We have corrected the approach of Lindzen and Choi (2009), based on all the criticisms made of the earlier work (Chung et al., 2010; Murphy, 2010; Trenberth et al., 2010). First of all, to improve the statistical significance of the results, we supplemented ERBE data with CERES data, filtered out data noise with 3-month smoothing, objectively chose the intervals based on the smoothed data, and provided confidence intervals for all sensitivity estimates. These constraints helped us to more accurately obtain climate feedback factors than with the original use of monthly data. Next, our new formulas for climate feedback
and sensitivity reflect sharing of tropical feedback with the globe, so that the tropical region is now properly identified as an open system. Last, the feedback factors inferred from the atmospheric models are more consistent with IPCC-defined climate sensitivity
than those from the coupled models. This is because, in the presence of cloud-induced radiative changes altering SST, the climate feedback estimates by the present approach tends to be inaccurate. With all corrections, the conclusion still appears to be
that all current models seem to exaggerate climate sensitivity (some greatly). Moreover, we have shown why studies using simple regressions of ΔFlux on ΔSST serve poorly to determine feedbacks.
To respond to the criticism of our emphasis on the tropical domain (Murphy, 2010; Trenberth et al., 2010), we analyzed the complete record of CERES for the globe (Dessler, 2010) (Note that ERBE data is not available for the high latitudes since the field-of-view is between 60oS and 60oN). As seen in the previous section, the use of the global CERES record leads to a result that is basically similar to that from the tropical data in this
study. The global CERES record, however, contains more noise than the tropical record.
This result lends support to the argument that the water vapor feedback is primarily restricted to the tropics, and there are reasons to suppose that this is also the case for cloud feedbacks. Although, in principle, climate feedbacks may arise from any
latitude, there are substantive reasons for supposing that they are, indeed, concentrated mostly in the tropics. The most prominent model feedback is that due to water vapor, where it is commonly noted that models behave roughly as though relative humidity
were fixed. Pierrehumbert (2009) examined outgoing radiation as a function of surface temperature theoretically for atmospheres with constant relative humidity. His results are shown in Fig. 13.
Fig. 13. OLR vs. surface temperature for water vapor in air, with relative humidity held fixed. The surface air pressure is 1 bar. The temperature profile in the model is the water/air moist adiabat. Calculations were carried out with the Community Climate Model radiation code (Pierrehumbert, 2009).
Specific humidity is low in the extratropics, while it is high in the tropics. We see that for extratropical conditions, outgoing radiation closely approximates the Planck black body radiation (leading to small feedback). However, for tropical conditions, increases in outgoing radiation are suppressed, implying substantial positive feedback. There are also reasons to suppose that cloud feedbacks are largely confined to the tropics. In the
extratropics, clouds are mostly stratiform clouds that are associated with ascending air while descending regions are cloudfree. Ascent and descent are largely determined by the large scale wave motions that dominate the meteorology of the extratropics, and for these waves, we expect approximately 50% cloud cover regardless of temperature (though details may depend on temperature). On the other hand, in the tropics, upper level clouds, at least, are mostly determined by detrainment from cumulonimbus towers, and cloud coverage is observed to depend significantly on temperature (Rondanelli and Lindzen, 2008).
As noted by LCH01, with feedbacks restricted to the tropics, their contribution to global sensitivity results from sharing the feedback fluxes with the extratropics. This led to inclusion of the sharing factor c in Eq. (6). The choice of a larger factor c leads to
a smaller contribution of tropical feedback to global sensitivity, but the effect on the climate sensitivity estimated from the observation is minor. For example, with c = 3, climate sensitivity from the observation and the models is 0.8 K and a higher value
(between 1.3 K and 6.4 K), respectively. With c = 1.5, global equilibrium sensitivity from the observation and the models is 0.6 K and any value higher than 1.6 K, respectively. Note that, as in LCH01, we are not discounting the possibility of feedbacks in the extratropics, but rather we are focusing on the tropical contribution to global feedbacks. Note that, when the dynamical heat transports toward the extratropics are taken into account, the overestimation of tropical feedback by GCMs may lead to even greater overestimation of climate sensitivity (Bates, 2011).
This emphasizes the importance of the tropical domain itself. Our analysis of the data only demands relative instrumental stability over short periods, and is largely independent of long term drift. Concerning the different sampling from the ERBE and CERES instruments, Murphy et al. (2009) repeated the Forster and Gregory (2006) analysis for the CERES and found very different values than those from the ERBE. However, in this
study, the addition of CERES data to the ERBE data does little to change the results for ΔFlux/ΔSST – except that its value is raised a little (as is also true when only CERES data is used.). This may be because these previous simple regression approaches include
the distortion of feedback processes by equilibration. In distinguishing a precise feedback from the data, the simple regression method is dependent on the data period, while our method is not. The simple regression result in Fig. 7 is worse if the model
integration time is longer (probably due to the greater impact of increasing radiative forcing).
Our study also suggests that, in current coupled atmosphereocean models, the atmosphere and ocean are too weakly coupled since thermal coupling is inversely proportional to sensitivity (Lindzen and Giannitsis, 1998). It has been noted by Newman et al. (2009) that coupling is crucial to the simulation of phenomena like El Niño. Thus, corrections of the sensitivity of current climate models might well improve the behavior of coupled
models, and should be encouraged. It should be noted that there have been independent tests that also suggest sensitivities less than predicted by current models. These tests are based on the response to sequences of volcanic eruptions (Lindzen and Giannitsis, 1998), on the vertical structure of observed versus modeled temperature increase (Douglass, 2007; Lindzen, 2007), on ocean heating (Schwartz, 2007; Schwartz, 2008), and on
satellite observations (Spencer and Braswell, 2010). Most claims of greater sensitivity are based on the models that we have just shown can be highly misleading on this matter. There have also been attempts to infer sensitivity from paleoclimate data (Hansen
et al., 1993), but these are not really tests since the forcing is essentially unknown given major uncertainties in clouds, dust loading and other factors. Finally, we have shown that the attempts to obtain feedbacks from simple regressions of satellite measured outgoing radiation on SST are inappropriate.
One final point needs to be made. Low sensitivity of global mean temperature anomaly to global scale forcing does not imply that major climate change cannot occur. The earth has, of course, experienced major cool periods such as those associated with ice ages and warm periods such as the Eocene (Crowley and North, 1991). As noted, however, in Lindzen (1993), these episodes were primarily associated with changes in the equatorto-
pole temperature difference and spatially heterogeneous forcing. Changes in global mean temperature were simply the residue of such changes and not the cause.
