Impact of dataset choice on calculations of the short-term cloud feedback

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1 JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, , doi: /jgrd.50199, 2013 Impact of dataset choice on calculations of the short-term cloud feedback A. E. Dessler 1 and N.G. Loeb 2 Received 19 August 2012; revised 8 January 2013; accepted 17 January 2013; published 11 April [1] Dessler [2010, hereafter D10] estimated the magnitude of the cloud feedback in response to short-term climate variations and concluded that it was likely positive, with an average magnitude of W/m 2 /K. This paper investigates the sensitivity of D10 s results to the choice of clear-sky top-of-atmosphere flux (ΔR clear-sky ), surface temperature (ΔT s ), and reanalysis data sets. Most of the alternative ΔR clear-sky data sets produce cloud feedbacks that are close to D10, differing by W/m 2 /K. An exception is the Terra SSF1deg ΔR clear-sky product, which produces an overall negative cloud feedback. However, a critical examination of those data leads us to conclude that that result is due to problems in the Terra ΔR clear-sky arising from issues with cloud clearing prior to July Eliminating the problematic early portion yields a cloud feedback in good agreement with D10. We also present an alternative calculation of the cloud feedback that does not require an estimate of ΔR clear-sky, and this calculation also produces a positive cloud feedback in agreement with D10. The various ΔT s data sets produce cloud feedbacks that differ by as much as 0.8 W/m 2 /K. The choice of reanalysis, used as a source of ΔR clear-sky or as adjustments for the cloud radiative forcing, has a small impact on the inferred cloud feedback. Overall, these results confirm the robustness of D10 s estimate of a likely positive feedback. Citation: Dessler, A. E., and N. G. Loeb (2013), Impact of dataset choice on calculations of the short-term cloud feedback, J. Geophys. Res. Atmos., 118, , doi: /jgrd Introduction [2] The cloud feedback remains one of the stubborn uncertainties in climate science. Dessler [2010, hereafter D10] estimated the cloud feedback in response to short-term climate variations over the past decade and obtained an average value of the cloud feedback of W/m 2 /K, thereby ranging from a weakly negative to strongly positive cloud feedback. [3] D10 used a method described by Soden et al. [2008] and Shell et al. [2008] to isolate ΔR cloud, that part of the top-of-atmosphere (TOA) flux anomaly due to cloud anomalies. Briefly, D10 started with a calculation of the cloud radiative forcing anomaly (ΔCRF), which is the difference between clear-sky and all-sky TOA flux anomalies. The clearsky flux anomaly ΔR clear-sky is the flux that would occur if clouds were instantaneously removed from the atmosphere, but all other parameters stayed the same. ΔR clear-sky cannot be directly measured in the presence of clouds, so indirect methods must be used to determine the global average value. D10 used ΔR clear-sky calculated by two modern reanalyses. 1 Department of Atmospheric Sciences, Texas A&M University, College Station, TX, USA. 2 NASA Langley Research Center, Hampton, VA, USA. Corresponding author: A. E. Dessler, Department of Atmospheric Sciences, Texas A&M University, College Station, TX, USA American Geophysical Union. All Rights Reserved X/13/ /jgrd [4] ΔCRF is then adjusted (using reanalysis meteorological fields) to account for cloud masking from temperature (ΔT), water vapor (Δq), and surface albedo (Δa) anomalies, yielding ΔR cloud. Once ΔR cloud is obtained, it is regressed against the global average surface temperature anomaly ΔT s, with the slope equal to the cloud feedback. [5] D10 calculated the cloud feedback in response to shortterm climate variations (mainly El Nino-Southern Oscillation or unforced monthly fluctuations relating to weather). While the short-term cloud feedback in an individual climate model is a poor predictor of that model s long-term feedback [D10] and therefore doesn t necessarily inform us about the equilibrium climate sensitivity, it nevertheless provides a useful test for climate models. Previous analyses have shown that, on average, climate models do a reasonable job of simulating the observed short-term cloud feedback [Dessler, 2013]. 2. Sensitivity Calculations [6] Table 1 reproduces D10 s calculation of the cloud feedback over the period March 2000 to June 2011, but using seven ΔT s data sets. For these calculations, the all-sky flux anomaly ΔR all-sky is from the Clouds and the Earth s Radiant Energy System (CERES) [Wielicki et al., 1996] SSF1deglite_Ed2.6 monthly average product (hereafter, SSF1deg) from NASA s Terra satellite. ΔR clear-sky and the meteorological fields used to adjust ΔCRF are from two modern reanalysis systems (ERA-interm [Dee et al., 2011] and MERRA [Rienecker et al., 2011]). The change in radiative forcing ΔF 2821

