Abstract

Using the climate feedback response analysis method, the authors examine the individual contributions of the CO2 radiative forcing and climate feedbacks to the magnitude, spatial pattern, and seasonality of the transient surface warming response in a 1% yr−1 CO2 increase simulation of the NCAR Community Climate System Model, version 4 (CCSM4).

The CO2 forcing and water vapor feedback warm the surface everywhere throughout the year. The tropical warming is predominantly caused by the CO2 forcing and water vapor feedback, while the evaporation feedback reduces the warming. Most feedbacks exhibit noticeable seasonal variations; however, their net effect has little seasonal variation due to compensating effects, which keeps the tropical warming relatively invariant all year long. The polar warming has a pronounced seasonal cycle, with maximum warming in fall/winter and minimum warming in summer. In summer, the large cancelations between the shortwave and longwave cloud feedbacks and between the surface albedo feedback warming and the cooling from the ocean heat storage/dynamics feedback lead to a warming minimum. In polar winter, surface albedo and shortwave cloud feedbacks are nearly absent due to a lack of insolation. However, the ocean heat storage feedback relays the polar warming due to the surface albedo feedback from summer to winter, and the longwave cloud feedback warms the polar surface. Therefore, the seasonal variations in the cloud feedback, surface albedo feedback, and ocean heat storage/dynamics feedback, directly caused by the strong annual cycle of insolation, contribute primarily to the large seasonal variation of polar warming. Furthermore, the CO2 forcing and water vapor and atmospheric dynamics feedbacks add to the maximum polar warming in fall/winter.

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.

Fig. 1.

Zonal mean of surface temperature change, , (in K) at the time of CO2 doubling, in a transient 1% yr−1 CO2 increase simulation of the NCAR CCSM4. The shading corresponds to the simulated surface temperature change given by the NCAR CCSM4 global warming simulations. Contours correspond to the sum of all partial temperature changes derived from the CFRAM analysis (sum of Figs. 28).

Fig. 1.

Zonal mean of surface temperature change, , (in K) at the time of CO2 doubling, in a transient 1% yr−1 CO2 increase simulation of the NCAR CCSM4. The shading corresponds to the simulated surface temperature change given by the NCAR CCSM4 global warming simulations. Contours correspond to the sum of all partial temperature changes derived from the CFRAM analysis (sum of Figs. 28).

3. CFRAM

The CFRAM technique (LC09; CL09), formulated for quantifying contributions to the 3D global warming pattern, is applied to the transient CCSM4 climate response. The CFRAM is based on the energy balance equation of the coupled atmosphere–surface system, similar to the partial radiative perturbation (PRP; Wetherald and Manabe 1988) and radiative kernel methods (Soden and Held 2006; Soden et al. 2008). The CFRAM goes beyond traditional feedback diagnostic methods by considering the temperature response to energy perturbations over the entire atmospheric column and surface instead of just focusing on radiative energy perturbations at the top of the atmosphere (TOA), and by considering the contributions of both radiative and nonradiative feedback processes explicitly, whereas the TOA-based feedback analysis can only consider radiative feedback processes with nonradiative feedback processes hidden in the “lapse-rate” feedback (LC09; CL09). At a given location, the atmospheric column is divided into M layers with the convention that the first layer represents the top layer of the atmosphere (for CCSM4, M = 26) and the surface (either land or ocean) is the (M + 1)th layer. The CFRAM equation is derived from the atmosphere–surface column energy balance equation (LC09; CL09) and at each grid point can be written as1

