Abstract

This study performs offline, partial radiative perturbation calculations to determine the geographical distributions of climate feedbacks contributing to the top-of-atmosphere (TOA) radiative energy budget. These radiative perturbations are diagnosed using monthly mean model output from the NCAR Community Climate System Model version 3 (CCSM3.0) forced with the Special Report Emissions Scenario (SRES) A1B emission scenario. The Monte Carlo Independent Column Approximation (MCICA) technique with a maximum–random overlap rule is used to sample monthly mean cloud frequency profiles to perform the radiative transfer calculations. It is shown that the MCICA technique provides a good estimate of all feedback sensitivity parameters. The radiative perturbation results are used to investigate the spatial variability of model feedbacks showing that the shortwave cloud and lapse rate feedbacks exhibit the most and second most spatial variability, respectively. It has been shown that the model surface temperature response is highly correlated with the change in the TOA net flux, and that the latter is largely determined by the total feedback spatial pattern rather than the external forcing. It is shown by representing the change in the TOA net flux as a linear combination of individual feedback radiative perturbations that the lapse rate explains the most spatial variance of the surface temperature response. Feedback spatial patterns are correlated with the model response and other feedback spatial patterns to investigate these relationships. The results indicate that the model convective response is strongly correlated with cloud and water vapor feedbacks, but the lapse rate feedback geographic distribution is strongly correlated with the climatological distribution of convection. The implication for the water vapor–lapse rate anticorrelation is discussed.

1. Introduction

There is overwhelming evidence that anthropogenic climate change has occurred in the twentieth century and will continue to occur in the future, even if CO2 emissions were brought to zero today (Solomon et al. 2007). Thus, there is great need to study how the climate system has responded and will respond to increasing greenhouse gases. The current best estimate of climate sensitivity to the doubling of CO2 presented by the Intergovernmental Panel on Climate Change (IPCC) in the Fourth Assessment Report (AR4) is approximately +3.0 K with a likely range of +2.0 to +4.5 K (Solomon et al. 2007). Indeed, there is large uncertainty in this projection, suggesting a need for a better understanding of the climate system response to an external forcing. The community consensus is that intermodel differences in climate feedback strengths are responsible for the large uncertainties in climate sensitivity, with clouds being the most uncertain (Colman 2003; Stephens 2005; Bony et al. 2006; Soden and Held 2006; Soden et al. 2008). As a result, the diagnosis, analysis, and intercomparison of climate feedback strengths in general circulation models (GCMs) are important endeavors to a better understanding of climate sensitivity.

Climate feedback strength is represented by a feedback sensitivity parameter defined as the ratio of global mean radiative perturbation from an individual feedback process to the global mean surface temperature response, in W m−2 K−1. Any variable within the climate system that can alter the top-of-atmosphere (TOA) energy balance—including temperature, water vapor, clouds, and surface albedo—represents a climate feedback mechanism. The sum of individual climate feedback sensitivity parameters equals the total climate feedback parameter, namely:

 
formula

In (1), λ is the climate feedback parameter and λy represents climate feedback sensitivity parameters, where y is either T, r, C, or α referring to temperature, water vapor, cloud, and surface albedo, respectively. Equation (1) stems from simple linear arguments used to gain insight into GCM response to any radiative forcing (e.g., Hansen et al. 1984; Wetherald and Manabe 1988; Zhang et al. 1994; Colman et al. 1997; Watterson et al. 1999; Colman 2002; Soden and Held 2006; Zhu et al. 2007; Soden et al. 2008; Shell et al. 2008; Lu and Cai 2009a).

Recently, several model intercomparison studies have used (1) to describe the mean strength of individual climate feedback strengths and intermodel range. Colman (2003) compiled previously published results of climate feedback strengths from a number of different models. Soden and Held (2006) intercompared a set of coupled ocean–atmosphere models forced with the IPCC Special Report Emissions Scenario (SRES) A1B. The current best estimate of climate feedback strengths are λr = +1.80 ± 0.18, λC = +0.69 ± 0.38, λα = +0.26 ± 0.08, and λT = −0.84 ± 0.26 W m−2 K−1 (Soden and Held 2006; Bony et al. 2006; Randall et al. 2007).

These climate feedback strengths indicate a moderate intermodel spread in all feedbacks. Bony et al. (2006) made a recommendation that narrowing the feedback intermodel spread may be obtained by improving our understanding of the related physical processes. Clement et al. (2009) present an exemplary analysis that tests model physical processes linked to low-cloud feedback through correlation analysis. However, most climate feedback model intercomparisons are centered on global mean feedback sensitivity parameters. It is impossible to infer physical relationships between feedbacks and processes at this scale. Comparing only global mean feedback strengths allows for compensating model differences to mask feedback differences. This study advocates analyzing feedback geographic distributions as one method for isolating physical processes contributing to intermodel spread.

