Radiative kernels have become a common tool for evaluating and comparing radiative feedbacks to climate change in different general circulation models. However, kernel feedback calculations are inaccurate for simulations where the atmosphere is significantly perturbed from its base state, such as for very large forcing or perturbed physics simulations. In addition, past analyses have not produced kernels relating to prognostic cloud variables because of strong nonlinearities in their relationship to radiative forcing. A new methodology is presented that allows for fast statistical optimizing of existing kernels such that accuracy is increased for significantly altered climatologies. International Satellite Cloud Climatology Project (ISCCP) simulator output is used to relate changes in cloud-type histograms to radiative fluxes. With minimal additional computation, an individual set of kernels is created for each climate experiment such that climate feedbacks can be reliably estimated even in significantly perturbed climates.
This methodology is applied to successive generations of the Community Atmosphere Model (CAM). Increased climate sensitivity in CAM5 is shown to be due to reduced negative stratus and stratocumulus feedbacks in the tropics and midlatitudes, strong positive stratus feedbacks in the southern oceans, and a strengthened positive longwave cirrus feedback. Results also suggest that CAM5 exhibits a stronger surface albedo feedback than its predecessors, a feature not apparent when using a single kernel. Optimized kernels for CAM5 suggest weaker global-mean shortwave cloud feedback than one would infer from using the original kernels and an adjusted cloud radiative forcing methodology.
Feedback processes in the climate system have the potential to amplify or dampen an initial radiative perturbation, such as that due to increased greenhouse gas concentrations. However, observations of feedback magnitudes are often confounded by natural variability, nonequilibrium conditions, and time-scale dependency (Bony et al. 2006; Knutti and Hegerl 2008). Isolating feedback processes in model simulations where forcing, feedback, and climate response can be distinguished is thus key to understanding differing model responses to anthropogenic forcing and the resulting uncertainties in projections of future climate.
In the present study, feedbacks are defined as processes that can alter the radiative balance of the system on a multiyear to century time scale and are themselves a function of temperature. In reality, this will be a mix of “true” feedbacks where the radiative balance is a function of global-mean temperature and “rapid” adjustments, which are purely a function of greenhouse gas concentration (Gregory and Webb 2008). A positive feedback indicates an amplification of warming: that is, a decrease in outgoing longwave (LW) or shortwave (SW) radiative flux at the top of the atmosphere (TOA). Net global feedbacks can be summarized by the feedback parameter (λ; units of W m−2 K−1), which is the change in net TOA fluxes associated with changes in feedback variables, which themselves are functions of global average surface air temperature.
A number of studies have demonstrated techniques for separating the net global climate feedback into components. Cess and Potter (1988) separated TOA fluxes into two components, relating to changes in “clear sky” fluxes (derived by simulating a cloud-free atmosphere in a repeat run of the model’s radiation code) and a residual “cloud radiative forcing” (CRF) term. This calculation can be misleading as changes in noncloud fields such as surface albedo, atmospheric temperature, and humidity can cause changes in CRF (Zhang et al. 1994; Soden et al. 2004).
Another technique known as partial radiative perturbation (PRP; Wetherald and Manabe 1988; Colman 2003) substitutes individual fields Xi (e.g., water vapor, cloud distribution, and atmospheric temperatures) from a climate change simulation into a control simulation and assumes that λ can be separated into components λi, such that
where δF is the change in net outgoing radiative flux between the two cases and Ts is the global-mean surface air temperature. However, if different parameters such as humidity and cloud cover are spatially correlated, Eq. (3) is not valid, and an additional simulation is required to perform a spatial decorrelation (Colman et al. 1997).
Given that a full PRP calculation is computationally expensive, the authors of Taylor et al. (2007) proposed a version of the methodology, referred to as “approximate partial radiative perturbation” (APRP), which uses a simplified, single-layer model of shortwave radiation in the atmosphere. Similar calculations were proposed by Winton (2006) and Yokohata et al. (2005). A small number of parameters in the simple model are used to approximate surface absorption and atmospheric scattering in the target GCM, allowing an approximate decomposition of shortwave feedbacks within the GCM. This technique cannot be applied to longwave feedbacks as simply because the vertical profile of atmospheric temperature and humidity is important for TOA longwave radiative balance, rendering the single-layer assumption insufficient. The technique is also unable to decompose cloud feedbacks further into cloud property changes.
The “radiative kernel” technique (Soden et al. 2008) performs a feedback decomposition by linearizing the TOA radiative fluxes about a control state as a function of the different fields Xi,
The kernel Ki for a given grid point, model level, and month is derived by making small perturbations δXi in each variable Xi and measuring the resulting changes in TOA fluxes δFL and δFS. The longwave and shortwave partial radiative changes due to changes in a specific variable Xi in a climate change simulation may then be reconstructed by summing the product of the variable change ΔXi and the kernels and , respectively, over vertical levels. In additional to the regular “all sky” kernels, clear-sky kernels, for use in calculating changes in clear-sky fluxes for an experiment, can be derived by setting the cloud fraction (CF) to zero but holding all other variables constant while performing the radiative transfer calculation. Soden et al. (2008) calculate feedbacks over the model troposphere only, making the implicit assumption that the net dynamical heating of the stratosphere is unchanged in the climate change simulation and decreasing the sensitivity of the technique to the height of the tropopause.
Kernels have been derived for a number of noncloud variables, including surface albedo and temperature, atmospheric temperature and humidity, and CO2 concentrations. The technique can thus easily be used to calculate noncloud feedbacks and flux changes. However, a significant limitation of the technique is that there is not a “cloud kernel” that relates changes in cloud properties to their radiative effects. Traditional kernel calculations require the perturbed variable to be a prognostic variable in the model, which in the case of clouds would be cloud liquid water and ice on model levels, cloud fraction, effective radius, etc. However, Soden and Held (2006) show that prognostic cloud variables have a nonlinear relationship with the TOA radiative fluxes, rendering the traditional kernel approach inappropriate.