 
formula

The left-hand side (LHS) represents a vector containing the change in temperature at each atmospheric layer and at the surface layer. Each term inside the curly brackets represent an energy flux convergence perturbation in each of the atmospheric layers and the surface layer in units of W m−2. In this equation, ΔFext is the change in radiative energy flux convergence at each atmospheric layer and at the surface layer due to the CO2 forcing alone; the vector S represents the solar radiation absorbed by the mth atmospheric layer for mM and at the surface layer (m = M + 1); R is the net infrared radiative flux divergence at each atmospheric layer and at the surface layer; Δwv(SR) and Δc(SR) correspond to the vertical profiles of changes in radiative flux convergence due to changes in atmospheric water vapor and cloud properties, respectively; ΔalbS is the vertical profile of changes in solar energy absorbed by atmospheric layers and the surface layer due to changes in surface albedo; ΔErr(SR) is the error in the offline radiative transfer calculation (to be discussed further below); and ΔQLH and ΔQSH are changes in the energy convergence at the surface due to changes in latent and sensible heat fluxes. Also, ΔQLH = (0, …, 0, −ΔLH)T and ΔQSH = (0, …, 0, −ΔSH)T, where LH and SH denote surface turbulent latent and sensible heat fluxes, respectively, following the sign convention that positive values mean upward energy flux leaving from the surface to the atmosphere; ΔQatmos_dyn represents the vertical profile of the change in convergence of energy into the mth layer due to nonradiative processes mainly associated with 1) convective/large-scale vertical transport of energy into the mth layer from other layers in the same column, 2) horizontal transport of energy into the mth layer of the column from its neighbor columns at the same mth layer, and 3) changes in sensible and latent heat fluxes into the atmosphere, and is zero for the surface layer by definition; and ΔQocn_dyn+storage represents the change in the nonradiative energy flux convergence mainly associated with changes in the oceanic heat transport and heat storage, and this term is nonzero only for the surface layer. Further, (∂R/∂T) is called the Planck feedback matrix, whose jth column represents the vertical profile of the change in divergence of LW radiative energy fluxes due to a 1-K warming at the jth layer alone. Readers may consult Fig. 1 of LC09 for an illustration of (∂R/∂T).

Equation (1a) is for an analysis of the temperature change at every layer in the atmosphere and at the surface. For this study, we only study the seasonal surface temperature response (ΔTM+1), which is evaluated according to

 
formula

where the right-hand side (RHS) is the same as before, except is a row vector corresponding to the (M + 1)th or last row of . In (1b) the last row of the inverse Planck feedback matrix is multiplied with each of the terms on the RHS of (1b) in brackets to obtain the partial surface temperature changes due to the CO2 forcing alone and respective feedbacks:

 
formula

For an easy reference, partial temperature changes are denoted as with the superscript x representing one of the nine superscripts from (1b). Solving (2) grid point by grid point enables us to obtain the individual contributions of the forcing alone and feedbacks to the simulated surface warming. Comparing the total sum of all individual contributions with the actual surface temperature change predicted by the original CCSM4 simulations verifies the accuracy of the CFRAM decomposition, since it is calculated independently without any need for a priori knowledge of the model simulated surface temperature change. In (2), it is assumed the surface temperature change caused by a change in energy flux convergence at the surface is that needed to balance the change in energy flux convergence through a change in thermal emission.

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.

Standard CCSM4 outputs include 3D solar heating and LW cooling rates in the atmosphere and all radiative energy fluxes at the surface. The solar heating and LW cooling rates in the CCSM4 outputs are provided in units of K day−1. We have converted the heating/cooling rates in each atmospheric layer to units of W m−2 from units of K day−1 by multiplying the heating/cooling rates with a factor equaling to (cpδm)/86 400, where cp is heat capacity of air at constant pressure, 86 400 is the length of a day in seconds, and δm is the monthly climatological mean mass of the atmospheric layer under consideration. These outputs enable us to directly quantify the errors in the offline calculations defined as

 
formula

where the superscript CCSM4 indicates the results are derived directly from CCSM4 output and the terms without the superscript are derived from the offline calculation. This is the error taken into account in (1). Note that the errors calculated from (3) are not due to the linearization of the radiative transfer model, but are from (i) differences between the radiation models used, (ii) using 20-yr monthly mean fields as inputs for our offline radiation calculations versus instantaneous fields, and (iii) the conversion from the unit of K day−1 to W m−2, which should be done before taking any time mean since δm changes with time. Note that (iii) also introduces errors in inferring the dynamical heating field in the atmosphere from the mean CCSM4 solar heating and LW cooling rate output. Previous studies, discussed later, indicate that the main source of error is due to (ii), which represents the total impacts of submonthly variations of all the radiative processes (i.e., diurnal cycle) neglected by the use of monthly mean data. As far as we know, only Taylor et al. (2013) has attempted to explicitly calculate the 3D pattern of the error term whereas other studies only examined the error pattern at the TOA (e.g., Shell et al. 2008). As discussed later, the comparison of the error pattern with each of the partial temperature changes caused by the forcing and feedbacks enables us to identify the impact of using the long time mean field in estimating the strength and spatial pattern of each feedback process.