Colman (2002) presented geographic distributions of climate feedbacks showing significant geographic variability. Additionally, Colman (2002) spatially correlated the radiative perturbations with model responses and showed that 1) water vapor height feedback and convective response are correlated, 2) contributions to longwave feedbacks from changes in cloud amount and height are uncorrelated, and 3) longwave cloud feedback due to a change in cloud height is correlated strongly with changes in convection. Other investigations of spatial feedback and spatial variability include Winton (2006) for surface albedo feedback, and Soden et al. (2008) and Shell et al. (2008) for all feedbacks. Colman’s (2002) results are instructive, indicating the model physical processes with the most influence on climate feedbacks and, therefore, climate sensitivity.

Boer and Yu (2003) analyzed local contributions to model climate feedbacks using the Canadian Centre for Climate Modeling and Analysis GCM. One major outcome was that the surface temperature response spatial pattern is largely explained by the spatial pattern of TOA feedback radiative perturbations, not the external forcing. Thus, analyzing individual TOA feedback geographic distributions provides insight about regional surface temperature response.

The purpose of this study is to investigate the geographic distribution of annual mean climate feedback radiative perturbations in the National Center for Atmospheric Research (NCAR) Community Climate System Model version 3 (CCSM3.0). Section 2 discusses the model characteristics and the prescribed forcing. Additionally, a detailed description of the TOA radiative perturbations calculation technique is presented. The technique is devised to perform a direct cloud feedback calculation, which is not possible using radiative kernels (e.g., Soden and Held 2006; Soden et al. 2008; Shell et al. 2008). A comparison with the approach in Soden et al. (2008) and Shell et al. (2008) is presented as a mutual verification of the techniques. The geographic distribution results and a feedback spatial variability discussion are presented in section 3. In section 4, insight into feedback spatial patterns is provided through discussions explaining the surface temperature response pattern and the apparent anticorrelation between water vapor and lapse rate feedbacks. Last, section 5 presents a summary and conclusions.

2. Methodology

a. Model characteristics and forcing

The NCAR CCSM3.0, hereafter CCSM3.0, is a coupled climate model comprising atmosphere, land, ocean, ice, and sea ice models. Readers are referred to Collins et al. (2004) and Collins et al. (2006) for a model technical review and validation of the model control climate state, respectively. The CCSM3.0 simulation used in this study was forced with the SRES A1B forcing (Solomon et al. 2007) with T85, 1.41° × 1.41°, resolution. The simulation represents a moderate increase of greenhouse gases throughout the twenty-first century from 360 to 689 ppmv after 100 years. The SRES A1B emissions scenario is chosen in this study to facilitate comparison with Soden and Held (2006).

b. Feedback calculation

Radiative perturbations were obtained using offline radiative transfer calculations, referred to as the partial radiative perturbation (PRP) technique (Wetherald and Manabe 1988). Radiative perturbations are defined as positive downward, such that a positive (negative) radiative perturbation represents a positive (negative) feedback. The technique is computationally expensive but is a direct determination of feedback radiative perturbations.

The PRP technique is elucidated by a first-order Taylor series expansion. Let us define R as the net flux at TOA, which is dependent on temperature, CO2 concentration, water vapor specific humidity, surface albedo, and cloud properties denoted by T, x, r, α, and C, respectively. Let us consider R1, the net flux at TOA of the initial equilibrium climate (denoted with subscript 1), and R2, the net flux at TOA of the perturbed climate state (denoted with subscript 2). We can approximate R2 using the first-order Taylor series expansion of R about R1 as

 
formula

In (2), O(2) denotes the higher-order terms. Moving R1 to the lhs and taking a long time mean, the total time mean TOA radiative perturbation ΔRtot is equal to the sum of external radiative forcing and feedbacks:

 
formula

In (3), the overbar stands for long time averaging. We have followed convention (e.g., Wetherald and Manabe 1988; Soden and Held 2006), separating the total temperature feedback into surface temperature response and lapse-rate terms. The lapse rate feedback is calculated as the difference between the total temperature and surface temperature response radiative perturbations following Wetherald and Manabe (1988):

 
formula

In (4), Γ refers to the vertically nonuniform contributions to the total temperature feedback. Equation (3) can be rewritten in a shorthand manner considering equilibrium:

 
formula

where the angled brackets, 〈·〉, denote global, long time average, and 〈ΔR= 0. From (5), the system response radiative perturbations, lhs, must balance the sum of the external forcing and individual feedback radiative perturbations.

Radiative perturbations are calculated using monthly model output at each grid point. Specifically, the terms in (5) are calculated according to (before carrying out the global averaging)

 
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In (6)(10), i represents the model grid point, j represents month index, and N represents the total number of years. The first and second terms on the rhs of (6)(10) represent the perturbed and control TOA radiative fluxes, respectively. The control climate state is defined as the first 11 years, 2000–10, of the model simulation, and the perturbed climate state is the first 11 years of the twenty-second century, 2100–10, following Soden and Held (2006). This definition of control and perturbed climate is adopted to facilitate comparison with Soden and Held (2006). It is important to note that the model climate is not in equilibrium state: 〈ΔRt〉 = 0.991 W m−2.

