1. Introduction
A range of climate models with varying complexity, from simple climate models to sophisticated coupled general circulation models (GCMs), have indicated a warming of the climate in simulations forced by an increase in CO2 concentration (e.g., Manabe and Wetherald 1975; Ramanathan et al. 1979; Meehl et al. 2007). However, there is a substantial intermodel spread in GCMs causing uncertainty in future climate projections forced by an increase in CO2 (Bony et al. 2006; Meehl et al. 2007). Gaining an understanding of the seasonality of the climate forcing and feedbacks is of utmost importance for understanding the full climate response to a forcing (Ramanathan et al. 1979; Colman 2003; Lu and Cai 2009a; Taylor et al. 2011b). In particular, understanding the feedbacks responsible for the seasonality of the polar regions is critical because the polar regions are the most climatically sensitive areas (Solomon et al. 2007).
Surface polar warming amplification (PWA) has been a robust feature of the polar response in climate simulations forced by increased CO2 (e.g., Manabe and Wetherald 1980; Meehl et al. 2007; Lu and Cai 2010; Taylor et al. 2013). Studies of PWA seasonality indicate that the largest warming occurs in fall/winter with minimum warming in summer (e.g., Manabe and Stouffer 1980; Hansen et al. 1984; Holland and Bitz 2003; Meehl et al. 2007; Lu and Cai 2009a). Contributions to surface PWA are made by numerous physical processes. The surface albedo feedback (SAF) is thought to be the leading contributor to PWA (Manabe and Wetherald 1975; Ramanathan et al. 1979; Taylor et al. 2013). As mentioned above, the largest warming is seen away from summer, when SAF is most effective, suggesting that SAF might not be the primary contributor. Despite this difference in seasonality the SAF is still thought to be the primary contributor to PWA, but indirectly through the release in winter of the extra heat energy stored in the ocean in summer and through ice thickness reduction causing warming in fall/winter (Manabe and Stouffer 1980; Holland and Bitz 2003; Hall 2004). Other studies place SAF as an important but secondary factor in causing PWA, with longwave (LW) feedback being the leading contributor to PWA (e.g., Winton 2006; Lu and Cai 2009a; Pithan and Mauritsen 2014). Additionally, it is thought that the LW feedback through its interaction with sea ice retreat is primarily responsible for the winter warming maximum in the Arctic (Bintanja and van der Linden 2013). Cloud feedback is also thought to play an important role in PWA (e.g., Vavrus 2004), especially during polar night when only the LW effects of clouds are important and an increase in polar clouds causes an enhancement of the downward LW radiation to the surface (Holland and Bitz 2003). Additionally, changes in atmospheric poleward heat transport are also thought to be an important contributor to PWA (Alexeev et al. 2005; Cai 2006; Cai and Lu 2007; Lu and Cai 2010; Cai and Tung 2012).
In this study, we directly attribute the importance of the CO2 forcing and various feedbacks in establishing the seasonal variation of the warming pattern by quantifying the partial temperature changes induced by each. Most of the studies cited above use indirect methods, such as regression, correlation, or other statistical methods, to attribute the feedbacks responsible for PWA, particularly when analyzing the seasonal warming pattern (e.g., Bintanja and van der Linden 2013). This study focuses on the seasonal surface temperature response to CO2 doubling from preindustrial levels, at the time of CO2 doubling (hereafter referred to as the transient response), simulated by the National Center for Atmospheric Research (NCAR) Community Climate System Model, version 4 (CCSM4). Using the coupled atmosphere–surface climate feedback-response analysis method (CFRAM; Lu and Cai 2009b, hereafter LC09; Cai and Lu 2009, hereafter CL09), the individual temperature contributions of the CO2 forcing alone and radiative and nonradiative feedbacks to the seasonal pattern of the total surface temperature response are investigated. This study is a continuation of Taylor et al. (2013), who investigated the roles of the CO2 forcing and feedbacks in causing the annual mean atmospheric and surface temperature changes in the same CCSM4 simulation. This study goes further by attributing the contribution of feedbacks to the annual cycle of surface temperature change, and demonstrating the importance of taking the seasonality of climate feedbacks into account.
