This study employs two climate models: an atmosphere-ocean general circulation model (AOGCM) with and without a dynamic vegetation component, referred to as MIROC4mV and MIROC4m, respectively. The dynamic vegetation here means the vegetation type is computed in the model based on simulated climate, incorporating the interaction between climate and the geographic distribution of vegetation. We begin with a brief description of MIROC4m. MIROC4m is an AOGCM that consists of the atmosphere, ocean-sea ice, and land surface components interacting with each other through exchanges of energy, water, and momentum (K-1 model developers, 2004). The atmospheric model component is based on the primitive equations and has a horizontal resolution limited by the T42 spectral truncation (∼ 2.8° × 2.8°), with 20 vertical levels. The land surface component has the same horizontal resolution as the atmospheric component, with one canopy layer, five soil layers, and a maximum of three snow layers. The ocean model component is based on the primitive equations under the Boussinesq approximation. It has a horizontal resolution of 1.4° in longitude and varies from 0.56 to 1.4° in latitude (with higher resolution toward the equator), comprising 43 vertical levels. The sea ice model component, which computes thermodynamic and dynamic processes, uses the same horizontal resolution as the oceanic component. Fourier filtering is applied to the ocean grids at NH high latitudes to reduce computational cost, as the zonal grid spacing converges toward the North Pole. We note that this filter smooths the large-scale zonal feature in sea ice variables. This climate model runs computationally efficiently and has been used in many paleoclimate studies (e.g., Chan and Abe-Ouchi, 2020; Kuniyoshi et al., 2022; Sherriff-Tadano et al., 2023). As stated in the Introduction, Sherriff-Tadano et al. (2023) is particularly relevant, as they demonstrated the importance of cloud parameterization in the LGM climate, which is employed in the current study.

MIROC4mV is a model that couples MIROC4m with the dynamic vegetation component (LPJ-DGVM) (O'ishi et al., 2009; Sitch et al., 2003). Dominant vegetation is represented by the most frequent plant functional type and is determined annually for each grid cell based on monthly temperature, precipitation, and sunlight, averaged over the most recent 20 years. The prescribed atmospheric CO₂ concentration also affects plants through fertilization. These variables are passed from the atmospheric component to the LPJ-DGVM, and the diagnosed vegetation type is then passed to the land surface component. By doing so, it is possible to simulate the interaction between climate and vegetation changes. This vegetation-coupled climate model has also been used in previous studies. As stated in the Introduction, O'ishi et al. (2021) are particularly relevant, as they demonstrated the importance of vegetation feedback for LIG Arctic warming, and Hirose et al. (2025) are relevant, as they identified remnant glacial ice sheets as a critical factor in the diversity of past interglacials.

We examine differences in the climate response to external forcing using two cloud parameter sets, “S” and “L”, introduced by Sherriff-Tadano et al. (2023) as models “A” and “C,” respectively. As defined below, “S” is named after more solid water and “L” after more liquid water at the same temperature. Three parameter values are different between the two sets: (a) the lowest temperature (Tice in Eq. 1) at which supercooled liquid water droplets can exist; (b) a coefficient of autoconversion rate for rain (α in Eq. 2); and (c) a coefficient of ice sedimentation rate (V0 in Eq. 3). Note that the actual values are summarized in Table 1.

In MIROC4m, SLF, taking the range from 0 to 1, is parameterized in such a way that all cloud particles are solid below Tice and liquid above 0 °C, and SLF is linearly interpolated in-between (Ogura et al., 2008): 1SLF(T)=0T≤TiceT-Tice/0-TiceTice<T<010≤T where the unit for T and Tice is in °C. The difference between cloud parameter sets S and L in SLF exists for the range between -28 and 0 °C, and SLF is always larger in L, meaning that more cloud liquid water exists in L with a given amount of total cloud water (Fig. 1). The original setting of the model follows the temperature dependency of cloud phase in S. Still, L is designed to be closer to the empirical relationship between temperature and cloud phase, obtained from recent satellite-based observations (Fig. 4 in Sherriff-Tadano et al., 2023).