Monthly mean thermodynamic variables are commonly used in diagnostic feedback calculations and are not expected to impact the local radiative perturbations (e.g., Shell et al. 2008; Wetherald and Manabe 1988). Wetherald and Manabe (1988) used 3-month averages of atmospheric thermodynamic variables to calculate radiative perturbations. Shell et al. (2008) computed radiative perturbation feedbacks using monthly mean model output and compared them against every time-step model-output calculations. They found small differences of ~10%. The biggest concern is the use of monthly mean cloud properties.

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 the model grid box into a number of subcolumns and then generating cloud profiles for each. The main MCICA assumptions are 1) 3D horizontal radiative transport is neglected, and 2) the subcolumns are small enough that the cloud fraction within a layer is either 0 or 1. To generate the necessary subcolumn cloud profiles, a maximum–random overlap cloud generator (Raisanen et al. 2004) is used. Raisanen et al. (2004) demonstrated the application of the stochastic cloud generator to cloud liquid and ice water profiles. The approach requires a probability distribution, but only monthly mean cloud properties were archived for this simulation. Therefore, monthly mean cloud liquid and ice water path values are used instead of arbitrarily assuming a distribution of the model-generated cloud liquid and ice water paths, which could easily bias the calculations.

Last, cloud particle effective radius is determined using the CCSM3.0 parameterization. For liquid water, the effective radius is a function of land surface type and layer temperature, whereas for ice water, the effective radius is only a function of temperature (Collins et al. 2004). More detailed information of the model-generated cloud liquid water path, ice water path, and cloud particle effective radius distributions would be beneficial for future investigations, and would be useful in identifying intermodel differences in cloud feedback strengths.

Using this MCICA variation, the terms inside the summation operator on the right-hand side of (6)(10) are calculated according to

 
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respectively. In (11)(16), a new index for the cloud profile, k, is the kth generated subcolumn. Perturbed and control fluxes for a month are the average flux, calculated using M subcolumns.

The choice of M = 100 was determined empirically as a compromise between computational cost and convergence of the radiative transfer calculation. Several experiments using monthly data were performed varying the number of subcolumns from 10 to 5000 to test the sensitivity to radiative perturbations. The variation in the meridional mean water vapor radiative perturbation resulting from varying the number of subcolumns was less than 1%, or 0.02 W m−2. For individual grid points, the largest variations in the monthly mean water vapor radiative perturbations were 12%, or 0.5 W m−2. The results for the water vapor radiative perturbation represent the temperature and forcing results as well. Cloud and surface albedo radiative perturbations exhibited more variability. The meridional mean variations were 10%, and the global mean sensitivity to the number of subcolumns is smaller.

The linear approximation has been tested extensively (e.g., Soden and Held 2006), and Fig. 1 shows a linearity test for the MCICA technique. The ΔRtot [lhs of (3)] is an offline radiative transfer calculation where all climate variables are perturbed simultaneously and is represented by color contours in Fig. 1. The sum of individual feedbacks ΔRind [rhs of (3)], is represented by black contours in Fig. 1. If the linearization methodology is valid, then there will be overlap between ΔRtot and ΔRind contours. This is largely the case and provides confidence in the methodology. Additional confidence is provided by the good reproduction of the model-simulated TOA net radiative response (Fig. 2). Moreover, the proposed methodology is beneficial because it allows a direct cloud feedback calculation. Radiative kernel cloud feedback calculation methods (Soden and Held 2006; Soden et al. 2008; Shell et al. 2008) are not a direct calculation and rely on either residual or adjustment methods. This point will be discussed further below.

Fig. 1.

Annual mean ΔR (W m−2) for all perturbations simultaneously calculated (color contours) and sum of the individually calculated offline radiative perturbations using monthly mean model output (black contours). Contour interval is 5 W m−2. Positive values correspond to increased downwelling TOA net flux.

Fig. 1.

Annual mean ΔR (W m−2) for all perturbations simultaneously calculated (color contours) and sum of the individually calculated offline radiative perturbations using monthly mean model output (black contours). Contour interval is 5 W m−2. Positive values correspond to increased downwelling TOA net flux.

Fig. 2.

Annual mean model ΔR (W m−2). Positive values correspond to increased downwelling TOA net flux. Contour interval is 5 W m−2.

Fig. 2.

Annual mean model ΔR (W m−2). Positive values correspond to increased downwelling TOA net flux. Contour interval is 5 W m−2.

The adjustment method (Soden et al. 2008; Shell et al. 2008) is presented here (Fig. 6) as a mutual test of the methodologies. The adjustment method takes the difference between the perturbed and control climate net cloud radiative forcing (CRFNET), hereafter ΔCRFNET, and applies a “cloud masking” correction. The CRFNET is defined as the TOA net all-sky flux minus the TOA net clear-sky flux. Both methodologies reveal very similar δRC_NET spatial patterns (see Figs. 4 and 6). The global, annual-mean-adjusted ΔCRFNET is +0.290 W m−2, similar to our result δRC_NET = +0.222 W m−2. This comparison provides additional verification of the MCICA methodology and provides further justification for the indirect cloud feedback calculations.