This paper focuses on the attribution of feedbacks on a single model, namely the CCSM4. However, the strengths and even the seasonal pattern of feedback partial temperature changes may vary among GCMs. Thus the analysis and conclusions on the individual feedback contributions to the total seasonal warming response may be model dependent. However, the robustness of the total seasonal warming pattern among a large body of model simulations (Chapman and Walsh 2007) suggests that the general characteristics of the individual partial temperature changes may well be similar among different models. Furthermore, considering that there has been no other study using the CFRAM to attribute the seasonal pattern of individual temperature change contributions to the seasonality of the total warming pattern, it is important to quantify and analyze them in at least one GCM to further our understanding of feedbacks.
The remainder of this paper is organized as follows. Section 2 describes the model characteristics and the setup of the climate simulations, as well as the temperature response of the simulations. A description of the attribution method, the CFRAM, is given in section 3. Section 4 reports on the individual contributions of the different feedbacks to the seasonal warming pattern, their contributions to the seasonality of the warming in the polar regions and the tropics, and their contributions to the polar warming asymmetry between hemispheres. Section 5 discusses the pronounced seasonality of the polar regions and its cause. Finally, a summary of our main findings is provided in section 6.
2. Model simulation and response
The data used in this study are derived from the climate simulations of the NCAR CCSM4. The atmospheric component of CCSM4 is the Community Atmospheric Model version 4 (CAM4) with a finite volume dynamic core, 1° horizontal resolution, and 26 vertical levels. The ocean model is the Parallel Ocean Program version 2 (POP2) with 1° horizontal resolution enhanced to 0.27° in the equatorial region and 60 levels vertically. The CCSM4 is also made up of the Community Land Model version 4 (CLM4), and the Community Sea Ice Code version 4 (CICE4). Please see Gent et al. (2011) for more CCSM4 details. Two model simulations are analyzed: 1) a preindustrial control simulation and 2) a simulation with a 1% yr−1 increase in the CO2 concentration. The CCSM4 preindustrial control simulation runs for 1300 years holding all forcings constant at year 1850 levels, with a CO2 concentration of 284.7 ppm. After year 200, the preindustrial run reaches a quasi-equilibrium state as indicated by the small global mean temperature trend afterward. Therefore, we use the 20-yr mean between years 311 and 330 in the preindustrial control simulation to define the climatological annual cycle of the control climate simulation. The 1% yr−1 CO2 increase simulation branches out at year 251 of the preindustrial control simulation. In this transient simulation, the CO2 increases 1% yr−1 until the CO2 concentration quadruples. We then define the difference between the 20-yr mean annual cycle centered at the time of CO2 doubling, which corresponds to years 61–80 of the transient simulation (corresponding to the same 20-yr span as the control run), and the climatological annual cycle of the control simulation as the transient climate response to the CO2 forcing.
Shown in Fig. 1 is the zonal mean surface temperature (hereafter referred to as the surface temperature) difference between the two simulations as a function of calendar month and latitude. The key features of the surface temperature response are 1) a warming throughout the globe, 2) large seasonality in the polar warming pattern, 3) weak seasonality in the warming pattern of the tropics, 4) maximum PWA in fall/winter and minimum PWA in summer, and 5) greater PWA in the NH than in the SH.