Cloud feedback analysis using the kernel technique has been attempted in two ways. Soden and Held (2006) used the all-sky kernels to calculate all noncloud related changes in radiative flux and attributed the residual flux change to cloud feedbacks. Shell et al. (2008) introduced “adjusted change in cloud radiative forcing” (AΔCRF), an update on the traditional measure of feedbacks based on the CRF. The AΔCRF calculation corrects cloud-masking effects, to first order, using the difference between clear-sky and all-sky kernels. This technique, however, cannot relate cloud properties to cloud feedbacks, which is a significant concern given that the longwave and shortwave cloud feedbacks exhibit more intermodel spread than any other radiative feedbacks both for recent models in the third Coupled Model Intercomparison Project (CMIP-3) archive and historically (Charney et al. 1979). In addition, if there are large differences between the cloud distributions in the model with which the kernel was derived (source model) and the model or state to which the kernel has been applied (target model), then the masking correction is likely to be biased.
A recent study, Zelinka et al. (2012), demonstrated one methodology for creating cloud radiative kernels based upon output from the International Satellite Cloud Climatology Project (ISCCP) simulator. The ISCCP simulator (Webb et al. 2001; Klein and Jakob 1999; Lin and Zhang 2004) simulates a satellite-based retrieval within a GCM. ISCCP algorithms divide each grid cell in the GCM into a number of subcolumns, using cloud overlap assumptions to estimate a subgrid-scale cloud distribution. The simulator mimics a satellite retrieval within the GCM to produce cloud fields that are analogous to observed products (for an extensive description, see Pincus et al. 2006). ISCCP products include the column optical depth τ, cloud-top pressure (CTP), and cloud amount, which together can coarsely describe the radiative effects of clouds from satellite data (Schiffer and Rossow 1983). The product uses visible (VIS) and infrared (IR) radiances to derive various cloud properties, including a joint histogram of cloud fraction for CTP and τ, with 7 bins in each quantity, allowing for 49 different cloud fraction types in each scene.
Zelinka et al. (2012) use an offline radiation code to calculate the radiative impact of different cloud histogram bins. For each ISCCP cloud type and for each kernel grid point, the authors simulate that cloud in an atmospheric column with temperature and water vapor profiles taken from a reference base state. The results of the study show that, in some models, there is a linear (or approximately so) relationship between ISCCP cloud fractions and cloud radiative forcing. Although this may seem contradictory to the findings of Soden and Held (2006), the linear relationship exploited in Zelinka et al. (2012) relies on particular features of the ISCCP dataset. Because the product simulates a satellite view of the atmosphere, it includes only information about clouds that contributes to the TOA budget and is unable to determine cloud depth, base, or vertical structure. The ISSCP data therefore already eliminate many of the nonlinearities that have plagued previous studies because redundant information has been removed by the simulator. Only the cloud layers that impact the TOA radiative fluxes are included, which is exactly why the ISCCP product is a suitable candidate for use with a radiative kernel. However, the accuracy of the technique is dependent upon the target model, which suggests that systematic differences between the radiative transfer code used to derive the kernel and that used in the GCM may result in errors.
In this paper, we will demonstrate an alternative methodology for statistically deriving a complete set of both cloud and noncloud radiative kernels directly from climate model output, thus eliminating errors due to systematic differences between the model or state in which the kernel was derived and the model to which the kernel is applied. The advantage of the statistical approach is that the method can potentially relate any variable, whether prognostic or diagnostic, to TOA fluxes, provided that a robust and well-constrained relationship exists. Such an approach, if derived from the model simulations we wish to analyze, can eliminate potential inaccuracies that arise from systematic differences between the kernel reference state and the target model. Furthermore, by using the ISSCP simulator, we can attribute cloud feedbacks to changes in specific cloud properties.
2. Kernel optimizing methodology
The kernel methodology allows efficient comparison of feedbacks in a number of climate models, but it is valid only while the linear assumptions are accurate. Linear kernels do not depend on the base state or radiative transfer code used in their generation. Soden et al. (2008) demonstrated that kernels derived in the Community Climate System Model (CCSM), Geophysical Fluid Dynamics Laboratory (GFDL), and Bureau of Meteorology Research Centre (BMRC) models were qualitatively similar. They found that the feedbacks calculated for a range of CMIP-3 simulations were relatively insensitive to the choice of kernel used, typically agreeing within 5%. However, the surface albedo feedbacks showed a 30% difference in magnitude with the National Center for Atmospheric Research (NCAR) and BMRC kernels, suggesting a dependence on base state.
In addition, the assumption of linearity will break down if the climate differs too much from the original model. Sanderson et al. (2010) showed that kernels derived in the Community Atmosphere Model (CAM) could not accurately reproduce radiative fluxes in some perturbed parameter simulations with significantly different atmospheric temperature or humidity profiles. Similarly, Jonko et al. (2012) showed that radiative kernels derived in a present-day control simulation were not able to reproduce top-of-atmosphere fluxes when the model was subjected to a very large forcing, such as simulations where CO2 concentrations were set to 8 times present-day levels.
Such issues can be avoided by using a PRP calculation or by rederiving kernels for climates that are significantly different from the base model, but both of these options require significant additional computation time plus much additional saved output (i.e., a complete base-state description for the purposes of the radiative transfer calculation). In cases when one wishes to contrast feedbacks in a large number of climate simulations, such as those in the Coupled Model Intercomparison Project, it is highly desirable to use a kernel analysis technique that requires only the output from the climate change simulations.
To this end, we propose a methodology whereby a preexisting radiative kernel may be statistically optimized using information contained within the climate change simulation itself. We consider first the longwave all-sky kernel KL, which when multiplied by the field changes outlined in Table 1 produces TOA longwave flux changes for each variable i. Each field Xi is defined as monthly means (for a given month m) on a latitude, longitude (x, y) grid for a number of years t. Some variables such as atmospheric temperature and humidity are also defined on model levels z, while output from the ISCCP kernel is given for 49 different cloud fraction types defined on 7 CTP and 7 τ bins.
