We explore annual and seasonal changes in moist static energy transport (MSE) into the Arctic over the 21st century as projected by the National Center for Atmospheric Research Community Climate System Model, version 3. Self-organizing maps are used to assess changes in MSE and its components—the latent heat flux and dry static energy flux (DSE)—across 70°N. These are computed from multilevel fields of specific humidity, meridional wind, geopotential, and temperature spanning periods in the 20th century (1960 to 1999) and the 21st century (2070 to 2089). The 21st century simulation incorporates the Special Report on Emission Scenarios A2 scenario. A strong decrease in tropospheric DSE of about 9% by the end of 21st century offsets an increase in latent heat flux of about 20% relative to its 20th century average. The combined changes result in a total annual decrease in tropospheric MSE of about 3% by the late 21st century. The difference, while statistically not significant, represents a weak negative feedback on Arctic amplification. Self-organizing maps also allow an attribution of changes in MSE to factors related to varying atmospheric dynamics and/or thermodynamics. A positive contribution to the MSE related to more frequent low pressure systems in high latitudes (dynamic factor) occurs in all seasons, particularly in the summer. The decrease in DSE is mainly due to a weakened poleward temperature gradient (thermodynamic factor) during all seasons except summer, which in turn is caused by amplified warming at high latitudes as a result of increased greenhouse gases.
 Large changes have occurred in the Arctic during recent decades. Sea ice, glaciers, and permafrost are declining [e.g., Stroeve et al., 2012; Sharp et al., 2011; Romanovsky et al., 2011], patterns of rain and snowfall are shifting [Finnis et al., 2007; Brown and Robinson, 2011], runoff is increasing [Peterson et al., 2002; Holland et al., 2007], and tundra vegetation is becoming shrubbier [Tape et al., 2006; Chapin et al., 2005], to name only a few. These transitions add to the growing body of evidence suggesting that the Arctic is heading toward a new state. Moreover, there are no obvious mechanisms within the Arctic system that can reverse this trajectory [Francis et al., 2009]. The motivation for this study is to explore some of the linkages between the Arctic and global climate system that may influence the sign and pace of high-latitude change.
 One such mechanism is the poleward transport of atmospheric moist static energy (MSE), comprising sensible heat, latent heat, and geopotential energy. In the 20th century climate, this component of the Arctic's energy budget supplied approximately 98% of the net radiation annually exchanged with outer space north of 70°N [Nakamura and Oort, 1988; Overland et al., 1996]. The annual-mean contribution from surface exchanges was small, but seasonal variations, alternating from an input to the ocean during summer to a net loss during winter, strongly influenced seasonal changes in Arctic heat storage [Serreze et al., 2007a, 2007b]. As global-mean warming continues, the Arctic response will be more pronounced than in lower latitudes because of the predominantly positive feedback involving ice and snow [e.g., Serreze and Francis, 2006a, 2006b]. The amplified Arctic warming suggests that the lower-tropospheric poleward temperature gradient will relax, poleward advection of sensible heat will decrease, and Arctic warming will weaken. Although climate model simulations support this reasoning, they also suggest that increases in the poleward transport of latent heat will compensate to some extent for the reduction in sensible heat transport [Alexeev et al., 2005; Hwang and Frierson, 2011]. Observational evidence only adds to the importance of understanding and predicting poleward energy transport, as changes in the atmospheric northward energy transport can influence Arctic surface air temperatures [Graversen, 2006].
 This study explores how the tropospheric moist static energy flux is projected to change in the late 21st century as the concentration of atmospheric CO2 continues to increase. We utilize a neural network technique called self-organizing maps (SOMs) [Kohonen, 2001] to analyze sea-level pressure fields from one simulation by the National Center for Atmospheric Research Community Climate System Model, version 3 (NCAR CCSM3), during the late 20th century (1960–1999) and late 21st century (2070–2089). The SOM technique is selected for this analysis because it reduces large data sets into representative, fundamental patterns organized in a matrix of 2-D fields—geographic maps in this case—that are expressed in a visual and intuitive rendering. The maps are situated in the matrix relative to one another according to their similarity. For each circulation pattern identified by the SOM, we derive the tropospheric latent heat flux (LH) and the flux of dry static energy (DSE) across 70°N. An approach developed by Cassano et al.  is used to assess the portion of change in each of these fluxes that can be attributed to changes related to dynamics, another related primarily to thermodynamics, and a third to the interaction of the two.
