The climate model chosen for this study is the CESM v1.2.2, a fully coupled atmosphere–ocean general circulation model with sea ice, land, and runoff components. The CESM and Community Climate System Model (CCSM) family has been widely utilized in paleoclimate studies. Our particular configuration utilizes the Community Atmosphere Model version 5 (CAM5). The land and atmosphere models have an approximate resolution of 1.9∘ latitude by 2.5∘ longitude with 30 hybrid coordinate vertical layers in the atmosphere. The ocean and sea-ice grids are comprised of an orthogonal curvilinear grid at nominally 1∘ resolution with the North Pole displaced over Greenland to avoid singularities in flux calculations in the Arctic Ocean.

Fixed present-day ice sheet topography was assumed for all MIS-11 time slice experiments, and therefore the land ice model component was disabled. This is perhaps the largest assumption of these simulations, but enables isolation of the effects of changing orbital and GHG forcings on the simulated climate. Options for applying different ice sheet configurations were also severely limited by the sparse Greenland ice-core data extending back through MIS-11, and only a small number of modeling studies have produced transient reconstructions (e.g., Robinson et al., 2017). CESM version 1 and CAM5 have a well-documented high-latitude cold bias due to a combination of anomalously strong high-latitude circulation features and radiative effects (e.g., Wang et al., 2019); however, our simulations are internally consistent, as the same core model configuration is merely compared with different parameters.

A control run was conducted which adheres to the standards set forth by the Paleoclimate Modelling Intercomparison Project 4 (PMIP4) for a preindustrial baseline (Otto-Bliesner et al., 2017). This simulation was integrated for 2500 years to enable full equilibration of the surface climate and quasi-equilibration of deep-ocean temperatures. The experimental MIS-11 runs were branched from year 1500 of the control integration, with only orbital and GHG parameters altered as described below.

The time slice technique (see e.g., Stone et al., 2013; Rachmayani et al., 2017) was utilized in this study, as transient simulations of 20 kyr duration or more remain prohibitively expensive in a relatively high-resolution AOGCM. Each selected slice is integrated for 1000 years at constant forcing conditions, enabling effective equilibrium of the surface climate (entire atmosphere and upper portion of the oceans) at conditions representative of the selected time. This timescale is insufficient for complete equilibration of the deep oceans. However, as the Greenland ice sheet does not have large ice shelves grounded at or below sea level, this is judged unimportant for our study (cf. Varma et al., 2016). Temperature trends in the deep ocean are also modest in our simulations, with typical drift being on the order of 0.05 ∘C per century below 1000 m depth. The 1000 years of each experiment consist of 900 years of spin-up time, then the final century is treated as the equilibrated period. All results presented are therefore 100-year time series or averages from the end of each simulation. The time slices were chosen to align approximately with minima and maxima in precession (which has a powerful modulating effect on the seasonal distribution of insolation) during the warm interglacial period of MIS-11. Intermediate 5 kyr steps were also selected to ensure fuller coverage of the period of interest. The characteristic parameters of each time slice and the preindustrial control run are detailed in Table 1.

For each experimental simulation, orbital parameters were calculated following Laskar et al. (2004) at the representative time period. Greenhouse-gas concentrations were obtained from the European Project for Ice Coring in Antarctica (EPICA) record, primarily consisting of data from Dome C (Siegenthaler et al., 2005; Lüthi et al., 2008). Following the experimental setup detailed in Otto-Bliesner et al. (2017), a nominal +23 ppb adjustment was applied to Antarctic CH4 values, accounting for the fact that methane persistently exists in higher concentrations in the Northern Hemisphere during interglacials. GHG values represent means of a 5 kyr window around the representative time (i.e., 423 ka GHG values are given by a mean of all values between 425.5 and 420.5 ka), which accounts for the inherent uncertainty in GHG values due to short-term variability (centennial and millennial scale) and the analysis techniques.

