Abstract

A simple technique is proposed for calculating global mean climate forcing from transient integrations of coupled atmosphere–ocean general circulation models (AOGCMs). This “climate forcing” differs from the conventionally defined radiative forcing as it includes semidirect effects that account for certain short time scale responses in the troposphere. First, a climate feedback term is calculated from reported values of 2 × CO2 radiative forcing and surface temperature time series from 70-yr simulations by 20 AOGCMs. In these simulations carbon dioxide is increased by 1% yr−1. The derived climate feedback agrees well with values that are diagnosed from equilibrium climate change experiments of slab-ocean versions of the same models. These climate feedback terms are associated with the fast, quasi-linear response of lapse rate, clouds, water vapor, and albedo to global surface temperature changes. The importance of the feedbacks is gauged by their impact on the radiative fluxes at the top of the atmosphere. Partial compensation is found between longwave and shortwave feedback terms that lessens the intermodel differences in the equilibrium climate sensitivity. There is also some indication that the AOGCMs overestimate the strength of the positive longwave feedback.

These feedback terms are then used to infer the shortwave and longwave time series of climate forcing in twentieth- and twenty-first-century simulations in the AOGCMs. The technique is validated using conventionally calculated forcing time series from four AOGCMs. In these AOGCMs the shortwave and longwave climate forcings that are diagnosed agree with the conventional forcing time series within ∼10%. The shortwave forcing time series exhibit order of magnitude variations between the AOGCMs, differences likely related to how both natural forcings and/or anthropogenic aerosol effects are included. There are also factor of 2 differences in the longwave climate forcing time series, which may indicate problems with the modeling of well-mixed greenhouse gas changes. The simple diagnoses presented provides an important and useful first step for understanding differences in AOGCM integrations, indicating that some of the differences in model projections can be attributed to different prescribed climate forcing, even for so-called standard climate change scenarios.

1. Introduction

With both the increase in computer power and a more complete representation of the many interactions in the climate system, climate models have become increasingly complex. Consequently, understanding their responses can often be just as difficult as understanding climate change in the real world. Radiative forcing and climate sensitivity were key concepts developed in the early days of climate modeling to aid understanding of the global mean temperature response (Houghton et al. 2001). These concepts remain valuable today, but forcing and climate sensitivity are more difficult to diagnose in more advanced models (Gregory et al. 2004).

In this paper we propose and validate a methodology for calculating both the global mean climate forcing time series and the climate feedback in coupled atmosphere–ocean general circulation model (AOGCM) simulations. We analyze recent simulations carried out in support of the Intergovernmental Panel of Climate Change (IPCC) Fourth Assessment Report. Importantly, these global time series can be calculated from routinely archived model output. To aid the understanding of intermodel differences in both twentieth- and twenty-first-century simulations, we also diagnose forcings and climate feedback terms from the current AOGCMs and provide a brief discussion of some of the more interesting findings. At each stage of our analysis, we analyze all available AOGCM output in the IPCC database.

2. Approach

The approach relies on a simple globally averaged linear-forcing feedback model. We adopt the Gregory et al. (2004) terminology, where the net flux imbalance of the climate system (N) is related to the radiative forcing (Q), a climate feedback term (Y), and the globally averaged surface temperature change (ΔTs):

 
formula

The climate feedback factor (Y) is the inverse of the climate sensitivity. As interpreted here, the equation is approximate as it only considers climate feedbacks that turn out to be proportional to global mean temperature changes (i.e., it considers the part of the energy budget from clouds, water vapor, surface albedo, and lapse rate change that are proportional to global mean temperature change). These temperature changes are largely governed by the ocean mixed layer relaxation time. Therefore this equation may not accurately reflect the impact of more slowly responding aspects of climate, such as ice sheets or the carbon cycle.