Section 2 describes the data sets and a brief overview of the SOM technique. Section 3 explains the master SOM, followed by an analysis of future changes in DSE, LH, and MSE, and an approximate attribution of those changes. Conclusions and future directions are discussed in section 4.
2 Data and Methodology
2.1 Data Sets
 Multilevel, six-hourly fields of specific humidity, temperature, geopotential, and meridional wind were obtained for a single run of the NCAR CCSM3 with horizontal resolution of about 1.4°. Major features of the model's hydrological cycle compare well to observations [Hack et al., 2006]. The 21st century simulation incorporates the Special Report on Emission Scenario (SRES) A2 scenario [Nakicemovic and Swart, 2000], which appears to be the most representative of actual emissions [Rahmstorf et al., 2007; Pielke et al., 2008]. Realistic forcing is applied before 1990, after which the A2 scenario is employed. Additional details about the model and the A2 scenario are available in Collins et al. [2006a] and Skific et al. [2009a].
 The original six-hourly data were reduced in size by subsetting from global coverage to the region north of 60°N, using daily output (1200 UTC), and focusing on the troposphere. Data were converted from hybrid levels to pressure levels. Levels above 300 hPa were not included in this analysis because model fields near and above the tropopause are less reliable [Cordero and Forster, 2006], as are validation data from reanalyses and rawinsondes. In addition, over two thirds of the atmospheric mass and virtually all of the water vapor in the Arctic atmosphere exists in the troposphere (see section 3 for more detail). The time slices used in this study span 1960–1999 from the 20th century experiment (20C3M), as well as 2010–2030 and 2070–2090 from the SRES A2 scenario. The latter two periods were chosen to be consistent with results from the Arctic Climate Assessment Report [ACIA, 2004, www.acia.uaf.edu;] [Serreze and Francis, 2006a, 2006b], to represent the so-called emerging and mature greenhouse states. Sea-level pressure (SLP) fields are extracted for the same time periods. The emerging time interval from 2010 to 2030 is used only to increase the number of daily samples to train the SOM algorithm. The SLP fields are interpolated from the original 1.4° × 1.4° grid to a 200 km × 200 km equal area-scalable Earth grid [Armstrong et al., 1997] (http://nsidc.org/data/ease/), covering the area north of 60°N with 51 × 51 grid points. Daily fields of SLP from the European Centre for Medium-Range Forecasts Reanalysis (ERA-40) [Uppala et al., 2005] were also interpolated to the equal area-scalable Earth grid and were used to construct the SOM and to validate the model results for the 20th century. The results of this validation are presented in Skific et al. [2009a] and will be described here only briefly.
2.2 Self-Organizing Maps
 A self-organizing map (SOM) algorithm is a neural-network technique that attempts to reduce the dimensions of a large data set by organizing it into a two-dimensional array or matrix [Kohonen, 2001]. For this study, the data set used for the SOM analysis consists of a time series of 2-D fields of SLP over the Arctic from both ERA-40 and CCSM3. The SOM algorithm organizes the daily fields into clusters of similar maps by identifying SLP patterns that represent the range present in the original data set. The 2-D maps in the SOM matrix provide a more intuitive rendering of pattern characteristics and their relative frequency of occurrence than is achieved by other statistical tools, such as empirical orthogonal functions.
 A brief description of the SOM method is presented here; see Skific et al. [2009a] for further detail. The initial step creates a first-guess set of maps consisting of an arbitrary number of SLP patterns, which are called reference vectors. Each of these vectors has a position or node assigned on a two-dimensional array. The size of the matrix is chosen to balance having enough nodes to capture the important features in the data while being small enough to visually interpret the patterns and display them conveniently. In this study, we use a 7×5 matrix; the results are insensitive to small changes in this size [Skific et al., 2009a]. The first-guess reference vectors are the two eigenvectors, derived from the covariance matrix of the SLP fields with the largest eigenvalues. These eigenvectors are placed in the corners of the map, with the central cluster corresponding to the mean of the data set. The rest of the reference vectors are then derived by using linear interpolation. The vectors are then “trained” by presenting each daily field to the SOM, and the similarity between the data sample and each of the reference vectors is then calculated, usually as a measure of Euclidean distance in space. The “best match” reference vector is identified and further refined in an iterative process through which the centroids of the clusters of daily maps matched to each node are modified to minimize the distances between the samples and the reference vectors. The resulting clusters of maps that define each node become organized on a two-dimensional array in such a way that more similar patterns are placed closer together, while those less similar are farther apart, allowing a more intuitive interpretation of patterns and their relationship to each other in the matrix. Once all the SLP anomaly fields have been assigned to a node, the frequencies of occurrence can be determined, i.e., the fraction of daily fields that reside in each cluster.
