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  • View in gallery

    Schematic of the temperature feedback loop: The atmosphere-initiated temperature feedback loop amplifies the direct atmospheric (a) warming or (b) cooling due to the forcing and/or nontemperature feedbacks; the surface-initiated temperature feedback loop amplifies the direct surface (c) warming or (d) cooling due to the forcing and/or nontemperature feedbacks.

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    The annual- and zonal-mean (partial) surface temperature changes (K) due to the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) ocean dynamics feedback plus heat storage, (f) surface latent heat flux feedback, (g) surface sensible heat flux feedback, (h) offline error, and (i) temperature feedback. In (j), the sum of (a)–(i) is the red curve and the simulated surface temperature change is the black curve.

  • View in gallery

    The annual- and zonal-mean changes in surface energy flux convergence (W m−2) due to the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) ocean dynamics feedback plus heat storage, (f) surface latent heat flux feedback, (g) surface sensible heat flux feedback, (h) offline error, (i) temperature feedback, and (j) sum of (a)–(i).

  • View in gallery

    The annual- and zonal-mean meridional profile of the inverse of the partial derivative of surface energy flux divergence with respect to surface temperature (∂Rs/∂Ts)−1 (units: K m2 W−1).

  • View in gallery

    The annual- and zonal-mean surface PTCs (K) due to the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) atmospheric dynamics feedback, (f) ocean dynamics feedback plus heat storage, (g) surface latent heat flux feedback, (h) surface sensible heat flux feedback, and (i) offline error. The black and red curves are the direct and indirect contributions of the above processes, respectively.

  • View in gallery

    The sum of direct and indirect contributions (solid black curves; K) to the surface temperature response by the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) atmospheric dynamics feedback, (f) ocean dynamics feedback plus heat storage, (g) surface latent heat flux feedback, (h) surface sensible heat flux feedback, and (i) offline error.

  • View in gallery

    (a) The net surface temperature change (K) at each iteration of the temperature feedback loop associated with the direct surface temperature change caused by the surface albedo feedback. (b) The surface temperature change (K) given by each iteration of the temperature feedback loop associated with the surface albedo feedback. The value for iteration zero corresponds to the direct surface temperature change due to the surface albedo feedback (abscissa is number of temperature feedback loop iterations; ordinate is the surface temperature change).

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Isolating the Temperature Feedback Loop and Its Effects on Surface Temperature

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  • 1 Department of Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee, Florida
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Abstract

Climate feedback processes are known to substantially amplify the surface warming response to an increase of greenhouse gases. When the forcing and feedbacks modify the temperature response they trigger temperature feedback loops that amplify the direct temperature changes due to the forcing and nontemperature feedbacks through the thermal–radiative coupling between the atmosphere and surface. This study introduces a new feedback-response analysis method that can isolate and quantify the effects of the temperature feedback loops of individual processes on surface temperature from their corresponding direct surface temperature responses.

The authors analyze a 1% yr−1 increase of CO2 simulation of the NCAR CCSM4 at the time of CO2 doubling to illustrate the new method. The Planck sensitivity parameter, which indicates colder regions experience stronger surface temperature responses given the same change in surface energy flux, is the inherent factor that leads to polar warming amplification (PWA). This effect explains the PWA in the Antarctic, while the direct temperature response to the albedo and cloud feedbacks further explains the greater PWA of the Arctic. Temperature feedback loops, particularly the one associated with the albedo feedback, further amplify the Arctic surface warming relative to the tropics. In the tropics, temperature feedback loops associated with the CO2 forcing and water vapor feedback cause most of the surface warming. Overall, the temperature feedback is responsible for most of the surface warming globally, accounting for nearly 76% of the global-mean surface warming. This is 3 times larger than the next largest warming contribution, indicating that the temperature feedback loop is the preeminent contributor to the surface warming.

Corresponding author address: Ming Cai, Department of Earth, Ocean, and Atmospheric Science, Florida State University, 1017 Academic Way, LOVE Building, Room 423, Tallahassee, FL 32306. E-mail: mcai@fsu.edu

Abstract

Climate feedback processes are known to substantially amplify the surface warming response to an increase of greenhouse gases. When the forcing and feedbacks modify the temperature response they trigger temperature feedback loops that amplify the direct temperature changes due to the forcing and nontemperature feedbacks through the thermal–radiative coupling between the atmosphere and surface. This study introduces a new feedback-response analysis method that can isolate and quantify the effects of the temperature feedback loops of individual processes on surface temperature from their corresponding direct surface temperature responses.

The authors analyze a 1% yr−1 increase of CO2 simulation of the NCAR CCSM4 at the time of CO2 doubling to illustrate the new method. The Planck sensitivity parameter, which indicates colder regions experience stronger surface temperature responses given the same change in surface energy flux, is the inherent factor that leads to polar warming amplification (PWA). This effect explains the PWA in the Antarctic, while the direct temperature response to the albedo and cloud feedbacks further explains the greater PWA of the Arctic. Temperature feedback loops, particularly the one associated with the albedo feedback, further amplify the Arctic surface warming relative to the tropics. In the tropics, temperature feedback loops associated with the CO2 forcing and water vapor feedback cause most of the surface warming. Overall, the temperature feedback is responsible for most of the surface warming globally, accounting for nearly 76% of the global-mean surface warming. This is 3 times larger than the next largest warming contribution, indicating that the temperature feedback loop is the preeminent contributor to the surface warming.