Model output is expressed as a sum of climatological means and an anomaly time series ΔXi(x, y, z, m, t) (corresponding to the kernel input column in Table 1). Preexisting atmospheric kernels are taken from Shell et al. (2008), and the ISCCP kernels are taken from Zelinka et al. (2012), but we introduce small zonally symmetric perturbation terms , which are initially unknown. The zonal assumption allows each longitudinal point to be treated as a separate sample in the optimization, such that the total number of samples is the product of the number of years and the number of longitudinal points, which makes the problem well constrained even for relatively short time series. The longwave TOA flux anomaly ΔFL(x, y, m, t) is obtained directly from the output of the simulation to be studied. We define an error in the kernel calculation εL(y, m) for the longwave flux reconstruction,
where nx is the number of longitudinal points and nt is the number of years in the time series. The sum-squared error in the expression is thus normalized by the interannual variance of the zonal-mean flux such that εL is unitless.
We seek a solution for that minimizes the error term εL. This minimization is computed numerically, simultaneously for all kernel components in each latitude band. We use the well-tested Broyden–Fletcher–Goldfarb–Shanno–quasi-Newton method (Fletcher and Powell 1963). After making an initial guess for (in this case, zero throughout), the algorithm approximates the Hessian matrix of second derivatives. The search direction is then obtained using Newton’s method, and the algorithm uses a line search to determine the appropriate step length. The process is repeated until a stopping condition is satisfied, either by reaching the maximum allowed number of iterations N (discussed below) or if the logarithm of εL changes by less than 10−6 on successive iterations.
One concern with a methodology such as this would be that the minimization procedure was overfitting to the data provided. We perform a simple test to demonstrate that this is not the case. The climate change simulation in question is a 20-yr double-CO2 experiment. To test for overfitting, the algorithm is trained using a 5-yr period of anomaly values from years 10–15 in the double-CO2 simulation. We then use the period from years 16–20 as a validation period. The optimal value of N is determined by minimizing εL for the validation period. We find the validation error is minimized with N values of about 3000 or greater (not shown), indicating that the system is not prone to overfitting. This is expected in this example, given that each latitude band has 85 and 67 unknowns for the longwave and shortwave kernels, respectively, and has 2560 data points with which to constrain them. Given confidence that the problem is well defined and not subject to overfitting, we can proceed with using the same time period (in this case, years 16–20 of the double-CO2 simulation) to evaluate both the kernels and the feedbacks in the simulation.
b. Constrained optimization
The methodology shown thus far can be used to create kernels directly from a climate change simulation. However, because the kernels are purely statistical, they can potentially show unphysical properties. For example, when certain feedbacks are highly correlated (e.g., the water vapor and atmospheric temperature feedback), the statistical methodology outlined cannot detect the degree of compensation between the two feedbacks. For the cloud kernels, some cloud types are much more common than others, which leads to a lack of signal to constrain certain elements of the kernel. Because the cloud types are rare, they have little effect on any net radiative feedback, but the resulting kernels can show unphysical features such as a decrease in outgoing (reflected) shortwave radiation for an increase in cloud fraction.
There are several possible ways to address this problem, with one being to use a constrained optimization algorithm in which one can specify ranges of kernel values that are physically plausible. However, it was found that consistent and physically plausible results could be obtained through the use of an additional term to limit the magnitude of kernel anomaly terms relative to the original kernel,
We define rL(y, z, m) as a unitless value that represents the ratio of the squared magnitude of the perturbation with respect to the variance of the original kernel value around the latitude band. For the cloud kernels, where the original Zelinka et al. (2012) kernels are already zonally symmetric, the variance term is replaced by the square of the absolute kernel value. The minimization is thus performed for combined metrics,
The free variable a sets the relative importances of the kernel perturbation and the TOA flux errors being minimized. If a = 0, the optimal solution is found for for all i. In lima→∞, the size of the perturbation is unimportant and only the errors in TOA fluxes determine the optimization. The value of a is arbitrary; a larger value reduces the error in TOA flux reproduction but also potentially allows some unphysical features to appear in the optimized kernels. For the noncloud kernels, a is set to 10, such that the small perturbation term becomes dominant only if the squared perturbation is larger than 10 times the latitudinal variance of the original kernel. For the cloud kernels, a is set to 1, so the small perturbation term is dominant if the perturbation is larger than the original kernel value itself.
The above example shows the optimization process for longwave kernels, but shortwave kernel optimization can be performed in a similar fashion, using the climate fields listed in Table 2. If one requires optimized clear-sky kernels (e.g., to calculate an optimized cloud radiative forcing), the process is similar, but the ISCCP kernels are omitted and clear-sky fluxes are used in place of the TOA flux ΔFL(x, y, m, t).
3. Optimized kernels
To test the methodology outlined above, we perform the all-sky kernel optimizing procedure for three successive generations of the CAM (the atmospheric model component of CCSM), which have successively higher equilibrium climate sensitivities to a doubling of CO2. The CAM 3.0 (CAM3; Collins et al. 2004) simulations are run at a spectral resolution of T42, roughly equivalent to 2.8° × 2.8° latitude–longitude, and this version of the model has a climate sensitivity of 2.5 K (Bitz et al. 2012). The CAM 4.0 simulations (CAM4; Neale et al. 2012, manuscript submitted to J. Climate) feature a finite volume dynamical core at 1° resolution (Lin 2004), an updated convection scheme with convective plume dilation (Raymond and Blyth 1992), and convective momentum transports (Richter and Rasch 2008), with a higher climate sensitivity of 3.1 K (Bitz et al. 2012). The CAM 5.0 simulations (CAM5; P. Rasch et al. 2011, personal communication) share the same convection scheme as CAM4, but many other components of the model are changed. This model exhibits the largest climate sensitivity at 4.1 K (Gettelman et al. 2012). For the purposes of this analysis, all models are interpolated onto the CAM3 grid, which is also consistent with the initial kernels derived in Shell et al. (2008) and Zelinka et al. (2012).