 The SOM method is applied to finding dominant patterns in the daily sea-level pressure anomaly fields from ERA-40 (1958–2001) and from CCSM3 for periods 1960–1999, 2010–2030, and 2070–2089 for the region north of 60°N. Fields from the period of 2010–2030 are included in the SOM training to increase the number of steps in the final convergence phase, which must be sufficiently long to achieve good statistical accuracy [Kohonen, 2001]. Daily SLP anomalies are created by subtracting the domain-averaged SLP for each daily map from the SLP at each grid point on that day. As argued by Cassano et al. , these anomalies are a better representation of the SLP patterns, because eliminating the daily mean focuses the classification procedure on pressure gradients, which are a better representation of circulation features. Areas of elevation higher than 500 m are removed from the fields because pressure reduction to sea level in the areas of high elevation can lead to unrealistic patterns.
 Ascribing a particular daily SLP sample to a specific circulation pattern in the SOM is also useful for analyzing associated variables for the same days as those in each cluster, enabling the description of conditions associated with a specific circulation regime. In this study, we apply this technique to investigate the characteristics and changes in the horizontal energy fluxes across 70°N. Details of this procedure are available in Skific et al. [2009a, 2009b].
3 Poleward Energy Fluxes
 To calculate the total latent heat flux LH across 70°N in units of W m–2, we follow the equation given in Overland et al. :
where the operator [A] indicates a zonal mean, is a time mean, g is gravity (g = 9.8 ms–1) and L is the latent heat of vaporization (L = 2.5×106J kg–1). After calculating the zonal mean of the time-averaged meridional moisture flux for each tropospheric level, we integrate the level-mean values over the latitude band. The expressions are then integrated vertically and divided by the area north of 70°N to obtain units of W m–2.
 An analogous expression is used to calculate the dry static energy flux (DSE) across 70°N consisting of the sum of sensible heat and geopotential energy fluxes
where cp is the specific heat of air under constant pressure (cp = 1000 Jkg–1K–1), T is temperature, and z is geopotential height. To obtain units of W m–2, we integrate values of vT and vz at each level over the latitude band, then integrate vertically, and finally divide this quantity by the area north of 70°N. The moist static energy flux (MSE) across 70°N is the sum of the dry static energy flux and latent heat flux.
3.1 SOM of Arctic SLP Patterns
 The self-organizing map of SLP anomalies north of 60°N is presented in Figure 1. The matrix of maps represents the dominant circulation regimes in which the atmosphere tends to reside according to the data sets used to create it, and is hereafter called the “master SOM.” Familiar features in the high-latitude pressure fields are evident, such as the Icelandic and Aleutian low-pressure centers typical of winter (bottom right), Beaufort highs (upper right), and central-Arctic lows of summer (bottom left). Less distinct patterns are located near the center of the SOM. The frequency of occurrence (FO) is defined as the percent of days that belong to a particular cluster out of the total number of daily fields (Figure 2a). Values of FO that are significantly different (>95% confidence) from an expected value for a random binomial distribution (i.e., 100% ÷ 35 = 2.86%) are assessed using the approach described in Skific et al. [2009a]. The confidence test includes an adjustment for the serial correlation and consequent reduction in degrees of freedom by dividing the number of samples by 7, as the atmosphere tends to maintain a circulation regime for approximately one week. This results in a higher threshold for determination of a significance level. For more details see Skific et al. [2009a] and Cassano et al. .
