC4m. In MIROC4m there is a fixed albedo of 0.5 for bare sea ice, with higher albedo for snow-covered sea ice that furthermore varies according to ambient surface air temperature . Of the six models that do not use a radiative transfer scheme to internally simulate sea ice albedo (those except NorESM-L and CCSM4), only GISS-E2-R has an albedo minimum lower than 0.5. However, this model allows the albedo to vary between 0.44 and 0.84 . All other models also allow the sea ice albedo to vary, and consequently MIROC4m has a lower overall albedo. This may help to explain the ability of MIROC4m to simulate an ice-free mid-Pliocene summer, despite simulating one of the highest winter sea ice extents for both pre-industrial and mid-Pliocene.

As the parameterisation of sea ice albedo is kept unchanged between pre-industrial and mid-Pliocene simulations, differences in the parameterisation between the models should have similar effects in both simulations. However, if there is a temperature threshold above which the ice–albedo feedback becomes more dominant in some of the models, then this could explain the different influence of the sea ice parameterisation on pre-industrial and mid-Pliocene simulations.

General circulation models are tuned to best reproduce modern-day climate conditions, and parameterisations are based on modern observations . When simulating the climate of time periods with different climate states, such as the mid-Pliocene, models that are tuned towards present-day conditions may be biased in some regions. However, it is disputed to which extent the adjustment of parameters, such as sea ice albedo, within the limits of observational uncertainties can affect the overall sea ice cover and compensate for other shortcomings in the model .

describe the characteristics of Arctic sea ice simulated by the CMIP5 ensemble for the time period from 1979 to 2010 as being related in a “complicated manner” to the simulated future change in September Arctic sea ice extent. Figure  demonstrates, based on correlation values, that some combinations of sea ice characteristics in the pre-industrial and mid-Pliocene simulations are much more strongly related to each other than others. In Sect.  it was highlighted that the differences in the PlioMIP models' simulation of sea ice for 1979–2005 in CMIP5 are not consistent with the differences in pre-industrial or mid-Pliocene simulations in the PlioMIP ensemble.

All of the models that simulate thinner pre-industrial summer sea ice than the ensemble mean also simulate ice-free conditions during the mid-Pliocene summer, with the exception of HadCM3. demonstrate that the thickness of sea ice in control simulations has a stronger influence on the climate state of the Northern Hemisphere polar region in simulations of future climates than sea ice extent. find that those CMIP5 models that predict an earlier disappearance of September Arctic sea ice generally have a smaller initial September sea ice extent. In PlioMIP, mean summer pre-industrial sea ice thicknesses have correlation coefficients of 0.81 and 0.82 with mean summer mid-Pliocene sea ice extents and thicknesses, respectively. Mean summer pre-industrial sea ice extents, on the other hand, show weaker correlations with mean summer mid-Pliocene sea ice extents and thicknesses, with respective correlation coefficients of 0.47 and 0.51. The relatively thin pre-industrial summer sea ice simulated in PlioMIP by COSMOS, GISS-E2-R, MIROC4m, and NorESM-L therefore appears to be an important factor for the ability of those models to simulate an ice-free mid-Pliocene summer. An exception is HadCM3, which simulates perennial sea ice in the mid-Pliocene, despite simulating relatively thin (within the PlioMIP ensemble) pre-industrial sea ice.

In the mid-Pliocene simulations, the correlation coefficient between Arctic surface temperatures and simulated sea ice extent is much higher than the corresponding correlation coefficient in the pre-industrial simulations (Fig. a, b). Pre-industrial sea ice is thicker than mid-Pliocene sea ice, which could explain the lower sensitivity of the pre-industrial sea ice extent to surface temperatures. However, similar differences in correlation strength between the pre-industrial and mid-Pliocene simulations are also seen for mean sea ice volume (Fig. , c,d), so there is no strong relationship between warmer pre-industrial simulations and those with less total ice.

In the pre-industrial simulations, much of the ocean north of 60∘ N is fully covered with sea ice, so all SSTs will be -1.8 ∘C. The uniformity of the SSTs in this region could be a plausible explanation for the weak correlation between the overall Arctic sea ice extents and SSTs north of 60∘ N in the pre-industrial simulations of the PlioMIP ensemble. The reduced sea ice coverage in the mid-Pliocene simulations, particularly during the summer months, enables, on the other hand, a greater range of possible SST values. This is potentially the reason for a much stronger correlation with the simulated mid-Pliocene sea ice extents (Fig. ). In the models, the presence of ice in a grid box, even at low concentrations, restricts the warming in the ocean. Larger parts of the ocean are ice-free for longer periods in the year in the mid-Pliocene simulations than in the pre-industrial simulations, meaning longer periods in the mid-Pliocene simulations where the ocean can warm. This will in turn affect the warming of the atmosphere in the models, and so is a possible reason for better correlation between sea ice extent and surface temperatures in the mid-Pliocene simulations.