To measure the climate response to greenhouse gas forcing in each of the models, we couple the atmospheric model to a thermodynamic slab ocean and consider simple experiments where carbon dioxide levels are instantaneously doubled from preindustrial levels. We choose these simple, idealized experiments to ensure that the forcing in each of the models is as similar as possible. Note, however, that the double-CO2 experiment does not separate true feedbacks from “fast” feedbacks due to the greenhouse gas concentrations alone, which by some definitions are considered part of the forcing (Gregory and Webb 2008; Andrews and Forster 2008). In the following calculations, we use climatological monthly means from a 30-yr control slab ocean simulation with preindustrial CO2 concentrations to derive a reference state. The climate change state is taken as years 15–20 of a double-CO2 simulation, where anomalies from the reference state are used for the kernel calculation.
Note that the optimized kernels are dependent on the particular experiment, in this case a doubled CO2 experiment. Differences between the original kernels and the optimized kernels can be due to different base (control) states as well as the changes in feedback variables between the control and doubled CO2 state. Thus, optimized kernels are only for these particular model–experiment combinations and may differ if another model or climate change scenario is used. The CAM3 kernels (Shell et al. 2008) were derived with an atmospheric GCM driven by climatological fixed SSTs, while in this case we use a thermodynamic slab ocean. Hence, there may be some differences between the base state used to calculate the original CAM3 kernel and control state of our CAM3 simulation, which will influence the optimized kernel, as well as the changing radiative effects of the feedback variables between the control and doubled CO2 simulations of this experiment.
a. Noncloud kernels
Considering first the all-sky atmospheric temperature kernels (see Figs. 1a–d), the optimized CAM3 and CAM4 kernels both show decreased sensitivity to midtropospheric tropical temperature change, coupled with decreased sensitivity to water vapor in the same region (Figs. 1e–h). This effect is present only when the double-CO2 simulation is used to optimize the kernels and is present in CAM3 and CAM4 (and not CAM5), because they both exhibit strong increases in tropical convection upon CO2 doubling (Neale et al. 2012, manuscript submitted to J. Climate). This causes a large increase in detrained water vapor in the tropical Pacific upon warming, especially the Pacific warm pool, which forms high clouds (the effects of this can be seen in Figs. 8a,b). The increased cloudiness makes the top-of-atmosphere longwave radiative balance less sensitive to temperatures lower in the atmosphere than the original Shell et al. (2008) kernels would suggest. This effect can be seen in Jonko et al. (2012), where the atmospheric temperature kernel derived in an 8 times CO2 CAM3 climate shows lower values in the tropical lower troposphere; hence, the original kernel overestimates the contribution of the tropical lower troposphere to atmospheric temperature feedback. At high latitudes, the optimized atmospheric temperature kernels all show slightly less negative values in the troposphere. This decrease is compensated in the net longwave TOA balance by larger negative values for the longwave surface temperature kernel (Fig. 2a).
CAM3, CAM4, and CAM5 show successively larger high-latitude surface albedo kernel values after optimizing, implying an increase in the sensitivity of top-of-atmosphere shortwave fluxes to surface albedo (Fig. 2b). Because there are few changes to the atmospheric model between CAM3 and CAM4, apart from the convection scheme, the difference between CAM3 and CAM4 albedo kernels is due to the changes in sea ice and surface snow parameterizations, which influence the base-state surface albedo. However, the increasing albedo kernel value between CAM4 and CAM5 is seen primarily in the Arctic late-summer–fall season and is due to the changes in the control state Arctic cloud distribution, which alter the all-sky TOA flux sensitivity to surface properties. We can confirm this by examining the clear-sky kernels (not shown), which do not significantly change between CAM4 and CAM5. Recent results (Kay et al. 2012) show that the control Arctic state of CAM4 exhibits significantly greater liquid cloud water paths and cloud optical depths than seen in CAM5. In the summer, when surface albedo feedbacks are relevant, the authors find the visible cloud optical depths in CAM4 to be 5 times greater than those found in CAM5. This allows more radiation to reach the surface in CAM5, thus increasing the importance of surface albedo on top-of-atmosphere energy balance, which implies that the CAM5 optimized albedo kernel has greater amplitudes in the Arctic than CAM4 or CAM3 (Fig. 2b). Thus, for a given change in surface albedo, the effect on the shortwave TOA flux is amplified in CAM5, and this is shown using the optimized kernel. These results are consistent with the APRP calculation presented in Kay et al. (2012), which also indicates significantly stronger Arctic surface shortwave feedbacks in CAM5, likely primarily due to a change in cloud properties. In the continental Antarctic, the optimized all-sky surface albedo kernels are similar for each of the three models. However, over the ice-covered Southern Ocean, we see similar optimized kernels to the Arctic case, with increasing shortwave TOA flux sensitivity to surface albedo in CAM3, CAM4, and CAM5.
b. ISCCP kernels
Throughout this discussion, we use the standard ISCCP cloud-type definitions established in Rossow and Schiffer (1999) and summarized in Fig. 3a. Global- and annual-mean optimized ISCCP kernels for the doubled CO2 experiment are plotted in Fig. 3 (the actual kernels are zonally symmetric). Longwave cloud kernels from Zelinka et al. (2012) are plotted in Fig. 3e, while the changes due to optimization are shown in Figs. 3f–i. The optimizing process has only a subtle effect on the global-mean values, with no significant changes from the Zelinka et al. (2012) kernels. In contrast, Figs. 3k–m show the difference between optimized shortwave cloud kernels and the Zelinka et al. (2012) kernels. Note that the differences are multiplied by 10 for clarity. The broad features of the original kernels are retained, with a larger radiative impact for an increase in optically thick cloud fractions and relatively little dependence on cloud-top pressure. However, in a detailed study of kernel differences, several model-specific features emerge. The optimized kernels for CAM3 and CAM4 are largely identical, with a decreased shortwave sensitivity to cirrus and deep convective clouds and a slightly increased sensitivity to stratus. The CAM5 optimization, in contrast, shows a stronger decrease in shortwave sensitivity to stratocumulus, but little change to the high cirrus or deep convective kernel values.