2 Table 1. Values of the Cloud Feedback Using the Adjusted ΔCRF a Reanalysis Used for Adjustments and ΔR clear-sky Surf. Temp. Total Longwave Shortwave Total Longwave Shortwave ERA ERA skin ERA ERA 2 m ERA MERRA skin ERA MERRA 2 m ERA GISS ERA NCDC ERA HadCRU MERRA ERA skin MERRA ERA 2 m MERRA MERRA skin MERRA MERRA 2 m MERRA GISS MERRA NCDC MERRA HadCRU a Values of the cloud feedback (W/m 2 /K) obtained using the adjusted ΔCRF method and using meteorological fields, including ΔR clear-sky and adjustments to ΔCRF, from two different reanalyses (ERA-Interim and MERRA). Seven different surface temperature data sets are used: ERA-Interim and MERRA surface skin temperature and 2 m air temperature, and surface temperatures from GISTEMP [Hansen et al., 2010], NCDC [Smith et al., 2008], and Had- CRUT4 [Morice et al., 2012]. All calculations use terra SSF1deg ΔR all-sky. The terra period is February 2000 to June 2011, while the aqua period is July 2002 to June Uncertainties are the 2s statistical uncertainty of the regression between ΔR cloud and ΔT s. caused primarily by changes in long-lived greenhouse gases over this period is assumed to be W/m 2 [e.g., Solomon et al., 2011]. [7] The inferred total cloud feedback (shortwave (SW) plus longwave) during the Terra period (March 2000 June 2011) averages W/m 2 /K, with estimates ranging from to W/m 2 /K. D10 s estimate falls in the middle of the values in Table 1. The uncertainty of each individual calculation in Table 1 is the statistical uncertainty of the regression between ΔR cloud and ΔT s. This is the dominant uncertainty the uncertainty due to the data going into the calculation is smaller (discussed in more detail later). In particular, spurious trends in the CERES ΔR all-sky and in the reanalysis fields could cause additional errors, but D10 estimated they were small because the feedback is a regression vs. ΔT s, and warm and cold years occur throughout the time series. Our analysis is also insensitive to our estimate of ΔF varying ΔF by 100% (0.25 W/m 2 /K) changes the average cloud feedback by less than 0.03 W/m 2 /K. [8] Table 2 shows the same calculation as in Table 1, but using Terra SSF1deg ΔR clear-sky. Over the TERRA period, this calculation yields much lower estimates of the cloud feedback [also pointed out by Masters, 2012], with the inferred cloud feedback ranging from 0.75 to W/m 2 / K, with an average value of 0.38 W/m 2 /K. In other words, using Terra SSF1deg as a source of ΔR clear-sky produces a cloud feedback ~0.9 W/m 2 /K lower than the results in D10 and Table 1. [9] To help explain this difference, we have also calculated the cloud feedback using SSF1deg ΔR clear-sky and ΔR all-sky from CERES instruments onboard NASA s Aqua satellite (these data cover the Aqua period: July 2002 June 2011). Table 3 shows the corresponding cloud feedback values using these data. The cloud feedback values range from to W/m 2 /K, with an average of W/ m 2 /K. This disagrees with that calculated from Terra SSF1deg ΔR clear-sky (Table 2), but agrees well with the calculations using the results of D10 and Table 1. [10] We have also calculated the cloud feedback using the CERES Energy Balanced and Filled product (EBAF Ed2.6r) [Loeb et al., 2009, 2012]. Table 4 shows that using the EBAF ΔR clear-sky and ΔR all-sky, the cloud feedback ranges from Table 2. Values of the Cloud Feedback Using the Terra SSF1deg Product a Reanalysis Used for Adjustments Surf. Temp. Total Longwave Shortwave Total Longwave Shortwave ERA ERA skin ERA ERA 2 m ERA MERRA skin ERA MERRA 2 m ERA GISS ERA NCDC ERA HadCRU MERRA ERA skin MERRA ERA 2 m MERRA MERRA skin MERRA MERRA 2 m MERRA GISS MERRA NCDC MERRA HadCRU a Same as Table 1, but ΔR clear-sky comes from the terra SSF1deg product. 2822

