Clim Dyn (2010) 35:1219–1236 DOI 10.1007/s00382-009-0661-1 Climate feedbacks determined using radiative kernels in a multi-thousand member ensemble of AOGCMs Benjamin M. Sanderson Æ Karen M. Shell Æ William Ingram Received: 6 March 2009 / Accepted: 1 September 2009 / Published online: 17 September 2009 Ó Springer-Verlag 2009 Abstract The use of radiative kernels to diagnose climate positive values such that none of the perturbed models feedbacks is a recent development that may be applied to exhibit a net negative cloud feedback. The perturbed existing climate change simulations. We apply the radia- physics ensemble contains fewer models with strong tive kernel technique to transient simulations from a multi- negative shortwave cloud feedbacks and has stronger thousand member perturbed physics ensemble of coupled compensating positive longwave feedbacks. A principal atmosphere-ocean general circulation models, comparing component analysis used to identify dominant modes of distributions of model feedbacks with those taken from the feedback variation reveals that the perturbed physics CMIP-3 multi GCM ensemble. Although the range of clear ensemble produces very different modes of climate sky longwave feedbacks in the perturbed physics ensemble response to the multi-model ensemble, suggesting that one is similar to that seen in the multi-GCM ensemble, the may not be used as an analog for the other in estimates of kernel technique underestimates the net clear-sky feed- uncertainty in future response. Whereas in the multi-model backs (or the radiative forcing) in some perturbed models ensemble, the first order variation in cloud feedbacks with significantly altered humidity distributions. In addi- shows compensation between longwave and shortwave tion, the compensating relationship between global mean components, in the perturbed physics ensemble the short- atmospheric lapse rate feedback and water vapor feedback wave feedbacks are uncompensated, possibly explaining is found to hold in the perturbed physics ensemble, but the larger range of climate sensitivities observed in the large differences in relative humidity distributions in the perturbed simulations. Regression analysis suggests that ensemble prevent the compensation from holding at a the parameters governing cloud formation, convection regional scale. Both ensembles show a similar range of strength and ice fall speed are the most significant in response of global mean net cloud feedback, but the mean altering climate feedbacks. Perturbations of oceanic and of the perturbed physics ensemble is shifted towards more sulfur cycle parameters have relatively little effect on the atmospheric feedbacks diagnosed by the kernel technique. B. M. Sanderson (&) Keywords Feedbacks Á Kernel Á Climate Á Sensitivity Á National Center for Atmospheric Research, Ensemble Á PPE Á Perturbed physics Á 1850 Table Mesa Dr, Boulder, CO 80305, USA e-mail: [email protected]; [email protected] Climateprediction.net Á CMIP K. M. Shell College of Oceanic and Atmospheric Sciences, 1 Introduction Oregon State University, Corvallis, USA W. Ingram The temperature response of the climate system to Atmospheric, Oceanic and Planetary Physics, anthropogenic greenhouse gas forcing scenarios is a critical University of Oxford, Oxford, UK factor in assessing the impacts of those possible future W. Ingram paths on society and the wider environment (Caldeira et al. Met Office Hadley Centre, Exeter, UK 2003). This temperature response can be estimated by 123 1220 B. M. Sanderson et al.: Climate feedbacks determined using radiative kernels observing past changes in atmospheric forcing and the cloud feedbacks inferred by changes in CRF include some resultant change in global or regional climates (Hall and of the effects of changes in water vapor and temperature Qu 2006; Forster and Gregory 2006), or by examining the distribution in addition to changes in the cloud distribution. response of General Circulation Models (GCMs) in simu- In the PRP technique, an assumption of linearity allows lations of different scenarios at both global (Knutti et al. k to be separated into components, such that: X 2008; Yokohata et al. 2008) and regional scales (Murphy k ¼ kX; ð2Þ et al. 2007; Webb et al. 2006). The interpretation of GCM X simulations is complicated when evaluating the differing responses of GCMs from the world’s major climate where kX is the radiative response to a parameter X (for modeling centers—raising questions both of how this example, surface albedo, atmospheric temperature or spread should be represented probabilistically (Tebaldi and humidity): Knutti 2007) and how the differences in GCM response dðF À QÞdX kX ¼ ð3Þ relate to feedbacks in the climate system. dX dTs 1.1 Feedback analysis in multi-GCM