It should be noted that the optimization algorithm cannot provide information about cloud types that do not occur frequently in the training dataset. To illustrate, Figs. 3b–d show global-mean cloud fractions for ISCCP cloud types in the control simulations of CAM3, CAM4, and CAM5. When the algorithm was used without the prior estimate of Zelinka et al. (2012), it was found that the kernel was poorly constrained for cloud types with low frequencies. This can lead to physically implausible kernels in the unsampled regimes (although, in practice, as long as the cloud types do not appear in the climate change simulation, these errors would not propagate to the calculated feedbacks). The use of the Zelinka et al. (2012) prior estimate results in more physically plausible kernels, because the unsampled regions are not significantly altered from the initial estimate.
4. Feedbacks in climate change simulations
Equilibrium field changes are the difference between a climate change state and the control state. We take the climate change state to be represented by the 5-yr monthly average of model output between years 15 and 20 of the equilibrium double-CO2 simulation. The control state is taken to be the 30-yr monthly average of the simulation produced by the same model with present-day CO2 concentrations. The final feedback values are thus calculated as a product of the field changes and the kernels, divided by the global-mean surface temperature change.
We first address the question of validation, whether the all-sky cloud and noncloud kernels can reproduce the model-generated fluxes in the double-CO2 simulation. Reproducing the all-sky TOA fluxes is a necessary condition for validating the kernel-generated fluxes (although not necessarily sufficient, as only the total and not the partitioning of the different field effects is validated).
Figures 4a–c show the performance of the optimized kernels in each model in the reproduction of the mean all-sky flux anomalies between control simulations and years 15–20 in the double-CO2 simulations. In all cases, the correlation between actual flux change and kernel-reproduced flux change is greater than 0.97 (which effectively represents the limiting accuracy of the fluxes reproduced from zonal-mean kernel perturbations), with slopes ranging from 0.94 to 1.00. Figures 4d–f shows the performance of the original Shell et al. (2008) and Zelinka et al. (2012) kernels, which perform better at reproducing SW TOA fluxes in CAM3 and CAM4 than in CAM5, where the original kernels systematically underestimate the shortwave feedback at high latitudes, largely due to the CAM5 biases in the all-sky surface albedo feedback discussed in the previous section. For all three models, however, the optimizing process successfully decreases the error reproducing the all-sky flux changes between single- and double-CO2 equilibrium states.
a. Noncloud feedbacks
A comparison of global-mean climate feedbacks in the double-CO2 experiments reveals a number of properties of the three models (Fig. 5). A number of feedbacks are not significantly altered through the optimizing process. The shortwave water vapor feedback, for example, remains unchanged after optimizing in all three models. The atmospheric temperature feedbacks and longwave water vapor feedbacks do exhibit some small changes after optimizing in CAM3 and CAM4 because of the altered tropical atmospheric temperature and water vapor kernel values shown in Fig. 1. In each case, both the (negative) temperature and (positive) water vapor kernels are weakened slightly in the tropics because of increased tropical upper-tropospheric water vapor in the double-CO2 state in these models. In addition, CAM3 also exhibits an increase in tropical high cirrus. These kernel changes lead to the reduction in the global atmospheric temperature and longwave humidity feedback values seen in Fig. 5. In CAM4, these effects are compensating, but in CAM3 the change in the temperature feedback exceeds the opposing change in the water vapor feedback. This reduces the (negative) longwave feedback due to noncloud effects, which leads to a weakening of the (positive) derived longwave cloud feedbacks after kernel optimizing, as discussed in the next section.
Figure 5 shows there is a significant and model-dependent change in the global-mean surface albedo feedbacks derived using the original and optimized kernels. As explained in section 2, the zonal surface albedo kernels show significant model dependency. We see an increasingly strong albedo feedback moving from CAM3 (0.26 W m−2 K−1) to CAM4 (0.32 W m−2 K−1) and CAM5 (0.45 W m−2 K−1), in contrast to the results using the original kernels, which suggest a slight decrease in feedback strength for the later models.
b. Global cloud feedbacks
For evaluation of global-mean cloud feedbacks (Fig. 5), we consider a number of metrics that are already published in the literature, in addition to the new ISCCP cloud kernels. All the methods show a broadly similar picture, with considerably more positive shortwave cloud feedbacks in CAM5 than we find in either CAM3 or CAM4. This is consistent with the findings of other recent work studying the climate sensitivity and feedbacks in both CAM4 (Bitz et al. 2012) and CAM5 (Gettelman et al. 2012); however, as discussed below, we find that the latter likely overestimates the strength of the shortwave cloud feedback in CAM5). All analyses show global-mean longwave feedbacks becoming slightly less positive between CAM3 and CAM4 but changing little between CAM4 and CAM5. Optimizing the ISCCP kernel does not significantly change global-mean cloud feedback values from those obtained with the Zelinka et al. (2012) kernels, though this result may depend on the particular climate change scenario.
Comparing the individual analysis techniques shows some minor differences. Perhaps the simplest metric of cloud feedback is the change in cloud radiative forcing (ΔCRF) per unit global temperature change (asterisks in Fig. 5), which tends to have a negative bias in the shortwave and longwave cloud feedback in all models because of masking effects of both changing surface albedo and humidity on the shortwave budget. AΔCRF (open squares) attempts to correct for these biases using the difference between the feedbacks calculated using the clear-sky and all-sky radiative kernels of Shell et al. (2008). An alternative is the residual approach (open diamonds in Fig. 5), where all-sky kernels are used to account for all noncloud changes in radiative flux and the residual TOA fluxes are attributed to clouds. In practice, we find that the latter two approaches yield similar global-mean results in all three models. To aid in understanding differences among the various techniques, we also calculate AΔCRF and the residual using the optimized noncloud kernels (filled symbols) rather than the Shell et al. (2008) kernels.