The nonradiative energy fluxes included in the standard CCSM4 output are associated with turbulent fluxes at the surface (i.e., surface sensible heat and latent heat fluxes). All other nonradiative fluxes, such as those associated with convective and large-scale advective energy transport, are not standard output, but can be estimated by taking advantage of the energy balance equation. Nonradiative energy flux perturbations and changes in heat storage are inferred using 3D solar heating and LW cooling rates in an atmospheric layer m (1 ≤ mM) from the standard output of the CCSM4 as

 
formula

where is the change in heat storage at atmospheric layer m. In (4), the nonradiative or atmospheric dynamical energy flux perturbation is used to approximate the contributions from both the dynamical and heat storage term; since the heat storage term in the atmosphere is quite small, it is assumed to be negligible. At the surface layer (m = M + 1), we can evaluate the changes in net downward solar and LW radiation fluxes at the surface (m = M + 1) and surface latent and sensible heat fluxes derived from the CCSM4 standard output, namely . Over ocean, this term can be used to infer the change in net convergence of nonradiative energy fluxes by the ocean dynamics and ocean heat storage, namely,

 
formula

where is the change in heat storage at the surface layer. Over land, should be close to zero because of the small land heat storage and the near absence of energy transport for land (i.e., energy transport by river and stream is negligible). For this reason, we simply refer to as changes in ocean dynamics and ocean heat storage.

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 (; Fig. 2a) is due primarily to the seasonal and meridional profile of the climatological mean water vapor and low-level clouds.2 The presence of water vapor in the unperturbed time mean state limits the effectiveness of the CO2 doubling due to the overlapping between H2O and CO2 absorption bands (Lu and Cai 2010). In the tropics, the great abundance of water vapor in the lower troposphere results in a strong absorption of the extra downward thermal radiation due to the CO2 doubling from the air above, causing a smaller increase in the downward LW flux at the surface in the tropics than in polar regions (Cai and Tung 2012). The presence of low-level clouds in the unperturbed time mean state has a similar effect on the strength of the external forcing at the surface; that is, is weaker in the place where low-level clouds are abundant (Taylor et al. 2013). Because the seasonal cycle of water vapor follows the temperature closely (per the Clausius–Clapeyron relation), such overlapping effect can explain the seasonal variation of , namely minimum in warm season and maximum in cold season except over the Antarctic where the unperturbed time mean water vapor is scarce all year. As discussed in Cai and Tung (2012) and Taylor et al. (2013), there is also a so-called temperature effect: namely, that the increase in the downward thermal radiation at the surface due to an increase in CO2 is stronger when/where the air temperature itself (assuming the same water vapor and cloud amount) is warmer. The temperature effect is secondary and is dominant only at the place where the atmosphere is very dry. The temperature effect explains why over the Antarctic, where the air is very dry all year round, is maximum in warm season and minimum in cold season, which is opposite to the rest of the world.

Fig. 2.

(a) Radiative energy flux convergence perturbation at the surface, , in units of W m−2. (b) Partial surface temperature change (in K) due to the external forcing alone, .

Fig. 2.

(a) Radiative energy flux convergence perturbation at the surface, , in units of W m−2. (b) Partial surface temperature change (in K) due to the external forcing alone, .

The partial surface temperature change due to the external forcing alone (; Fig. 2b) follows the pattern of . Note that shows a warming throughout with largest warming in the polar regions and smallest in the tropics. In terms of seasonal variation, tends to have a maximum in winter and minimum in summer except over the SH high latitudes where the maximum is in summer and minimum in winter. Because of the thermal radiative coupling between the atmosphere and surface, is also affected by the external forcing in the atmosphere. Specifically, the lower tropospheric warming due to the external forcing alone in the atmosphere causes an increase in the downward LW flux, which contributes additional surface warming on top of the warming due to . In the NH, the lower troposphere warms more in polar regions than in the tropics [not shown here but see Fig. 2c of Taylor et al. (2013) as an example], so the thermal radiative coupling amplifies the polar warming due to more than it does so in the tropics. This also occurs in the SH equatorward of 60°S. Over the Antarctic, the external forcing in the lower troposphere is negative (not shown; see Taylor et al. 2013), which implies the direct effect of the external forcing is a cooling of the lower troposphere. As a result, this thermal radiative coupling effect acts to reduce the surface warming caused by . Note that the seasonal cycle and meridional profile of the unperturbed time mean surface temperature also plays a role in causing . According to the Stefan–Boltzmann feedback, which is inversely proportional to the cubic of the unperturbed time mean surface temperature, for the same forcing, the temperature response is smaller in a warmer place than in a colder place (Hartmann 1994).