A complication arises in the coupled-model sensitivity experiments because a single-parameter perturbation disturbs the global energy balance of the Earth, leading the model to drift away from the realistic modern climate. To avoid this issue, Sherriff-Tadano et al. (2023) also adjusted the two other cloud parameter values. Rain rate Prain is parameterized as 2Prain=-∂lL∂t=αρlL2β+γNcρlL+CcFplL, where lL is the cloud liquid water content, ρ is the air density, Nc is the cloud droplet number concentration, Fp is the precipitation flux from the layer above, and α, β, γ and Cc are constants (Ogura et al., 2008). In the cloud parameter set L, the coefficient associated with autoconversion rate α in Eq. (2) is increased compared to set S (Table 1). Ice sedimentation rate Pice is parameterized as 3Pice=-∂lF∂t=V0ρlFδΔzlF. where lF is the cloud ice content, Δz is the thickness of the model layer, and V0 and δ are constants (Ogura et al., 2008). In the cloud parameter set L, the coefficient associated with ice sedimentation rate V0 in Eq. (3) is increased compared to set S (Table 1). The increase in both α and V0 generally reduces cloud amount.

We verified that the cloud liquid water has a longer mean lifetime than cloud ice water in the model (Fig. S1 in the Supplement), which is qualitatively consistent with the discussion in the Introduction. Therefore, an increase in SLF is expected to result in a larger cloud amount when averaged over a specific period.

Since the shape and precession phase of the Earth's orbit around the Sun are different at LIG from PI, the angular velocity, which depends on the Sun-Earth distance, differs between the two experiments for each season. The astronomical season may be defined by the angle from the moving vernal equinox, e.g., 90° for the summer solstice. Applying a modern calendar to both LIG and PI yields a comparison of slightly shifted seasons. To minimize this undesired effect, we used the calendar adjustment introduced by Bartlein and Shafer (2019) for the monthly mean values. This adjustment enables us to more accurately evaluate the seasonal difference between LIG and PI, which is essential for comparing the simulation with proxies whose records are dominated by a specific season. While this adjustment is appropriate for comparing the model and data, differences in month length between the two periods (PI and LIG) may introduce issues in energy budget analysis, which relies on conservation, as noted by Sime et al. (2025). While our energy balance analysis, described in the next section, is applied independently for each month and the interpretation should not be affected by differences in month length, we also examined an alternative calendar definition: the mid-month date is defined according to the fixed-angle calendar, and the month length is fixed for 31 d, with 15 d before and after the mid-month date. The results change little and are presented in the Supplement. We also note that the calendar adjustments are not applied when calculating the annual mean values.

We applied the surface energy balance analysis to quantify the contributions of individual feedback processes to changes in surface temperature (ST), following Lu and Cai (2009). This method converts each energy-flux term in W m⁻² between the two experiments into a partial ST change in K, whose sum is an excellent approximation to the simulated ST change.

The energy balance equation at the surface may be given by 4N=1-aS↓+F↓-F↑-LE-H where S↓ is downward SW radiation with a being the surface albedo, and F↓ and F↑ are downward and upward LW radiation, respectively. H and LE are sensible and latent heat fluxes (positive upward), respectively, and N is the heat storage rate in the subsurface (e.g., heat uptake by the ocean and heat conduction into the soil layers).

The perturbation equation for the difference between the two experiments, denoted by Δ, is written as 54σT‾3ΔT≈ΔF↑=-ΔaS‾↓-ΔaΔS↓+1-a‾ΔS↓,clr+ΔF↓,clr+1-a‾ΔS↓,cld+ΔF↓,cld-ΔLE-ΔH-ΔN The overlines denote the average of the two paired experiments. Here, SW and LW radiation are decomposed into clear-sky and cloud (= total-sky - clear-sky) radiative effects. Dividing by 4σT‾3 on both sides, the ST change is expressed as the sum of 9 partial-change terms on the right side. It is symbolically written as 6ΔT=A+A⋅SW+SWclr+LWclr+SWcld+LWcld+LH+SH+Qs The physical meaning of each term is summarized in Table 4. While this diagnosis is made explicitly for the ST change rather than the SAT change, it is also helpful to understand the latter, as the two variables are thermally coupled. Indeed, changes in these two variables are nearly identical across all pairs of experiments compared in this study. Nevertheless, care must be exercised in the physical interpretation. For example, upward sensible heat flux cools the surface yet warms the air above. The upward heat flux from the subsurface to the surface represents the warming effect on the surface, which may be transferred to sensible and latent heat fluxes, warming the air above. Therefore, a warming from the subsurface term and a cooling from the evaporation and sensible terms imply atmospheric warming due to the release of heat from the ocean.