A sensitivity experiment was also conducted to ensure that the results of the time slice experiments were not dependent upon initialization. To this end, additional simulations for 418 ka were conducted, branching from year 500 of the preindustrial control run and from year 500 of the 423 ka run. A comparison of the equilibrated periods (final 100 years of each integration) showed that no statistically significant differences existed between them.

A number of correlation plots are presented in the results section. These present Pearson's r values, 95 % confidence intervals of the r values, and p values. Pearson's r is calculated with respect to the mean values of given quantities for each particular time slice. On interannual timescales, regional temperatures, eddy heat fluxes, etc. are noisy and influenced by a number of different factors. The most prudent comparison is therefore between the long-term mean patterns in each time slice simulation. When correlating 2 m air temperature and precipitation for all MIS-11 experiments, for example, the values correlated consist only of the six mean seasonal precipitation values from the time slices and the six mean seasonal temperature values from the time slices. The n for these correlations is therefore only six, and the degrees of freedom just four. In reality, 600 total seasonal values likely have a much greater number of degrees of freedom, although each time slice's 100 years of data is best classified as a red-noise time series and therefore does not have a full 100 degrees of freedom (Thomson, 1982). The significance of the correlations presented are therefore conservative.

Student's t tests are also employed to determine whether climatological changes between the time slice simulations and the preindustrial simulation are significant. For all variables tested, the seasonal values at each grid point and in each time slice are treated as an independent time series (n=100). This necessarily assumes spatial independence of each grid point. Critical values and p values are then obtained based on the effective degrees of freedom of each time series, reduced from 100 based on the lag-1 autocorrelation. The inherent assumption of normally distributed, spatially independent variables is not fully applicable for spatially coherent, non-normal variables like wind, eddy heat flux, and precipitation, but degrees of freedom are sufficiently large in all cases to ensure that t testing retains some explanatory power (Decremer et al., 2014). The 95 % confidence threshold presented in all figures here should not be considered as absolute, but an approximate representation of where anomalies are noteworthy.

The surface temperature response is the most obvious effect of the varying orbital and GHG conditions throughout MIS-11 (Fig. 1). Global-mean 2 m air temperatures were at or modestly above preindustrial levels for each of the 423–408 ka simulations (dark blue). As expected, the temperature pattern is considerably amplified over Greenland, with positive anomalies reaching 2–3 ∘C above preindustrial during the warmest period (413 ka). This result generally aligns well with the temperature anomalies over Greenland from two other recent studies utilizing EMICs for transient simulations of MIS-11. First, an ensemble of coupled REMBO-SICOPOLIS simulations with transient ice sheets was performed by Robinson et al. (2017), depicted in the gray line and shading in Fig. 1. Their simulations in turn rely on temperature anomalies derived from a transient climate simulation from the CLIMBER2 EMIC (Ganopolski and Calov, 2011). Our simulations deviate significantly from the these at the first time slice (423 ka), and to a lesser extent at 418 ka. This is most likely a result of our simulations assuming a fixed ice modern-day Greenland ice sheet, whereas the transient simulations still had greater Greenland and North American ice coverage from the previous glaciation. This is affirmed by further comparing our simulations to those of Yin et al. (2021), who utilized LOVECLIM1.3 with transient orbital and GHG forcing, but fixed present-day ice sheets. Near-surface air temperatures from their simulations (light red in Fig. 1) averaged around Greenland match our results very closely, including at 423 ka. Except for the discrepancies at 423 ka, differences between the fixed ice and fully transient simulations are otherwise minimal during MIS-11.

The spatial distribution and magnitude of boreal summer temperature anomalies across the North Atlantic sector also varied notably throughout the analysis period (Fig. 2). Anomalies as high as 4–5 ∘C above preindustrial are evident around northern Greenland and the Canadian Arctic during the peak warmth of 413–408 ka due to the combined effects of high insolation and regional feedback, including reduced sea-ice cover (not shown). More modest and relatively uniform warming is present across much of the rest of the Atlantic basin, with the exception being areas immediately surrounding the Mediterranean Sea. A narrow but stark band of 1–2 ∘C cool anomalies stands out in sub-Saharan Africa during the 423 and 413–408 ka simulations, the result of increased cloud cover and surface cooling induced by evaporation associated with enhanced monsoonal and intertropical convergence zone (ITCZ) convection. Also evident is the abrupt return of surface air temperatures to near-preindustrial conditions by 403 ka and substantial cool anomalies by 398 ka, consistent with conditions potentially favorable for renewed glaciation.

