1. Introduction
Radiative forcing F is the change in the net downward heat flux (W m−2) into the climate system caused by an agent of climate change, such as an alteration to the atmospheric concentration of carbon dioxide or aerosol. The concept is useful because the magnitude of climate change that would be caused by different agents can often be estimated, without running a climate model, from their radiative forcings. Precise radiative forcings can be evaluated from detailed radiative calculations with less computation than required for a climate simulation and can be compared without the complication of climate variability.
The magnitude of climate change is quantified by the change in global-mean surface air temperature change ΔT from the initial state. General circulation model (GCM) experiments show that ΔT ∝ F in a steady state. GCMs give a wide range of values (Cubasch et al. 2001) for the constant α (W m−2 K−1) in the formula F = αΔT. This α is called the “climate feedback parameter” and is sometimes quoted equivalently as the “climate sensitivity parameter” 1/α (K W−1 m2). Several analyses have been undertaken that use observed mean climate or climate change to constrain the climate sensitivity parameter of the real world (e.g., Gregory et al. 2002; Murphy et al. 2004; Forster and Gregory 2006; Forest et al. 2006; Hegerl et al. 2006).
Thus, steady-state global-mean climate response is determined jointly by forcing F and feedback α. This factorization is useful to the extent that feedback is model dependent but the same in a given model for all forcing agents, while forcing is model independent but depends on the forcing agent (Hansen et al. 2005).
The relationship between ΔT and F is an expression of the energy balance of the climate system. As the climate changes in response to the forcing agent, for example, by warming when the CO2 concentration has been raised, it produces a radiative response H = αΔT, which opposes the imposed F so that the net heat flux into the climate system N = F − H = F − αΔT. In the perturbed steady state N = 0 ⇒ F = αΔT since no more heat is being absorbed. Here, N is most conveniently measured as the net downward radiative flux at the top of the atmosphere (TOA).
The separation into forcing and feedback may appear to be arbitrary since both the radiative forcing F and the radiative response H = αΔT are consequences of imposing the forcing agent. The radiative forcing is sometimes defined as global-mean net downward change in radiative flux at the tropopause caused instantaneously when the forcing agent is imposed, but this definition is thought inadequate in the following most important cases.
Carbon dioxide since raising the CO2 concentration increases the rate at which the stratosphere radiates heat. It adjusts by a temperature decrease taking a few months. This reduces the net downward tropopause radiation.
Aerosol since only the “direct” effect is instantaneous. Aerosols in the atmosphere also alter the occurrence and optical properties of clouds, which in turn have an “indirect” radiative effect, but these changes are not instantaneous.
Special treatments have been developed for these and other cases to include in F those effects which are considered to be part of the forcing. This is done partly because the resulting values for F are more nearly model independent and hence useful for comparative studies of the climatic effects of different forcings (e.g., Shine et al. 2003; Hansen et al. 2005).
The arbitrariness of what to count as forcing in a given model is a consequence of looking only at steady-state changes, from which it is not possible to distinguish between effects driven directly by the forcing agent and those associated with global climate change. Suppose that two different definitions of CO2 forcing (for instance, including or excluding stratospheric adjustment) give values of F and F′ for a doubling of CO2. The GCM is run to steady state with doubled CO2, and the diagnosed temperature change ΔT2×, called the “equilibrium climate sensitivity,” is used to calculate two different values of the feedback parameter α = f /ΔT2× and α′ = F′/ΔT2×. Using either of these values, we predict that twice the forcing will give twice the temperature change: ΔT = (2F)/α = (2F′)/α′ = 2ΔT2×. Both forcing and feedback can be multiplied by any factor in this way without changing our predictions for the steady state.
The distinction of forcing and feedback is not arbitrary if we assume that the concepts should apply to time-dependent climate change since different choices of (F, α) giving the same steady-state ΔT lead to different predictions of the heat flux into the climate system for a given ΔT: N = F − αΔT = (f /F′)(F′ − α′ΔT) ≠ F′ − α′ΔT. Since we regard “forcing” as the change in N caused directly by the forcing agent and climate feedback as being the change in N due to the response of the system to the forcing, time dependence therefore suggests a practical way to evaluate forcing: F is the limit of N as ΔT → 0, where ΔT is measuring “climate response.” This defines the forcing as the net heat flux into the climate system caused by the forcing agent without any climate response yet having occurred. The distinction between forcing and feedback is thus made according to time scale. The radiative response of the climate system is distinguished from the forcing because the former develops over longer time scales: years if only the mixed layer of the ocean is considered or centuries if the full ocean.
Gregory et al. (2004) showed that, when N is plotted against ΔT for a fixed forcing of the Hadley Centre slab climate model version 3 (HadSM3, see also section 2a), a straight line gives a good fit, as would be expected from N = F − αΔT if α is constant. (In a more complex system, α might depend on climate and hence not be constant.) The N intercept is the forcing F, following the prescription F = limΔT→0N. Forcings such as stratospheric adjustment to CO2 and the indirect forcing by aerosols are effects that develop quickly (over months or less) after the forcing agent is added. Consequently, if means over long enough periods are used for the regression, F includes these influences on forcing. Although stratospheric adjustment and aerosol forcing develop over periods of less than a year, it is convenient to use periods of a year or longer for the analysis so that the seasonal cycle does not have to be considered. Gregory et al. used annual or decadal means.