Figure 2 shows the difference in annual mean SAT between PIvL and PIvS, highlighting the impact of cloud parameterization on preindustrial simulations. The global, annual mean SAT is 13.9 and 14.6 °C in PIvS and PIvL, respectively. Note that comparisons with a global atmospheric reanalysis dataset are presented in Fig. A1. PIvL is generally warmer than PIvS, except in regions around Antarctica, as discussed in Sect. 6. This spatial pattern difference is similar to what was shown in Sherriff-Tadano et al. (2023), in which observed modern vegetation is prescribed. The warmer tropics in PIvL than PIvS are attributable to more solar radiation reaching the surface due to less cloud amount (not shown), which is caused by the higher efficiency of autoconversion rate with the cloud parameter set L (Sect. 2.2). In the Arctic region, defined here as north of 60° N, PIvL is warmer than PIvS by 1.1 °C. There is, however, little difference in the simulated vegetation distribution between PIvS and PIvL (Fig. 3a and b). We note that the PIvS vegetation is consistent with O'ishi et al. (2021), which used the identical cloud parameterization but a slightly different value for the ocean's eddy isopycnal thickness diffusivity of the Gent-McWilliams parameterization. Factors contributing to the Arctic SAT difference between the two cloud parameterizations were not investigated in Sherriff-Tadano et al. (2023), which focused on the Southern Ocean. Figure 4 shows the partial contribution of individual components to the total ST difference in the Arctic, as diagnosed by the diagnosis method described in Sect. 4.2. Note that the SAT difference is almost indistinguishable from the ST difference (not shown). The ST difference stands out from October to January, with a peak in November (2.8 °C). Conversely, the difference diminishes during the summer. The figure shows a dominant positive contribution from the LW cloud radiative effect, although the SW cloud radiative effect is not negligible in some months.

When focused on the November SAT in the region north of 70° N, covering most of the Arctic Ocean, PIvL (-17.43 °C) appears to be a better match to the ECMWF ERA5 reanalysis dataset (-17.62 °C for 1980–1999; Hersbach et al., 2020) than PIvS (-19.89 °C). However, as Sime et al. (2025) stress, it is important to consider the differences between present-day and preindustrial conditions. The difference between the 1980–1999 average and the 1850–1899 average is 1.05 °C in the long-term NOAA 20CRv3 reanalysis dataset (Slivinski et al., 2021). Thus, PIvL and PIvS may contain a similar magnitude of errors of about 1 °C with opposite signs. Note that the 1980–1999 average differs by 1.29 °C between ERA5 and 20CRv3 reanalyses, which is comparable to, or slightly larger than, the estimated model biases.

Figure 5 shows annual mean differences in cloud liquid water path (LWP) and low-level cloud cover for the Arctic between PIvL and PIvS. Except for the northern North Atlantic, larger LWP and low-level cloud cover are simulated in PIvL. The larger LWP in PIvL was expected as SLF is parameterized to be larger below 0 °C in PIvL compared to PIvS (Sect. 2.2). As the precipitation efficiency is significantly lower for cloud water than for cloud ice in the model (Fig. S1), the average lifetime of cloud water becomes longer. Consequently, the Arctic low-level cloud cover also increases in PIvL compared to PIvS. The final simulated difference, of course, is modified by feedbacks, such as changes in sea ice cover. The difference in low-level cloud cover is far more pronounced than that of middle and high clouds (not shown). Additionally, the downward LW radiation from low-level clouds is more effective in warming the surface, as the emission temperature at lower altitudes is higher than at higher altitudes. The dominant influence of temperature-cloud phase parameter, rather than other perturbed cloud parameters was verified with additional AGCM experiments as described in Appendix A.

Figure 6a and b show September sea-ice concentrations for PIvS and PIvL, respectively. Note that the minimum in sea ice area occurs in August (ice extent is comparable between August and September) in the PI simulations; September was shown here for the later comparison because it is the month of minimum sea ice area/extent in the LIG simulations. The smaller area of sea ice cover in PIvL is consistent with the warmer Arctic in PIvL. Additionally, the sea ice of PIvL is overall thinner than that of PIvS, with a difference of up to 30 cm in the Central Arctic (Fig. 7a and b). This difference in sea ice thickness will later be shown to be important to understanding the sea ice distribution difference in LIG simulations.

The cold bias and excessive sea ice cover in the Barents and Kara Seas show some improvement in PIvL compared to PIvS, based on sea ice and global atmospheric reanalysis datasets (HadISST2 – Titchner and Rayner, 2014, and ERA5 in Fig. A1, respectively). We note, however, that both versions suffer equally from a significant warm bias over North America (Fig. A1) and a lack of Arctic sea ice along the North American coast, regardless of the applied cloud parameterization.