Our own analysis, based on the new ISCCP kernels (closed circles in Fig. 5), shows rather similar results to the optimized adjusted CRF values (closed squares) in most cases. In the case of CAM3, the optimized kernels indicate a slightly weaker longwave cloud feedback than is obtained using the residual (red open diamond) or adjusted CRF approach (red open square) with the original Shell et al. (2008) kernels. This is a direct effect of the overestimation by the original kernels of the negative atmospheric temperature feedback in CAM3 (discussed in the previous section), which causes the residual (positive) longwave cloud feedback to be too large. Also, because this temperature kernel bias is associated with a change in high cloud cover upon CO2 doubling, it affects the all-sky kernel but not the clear-sky kernel (not shown). Thus, the (negative) all-sky noncloud LW feedback is biased negative (too large), while the clear-sky LW feedback is essentially the same as that obtained using the optimized kernels. The LW adjustment to ΔCRF, which makes it more positive, is therefore larger for the original kernels, resulting in a positively biased estimate of AΔCRF. Thus, even the AΔCRF method (using the original kernels) cannot correct for the bias and produces a similar result to the residual method.
In the shortwave, the optimizing process has the most dramatic effect on CAM5 cloud feedbacks, where cloud feedback estimates using our optimized ISCCP kernels or the original Zelinka et al. (2012) kernels suggest that shortwave cloud feedbacks are almost 40% weaker than one would infer from either the residual approach (open diamonds) or the adjusted CRF approach (open squares) using the original Shell et al. (2008) kernels. This decrease in estimated feedback is at least partly due to the optimized surface albedo kernel. As discussed in the previous section, the optimized kernels produce a stronger surface albedo feedback in CAM5 than the original kernels. Using the residual method would therefore overestimate the strength of the shortwave cloud feedback by the same amount. We demonstrate this by recalculating the residual cloud feedback with the optimized kernels (closed diamonds), which removes the bias compared with the cloud-kernel results. Also, because the optimization influences the all-sky kernel but not the clear-sky kernel, this change influences the AΔCRF. If we use the original Shell et al. (2008) kernel to derive a shortwave AΔCRF for CAM5, we find the results indicate a global-mean value of 0.66 W m−2 K−1, but when using the CAM5 optimized noncloud kernels the value reduces to 0.47 W m−2 K−1. This occurs because the difference between the all-sky albedo kernel and the clear-sky albedo kernel is reduced after the CAM5 optimization, which reduces the (positive) kernel adjustment made to the ΔCRF. This result implies that the results of Gettelman et al. (2012), which use the Shell et al. (2008) kernels to derive AΔCRF, overestimate the strength of the shortwave cloud feedback in CAM5 by almost 40%. Bitz et al. (2012) also use the Shell et al. (2008) kernels but only analyze CAM4 feedbacks, where we find the errors in the AΔCRF calculation to be much smaller.
In summary, our results suggest that the use of the original CAM3 noncloud kernels with either the adjusted CRF method or the residual method in CAM5 will result in the derived surface albedo feedback being overly weak and the derived shortwave cloud feedback being overly strong. Also, using the original CAM3 kernels will produce a too positive longwave AΔCRF and a too negative longwave atmospheric temperature feedback in the CAM3 double-CO2 experiment. These biases can be eliminated by using the optimized noncloud kernels in the calculations or by using the ISCCP-kernel-calculated feedback. In the scenarios and models considered here, optimizing the Zelinka et al. (2012) kernels does not significantly alter global-mean cloud feedbacks.
c. Cloud-type feedbacks
In contrast to the other methodologies considered, using ISCCP-kernel-derived cloud feedbacks allow us to break down the feedback into different regions and cloud types as in Zelinka et al. (2012). Figure 6 shows the global-mean cloud feedbacks in CAM3, CAM4, and CAM5 partitioned into ISCCP cloud types. These plots are produced by taking the product of the cloud fraction changes between control and double-CO2 simulations and the longwave and shortwave cloud kernels. Global feedbacks in Figs. 6d–m are calculated on a gridpoint basis and then averaged globally. Before one even considers the feedbacks, it is clear from the cloud fraction changes in Figs. 6a–c that there are many more similarities between CAM3 and CAM4 than there are between CAM3 or CAM4 and their successor. CAM5 exhibits large cloud fraction changes in the optically thin regimes with τ < 0.3 (Fig. 6c). This is primarily because CAM5 simulates more of these optically thin cloud types in its control climate (see Fig. 3d and Kay et al. 2012). However, because the shortwave and longwave kernel values are small for this regime (Figs. 3e,i,j,m), the radiative effect of the cloud changes is also small (Fig. 6j).
In most regimes, taking the product of global-mean cloud fraction changes and global-mean kernels yields a reasonable estimate of the net global feedback for that regime, but there are some exceptions. For example, in CAM5 for the stratocumulus regime, the globally averaged shortwave kernel is mixed. For high stratocumulus (CTP < 800 hPa and 3.6 < τ < 23), there is a decrease in global-mean cloud fraction (Fig. 6c) and a corresponding strong positive shortwave feedback (Fig. 6f). However, for lower stratocumulus with CTP > 800 hPa, there is an increase in global cloud fraction and a positive shortwave global feedback, even though the globally averaged shortwave kernel is negative throughout. This can be explained by considering the zonal pattern of low-level stratocumulus change in CAM5 upon CO2 doubling. The model loses low stratocumulus in the midlatitudes but gains them poleward of 60°N and 60°S. The shortwave cloud kernel is negative at all latitudes for stratocumulus cloud types (not shown), but the amplitude is greater for lower latitudes where annual-mean insolation is higher. Thus, the high-latitude stratocumulus cloud fraction change has only a small effect on the global feedback because the kernel values are relatively small in these regions.