Corresponding author address: Ming Cai, Department of Earth, Ocean, and Atmospheric Science, Florida State University, 1017 Academic Way, LOVE Building, Room 423, Tallahassee, FL 32306. E-mail: mcai@fsu.edu

1. Introduction

The Intergovernmental Panel on Climate Change Fifth Assessment Report indicates the equilibrium climate sensitivity1 is likely in the range from 1.5° to 4.5°C with high confidence and that the transient climate response2 is likely in the range from 1° to 2.5°C (Collins et al. 2013). Most of the surface warming, however, cannot be directly attributed to the increase of carbon dioxide (CO2). In response to an increase of CO2 the complex energy exchanges among the atmosphere, ocean, and land are changed. The perturbed variables of the climate system can amplify or suppress the surface warming response to the CO2 forcing alone (i.e., without feedbacks). It is these climate feedbacks, triggered by the CO2 forcing, that account for most of the global surface warming response (Hansen et al. 1984; Wetherald and Manabe 1988; Zhang et al. 1994; Colman 2003; Soden and Held 2006; Taylor et al. 2013; Yoshimori et al. 2014).

When the forcing and climate feedbacks modify the temperature response, in the atmosphere or at the surface, the thermal longwave (LW) emission by the atmosphere and surface is also altered. This change in thermal LW emission due to temperature changes is known as the temperature feedback. In the conventional top-of-atmosphere (TOA) feedback-analysis framework the temperature feedback is typically decomposed into a uniform temperature response equal to the surface temperature change (also referred to as the Planck feedback) and a lapse-rate feedback, which describes the deviation of the temperature response from uniformity (Wetherald and Manabe 1988; Colman 2002, 2003; Soden and Held 2006; Soden et al. 2008; Taylor et al. 2011). From the TOA perspective, the temperature feedback is a negative feedback as the general warming of the atmosphere and surface lead to an increase of the outgoing longwave radiation (e.g., Soden et al. 2008).

The climate feedback-response analysis method (CFRAM; Lu and Cai 2009a; Cai and Lu 2009) uses a different climate feedback framework than that used in traditional TOA climate feedback-analysis methods such as the partial radiative perturbation (PRP) method (Wetherald and Manabe 1988) and the radiative kernel method (Soden and Held 2006; Soden et al. 2008). Unlike the traditional TOA climate feedback framework, the CFRAM analysis is a three-dimensional analysis that includes nonradiative feedbacks as well as radiative feedbacks. The CFRAM allows for a calculation of the individual (partial) temperature change contributions of the external forcing alone and each of the radiative and nonradiative feedback processes to the (total) 3D temperature response as offline and postprocess diagnostic quantities without rerunning the original climate model. Furthermore, these (partial) temperature changes (PTC) are additive and the summation of all of them can be directly compared to the (total) temperature change derived from the original climate simulations; since the PTCs are calculated with no need for a priori knowledge of the simulated (total) temperature change, the sum of all PTCs can be compared to the simulated temperature change to validate the accuracy of the CFRAM analysis.

According to Cai and Lu (2009), the lapse-rate feedback (or temperature feedback) as defined in the TOA context is representative of multiple physical and dynamical feedback processes and thus not easily interpretable. This limitation is overcome in the three-dimensional CFRAM analysis, since the multiple physical and dynamical feedback processes lumped into the lapse-rate feedback (i.e., temperature feedback) are studied separately. Therefore, the individual PTCs due to the forcing and each of the nontemperature feedbacks include a temperature feedback associated with each of the different processes. Consequently, the forcing PTC in the CFRAM analysis is not a true no feedback calculation as the temperature feedback effects associated with the forcing are included in the forcing PTC. To uncover this hidden effect in the CFRAM this study develops and introduces a new feedback-analysis method, based on the same feedback framework as the CFRAM, to isolate the temperature feedback effects on surface temperature from those due directly to the forcing and nontemperature feedbacks.

The next section gives a conceptual understanding of the temperature feedback loop. Section 3 describes the mathematical formulation of the new feedback-analysis method used to isolate and quantify the temperature feedback effects on surface temperature and the model simulations it is applied to. The results of the analysis are then presented and discussed in sections 4 and 5, followed by a discussion on the temperature feedback loop strength in section 6. Finally, the paper ends with a summary and concluding remarks in section 7.

2. The temperature feedback loop

As stated previously, the thermal LW emission is altered when the forcing and nontemperature feedbacks modify the atmospheric or surface temperature. The change in thermal LW emission further modifies the atmospheric and surface temperature response through the thermal–radiative coupling between the surface and atmosphere. Thus, when the forcing or nontemperature feedbacks change the temperature response in the atmosphere–surface column a temperature feedback loop is triggered.

There are four different possible configurations for the temperature feedback loop (Fig. 1). The forcing or nontemperature feedback can directly change the energy flux convergence in the atmosphere (Figs. 1a,b), at the surface (Figs. 1c,d), or both. For example, if the forcing or nontemperature feedback directly increases (decreases) the atmospheric energy flux convergence the atmosphere warms (cools), which then increases (decreases) the LW emission to the surface. This augments (reduces) the absorption of LW radiation at the surface, which enhances (reduces) the surface energy flux convergence and warms (cools) the surface. The warming (cooling) of the surface in turn enhances (reduces) the LW emission to the atmosphere, which increases (decreases) the absorption of LW radiation in the atmosphere. The temperature feedback loop is closed as the increase (decrease) of energy flux convergence in the atmosphere amplifies the warming (cooling) of the atmosphere. The temperature feedback loop would then continue to cycle further amplifying the atmospheric and surface warming (cooling). Similarly, a direct change of the surface energy flux convergence by the CO2 forcing or nontemperature feedback would trigger the same type of temperature feedback loop except the temperature feedback loop begins at the surface (Figs. 1c,d). The surface-initiated temperature feedback loop amplifies the initial surface warming (cooling) associated with a positive (negative) energy flux convergence perturbation at the surface and warms (cools) the atmosphere. A common textbook explanation of the greenhouse effect (e.g., Petty 2006) will include a statement on how the infrared emission by the surface gets absorbed by the atmosphere and reradiated downward toward the surface and absorbed, thus leading to a higher surface temperature. The temperature feedback loop is the manifestation of this process and thus exemplifies the greenhouse effect.