Fig. 3.

(top left) Annual mean δRx (W m−2) with contour interval of 0.5 W m−2 and (top right) δRr (W m−2) with contour interval of 2.0 W m−2. (bottom left) δRΓ (W m−2) contour interval of 2.5 W m−2, and (bottom right) δRα (W m−2) with contour interval of 5.0 W m−2. Positive values correspond to increased downwelling TOA flux.

Fig. 3.

(top left) Annual mean δRx (W m−2) with contour interval of 0.5 W m−2 and (top right) δRr (W m−2) with contour interval of 2.0 W m−2. (bottom left) δRΓ (W m−2) contour interval of 2.5 W m−2, and (bottom right) δRα (W m−2) with contour interval of 5.0 W m−2. Positive values correspond to increased downwelling TOA flux.

Fig. 4.

(top left) Annual mean δRC_LW (W m−2), (top right) δRC_SW, and (bottom) δRC_NET. Contour intervals are 5 W m−2. Positive values correspond to increased downwelling TOA flux.

Fig. 4.

(top left) Annual mean δRC_LW (W m−2), (top right) δRC_SW, and (bottom) δRC_NET. Contour intervals are 5 W m−2. Positive values correspond to increased downwelling TOA flux.

Fig. 5.

Summary of selected model climate responses defined by the difference between the mean of the perturbed and control decades: (top left) high-cloud (clouds at pressures < 400 hPa) area fraction, (top right) low-cloud (clouds at pressures >700 hPa) area fraction, and (bottom) convective precipitation.

Fig. 5.

Summary of selected model climate responses defined by the difference between the mean of the perturbed and control decades: (top left) high-cloud (clouds at pressures < 400 hPa) area fraction, (top right) low-cloud (clouds at pressures >700 hPa) area fraction, and (bottom) convective precipitation.

Fig. 6.

Annual mean TOA-adjusted ΔCRFNET estimated δRC_NET (W m−2). Contour interval is 5 W m−2. Positive values correspond to increased downwelling TOA flux.

Fig. 6.

Annual mean TOA-adjusted ΔCRFNET estimated δRC_NET (W m−2). Contour interval is 5 W m−2. Positive values correspond to increased downwelling TOA flux.

3. Geographic distribution of forcing and feedback TOA radiative perturbations

Typically, discussions of intermodel differences in climate sensitivity only involve global, annual mean climate feedback strengths. As indicated in Fig. 2, the total net TOA radiation response pattern ΔRtot is highly location dependent with a standard deviation σΔRtot of 10.54 W m−2. The spatial pattern of the CO2 forcing and the individual feedbacks will be presented next and the attribution of ΔRtot spatial variability σΔRtot will be discussed.

a. CO2 forcing

The CO2 external forcing δRx (Fig. 3, upper panel) ranges from +3.6 to +0.4 W m−2, with 〈δRx〉 = +2.28 W m−2. The 〈δRx〉 calculated here is less than the typical +4 W m−2 value for doubled CO2 (Hansen et al. 1984). This mainly results from calculating TOA radiative fluxes instead of tropopause fluxes, but also because the radiative forcing in this scenario is not quite doubled. The tropical δRx is more than 3 times larger than that near the poles, with the largest values of δRx occurring in warm, dry regions where cloud coverage is scarce. The δRx minima occur over mountain ranges (i.e., Himalayan Mountains) and near the poles where temperature is cold and water vapor in the mean climate state is scarce (Lu and Cai 2009b). The mean state cloud distribution is responsible for the tropical zonal asymmetry. This feature indicates that model control climate, especially cloud properties, significantly affects δRx magnitude and spatial distribution.

b. Clouds

The δRC_LW, δRC_SW, and δRC_NET geographic distributions (Fig. 4) show large spatial variations. The δRC_LW has large positive TOA values in the equatorial Pacific region exceeding +20 W m−2 and smaller values in the extratropics. The 〈δRC_LW〉 is +0.776 W m−2, representing λC_LW = +0.367 W m−2 K−1. The positive tropical δRC_LW dominates the global longwave (LW) cloud feedback; 40% of the 〈δRC_LW〉 comes from equatorward of 30°, and the maximum δRC_LW region in the equatorial Pacific Ocean accounts for ~25% of 〈δRC_LW〉. The strong positive equatorial Pacific δRC_LW is due to high-cloud coverage increases (Fig. 5).

A strong negative δRC_SW (Fig. 4) is shown over the equatorial Pacific Ocean exceeding −30 W m−2 that opposes the strong positive δRC_LW. Negative δRC_SW in this region is related to high-cloud (clouds at pressures less than 400 hPa) and low-cloud (clouds at pressures greater than 700 hPa) increases (Fig. 5). Several subtropical regions—including the United States and South American west coasts, the southern African continent, and the subtropical Atlantic Ocean—show negative δRC_SW from increased low cloud (Fig. 5), which drives 〈δRC_SW〉 = −0.554 W m−2 and λC_SW = −0.262 W m−2 K−1. These cloud regimes do not have a δRC_LW-offsetting counterpart, making significant contribution to 〈δRC_NET〉.