Estimates of radiative forcing, linear global feedback, and climate sensitivity are commonly used to summarize the causes of and to quantify the reasons for climate change, as well as to predict quantitatively future climate change. Several papers, however, suggest that these simple forcing response relationships are both inaccurate and unhelpful (e.g., Boer and Yu 2003; Aires and Rossow 2003; and especially the critical review of Stephens 2005). Nevertheless, we contend that a simple model remains useful, and furthermore such models provide a useful framework for more regionally based feedback analyses, such as the linear global feedback analysis commonly used to examine and diagnose model feedback differences (e.g., Cess et al. 1996; Colman 2003; Soden and Held 2006; Bony et al. 2006). These papers and others provide many useful insights into cloud, water vapor, and other feedbacks, and the way they are represented within climate models. Global mean radiative forcing has also been extensively used to compare climate change mechanisms (e.g., Houghton et al. 2001). Even in today’s sophisticated GCMs, global mean radiative forcing is a useful predictor of global mean temperature response, and forcings with very different spatial patterns can have similar patterns of surface temperature change (e.g., Forster et al. 2000; Joshi et al. 2003; Hansen et al. 2005). Reporting findings from several studies, Houghton et al. (2001) concluded that responses to individual radiative forcings could be linearly added to gauge the global mean response, but not necessarily the regional response. Since then, studies based on both equilibrium and/or transient integrations by several different GCMs have found no evidence of important nonlinearities in the global-scale climate response to changing concentrations of greenhouse gases and sulfate aerosols (Boer and Yu 2003; Gillett et al. 2004; Matthews et al. 2003; Meehl et al. 2004). Two of these studies also examined several other forcing agents without finding evidence of a nonlinear response (Meehl et al. 2004; Matthews et al. 2003). In all four studies, even the regional responses typically add linearly. However, some studies have found marked nonlinearity for large negative solar radiative forcing (e.g., Hansen et al. 2005). For the radiative forcings analyzed here, however, which are relatively small and positive, we believe a linear-forcing-response assumption is justified.

Using Eq. (1), Gregory et al. (2004) employed a simple regression technique to estimate in slab and coupled versions of the Hadley Centre GCM both the global mean climate forcing and the climate sensitivity from experiments with constant forcing. Conceptually the energy balance (N) is perturbed by an initial forcing (Q); this in turn causes the climate to respond (ΔTs), eventually returning N to zero at a new equilibrium state. Gregory et al. (2004) regressed N against ΔTs to diagnose Q from the intercept and Y from the slope of the regression line. They found that the estimate of both climate forcing (Q) and climate feedback (Y) agreed with that calculated by other methods. They also noted, however, that this “climate forcing” could be different from the conventional radiative forcing as it allowed aspects of short-term climate response in the troposphere (e.g., a semidirect aerosol effect). As usually defined, radiative forcing does not allow the tropospheric climate state to change, but it does allow for the stratosphere to adjust (Houghton et al. 2001).

Forster and Gregory (2006) extended the Gregory et al. (2004) approach to look at transient observations of the terms in Eq. (1). They specified a time series for Q and then used Eq. (1) to diagnose Y from transient observations of N and ΔTs during 1985–1996, when N was measured by the Earth Radiation Budget Satellite. This paper extends the same methodology one stage further. It employs Eq. (1) to diagnose both Y and Q in transient integrations of AOGCMs. First, Y values are diagnosed from integrations where CO2 is increased by 1% yr−1 and where the forcing due to a doubling of CO2 concentration is known. Then these Y values are used to diagnose the climate forcing time series (Q) in both twentieth-century integrations and the Special Report on Emission Scenarios (SRES) A1B (Nakicenovic and Swart 2000) future scenario integrations. In extending the methodology to transient integrations with changes in multiple radiative forcing agents, we make two assumptions in addition to those in Gregory et al. (2004): we assume that the climate sensitivity does not vary over the time period of the integration and also that the climate sensitivity associated with multiple forcing agents is similar to that for carbon dioxide alone.

On long time scales (∼500 yr), there is evidence from AOGCMs that climate sensitivity can evolve with time. To monitor the changes, an “effective” climate sensitivity has been used to describe an instantaneous climate sensitivity diagnosed from the strengths of climate feedbacks at any point in the integration. Senior and Mitchell (2000) and Gregory et al. (2004) found in different versions of the Hadley Centre model that the effective climate sensitivity increased with time and that this was associated with the deep ocean slowly warming. In the Third Hadley Centre Coupled Ocean–Atmosphere General Circulation Model (HadCM3) the effective climate sensitivity increased after ∼500 yr (Gregory et al. 2004). We assume that for the ∼200-yr integrations described here, climate sensitivity is invariant for each AOGCM: tests described in section 5 of this paper support this assumption.