Zonal mean of surface temperature change, 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
3. CFRAM
The Fu–Liou radiative transfer model (Fu and Liou 1992, 1993) is used for all radiation calculations in (1) for each longitude–latitude grid point using the 20-yr monthly mean outputs from the control and transient climate simulations. Clouds are handled in this study using a variation of the Monte Carlo Independent Column Approximation (MCICA; Pincus et al. 2003) used previously by Taylor et al. (2011a,b) to diagnose cloud feedback; MCICA is performed by subdividing each model grid box into 100 subcolumns and then generating cloud profiles for each. The subcolumn cloud profiles are generated using a maximum-random overlap cloud generator (Raisanen et al. 2004) based on the monthly mean climatological cloud properties (fractional cloud area, liquid and ice cloud mixing ratios) derived from the CCSM4 simulations. Radiative terms on the RHS of (1) are evaluated by taking the perturbed 20-yr monthly mean field of the radiative process in question, with all other variables being held at their unperturbed 20-yr monthly mean fields, and using these fields as input in our offline radiative flux calculations (CL09). Calculating each radiative term on the RHS of (1), using the Fu–Liou radiative transfer model, over all grids results in a series of 3D radiative energy flux perturbations. As was shown in Taylor et al. (2013, their Fig. 1), using the same radiative transfer model, the linearity assumption invoked by the CFRAM method has been validated.
Figure 1 demonstrates that the total surface temperature change (contours), obtained from the summation of the partial temperature changes derived from the CFRAM, matches up well with the model simulated surface temperature change (shading). This further validates the linearity assumption and gives us confidence in the CFRAM results.
4. Attribution of the seasonal zonal mean surface warming pattern
a. CO2 forcing
The seasonal and meridional pattern of the external forcing at the surface (
(a) Radiative energy flux convergence perturbation at the surface, 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
The partial surface temperature change due to the external forcing alone (
Even though 
b. Water vapor feedback
The surface temperature response due to the water vapor feedback, 
(a) Partial surface temperature change (in K) due to the water vapor feedback, 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
c. SAF
The SAF is mainly associated with changes in snow/ice coverage and therefore it is important only in cold places, such as the polar regions. As climate warms, there is a reduction of the surface albedo in polar regions due to the melting of snow/ice. Regardless of whether the reduction of the surface albedo is a seasonal or year-round phenomenon, the SAF in the polar regions is nearly absent during winter because of the lack of sunlight. This explains why the warming due to the SAF (
As in Fig. 3a, but due to the surface albedo feedback, 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
The SAF difference between the two hemispheres is mainly attributed to the larger ice melting that occurs in the NH, which causes a larger reduction of the albedo than in the SH (not shown), allowing for more solar radiation to be absorbed, which represents a stronger SAF. Secondary factors include the latitudinal location of the ice melting, which the insolation is dependent on, and the unperturbed time mean clouds that reduce the SW radiative flux at the surface. Overall, the annual cycle of 
d. Cloud feedback
Unlike other radiative feedbacks that are dominated by either LW or shortwave (SW) effects, changes in clouds affect both the reflection of SW radiation and the absorption and emission of LW radiation. Therefore, it is useful to decompose the partial temperature change due to the cloud feedback (
(a) Partial surface temperature changes (in K) due to the net cloud feedback (
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
Both 
In the polar regions, the dominance of 
In comparison to Fig. 1, we conclude that the cloud feedback contributes greatly to the seasonal and meridional pattern of the total warming by a general reduction of the warming due to the CO2 forcing and the water vapor feedback in the tropics, and by a stronger amplification of the polar warming in fall/winter.