The 〈δRC_NET〉 and λC are +0.222 W m−2 and +0.105 W m−2 K−1, respectively, and result from a large cancellation between δRC_LW and δRC_SW. This is evident in the tropical western Pacific, where δRC_LW and δRC_SW largely cancel (Fig. 4). Conversely, the eastern tropical Pacific small positive δRC_LW and δRC_SW collectively contribute to a positive δRC_NET. Strong negative δRC_SW in the subtropics combine with a weak negative δRC_LW to contribute significantly to negative δRC_NET. In the midlatitudes, regions of positive and negative δRC_NET largely offset in the global mean. The Northern Hemisphere polar region shows a predominantly positive δRC_NET with a few areas of weak negative δRC_NET. The overall small positive 〈δRC_NET〉 is determined by a cancellation between positive tropical δRC_NET along the intertropical convergence zone and negative subtropical δRC_NET. In other words, 〈δRC_NET〉 is the small difference between opposing radiative perturbations due to increased tropical high and subtropical low clouds.

c. Water vapor

The water vapor feedback is mainly zonally uniform, with largest values in the tropics decaying rapidly toward the poles (Fig. 3). The δRr shows some interesting structure with very large values in the central equatorial Pacific. This result is different from Colman (2002), which shows a local minimum in the region, but Soden et al. (2008) multimodel ensemble results indicate a similar maximum. The 〈δRr〉 and λr are equal to 3.846 W m−2 and 1.82 W m−2 K−1, respectively, representing slightly larger values than Soden and Held (2006), but are within uncertainties bounds due to methodological differences. The water vapor feedback will be revisited in section 4, where the anticorrelation with the lapse rate feedback will be discussed.

d. Lapse rate

The δRΓ varies from negative in the tropics to positive near the poles (Fig. 3). The 〈δRΓ〉 and λΓ are −1.842 and −0.87 W m−2 K−1, respectively. Pointed out by Cai (2006) and Cai and Lu (2007), this δRΓ variation from negative in low latitudes to positive in high latitudes mainly represents stronger tropical evaporation and convective feedbacks that reduce surface warming and positive high-latitude large-scale dynamical feedback associated with stronger poleward energy transport. From correlation analysis, a relationship between δRΓ, the planetary boundary layer height (PBLH), and low-cloud area fraction response in high latitudes is shown in Figs. 7 and 8. The correlation strength between these quantities is highly latitude dependent, showing the strongest correlation in high latitudes. In light of this, the results shown in Figs. 7 and 8 illustrate a coherent positive coupling between local feedbacks (boundary layer and low-level clouds) and nonlocal feedbacks (horizontal energy transport).

Fig. 7.

Scatterplot of δRΓ (W m−2) on the x axis vs planetary boundary layer height response (m) on the y axis for various latitude regions. The correlation coefficient (r) is given for each region.

Fig. 7.

Scatterplot of δRΓ (W m−2) on the x axis vs planetary boundary layer height response (m) on the y axis for various latitude regions. The correlation coefficient (r) is given for each region.

Fig. 8.

As in Fig. 7, but for δRΓ (W m−2) vs the percent change in low-cloud area fraction.

Fig. 8.

As in Fig. 7, but for δRΓ (W m−2) vs the percent change in low-cloud area fraction.

Physically, the high-latitude positive correlation between the PBLH and δRΓ could be explained considering that increased surface warming is generally associated with a deeper surface mixed layer and an increased PBLH. An increased PBLH would in turn lead to a further positive feedback on the surface temperature, due to the deepening of the well-mixed layer, corresponding to a positive δRΓ. The PBLH parameterization may represent a link between the δRP and δRΓ, suggesting that δRΓ may be dependent upon the boundary layer parameterization, and therefore be responsible for some intermodel differences in λΓ.

e. Albedo

The δRα (Fig. 3) is mainly a high-latitude feedback with strongest contributions from the Northern Hemisphere—84%. Winton (2006) found a similar result, reporting 75% of 〈δRα〉 is from the Northern Hemisphere. The 〈δRα〉 is +0.503 W m−2 and λα is +0.238 W m−2 K−1. Large values of δRα occur in the Tibetan Plateau region because of reduced snow cover and in the Arctic because of sea ice melt. The contribution to the 〈δRα〉 separated by surface type indicates that in the CCSM3.0, 55% of λα is due to land snow changes and the remaining 45% is due to sea ice melt.