In this paper we pursue these ideas somewhat further. We argue that this way of distinguishing forcing and feedback is useful in explaining differences in climate response among GCMs and is consistent with the recently proposed methods of Hansen et al. (2002, 2005) and Shine et al. (2003) for evaluating the forcing.
2. Forcing and feedback diagnosed from time-dependent climate change
The climate radiative response arises from a number of feedback processes. A conventional decomposition H = Σi Hi at the TOA is into longwave and shortwave radiation (terrestrial and solar) and clear sky and cloud (Cess and Potter 1988). Gregory et al. (2004) did not show components of H but, if H ∝ ΔT, it is reasonable to expect that the individual Hi ∝ ΔT as well so that Ni = Fi + YiΔT, where Fi are the components of forcing and Yi the individual climate feedback parameters. (Note that we choose to write Yi with the opposite sign to α so that α = −ΣiYi, because that suits their physical interpretation below. The notation is summarized in Table 1.) A linear dependence of the Ni on ΔT has been shown by Stowasser et al. (2006) and Lambert and Faull (2007) for GCMs forced with increased insolation and by Forster and Gregory (2006) for observed changes in TOA radiation in recent years.
In GCMs the clear-sky components are obtained from a diagnostic radiative calculation (i.e., not affecting model evolution) with clouds assumed to be absent, and the cloud components as the difference between the radiation calculations with and without clouds. The sum of clear-sky and cloud components is called “all sky.” The cloud components of N are often referred to as “cloud radiative forcing,” a term that we prefer to avoid because it is confusing. Because clouds are cooler than the surface, especially high clouds, they have a greenhouse effect, meaning that TOA outgoing longwave radiation is reduced compared to clear-sky conditions since the radiation emanating from clouds is less than from the lower, warmer levels of the atmosphere that they obscure. On the other hand, clouds at all levels generally have higher albedo than the surface and increase the TOA outgoing shortwave radiation.
a. HadSM3 model
Using the HadSM3 model, an experiment is carried out in which CO2 is instantaneously quadrupled. We refer to this as a “transient experiment.” HadSM3 comprises the Hadley Centre Atmosphere Model version 3 (HadAM3) coupled to a “slab” ocean, that is, a mixed layer with prescribed horizontal heat convergence (Williams et al. 2001). The version of HadSM3 used here is not identical with that used by Gregory et al. (2004), but our results are consistent with theirs and for the purpose of this work we regard them as the same model, which we call “standard HadSM3.” [The present version includes the sulfur cycle, which was added by Murphy et al. (2004); we have no evidence of significant differences caused by this to our results.]
In the transient experiment, the climate initially evolves rapidly, the rate of change decreasing as the new steady state is approached. Figure 1a shows that changes in longwave/shortwave clear-sky/cloud Ni separately depend linearly on ΔT. (All quantities are differences from a control run with unchanged CO2.) Regressions are made from the first 20 years of data, during which the 4 × CO2 steady state is largely achieved (cf. Gregory et al. 2004). The regression coefficients are shown in Table 2. The forcings Fi have been divided by 2 to make them apply to 2 × CO2. The uncertainties (shown as one standard error) have been calculated assuming 10 degrees of freedom, on the basis of the autocorrelation in the time series.
The majority of F (the N intercept) is longwave clear-sky FLN, as expected for CO2. As noted in section 1, forcings diagnosed in this way include stratospheric adjustment; the instantaneous forcing is larger than the adjusted forcing (e.g., Cess et al. 1993; Myhre et al. 1998). The longwave clear-sky YLN is the largest Yi (in magnitude) and includes the blackbody, water vapor, and lapse rate feedbacks (separately quantified by Colman et al. 2001; Colman 2003). Their sum is negative and dominates Σi Yi, so α > 0 as required for stability, that is, overall negative feedback. (The sign convention for the Yi is chosen so that a positive Yi enhances the warming.)
The instantaneous shortwave forcing at the tropopause is negative because of increased shortwave absorption by CO2 in the stratosphere. Part of the stratospheric adjustment is a compensating increase in longwave radiation, mostly to space. The sum of adjusted shortwave and longwave forcing must be the same at the TOA and tropopause because the heat content of the stratosphere changes negligibly after the adjustment is complete, but the partition of the forcing between longwave and shortwave is different at the two levels because of shortwave absorption and longwave emission by the stratosphere. At the top of the atmosphere, the shortwave forcing is positive. However, it is small in any case, being only ∼4% of the adjusted longwave forcing at the tropopause (Myhre et al. 1998). The (stratosphere adjusted) TOA FSN in HadSM3 is ∼2% of FLN. The shortwave clear-sky YSN is an important positive feedback, caused by the reduction of surface albedo as the area of snow and ice contracts and increased absorption by water vapor.