e. Atmospheric and oceanic dynamics plus heat storage feedbacks
As stated earlier, the atmospheric dynamics feedback estimated using (4) provides the 4D pattern (3D + seasonal cycle) of the lump sum of changes in the energy flux convergence due to all nonradiative processes, including convective/large-scale vertical energy transport, horizontal energy transport, and sensible and latent heat fluxes into the atmosphere (also atmospheric heat storage term, which is assumed very small). This term is zero at the surface by definition. Therefore, the partial surface temperature change due to the atmospheric dynamics feedback (
As in Fig. 3a, but due to (a) atmospheric dynamics feedback, 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
Shown in Fig. 6b is 
f. Sensible and latent heat flux feedbacks
Figures 7a and 7b show 
As in Fig. 3a, but due to the (a) sensible heat flux feedback, 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
The warming and cooling patterns of 
g. Errors due to offline calculations
All radiative feedback decomposition techniques (e.g., PRP and radiative kernel methods) performed offline using time mean data contain errors in their offline radiative calculations, which are quoted as being ~23% and ~2% in magnitude (global average) for the clear-sky SW and LW anomalies, respectively, in the radiative kernel method (Shell et al. 2008). We note here that if the radiative feedback decomposition technique is performed online, there is no offline error to speak of, but the computational cost is increased substantially. These errors are speculated to originate from the use of time mean clouds in the offline radiative transfer calculations versus using instantaneous clouds (Wetherald and Manabe 1988; Taylor and Ghan 1992; Kato et al. 2011; Song et al. 2014). Previous CFRAM studies (Lu and Cai 2010; Cai and Tung 2012), which use time mean data in their radiative flux calculations but have no clouds (or albedo changes) in their GCM simulations, show small to negligible offline error. This indirectly supports the notion that the use of time mean clouds is indeed the cause of this error. Additionally, Song et al. (2014) used the same radiative transfer model for both the GCM simulations and the offline radiative transfer calculations, and still found a substantial error when annual mean data were used as input in the offline radiative calculations. However, when hourly data were used as input, the accuracy of the offline radiative flux calculation was much improved, with a quoted global mean difference between the total radiative flux change given by the runtime simulation and that given by the offline radiative calculation, with hourly input data, of only −2.5 × 10-5 W m−2 (Song et al. 2014). This all points to the use of time mean data as the main cause of the offline error.
Here we explicitly quantify the error due to the offline radiative calculations, namely 
(a) The net error in our radiative partial temperature change calculations due to the error in our offline radiative heating calculations with respect to the CCSM4 simulated radiative heating rates, 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
To obtain a measure of which radiative feedback processes have larger errors in their partial temperature change calculation due to the use of time mean data, a correlation analysis is carried out. Large correlations would indicate that these errors are largely attributable to errors in the partial temperature change calculation of that specific radiative feedback. The small correlations between 
Correlations between (a) 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
Next, we wish to see if any of the interpretations made above for the cloud and albedo feedbacks are changed by the inclusion of the offline error. The error in boreal polar summer is smaller in magnitude than the warming of 
(a) Sum of 
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
h. Seasonality of polar warming
Figure 11 shows the seasonal cycle of the contributions (bars) of the CO2 forcing alone and each feedback to the total mean warming (red line) in polar regions (from 60° to 90°N for the NH and 60° to 90°S for the SH). In polar regions we observe a pronounced seasonality with largest warming occurring in fall/winter and minimum warming in summer. During polar summer, there exists a large cancellation between the LW and SW cloud feedbacks and between the SAF and ocean heat storage/dynamics feedback, leading to a polar warming minimum, and establishing that the warming in summer is primarily caused by the CO2 forcing and water vapor feedback. During fall/winter, the warming contributions from the CO2 forcing alone and many of the feedbacks collectively give rise to the warming maximum due to the lack of cancellations. The leading terms causing the warming maximum in fall/winter are the CO2 forcing, the ocean heat storage/dynamics feedback, and the LW cloud feedback.
Mean partial surface temperature changes due to the forcing alone and each of the feedbacks in (a) Northern Hemisphere (NH; 60°–90°N) and (b) Southern Hemisphere (SH; 60°–90°S). Sum of color bars in (a) and (b), for each month, equals the red line, which is the mean total surface temperature change in each of the polar regions, respectively. In (b) the months go from July to June, so as to match up the seasons with the NH and easily compare with (a). (units: K).
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
i. Polar warming asymmetry between NH and SH
The relative annual and seasonal contributions of individual feedbacks to AI are summarized in Fig. 12. Albedo feedback is the primary contributor to the larger warming of the Arctic than the Antarctic during spring and summer, reflecting the larger reduction of albedo in the Arctic. During polar summer the offline error indicates a large negative AI; as discussed in section 4g, this is a result of an overestimation of the albedo feedback, implying that the large positive AI of albedo feedback could be substantially smaller in summer, although it would still have the largest positive AI. Other important contributors to the larger warming of the Arctic than the Antarctic, in summer, include the water vapor and ocean heat storage/dynamics feedbacks. However, the summer polar warming asymmetry between the two hemispheres is largely suppressed by the sensible and latent heat flux feedbacks.