f. Attribution of total variance

The attribution of spatial variance is straightforward in this situation, since ΔRtot can be written as a linear combination of these individual partial radiative perturbations. For more details see Boer and Yu (2003). In the CCSM3.0, the lapse rate feedback explains the largest percent, 47%, of σΔRtot, and is the second most variable feedback: σδRΓ = 10.58 W m−2. The albedo feedback explains 32% of σΔRtot with a moderate spatial variability: σδRα = 4.95 W m−2. One expectation of this analysis was that the cloud feedbacks would have a large spatial variability and explain a large portion of σΔRtot. The largest spatial variability is δRC_SW with σδRC_SW = 11.1 W m−2, with smaller variability in δRC_LW and δRC_NET, σδRC_LW = 5.48 W m−2, and σδRC_NET = 6.26 W m−2, respectively. Clouds, however, explain only 23% of σΔRtot, shortwave (SW) contributing 16% and LW contributing 7%. The δRx is the least variable (σδRx = 0.31 W m−2) explaining 2% σΔRtot. The spatial δRr variability is the smallest of any feedback: σδRr = 2.85 W m−2. The water vapor feedback spatial pattern explains −2% of σΔRtot. The negative value results from a negative spatial correlation between δRr and ΔRtot. This represents a weakness in the explained variance methodology. The conclusion remains: the water vapor feedback does not contribute to σΔRtot, and operates uniformly across latitude bands.

4. Discussion

a. Explaining the spatial surface temperature response pattern

The surface temperature response spatial distribution is driven by the net TOA response pattern, not the forcing, and climate feedbacks act to localize the surface temperature response to the quasi-uniform CO2 forcing (Boer and Yu 2003). From a scatterplot of (ΔRtotδRP) versus δRP (Fig. 9) one can see that globally ~80% of the spatial pattern of the surface temperature response is explained by total feedbacks. Removing δRx decreases the explained variance by only a few percent (not shown), as shown by Boer and Yu (2003). The remaining ~20% of the surface temperature response pattern is explained by changes in horizontal energy transport. Thus, the feedback spatial distribution provides insight into the regional processes driving surface temperature response.

Fig. 9.

As in Fig. 7, but for δRP (W m−2) vs ΔRtot (W m−2).

Fig. 9.

As in Fig. 7, but for δRP (W m−2) vs ΔRtot (W m−2).

Robust surface temperature response features are evident from δRP (Fig. 10), including larger high-latitude warming and larger land surface temperature response. The surface temperature response is directly related to δRP, where more negative values indicate stronger surface warming. Other interesting features of the CCSM3.0 model results include warming asymmetries between the northern high latitudes (NHL) versus the southern high latitude (SHL), and a zonal warming asymmetry in the equatorial Pacific. Further, surface temperature differences between high- and low-latitude land and ocean seem to be opposite: land warms more than ocean in the tropics and ocean warms more than land in the high latitudes.

Fig. 10.

Annual mean δRP (W m−2). The contour interval is 2.5 W m−2. Negative values correspond to an increase of upward TOA longwave radiation due to surface warming.

Fig. 10.

Annual mean δRP (W m−2). The contour interval is 2.5 W m−2. Negative values correspond to an increase of upward TOA longwave radiation due to surface warming.

The global surface temperature response spatial pattern is mostly explained by the lapse-rate and surface albedo feedbacks, as shown in section 3. The local polar surface albedo feedback is partially responsible for this region’s surface temperature response; however, it cannot explain the seasonality (e.g., Lu and Cai 2009b). From the zonal mean perspective, the lapse rate feedback accounts for most of the surface temperature response pattern. Figure 11 is a zonal mean plot of several feedbacks showing the lapse rate feedback meridional transition from negative to positive. Thus, the lapse rate feedback explains most of the warming differences between low and high latitudes.

Fig. 11.

Zonal-annual mean δRΓ (brown), δRC_SW (red), δRC_LW (green), δRC_NET (black), and δRr (blue) (W m−2).

Fig. 11.

Zonal-annual mean δRΓ (brown), δRC_SW (red), δRC_LW (green), δRC_NET (black), and δRr (blue) (W m−2).

The temperature increases in the NHL exceed 8 K over large regions, whereas the maximum SHL increases are approximately 5 K. Overall, NHL has stronger surface albedo, lapse-rate, and water vapor feedbacks, as illustrated in Fig. 4. Based upon the feedback strengths, the NHL must warm more than the SHL, assuming dynamical heat transport changes are similar. Spatially, the NHL spatial temperature response pattern exhibits a large warming centered around the pole, decreasing southward. Alternatively, the SHL response is a broad warming with a local maximum around 315°E longitude. These spatial warming patterns follow combined lapse-rate and surface albedo feedback pattern. The root cause of the hemispheric differences must be linked to the underlying surface type: ocean in NHL and continent in SHL. A reinforcement of the previous statement is illustrated by the weaker Greenland warming response. The polar lapse-rate and surface albedo feedbacks seem to behave differently over land versus ocean, tending to be stronger over ocean and weaker over ice-covered continent.