Figure 8a and b show the difference in summer SAT between the LIG and PI simulations. The estimate from proxy records (Guarino and Sime, 2022) is also presented. Note that this family of proxy datasets has been used previously and updated for the model-data comparison (CAPE, 2006; Guarino et al., 2020; Sime et al., 2023). Both ΔLIGvS and ΔLIGvL generally capture the strong summer warming at LIG, with some overestimation over Alaska and underestimation over Greenland. The root mean squared error is 1.8 °C for ΔLIGvS and 1.9 °C for ΔLIGvL, and they are comparable. It is difficult to draw a definitive conclusion about the superiority of S vs. L, given the uncertainty in proxy reconstructions and the limited number of sample locations.

The annual mean SAT at LIG is warmer than PI in the Arctic (to the north of 60° N) by 2.7 °C for ΔLIGvS and by 3.1 °C for ΔLIGvL, slightly larger with the cloud parameter set L. It is also compared with the proxy-based estimate (Turney and Jones, 2010; Capron et al., 2017) in Fig. S7. It is important to note that the dataset of Turney and Jones (2010) was compiled from the locally warmest timing within a wide period spanning approximately 13 000 years, from 129 to 116 ka BP. The assumption that peak warmth at LIG was simultaneous has been challenged, and the validity of comparison with 127 ka BP simulations for the model assessment has been questioned (Capron et al., 2014, 2017). Nevertheless, the comparison is referenced here because the impact of cloud phase representation on SAT is more critical in winter, rather than summer, and it is important to point out that the discrepancy of simulation with this dataset, shown by O'ishi et al. (2021), remains substantial even with the alternative cloud phase representation. We must wait for a well-dated dataset for a more quantitatively solid comparison.

Figure 6c and d show September sea-ice concentration for LIG simulations, LIGvS and LIGvL, respectively. The area of sea ice cover decreases compared to the corresponding PI simulations. The reduction of sea ice cover in LIGvL is, however, much more drastic than that in LIGvS. Figure 6c and d compare two different sea ice cover reconstruction datasets with these LIG simulations: those from Kageyama et al. (2021) and Vermassen et al. (2023). At one location (PS92/039-2: 81.92° N, 13.83° E), identified as ice-covered in summer by the Kageyama et al. (2021) compilation, sea ice is present in LIGvS but absent in LIGvL simulations. On the contrary, overall simulated sea ice cover in LIGvL is much closer to the Vermassen et al. (2023) compilation and a nearly ice-free summer Arctic as suggested by Malmierca-Vallet et al. (2018) and Sime et al. (2023). Notice that the difference in ice thickness in the Central Arctic between LIGvS and LIGvL is as much as 27 cm (Fig. 7c and d), which is close to the difference between PIvS and PIvL (Fig. 7a and b). This implies that whether sea ice remains in summer at LIG in these simulations is sensitive to the simulated sea ice thickness under modern conditions. In addition, the annual mean Arctic warming for ΔLIGvL is larger than that for ΔLIGvS, which may further help to simulate a smaller summer sea ice cover in LIGvL.

As discussed in Sect. 5.2, there is a discernible annual mean SAT difference between ΔLIGvL and ΔLIGvS. Nevertheless, the simulated vegetation distributions for LIGvS and LIGvL are similar, in which the area covered by tundra at NH high latitudes in PI simulations is replaced by boreal deciduous forest in LIG simulations (Fig. 3c and d). Similarly, the area covered by boreal conifer forest at NH mid-latitudes in PI simulations is replaced by grassland in LIG simulations. The former change is particularly effective at altering surface albedo and the consequent warming, as discussed by O'ishi et al. (2021).

Figure 9a shows the partial contribution of individual components to the total ST difference over the Arctic Ocean for ΔLIGvS according to the diagnosis method described in Sect. 4.2. LIGvS is warmer than PIvS in the Arctic from April to December, with a peak warming in October. From May to August, the dominant warming factors are changes in downward clear-sky SW and LW radiation and in surface albedo. The increase in clear-sky SW radiation is expected and reflects differences in summer insolation at the top of the atmosphere (TOA) driven by variations in astronomical parameters. The increase in clear-sky LW radiation is caused by increased air temperature and/or water vapor. The net decrease in subsurface heat uptake (positive Qs term) and the net increase in upward surface latent and sensible heat fluxes (negative LH and SH terms), which are respectively tagged with surface warming and cooling from October to December, imply atmospheric warming via heat transfer from the ocean to the atmosphere. The mechanism of warming involving these processes is consistent with many previous studies: stronger insolation at LIG reduces sea ice cover, and the ocean mixed layer absorbs more heat in summer and releases it to the atmosphere in autumn-winter (e.g., O'ishi et al., 2021; Sicard et al., 2022; Hirose et al., 2025). It is important to note that the LW cloud radiative effect contribution to surface warming is not negligible from September to November, consistent with the increase in low-level cloud cover in autumn (Fig. 10a).