Seasonal and annual mean contributions of individual feedbacks to the warming asymmetry between the NH polar region (60°–90°N) and the SH polar region (60°–90°S), as defined by the AI. See text for the definition of the AI. Corresponding seasons between the NH and SH are compared.
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
During polar fall and winter, when the largest polar warming difference between the two hemispheres is seen in terms of magnitude, there is no clear primary contributor to the larger warming of the Arctic (Fig. 12). In fall, the greatest positive AI values are given by the cloud, ocean heat storage/dynamics, water vapor, atmospheric dynamics, and sensible heat flux feedbacks, which are in turn suppressed mainly by the latent heat flux feedback. In winter, the ocean heat storage/dynamics and sensible heat flux feedbacks are the primary contributors to the larger warming of the Arctic, as they have the greatest positive AI values. Overall, Figs. 11 and 12 indicate that in general the large polar warming asymmetry seen during fall and winter (in magnitude) is a result of the larger amplitude of positive feedbacks in the NH polar region as compared with the SH polar region.
Annual mean results indicate the primary contributor to the hemispheric polar warming asymmetry is the SAF, favoring a larger warming of the Arctic. Other important contributors to the larger warming of the Arctic are the water vapor, ocean heat storage/dynamics, cloud, and atmospheric dynamics feedbacks. The main suppressor of the hemispheric polar warming asymmetry, annually, is the latent heat flux feedback.
j. Seasonality of the tropics
Figure 13 shows the mean partial temperature contribution of the forcing itself and each feedback in the area of the tropics (defined to be between 0° and 23.5° in the NH and SH). The main contributors to the tropical warming are 
Mean partial surface temperature changes due to the forcing alone and each of the feedbacks in the tropics: (a) the NH tropics, defined to be from 0° to 23.5°N, and (b) the SH tropics, defined to be from 0° to 23.5°S. Sum of color bars, for each month, equals the red line, which is the mean total surface temperature change in the tropics. (units: K).
Citation: Journal of Climate 27, 14; 10.1175/JCLI-D-13-00658.1
5. Discussion
Figure 11 demonstrates the SAF has its maximum warming contribution in summer and minimum contribution in winter, which is almost opposite that of the seasonal cycle of the polar surface warming pattern. When an annual mean is taken for the SAF, the large warming in summer is what leads to its large value in the annual mean (e.g., Taylor et al. 2013). Important contributors to the PWA pattern such as ocean heat storage and cloud feedback have cooling contributions in summer, which offset the warming contributions in fall/winter when taking an annual mean. Their contributions to PWA are thus “hidden” and seem small in the annual mean approach. This highlights the importance of taking into account the seasonality of individual feedbacks to further our understanding of climate change.
While the SAF is not directly responsible for the PWA pattern, this does not indicate it cannot play an indirect role. The main reason polar summer does not experience the largest warming is due to the ocean storage of the extra solar energy absorbed by the surface due to the SAF, offsetting the large warming contribution of the SAF. The ocean heat storage then releases this energy in fall/winter, when the SAF is small or absent, substantially contributing to the warming maximum. Thus, it is through its interaction with ocean heat storage that the SAF indirectly contributes to the PWA pattern. This process was also described by Screen and Simmonds (2010) to describe the seasonal PWA pattern using reanalysis data.