Inevitably, these results contain some bias introduced by using a fixed modern-day Greenland ice sheet in the simulations. In addition to the aforementioned warmth at 423 ka, temperature anomalies are likely somewhat underestimated over Greenland itself for later analysis periods, as the lowering and partial removal of ice surfaces would have enabled even warmer conditions. Additionally, changes in Greenland topography may also induce further warming on local to regional scales due to katabatic winds (Merz et al., 2014). These potential biases are particularly relevant for the 413–398 ka time slices, when the ice sheet was likely smaller than the present day.

Regardless of the exact magnitude of summer warming during MIS-11, the signal for large, statistically significant warming at high latitudes is robust. One clear consequence of strong warming at high latitudes, especially when paired with tropical surface cooling over Africa, is the reduction of the mean Equator-to-pole surface temperature gradient, and thus the contribution of the thermal wind balance to the geostrophic flow. A dynamic adjustment of baroclinic processes is therefore to be expected, including attendant changes in jet stream and baroclinic eddy behavior.

Particularly robust changes are present in the lower-tropospheric meridional eddy heat flux (EHF) anomalies across the North Atlantic sector. Note that future references to baroclinicity, meridional temperature gradients, or eddy heat fluxes in this text are concerning only lower-tropospheric quantities, and EHF in general refers to the meridional flux of heat by atmospheric eddies. Figure 3 illustrates the mean patterns of total (transient plus stationary) boreal (sensible) summer eddy heat flux anomalies relative to the preindustrial control simulation. Stationary eddy heat fluxes are defined as v∗‾T∗‾, where v∗ and T∗ are the zonally anomalous meridional wind and temperature, respectively, with anomalies calculated at daily intervals and at the 700 hPa atmospheric pressure level before being averaged to seasonal values. Transient eddy heat fluxes are likewise defined as v′T′‾, or the product of the time-anomalous meridional wind and temperature. The total EHF is simply the sum of the transient and stationary meridional eddy heat fluxes and is, in effect, representative of the heat-advecting effects in the lower-to-middle troposphere of the atmospheric waves captured in the model. Over the large majority of the analysis domain, total meridional EHF anomalies are dominated by the transient eddy component (not shown). The values represented in the figure are averages of all the June–July–August (JJA) days in the 100-year period, relative to the preindustrial simulation.

Two features in the total meridional EHF anomaly fields stand out. First, the couplet of positive and negative anomalies over southwestern Europe and the central Mediterranean during 423–408 ka is indicative of a robust shift in the favored storm track. Positive EHF anomalies are indicative of either an increased and anomalous meridional temperature gradient or frequent large southerly wind anomalies (transient or stationary), or more likely, some combination thereof. Given that the mean temperature gradient appears unchanged or even slightly weaker (Fig. 2), the likely source of this anomaly is increased frequency and/or intensity of wave activity and meridional transport in this region. Conversely, reductions exist over the central Mediterranean, consistent with a shift in baroclinic wave activity away from this region. Considered together, the strong anomaly couplet (for all periods except 398 ka) over Europe and the Mediterranean represents a northwestward shift in the mean storm track over the eastern Atlantic.

A second region of widespread and statistically significant reduction in total eddy heat fluxes is present over much of Greenland and the open North Atlantic. The magnitude is overall smaller than the anomalies over Europe and the Mediterranean, but rather than marking a simple shift or intensification of the preindustrial pattern, it appears to resemble an entirely different wave pattern. Meridional heat flux from eddies is clearly reduced in the MIS-11 simulations (except 398 ka) in a broad area extending from the Canadian Maritime Provinces up through much of Greenland, a region that experiences relatively large meridional EHF in the preindustrial mean (black contours in Fig. 3). As will be discussed in Sect. 3.3, this is a clear indication of an altered storm track across the North Atlantic.