The cloud components of forcing are surprising. Though of a smaller magnitude than FLN, both FLC and FSC are significantly different from zero at the 5% level: FLC < 0 and FSC > 0. As these terms have similar sizes, the net F = 3.3 ± 0.2 W m−2 is not very different from the clear-sky forcing. The partition of F into longwave FL = 2.52 ± 0.16 W m−2 and shortwave FS = 0.78 ± 0.10 W m−2 is affected, however, FS being about 25% of F, a much larger fraction than in the clear sky.
It is notable that NSC has relatively large interannual variability, leading to a bigger uncertainty in FSC than in the other Fi. A similar point was made by Colman et al. (2001). This suggests that internal variability of the climate system has its largest effect on the radiation budget through fluctuations in low cloud, which has a shortwave but not a large longwave radiative effect. The same suggestion has been made regarding observed TOA variations (Forster and Gregory 2006).
We interpret the nonzero FLC and FSC as evidence of adjustment of clouds to the extra CO2 in the atmosphere. We suggest that this is caused by rapid local changes to the vertical temperature profile of the atmosphere due to the altered radiative heating, with consequent changes to stability, vertical mixing, and the moisture profile, analogous to the changes causing the indirect and semidirect aerosol forcings. We refer to these induced cloud contributions to F as “tropospheric adjustment” of CO2 forcing. They are like stratospheric adjustment in that they occur in much less than a year, in response to the elevated CO2 concentration. It would be valuable to examine the processes of tropospheric adjustment in more detail, for instance by analysis of the heating rates and fluxes through the depth of the atmosphere, as was done by Sokolov (2006), who also comments on the contribution of tropospheric adjustment to forcing.
The method used to partition fluxes into clear sky and cloud can give misleading results (Soden et al. 2004). Increasing the CO2 concentration instantaneously reduces atmospheric longwave emission but has no instantaneous effect on cloud longwave emission, so the instantaneous all-sky longwave forcing of CO2 is smaller than it would be for clear skies. The difference between all sky and clear sky contributes to FLC. However, this cloud “masking” effect is considerably smaller than our FLC. Instantaneous all-sky forcing (sum of longwave and shortwave) is 0.16 W m−2 (4%) smaller than clear sky in the Bureau of Meteorology Research Centre (BMRC) GCM (Colman et al. 2001). Instantaneous all-sky longwave forcing is on average 14% smaller than clear sky in the set of GCMs analyzed by Cess et al. (1993). In our results for HadSM3 (Table 2), however, longwave all-sky (not instantaneous, i.e., after tropospheric adjustment) FL = FLN + FLC is ∼30% smaller than FLN (on average 25% in the set of models considered in section 2b). The nonzero FSC is even less likely than FLC to be a cloud-masking effect since the instantaneous clear-sky shortwave CO2 forcing is much smaller than the longwave and smaller than FSC itself in magnitude. We therefore think that FC ≡ FLC + FSC is not an artifact of cloud masking.
The cloud feedbacks YLC and YSC are rather weak, especially the latter; that is, the regression lines are almost flat. Most of the changes in cloud are the rapid tropospheric adjustment. The changes in cloud due to changing climate, as measured by ΔT, are relatively small. The usual feedback calculations done from the steady state count all cloud changes as feedback, but this time-dependent calculation indicates that most should be regarded as forcing.
Murphy et al. (2004) and Webb et al. (2006) constructed ensembles of modified versions of HadSM3 by varying parameters, with the aim of quantifying the systematic uncertainty in climate feedbacks. The second ensemble (Webb et al. 2006) varied 26 parameters in combination. From this ensemble we identified one model, which we refer to as “modified HadSM3,” having a particularly low ΔT2× of 2.5 K. Two 4 × CO2 experiments were done with modified HadSM3, and their results were averaged together year by year so as to reduce the influence of interannual variability. The plot of Ni against ΔT is shown in Fig. 1b and the regression results in Table 2.
There are no statistically significant differences at the 5% level between the corresponding feedback parameters of standard and modified HadSM3. (The uncertainties are generally smaller for the modified model because they are calculated from an ensemble of two experiments.) The reason for the lower ΔT2× is therefore not different climate feedback, according to our definition, but lies in FSC, which is positive (+ 0.71 ± 0.12 W m−2) in the standard HadSM3 and negative (−0.27 ± 0.30 W m−2) in the modified model. The difference between the values is significant at the 5% level. Webb et al. (2006) show that variants of HadSM3 that have low ΔT2× in the ensemble of which our two versions are members generally show increases in the amount and optical thickness of low clouds, which tend to have a negative radiative effect dominated by shortwave. The other Fi are indistinguishable between the two models. Consequently, CO2 has a smaller F = 2.6 ± 0.3 W m−2 for 2 × CO2 in the modified HadSM3, significantly less at the 5% level than the standard HadSM3 value.
b. Intercomparison of climate models
In connection with the Fourth Assessment Report (AR4) of the Intergovernmental Panel on Climate Change, a large database of results from many GCMs has been assembled. This database, known as the “Coupled Model Intercomparison Project Phase 3 (CMIP3),” includes experiments done with several other slab models under instantaneous doubling of CO2 and their corresponding control experiments. For some slab models, the CMIP3 database unfortunately contains only a sample of years from the steady state with 2 × CO2, omitting the initial period of warming, which is of interest to us here, but which was not included in the protocol for CMIP3 experiments. The Cloud Feedback Model Intercomparison Project (Webb et al. 2006) collected data with this initial period from several slab models, including two versions with different cloud physics of the Model for Interdisciplinary Research on Climate 3.2 (MIROC3.2) slab model denoted as low climate sensitivity (LS) and high climate sensitivity (HS). The former model is in the CMIP3 database; the latter is described by Ogura et al. (2006, manuscript submitted to J. Meteor. Soc. Japan).