The strong seasonality of 
6. Summary and conclusions
The CFRAM technique is used to attribute the individual contributions of the CO2 forcing alone, and radiative and nonradiative feedback processes to the surface temperature change at the time of CO2 doubling, in a transient 1% yr−1 CO2 increase simulation of the NCAR CCSM4. The results indicate that the model-simulated (total) surface temperature response demonstrates a warming throughout, but does not exhibit the same seasonal pattern and amplitude as 
The water vapor feedback and the CO2 forcing alone are responsible for most of the warming in the tropics, with the latent heat flux feedback acting as the main suppressor of the warming. The lack of seasonality in the total temperature response of the tropics is explained by compensating contributions between feedbacks, which keep the net warming nearly uniform. Unlike the tropics, the polar regions demonstrate a pronounced seasonal variation in 
It must be restated that these results are for a transient response, meaning the thermal adjustment of the ocean from the transient to equilibrium state can modify this seasonal picture for the equilibrium response. In the future, a comparison with the equilibrium response would be informative, as it would give an in depth look at how the oceanic thermal adjustment to equilibrium changes the seasonal pattern and amplitude of each of the partial temperature changes due to feedbacks. In addition, we also emphasize that the results discussed here are only of a single model. It is likely that the detailed results are model dependent. Thus, in the future it would be valuable to have an intermodel comparison to test the robustness of the results presented here. However, the robustness of the seasonal cycle of the total surface warming pattern due to a doubling of CO2 among CGCMs gives us confidence that the general features revealed in this study will remain unchanged.
The authors are grateful for the insightful and constructive comments from the anonymous reviewers. This research was in part supported by research grants from the National Science Foundation (ATM-0833001), the DOE Office of Science Regional and Global Climate Modeling (RGCM) program (DE-SC0004974), the NOAA CPO/CPPA program (NA10OAR4310168), and the NASA Living With a Star Program (NNX13AF91G). Portions of this study were supported by the Office of Science (BER), U.S. Department of Energy, Cooperative Agreement DE-FC02-97ER62402, and the National Science Foundation.
REFERENCES
Alexeev, V. A., , P. L. Langen, , and J. R. Bates, 2005: Polar amplification of surface warming on an aquaplanet in “ghost forcing” experiments without sea ice feedbacks. Climate Dyn., 24, 655–666, doi:10.1007/s00382-005-0018-3.
Bintanja, R., , and E. C. van der Linden, 2013: The changing seasonal climate in the Arctic. Sci. Rep., 3, 1556, doi:10.1038/srep01556.
Bony, S., and Coauthors, 2006: How well do we understand and evaluate climate feedback processes? J. Climate, 19, 3445–3482, doi:10.1175/JCLI3819.1.
Cai, M., 2006: Dynamical greenhouse-plus feedback and polar warming amplification. Part I: A dry radiative-transportive climate model. Climate Dyn., 26, 661–675, doi:10.1007/s00382-005-0104-6.
Cai, M., , and J. Lu, 2007: Dynamical greenhouse-plus feedback and polar warming amplification. Part II: Meridional and vertical asymmetries of the global warming. Climate Dyn., 29, 375–391, doi:10.1007/s00382-007-0238-9.
Cai, M., , and J. Lu, 2009: A new framework for isolating individual feedback processes in coupled general circulation climate models. Part II: Method demonstrations and comparisons. Climate Dyn., 32, 887–900, doi:10.1007/s00382-008-0424-4.
Cai, M., , and K.-K. Tung, 2012: Robustness of dynamical feedbacks from radiative forcing: 2% solar versus 2 × CO2 experiments in an idealized GCM. J. Atmos. Sci., 69, 2256–2271, doi:10.1175/JAS-D-11-0117.1.
Chapman, W. L., , and J. E. Walsh, 2007: Simulations of Arctic temperature and pressure by global coupled models. J. Climate, 20, 609–632, doi:10.1175/JCLI4026.1.
Colman, R., 2003: Seasonal contributions to climate feedbacks. Climate Dyn., 20, 825–841, doi:10.1007/s00382-002-0301-5.
Fu, Q., , and K. N. Liou, 1992: On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres. J. Atmos. Sci., 49, 2139–2156, doi:10.1175/1520-0469(1992)049<2139:OTCDMF>2.0.CO;2.