As implied by comparing the eddy heat flux and surface temperature maps, a strong negative correlation exists between the temperature averaged over Greenland and its immediate surroundings (the region enclosed by the green box in the top-left panel of Fig. 2) and the mean eddy heat flux over the North Atlantic region (the larger region enclosed by the green box in Fig. 3). The strength of this relationship is also strongly dependent on the season (Fig. 4). While both boreal winter-mean and summer-mean EHF–temperature relationships exceed the 95 % confidence threshold, the correlation is much stronger and has a much narrower confidence interval in boreal summer. This can be partly explained by the much larger magnitude and variability of seasonal-mean North Atlantic eddy heat fluxes in winter, but is also indicative of a more robust dynamic response in the summer season.

While reduced meridional temperature gradients play a role in reducing eddy heat fluxes, changes in eddy activity are the dominant cause. Eddy activity in the midlatitudes has a symbiotic relationship with the jet stream, which both drives and is driven by wave activity. An attendant change is therefore expected in jet behavior, which is apparent in the daily jet frequency matrices (Fig. 5). A clear shift in the favored latitude and strength of the boreal summer North Atlantic jet is evident, with weaker and lower-latitude daily maximum 300 hPa winds clearly favored in the 418, 413, and 408 ka experiments. These three warm periods also show a slight reduction in the frequency of low-latitude jet maxima, denoted by the slight negative frequency anomalies on the lower flank of the robust couplet. This is consistent with a decreasing tendency towards wind maxima in the typical (modern) latitude of the subtropical jet, an observation which is further supported by the presence of negative mean 300 hPa wind anomalies (Fig. 6).

Thus, both purely eddy-driven high-latitude jet maxima and purely subtropical jet maxima are reduced (the southern flank subtropical wind weakening is even more clearly visible in the u component of the wind field; not shown), with the dominant state instead emerging as a broad hybrid eddy–thermal jet in the midlatitudes. Son and Lee (2005) used an idealized aquaplanet model simulation to demonstrate that either weakened midlatitude baroclinicity or stronger tropical ascent could cause the jet to transition to a unified state. Interestingly, both mechanisms are present during MIS-11 boreal summers in our considerably more realistic simulations. As discussed in Sect. 3.1, baroclinicity changes are clear in the temperature anomaly patterns (Fig. 2) and additionally implied by the robust negative correlation between jet strength and mean 2 m air temperature over the North Atlantic (Fig. 7). As will be discussed further in Sect. 3.5, the band of tropical cooling over Africa is a result of increased convection, cloud cover, and evaporative surface cooling, thus indicating enhanced tropical ascent.

Notably, the region with the large couplet in EHF anomalies over western Europe and the Mediterranean (Fig. 3) corresponds approximately with the largest changes in jet stream wind strength (Fig. 6). Since the changes in EHF are dominated by the transient component, it is clear that the emergence of these anomalies is associated with a significantly altered North Atlantic storm track. A more baroclinically active JJA storm track across this region appears to be the consequence of the merged jet state, which is also consistent with the trapping of atmospheric waves equatorward of a merged jet (e.g., Nakamura and Sampe, 2002). Reduced baroclinic eddy activity on the poleward flank of the merged jet explains the existence of the opposite state (reduced EHF) across much of the open North Atlantic. The contrast is made clear by examining the 300 hPa wind (Fig. 6) and total eddy heat flux maps (Fig. 3). During 423–403 ka, large reductions in EHF are present across the central and North Atlantic in association with the weakened polar jet to varying degrees; in cooler-than-preindustrial 398 ka, these have been replaced by small positive anomalies in association with the return to a split-jet state.