ensembles Colman et al. (1997) point out that this assumption is incorrect if different parameters are spatially correlated (as Feedbacks occur when changes in state (caused by an is the case for humidity and cloud cover). This problem can initial forcing) further force the system. At equilibrium, the be accounted for by explicitly decorrelating the result using anthropogenic forcing at the top of atmosphere (G) must be a further independent simulation. An alternative solution balanced by changes in the outgoing longwave (F) and proposed by Soden et al. (2008) is to consider changes in absorbed shortwave (Q) fluxes such that: the mean state of X between a control simulation and a climate change simulation and shift the distribution in the DðF À QÞ control simulation by that difference—thus preserving any G ¼ DTs ¼ kDTs; ð1Þ DTs correlations present between variables in the control. Perturbing the variable X by a small amount dX and where k is the global feedback parameter and Ts is the global mean surface temperature, making the assumption observing the top of atmosphere flux change d(F - Q) of a linear relationship between radiative response and gives a radiative kernel which gives the differential surface temperature. response, without the computational expense of the full The identification and separation of feedbacks in climate radiation code: models has been identified as an essential step in under- oF FðX þ dXÞFðXÞ ðXÞdX ¼ KX dX; ð4Þ standing and constraining the future climate system oX LW response (Bony et al. 2006). In recent years, various o techniques have been proposed in order to achieve this Q X QðX þ dXÞQðXÞo ðXÞdX ¼ KSW dX; ð5Þ goal. The explicit separation of feedbacks and forcing in a X zero-dimensional global climate model was explored in the where 4 and 5 describe the longwave and shortwave ker- pioneering work of Hansen et al. (1985). Separation of nels KLW and KSW, respectively. The kernel must have the clear sky and cloudy sky feedbacks, however, was achieved same dimensions as the variable X itself, hence if X rep- by Cess and Potter (1988) in a simple but effective and resents atmospheric temperature on model levels, then the often emulated experiment examining the response of the kernel must be also be defined on model levels and must be all sky and clear sky radiative budget to a 2 K perturbation explicitly calculated by perturbing the temperature of each in sea surface temperature. The difference between the all- model level in turn and observing the top of atmosphere sky and clear sky response is then said to be the cloud response. The product of the kernel and the perturbation radiative forcing (CRF). field DX gives the ‘‘field effect’’, which when integrated Wetherald and Manabe (1988) introduced the technique vertically gives the radiative top of atmosphere response. later referred to as the partial radiative perturbation (PRP) The methodology allows the decomposition of atmospheric technique used more recently in Colman (2003), which response to forcing in a similar fashion to the PRP tech- uses offline calculations to examine the radiative effect of nique, but does not require each variable to be individually individual variables (such as water vapor, cloud distribu- perturbed in each GCM analyzed—thus allowing the tion and atmospheric temperatures) by taking the variable authors to analyze the stock simulations produced for the from the climate change simulation and substituting it into World Climate Research Programme’s Coupled Model a control simulation. It was noted by Zhang et al. (1994) Inter-comparison Project Stage 3 (CMIP-3). and Soden et al. (2004) that the CRF and PRP techniques Soden et al. (2008) used radiative kernels to isolate produce different estimates for cloud feedback because the different tropospheric feedbacks in the CMIP-3 ensemble, 123 B. M. Sanderson et al.: Climate feedbacks determined using radiative kernels 1221 and stratospheric levels are not included in their integra- Therefore, it is of some value to study versions of the GCM tion. However, fluxes in Soden et al. (2008) are calculated where the parameters are ‘de-tuned’ to values that are still at the top of the model atmosphere, thereby assuming that physically plausible but perhaps not optimal. Such an the net dynamical heating of the stratosphere is unchanged experiment produces a large number of simulations, and in the simulation, but decreasing the sensitivity of the thus relatively few ‘perturbed physics ensembles’ have technique to the height of the tropopause. Some earlier been created, but using those which do exist to study cli- studies (Colman (2003; Held and Soden 2000) calculated mate feedbacks allows the physical feedback processes to feedbacks over the entire atmospheric column, which