Fu, Q., , and K. N. Liou, 1993: Parameterization of the radiative properties of cirrus clouds. J. Atmos. Sci., 50, 2008–2025, doi:10.1175/1520-0469(1993)050<2008:POTRPO>2.0.CO;2.
Gent, P. R., and Coauthors, 2011: The Community Climate System Model version 4. J. Climate, 24, 4973–4991, doi:10.1175/2011JCLI4083.1.
Hall, A., 2004: The role of surface albedo feedback in climate. J. Climate, 17, 1550–1568, doi:10.1175/1520-0442(2004)017<1550:TROSAF>2.0.CO;2.
Hansen, J., , A. Lacis, , D. Rind, , G. Russell, , P. Stone, , I. Fung, , R. Ruedy, , and J. Lerner, 1984: Climate sensitivity: Analysis of feedback mechanisms. Climate Processes and Climate Sensitivity, Geophys. Monogr., Vol. 29, Amer. Geophys. Union, 130–163.
Hartmann, D. L., 1994: Climate sensitivity and feedback mechanisms. Global Physical Climatology, D. L. Hartmann, Ed., International Geophysics Series, Vol. 56, Academic Press, 229–253.
Holland, M. M., , and C. M. Bitz, 2003: Polar amplifications of climate change in coupled models. Climate Dyn., 21, 221–232, doi:10.1007/s00382-003-0332-6.
Ingram, W. J., , C. A. Wilson, , and J. F. B. Mitchell, 1989: Modeling climate change: An assessment of sea ice and surface albedo feedbacks. J. Geophys. Res., 94, 8609–8622, doi:10.1029/JD094iD06p08609.
Kato, S., and Coauthors, 2011: Detection of atmospheric changes in spatially and temporally averaged infrared spectra observed from space. J. Climate, 24, 6392–6407, doi:10.1175/JCLI-D-10-05005.1.
Li, C., , D. Notz, , S. Tietsche, , and J. Marotzke, 2013: The transient versus the equilibrium response of sea ice to global warming. J. Climate, 26, 5624–5636, doi:10.1175/JCLI-D-12-00492.1.
Lu, J., , and M. Cai, 2009a: Seasonality of polar surface warming amplification in climate simulations. Geophys. Res. Lett., 36, L16704, doi:10.1029/2009GL040133.
Lu, J., , and M. Cai, 2009b: A new framework for isolating individual feedback processes in coupled general circulation climate models. Part I: Formulation. Climate Dyn., 32, 873–885, doi:10.1007/s00382-008-0425-3.
Lu, J., , and M. Cai, 2010: Quantifying contributions to polar warming amplification in an idealized coupled general circulation model. Climate Dyn., 34, 669–687, doi:10.1007/s00382-009-0673-x.
Manabe, S., , and R. T. Wetherald, 1975: The effects of doubling the CO2 concentration on the climate of a general circulation model. J. Atmos. Sci., 32, 3–15, doi:10.1175/1520-0469(1975)032<0003:TEODTC>2.0.CO;2.
Manabe, S., , and R. J. Stouffer, 1980: Sensitivity of a global climate model to an increase of CO2 concentration in the atmosphere. J. Geophys. Res., 85, 5529–5554, doi:10.1029/JC085iC10p05529.
Manabe, S., , and R. T. Wetherald, 1980: On the distribution of climate change resulting from an increase in CO2 content of the atmosphere. J. Atmos. Sci., 37, 99–118, doi:10.1175/1520-0469(1980)037<0099:OTDOCC>2.0.CO;2.
Meehl, G. A., and Coauthors, 2007: Global climate projections. Climate Change 2007: The Physical Science Basis, S. Solomon et al., Eds., Cambridge University Press, 747–846.
Pincus, R., , H. W. Barker, , and J.-J. Morcette, 2003: A fast, flexible, approximate technique for computing radiative transfer in inhomogeneous cloud fields. J. Geophys. Res., 108, 4376, doi:10.1029/2002JD003322.