 The FOs of 20th century CCSM3 SLP patterns (annual mean in Figure 2a and seasonal means in Figure 2b) suggest that the bordering clusters, which tend to feature pronounced gradients, occur more frequently during fall through spring than those positioned in the middle of the SOM. Patterns in the left-middle of the master SOM represent mainly summer conditions, characterized by relatively weak pressure systems. While the distribution of FOs for the model fields does not reveal a dominance of any particular group of clusters, the real atmosphere does exhibit a preference for the regimes appearing in the middle of the SOM, which are characterized by moderate high pressure over the central Arctic. Figure 3 presents the seasonal differences in FO between the 20th-century time slice from the CCSM3 realization and that from ERA-40. The clusters in the upper-middle portion of the master SOM, characterized by moderate high pressure over the central Arctic, appear more frequently in ERA-40 during fall through spring, while the CCSM3 patterns in the bordering clusters have a higher FO. In summer, the modeled fields have a higher FO of patterns with strong low pressure in the central Arctic (left side of the SOM). These differences are consistent with the assessment of Arctic atmospheric circulation in CCSM3 by DeWeaver and Bitz . Although the differences in the distribution frequencies and SLP climatologies appear substantial, one should note that this comparison is between two single realizations of the 20th century climate, and some differences would be expected between any two representations. Studies by Cassano et al.  and Chapman and Walsh  found that the CCSM3 model is one of the most realistic of the group participating in the Intergovernmental Panel on Climate Change Fourth Assessment Report for simulating Arctic atmospheric circulation, and Skific et al. [2009a] also found that this model simulation realistically simulates 20th century moisture flux across 70°N.
3.2 Attribution of Annual and Seasonal Changes in Moist Static Energy Flux
 In this section, we explore mechanisms leading to annual and seasonal changes in the CCSM3 moist static energy flux across 70°N from the 20th century to the late 21st century. The MSE is separated into contributions from the dry static energy flux (DSE) and the latent heat flux (LH).
3.2.1 Dry Static Energy Flux
 The total percentage change in the annual-mean dry static energy flux, and that for each season, is presented in the top panel of Figure 4. As expected, the total flux decreases by the end of the 21st century in this model simulation by about 5.8 Wm–2 (9%). The DSE decreases in all seasons.
 To better understand the causes of these changes, we apply an attribution method introduced by Cassano et al.  in their investigation of changing net precipitation in the Arctic. The method separates contributions owing to changes in the FO of each atmospheric circulation pattern in the SOM from changes in the variable of interest (in this case, energy fluxes) associated with each of the fixed circulation patterns in the SOM. Effects of interactions between these changes are also accounted for. The future, domain-averaged value of a quantity is calculated as the mean of the quantity for all samples that belong in a particular cluster. In equation ((1)) below, xi is the cluster-averaged value for node i (i = 1 to N, where N = 35 in this study) during the initial time period, Δxi is the change in its cluster-averaged value between the two time periods, fi is the frequency of occurrence of node i during the initial time period, and Δfi is the change in node frequency between the two time periods.
 Expansion results in the following:
where the first term on the right of equation ((2)) represents the effects of changing FO for each pattern in the SOM. This term is called the dynamic factor. The second term captures changes in a variable within a SOM cluster that are separate from effects of changing circulation. Because changes in energy fluxes within a particular pattern are likely to be caused by primarily (but not exclusively) thermodynamic effects—i.e., changing poleward temperature/geopotential gradients for DSE and moisture gradients for the latent heat transport—we refer to this term as the thermodynamic factor. The third term captures a combination of the two, and tends to be relatively small.
 The change in annual FO Δfi from the late 20th century (1960–1999) to the late 21st century (2070–2089) is shown in Figure 5a, with seasonal changes presented in Figure 5b. The FO of the patterns on the left and upper right side of the master SOM increase in the future. Patterns in the middle, characterized by weak or moderate high pressure over the Arctic, decrease in FO in this model simulation. These changes suggest that by the end of the 21st century, the Arctic will experience generally lower pressure and likely increased storminess. The cluster-averaged annual DSE across 70°N, xi, for the 20th century is shown in Figure 6a, with seasonal values presented in Figure 6b. Cluster-averaged values are means of the all of the daily samples that belong in a particular cluster. The largest transports of DSE occur for patterns with pronounced low pressure in the North Atlantic that are found along the right of the master SOM and for those with low pressure over the central Arctic on the left. Patterns in the middle with high pressure over the central Arctic generally do not bring much DSE into high latitudes. Because poleward temperature gradients are projected to decrease, the temporal change in the cluster-averaged DSE Δxi is negative for all clusters (not shown), and thus the thermodynamic factor in equation ((2)) is also negative.
