In simulations of 21st century climate, it is argued that changes in midlatitude near-surface moisture and temperature could explain the autumn midtropospheric Arctic warming. The argument is based on a comparison between the Arctic midtropospheric warming and theoretical estimates in which synoptic scale transient eddies propagate near-surface warming anomalies along either dry potential temperature surfaces or equivalent (moist) potential temperature surfaces. In most models, it is observed that the Arctic midtropospheric warming can be obtained from the propagation of midlatitude near-surface warming anomalies according to a dynamic that is intermediate between the dry and moist theories. While many models follow more closely the moist theory, few follow more closely the dry theory. This finding suggests that, as for the tropical atmosphere, theories of high-latitude midtropospheric warming based on changes in poleward heat fluxes should include a moist component.
 In recent decades, the midtroposphere has warmed faster in the Arctic than in the Northern Hemisphere midlatitudes, particularly during September-October-November (SON) [Screen and Simmonds, 2010]. Climate model simulations suggest that the SON warming of the Arctic midtroposphere (AMT) is mostly driven by enhanced poleward eddy heat transport rather than, for example, enhanced Arctic surface heat fluxes [Graversen and Wang, 2009; Screen et al., 2012]. Theoretical studies using idealized Global Climate Models and Energy Balance Models support these results and show that moisture is an important component of the enhanced heat fluxes [Schneider et al., 1999; Alexeev et al., 2005]. The underlying large-scale dynamics responsible for these enhanced heat fluxes remains not well understood. We postulate that the eddy-driven transport along isentropic surfaces relates the near-surface midlatitude warming to the AMT warming. We show evidence of this link and demonstrate that it could explain the AMT warming in simulations of 21st century climate with strong greenhouse warming.
 Midlatitude atmospheric energy transport is dominated by transient eddy transport. During SON, eddy-sensible heat transport accounts for 50–70% of the total SON transient eddy heat convergence, and eddy latent heat transport accounts for the remainder [Trenberth and Stepaniak, 2003]. Transient eddies, which have their genesis in baroclinic instability, flatten isentropic surfaces by transporting isentropic layer mass [Johnson, 1989; Held and Schneider, 1999]. This results in a net poleward transport of heat and highlights the interaction between the stratification (the vertical gradient of entropy or potential temperature θ) and eddy heat transport.
 The midlatitude stratification is largely set by meridional gradients of surface equivalent (moist) potential temperature θe [Juckes, 2000; Pauluis et al., 2011]. When condensation and precipitation occur within the warm conveyor belt of synoptic eddies [Eckhardt et al., 2004], ascending parcels convert their θe into θ along trajectories aligned with surfaces of constant θe. Parcels returning in the equatorward branch of synoptic eddies are dry and therefore follow surfaces of constant θ until they are reinjected into the planetary boundary layer (PBL). These motions give rise to the vigorous moist overturning circulation observed in the midlatitudes [Laliberté et al., 2012] and connect the midtropospheric heat content to surface heat fluxes along a combination of slanted dry and moist isentropes. Frierson  showed that this connection between surface θe and the stratification holds for the response to climate change in simulations of the 21st century.
 Because isentropic surfaces in the AMT intersect the PBL in the midlatitudes (see Figure 1), it might be expected that variability in the AMT is connected, via isentropic mass transport, to midlatitude surface processes. Indeed, modeling evidence suggests lower latitude near-surface warming can warm and moisten the AMT [Vavrus et al., 2011; Screen et al., 2012]. In the cited studies, it was shown that climate simulations forced with climatological sea surface temperature (SST) and observed sea ice loss exhibit only surface-amplified Arctic warming and little moistening in the AMT. By contrast, it was shown that simulations forced with the observed warming of midlatitude SST and climatological sea ice warmed, moistened, and increased cloud in the AMT.
 Net poleward heat fluxes into the Arctic have been shown to remain mostly unchanged in simulations with greenhouse warming [Hwang et al., 2011; Kay et al., 2012]. In those studies, the increase in poleward latent heat fluxes is compensated by a decrease in poleward sensible heat fluxes. The robust increase in latent heat fluxes indicates that moisture is playing an important role in the redistribution of warming anomalies to the Arctic.
 This paper is structured as follows. In section 2, we describe the data and the methods used in this study, and in section 3 we present our results. We conclude in section 4 where we discuss the implications our analysis might have on our understanding of the role played by large-scale dynamics on Arctic warming in a changing climate.