Fig. 1.
Fig. 1.

Schematic of the temperature feedback loop: The atmosphere-initiated temperature feedback loop amplifies the direct atmospheric (a) warming or (b) cooling due to the forcing and/or nontemperature feedbacks; the surface-initiated temperature feedback loop amplifies the direct surface (c) warming or (d) cooling due to the forcing and/or nontemperature feedbacks.

Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0287.1

The temperature feedback loop is a positive feedback that amplifies the initial temperature change of the atmosphere and/or surface. Consequently, the surface-initiated temperature feedback loop will always enhance the direct surface PTCs caused by the external forcing and nontemperature feedbacks, while the atmosphere-initiated temperature feedback loop will always amplify the direct atmospheric PTCs. If the direct temperature change by a given forcing or nontemperature feedback is of the same sign in both the surface and atmosphere, the surface-initiated and atmosphere-initiated temperature feedback loops will be of the same sign and the direct atmospheric and surface PTCs will be further amplified. On the other hand, if the direct temperature changes in the surface and atmosphere by a given forcing or nontemperature feedback are of opposite signs, the surface-initiated and atmosphere-initiated temperature feedback loops will work against each other. Since the forcing and nontemperature feedbacks trigger these temperature feedback loops, the temperature feedback effects on atmospheric and surface temperature can be thought of as the indirect effects of the forcing and nontemperature feedbacks.

3. Surface version of the CFRAM

Isolating the effect of the temperature feedback loop on surface temperature from their corresponding direct surface temperature responses can be achieved by the surface version of the CFRAM, which is referred to as the surface feedback-response analysis method (SFRAM). The energy budget perturbation in response to an external forcing for the whole atmosphere–surface column (at a grid point) is given by
e1
where is the change in the tendency or heat storage term, Δ(SR) is the change in net radiative energy flux convergence, and ΔQ is the change in energy flux convergence due to all nonradiative processes, all in units of watts per square meter. This is a vector equation with (M + 1) elements, which consists of M atmospheric layers and a single surface layer at each horizontal grid point. Unlike Lu and Cai (2009a), we have included the heat storage term, , since we are not limiting our focus to the annual-mean equilibrium response [for which ]. If we assume Δ(SR) is small, we can linearize it according to
e2
where ΔFext is the change in radiative energy flux convergence at each atmospheric layer and at the surface layer due to the CO2 forcing alone; Δwv(SR) and Δcld(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; and is the vertical profile of changes in net LW radiative flux divergence due to changes in atmospheric and surface temperatures. The quantity (∂R/∂T) is called the Planck feedback matrix whose mth column represents the change in LW radiative divergence at the mth layer due to a 1-K warming at the jth layer alone (where j is a dummy variable representing a single atmospheric layer or the surface layer). Readers may consult Fig. 1 in Lu and Cai (2009a) for an illustration of (∂R/∂T). After a substitution of (2) into (1) and some rearrangement, (1) becomes
e3a
e3b
where the equation is written in both vector-matrix notation (3a) and summation notation (3b). The summation notation of (3b) indicates that there are actually M + 1 equations implicit in the vector-matrix notation corresponding to energy balance equations for each of the M + 1 layers (M atmospheric layers plus the surface layer)3.
This is the point where the CFRAM and SFRAM derivations diverge. For the CFRAM derivation the next and final step would be to take the inverse of the Planck feedback matrix and multiply it to both sides of (3a). Therefore, the CFRAM is just a way to solve for the vertical profile of (total) temperature change at each atmospheric layer and at the surface layer using matrix algebra to solve the system of equations. The matrix multiplication of with each of the terms in vector-matrix notation on the right-hand side (rhs) of (3) gives the vertical profile of the partial temperature changes of the external forcing alone and each of the radiative and nonradiative feedbacks (Lu and Cai 2009a). For the SFRAM derivation, on the other hand, the focus is exclusively on the surface energy budget, which is equivalent to setting m = M + 1 (M + 1 is the surface layer) in (3b), leading to
e4
where the summation in (3b) has been expanded to isolate the surface temperature change. It follows that one can solve for just the surface temperature change according to
e5
where the subscript M + 1 has been substituted for s to signify the surface layer. The terms in brackets in (5) are just the changes in surface energy flux convergence due to the external forcing (ext), water vapor changes (wv), changes in cloud properties (cld), surface albedo changes (alb), nonradiative changes (non-rad), air temperature changes, and changes in surface heat storage. The quantity is similar to the Planck feedback parameter and is actually just one element of the Planck feedback matrix used in the CFRAM. The multiplication of with each of the terms in the brackets of (5) gives the surface PTC of the external forcing alone and feedbacks,
e6
where x represents one of the terms in the brackets of (5). The sum of the individual contributions of the external forcing alone and feedbacks add up to the total surface temperature change. Since there is no explicit a priori need for the surface temperature change information from the model output, the total surface temperature change given by the SFRAM analysis can be compared to that given by the model simulations to serve as validation of the accuracy of the SFRAM analysis.

The reason the surface layer (m = M + 1) is chosen instead of any atmospheric layer in going from (3a) and (3b) to (4) is based on physical rather than mathematical principles. A fundamental principle of the CFRAM and SFRAM climate feedback framework is that a change in energy flux convergence at any specific layer (surface or atmosphere) will cause a heating or cooling of that specific layer (i.e., the climate response). The only assumption made in the CFRAM and SFRAM calculations is that the temperature change will be such that the associated infrared radiation change will balance the change in energy flux convergence of that layer. This occurs for all layers and since for the SFRAM calculation we are only interested in the surface temperature change, it makes sense to use the surface layer, since the energy flux perturbations at the surface layer cause the surface temperature change.