In addition to SATs and SSTs, there are of course other atmospheric and oceanic influences on the simulation of Arctic sea ice. The Atlantic meridional overturning circulation (AMOC) contributes significantly to poleward oceanic heat transport and has been shown to have a strong impact on Arctic sea ice (e.g. ). analyse the simulation of the AMOC in both pre-industrial and mid-Pliocene simulations of the PlioMIP ensemble and find that there is little difference between each model's pre-industrial and mid-Pliocene AMOC simulation. There is no consistent change in northward ocean heat transport, with half the models simulating a slight (less than 10 %) increase and half simulating a slight decrease (less than -15 %). Of the models which simulate increased northward ocean heat transport (COSMOS, GISS-E2-R, IPSLCM5A, and MRI-CGCM), only two (COSMOS and GISS-E2-R) simulate an ice-free mid-Pliocene summer. This suggests that the influence of AMOC and northward oceanic heat transport on the ensemble variability in sea ice in the mid-Pliocene simulation of PlioMIP is not the most important factor.

An analysis of multi-decadal variability influence on Arctic sea ice extent in selected CMIP3 simulations (covering 1953–2010) by showed a significant correlation between Arctic sea ice extents and Atlantic Multi-decadal Oscillation (AMO) indices. and demonstrate evidence of the North Atlantic Oscillation (NAO) on Arctic sea ice. Table  shows annual and decadal correlations between Arctic sea ice extent and AMO and NAO indices for simulations from three PlioMIP models (CCSM4, HadCM3, and NorESM-L).

All three models show a small but significant (at 90 % level) correlation between the pre-industrial annual Arctic sea ice extents and the NAO indices. The correlation coefficients at the decadal timescale are increased for both HadCM3 and NorESM-L but are not significant for any of the models. None of the correlations between mid-Pliocene Arctic sea ice extents and NAO indices are significant at the 90 % level. The correlations between pre-industrial Arctic sea ice extents and AMO indices are all not significant at the 90 % level. For the mid-Pliocene simulations, only the correlation between the annual Arctic sea ice extents and AMO indices from the CCSM4 simulations is significant at the 90 % level.

There is no significant correlation between decadal sea ice extents and NAO/AMO indices in the three models shown, and so it is unlikely that differences in the mean sea ice extents (representing averages representing between 30 and 200 years' worth of climatology) between different models and simulations can be explained by different influences of these variability indices. To more thoroughly investigate this would require much longer time series from all the modelling groups, which are not available. A comprehensive analysis of the relationships between variability indices and sea ice in the PlioMIP simulations is beyond the scope of this paper.

Patterns of ice thicknesses are strongly influenced by the motion of sea ice in the models. In each model, the equations used to determine sea ice motion account for stresses on the ice from surface winds and ocean currents, with the exceptions of HadCM3, which does not take surface winds into account , and MRI-CGCM, where the ocean currents are not taken into account in determining ice motion .

Figure  shows the mean annual 10 m surface winds and sea ice thicknesses for the IPSLCM5A and MIROC4m simulations. In MIROC4m, the dominant wind direction between 90 and 180∘ E over the Arctic Basin is towards the northern coast of eastern Siberia, where a build-up of thicker ice is present. Similarly, in IPSLCM5A (Fig. ), the dominant wind direction is towards the north of Greenland and the Canadian Arctic Archipelago, where the thickest ice is. Mean annual 10 m winds and sea ice thicknesses for all simulations (excluding CCSM4, for which 10 m winds are not an output) are included in the Supplement.

In HadCM3, the ocean surface currents form a vortex in part of the Arctic Basin (Beaufort Gyre), where the thickest sea ice is present in both simulations (see Fig. ). Given that the sea ice motion is entirely determined by the surface ocean current, its influence on the spatial pattern of sea ice thickness is clear. If sea ice motion were instead determined by surface wind stresses in addition to the ocean currents (which do not have the same patterns in HadCM3), this should result in a different configuration of sea ice in the Arctic basin, and would likely affect the location of the sea ice margins simulated by the model. Mean annual surface ocean currents and sea ice thicknesses for all simulations are included in the Supplement.

Understanding the more precise influences of winds and ocean currents on the modelled sea ice and the causes of differences between models, as well as different simulations with the same model, would require a far more extensive analysis. Differences in seasonal, as well as annual patterns, alongside atmospheric circulations at higher levels, may be explored in further work.