2 Data and Methods
 We use Coupled Model Intercomparison Project 5 (CMIP5) multimodel ensemble output from the historical and rcp45 experiments [Taylor et al., 2012] (see table in Supporting Information). We select the monthly temperature T, monthly specific humidity q, and monthly relative humidity on the 850, 700, 600, 500, and 400 hPa pressure levels for years 1979–2005 of the historical experiment and years 2006–2099 of the rcp45 experiment. We remap these variables onto an N48 Gaussian grid using first-order conservative interpolation, and we calculate the potential temperature θ and equivalent (moist) potential temperature θe:
where Lv is the latent heat of vaporization and cp is the specific heat of air. To compute θe, we use an ideal gas representation of moist air where the effect of ice is included by replacing the latent heat of vaporization Lv by the latent heat of sublimation Ls for temperatures below freezing. To compute Lv and Ls, we follow Emanuel  and use the saturation vapor pressure e∗ in eq. (4.4.14) above the freezing temperature and e# in eq. (4.4.15) below the freezing temperature.
 We calculate the zonal-mean T, , θ, and θe; for the remainder of this study, we refer only to zonal-mean quantities. We compute the multimodel mean (MODEL-MEAN) by averaging the zonal-mean T, , θ, and θe from the r1i1p1 realization across models. The identifier r1i1p1 is a shorthand notation for a CMIP5 model simulation, where the number following “r” indicates the realization number and the number following “i” indicates the initialization (typically changing only for decadal-prediction runs). The number following “p” indicates the parametrization number and serves to distinguish two simulations that differ only in their physical parametrizations.
 Finally, we compute climatological averages of T, , θ, and θe over the period 1979–2005 of the historical experiment, denoted as , , and . We also compute climatological averages over the period 2080–2099 of the rcp45 experiment, denoted as , , , and . Note that in Figure 2, we highlight the results of IPSL-CM5A-LR (four realizations mean) and CANESM2 (five realizations mean). For SON, the IPSL-CM5A-LR is an example of a model following the moist theory closely, while the CANESM2 is similar to the MODEL-MEAN case. We explain in Appendix 5 how the ensemble average for these two models is computed.
 In our analysis, we identify the 850 hPa pressure level as the near surface. This minimizes the influence of errors originating from the model-level to pressure-level interpolation and associated with the treatment of the surface boundary. In addition, the 850 hPa level corresponds roughly to the top of the PBL and, within the PBL, both θ and θe are regularly homogenized in the vertical by boundary layer dynamics (Stevens, 2005). As a consequence, their 850 hPa value are often close to their surface value.
 In the top row of Figure 1, we plot for the historical experiment during SON in contours, and we show the change in climatological potential temperature between the rcp45 and historical experiments in shading. In all three cases, δθ increases with height between 30 N and 65 N, indicating that the midlatitude bulk stratification increases.
 The three cases presented in Figure 1 exhibit a range of Arctic amplification of warming on the 850 hPa pressure level. The amplification is strong in the CANESM2 and the MODEL-MEAN cases, and their high-latitude bulk stratification decreases over the 21st century. This observation is not true for the IPSL-CM5A-LR, where Arctic amplification of warming on the 850 hPa pressure level is weak. As a consequence, its high-latitude bulk stratification increases over the 21st century.
 In the bottom row of Figure 1, we show climatological profiles and warming profiles similar to the top row but with the equivalent (moist) potential temperature replacing the dry potential temperature. Poleward of 55 N, gradients of δθe along lines of constant are weak, suggesting that the large-scale dynamics has homogenized changes of δθe along moist isentropes. In the CANESM2 and MODEL-MEAN, changes δθe along the curve defined by K are weaker in the AMT than at 850 hPa. This illustrates that for these two cases gradients of δθe along lines of constant are slightly negative. The opposite is true for θ, where gradients of δθ along lines of constant are stronger in the AMT than at 850 hPa for the three cases.
 To quantify this observation, we compare the simulated AMT temperature anomalies δT with dry and moist theories for the propagation of midlatitude near-surface warming anomalies. The dry theory propagates the 850 hPa warming along dry isentropes (δTθ), and the moist theory () propagates the 850 hPa warming along moist isentropes. The mathematical method used to obtain δTθ, , and δT is described in Appendix.