The relative impact of various forcing agents on climate is quantified by their so-called efficacy—the response of climate to a given forcing agent relative to its response to an equivalent radiative forcing of carbon dioxide (e.g., Hansen et al. 2005). Slab GCM integrations have shown that while different forcing mechanisms can have different efficacies (e.g., Joshi et al. 2003; Hansen et al. 2005), realistic twentieth-century forcing mechanisms have efficacies within ∼25% of that associated with an equivalent carbon dioxide change. Furthermore, as the majority of the radiative forcing in the twentieth and twenty-first centuries was, and is expected to be, associated with carbon dioxide, the efficacy of the combined forcings over these integrations would be expected to be close to 1.0. Hansen et al. (2005) found, for example, an efficacy for combined twentieth-century forcings of between 0.99 and 1.11 (depending on their evaluation methodology). For our purposes, these findings therefore justify the use of a single value for climate sensitivity.

In our analysis, the efficacy cannot be determined specifically, but instead it is incorporated into the forcing estimate (i.e., our estimate of forcing is effectively scaled by the efficacy). Likewise, because the semidirect effect, along with stratospheric adjustment, involve feedbacks that are generally not proportional to surface temperature response, incorporating them into the adjusted forcing, which is inferred by our method, allows one to use Eq. (1) to predict future climate change more accurately. As pointed out by Shine et al. (2003) and Hansen et al. (2005), it is the effective climate forcing, after stratospheric adjustment and after accounting for various semidirect effects and different efficacies, which is most accurate in estimating future climate responses. Imagine, for example, that the atmosphere alone (perhaps through some cloud change unrelated to any surface temperature response) quickly responds to a large radiative forcing to restore the flux imbalance at the top of the atmosphere, yielding a small effective climate forcing. In this case the ocean would never get a chance to respond to the initial radiative forcing, so the resulting climate response would be small and this would be consistent with our diagnosed effective climate forcing rather than the conventional radiative forcing.

3. Data

This study employs AOGCM model output obtained from the IPCC data archive (see online at http://www-pcmdi.llnl.gov/ipcc/about_ipcc.php). Among the variables found in this archive are monthly mean surface temperature and shortwave (SW) and longwave (LW) components of N (measured at the top of the atmosphere). As of March 2006, each model analyzed in this study had archived a preindustrial control integration, a 1% yr−1 CO2 increase integration, a twentieth-century integration, and a SRES A1B integration. The SRES A1B integration is forced by one of the standard twenty-first-century scenarios for increases in greenhouse gases (Nakicenovic and Swart 2000). A long preindustrial control integration was run for each model. At some point partway through the control integration, the 1% yr−1 CO2 increase simulation was initiated, as was the twentieth-century-forcing simulation.1 The SRESA1B simulation then started from the endpoint of the twentieth-century simulation. Although results from multiple simulations were available from some models, only one of the ensemble members (run 1) from each model is analyzed here.2 To correct for unforced model drift, the preindustrial control simulations are run for at least 220 yr beyond the time when the other scenarios began. For each model we diagnose the linear drift in N and ΔTs from the corresponding long control simulation and this drift was subsequently subtracted from the corresponding segments of the forced integration time series. Drifts were smaller than 10% of the climate change signal in all but five of the models analyzed. Results reported here are based exclusively on global and annual averages calculated from gridded monthly mean data. Table 1 lists the models and summarizes the forcing agents included in each. (Further details of the models used and the integrations can be found online at http://www-pcmdi.llnl.gov/ipcc/info_for_analysts.php.)

Table 1.

The models used in this paper and the summary of their included radiative forcings (indicated by a “Y”), following Santer et al. (2005): well-mixed greenhouse gases (G), tropospheric and stratospheric ozone (O), sulfate aerosol direct effects (SD); sulfate aerosol indirect effects (SI), black carbon (BC), organic carbon (OC), mineral dust (MD), sea salt (SS), land use change (LU), solar irradiance (SO), volcanic aerosols (VL), and volcanic aerosols modeled as a solar constant change (Y*). (Further model details can be found online at http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php)

The models used in this paper and the summary of their included radiative forcings (indicated by a “Y”), following Santer et al. (2005): well-mixed greenhouse gases (G), tropospheric and stratospheric ozone (O), sulfate aerosol direct effects (SD); sulfate aerosol indirect effects (SI), black carbon (BC), organic carbon (OC), mineral dust (MD), sea salt (SS), land use change (LU), solar irradiance (SO), volcanic aerosols (VL), and volcanic aerosols modeled as a solar constant change (Y*). (Further model details can be found online at http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php)
The models used in this paper and the summary of their included radiative forcings (indicated by a “Y”), following Santer et al. (2005): well-mixed greenhouse gases (G), tropospheric and stratospheric ozone (O), sulfate aerosol direct effects (SD); sulfate aerosol indirect effects (SI), black carbon (BC), organic carbon (OC), mineral dust (MD), sea salt (SS), land use change (LU), solar irradiance (SO), volcanic aerosols (VL), and volcanic aerosols modeled as a solar constant change (Y*). (Further model details can be found online at http://www-pcmdi.llnl.gov/ipcc/model_documentation/ipcc_model_documentation.php)