The variation of N with ΔT for eight slab models is shown in Fig. 2. Results for the slab version of the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model, version 3.1 [CGCM3.1(T63)] are very similar to those of the corresponding lower-resolution T47 model shown. Like standard and modified HadSM3, all these models yield good straight lines, indicating time-independent forcing F and climate feedback parameter α. This is a notable result, because it shows that H ∝ ΔT in all climate states of these slab models, not only in steady states. However, there is evidence from coupled atmosphere–ocean GCMs (AOGCMs) that climate feedbacks are somewhat dependent on climate state (Senior and Mitchell 2000; Boer and Yu 2003a), probably because some aspects of the geographical pattern of surface climate change evolve slowly, on the time scales of ocean climate change, and N versus ΔT then deviates from a straight line (Gregory et al. 2004). Such behavior reopens the issue of distinguishing forcing from feedback on this multicentury time scale, but we do not pursue the question here.
The main qualitative features of the regression coefficients are also common among models (Table 2). The clear-sky longwave components are most similar across models, with coefficients of variation (standard deviation divided by mean) of 6% in YLN and 8% in FLN. In most models, the clear-sky shortwave FSN is not significantly different from zero at the 5% level. The net forcing F = 3.7 ± 0.3 W m−2 agrees with the forcings of 3.71 W m−2 calculated by Myhre et al. (1998), and 3.7 ± 0.2 W m−2 reported by Forster and Taylor (2006) for a different set of GCMs.
All of the models show nonzero cloud components of forcing, both longwave FLC and shortwave FSC, that tend to compensate to some extent, as in standard HadSM3. In all models, FLC is significantly less than zero at the 5% level. In most models, FSC is positive, but it is significantly greater than zero in only a few cases. In all but two models FC = FLC + FSC is negative, so the net troposphere-adjusted forcing F < FN(= FLN + FSN): the exceptions are CGCM3.1(T47) and MIROC3.2(LS), which have unusually large FSC ≃ +1 W m−2. The ensemble-mean FC = −0.4 ± 0.5 W m−2. The mean is significantly less than zero at the 5% level if the 10 models are regarded as independent instances from a common distribution so that the standard error of the mean is
Stowasser et al. (2006) applied the method of Gregory et al. (2004) to three AOGCMs forced by increased insolation. Their results also give evidence of a negative FC (they do not distinguish longwave and shortwave), which reduces the net solar forcing in the Climate System Model version 1 (CSM1) and Community Climate System Model version 2 (CCSM2) AOGCMs (the stars in their Fig. 3 point to a negative intercept on the N axis, which they call 〈R′〉). The omission of FC from the forcing could account for the apparent inconstancy of the climate sensitivity and feedback parameters calculated by Stowasser et al. (2006) in these two models (their Figs. 1 and 2), whereas they find a more constant α for CGCM3, which has a small FC (Lambert and Faull 2007).
Modified HadSM3 has the smallest ΔT2× = 2.5 K; its net climate feedback parameter α matches the ensemble mean of about 1.0 W m−2 K−1, but its negative FSC is unusual. CCSM3 also has FSC < 0 and, consequently, the second lowest ΔT2× = 2.7 K, since it also has a typical α. The tropospheric adjustment to CO2 thus appears to be a substantial influence on climate sensitivity. Net forcing F has a coefficient of variation of 14%, to which FSC makes the largest contribution.
Cloud shortwave feedback YSC is significantly different from zero at the 5% level only in MIROC3.2(HS). That is, with the exception of this one model, the shortwave radiative response to CO2 due to clouds is not a climate feedback; it may depend on the CO2 concentration, but not on global warming. The longwave radiative response due to clouds is a combination of generally negative forcing with generally positive feedback, but this feedback is small compared with YLN and YSN. From the statistics of the ensemble, YLC is −7 ± 7% of YLN, but FLC is −23 ± 6% of FLN.
Our analysis for CCSM3 differs from that of Kiehl et al. (2006) for the same slab model (although at different resolution: T85 here and T42 in their paper). They obtain a similar ΔT2× = 2.5 K but a forcing of 3.58 W m−2 from regression on an N versus ΔT plot (their Fig. 1) like ours (our Fig. 2a), whereas we obtain F = 2.93 ± 0.23 W m−2. On their plot N ≃ 1 W m−2 in the final steady state, but we would expect it to be zero. This imbalance should have been subtracted, shifting the values in their Fig. 1 downward by ∼1 W m−2 and reducing their forcing estimate to agree with ours (J. T. Kiehl 2006, personal communication). This adjustment does not affect the slope and hence the estimate of the climate feedback parameter, for which we both obtain α = 1.1 W m−2 K−1. It is also notable that the scatter in their plot is larger and the correlation coefficient consequently lower than in ours.