Lu and Cai (2009a) show that the lapse rate feedback is a consequence of using the TOA feedback perspective, and is actually portions of other feedbacks. Moreover, the high-latitude lapse rate feedback is mainly driven by dynamical transport of moist static energy (Lu and Cai 2009b). We conclude that the overall high-latitude positive lapse rate feedback is driven by large-scale atmospheric transport (nonlocal feedbacks), while the local thermodynamics drives the zonal asymmetry. With regards to the land versus ocean lapse rate feedback differences, it is difficult to ascertain the contributing feedbacks to the lapse rate feedback without additional analysis.

The equatorial Pacific zonal warming asymmetry is characterized by stronger warming in the central and eastern equatorial Pacific (CEEP) than the western equatorial Pacific (WEP). The asymmetry is driven by the total feedback, not any individual, and may result from a link between the water vapor, lapse-rate, and cloud feedbacks discussed in the next section. The CEEP exhibits strong net cloud and water vapor feedback and a weaker lapse-rate damping than the WEP. The overall spatial response pattern closely follows the lapse rate feedback, which matches the base state convective precipitation. This suggests that the warming asymmetry is related to the convective base state.

The tropical land versus ocean warming differences are opposite to the high latitudes. For instance, the warming of the tropical South America (TSAM), central Australia (CA), and South Africa (SA) land areas is 1–2 K more than nearby oceans. Part of the warming difference results from the nonequilibrium state, since oceans warm more slowly than land. However, the results show differences between ocean and land total feedback strengths. There is a tendency for less negative lapse rate feedback over land than ocean for a given zonal region, evident from the zonal mean anomalies of the lapse rate feedback in Fig. 12 (upper panel). The zonal mean net cloud feedback anomalies (Fig. 12) indicate no consistent zonal differences between land and ocean. The lapse rate feedback contributes most to the tropical land versus ocean warming differences, tending to be more positive over land than ocean regions. This result is opposite to the high-latitude result, where the ocean feedback was more positive. Separating the lapse rate feedback by surface type, the land lapse-rate is always closer to zero than the ocean feedback. Thus, the lapse rate feedback over ocean is always larger than over land in the absolute sense.

Fig. 12.

Zonal mean anomalies of (top) δRΓ (contour interval 2.0 W m−2) and (bottom) δRC_NET (contour interval 5.0 W m−2).

Fig. 12.

Zonal mean anomalies of (top) δRΓ (contour interval 2.0 W m−2) and (bottom) δRC_NET (contour interval 5.0 W m−2).

b. Water vapor–lapse rate feedback anticorrelation

Recent model feedback intercomparison studies consider the global mean water vapor and lapse rate feedbacks as a combined feedback. The main reason for the combination is the reduced intermodel spread when the two feedbacks are combined (Colman 2003; Soden and Held 2006; Bony et al. 2006). Hansen et al. (1984) explained that the combined water vapor–lapse rate feedback must have opposing signs because of convective effects. The cancellation results from the upward transport of energy and water vapor by convection, where warming and moistening of the upper troposphere corresponds to negative lapse-rate and positive water vapor feedbacks. In the tropics where convection is frequent, this explanation suggests a clear cancellation between the lapse rate and water vapor feedbacks. However, this explanation is not consistent in high latitudes where the lapse rate and water vapor feedbacks have the same sign.

The tropical cancellation is obvious from zonal mean lapse-rate and water vapor radiative perturbations (Fig. 11) where the water vapor feedback is positive and the lapserate feedback is negative. Considering the spatial distribution, there is negligible spatial correlation between the two feedbacks, suggesting that the mechanism driving the tropical mean cancellation may not be straightforward. Figure 13 shows the average δRΓ within 2.0 W m−2-wide δRr bins and suggests a partial cancellation of the tropical water vapor and lapse rate feedback. Under weaker water vapor feedback, the lapse rate feedback is positive with large variability, indicated by the width of the bars representing ±1σ. The stronger water vapor feedback regions, largely found in the tropics, have a less variable, negative lapse rate feedback.

Fig. 13.

Mean (top) δRΓ and (bottom) δRC_LW within 2.0 W m−2 wide δRr bins. The bars centered on each bin average represent ±1 std dev.

Fig. 13.

Mean (top) δRΓ and (bottom) δRC_LW within 2.0 W m−2 wide δRr bins. The bars centered on each bin average represent ±1 std dev.