Interestingly, correlations between EHF anomalies and jet characteristics fail to paint quite so clear a picture. While hints of a relationship between jet latitude and North Atlantic-mean EHF (mean over a box spanning 40–80∘ N and 70∘ W–0∘ E) exist, the correlation does not reach significance at the 95 % confidence level (Fig. 8). However, EHF exhibits a strong positive correlation with boreal summer jet strength in the North Atlantic. Our simulations indicate that split-jet states are associated with higher absolute maximum jet strengths. Therefore, the strong positive correlation between higher maximum jet velocities and North Atlantic meridional EHF implies greater EHF during split-jet regimes, and reduced EHF during the prevailing merged-jet regime of MIS-11 boreal summers.

Precipitation across the Greenland ice sheet is highly seasonal, predominantly driven by extratropical cyclones, and strongly enhanced along major orographic features, particularly in the southeast (Chen et al., 1997). With such a pronounced change in eddy behavior (extratropical cyclones) as a result of the shifted jet, a logical consequence would seem to be a positive correlation between jet strength and precipitation over Greenland. However, exactly the opposite appears to be the case (Fig. 9), with a significant but small negative trend in precipitation associated with higher North Atlantic wind maxima based on time slice means. A considerable amount of noise exists among the individual annual values, however, so this result should be treated with some caution. As is the case with the EHF correlations (Fig. 8), only the relationship between maximum jet velocity and precipitation obtains 95 % significance.

Competing effects appear to be influencing precipitation over Greenland in these simulations: intuitively, increases in eddy heat flux should correspond to increases in eddy moisture flux (EMF). However, comparing the jet state to total EMF over the North Atlantic directly results only in a statistically insignificant correlation (not shown). On the other hand, we have demonstrated that warmer North Atlantic temperatures are associated with weaker jets, and lower-tropospheric air temperature places a strong cap on atmospheric moisture. The apparent negative correlation between maximum jet winds and precipitation over Greenland (Fig. 9) therefore appears to be overwhelmingly driven by the inverse relationship between temperatures over Greenland and jet strength. Behavioral changes in the jet and eddies exhibit only a secondary influence.

Spatially, the largest boreal summer precipitation changes across the analysis domain appear to be related to the strength of the African monsoon (Fig. 10). Specifically, a drying is noted across much of the midlatitude Atlantic and much of central and southern Europe, consistent with the general shift of the preferred storm track and suggestive of increased subsidence from the poleward flank of the Hadley cell. The magnitude of subtropical drying appears to be roughly proportional to the increase in precipitation over sub-Saharan Africa, strongly suggesting the influence of tropical convection on the altered jet state. Precipitation increases across west/central Africa associated with the increased monsoon are evident through the 423–403 ka periods, peaking at over 175 % of preindustrial under 408 ka conditions. Attendant decreases of around 5 %–25 % over Europe, 25 %–50 % for most of the Mediterranean, and 5 %–25 % across the Caribbean and western subtropical Atlantic are also evident during 413 and 408 ka. The largest monsoon precipitation increases appear to occur at 418 and 408 ka, roughly corresponding with the periods of most negative precession (perihelion occurring near/during boreal summer).

Over Greenland, boreal summer precipitation changes during the warm 423–408 ka period resemble that of orographic precipitation during dominant westerly/northwesterly wind regimes: positive precipitation anomalies along the western slopes and negative anomalies along and just off the southeastern coast. In absolute terms, these anomalies are relatively small, on the order of 0.1–0.3 mm d-1, but constitute statistically significant 5 %–25 % increases. In the annual mean, however, a near-opposite pattern emerges in precipitation anomalies for southeastern Greenland (Fig. 11). Simulated annual average precipitation rates increase there by 5 %–15 % for the 418–408 ka period. Since the bulk of the southeastern Greenland precipitation increase occurs in the cool season, it occurs overwhelmingly as snow (not shown but confirmed by model precipitation-type output), and therefore contributes to an increase in the mass balance of the ice sheet across southeastern regions.