3 Table 3. Values of the Cloud Feedback Using the Aqua SSF1deg Product a Reanalysis Used for Adjustments Surf. Temp. Total Longwave Shortwave ERA ERA skin ERA ERA 2 m ERA MERRA skin ERA MERRA 2 m ERA GISS ERA NCDC ERA HadCRU MERRA ERA skin MERRA ERA 2 m MERRA MERRA skin MERRA MERRA 2 m MERRA GISS MERRA NCDC MERRA HadCRU a Same as Table 1, but ΔR all-sky and ΔR clear-sky come from the aqua SSF1deg product. The time period covered by these data is the aqua period, July 2002 to June to W/m 2 /K, with an average of W/m 2 /K. This value is lower than D10 s, but still predicts that a positive cloud feedback is more likely than not. [11] It should be emphasized that the differences in the cloud feedbacks in Tables 2, 3, and 4 arise because of differences in ΔR clear-sky,notδr all-sky. ΔR all-sky in the three CERES data sets agree well, and varying just the ΔR all-sky changes the inferred cloud feedback by less than ~0.1 W/m 2 /K. [12] Table 6 summarizes these results. Only the calculation using Terra SSF1deg ΔR clear-sky produces a strongly negative cloud feedback. The other calculations generally agree with D10 that the cloud feedback is positive, although the cloud feedback obtained using EBAF is clearly lower than the other calculations. In the next section, we will explore the reasons that the Terra SSF1deg and, to a lesser extent, EBAF produce these divergent results. 3. Impact of Reduced MODIS Data Availability Early in the Terra Mission [13] We begin by showing in Figure 1 anomalies of the longwave component of ΔR clear-sky from Terra SSF1deg and from EBAF averaged over 30 S 30 N, 60 S 60 N, and for the entire globe between March 2000 and December Least-square regression trends are also plotted for each curve. For all three latitude ranges, the linear trends from the two data sets are within 0.05 W/m 2 /decade. [14] In the SW, however, the picture is different. Figure 2 shows that the Terra SSF1deg slopes are lower than EBAF by about ~0.2 W/m 2 /decade for the 30 N 30 S latitude range and ~0.4 W/m 2 /decade for the 60 N 60 S and global averages. These differences in slope are almost entirely due to large positive anomalies in the Terra SSF1deg data prior to July [15] These large positive anomalies in the Terra SSF1deg SW ΔR clear-sky prior to July 2001 can be traced to the Moderate Resolution Imaging Spectroradiometer (MODIS) data, which are used to identify cloud-free CERES footprints for the calculation of ΔR clear-sky. Prior to July 2001, electronics problems in the Terra MODIS [Barnes et al., 2003] limited the availability of MODIS data for use in CERES processing. While both EBAF and Terra SSF1deg ΔR clear-sky are affected by this, the impact is more pronounced in the SW than in the longwave and more pronounced in the Terra SSF1deg than in EBAF. The different impacts occur because SSF1deg analyzes only completely clear footprints while EBAF augments these clear footprints with contributions from mixed clear and cloudy footprints [Loeb et al., 2009]. Table 4. Values of the Cloud Feedback Using the CERES EBAF Product a Reanalysis Used for Adjustments Surf. Temp. Total Longwave Shortwave Total Longwave Shortwave ERA ERA skin ERA ERA 2 m ERA MERRA skin ERA MERRA 2 m ERA GISS ERA NCDC ERA HadCRU MERRA ERA skin MERRA ERA 2 m MERRA MERRA skin MERRA MERRA 2 m MERRA GISS MERRA NCDC MERRA HadCRU a Same as Table 1, but ΔR all-sky and ΔR clear-sky come from the CERES EBAF product [Loeb et al., 2009]. 2823

4 Figure 1. Anomalies of the longwave component of ΔR clear-sky from (a) CERES SSF1deg-Month-lite_Terra_Ed2.6 and from (b) CERES EBAF-TOA_Ed2.6r averaged over 30 S 30 N, 60 S 60 N, and for the entire globe between March 2000 and December Least-square regression trends are calculated for each curve. [16] Figure 3 demonstrates the influence of the sampling in these two data sets by plotting Terra SSF1deg minus EBAF SW ΔR clear-sky against the differences between the SSF1deg-sampled and actual average snow/ice percent coverage for 60 S 90 S and 60 N 90 N. Snow/ice percent coverage is calculated using daily snow/ice percent coverage maps from the National Snow and Ice Data Center. The subsampled mean percent coverage is determined by averaging