4. CO2 radiative forcing

Although radiative forcings are not routinely calculated in coupled models, nine of the 20 models used here have submitted a calculation for the 2 × CO2 radiative forcing to the IPCC model data archive. These radiative forcings are presented in Table 2, along with the line-by-line model estimates of Myhre et al. 1998 (used for the Houghton et al. 2001 standard). Instantaneous and adjusted (i.e., after stratospheric adjustment) radiative forcings for clear skies and all skies were calculated by the modeling groups. The average forcing from the nine models agrees very well with the line-by-line model estimate. However, there is a ∼25% spread in the LW radiative forcing between models, and, where included, models have very different SW radiative forcings. Also bear in mind that the other modeling groups have not recorded radiative forcings, so the 20 model spread could still be larger.

Table 2.

The 2 × CO2 radiative forcings computed by the AOGCM groups. The LW adjusted all-sky (ADJ) and instantaneous clear sky (CLR-INST) are shown, where “adjusted” refers to forcing calculated after stratospheric adjustment. The SW instantaneous all-sky forcing (INST) and NET adjusted forcing (ADJ) are also shown. The Myhre et al. (1998) values are from a reference line-by-line model. These reference RF values are assumed for AOGCMs that do not diagnose their own RF values

The 2 × CO2 radiative forcings computed by the AOGCM groups. The LW adjusted all-sky (ADJ) and instantaneous clear sky (CLR-INST) are shown, where “adjusted” refers to forcing calculated after stratospheric adjustment. The SW instantaneous all-sky forcing (INST) and NET adjusted forcing (ADJ) are also shown. The Myhre et al. (1998) values are from a reference line-by-line model. These reference RF values are assumed for AOGCMs that do not diagnose their own RF values
The 2 × CO2 radiative forcings computed by the AOGCM groups. The LW adjusted all-sky (ADJ) and instantaneous clear sky (CLR-INST) are shown, where “adjusted” refers to forcing calculated after stratospheric adjustment. The SW instantaneous all-sky forcing (INST) and NET adjusted forcing (ADJ) are also shown. The Myhre et al. (1998) values are from a reference line-by-line model. These reference RF values are assumed for AOGCMs that do not diagnose their own RF values

Houghton et al. (2001) and Myhre et al. (1998) give a simple, but accurate, formula for the radiative forcing from CO2 changes of QCO2(NET) = 5.35. ln(C/Co), where Co is the unperturbed concentration and C is the perturbed concentration of CO2. This formula gives the 2 × CO2 radiative forcing value shown in Table 2. We use the SW and LW split of the 2 × CO2 NET forcing from Myhre et al. (1998; see Table 2) with this simple formula to obtain LW and SW time series of radiative forcing for a 1% yr−1 CO2 increase. Thus, the model radiative forcing time series are represented by QCO2(LW) = fyear[5.57.ln(1.01)]; QCO2(SW) = fyear[−0.22.ln(1.01)], where year is the number of years since the start of the integration (up to 70 yr, the time of CO2 doubling) and f is the ratio of the models’ 2 × CO2 radiative forcing estimate to the IPCC/Myhre et al. (1998) value. Many models continued their integration for an additional 150 yr, keeping CO2 constant after year 70. For models that did not record their 2 × CO2 radiative forcing, time series were generated assuming f = 1.

5. Climate sensitivities

Twenty AOGCMs provided flux and temperature data from their 1% yr−1 CO2 increase integration, allowing us to calculate the feedback strength, as gauged by Y. After the drift in the control climate integration was subtracted from the 1% yr−1 CO2 integration, the first 70 yr of the N and ΔTs time series were calculated as the difference from the beginning of the runs. With Eq. (1) applied separately to the SW and LW components of radiation, values of Y and their statistical uncertainty are calculated, based on the Q time series from section 4, by regressing QN against ΔTs (Fig. 1 and Table 3). Ordinary least squares (OLS) regression is used. The autocorrelations in the QN time series were high. Lag-1 correlations were typically 0.9 in the LW and 0.8 in the SW. These autocorrelations are accounted for when evaluating the statistical uncertainties. Forster and Gregory (2006) give extensive justification for the use of OLS regression within this climate modeling framework. Their argument is based on the reasoning that ΔTs is the likely driver for most of the changes in N. In practice the choice of regression model made little difference to the overall results, especially in the LW.