The Goddard Institute for Space Studies Model E-R (GISS-ER) has FLN considerably larger than for any other model, and consequently the largest F = 3.8 ± 0.3 W m−2. For this model, Hansen et al. (2005) report the same ΔT2× as ours and a forcing of 4.11 W m−2 obtained by a different method (see below). The strong forcing is countered by an unusually strong (negative) YLN and accompanied by an unusually weak (positive) YSN, leading to the third smallest ΔT2× = 2.7 K.
MIROC3.2(HS) has the largest ΔT2× = 6.3 K by a substantial margin, due mostly to its exceptionally strong positive YSC. Its other forcing and feedback components are typical. The Met Office Hadley Centre Global Environmental Model version 1 (UKMO-HadGEM1) has the second largest ΔT2× = 4.5 K, mostly due to its strong YSN, largely caused by strong sea ice sensitivity to warming (Johns et al. 2006). UKMO-HadGEM1 shares with the Meteorological Research Institute Coupled General Circulation Model, version 2.3.2 (MRI CGCM2.3.2) the feature that FSN < 0. In a way analogous to the tropospheric adjustment of clouds, this indicates some change affecting clear-sky shortwave absorption (e.g., in water vapor or surface albedo), which comes about much more rapidly than global climate change in response to CO2 (see section 4 for further comment on this).
The ensemble standard deviation of ΔT2× is 1.1 K. If we exclude MIROC3.2(HS) and UKMO-HadGEM1, the two models with a high ΔT2× due to large shortwave feedbacks, the standard deviation is reduced to 0.5 K, which is due roughly equally to uncertainty in F and α (combined in quadrature). If all 10 models had the ensemble-mean FN and α, the standard deviation of ΔT2× would be 0.5 K due to the spread in FC alone.
3. Forcing diagnosed by preventing climate feedback
An independent method to evaluate the forcing is by running an experiment in which the forcing agent is included but climate feedback is inhibited by not allowing surface temperatures to change. The advantage of this approach is that forcing can be evaluated to arbitrary precision by running a long enough experiment. The disadvantages compared with the regression approach are that this special experiment is needed and that it gives no information about feedbacks.
In such an experiment ΔT = 0 ⇒ N = F − αΔT = F, so the forcing is diagnosed as the change in net downward TOA radiation. Hansen et al. (2002) proposed the method, which they implemented by prescribing observed sea surface temperatures and sea ice; we will call this a “fixed SST experiment.” Global climate change is not completely prevented since land surface conditions are allowed to evolve. Hansen et al. (2005) corrected for this by evaluating F = N* + αΔT* [the asterisk is for fixed-SST experiment, equivalent to their Eq. (1)]. This assumes that the climate feedback parameter in a fixed-SST experiment is the same as in a transient experiment; this is unlikely to be exactly true since feedbacks over sea areas have largely been inhibited. Hence α may not be the appropriate feedback parameter for the correction.
Shine et al. (2003) avoided the problem by fixing land surface temperatures as well. This is technically more difficult to do in a GCM because it interferes with the rapid coupling of the atmospheric boundary layer to land surface temperatures and hydrology during the diurnal cycle and synoptic variation. Such interference is believed to be less severe over the sea, which has a greater heat capacity and a constantly moist surface. (However, this perception might partly result from the rather simple representation that most AOGCMs employ for the near-surface vertical structure of the ocean mixed layer.)
Both Shine et al. (2003) and Hansen et al. (2005) use observed surface temperatures. Climate feedbacks are somewhat dependent on climate state (Senior and Mitchell 2000; Boer and Yu 2003a; Gregory et al. 2004) and the same may be true for climate forcing. Consequently, it might be better to use the model’s own control climatology for surface temperature in such experiments. This should be very similar over the sea since slab models are calibrated to reproduce observed SST, but could differ over the land. We have not investigated this issue further.
We suppose that the same value of forcing should be obtained by preventing climate feedback in a fixed-SST experiment (this section), as by regressing to the limit of zero climate change in a transient experiment (section 2). Shine et al. (2003) and Hansen et al. (2005) do not consider components of TOA forcing, but we presume that they can also be diagnosed in fixed-SST experiments according to Fi = N*i. These suppositions are tested by carrying out fixed-SST experiments for standard and modified HadSM3. Each experiment comprises two integrations—one with control CO2 and one with 2 × CO2—and each Ni is evaluated as the difference between time means in the two integrations.
Table 3 and Fig. 3 compare the forcings in standard and modified HadSM3 using the regression and fixed SST methods. The results qualitatively confirm the hypothesis that the methods agree since in either model the difference between the two methods for each of the components is much less than the differences among the four components. However, the fixed SST method tends to give less negative and more positive forcings, and the differences between the methods are statistically significant at the 5% level in many cases. The correction proposed by Hansen et al. (2005) would further increase the fixed SST net forcing. The integrations are 20 years long or more, but the uncertainties have been calculated assuming 10 degrees of freedom to allow for interannual autocorrelation, as for the regression method.
Nonetheless, the fixed SST method agrees with the regression method that the net forcing F in modified HadSM3 is significantly less than in standard HadSM3 and that this is mostly due to FSC. This agreement supports our conclusions from section 2 that tropospheric adjustment to CO2 is responsible for the low ΔT2× of modified HadSM3.