regions with a valid daily SSF1deg SW ΔR clear-sky. Each point in Figure 3 represents a monthly mean anomaly. [17] Both60 N 90 N (Figure 3a) and 60 S 90 S (Figure 3b) show a correlation, demonstrating that reduced sampling of clear scenes by the coarser resolution SSF1deg product leads to differences in SW ΔR clear-sky compared to EBAF. This tendency, combined with reduced MODIS data availability prior to July 2001, increased the variability in monthly SW ΔR clear-sky in SSF1deg. After July 2001, MODIS data availability is more complete, and clear-sky SW TOA flux anomalies in Terra SSF1deg are more robust (Figure 2a). Independent analysis of the Aqua period confirms the robustness of the CERES values for this period [Susskind et al., 2012]. [18] To verify this, we recalculated the cloud feedback for all data sets over the Aqua period (July 2002 June 2011), thereby excluding the affected portion of the Terra SSF1deg and EBAF ΔR clear-sky time series. Results are listed in Tables 1, 2, and 4. Table 6 summarizes these results and shows that eliminating the early part of the time series brings the cloud-feedback estimates from Terra SSF1deg and EBAF into much better agreement with the other data sets. The other data sets show little sensitivity to the change in time period, which provides additional support for this explanation. Figure 2. Same as Figure 1, but for the shortwave component of ΔR clear-sky. 4. An Alternative Calculation [19] In addition to the method used by D10 (and which was used in all the calculations in Tables 1 4), which we will call the the adjusted ΔCRF method, there is an alternative approach to calculating the cloud feedback that does not require any estimate of ΔR clear-sky. This alternative calculation starts with the all-sky flux anomaly ΔR all-sky and subtracts off the components of the flux anomaly due to ΔT, Δq, and Δa, as Figure 3. Scatter plot of the difference between Terra SSF1deg and EBAF ΔR clear-sky vs. the difference between SSF1deg-sampled and actual snow/ice percent. (a) Averaged over 60 N 90 N and over April through August, , (b) averaged over 60 S 90 S and over November through February,

5 well as the change in radiative forcing [Soden et al., 2008, equation (24)]: ΔR cloud ¼ ΔR all-sky ΔR T ΔR q ΔR a ΔF (1) where ΔR x is that part of the TOA all-sky flux anomaly due to anomalies in x (x = T, q, and a). We will refer to this approach as the subtraction method, and Soden and Held [2006] used it in their calculation of the cloud feedback. The important point here is that the subtraction method does not require an estimate of ΔR clear-sky, so uncertainties or errors in that parameter will not affect the results. [20] Table 5 shows estimates of the cloud feedback obtained using the subtraction method, and the results are summarized in Table 6. In these calculations, ΔR all-sky are from Terra SSF1deg, and ΔR T, ΔR q,andδr a are estimated by combining the radiative kernels of Soden et al. [2008]withΔT, Δq, and Δa anomalies obtained from reanalyses. [21] These calculations yield an average cloud feedback strength of W/m 2 /K, with estimates ranging from to W/m 2 /K. This is in excellent agreement with the conclusion of D10 that the cloud feedback over this period is likely positive. [22] Spurious trends in the reanalyses [Bengtsson et al., 2004] or ΔR all-sky are unlikely to cause large errors in these calculations [D10]. The uncertainty in the cloud feedback due to uncertainty in ΔF is larger for the subtraction method than the adjusted ΔCRF method, but still relatively unimportant varying ΔF by0.25 W/m 2 /K (100%) changes the inferred cloud feedback by ~0.1 W/m 2 /K. Uncertainties due to the radiative kernels are harder to assess, but kernels computed by different groups using different models show good agreement [Soden et al., 2008; Shell et al., 2008], giving us some confidence in these calculations. 