 To elucidate seasonal changes and their attributions, we calculate and present the components of the three terms in equation ((2)) for each season. The FOs (fi) for the 20th century, along with statistically significant differences from a uniform distribution, are shown in Figure 2b, and the corresponding cluster-averaged DSE (xi) for the 20th century is displayed in Figure 6b. Summer patterns tend to occupy clusters toward the left of the master SOM more frequently, which are characterized by either a relatively diffuse pressure patterns or weak-to-moderate low pressure over the central Arctic. In winter there is a clear dominance of the clusters to the right of the SOM, corresponding to a strong Icelandic low in the Atlantic sector, a well-developed Aleutian low in the Pacific, and high pressure over the western Arctic. Spring and autumn FOs are relatively evenly distributed throughout the SOM matrix. A common characteristic in the seasonal cluster-averaged DSE (Figure 6b) is weak energy transport for the clusters in the middle and stronger energy transport for those along the left and particularly right of the SOM. Low pressure over the central Arctic generally favors increased DSE across 70°N. The clusters in the right side of the SOM, associated with low pressure in the Atlantic sector, generate strong transport in the winter and fall season. The energy flux is generally the weakest in summer when the poleward temperature gradient and horizontal sensible heat flux are also weakest. Interestingly, DSE is strong in the fall season, almost comparable to winter transport in this model simulation.
 The changes from the 20th to late 21st century by season are presented in Figure 5b (Δfi). Circulation patterns in the left side of the master SOM (low pressure over the Arctic) are projected to become more frequent in all seasons, particularly during summer. The patterns in the right of the SOM (low pressure in the Atlantic sector and eastern Arctic) will also occur more frequently. Patterns in the middle of the SOM (high pressure over the central Arctic) are projected to become less frequent in all seasons, particularly in the summer.
 Using the attribution method described previously, we derive each of the terms in equation ((2)) to obtain the contributions to the total change in DSE by the dynamic, thermodynamic, and combined factors. The first column in Figure 7 presents the annual and seasonal results. The DSE across 70°N decreases by about 5.8 W m–2 (9%), which is driven by the reduction in the thermodynamic term. The dynamic factor increases slightly owing to an increased frequency of circulation patterns that are characterized by low pressure in the central Arctic and North Atlantic sector by the end of the 21st century. These pressure patterns favor stronger northward transport of sensible heat and geopotential energy. The largest changes in the dynamic term occur in fall and summer, but are relatively small compared to the thermodynamic term. The reduction in the thermodynamic term arises from the general decrease in cluster-average fluxes (Figure 5b). DSE decreases most in fall and winter, consistent with stronger Arctic amplification during these seasons [Serreze and Francis, 2006a]. The reduction is driven mainly by the reduction in eddy transport, which acts to suppress initial perturbations in the meridional temperature gradient [Held and Soden, 2006; Hartmann, 1994]. Amplification is weaker in summer [Teng et al., 2006], so the reduction in poleward temperature gradient is smaller than in other seasons. The contribution by the combined factor to the total change, both annually and seasonally, is small.
3.2.2 Latent Heat Flux
 Changes in latent heat flux (LH) across 70°N were discussed in detail in Skific et al. [2009a]. The results are summarized here but from a different perspective, consistent with that for the dry static energy flux.
 Daily fields of LH are associated with particular circulation patterns in the SOM as described for the DSE. The cluster-averaged values of the LH across 70°N are presented in Figure 8a. There are many similarities between this and the cluster-averaged DSE shown in Figure 6a. Red areas correspond to clusters in the master SOM characterized by strong low pressure in the north Atlantic and central Arctic, both of which tend to advect large quantities of moisture poleward. The seasonal contributions to the 20th century cluster-average LH appear in Figure 8b. The largest poleward transports of moisture occur in the summer, primarily because of the deeper moist layer and more poleward wind vectors [Groves and Francis, 2002], which together lead to stronger advection in upper levels. Once again, the patterns in the right half and far left of the SOM contribute most. Even though the temperature gradient is weak during summer, the gradient in moisture is strong and cyclones penetrate farther northward, driven by baroclinicity that is sustained by land/ocean differential heating and augmented by the coastal orography [Serreze and Barry, 2005]. The LH is weakest during winter, because specific humidity is low and the moist layer is shallow and often capped by a strong surface-based inversion. Clusters in the lower right of the master SOM, corresponding to low centers in the North Atlantic and Pacific, are effective in transporting moisture during all seasons. These systems become well developed and particularly vigorous in the winter when baroclinicity is enhanced by strong north-to-south, land-sea, and ocean-atmosphere temperature gradient. As in the case for the DSE, patterns in the middle of the SOM (associated with high pressure over central Arctic) are associated with weak moisture transport in all seasons.