To speculate why the lapse rate and water vapor feedbacks, both driven by convection, are not spatially correlated, we consider the slowing of the tropical mean circulation. Slower Hadley and Walker cell circulations are a robust model result, this suggests a direct consequence of more efficient upward energy transport (Held and Soden 2006). The lapse rate feedback spatial pattern closely matches the model base state distribution of tropical convection, not the response. This suggests that regions where convection is already frequently occurring act to transport energy vertically, producing the lapse rate feedback with little change in spatial extent. Without a change in the spatial extent of convection, deep convection must become more efficient at vertical energy transport, consistent with Held and Soden (2006). The region of strongest water vapor feedback is located in the central equatorial Pacific (CEP), collocated with a large high-cloud increase. It is possible that increased cirrus clouds from convective detrainment could moisten the CEP upper troposphere even in the presence of a weaker mean circulation and produce a strong water vapor feedback. Figure 13 (lower panel) shows the average δRC_LW within 2.0 W m−2-wide δRr bins, showing more positive δRC_LW under stronger water vapor feedback. It is impossible, however, to determine causation in this context and we are unsure whether the increased water vapor resulted in more high clouds or if more detrained high clouds lead to more upper-tropospheric water vapor. Despite the lack of spatial correlation, it seems plausible that convection drives a physically consistent tropical cancellation between the lapse-rate and water vapor feedbacks. A small portion of the apparent discrepancy results from clouds masking the tropical western Pacific clear-sky water vapor feedback. The resulting correlation becomes negative but is still small: r = −0.28. Further, the anticorrelation becomes slightly stronger (r = −0.35) when considering only convection regions.

5. Summary and conclusions

This study presented a detailed investigation of the climate feedback geographic distributions within the CCSM3.0 at TOA. The individual feedback radiative perturbations were determined using monthly mean model output and offline radiative transfer calculations. The unique feature of the radiative feedback calculations presented is that by applying a variation of the MCICA technique, monthly mean clouds properties can be used in model feedback diagnosis. This technique was shown to provide a good estimate of all feedback radiative perturbations and strengths, and obtained results similar to Soden and Held (2006). The two estimates were generally within the uncertainty range of ~10% quoted by Soden and Held (2006), accounting for methodological and radiative transfer model differences.

The CCSM3.0 cloud feedback sensitivity parameter was diagnosed as being small and positive: +0.105 W m−2 K−1. This result is significantly smaller than the Soden and Held (2006) ensemble mean value (+0.68 W m−2 K−1) but is essentially the same feedback strength Soden and Held (2006) diagnosed for the CCSM3.0 (+0.14 W m−2 K−1) using a different method. This reaffirms the small, positive cloud feedback in CCSM3.0. Additionally, this result provides a validation of the MCICA methodology for this application. The global mean cloud feedback is the difference between a positive tropical cloud feedback and a negative subtropical cloud feedback due to increased tropical and subtropical high and low clouds.

The SW cloud feedback spatial variability was found to be the most variable feedback and the lapse rate feedback was found to be the second most variable. The LW and net cloud feedback spatial variability was moderate. The net cloud feedback spatial variability was much closer to the LW than the SW cloud feedback, indicating that the LW acts to reduce the spatial variability of the SW. The lapse-rate, surface albedo, and net cloud feedback explained 47%, 32%, and 23% of the surface temperature response. The small explained variance by the net cloud feedback was a surprising result since the spatial variability of the SW cloud feedback was large. The external forcing and water vapor feedback both exhibit little spatial variability and do not contribute to the regional surface temperature response.

This study found strong correlation between the model convective base state and the tropical lapse rate feedback. Additionally, positive tropical cloud and water vapor feedbacks strongly correlate with the model convective response. These correlations have implications to the model surface temperature response and the anticorrelation between water vapor and lapse rate feedback. There are indications that particular features of the model control climate may dictate the spatial surface temperature response. It is then logical to speculate that the model control climate could dictate the model climate sensitivity. One way we plan on testing this assertion is through a multimodel intercomparison.

The water vapor and lapse rate feedbacks have recently been combined to show a reduction in the intermodel spread. The physical cause for such an anticorrelation is thought to be due to convection and is evident in the tropical zonal mean radiative perturbation. However, the feedback spatial distributions are not spatially correlated. We conclude that the lack of spatial correlation between the two feedbacks does not indicate that convection is not a link between the feedbacks. It seems that the tropical mean circulation changes may act to separate regions of strong lapse-rate and water vapor feedback.

This study focused on the diagnosis of climate feedback radiative perturbations at TOA. However, such an analysis can also be applied to each atmospheric layer investigating the vertical distribution of climate feedback-related atmospheric heating. Taylor (2010) carried out the analysis for the CCSM3.0, and in a future paper we plan to describe results from those calculations.

A benefit of analyzing the geographic distribution of the radiative contributions to global feedbacks is that local radiative perturbations and feedback processes can be linked to physical processes within a GCM. It would then be beneficial to perform similar analyses on a broader range of models. However, not all of the necessary model output is currently being archived, particularly cloud information, from the IPCC simulations. This analysis is beginning to link the geographic distribution of climate feedbacks to physical processes within the model. The linking of physical processes to model climate feedbacks is a necessary step toward understanding GCM climate feedbacks, reducing uncertainties in model feedback strengths, and understanding the influence of model parameterizations on model climate sensitivity.

Acknowledgments

The Office of Biological and Environmental Research of the U.S. Department of Energy supported this research under Grant DE-FEG02-02ER63338 as part of the Atmospheric Radiation Measurement Program. Also, we thank the two anonymous reviewers for their helpful comments. We acknowledge that The Florida State University shared High-Performance Computing facility and staff for contributions to results presented in this paper.

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