5. Summarizing the Impact of Different Data Sets [23] It is clear that the choice of input data set can significantly affect the inferred cloud feedback. The impact of the choice of ΔR clear-sky data can make a very large difference, even changing the sign of the feedback from positive to negative [Masters, 2012]. Much of this variation, however, is due to problems in the Terra SSF1deg and EBAF ΔR clear-sky data (as discussed earlier). If we focus on the Aqua period, thereby excluding the troublesome portions of those data, Table 6 shows that the choice of ΔR clear-sky data set leads to relatively small variations in the cloud feedback of W/m 2 /K. [24] The choice of ΔT s matters much more. Table 7 summarizes the cloud feedback calculated from each ΔT s data set, showing differences of ~0.8 W/m 2 /K. This helps explain the low values of the cloud feedback found by Masters [2012]. In that paper, there was an emphasis on two particular ΔT s data sets, ERA 2 m air temperatures and GISTEMP, which produce lower values of the cloud feedback than other ΔT s data sets. [25] In the adjusted-δcrf calculations, the adjustment terms are calculated from reanalysis meteorological fields. Which reanalysis is used has little impact on the calculated Table 5. Values of the Cloud Feedback Using the Subtraction Method a Reanalysis Used for Calculation Surf. Temp. Total Longwave Shortwave Total Longwave Shortwave ERA ERA skin ERA ERA 2 m ERA MERRA skin ERA MERRA 2 m ERA GISS ERA NCDC ERA HadCRU MERRA ERA skin MERRA ERA 2 m MERRA MERRA skin MERRA MERRA 2 m MERRA GISS MERRA NCDC MERRA HadCRU a Same as Table 1, but values of the cloud feedback (W/m 2 /K) are obtained using the subtraction method. Table 6. Average of the Total Cloud Feedback Values From Tables 1 5 a Clear-sky Data Source Avg. Cloud Feedback Avg. Cloud Feedback Avg. ERA Avg. MERRA Table 1 reanalysis Table 2 Terra SSF1deg Table 3 Aqua SSF1deg N/A Table 4 EBAF Table 5 subtraction a Average of the total cloud feedback values from Tables 1 5. The uncertainty is two standard deviations of the ensemble of slopes from these tables (it does not include the statistical uncertainty of the fits). The terra period covers March 2000 June 2011, the aqua period covers July 2002 June The average ERA and MERRA columns are the average of the feedbacks using those reanalyses for the ΔCRF adjustments. All units are W/m 2 /K. 2825

6 Table 7. Average of the Ensemble of Total Cloud Feedbacks Calculated Using a Single Surface Temperature Data Set, Derived From Values in Tables 1-5 a Surface Temperature ERA MERRA ERA skin ERA 2 m MERRA skin MERRA 2 m GISS NCDC HadCRU a Average of the ensemble of total cloud feedbacks calculated using a single surface temperature data set, derived from values in Tables 1 5. The uncertainty is two standard deviations of the ensemble of slopes from each temperature data set (it does not include the statistical uncertainty of the fits). The feedbacks are calculated over the aqua period, July 2002 June The averages are broken into ERA and MERRA, Which is the reanalysis used for the ΔCRF adjustments. All units are W/m 2 /K. cloud feedback generally less than 0.05 W/m 2 /K. In the subtraction method calculation, Table 6 shows that the choice of reanalysis is more important, leading to variations of 0.33 W/m 2 /K. [26] Combining in quadrature the variations in the cloud feedback due to the choice of the ΔR clear-sky (0.15 W/m 2 /K) and ΔT s data sets (0.4 W/m 2 /K) produces an estimate of the uncertainty in the cloud feedback due to the choice of these data sets of ~ W/m 2 /K. The uncertainties listed in Tables 1 5 are the statistical uncertainty of the ΔR clear-sky vs. ΔT s linear regression, which is typically 0.7 W/m 2 /K. Combining these yields a total uncertainty of W/m 2 /K, with most of this coming from the statistical uncertainty in the fit. 6. Conclusions [27] In D10, an estimate of the cloud feedback in response to short-term climate variations over the decade of the 2000s was presented. That paper concluded that the cloud feedback was likely positive, with a magnitude of W/m 2 /K. In this paper, we have investigated the sensitivity of D10 s conclusion to the choice of ΔR clear-sky, ΔT s, and reanalysis data sets used in the calculation. These results, when appropriately weighted by a critical evaluation of the relative strengths of the data sets, strongly support the conclusion of D10 of the existence a likely positive cloud feedback. [28] The different ΔR clear-sky data sets produce a wide range of cloud feedbacks, extending from negative to positive. However, much of this range is due to problems early in the Terra SSF1deg and EBAF ΔR clear-sky time series. Excluding those