 In the top row of Figure 2, we show the SON vertical profile of these three quantities averaged over the polar cap (70 N–90 N). Between 600 and 400 hPa, the simulated AMT warming δT (blue) is larger than δTθ (green) but smaller than (red) for the three cases. Warming in the AMT is therefore bounded below by the warming expected from dry dynamics and bounded above by the warming expected from moist dynamics. IPSL-CM5A-LR has , whereas the AMT warming in the CANESM2 and in the MODEL-MEAN lies between the dry and moist propagation theories.
 In the bottom row of Figure 2, we show the 21st century time series of AMT warming averaged over 600–400 hPa for the three cases. For the IPSL-CM5A-LR case, interannual variability makes δT (blue) and (red) statistically indistinguishable. Both are nevertheless well separated from δTθ (green). For the CANESM2 and the MODEL-MEAN cases, the interannual variability is small enough to easily distinguish all three time series by the end of the 21st century. In the three cases, the separation between δTθ and only becomes large compared to the interannual variability around 2025. This remark suggests that another decade of observations will be required before the secular warming driven by rising greenhouse gases makes the dry and moist theories statistically distinguishable.
 To quantify the relationship between the simulated AMT warming and that predicted by the moist and dry theories, we diagnose the response as a mixture of dry and moist warming:
 In a model with α ≈ 0.0, the AMT warming can be inferred from midlatitude warming by assuming that synoptic eddies propagate 850 hPa sensible heat anomalies along surfaces of constant . On the other hand, in a model with α ≈ 1.0 (e.g., IPSL-CM5A-LR), the AMT warming can be inferred from midlatitude warming by assuming that synoptic eddies propagate 850 hPa total heat anomalies (sensible plus latent) along surfaces of constant .
 For realization r1i1 of each parameterization and for each model, we compute three α values based on the following formula:
where [⋅] average over 2080–2099 and a spatial average over the polar cap. The first two α values are computed using the quantities [δT], [δTθ], and at pressure levels 600 and 400 hPa, respectively; the third α value is computed using the quantities [δT], [δTθ], and further averaged over pressure levels 600, 500, and 400 hPa. In Figure 3, we identify the α value at 600 hPa by a downward triangle and the α value at 400 hPa by an upward triangle. We identify the third α value with the symbol × in Figure 3 and denote it by α×. For all but one combination of models and levels, α is positive (α is negative at 400 hPa for GISS-E2-R). All but five models have all of their α values lower than 1.0. Of these five models, four have their α× value higher than 1.0 and one, the HADGEM2-ES, has an α× value of 0.86 but with an α value at 600 hPa of 1.01. Twenty-five models out of 33 have an α× value greater than 0.5, and 17 models out of 33 have their three α values between 0.5 and 1.0. This shows that most models tend to warm in accordance with a dynamic that is closer to the moist theory than to the dry theory during SON. The IPSL-CM5A-LR has the highest α× value that is less than 1.0. The CANESM2 has α values that are similar to the MODEL-MEAN.
 The α values measure the relative contribution of dry and moist dynamics to the AMT warming in the rcp45 scenario over the 21st century, assuming that only non-Arctic sources are responsible for the warming. An α× value close to 0.5 indicates that both propagation theories would contribute in equal proportions to the AMT warming. The CANESM2 with α× ≈ 0.6 and the MODEL-MEAN with α× ≈ 0.7 are examples of this mixed behavior. More than half of the models (19 out of 33) have an α× value between 0.25 and 0.75, which makes mixed propagation the predominant behavior among models. The same analysis using annual-mean data instead of SON mean is shown in th right panel of Figure 3. Thirty out of 33 models have an α× value between 0.25 and 0.75, with no models below 0.33. Moreover, no model has an α× value above 0.86. These statistics are consistent with the finding that during SON from 40 N to 60 N, about half of the observed moist overturning circulation is driven by latent heat fluxes ascending in transient eddies [Shaw and Pauluis, 2012, Fig. 16]. This result is also confirmed by the analysis of Laliberté et al. , where it is shown that the poleward branch of midlatitude eddies follows moist dynamics, and the equatorward branch follows dry dynamics.
 We have shown that it is possible to constrain the intermodel spread of Arctic midtropospheric warming in simulations of the 21st century using midlatitude changes in near-surface temperature and latent heat content. We obtained this result by investigating how dry and moist dynamics communicate near-surface warming anomalies to the midtroposphere. We postulated that in the dry regime near-surface warming anomalies in θ should be homogenized along climatological dry isentropes on seasonal time scales by synoptic eddies. We then argued that in this regime the AMT warming should be close to the near-surface midlatitude warming. In the moist regime, the dynamics of midlatitude synoptic eddies no longer redistributes mass along surfaces of constant potential temperature since the latent heat release associated with condensation and precipitation introduces large diabatic fluxes.