Figure 11 shows the changes in sea ice concentration in August and September and low-level cloud cover in September and October for ΔLIGvS (north of 60° N). It appears that regions of sea ice retreat in August and September loosely coincide with the areas of cloud increase in September and October, respectively. The match is firmer in the zonally elongated region to the north of Spitsbergen and the region from the Laptev Sea to the Canadian Archipelago in Fig. 11b and d. While we do not fully understand the reason for this one-month delay in response, the previous study by Abe et al. (2016) reported a similar relationship between shrinking sea ice and increasing cloud cover in a 1976–2005 simulation using a different version of the MIROC model. In their study, a decrease in September sea-ice cover leads to increased upward heat and moisture fluxes through the open-water surface. As the air-sea temperature difference rises in October, these fluxes further intensify, resulting in an apparent one-month lag between the decrease in sea ice and the increase in cloud cover. Although radiative forcing and climate conditions differ from ours, Fig. 11 is qualitatively consistent with their argument.

The description above is consistent with the seasonal evolution of atmospheric and upper-ocean temperature anomalies shown in Fig. 12a, where anomalous ocean heat content increases in summer and decreases in autumn. It is worth noting that summer warming extends to the upper troposphere, whereas autumnal warming is confined to the near-surface layers, qualitatively consistent with Sicard et al. (2022, Fig. 8). In winter, the ocean is slightly warming, and cooling occurs in the atmosphere.

Figure 9b shows the partial contribution of individual components to the total ST difference in the Arctic for the difference between ΔLIGvL and ΔLIGvS. The net increase in subsurface ocean heat content in summer (negative Qs term), along with the albedo feedback (positive A term), and the net decrease in subsurface ocean heat content in winter (positive Qs term), indicate enhanced heat exchange between the ocean and the atmosphere with reduced sea ice cover. From October to December, the difference between ΔLIGvL and ΔLIGvS is caused primarily via downward LW cloud radiative effect, consistent with a marked difference in low-level cloud cover increase in ΔLIGvL (Fig. 10b) than ΔLIGvS (Fig. 10a). Figure 13a and b show the difference of the difference, i.e., ΔLIGvL - ΔLIGvS, in LWP and low-level cloud cover, respectively, for the average from October to December. Overall, positive anomalies are observed. As discussed above, the increases in LWP and low-level cloud cover in LIG simulations are likely associated with decreased sea ice cover relative to PI simulations. As the reduction in sea ice cover is much larger in ΔLIGvL than in ΔLIGvS, a larger cloud response occurs in ΔLIGvL. In addition, air temperatures drop below -15 °C in November and December across large areas of the Arctic, even near the surface at LIG. As the cloud parameterization allows SLF to have non-zero values below -15 °C only in the cloud parameter set L, the distinct increase in LWP in the LIG simulation compared to the PI simulation is observed for ΔLIGvL in November and December. Therefore, the positive anomalies in Fig. 13a and b are simulated due to a larger decrease in sea ice cover (Fig. 13c) and the allowance of mixed-phase clouds at lower temperatures by the cloud parameter set L. The dominant influence of the temperature-cloud phase parameter, rather than other perturbed cloud parameters, was verified through additional AGCM experiments and is described in Appendix A.

The description above is consistent with the seasonal evolution of atmospheric and upper-ocean temperature differences shown in Fig. 12b, where anomalous ocean heat content increases in summer and decreases in autumn. The contrasting weaker summer and stronger winter signals in the ocean temperature in Fig. 12b, relative to Fig. 12a, are striking, although a larger portion of the difference originates from the PI simulations. The warming signal is also evident in the winter atmosphere in Fig. 12b. These signatures are related to the cloud-phase representaion, which helps sustain the warmer ocean through winter and thereby potentially impacts sea ice growth. Both a larger reduction in sea ice cover and stronger cloud feedback in the model with cloud parameter set L functionally contribute to warmer conditions relative to the model with cloud parameter set S. However, given the limitations in disentangling both effects in coupled atmosphere-ocean model simulations, each effect, particularly on sea ice growth and loss, is not quantified separately in the current study. A model capable of ice mass tendency diagnostics, as suggested by Keen et al. (2021) and Sime et al. (2025), would help explore this aspect.