Even though bears some similarities with the total surface temperature change shown in Fig. 1, the differences in the magnitude of the warming and even in the pattern itself indicate that feedbacks play a major role in modifying the warming pattern due to the external forcing alone.

b. Water vapor feedback

The surface temperature response due to the water vapor feedback, , is positive everywhere for all seasons (Fig. 3a). The largest warming is found in the tropics and its amplitude tends to decrease with latitude, which acts to increase the equator-to-pole temperature gradient. Seasonally larger warming usually occurs during the warm season, particularly in the NH. The seasonal and spatial warming pattern of follows the change in the column water vapor content (Fig. 3b), with the largest (smallest) warming typically collocated with the largest (smallest) increase in water vapor. It is very evident that both the seasonal and spatial patterns of bear little resemblance with the total warming (Fig. 1), even though it is the largest contributor to the global mean warming. These results are qualitatively in agreement with those presented by Colman (2003) and Taylor et al. (2011b) for the water vapor feedback using the PRP method.

Fig. 3.

(a) Partial surface temperature change (in K) due to the water vapor feedback, . (b) Zonal mean column water vapor content change (in kg m−2) at the time of CO2 doubling, in a transient 1% yr−1 CO2 increase simulation of the NCAR CCSM4.

Fig. 3.

(a) Partial surface temperature change (in K) due to the water vapor feedback, . (b) Zonal mean column water vapor content change (in kg m−2) at the time of CO2 doubling, in a transient 1% yr−1 CO2 increase simulation of the NCAR CCSM4.

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 (; Fig. 4) is found mainly in the polar regions and is largest in summer. The seasonal and meridional pattern of is quite similar to the seasonal cycle of the SAF found in other studies (e.g., Colman 2003; Lu and Cai 2009a; Taylor et al. 2011b), indicating a robust seasonal cycle for the SAF.

Fig. 4.

As in Fig. 3a, but due to the surface albedo feedback, (units: K).

Fig. 4.

As in Fig. 3a, but due to the surface albedo feedback, (units: K).

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 is opposite to the total polar warming annual cycle even though it greatly contributes to the annual mean PWA.

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 (; Fig. 5a) into its SW (; Fig. 5c) and LW (; Fig. 5d) components.

Fig. 5.

(a) Partial surface temperature changes (in K) due to the net cloud feedback (). (b) The transient response of the zonal mean column cloud liquid water path (in g m−2). Also shown are the (c) shortwave () and (d) longwave () components of (units: K).

Fig. 5.

(a) Partial surface temperature changes (in K) due to the net cloud feedback (). (b) The transient response of the zonal mean column cloud liquid water path (in g m−2). Also shown are the (c) shortwave () and (d) longwave () components of (units: K).

Both and follow the pattern of the change in clouds (Fig. 5b) but with opposite sign. Specifically in the vast surface area outside the polar regions, in response to an increase in clouds (Fig. 5b), the LW cloud feedback acts to warm the surface whereas the SW cloud feedback cools it; the reverse can be said about the response to a decrease in clouds. This explains why the warming and cooling patterns of and away from the polar regions are similar but have opposite sign. The comparison of Figs. 5c and 5d indicates that, outside of the polar regions, the SW cloud feedback tends to dominate over the LW cloud feedback. As a result, the sign of the net cloud feedback or is determined by , which is responsible for a cooling in equatorial latitudes in response to an increase in clouds and warming in the vast area of subtropics and midlatitudes due to a decrease in cloud coverage there.

In the polar regions, the dominance of over the opposing pattern of still exists in summer. The net effect of the general increase in clouds over the Arctic and Antarctic rim in summer is a cooling. However, in winter, the SW effects of clouds become negligible because of the lack of insolation. Therefore the net cloud feedback is due solely to the LW cloud effect, contributing to a strong polar winter warming due to an increase in clouds. This effect was also described in Holland and Bitz (2003) as a possible contributor to polar warming; our results support this idea and promote the cloud feedback as an important contributor to the PWA during fall/winter.