Fig. 1.

The OLS regression of QN vs ΔTs, used to diagnose the Y terms, is shown for two models, based on the first 70 yr of data from their 1% yr−1 CO2 increase integrations. (top) CGCM3.1(T47) had one of the better constrained Y estimates. (bottom) In contrast, the FGOALS-g1.0 model had the least constrained estimate. (left to right) The Y–LW, Y–SW, and Y–NET regressions. The titles of each plot show the derived Y value and its 1σ uncertainty range, as calculated by the OLS regression.

Fig. 1.

The OLS regression of QN vs ΔTs, used to diagnose the Y terms, is shown for two models, based on the first 70 yr of data from their 1% yr−1 CO2 increase integrations. (top) CGCM3.1(T47) had one of the better constrained Y estimates. (bottom) In contrast, the FGOALS-g1.0 model had the least constrained estimate. (left to right) The Y–LW, Y–SW, and Y–NET regressions. The titles of each plot show the derived Y value and its 1σ uncertainty range, as calculated by the OLS regression.

Table 3.

In the first block of numbers AOGCM results are given for the diagnosed climate feedback (Y) terms and the 1 std dev uncertainties (see section 5). Note that all but the last column of values in this block come from the 1% yr−1 CO2 increase integrations. The values in the last column of this block come from doubled-CO2 equilibrium experiments performed with atmospheric models coupled to slab oceans. For these calculations 2 × CO2 radiative forcing estimates are taken from Table 2. The next block contains the diagnosed climate forcing values (Q) for year 2100 relative to preindustrial times (see section 6) obtained from the SRES A1B simulations. Values in the rightmost column are the globally averaged surface temperature changes at year 2100 relative to preindustrial times (see section 7). For comparison the last row in the table presents forcing values for the SRES A1B scenario presented in Houghton et al. (2001).

In the first block of numbers AOGCM results are given for the diagnosed climate feedback (Y) terms and the 1 std dev uncertainties (see section 5). Note that all but the last column of values in this block come from the 1% yr−1 CO2 increase integrations. The values in the last column of this block come from doubled-CO2 equilibrium experiments performed with atmospheric models coupled to slab oceans. For these calculations 2 × CO2 radiative forcing estimates are taken from Table 2. The next block contains the diagnosed climate forcing values (Q) for year 2100 relative to preindustrial times (see section 6) obtained from the SRES A1B simulations. Values in the rightmost column are the globally averaged surface temperature changes at year 2100 relative to preindustrial times (see section 7). For comparison the last row in the table presents forcing values for the SRES A1B scenario presented in Houghton et al. (2001).
In the first block of numbers AOGCM results are given for the diagnosed climate feedback (Y) terms and the 1 std dev uncertainties (see section 5). Note that all but the last column of values in this block come from the 1% yr−1 CO2 increase integrations. The values in the last column of this block come from doubled-CO2 equilibrium experiments performed with atmospheric models coupled to slab oceans. For these calculations 2 × CO2 radiative forcing estimates are taken from Table 2. The next block contains the diagnosed climate forcing values (Q) for year 2100 relative to preindustrial times (see section 6) obtained from the SRES A1B simulations. Values in the rightmost column are the globally averaged surface temperature changes at year 2100 relative to preindustrial times (see section 7). For comparison the last row in the table presents forcing values for the SRES A1B scenario presented in Houghton et al. (2001).

Figure 1 shows the results for the two models that had the best and worst fits to Y. All the models began their 1% yr−1 integration close to equilibrium (the origin on the graph). The derived Y values and their uncertainties are shown for all models in Table 3. Most models had a very good straightline fit to Y–LW, as illustrated by the coupled GCM version 3.1 (CGCM3.1) (T47) (Fig. 1). Likewise, the Y–NET value had small statistical uncertainties (Fig. 1 and Table 3). Importantly, no model obviously departed from a straightline fit; that is, Y appears constant over these 70 yr.