Pithan, F., , and T. Mauritsen, 2014: Arctic amplification dominated by temperature feedbacks in contemporary climate models. Nat. Geosci., 7, 181–184, doi:10.1038/ngeo2071.
Räisänen, P., , H. W. Barker, , M. F. Khairoutdinov, , J. Li, , and D. A. Randall, 2004: Stochastic generation of subgrid-scale cloudy columns for large-scale models. Quart. J. Roy. Meteor. Soc., 130, 2047–2067, doi:10.1256/qj.03.99.
Ramanathan, V., , M. S. Lian, , and R. D. Cess, 1979: Increased atmospheric CO2: Zonal and seasonal estimates of the effect on the radiation energy balance and surface temperature. J. Geophys. Res., 84, 4949–4958, doi:10.1029/JC084iC08p04949.
Screen, J. A., , and I. Simmonds, 2010: The central role of diminishing sea ice in recent Arctic temperature amplification. Nature, 464, 1334–1337, doi:10.1038/nature09051.
Shell, K. M., , J. T. Kiehl, , and C. A. Shields, 2008: Using the radiative kernel technique to calculate climate feedbacks in NCAR’s Community Atmospheric Model. J. Climate, 21, 2269–2282, doi:10.1175/2007JCLI2044.1.
Soden, B. J., , and I. M. Held, 2006: An assessment of climate feedbacks in coupled ocean–atmosphere models. J. Climate, 19, 3354–3360, doi:10.1175/JCLI3799.1.
Soden, B. J., , I. M. Held, , R. Colman, , K. M. Shell, , J. T. Kiehl, , and C. A. Shields, 2008: Quantifying climate feedbacks using radiative kernels. J. Climate, 21, 3504–3520, doi:10.1175/2007JCLI2110.1.
Solomon, S., and Coauthors, 2007: Technical summary. Climate Change 2007: The Physical Science Basis, S. Solomon et al., Eds., Cambridge University Press, 19–91.
Song, X., , G. J. Zhang, , and M. Cai, 2014: Quantifying contributions of climate feedbacks to tropospheric warming in the NCAR CCSM3.0. Climate Dyn., 42, 901–917, doi:10.1007/s00382-013-1805-x.
Taylor, K. E., , and S. J. Ghan, 1992: An analysis of cloud liquid water feedback and global climate sensitivity in a general circulation model. J. Climate, 5, 907–919, doi:10.1175/1520-0442(1992)005<0907:AAOCLW>2.0.CO;2.
Taylor, P. C., , R. G. Ellingson, , and M. Cai, 2011a: Geographical distribution of climate feedbacks in the NCAR CCSM3.0. J. Climate, 24, 2737–2753, doi:10.1175/2010JCLI3788.1.
Taylor, P. C., , R. G. Ellingson, , and M. Cai, 2011b: Seasonal variations of climate feedbacks in the NCAR CCSM3. J. Climate, 24, 3433–3444, doi:10.1175/2011JCLI3862.1.
Taylor, P. C., , M. Cai, , A. Hu, , J. Meehl, , W. Washington, , and G. J. Zhang, 2013: A decomposition of feedback contributions to polar warming amplification. J. Climate, 26, 7023–7043, doi:10.1175/JCLI-D-12-00696.1.
Vavrus, S., 2004: The impact of cloud feedbacks on Arctic climate under greenhouse forcing. J. Climate, 17, 603–615, doi:10.1175/1520-0442(2004)017<0603:TIOCFO>2.0.CO;2.
Wetherald, R. T., , and S. Manabe, 1988: Cloud feedback processes in a general circulation model. J. Atmos. Sci., 45, 1397–1416, doi:10.1175/1520-0469(1988)045<1397:CFPIAG>2.0.CO;2.
Winton, M., 2006: Amplified Arctic climate change: What does surface albedo feedback have to do with it? Geophys. Res. Lett., 33, L03701, doi:10.1029/2005GL025244.
Note that LC09 compares two annual mean equilibrium states. Here we deal with a transient response and a seasonal cycle, meaning the tendency term 
Note that 