suspect data brings the cloud-feedback estimate from all the data sets to close agreement, within ~ W/m 2 /K of each other and all close to D10. [29] We found that the different ΔT s data sets lead to large variations in the cloud feedback of ~0.8 W/m 2 /K. Averaging the estimates of the cloud feedback from different ΔT s data sets yields an average cloud feedback close to the estimate of D10. The choice of reanalysis data set introduces smaller variations. Overall, the total uncertainty in the cloud-feedback calculation is dominated by the statistical uncertainty in the fit between ΔR clear-sky and ΔT s. [30] We also presented an alternative calculation of the cloud feedback that does not require any estimate of the ΔR clear-sky. This calculation produces estimates of the cloud feedback that are virtually identical to D10 s. Putting everything together, this analysis provides strong evidence supporting D10 s contention that the short-term cloud feedback over the decade of the 2000s was likely positive. [31] Acknowledgments. This work was supported by NSF grant AGS to Texas A&M University. We thank Mark Zelinka and Troy Masters for their comments on this paper. References Barnes, W., X. Xiong, and V. Salomonson (2003), Status of Terra MODIS and Aqua MODIS, Adv. Space Res., 32, , doi: /s (03) Bengtsson, L., S. Hagemann, and K. I. Hodges (2004), Can climate trends be calculated from reanalysis data?, J. Geophys. Res., 109, D11111, doi: /2004jd Dee, D. P., et al. (2011), The ERA-Interim reanalysis: Configuration and performance of the data assimilation system, Q. J. R. Meteor. Soc., 137, , doi: /qj.828. Dessler, A. E. (2010), A determination of the cloud feedback from climate variations over the past decade, Science, 330, , doi: / science Dessler, A. E. (2013), Observations of climate feedbacks over and comparisons to climate models, J. Climate, 26, , doi: /jcli-d Hansen, J., R. Ruedy, M. Sato, and K. Lo (2010), Global surface temperature change, Rev. Geophys., 48, Rg4004, doi: /2010rg Loeb, N. G., B. A. Wielicki, D. R. Doelling, G. L. Smith, D. F. Keyes, S. Kato, N. Manalo-Smith, and T. Wong (2009), Toward optimal closure of the Earth s top-of-atmosphere radiation budget, J. Climate, 22, , doi: /2008jcli Loeb, N. G., S. Kato, W. Su, T. Wong, F. Rose, D. R. Doelling, J. R. Norris, and X. Huang (2012), Advances in understanding top-of-atmosphere radiation variability from satellite observations, Surv. Geophys., 33, , doi: /s Masters, T. (2012), On the determination of the global cloud feedback from satellite measurements, Earth Syst. Dynam., 3, , doi: /esdd Morice, C. P., J. J. Kennedy, N. A. Rayner, and P. D. Jones (2012), Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: The HadCRUT4 data set, J. Geophys. Res., 117, D08101, doi: /2011jd Rienecker, M. M., et al. (2011), MERRA - NASA s Modern-Era Retrospective Analysis for Research and Applications, J. Climate, 24, , doi: /jcli-d Shell, K. M., J. T. Kiehl, and C. A. Shields (2008), Using the radiative kernel technique to calculate climate feedbacks in NCAR s Community Atmospheric Model, J. Climate, 21, , doi: /2007jcli Smith, T. M., R. W. Reynolds, T. C. Peterson, and J. Lawrimore (2008), Improvements to NOAA s historical merged land-ocean surface temperature analysis ( ), J. Climate, 21, , doi: / 2007jcli Soden, B. J., and I. M. Held (2006), An assessment of climate feedbacks in coupled ocean-atmosphere models, J. Climate, 19, , doi: /jcli Soden, B. J., I. M. Held, R. Colman, K. M. Shell, J. T. Kiehl, and C. A. Shields (2008), Quantifying climate feedbacks using radiative kernels, J. Climate, 21, , doi: /2007jcli Solomon, S., J. S. Daniel, R. R. Neely, J. P. Vernier, E. G. Dutton, and L. W. Thomason (2011), The persistently variable background stratospheric aerosol layer and global climate change, Science, 333, , doi: /science Susskind, J., G. Molnar, L. Iredell, and N. G. Loeb (2012), Interannual variability of outgoing longwave radiation as observed by AIRS and CERES, J. Geophys. Res., 117, doi: /2012jd Wielicki, B. A., B. R. Barkstrom, E. F. Harrison, R. B. Lee, III, G. L. Smith, and J. E. Cooper (1996), Clouds and the Earth s Radiant Energy System (CERES): An Earth Observing System experiment, Bull. Am. Meteorol. Assoc., 77,

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