Even when the complete 220-yr integration was included in the analysis, most models still exhibited a constant Y–LW. Exceptions are shown in Fig. 2, where three models clearly exhibit temporal variation in Y–LW. Data after 70 yr were not available from the Hadley Centre, therefore we were unable to test the nonlinearities previously found with its models (see section 2). The Geophysical Fluid Dynamics Laboratory (GFDL) Coupled Model version 2.0 (CM2.0) has a response very similar to GFDL-CM2.1. In the Centre National de Recherches Météorologiques (CNRM) Coupled Model version 3 (CM3) the slope changes after 70 yr, which likely indicates that the specified forcing could be in error: we found that reducing the LW forcing by 10% improved the straightline fit. Only the Goddard Institute for Space Studies Model E-H (GISS-EH) shows a large departure from a constant value for Y–LW. Interestingly, the GISS Model E-R (GISS-ER; not shown) does not exhibit this nonlinearity. As there is no noticeable change in gradient after 70 yr and the 2 × CO2 forcing is known (see Table 2), errors in forcing are unlikely to be the cause. The variation in Y could be explained if the model’s ocean did not start near quasi equilibrium at the beginning of the integration and was undergoing significant adjustment over the analysis period (see Senior and Mitchell 2000). Analysis of global mean temperature trends in the preindustrial control integrations supports this theory. Over a 200-yr period the global mean surface temperature in the GISS EH model’s control integration cools by about 1 K, while the GISS ER model’s surface temperature does not have a trend.

Fig. 2.

Same as in Fig. 1, but for four models, based on 220 yr of data from their 1% yr−1 CO2 increase integration. In these simulations CO2 is held constant after year 70 when CO2 concentration reaches twice its initial value. (left to right) The Y–LW, Y–SW, and Y–NET regressions. The titles of each plot show the derived Y value and its 1σ uncertainty range, as calculated by the OLS regression. The first three rows are models that exhibited nonlinearities in their derived values. The CCSM3 model shown in the fourth row is illustrative of the majority of models that did not exhibit marked nonlinearities.

Fig. 2.

Same as in Fig. 1, but for four models, based on 220 yr of data from their 1% yr−1 CO2 increase integration. In these simulations CO2 is held constant after year 70 when CO2 concentration reaches twice its initial value. (left to right) The Y–LW, Y–SW, and Y–NET regressions. The titles of each plot show the derived Y value and its 1σ uncertainty range, as calculated by the OLS regression. The first three rows are models that exhibited nonlinearities in their derived values. The CCSM3 model shown in the fourth row is illustrative of the majority of models that did not exhibit marked nonlinearities.

For a further check of our results we compare the diagnosed Y–NET values given in Table 3 to values computed from actual equilibrium experiments from a slab version of the corresponding model. The global mean equilibrium surface temperature changes for 11 models were available. From the time series generated by each of these models, we selected years following the initial transient warming phase. The time series of annually and globally averaged surface temperature was plotted and the post “transient warming” years were identified by visual inspection. Then for those selected equilibrium periods, we calculated the difference between the multiyear mean for the control and 2 × CO2 runs, yielding the equilibrium temperature change. The NET radiative forcing from section 4 is then divided by these temperature changes, to obtain the Y–NET (2 × CO2) values that are shown in Table 3. Within the quoted statistical uncertainty there is an approximate correspondence between these equilibrium Y–NET (2 × CO2) values and the diagnosed Y–NET values in the table. Agreement would not be expected to be perfect, as the presence of an ocean model could readily modify the atmospheric feedbacks (Gregory et al. 2004).

Figure 3 graphically illustrates the range of derived Y values (from the 70-yr integrations) and their uncertainties. The figure compares Y values to the uncertain estimate from Earth Radiation Budget observations made in Forster and Gregory (2006). In the models, the range of Y–LW and Y–NET values is less than a factor of 2. Also, these values are always smaller than 3.3 W m−2 K−1, the value of Y for a blackbody response (sometimes referred to as the Stefan–Boltzmann radiative damping). This indicates a positive LW feedback. For some models their large positive LW feedback (smaller positive Y–LW) does not appear consistent with the Y–LW found from the observationally based estimate (Fig. 3). Forster and Gregory (2006) note that the sign of the observationally based estimate of LW cloud feedback is negative, in disagreement with most models, but the Y values derived from the observations are very uncertain.

Fig. 3.

(a) The Y–LW and Y–SW values and (b) Y–LW and Y–NET values derived from the 1% yr−1 CO2 increase model integrations. Shown as horizontal and vertical lines centered on each model estimate are 1σ uncertainty ranges from the OLS regression. Estimates based on observations are shown in black (from the work of Forster and Gregory 2006); these estimates have errors that extend beyond the plot boundaries.

Fig. 3.