The main advantage and motivation for the development of the SFRAM is the explicit calculation of the temperature feedback contribution to the (total) surface temperature change not included in the CFRAM analysis. The temperature feedback represents the warming or cooling of the surface due to an enhancement or reduction of the LW absorption at the surface, respectively, due to the net contribution of all the temperature feedback loops triggered by the forcing and nontemperature feedbacks (as described in section 2). The CFRAM includes the temperature feedback but does so implicitly. By explicitly separating the contribution of the temperature feedback to the surface temperature change, the SFRAM not only lets us analyze the importance of the temperature feedback but also gives insight into the direct effects (i.e., excluding the temperature feedback) of the external forcing and nontemperature feedbacks on the surface temperature. The SFRAM therefore gives the true no feedback contribution of the external forcing to the surface temperature change, unlike the CFRAM that includes the temperature feedback associated with the external forcing.

The temperature feedback contribution to the surface temperature change given by the SFRAM analysis is just the total sum of the indirect effects of the external forcing and nontemperature feedbacks. Considering the CFRAM analysis gives the atmospheric PTCs of the external forcing and nontemperature feedbacks and that these add up to the total atmospheric temperature change, we can use the SFRAM in conjunction with the CFRAM results to calculate the indirect effects of the external forcing and nontemperature feedbacks on surface temperature according to
e7
The terms on the rhs of (7) represent temperature feedbacks associated with the external forcing and each of the nontemperature feedbacks. Combining (7) with (6) the indirect surface PTCs of the external forcing and nontemperature feedbacks can be calculated. The surface PTCs given by the CFRAM analysis are thus equal to the sum of the direct and indirect PTCs of the external forcing and each of the nontemperature feedbacks given by the SFRAM analysis in conjunction with the CFRAM results; namely,
e8
Equation (8) allows for a separation and quantification of the direct (the first term in the square bracket) and indirect (the second term in the square bracket) contributions of the forcing and nontemperature feedbacks to the surface temperature response. Such analysis thus allows the climate community to understand how important the direct versus the indirect effects are and better explain the PTCs of the forcing and nontemperature feedbacks. Furthermore, the decomposition of the temperature feedback in (7) allows us to attribute how the external forcing and nontemperature feedbacks contribute to the (total) temperature feedback, giving a better understanding of the temperature feedback contribution to the surface temperature change.

4. Model data and application

a. Model characteristics and simulations

The data used in this study are derived from the climate simulations of the NCAR CCSM4. A brief description of the NCAR CCSM4 model and the climate simulations considered in this study has been provided previously by Sejas et al. (2014b). The same description is reproduced here merely for the sake of self-completeness in the interest of benefiting the readers of the present paper. The atmospheric component of the CCSM4 is the Community Atmosphere 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 Ice Code, version 4 (CICE4). Please see Gent et al. (2011) for more CCSM4 details.

In this study, 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 yr, 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, the 20-yr mean between years 311 and 330 in the industrial control simulation is used 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. 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 is defined as the transient climate response to the CO2 forcing (known as the transient response).

b. SFRAM application

The SFRAM application to the NCAR CCSM4 dataset follows similarly to the CFRAM application done to this same dataset in Taylor et al. (2013) and Sejas et al. (2014a,b). The Fu–Liou radiative transfer model (Fu and Liou 1992, 1993) is used for all offline radiation calculations in (8) 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); 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 (Räisänen 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 (8) 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 (Cai and Lu 2009).

The nonradiative term in (5) can be expanded into individual contributions by specific nonradiative processes if they are available from the output files of the model simulations. The standard CCSM4 output includes nonradiative energy fluxes associated with atmospheric turbulent motions at the surface [i.e., surface turbulent sensible (SH) and latent heat (LH) fluxes]. Therefore, we can expand in (5) into
e9
where ΔLH and ΔSH are the changes in surface latent and sensible heat fluxes, with the traditional sign convention that positive values mean an increase in upward energy flux going from the surface to the atmosphere; is the remaining change in surface energy flux convergence due to nonradiative processes. Over land, should be close to zero because of the near absence of energy transport for land; for this reason, we simply refer to as changes in energy flux convergence due to changes in ocean dynamics and latent heat of melting due to sea ice melting.
The CCSM4 does not output or the surface heat storage (i.e., the thermal inertia), but we can take advantage of the surface energy balance equation and calculate them together as a residual:
e10
where is the change in net radiative flux convergence at the surface derived from the CCSM4 output. Over land, is assumed negligible because of the small heat capacity of land. Therefore, represents changes in energy flux convergence due to changes in ocean dynamics, sea ice, and heat storage.
The SFRAM equation [i.e., (5)] as applied to the CCSM4 dataset thus becomes
e11
The , as explained in Taylor et al. (2013) and Sejas et al. (2014b), is the error in the offline radiative calculation as compared to that derived from the CCSM4 outputs,
e12
This error is caused by differences between the offline radiative transfer model and that used for the online CCSM4 simulations and the usage of 20-yr monthly mean fields as inputs for our offline radiative calculations versus instantaneous fields. Note that (12) has no linearization to speak of, so the error is not due to the linearization assumption. Song et al. (2014a,b) and Sejas et al. (2014b) indicate that the main cause of the error in the offline radiative calculations is the use of time mean cloud properties and albedo data, owing to the exclusion of the diurnal cycle.
To obtain the indirect contributions of the CO2 forcing and nontemperature feedbacks, the CFRAM results for the atmospheric PTCs are utilized and (7) applied; namely,
e13
Notice that (13) includes an atmospheric dynamics term, as it is only through the temperature feedback loop that the atmospheric dynamics alters the surface temperature. When (13) is substituted into (11), the sum of the direct and indirect PTCs of the CO2 forcing and nontemperature feedbacks is obtained.