4. Geographical distribution of forcing
Both the regression method of section 2 and the fixed SST method of section 3 can be used to obtain the geographical distribution of the components of forcing, as well as the global mean. Using the fixed-SST experiment, the TOA radiation fluxes Ni(x) = Fi(x) can be diagnosed from the model as functions of geographical location x (latitude–longitude). Alternatively, we can regress Ni(x, t) from the transient experiment at each point individually against global-mean surface air temperature change ΔT(t) and thus obtain a latitude–longitude field of the regression intercepts for ΔT = 0. This procedure is analogous to the treatment of global-mean Ni(t) to obtain the global-mean forcing. We interpret the field of intercepts as the geographical distribution Fi(x) of local contributions to the global-mean Fi. Note that only the global-mean ΔT is constrained to be zero by the regression method; there is no constraint on local surface air temperature change (see section 5).
The components of forcing for standard HadSM3 are compared in Fig. 4 (two left-hand columns). Some similarity is evident between the methods. There are substantial areas where the results are not statistically different from zero, especially in the cloud components, which have greater temporal variability. The dominant FLN is positive everywhere, has least geographical variation, and is larger at lower latitudes (Colman et al. 2001; Boer and Yu 2003b). The clear-sky shortwave FSN shows interesting features in the Arctic; both methods indicate significant forcing, but they give opposite signs.
The cloud components FLC and FSC result from tropospheric adjustment to CO2. They have the most pronounced geographical variation, with local values of magnitude >10 W m−2 greatly exceeding their global means of magnitude ∼1 W m−2. We noted that the global means of FLC and FSC tend to have opposite signs (Table 2), and this anticorrelation is evident geographically as well. In the control climate, high cold cloud causes a positive longwave (greenhouse) effect, which is opposed by a negative cloud shortwave (planetary albedo) effect. Figure 4 suggests that, when CO2 is added to the atmosphere, there are rapid changes in cloud, predominantly reductions. This produces opposing FLC and FSC at low latitudes (Webb et al. 2006; Sokolov 2006), which is particularly clear in the Pacific in the regression method. In midlatitudes, reduction in cloud has a weaker effect in the longwave because clouds are lower and at a more similar temperature to the surface, but it still has a substantial positive effect in the shortwave through reduction of albedo, shown by both methods across Eurasia and North America.
Components of forcing for modified HadSM3 are compared in Fig. 4 (two right-hand columns). For clear sky FLN and FSN are similar to the standard HadSM3. Both the regression and fixed SST methods show that the positive areas of FSC in northern midlatitudes are largely eliminated in the modified model. These differences are consistent with the negative global mean of FSC and hence explain the low ΔT2× of the modified model.
The regression method also shows differences in cloud components between the models in the Pacific subtropics: in modified HadSM3 positive areas appear in FLC, matched by negative areas in FSC. This suggests that tropospheric adjustment produces some increases in cloud at low latitudes in this model.
Fixed-SST experiments are not available from the CMIP3 database, but the regression method can be used to evaluate forcing and feedback geographically from the transient 2 × CO2 experiments. Statistical significance is worse than for our HadSM3 experiments, which use 4 × CO2, and hence show a larger signal. Preliminary inspection of the forcing fields (not shown) indicates that they share some general features with HadSM3. The clear sky longwave FLN is relatively uniform, and FLC and FSC have strong spatial variation, with anticorrelation at low latitudes. The clear-sky shortwave FSN exhibits large values at high latitudes, in the regions of the sea ice. In several models this forcing is negative, as was noted in section 2 for the global mean of MRI-CGCM2.3.2. In that model, the sea ice area initially expands and the surface air temperature falls slightly when CO2 is doubled. Further investigation would be needed to establish a physical explanation for this phenomenon.
5. Surface and tropospheric adjustment
The largest differences between the regression and fixed SST estimates of components of forcing in Table 3 and Fig. 3 are in FLC. Figure 4 suggests that this may arise from differences in the low-latitude Pacific, where the regression method shows pronounced FLC, predominantly negative in the standard HadSM3 and negative in large regions in the modified HadSM3, while the fixed SST method has much weaker features. By construction, both methods evaluate Fi = Ni for ΔT = 0, but they differ in how they impose ΔT = 0. In the fixed SST method, the local change must be zero everywhere over the sea, which is the majority of the world, but this is not required by the regression method. For example, for the standard HadSM3, regression indicates mean temperature change over land and sea, respectively, of +0.40 ± 0.05 and −0.16 ± 0.02 K for global ΔT = 0. This suggests the idea that the rapid adjustment to CO2 in a transient experiment may include changes in surface temperatures as well as in the troposphere. Tropospheric adjustment in a fixed-SST experiment might therefore be somewhat different because surface temperature change is largely inhibited.
Radiative forcing at the surface caused instantaneously by doubling of CO2 is much smaller than at the TOA (Collins et al. 2006) because the atmosphere is fairly opaque in the longwave. However, a continued difference between the surface and the TOA implies storage of heat in the atmosphere, which has a relatively small heat capacity. On a fairly short time scale of months, during which tropospheric and stratospheric adjustment takes place, this difference must be eliminated. Unlike the instantaneous forcing, the adjusted forcing is therefore identical at the surface, tropopause, and TOA (Shine et al. 2003; Hansen et al. 2005).