(a) The Y–LW and Y–SW values and (b) Y–LW and Y–NET values derived from the 1% yr−1 CO2 increase model integrations. Shown as horizontal and vertical lines centered on each model estimate are 1σ uncertainty ranges from the OLS regression. Estimates based on observations are shown in black (from the work of Forster and Gregory 2006); these estimates have errors that extend beyond the plot boundaries.

For all models, SW feedback is positive (i.e., Y–SW is negative). These values, however, are less constrained by the regression than the LW values, and for a few models the statistical uncertainties are too large to constrain the sign (Figs. 1, 2, 3 and Table 3). Forster and Gregory (2006) also noted similar difficulties in constraining Y-SW. Interestingly, there is some compensation between Y–SW and YLW, that is, those models with the largest positive SW feedback also have the smallest positive LW feedback (Fig. 3, Table 3). This may be attributable to differing strengths of their cloud amount feedback. In most models cloud fraction decreases as surface temperatures rise, this leads to a positive SW cloud feedback and negative LW cloud feedback (Cess et al. 1996; Bony et al. 2006). The 2 × CO2 equilibrium Y range (Fig. 3, Table 3) is similar to that from the range of model sensitivities quoted in Houghton et al. (2001).

The regression technique we use to derive Y values works considerably better here than it did for the constant forcing experiments in Gregory et al. (2004). In their experiments, N approached equilibrium so rapidly that only a few data points were available to constrain the statistics of the regression line. In the 1% yr−1 CO2 increase transient integrations of this paper, the Y values are much better constrained. There is also no evidence of a change in Y values over the 70-yr time period of the CO2 increase, and most models had no evidence of a change in Y over all +200 yr of the integration. These findings suggest that in most AOGCMs our simple forcing response concepts are still applicable. However, as long-term data were not available from the Hadley Centre models to evaluate Y values after 70 yr and the GISS EH model exhibited a significant nonlinear response, caution needs to be used when assuming an invariant Y, as we do in section 6 of this paper.

6. Derived climate forcings

In the final part of this paper we combine the N and ΔTs values from the twentieth- and twenty-first-century integrations (∼1880–2100) with the Y values already diagnosed in section 5 to find the time series of climate forcings, presented in Figs. 4 and 5. The models from section 5 contributed flux and temperature data for both a twentieth-century integration and an SRES A1B integration. Using these data, LW and SW components of the climate forcing Q are derived separately from Eq. (1). The total SW forcing includes a component due to any changes in the solar constant. This solar forcing is shown as the blue lines on the figures, as it can be diagnosed directly from changes in the models’ downward SW flux at the top of the atmosphere. For comparison, the figure also shows the radiative forcing time series for the twentieth century from Myhre et al. (2001) and for the twenty-first-century SRESmA1B scenario from Houghton et al. (2001, their appendix 2). A summary of the climate forcing changes over 50- and 100-yr intervals is shown in Fig. 6, and Table 3 shows, relative to the preindustrial control, the total climate forcing and surface temperature change up to year 2100.

Fig. 4.

Black lines show time series from 1850 to 2000 of diagnosed SW and LW climate forcing relative to the preindustrial control simulation. Results from 20 climate models and the Myhre et al. (2001) estimate are shown. Preindustrial values are ∼1850 for most models and 1750 for Myhre et al. (2001). The model name refers to the time series below it. Each of the time series begins near the corresponding zero line, and tick intervals are 1 W m−2. (left) The solar constant component, which is included in the plotted total SW climate forcing, is also shown separately as the blue line. For four models independent estimates of the radiative forcing are shown as the magenta lines

Fig. 4.

Black lines show time series from 1850 to 2000 of diagnosed SW and LW climate forcing relative to the preindustrial control simulation. Results from 20 climate models and the Myhre et al. (2001) estimate are shown. Preindustrial values are ∼1850 for most models and 1750 for Myhre et al. (2001). The model name refers to the time series below it. Each of the time series begins near the corresponding zero line, and tick intervals are 1 W m−2. (left) The solar constant component, which is included in the plotted total SW climate forcing, is also shown separately as the blue line. For four models independent estimates of the radiative forcing are shown as the magenta lines

Fig. 5.

Black lines show time series of diagnosed SW and LW climate forcing for the twenty-first century SRES A1B scenario. Results from 20 climate models and the Houghton et al. (2001) estimate based on SRES A1B tables are also shown. The model name refers to the time series below it. Each of the time series begins near the corresponding zero line, and tick intervals are 1 W m−2. Data in these time series have been smoothed with a 10-yr running mean filter. The magenta lines show the statistical error in the climate forcing diagnostic. These forcing time series are derived using the 1σ statistical uncertainty values of Y–SW and Y–LW in Eq. (1). (left) The solar constant component, which is included in the plotted SW climate forcing, is also shown separately as the blue line.