 The projected annual and seasonal changes in LH across 70°N from the 20th to the late 21st century are presented in the middle panel of Figure 4. By the end of the century, the annual LH increases by 3.3 W m–2 owing to increased atmospheric water vapor content and enhanced meridional moisture gradients. The largest increase in moisture transport occurs in summer (about 1.1 W m–2), which accounts for about 31% of the total change. Winter, spring, and fall contribute approximately 25%, 22%, and 22%, respectively.
 To better understand the causes of these changes, we again apply the method for separating contributions from the dynamic, thermodynamic, and combined terms in equation ((2)) to the total change by the end of the century. The total change in cluster-averaged LH Δxi is presented in Figure 9. It is obvious that by the late 21st century, latent heat flux increases in the majority of circulation patterns on the master SOM, as is also the case for the seasonal contributions (not shown). These changes will determine the sign of the thermodynamic term in equation ((2)) because the annual and seasonal FOs for the 20th century fi are always positive. The three terms in equation ((2)) are calculated for the LH using the same methodology as for the DSE.
 The second column of Figure 7 shows total annual and seasonal changes in the latent heat flux, along with contributions from the dynamic, thermodynamic, and combined terms. The thermodynamic factor clearly plays a dominant role and is responsible for approximately 80% of the total change in latent heat flux across 70°N, annually and in each season. Thermodynamic effects are caused by an increased atmospheric moisture content and poleward moisture gradient, both of which lead to a larger transport of poleward moisture. The dynamic term accounts for about 16% of the total annual change, while 3% is due to the combined term. The positive dynamic term is related to the statistically significant increase in FO of clusters to the left of the SOM, corresponding to low pressure over the central Arctic that generally transports substantial moisture into the Arctic. In addition, the FO decreases for patterns in the middle of the SOM, which are associated with high pressure over the central Arctic and generally bring little moisture poleward.
 The largest increase in poleward latent heat flux occurs in summer owing to the exponential relationship between saturation vapor pressure and temperature. In the warmer low latitudes, a given increase in temperature will lead to a relatively larger increase in saturation vapor pressure, and presumably vapor pressure, than that at higher latitudes for the same amount of warming, which results in an increased poleward specific humidity gradient. In summer, high-latitude poleward temperature gradients, and thus moisture gradients, are also sustained by regional land-ocean differential heating. The contribution by the dynamic term is largest in summer because statistically significant changes in FO tend to occur mainly for summer patterns (Figure 5b), which tend to favor a convergent circulation and larger poleward moisture fluxes.
 During fall the dynamic term plays a relatively large role in the total LH change (~30%) owing to the statistically significant increase in the FO of patterns with low pressure over the central Arctic and North Atlantic (Figures 5b and 7), both of which favor an increased poleward moisture transport (Figure 8b). The thermodynamic term still dominates, however, accounting for over half of the total increase in fall moisture transport. The combined factor accounts for a small but non-negligible portion of the change (14%). Physically this may arise through an increased surface flux of moisture owing to stronger, more poleward winds or perhaps a change in circulation owing to latent heat release through condensation.
 In spring and winter the total change in moisture flux from the 20th to late 21st century is governed mainly by the thermodynamic term. In winter, changes in the dynamic factor play the smallest role of any season—about 3% of the total winter increase (Figure 7). Although a statistically significant increase in FO of clusters in the upper right and left corners of the master SOM occurs in winter, these patterns do not have the potential to bring substantial amounts of moisture into the Arctic in the winter season (Figure 8b). These results clearly suggest that thermodynamic processes are responsible for the projected changes in the poleward latent heat flux in all seasons, with dynamics playing a secondary role.