 We postulated that in the moist regime, near-surface warming anomalies in θe should be homogenized along climatological moist isentropes on seasonal time scales by synoptic eddies. We therefore argued that in an atmosphere where the moist dynamics is dominant the AMT warming associated with poleward heat fluxes should not only be determined by the midlatitude near-surface warming but also by the increase in midlatitude near-surface latent heat content.
 We have expanded upon the analysis of Frierson  by arguing that, because midlatitude warming anomalies will propagate slantwise within synoptic eddies, midlatitude near-surface warming is a good predictor of AMT warming. We used a mathematical method that is similar to a linearization along climatological dry and moist isentropes. This explains why we could describe the 21st century AMT warming using monthly-averaged warming anomalies even if temperature anomalies typically propagate to the AMT with submonthly time scales [Graversen et al., 2008]. It is consistent with the conclusions of Laliberté et al.  in that neither the dry dynamics nor the moist dynamics by themselves can explain the AMT warming. This leads us to conclude that any theory of AMT warming based on changes in poleward heat fluxes should include a moist component and that the importance of the moist component is model-dependent.
 Our results appear to be in agreement with the increase in poleward latent heat fluxes into the Arctic observed in simulations with greenhouse warming analyzed by Kay et al. , but they cannot explain why the increase in latent heat fluxes is almost exactly compensated by a decrease in poleward sensible heat fluxes into the Arctic. It remains an open question why this compensation occurs.
 We have not quantified how local processes involving vertical heat fluxes could also affect the AMT warming. For example, the weakening of the Arctic surface temperature inversion over the 21st century [Deser et al., 2010] could contribute to the AMT warming by enhancing Arctic moist convection. The simulated AMT warming would then be larger than the AMT warming directly attributable to poleward heat fluxes. This would lead to an overestimation of α and might explain why three models have α values larger than 1.0 during SON.
 Many studies of Arctic climate change explain the amplification of surface warming by attributing it to reduced sea ice cover and increased ocean heat transport [Holland and Bitz, 2003; Serreze and Francis, 2006; Boé et al., 2009; Deser et al., 2010]. It has however been shown by Screen et al.  that midlatitude SST warming drives almost all of the SON AMT warning trends and contributes to about a quarter to a fifth of the surface Arctic warming. Our results along with the conclusions of Screen et al.  would therefore suggest that the increase in near-surface midlatitude latent heat content might be responsible for a significant portion of the surface Arctic warming. While our work highlights the possible role of midlatitude moist dynamics on the Arctic midtropospheric warming, it still remains an open question how this warming could be communicated to the Arctic surface.
Appendix A: Propagation of warming along isentropes
 For SON and for the annual-mean of every year at each point (ϕ, p) in the latitude and pressure plane, we set the propagated equivalent (moist) potential temperature to , where ϕ850, (ϕ, p) is the latitude at which the historical climatological moist isentrope passing through (ϕ, p) intersects the 850 hPa pressure surface. It can be found by solving the equation for each (ϕ, p). This task is accomplished by linearly interpolating along ϕ. Note that this expression involves climatological values from the historical experiment only. We convert into a temperature propagated along moist isentropes by solving for the temperature with a relative humidity equal to its climatological historical value in the thermodynamical expression for : . We then define anomalies from the historical climatology as . The propagated potential temperature , the temperature propagated along dry isentropes Tθ, and the associated anomalies δTθ are found similarly. We find the AMT warming anomalies by subtracting the climatological historical from the temperature T. In Figure 2, we use an ensemble average over multiple realizations by first computing the propagated anomalies for each realizations and then averaging , δTθ, and δT across the ensemble.
 We note that a different analysis method was tried in which δT, δTθ, and were computed using trends instead of differences between eras. It resulted in very similar α values.
 This work was supported by the Natural Sciences and Engineering Research Council (NSERC) G8 Research Initiative grant “ExArch: Climate analytics on distributed exascale data archives” as well as by an NSERC Strategic Project grant. We thank the Institut Pierre-Simon Laplace and the British Atmospheric Data Center for giving us access to their data and computing resources. We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in the Table provided in supplemental material) for producing and making available their model output. For CMIP, the U.S. Department of Energy's Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We thank Lawrence Mudryk for his numerous suggestions that have contributed to greatly improve this work. We acknowledge two anonymous reviewers for their thoughtful comments and suggestions.