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 (; Fig. 6a) is caused solely by the nonradiative energy flux perturbations in the atmosphere, an indirect effect through the thermal radiative coupling between the atmosphere and surface. In polar regions, is positive with a relatively small warming contribution for all seasons except the boreal fall season. The positive in polar regions is due to the enhanced downward LW radiation to the surface resulting from the dynamically induced atmospheric warming [not shown here, but see Fig. 8 of Taylor et al. (2013) as an example]. Part of the dynamically induced atmospheric warming over the polar regions could be due to an enhancement of the poleward atmospheric heat transport, as elucidated in Cai (2006). Additionally, the fall polar warming of the lower troposphere, as a result of the increase in sensible heat flux can add to the dynamically induced warming, possibly leading to the observed warming maximum for . Everywhere else is small with little seasonal variation. The slight cooling observed over the equatorial region results from a reduction in downward LW radiation due to a dynamically induced cooling of the lower troposphere likely caused by an increase in convection above the equatorial region (Taylor et al. 2013).

Fig. 6.

As in Fig. 3a, but due to (a) atmospheric dynamics feedback, , and (b) ocean dynamics plus heat storage feedback, (units: K).

Fig. 6.

As in Fig. 3a, but due to (a) atmospheric dynamics feedback, , and (b) ocean dynamics plus heat storage feedback, (units: K).

Shown in Fig. 6b is , the partial temperature change due to the ocean heat storage/dynamics feedback, which is large mainly in polar regions. This term has a pronounced seasonality in polar regions, demonstrating a substantial cooling contribution in summer and large warming in polar fall/winter. It is seen that the summer cooling of coincides with the summer warming of . Lu and Cai (2009a) also found the overlapping of the summer polar cooling due to changes in ocean heat storage with the summer polar warming of in the global warming simulations with a GFDL slab-ocean climate model. Because the seasonal patterns of the temperature change due to changes in ocean heat storage in Lu and Cai (2009a) are so similar to that shown in Fig. 6b, we tend to interpret most of the summer polar cooling of as the heat storage term, which stores the extra SW radiative energy absorbed at the open water surface after the melting of sea ice in polar summer. The storage term cools the surface substantially in summer, suppressing the summer polar warming. The large amount of heat energy stored is subsequently released during polar fall/winter, contributing substantially to the surface warming during this time period. Over the Southern Ocean, we see there is a dipole structure not seen in the Arctic during fall and winter. The cooling in the region north of the warming region is likely due to greater ocean heat uptake, but could also be due to changes in ocean dynamics (or a combination of both).

f. Sensible and latent heat flux feedbacks

Figures 7a and 7b show and , the partial temperature changes due to sensible and latent heat flux feedbacks, respectively. For the largest seasonality occurs in the polar regions, with no discernible seasonal variation in the tropics. The NH polar latitudes have a cooling maximum during fall/winter, with little contribution the rest of the year. The SH polar region also has a cooling maximum in fall/winter, but it is accompanied by a warming maximum north of it. In the NH midlatitudes a pronounced seasonal variation of is observed with a cooling in summer and warming in winter. On the other hand, has noticeable seasonality almost everywhere. In polar regions, the cooling of is similar to that of . The seasonal structure of the polar regions due to and particularly due to are quite similar to that shown in Lu and Cai (2009a), which shows the temperature change due to the combined effects of changes in sensible and latent heat fluxes.

Fig. 7.

As in Fig. 3a, but due to the (a) sensible heat flux feedback, , and (b) latent heat flux feedback, (units: K).

Fig. 7.

As in Fig. 3a, but due to the (a) sensible heat flux feedback, , and (b) latent heat flux feedback, (units: K).

The warming and cooling patterns of and follow the seasonality of the sensible and latent heat flux responses (not shown), respectively, where a warming (cooling) is due to a decrease (increase) in the sensible or latent heat flux. During fall/winter, the turbulent energy loss is greatest when the air temperatures are coolest relative to the temperature of the ocean surface. Since ice reduction has taken place over the polar regions during this time period, there is an increase in the amount of turbulent energy flux going from the surface to the atmosphere causing a cooling of the ocean surface. The wintertime warming over the subpolar regions for is caused by a decrease in sensible heat flux from the ocean to the atmosphere, while the summertime cooling at NH midlatitudes results from an increase in sensible heat flux from land to the atmosphere.

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 . Substantial negative error around ~3 K in magnitude is seen during polar summer in the NH (Fig. 8a). All other regions throughout the year demonstrate errors that are under ~1.5 K in magnitude. Separating into LW and SW components (Figs. 8b,c) demonstrates that and partially offset each other in the tropics. The large error during polar summer is mostly due to error in the SW offline radiative calculation, but adds to it. Positive and negative values indicate an overestimation or underestimation of the cooling or warming contributions by the CO2 forcing and radiative feedbacks due to the use of time mean fields.