3.2.3 Moist Static Energy Flux
 Changes in the poleward fluxes of latent heat and dry static energy in the troposphere, along with the mechanisms responsible for the changes, can be combined to evaluate total annual and seasonal change in the poleward moist static energy transport projected for the end of the 21st century. The percentage and actual change in MSE is presented in the bottom panel of Figure 4 and in Figure 7. In this model realization the total change in MSE across 70°N is small (about 2.5 W m–2 or 3%) and negative, driven primarily by a decrease in DSE. While the opposing changes in DSE and LH are statistically significant at the 95% confidence level, their combination (MSE) is not, although the value does agree with that obtained in a previous study by Hwang et al. . Even though the change in MSE is small, it suggests that as greenhouse gases increase, the MSE flux from low latitudes into the Arctic below 300 hPa will not have a large effect on Arctic amplification, and may actually weaken it, thereby constituting a negative feedback. However, this does not completely offset the Arctic warming in this model run, thus pointing to the role of sea-ice loss as well as increased clouds and water vapor, related to the substantial increase in LH, as the main drivers of future Arctic amplification.
 As for DSE and LH, we assess the contributions to MSE changes by the three terms in equation ((2)). A summary of the results appear in the right column of Figure 7. In the annual mean, the total MSE decrease results from a positive contribution from the dynamic term that is overwhelmed by the negative contributions from thermodynamics. Summer change (about 1%) is driven primarily by the dynamic term. During fall, winter, and spring, however, the smaller increases in the thermodynamic factor caused by LH are opposed by decreasing DSE owing mostly to a weakened equator-to-pole temperature gradient [Hwang et al., 2011]. Consequently, the MSE during these seasons (approximately 4%, 7%, and 1%, respectively) is reduced overall.
 Results presented to this point are derived from fluxes calculated for the layer below 300 hPa. To assess the contribution from fluxes above this level, we calculate MSE from the surface to the top of the atmosphere (TOA) as a residual from the CCSM3 monthly mean TOA and surface fluxes available in the PCMDI archive. The surface flux FSFC is the sum of net radiation and turbulent fluxes over the area north of 70°N, and the TOA flux. FTOA is the sum of upward longwave and net shortwave fluxes. The MSE crossing the imaginary wall at 70°N is the difference between FSFC and FTOA. Figure 10 presents the seasonal cycle of this residual MSE (blue line), FSFC (green line), and FTOA (red line) for the late 20th century (1960–1999) (solid) and the late 21st century (2070–2089) (dashed). The poleward MSE flux across 70°N decreases in the future, driven primarily by the decrease during late fall and winter, which agrees with our findings for the troposphere. Moreover, the total change in the MSE from the residual calculation is similar to that derived for the troposphere only (ΔMSE total = −3.3 W/m2), which indicates that the change in DSE above the tropopause does not contribute significantly to the total change. It may be that that lower tropospheric gradients of DSE are more important to eddy growth, while the gradients in the upper troposphere are less important for eddy growth and energy transfer. D. Frierson (personal communications, 2010) argues that under global warming conditions, DSE increases near the tropopause and in the lower stratosphere owing to a rising tropopause rather than to changes in gradients.
4 Discussion and Conclusions
 The projected reduction in DSE exceeds the increase in LH into the Arctic in this simulation. Held and Soden  analyzed an ensemble of fully coupled general circulation models (GCMs) forced by the SRES A1B scenario and found a general increase in MSE across 70°N. An earlier study by Manabe and Wetherald  explored the equilibrium responses of GCMs to warming and revealed only a partial compensation of a projected moisture transport increase by decreases in dry static energy. Hwang et al.  found that GCMs with larger Arctic amplification project that changes in MSE will be small and most likely decrease in the future. Because CCSM3 exhibits a relatively large Arctic amplification, our assessment of a decreased MSE by the end of the 21st century is consistent with Hwang et al. . Moreover, earlier studies suggest that CCSM3 stands out as one of the most realistic in simulating the Arctic system [Lipscomb, 2001; Bitz et al., 2012; Bitz and Lipscomb, 1999; Gerdes and Köberle, 2007; Stroeve et al., 2007]. Because sea ice thickness influences the Arctic response to greenhouse gas forcing [Holland and Bitz, 2003], it is likely that refined sea ice physics in CCSM3 contributes to its success in simulating sea ice loss. Bitz et al.  found that changes in sea-ice thickness, extent, and surface temperature in CCSM3 to be about double the mean change of models participating in the Coupled Model Intercomparison Project. This Arctic amplification contributes to a large decrease in DSE owing to a weakened poleward temperature gradient.