The adjustment of the net downward surface heat flux may involve changes to nonradiative fluxes, which can be evaluated like those at the TOA by regression against ΔT. Figure 5 indicates that in HadSM3 the largest part of surface forcing due to 2 × CO2 is a reduction in latent heat loss due to evaporation, with smaller contributions from increased net downward longwave and shortwave radiation, the latter being consistent with a reduction of cloud amount as an aspect of tropospheric adjustment. As the climate responds to the forcing by warming up, the net downward longwave flux increases because the atmosphere becomes warmer and moister. Net heat loss by the surface is achieved by a strong increase in evaporative cooling. The change in surface shortwave is small, consistent with weak cloud feedback. We note that global-mean changes in surface heat fluxes are dominated by changes over the sea, which covers most of the world, and changes over land have a different character as evaporation is limited by water availability. Since the surface fluxes are related to the near-surface tropospheric temperature profile, it would not be surprising if they were different in transient and fixed-SST experiments. A similar point is made by Lambert and Faull (2007) when comparing transient and fixed-SST experiments with increased insolation.
The basic distinction made in section 1 is between the rapid local response to the CO2, which we include in “forcing,” and the slow widespread response over a time scale set by the thermal inertia of the climate system, with a magnitude determined by “feedback.” An initial rapid response (for instance over continental interiors) might change the global-mean surface air temperature as well as the global-mean surface fluxes. However, the regression method could not then be used to evaluate it because it defines ΔT = 0 as indicating “no climate change.” The extension of the idea of tropospheric adjustment to include changes in the surface temperature and fluxes is an obvious extrapolation, but it needs careful consideration to understand what it means and whether it is useful.
6. Summary and conclusions
Gregory et al. (2004) proposed a method for diagnosing radiative forcing and climate feedback from transient climate change experiments, by regressing TOA radiative fluxes against global-mean surface air temperature ΔT. We have demonstrated that this method works in several GCMs for experiments with increased atmospheric CO2 concentrations and have extended it to separate the longwave/shortwave clear-sky/cloud contributions to forcing and feedback. The clear-sky forcing from this method gives reasonable agreement with radiative forcing calculations that allow for stratospheric adjustment.
The method suggests a practical distinction between forcing and feedback to be made on the basis of time scale, namely, that we should regard all radiative changes as forcing that come about rapidly compared with the time scale of climate change as measured by ΔT, for instance within much less than a year. Our definition of forcing due to CO2 includes not only its instantaneous greenhouse effect and stratospheric adjustment, but any other rapid adjustment of the system that may occur, in particular due to clouds. It is a familiar idea that the radiative effect of cloud changes may be counted as forcing since this is the case for the indirect and semidirect effects of aerosols. In all of the GCMs examined in the present work, CO2 also is found to induce small but statistically significant cloud forcing. Longwave forcing is usually negative and shortwave usually positive, so they compensate to some degree, but the sum is negative in most models. In some models the induced shortwave forcing is negative, leading to a substantially reduced net forcing by CO2 and a low ΔT2×. Extending the regression method to examine geographical variation provides further evidence for cloud changes.
We regard these cloud changes as a tropospheric adjustment of the forcing due to CO2. The usual interpretation would be to call them cloud feedbacks. We show, on the contrary, that shortwave cloud feedback is statistically insignificant in nearly all the models examined here, and radiative change caused by clouds depends on CO2 change rather than on the magnitude of global climate change (measured by ΔT). Further studies would be useful of how the differences in cloud parameterizations and simulated climates among models lead to different tropospheric adjustments.
We propose that the net forcing, including both tropospheric and stratospheric adjustment, could be called “effective” forcing, to distinguish it from “instantaneous” forcing. We have shown that this definition of forcing agrees fairly well with results from the method introduced by Hansen et al. (2002), and developed by Shine et al. (2003) and Hansen et al. (2005), of preventing climate feedback by fixing surface conditions in an experiment with the forcing agent included, in which case forcing can be diagnosed as the change in the TOA radiative flux. This agreement of methods is reasonable because, in different ways, they are both estimating the forcing as the change in TOA radiative flux when no global-mean temperature response to the forcing agent has occurred. A more detailed comparison of the methods is required to establish the differences. Since the surface temperatures are locally fixed in the method of Shine et al. and Hansen et al., the tropospheric adjustment, including changes in surface heat fluxes, may not be the same as implied by the regression method.
On account of tropospheric adjustment, the model spread in ΔT2× may be partly due to a spread of CO2 forcing, rather than entirely due to differences in the climate feedback parameter. Although this reattribution makes no difference to prediction of steady-state climate change, a correct separation of forcing and feedback is necessary for predicting time-dependent climate change. As shown in section 1, different pathways result from different choices of (F, α) that have the same ΔT2× = f /α: this is relevant to the use of simple climate models to emulate AOGCMs, for example. The possibility of tropospheric adjustment also affects interpretation of past change. If clouds respond directly to tropospheric adjustment due to CO2, they will “keep up” with rising concentrations, rather than lagging behind with global temperature change; cloud changes in recent decades may be part of the CO2 forcing rather than a response to it.