Fig. 8.

(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, . Also shown are the (b) longwave, , and (c) shortwave, , components of the net error (units: K).

Fig. 8.

(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, . Also shown are the (b) longwave, , and (c) shortwave, , components of the net error (units: K).

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 and and between and (not shown), in terms of both the LW and SW components as well as their sum, suggest that the estimations of and do not suffer greatly from the use of time mean fields. The high negative correlations between and and between and (Figs. 9a,b) indicate that most of the error is attributable to the use of time mean clouds in the calculation of and . The negative correlations imply that in general the warming and cooling of and have been overestimated. However, during boreal polar summer, where the error is largest, there is a large negative correlation between and (Fig. 9c) and relatively little correlation between and . Therefore the large error in boreal polar summer is primarily due to an overestimation of the warming due to the SAF, implying that the use of time mean albedo can also introduce substantial error, as previously pointed out by Ingram et al. (1989). These results are in agreement with those presented by Song et al. (2014), which also attributed their offline error (or residual) to the use of annual mean data in their calculation of the cloud and albedo feedbacks.

Fig. 9.

Correlations between (a) and , (b) and , and (c) and .

Fig. 9.

Correlations between (a) and , (b) and , and (c) and .

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 . Therefore, adding the error in boreal polar summer to changes the magnitude of the warming but not the explanation given for above. Similarly, the regions of high error correlation with and in general have larger magnitudes for and than the corresponding errors and . Thus the qualitative picture given for and above is mostly unchanged. Figures 10a and 10b demonstrate this by showing that the sum of , , and has a similar seasonal pattern as the sum of just and .

Fig. 10.

(a) Sum of and ; (b) sum of , , and (units: K).

Fig. 10.

(a) Sum of and ; (b) sum of , , and (units: K).

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.

Fig. 11.

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).

Fig. 11.

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).

i. Polar warming asymmetry between NH and SH

As indicated in previous studies (e.g., Li et al. 2013), the hemispheric mean warming asymmetry between the NH and SH is relatively small for both transient and equilibrium responses. However, when comparing just the polar regions of the two hemispheres, a clear and notable warming asymmetry is found (Fig. 1). Although the polar warming patterns are similar in both hemispheres, the amplitudes of the individual contributions are generally larger in the NH (Fig. 11). This leads to a warming asymmetry that favors a larger warming of the NH polar region than the SH polar region. To obtain a better sense of what feedbacks are responsible for the hemispheric polar warming asymmetry, we have defined an asymmetry index (AI) as follows:

 
formula

which calculates the ratio of the hemispheric polar warming asymmetry of an individual process x to the absolute value of the total hemispheric polar warming asymmetry. A positive AI represents a process that favors a larger warming of the NH polar region than the SH polar region, while a negative AI indicates the opposite.

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.

Fig. 12.

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.

Fig. 12.

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.

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 and , which have small seasonal variations. The largest negative feedback on the tropical surface warming is due to the evaporation (or latent heat flux) feedback. Although some feedback contributions to the total tropical temperature change, such as and , have a noticeable seasonality in the tropics, their seasonal variations largely cancel out. Therefore, the total warming is relatively uniform year-round at ~+1.3 K.

Fig. 13.

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).

Fig. 13.

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).

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 is primarily due to the large solar annual cycle over the polar regions. At first this might seem counterintuitive as the maximum of the solar annual cycle occurs in summer and the minimum in winter, which is almost opposite the seasonal cycle of . However, the importance of the solar annual cycle becomes clear once it is understood that it controls the seasonality of the SAF and ocean heat storage interaction and the net cloud feedback. The insolation maximum in summer leads to a near cancellation between the SAF and ocean heat storage terms and between SW and LW cloud feedbacks, which leads to the relatively small total warming observed in polar summer (as discussed in section 4i). During late fall/winter the lack of insolation in polar regions leads to small contributions by the SAF and SW cloud feedback to the total temperature change, which allows for a warming of the surface by the release of the extra solar energy absorbed in summer and by the LW cloud feedback due to the increase in clouds. Since other feedbacks do not experience as large seasonal variations as the net cloud feedback and the SAF and ocean heat storage interaction, the strong solar annual cycle in polar regions is primarily responsible for the pronounced seasonality of the total polar warming pattern.