 The results of this study suggest that the tropospheric latent heat flux across 70°N will increase by about 21% by the end of 21st century, but it is opposed by a larger decrease in DSE of about 9% from its 20th century average. The MSE is projected to decrease in all seasons except in summer. These combined changes yield a total decrease in the transport of tropospheric MSE of about 3% by the late 21st century that is not statistically significant. Hwang and Frierson  found a small increase in MSE across 40°N averaged across a number of model simulations of future conditions, but this signal weakened and became less consistent with latitude. Estimates of total atmospheric MSE transport across 70°N indicate that the change in MSE above the tropopause does not contribute significantly to the total change, but more research is needed to better understand how polar MSE transport varies with altitude as the climate warms. Based on this model realization, we conclude that a reduction in the MSE of about 3% in the late 21st century relative to the late 20th century in response to realistic increases in greenhouse gas concentrations act as a weak negative feedback to counteract Arctic warming.
 The SOM technique provides a means to separate causes for these changes into factors related to dynamics and/or thermodynamics. The change in the frequency of occurrence of fundamental atmospheric patterns, as identified by the SOM classification technique, contributes to an increase in MSE by the end of the 21st century. Patterns that feature predominant low pressure centers in the North Atlantic—and to a lesser extent in the Arctic—are effective in transporting MSE poleward, and their increased FO accounts for much of the positive dynamic contribution. However, the seasonal differences in the thermodynamic factors are more illuminating as to the mechanisms at work.
 The MSE in summer exhibits an increase (1% larger than the 20th century value). The FO of high-latitude cyclones increases most in the warm season, which accounts for most of the enhanced MSE. Two opposing thermodynamic effects nearly cancel each other: a weakening of the poleward temperature gradient in the future, which reduces the eddy sensible heat transport, makes a negative contribution, while the latent heat flux increases owing to a stronger poleward moisture gradient and higher water vapor content, a positive contribution.
 In fall, winter, and spring the pieces of the puzzle align very differently. In all three seasons the change in MSE is negative, with the largest decrease in the winter. While the contribution from LH is still positive and results almost exclusively from thermodynamic effects, it is overwhelmed by a negative contribution from the DSE. Polar amplification of warming in the future is responsible for this reduction, as advection of sensible heat is reduced. Our conclusion is consistent with results from Bitz et al.  who found that the CCSM3's projected decrease in DSE by the end of the 21st century is greater than the increase in northward LH.
 During the summer of 2004 a group of experts on various aspects of the Arctic climate system spent a week comparing recent observations and discussing possible implications for the future. They concluded that the Arctic system appeared to be headed for a new seasonally ice-free state [Overpeck et al., 2005]. They also suggested that there appeared to be no feedback mechanisms within the Arctic that were capable of diverting this trajectory, but that perhaps interactions with lower latitudes would eventually slow the pace of Arctic change. Changes in poleward energy transport were identified as one possible mechanism. The research presented in this study, although based on one realization from one model, provides evidence supporting this expectation. While this mechanism may slow the observed trajectory of change, warming is still expected to continue owing to changes in ocean circulation, clouds, sea ice, snow cover, and water vapor content. Further research is needed to determine whether other models simulate this relationship and ultimately whether MSE decreases over time in the real atmosphere as greenhouse gases continue to accumulate.
 We are grateful to two anonymous reviewers and to Dr. James Screen for providing excellent suggestions that greatly improved this manuscript. We also acknowledge and appreciate the technical support of Gary Strand from the National Center for Atmospheric Research for providing the CCSM3 daily outputs used in this study. Comments and valuable suggestions were provided by Dargan Frierson from the Department of Atmospheric Sciences, University of Washington and Steve Vavrus from the Center for Climatic Research, University of Wisconsin-Madison. Special thanks go to Teuvo Kohonen in the Department of Computer and Information Science at Helsinki University of Technology for his helpful advice in applying the self-organizing maps algorithm. This work is funded by the National Science Foundation, NSF ARC-0455262.