Figures 7a–c show that the spatial stratocumulus feedbacks in CAM3 and CAM4 are significantly different from CAM5. Both CAM3 and CAM4 show negative shortwave stratocumulus feedbacks off the western subtropical continental boundaries due to cloud fraction increases, but these are largely absent in CAM5. This, combined with the more extensive midlatitude stratocumulus loss in CAM5 compared to CAM3 or CAM4 means that the net global positive stratocumulus feedback in CAM5 (0.59 W m−2 K−1) is almost twice that of CAM3 (0.36 W m−2 K−1) or CAM4 (0.27 W m−2 K−1).
However, although the differences in stratocumulus response do account for some of the increase in CAM5 shortwave cloud feedback strength, a larger portion is attributable to the more optically thick stratus response (Figs. 7d–f). The successive models exhibit increasingly positive global-mean shortwave stratus feedbacks of −0.26, 0.10, and 0.58 W m−2 K−1 for CAM3, CAM4, and CAM5, respectively. In this regime, each of the models behaves rather differently. CAM3 exhibits global increases in stratus, with peaks in the tropics and subtropics and slight increases over land. CAM4 gains stratus in the tropical oceans but tends to lose stratus over land, while CAM5 shows mild stratus losses globally and large losses over midlatitude ocean regions. This difference in shortwave stratus feedback explains almost 60% of the variance in global shortwave cloud feedback between the three models.
The deep convective response affects both the longwave and shortwave feedbacks. Figures 7g–i and 8g–i show that the deep convective cloud response is stronger in CAM3 and CAM4 than in CAM5, although the spatial distribution of convective cloud response does differ between CAM3 and CAM4. In CAM3 and CAM4, the positive longwave deep convective feedbacks are partially compensated by the negative shortwave deep convective feedbacks, leaving net positive feedbacks of 0.18 and 0.14 W m−2 K−1, respectively. In CAM5, the deep convective cloud fraction increase is much smaller (Fig. 6c), making the net effect of deep convective clouds only −0.03 W m−2 K−1.
Also important for the longwave cloud feedback are differences among the models attributable to the cirrus and to some extent cirrostratus responses. For cirrus (Figs. 8a–c), CAM3 shows tropical increases and subtropical losses in cloud fraction, which results in a near zero net cirrus feedback of −0.03 W m−2 K−1. CAM4 shows global cirrus loss, which results in a slight negative feedback of −0.12 W m−2 K−1, while CAM5 shows a global increase in cirrus upon CO2 doubling, which results in a positive global longwave cirrus feedback of 0.31 W m−2 K−1.
The global-mean longwave cloud feedback is less positive in CAM5 than in its predecessors (Fig. 5). Although the longwave cirrus feedback is more positive in CAM5, this is more than cancelled out by the weaker longwave deep convective response. On the other hand, the strong negative shortwave deep convective cloud feedbacks in CAM3 and CAM4 combined with their smaller positive shortwave stratocumulus and more negative stratus feedbacks result in smaller shortwave cloud feedbacks when compared with CAM5. In CAM5, there are thus three factors that contribute to the stronger positive net shortwave cloud feedback: a global loss of stratus and stratocumulus, a lack of negative stratocumulus feedback off the western continental boundaries, and a lack of strong negative deep convective response.
Although we showed in Fig. 5 that the global-mean cloud feedbacks were not significantly influenced by the optimization of the Zelinka et al. (2012) kernels, there are some significant changes at the regional level, primarily for the shortwave feedbacks. For instance, in the CAM5 optimization, although the shortwave kernel sensitivity to both stratocumulus and stratus is decreased in the global mean (Fig. 3m), the sensitivity is actually increased for latitudes south of 30°S (not shown). Thus, when using the Zelinka et al. (2012) kernels, the shortwave stratus and stratocumulus feedbacks in the Southern Ocean appear to be 10%–15% weaker than when using the optimized kernels. In CAM5, these southern latitudes exhibit the most significant loss of stratus and stratocumulus (Figs. 7c,f), so this is the primary reason we see that global shortwave cloud feedbacks become slightly more positive after optimization (Fig. 5).
This study extends the radiative kernel feedback analysis such that information from climate change simulations is used to optimize existing radiative kernels. The modified technique produces more accurate approximations of feedback processes when the initial and/or final model state is significantly different from that in which the original kernel was derived. The optimizing process is statistical, finding optimal kernel values to minimize the error in the estimation of top-of-atmosphere fluxes while also avoiding spurious results by constraining kernel corrections to be small. This optimizing process estimates cloud radiative kernels by finding correlations between cloud fractions for different ISCCP-simulated cloud-top pressures and optical depths and the longwave and shortwave TOA fluxes. Previous studies have also used ISCCP data to measure TOA flux sensitivity to cloud distributions (Hartmann et al. 1992; Ockert-Bell and Hartmann 1992), but here we present a methodology that simultaneously estimates all cloud and noncloud components of a given change in TOA flux, given some initial estimates.
We demonstrate this methodology using doubled CO2 experiments with three successive generations of the Community Atmosphere Model with progressively higher equilibrium climate sensitivity to a doubling of CO2: CAM3 and CAM4 (2.5 and 3.1 K, respectively, according to Bitz et al. 2012) and CAM5 (4.1 K, as shown in Gettelman et al. 2012). Using a set of radiative kernels that were originally developed for CAM3, it is shown that all kernels are somewhat changed by the optimizing process, but the change is model dependent. We find that, in regions where the base-state cloud distribution has changed noticeably with respect to the CAM3 state, the new kernels show significant differences with respect to the original. For example, the values of the surface albedo kernel at high northern latitudes are larger in CAM5 than in CAM3 or CAM4, meaning that the TOA shortwave flux is more sensitive to a change in surface albedo. This can be explained by the fact that Arctic summer liquid water paths and cloud optical depths are decreased in CAM5 relative to its predecessors. This increase in Arctic kernel results in an approximately 50% larger global-mean surface albedo feedback in CAM5 than one would infer from using the original kernels.