Because of these implications, the correct distinction of forcing and feedback is not purely theoretical. If tropospheric adjustment is a real effect, it complicates the definition of these concepts. Rather than seeing this as an issue of terminology, let us concentrate on what is practically important. There are two main points. First, the distinction is most useful if it is made in such a way that the feedback parameter is the same for all kinds of forcing. Recent work (Shine et al. 2003; Hansen et al. 2005) suggests that including noninstantaneous effects in the forcing does have that effect. Second, if we include noninstantaneous effects, the distinction is bound to become rather blurred because there is no longer a clean separation into two time scales that we can obviously designate as forcing and response. The “adjustments” probably occur on various time scales. Our conclusion is therefore that analysis of the response to forcing should not be limited to the final steady states. Examination of time-dependent changes could provide further insight into the systematic uncertainty in model projections of climate change.
Acknowledgments
We thank Karl Taylor, Piers Forster, Glen Harris, Rowan Sutton, Buwen Dong, Jeff Kiehl, and Hugo Lambert for useful discussions, William Ingram and Jason Lowe for careful comments, which helped to improve the clarity and precision of the manuscript, and the referees for their positive and helpful reviews. Work at the Hadley Centre was supported by the U.K. Department for Environment, Food and Rural Affairs under Contract PECD 7/12/37 and by the Government Meteorological Research and Development Programme. Work at the Walker Institute was supported by the Climate Programme of the National Centre for Atmospheric Science (NCAS). We acknowledge the modeling groups for making their simulations available for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the CMIP3 and CFMIP model output, and the WCRP’s Working Group on Coupled Modelling (WGCM) for organizing the model data analysis activity. The WCRP CMIP3 and CFMIP multimodel datasets are supported by the Office of Science, U.S. Department of Energy.
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The evolution of annual-mean global-mean radiative fluxes N at the TOA with annual-mean global-mean surface air temperature change ΔT in experiments in which CO2 is instantaneously quadrupled using the standard and modified HadSM3 slab models; the results have been divided by 2 before plotting to make them applicable to 2 × CO2. The symbols show annual means and the lines are regressions.
Citation: Journal of Climate 21, 1; 10.1175/2007JCLI1834.1
(a)–(h) The evolution of annual-mean global-mean radiative fluxes N at the TOA with annual-mean global-mean surface air temperature change ΔT in experiments with various slab models in which CO2 is instantaneously doubled. Note that the panels all have different axis ranges. The key for the line styles and symbols is as in Fig. 1.
Citation: Journal of Climate 21, 1; 10.1175/2007JCLI1834.1
Comparison of components of forcing for 2 × CO2 evaluated using the regression method of Gregory et al. (2004) and the fixed SST method of Hansen et al. (2002) in two versions of the HadSM3 slab model.
Citation: Journal of Climate 21, 1; 10.1175/2007JCLI1834.1
Geographical distribution of components of 2 × CO2 forcing (W m−2) in standard HadSM3 (two left-hand columns) and modified HadSM3 (two right-hand columns) evaluated using the regression method of Gregory et al. (2004) and the fixed SST method of Hansen et al. (2002). Areas where the forcing is not significantly different from zero at the 5% level are uncolored.
Citation: Journal of Climate 21, 1; 10.1175/2007JCLI1834.1
The evolution of annual-mean global-mean surface fluxes with annual-mean global-mean surface air temperature change in an experiment with the standard HadSM3 model in which CO2 is instantaneously quadrupled. The results have been divided by 2 so that they apply to 2 × CO2. All fluxes are positive downward. Negative downward latent heat implies positive evaporation.
Citation: Journal of Climate 21, 1; 10.1175/2007JCLI1834.1
Summary of notation.
Regression of global-mean radiative fluxes Ni at the top of the atmosphere against global-mean surface air temperature ΔT in experiments with various slab models in which CO2 is instantaneously doubled: F is the intercept on the N axis (the forcing) and Y is the slope (the feedback parameter). (In the HadSM3 experiments, CO2 is quadrupled, and results for F have been divided by 2.) The uncertainties for individual models are ±1 standard errors from the regression. The uncertainties for the ensemble are ±1 standard deviations. The names of the models from the CMIP3 database are more properly the names of AOGCMs with the same atmosphere component as the slab models, e.g., “GISS-ER” here refers to the GISS-E atmosphere model coupled to a slab ocean, although actually GISS-ER is an AOGCM that includes GISS-E. The atmosphere model of HadSM3 is the same as that of the UKMO-HadCM3 AOGCM in the CMIP3 database. The atmosphere model of MIROC3.2(LS) is the same as that of the MIROC3.2(medres) AOGCM in the CMIP3 database, but MIROC3.2(HS) is not the same as MIROC3.2(hires) in the CMIP3 database.
Comparison of components of forcing for 2 × CO2 evaluated using the regression method of Gregory et al. (2004) and the fixed SST method of Hansen et al. (2002) in two versions of the HadSM3 slab model. The symbols indicate whether the methods are statistically consistent (≃) or not (≠)