5. Annual-mean attribution

a. Global mean

The global- and annual-mean PTCs of the CO2 forcing and feedback given by the SFRAM analysis are given in Table 1. The accuracy of the linearity assumption can be verified by comparing the sum of these PTCs with the simulated surface temperature change. The total surface temperature change estimated with the SFRAM is 1.66 K—a difference of only 0.02 K (~1% difference) as compared to the CCSM4 simulated surface temperature change of 1.64 K. The high accuracy of the SFRAM confirms the PTCs due to the CO2 forcing and feedbacks are indeed addable to the surface temperature change obtained from the original model runs.

Table 1.

Global-mean surface PTCs for the CO2 forcing and feedbacks given by the SFRAM analysis, plus their total sum.

Table 1.

The SFRAM results indicate the temperature feedback is by far the most important contributor to the global warming of the surface, with a warming contribution of 1.26 K. This is 3 times larger than the surface warming owing to the energy flux perturbation at the surface from the water vapor feedback (0.42 K), which is the second largest contributor to the surface warming. This is in stark contrast to feedback attribution studies using a TOA perspective, which indicates the water vapor feedback is the largest contributor to the global-mean surface warming (e.g., Hansen et al. 1984; Held and Soden 2000; Colman 2003; Bony et al. 2006; Taylor et al. 2011). Less important contributors to the global-mean surface warming are the CO2 forcing and surface albedo and cloud feedbacks. The CO2 forcing only warms the surface by 0.15 K, demonstrating that the feedbacks it triggers are responsible for the majority of the surface temperature response.

The main suppressor of the global surface warming is the evaporation feedback with a cooling contribution of −0.29 K. Followed closely behind by the cooling contribution of the ocean dynamics feedback plus heat storage (−0.23 K). The surface sensible heat flux feedback, on the other hand, contributes very little to the surface temperature change (−0.01 K). The offline error in the SFRAM calculation is also very small (0.07 K), indicating the results are reliable.

Once again this is in contrast to the TOA perspective, which indicates the lapse-rate feedback is the main suppressor of the global-mean surface warming (Hansen et al. 1984; Colman 2003; Bony et al. 2006). The results, however, are consistent with other surface perspective studies that indicate evaporation is enhanced in global warming simulations, as a result of the enhanced energy absorption by the surface and water vapor capacity of the warming atmosphere (e.g., Manabe et al. 1991; Liu et al. 2005; Sutton et al. 2007). As would be expected, this enhancement of evaporation occurs mainly over the ocean, which is why the evaporation feedback is the greatest suppressor of the ocean warming and also helps explain the greater land than sea warming in climate simulations (Manabe et al. 1991; Sutton et al. 2007; Sejas et al. 2014a). Since the ocean encompasses most of the global surface, it is no surprise that we find that the evaporation feedback is the greatest suppressor of the global-mean surface warming.

b. Zonal mean

The zonal- and annual-mean total surface temperature change estimated with the SFRAM (red curve in Fig. 2j) also matches up quite well with the simulated surface temperature change (black curve in Fig. 2j). These curves show the surface warms at all latitudes in response to the doubling of CO2. The warming is weakest in the tropics and strongest in polar regions, a phenomenon known as polar warming amplification (PWA). The surface warms because of an increase in (total) surface energy flux convergence, as seen by the similarity of the meridional structures (Fig. 3j vs Fig. 2j). The major difference between the change in surface temperature and energy flux convergence is that the Antarctic increase of surface energy flux convergence is not as amplified as the increase in surface temperature. The difference in structures is due to , as indicated by (11), which using the Stefan–Boltzmann law and assuming the surface acts like a blackbody can be approximated by
e14
where σ is the Stefan–Boltzmann constant. Equations (11) and (14) indicate that a colder surface will experience a larger temperature response than a warmer surface, given the same change in energy flux convergence at the surface. This is similar to the Stefan–Boltzmann feedback (Hartmann 1994) or Planck feedback (Pithan and Mauritsen 2014) from the TOA perspective. Overall, this implies that polar regions will experience a larger temperature sensitivity to changes in surface energy flux convergence than the tropics. Since this is an inherent property of the polar surface and not an actual feedback process, we refer to (14) as the Planck sensitivity parameter.
Fig. 2.
Fig. 2.

The annual- and zonal-mean (partial) surface temperature changes (K) due to the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) ocean dynamics feedback plus heat storage, (f) surface latent heat flux feedback, (g) surface sensible heat flux feedback, (h) offline error, and (i) temperature feedback. In (j), the sum of (a)–(i) is the red curve and the simulated surface temperature change is the black curve.

Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0287.1

Fig. 3.
Fig. 3.

The annual- and zonal-mean changes in surface energy flux convergence (W m−2) due to the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) ocean dynamics feedback plus heat storage, (f) surface latent heat flux feedback, (g) surface sensible heat flux feedback, (h) offline error, (i) temperature feedback, and (j) sum of (a)–(i).

Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0287.1

Figure 4 shows that the Antarctic is the most sensitive location experiencing up to a 0.4 K change in temperature for every 1 W m−2 change in surface energy flux convergence, which more than doubles that seen in the tropics, thus explaining the PWA in the Antarctic. The Arctic is also more sensitive to changes in surface energy flux convergence relative to the tropics, though substantially less sensitive than the Antarctic. Overall, the larger sensitivity of the polar regions is an important factor causing PWA.

Fig. 4.
Fig. 4.

The annual- and zonal-mean meridional profile of the inverse of the partial derivative of surface energy flux divergence with respect to surface temperature (∂Rs/∂Ts)−1 (units: K m2 W−1).

Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0287.1

From the sensitivity arguments above, we might expect the Antarctic to have greater PWA than the Arctic. The Arctic, however, while not as sensitive to changes in surface energy flux convergence as the Antarctic, experiences the largest increases in surface energy flux convergence by far (Fig. 3j). This explains why the Arctic experiences greater PWA compared to the Antarctic, even though the Antarctic is more sensitive. The Antarctic also experiences a larger increase in surface energy flux convergence relative to the tropics but only slightly. The PWA in the Antarctic is therefore mainly due to the large sensitivity of the Antarctic. In the Arctic the much greater increase in surface energy flux convergence, compared to the tropics, would lead to substantial PWA even if the sensitivity of the tropics were equal to that of the Arctic. Therefore, the larger sensitivity of the Arctic relative to the tropics just enhances the PWA of the Arctic.

The principal contributor to the larger increase in surface energy flux convergence in the Arctic relative to the tropics is the surface albedo feedback (Fig. 3c). Therefore, the surface albedo feedback is the feedback process that most contributes to the large PWA of the Arctic. While not all feedback studies find the surface albedo feedback to be the feedback that most contributes to PWA (e.g., Winton 2006; Pithan and Mauritsen 2014), our result is consistent with many previous studies (e.g., Manabe and Wetherald 1975; Hall 2004; Taylor et al. 2013). The cloud feedback and the temperature feedback are also important contributors to the larger increase of the surface energy flux convergence in the Arctic (Figs. 3d,i) and are, thus, notable contributors to the PWA of the Arctic (Figs. 2d,i). Lu and Cai (2009b), using a surface perspective, indicated that the LW radiative feedback was a larger contributor to PWA in the Arctic than the surface albedo feedback. This study indicates that this might be true if the contributions of the LW cloud feedback (not shown) and the temperature feedback are added up, since these would essentially account for the PWA contribution of the LW feedback. However, upon decomposition of the LW feedback, the surface albedo feedback is clearly the principal contributor.

6. Direct versus indirect contributions

The previous section demonstrated that the temperature feedback accounts for most of the surface warming in the tropics, midlatitudes, and polar regions (Fig. 2). The temperature feedback is thus by far the most important feedback in relationship to surface temperature. As mentioned previously, the temperature feedback can be thought of as the indirect effect of the external forcing and nontemperature feedbacks. Therefore, the results given in the previous section for the CO2 forcing and nontemperature feedbacks are the direct contributions of these processes to the surface temperature change. To better comprehend the large contribution of the temperature feedback to the surface warming, we must be able to attribute the individual contributions of the external forcing and feedbacks to the atmospheric warming. Fortunately, the CFRAM method allows for such an attribution by calculating the individual contributions of the forcing and feedbacks to the atmospheric warming (e.g., Cai and Lu 2009; Lu and Cai 2010; Cai and Tung 2012; Taylor et al. 2013; Song et al. 2014a; Yoshimori et al. 2014). Therefore, by using the CFRAM results in conjunction with the SFRAM, we can decompose the temperature feedback as in (7) and (13) into individual indirect contributions by the external forcing and nontemperature feedbacks.

Table 2 shows the global-mean contributions, respectively, of the CO2 forcing alone and nontemperature feedbacks to the surface PTC of the temperature feedback. Globally, the temperature feedback loops associated with the external forcing are the primary contributors (0.93 K) to the surface temperature change attributed to the (total) temperature feedback, followed by the temperature feedback loops associated with the water vapor feedback (0.78 K). The temperature feedback loops triggered by the latent heat flux feedback (−0.46 K) and ocean dynamics feedback plus heat storage (−0.39 K) reduce the surface warming caused by the (total) temperature feedback. The temperature feedback contribution to the surface temperature change is also shown to have very little offline error (0.01 K), so we will not discuss the offline error any further in this study. The reader may refer to Sejas et al. (2014b) for further discussion on the offline error in the NCAR CCSM4 dataset.

Table 2.

Decomposition of the global-mean surface PTC of the temperature feedback into “indirect” global-mean surface PTCs for the CO2 forcing and feedbacks given by the SFRAM analysis in conjunction with CFRAM.

Table 2.

Figure 5 (red lines) demonstrates the temperature feedback loops connected to the water vapor feedback are the primary contributors to the warming of the tropics by the (total) temperature feedback, with an important contribution by the temperature feedback loops triggered by the CO2 forcing as well. This is a result of the lower troposphere warming in the tropics being caused mostly by these two processes (Taylor et al. 2013). The polar surface warming caused by the (total) temperature feedback is mainly related to the surface albedo feedback, with valuable contributions by the temperature feedback loops triggered by the CO2 forcing and atmospheric dynamics feedback as well. The temperature feedback contribution to the Arctic PWA can be mainly ascribed to the temperature feedback loop associated with the albedo feedback.

Fig. 5.
Fig. 5.

The annual- and zonal-mean surface PTCs (K) due to the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) atmospheric dynamics feedback, (f) ocean dynamics feedback plus heat storage, (g) surface latent heat flux feedback, (h) surface sensible heat flux feedback, and (i) offline error. The black and red curves are the direct and indirect contributions of the above processes, respectively.

Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0287.1

In general, the indirect contributions of the CO2 forcing and nontemperature feedbacks are larger in magnitude than their corresponding direct contributions, demonstrating the strength of the temperature feedback loop. Since the temperature feedback contribution to the surface warming is equal to the sum of all indirect contributions by the CO2 forcing and nontemperature feedbacks, this partially explains why the temperature feedback contribution to the surface warming is substantially more important than any individual direct contribution. Global-mean estimates indicate the temperature feedback contribution (~1.26 K) to the surface warming is 3 times larger than even the sum of all direct contributions (~0.4 K).