The cloud radiative kernels are optimized from Zelinka et al. (2012). Although the optimizing methodology can be used in theory to derive kernels without a prior estimate, it was found that, in practice, the derived kernels with no prior estimate exhibited unphysical properties. The global-mean kernels show moderate differences from the originals, but the optimizing process did significantly reduce errors in the reproduction of top-of-atmosphere fluxes. Given that Zelinka et al. (2012) found that kernel performance was model dependent, we expect that the error reduction using the optimizing methodology could potentially be larger in other models, since the original noncloud kernels are based on CAM3.
The conventional kernel analysis approach is sensitive not only to systematic differences between the model used to derive the kernel and the target model but also to kernel dependencies on the model state. Jonko et al. (2012) found that, during a climate change simulation with a significant change in mean state, such as an octupling of present-day carbon dioxide levels, feedbacks calculated using kernels based on the present-day state or the 8 times CO2 state were both subject to significant errors. In fact, the authors found that the most accurate kernel was an average of the two kernels derived from the present-day state and from the 8 times CO2 state. In the present study, we postulate that the kernel optimizing method will effectively produce the best linear estimate of the feedbacks throughout the climate change simulation rather than linearizing about the initial or final state, and this is likely to be the most accurate approximation of feedbacks for the simulation in question, assuming only one kernel is used.
When applied to the successive generations of the Community Atmosphere Model, the cloud radiative kernels produce global-mean results that are broadly similar to those seen in previous studies. The dominant cause for the increase in climate sensitivity between CAM4 and CAM5 is the increase in net shortwave cloud feedback strength, which is positive in CAM4 but gets stronger in CAM5. However, this increase is significantly less than is obtained by using the shortwave adjusted cloud radiative forcing with the original CAM3 kernels as in Soden et al. (2008) and Gettelman et al. (2012), due to the change in base-state cloud distribution between CAM3 and CAM5.
Many multimodel studies of cloud feedback have shown that stratocumulus response is the dominant component of intermodel spread in the CMIP-3 ensemble (Bony et al. 2006; Webb et al. 2006). However, our analysis of the cloud feedbacks shows that a number of processes contribute to the increase in net cloud feedback seen in CAM5 compared to its predecessors. CAM5 exhibits a greater loss of both stratus and stratocumulus in midlatitude ocean regions with a doubling of CO2. CAM3 and CAM4 both display negative stratocumulus feedbacks off the western subtropical continental boundaries, but CAM5 does not. CAM3 and CAM4 have greater increases in deep convection, which cause compensating positive longwave and negative shortwave feedbacks. CAM5 has a much weaker convective response, which increases its net shortwave feedback and decreases its longwave feedback relative to its predecessors. Finally, CAM5 develops more cirrus cloud, resulting in a positive longwave cloud feedback. These conclusions are somewhat in agreement with the findings of Gettelman et al. (2012), who also find that it is stratus rather than stratocumulus clouds that primarily differentiate the cloud response of the two most recent versions of the CAM, but our findings suggest that the other factors detailed above may also play significant roles in increasing the CAM5 climate sensitivity.
A significant question that arises from this work is whether future kernel analyses should go to the additional trouble of deriving model- and experiment-specific kernels rather than using a single kernel for purposes. The results of our study indicate that this decision is dependent on the goals. Optimized kernels, aside from the manual effort involved in their computation, introduce an additional complication in interpreting differences in model feedbacks that are now attributable to both differences in the kernel and changes in the model state variables. In some cases, it might be desirable to make the approximation of a single kernel for ease of interpretation. Additionally, this technique requires that the ISCCP simulator is implemented in the model. However, as we have shown in this study, the kernel optimizing approach does convey some advantages; it allows a more exact reproduction of the top-of-atmosphere energy budget in a climate change simulation, within the limits of the linear assumptions made. In some cases, such as with the all-sky surface albedo kernel, we find that the optimized kernel produces significant differences in the derived feedbacks, which are justifiable and expected when one considers the climatologies of the different models used. The sensitivity of the albedo kernel is not unprecedented, given that this kernel was found to be the most uncertain of the all-sky kernels considered in Soden et al. (2008). The kernel optimizing approach is therefore recommendable in any situation when all-sky kernels produce significant errors in the reproduction of top-of-atmosphere fluxes, a test that can easily be conducted on a case-by-case basis using existing kernels.
This work presents a model- and experiment-specific kernel-based analysis of cloud feedbacks differentiated by cloud type and location, where we have restricted our consideration to the output from the ISCCP simulator. However, the most recent coordinated experiments in the Cloud Feedback Model Intercomparison Project include a number of additional satellite simulators, each with their own advantages and caveats, for the analysis of different cloud types. The basic methodology presented in this work could be extended to use data from these additional simulators in future work. Finally, our study as presented here has been entirely model centric, but given adequate observations could be used to compute cloud-induced radiative anomalies directly from satellite products.
We have demonstrated that some (but not all) feedbacks may require model- and experiment-specific kernels to provide the best estimates of climate feedbacks. Thus, another logical step would be to optimize model-derived kernels using observational or reanalysis fields to test the robustness of studies such as Dessler (2010), which seek to derive feedbacks directly from the observational record.
Many thanks to Mark Zelinka and an anonymous reviewer for their extensive and helpful comments. We thank Jennifer Kay for her contributions to the Arctic feedback discussion. Portions of this study were supported by the Office of Science (BER), U.S. Department of Energy, Cooperative Agreement DE-FC02-97ER62402, by National Science Foundation Grants ATM-0904092 and ARC-102299.
The National Center for Atmospheric Research is sponsored by the National Science Foundation.