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 , implying notable contributions from feedback processes to the seasonality of the surface temperature change.

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 with a minimum warming in summer and maximum in fall/winter. The large solar annual cycle is mainly responsible for the strong seasonality of the total polar warming pattern, as illustrated in section 5. In the tropics the solar annual cycle is small, which demonstrates why the picture given here for the tropics is similar to that given by the annual mean analysis of Taylor et al. (2013). In the polar regions the large solar annual cycle leads to a different picture for the seasonal approach versus the annual mean approach. Thus, it is in the polar regions where we benefit the most from the seasonal information of individual feedbacks.

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.

Acknowledgments

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

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:.
Bintanja
,
R.
, and
E. C.
van der Linden
,
2013
:
The changing seasonal climate in the Arctic
.
Sci. Rep.
,
3
,
1556
, doi:.
Bony
,
S.
, and Coauthors
,
2006
:
How well do we understand and evaluate climate feedback processes?
J. Climate
,
19
,
3445
3482
, doi:.
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:.
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:.
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:.
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:.
Chapman
,
W. L.
, and
J. E.
Walsh
,
2007
:
Simulations of Arctic temperature and pressure by global coupled models
.
J. Climate
,
20
,
609
632
, doi:.
Colman
,
R.
,
2003
:
Seasonal contributions to climate feedbacks
.
Climate Dyn.
,
20
,
825
841
, doi:.
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:.
Fu
,
Q.
, and
K. N.
Liou
,
1993
:
Parameterization of the radiative properties of cirrus clouds
.
J. Atmos. Sci.
,
50
,
2008
2025
, doi:.
Gent
,
P. R.
, and Coauthors
,
2011
:
The Community Climate System Model version 4
.
J. Climate
,
24
,
4973
4991
, doi:.
Hall
,
A.
,
2004
:
The role of surface albedo feedback in climate
.
J. Climate
,
17
,
1550
1568
, doi:.
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:.
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:.
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:.
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:.
Lu
,
J.
, and
M.
Cai
,
2009a
:
Seasonality of polar surface warming amplification in climate simulations
.
Geophys. Res. Lett.
,
36
,
L16704
, doi:.
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:.
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:.
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:.
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:.
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:.
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:.
Pithan
,
F.
, and
T.
Mauritsen
,
2014
:
Arctic amplification dominated by temperature feedbacks in contemporary climate models
.
Nat. Geosci.
,
7
,
181
184
, doi:.
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:.
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:.
Screen
,
J. A.
, and
I.
Simmonds
,
2010
:
The central role of diminishing sea ice in recent Arctic temperature amplification
.
Nature
,
464
,
1334
1337
, doi:.
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:.
Soden
,
B. J.
, and
I. M.
Held
,
2006
:
An assessment of climate feedbacks in coupled ocean–atmosphere models
.
J. Climate
,
19
,
3354
3360
, doi:.
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:.
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:.
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:.
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:.
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:.
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:.
Vavrus
,
S.
,
2004
:
The impact of cloud feedbacks on Arctic climate under greenhouse forcing
.
J. Climate
,
17
,
603
615
, doi:.
Wetherald
,
R. T.
, and
S.
Manabe
,
1988
:
Cloud feedback processes in a general circulation model
.
J. Atmos. Sci.
,
45
,
1397
1416
, doi:.
Winton
,
M.
,
2006
:
Amplified Arctic climate change: What does surface albedo feedback have to do with it?
Geophys. Res. Lett.
,
33
,
L03701
, doi:.

Footnotes

*

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

1

Note that LC09 compares two annual mean equilibrium states. Here we deal with a transient response and a seasonal cycle, meaning the tendency term is not zero, and thus has to be taken into account. The tendency term or heat storage term is part of the ΔQocn_dyn+storage term and assumed negligible in the atmosphere, as explained in the text below.

2

Note that shown in Fig. 2a is drastically different from that given by the TOA perspective, which is characterized with maximum forcing in tropics and subtropics and minimum in polar regions with little seasonal variation (e.g., Winton 2006; Taylor et al. 2011a,b). This is because the meridional profile of the external forcing at the TOA is determined by the reduction of the upward thermal radiation due to an increase in CO2, which tends to follow the poleward decreasing temperature profile in the unperturbed time mean state. However, is purely due to the increase of the downward thermal radiation at the surface due to an increase in CO2.