The sum of corresponding direct and indirect contributions (Fig. 5; sum of black and red lines) for the CO2 forcing and each feedback gives the net contribution (Fig. 6) of the CO2 forcing and each nontemperature feedback to the surface temperature response. Each sum is exactly equal to the individual surface PTCs of the CO2 forcing and feedbacks given by a CFRAM analysis, respectively, which can be verified by comparing our Fig. 6 results with the surface PTCs given by the CFRAM analysis of Taylor et al. (2013) on the same dataset. The temperature feedback is excluded, as it is taken into account through the indirect contributions of the CO2 forcing and feedback processes, which is why the CFRAM analysis does not include a temperature feedback. The CFRAM calculates the direct and indirect contributions jointly and, thus, are implicit in the analysis. This is why the CFRAM analysis attributes most of the global-mean warming to the water vapor feedback followed by the CO2 forcing instead of the temperature feedback.

Fig. 6.
Fig. 6.

The sum of direct and indirect contributions (solid black curves; K) to the surface temperature response by the (a) CO2 forcing alone, (b) water vapor feedback, (c) surface albedo feedback, (d) cloud feedback, (e) atmospheric dynamics feedback, (f) ocean dynamics feedback plus heat storage, (g) surface latent heat flux feedback, (h) surface sensible heat flux feedback, and (i) offline error.

Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0287.1

The advantage of the SFRAM is that we can separate and explicitly quantify the direct and indirect contributions of the forcing and feedback processes to the surface temperature response, furthering our understanding of how these processes, particularly through the thermal–radiative coupling (i.e., temperature feedback) between the surface and atmosphere, modify the surface temperature. The CFRAM has the advantage of attributing forcing and feedback contributions to the atmospheric temperature response as well as the surface temperature change. Of course the CFRAM advantage is utilized in the SFRAM analysis to separate the temperature feedback into indirect contributions. Therefore, they are synergetic approaches.

7. Strength of the temperature feedback loop

The SFRAM results clearly indicate that in general the indirect contributions of the forcing and nontemperature feedbacks to the surface temperature response are greater than their corresponding direct contributions. This is an important result that could not be deduced from the CFRAM analysis alone. To understand why the indirect PTCs are larger than the direct PTCs, the evolution of the temperature feedback loops triggered by the direct effect of the forcing and nontemperature feedbacks must be understood.

The CO2 forcing and nontemperature feedbacks indirectly modify the surface temperature through the surface-initiated temperature feedback loop, atmosphere-initiated temperature feedback loop, or both. If the forcing or nontemperature feedback directly affects the surface but not the atmospheric energy flux convergence, only a surface-initiated temperature feedback loop is triggered. For example, the ocean dynamics feedback plus heat storage and surface latent and sensible heat flux feedbacks amplify their direct effects on surface temperature exclusively through the surface-initiated temperature feedback loop. The surface albedo feedback has a very small direct effect on the atmospheric energy flux convergence, so its indirect effect on surface temperature is also through the surface-initiated temperature feedback loop. The surface-initiated temperature feedback loop amplifies the direct surface temperature change caused by these feedbacks, which is why these feedbacks have indirect surface PTCs with a similar meridional structure to their corresponding direct surface PTCs (Figs. 5c,f–h). On the other hand, if the forcing or nontemperature feedback directly affects the atmosphere but not the surface energy flux convergence, only an atmosphere-initiated temperature feedback loop is triggered. For example, the atmospheric dynamics has no direct effect on the surface temperature change but indirectly affects it through the atmosphere-initiated temperature feedback loop.

The CO2 forcing and the remaining nontemperature feedbacks indirectly modify the surface temperature change through both the surface-initiated and atmosphere-initiated temperature feedback loops. If the direct changes in energy flux convergence in the atmosphere and surface by the forcing or nontemperature feedback are of opposite signs, the surface-initiated temperature feedback loop amplifies the direct effect on surface temperature while the atmosphere-initiated temperature feedback loop suppresses it. This explains why the indirect PTCS are not always larger than the direct PTCs or even of the same sign. The cloud feedback, for example, directly warms the polar surface but indirectly cools it (Fig. 5d). If the signs are the same, however, both types of temperature feedback loops enhance the direct effect on surface temperature. This helps explain why the indirect PTCs are usually larger than the direct PTCs.

Amplification of the direct surface PTC by the atmosphere-initiated temperature feedback loop, however, is not necessary for the indirect surface PTC to be larger in magnitude than the direct surface PTC. Case in point, the direct surface PTCs of the feedbacks that have no atmosphere-initiated temperature feedback loop are generally smaller than the corresponding indirect PTCs (e.g., albedo feedback). Figure 7a demonstrates how after each iteration of the surface-initiated temperature feedback loop the direct warming by the surface albedo feedback gets continually amplified until it converges to a global-mean surface temperature change equal to that given by the sum of the direct and indirect effects (~0.42 K). As more iterations of the temperature feedback loop occur, the additional warming gets smaller and smaller as it asymptotically goes to zero (Fig. 7b), thus explaining the convergence of the global-mean surface temperature change caused by the albedo feedback in Fig. 7a. Furthermore, Fig. 7b demonstrates that each iteration of the temperature feedback loop contributes less to the surface warming than the direct contribution. The temperature feedback loop, however, goes through many iterations before it contributes negligibly to the surface temperature change, so the sum of all iterations of the temperature feedback loop (i.e., the indirect contribution) contributes more to the surface temperature change than the corresponding direct contribution of the forcing or nontemperature feedback.

Fig. 7.
Fig. 7.

(a) The net surface temperature change (K) at each iteration of the temperature feedback loop associated with the direct surface temperature change caused by the surface albedo feedback. (b) The surface temperature change (K) given by each iteration of the temperature feedback loop associated with the surface albedo feedback. The value for iteration zero corresponds to the direct surface temperature change due to the surface albedo feedback (abscissa is number of temperature feedback loop iterations; ordinate is the surface temperature change).

Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0287.1

The multiple iterations of the temperature feedback loop partially explain why the indirect surface PTCs are generally larger than the direct surface PTCs, but the reason multiple iterations of the temperature feedback loop are able to substantially amplify the surface temperature change before becoming negligible is due to the strength of the temperature feedback loop. The strength of the temperature feedback loop (i.e., the thermal–radiative coupling) is dependent on the unperturbed absorptance of the atmosphere and surface and the magnitude of the direct surface and/or atmospheric temperature change that triggers it. The surface is a near blackbody and the atmosphere has an abundance of strong absorbers such as water vapor, clouds, and CO2 and thus the strength of the temperature feedback loop is quite substantial—hence, explaining the greater contribution of the indirect than direct effects on surface temperature. The smaller the spectral windows in the LW domain and the larger the absorber amount in the atmosphere the stronger the temperature feedback is, given the same direct temperature change. The thick atmosphere (i.e., large amount of LW absorbers) of the earth’s climate system is thus the main reason why the temperature feedback is the most important contributor to the warming of the surface when forced by an increase of CO2.

8. Summary and conclusions

In this paper we introduced a surface version of the CFRAM, termed the SFRAM, to isolate and explicitly quantify the temperature feedback effects on surface temperature in a 1% yr−1 increase of CO2 simulation of the NCAR CCSM4 at the time of CO2 doubling (i.e., the transient response). The analysis indicates the temperature feedback is the most important contributor to the surface warming with a global-mean warming contribution of 1.26 K that accounts for ~76% of the total global-mean surface warming. This is 3 times larger than the next largest warming contribution, given by the water vapor feedback. This is a particularly poignant result as most climate feedback studies have indicated that the water vapor feedback is the main contributor to the global surface warming (e.g., Bony et al. 2006). The temperature feedback also accounts for most of the surface warming in the tropics, midlatitudes, and polar regions—consistent with the surface perspective results in Pithan and Mauritsen (2014), which show the (air) temperature feedback accounts for most of the surface warming in the tropics and the Arctic.

The SFRAM decomposition also indicates that the polar regions are more sensitive to increases in surface energy flux convergence, as polar regions will experience a greater surface warming relative to the tropics given the same increase in surface energy flux convergence. The PWA in the Antarctic is mainly a result of this larger sensitivity. Even though the Arctic is less sensitive than the Antarctic to changes in surface energy flux convergence, the PWA of the Arctic is greater, since the Arctic experiences the largest increases in surface energy flux convergence by far. The main contributor to this asymmetrical increase in surface energy flux convergence, relative to the tropics, is the surface albedo feedback. This is consistent with many PWA studies that cite the surface albedo feedback as the principal contributor to PWA (e.g., Manabe and Wetherald 1975; Hall 2004; Taylor et al. 2013). The temperature feedback is also found to contribute to the PWA of the Arctic.

The decomposition of the temperature feedback surface PTC into indirect contributions by the CO2 forcing and nontemperature feedbacks indicates that the temperature feedback loop associated with the CO2 forcing is the largest contributor to the global-mean surface warming ascribed to the temperature feedback. The warming in the tropics by the temperature feedback is mainly associated with the CO2 forcing and water vapor feedback, while the polar warming by the temperature feedback is predominately linked to the surface albedo feedback. In general, we found the indirect contributions of the CO2 forcing and nontemperature feedbacks to the surface temperature change were larger than their corresponding direct contributions.

The temperature feedback loop is a positive feedback that amplifies the direct PTC of the CO2 forcing and nontemperature feedbacks. The strength of the temperature feedback loop, though, is the main reason the indirect PTCs are larger in magnitude than the direct PTCs. The strength of the temperature feedback loop is dependent on both the unperturbed absorber amount in the atmosphere and surface and the direct temperature change that triggers it. The smaller the spectral windows in the LW domain and the larger the absorber amount in the atmosphere the stronger the temperature feedback will be, given the same direct temperature change. The great abundance of absorbers (e.g., water vapor) in the earth’s atmosphere and their absorption of LW radiation throughout the LW spectral domain thus explain the great strength of the temperature feedback and its predominant effect on the surface temperature response.

The SFRAM has thus shed light on the preeminent importance of the temperature feedback loop on surface temperature and hints at its great importance on the whole climate system. An important next step is to quantify the contribution of the temperature feedback on the atmospheric temperature change as well, since it is likely a dominant factor. A generalization of the SFRAM is needed to isolate the temperature feedback effects on the atmospheric temperature response and will be left for a future study. This generalization would be important since it will allow for a deeper understanding of the full (i.e., atmosphere and surface) temperature response to an external forcing and perhaps demonstrate the dominance of the temperature feedback loop on the climate system.

This study relies on the results of a single model. Previous studies indicate climate feedbacks have a notable model dependency (Colman 2003; Soden and Held 2006; Boé et al. 2009; Crook et al. 2011), so an equivalent analysis for other GCMs is required to test the robustness of the results and evaluate uncertainties. The dominant contribution to the surface warming by the temperature feedback loop suggests that intermodel differences in the absorber amount and composition in the unperturbed climate state can cause substantial differences in the surface warming response between different GCMs and should be studied in a future multimodel analysis.

Acknowledgments

This research was in part supported by grants from the National Science Foundation (AGS-1262173 and AGS-1354834) and NASA Interdisciplinary Studies Program Grant (NNH12ZDA001N-IDS).

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1

The equilibrium climate sensitivity is the annual global-mean surface temperature response to a doubling of the CO2 concentration once a climate model has reached equilibrium.

2

The transient climate response is the change in the annual global-mean surface temperature, averaged over a 20-yr period, centered at the time of CO2 doubling, in a climate model simulation in which CO2 increases at 1% yr−1.

3

To be clear, “T” is representative of temperature, while “t” is representative of time.

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