Fig. 5.

Black lines show time series of diagnosed SW and LW climate forcing for the twenty-first century SRES A1B scenario. Results from 20 climate models and the Houghton et al. (2001) estimate based on SRES A1B tables are also shown. The model name refers to the time series below it. Each of the time series begins near the corresponding zero line, and tick intervals are 1 W m−2. Data in these time series have been smoothed with a 10-yr running mean filter. The magenta lines show the statistical error in the climate forcing diagnostic. These forcing time series are derived using the 1σ statistical uncertainty values of Y–SW and Y–LW in Eq. (1). (left) The solar constant component, which is included in the plotted SW climate forcing, is also shown separately as the blue line.

Fig. 6.

Changes in the LW and SW climate forcing calculated from the 20 models and from Myhre et al. (2001) or Houghton et al. (2001), indicated by triangles. These forcing changes over 50 or 100 yr are differences between two 9-yr averages centered on the start and end years given.

Fig. 6.

Changes in the LW and SW climate forcing calculated from the 20 models and from Myhre et al. (2001) or Houghton et al. (2001), indicated by triangles. These forcing changes over 50 or 100 yr are differences between two 9-yr averages centered on the start and end years given.

The climate forcing time series we derive are contaminated by changes in N that are unrelated to surface temperature change. These fluctuations are largest in the SW and in the models where the same variations in N contributed most to the uncertainty in Y. Their effect on the forcing time series can clearly be seen in the unsmoothed data presented in Fig. 4. They appear to be of a small enough magnitude and occur over a sufficiently short time scale not to mask the major features of the time series. The diagnosed SW and LW climate forcing time series for the twentieth century have been verified for the two modeling groups (four models) that were able to provide time series of radiative forcings used in their model simulation; these were produced by offline radiative transfer codes and are shown as magenta lines in Fig. 4 for the Model for Interdisciplinary Research on Climate (MIROC) models (T. Takemura 2005, personal communication) and the GISS models (J. Hansen 2005, personal communication). These radiative forcings were provided as individual time series for each major forcing agent and these time series were then combined to obtain estimates of total SW and LW radiative forcings. The reported well-mixed greenhouse gas forcing was assumed to be LW only and the reported aerosol and solar forcings were assumed to be SW only; ozone and volcanism were taken to be composed of SW and LW components, which are estimated using the reported net forcing, partitioned according to Houghton et al. (2001, their chapter 6). Figure 4 shows that the groups’ forcing estimates agree very well with that diagnosed using our simple methodology. For the GISS models there is a small discrepancy (∼10%) between our diagnosed forcing estimate and the radiative forcing provided by the GISS group. Given that Hansen et al. (2005) found a twentieth-century efficacy close to 1.0 with the same model, the difference is unlikely to be due to an efficacy effect.

By inspecting the SW and solar forcing results for the twentieth century, it is easy to identify the models that include natural forcings in their integrations (also see Table 1). Solar forcings are directly diagnosed from the downward solar flux, and the volcanic forcing manifests itself as a series of negative spikes. The solar and volcanic forcing signals are similar in size and shape in most models that incorporate them (Fig. 4 and Table 1). However, the volcanic forcing is too small in the Japanese Meteorological Research Institute Coupled GCM version 2.3.3 (MRI-CGCM2.3.2) model, which incorporates it as a change in the solar constant. Several models have a negative total SW forcing, presumably due to scattering by tropospheric aerosols (see Table 1). The strength of this aerosol effect differs greatly between the models and some, such as the two GFDL and CCSM3 models, do not appear to have a significant NET tropospheric SW forcing (Fig. 4); this is likely due to a cancellation effect between scattering sulfate aerosols and absorbing black carbon aerosols, as both types are included in these models (see Table 1). Overall these differences in included SW forcing agents described in Table 1 (e.g., aerosols, solar, and volcanic effects) lead to a wide range in the SW forcings for the twentieth century (Fig. 6).

Compared to the range of SW forcings, the LW forcings for the twentieth century are in better agreement with each other and are similar to the estimates of Myhre et al. (2001). The shapes of the different LW Q time series are similar (Fig. 4), but the magnitude of the estimated forcing still differs by a factor of 2; compare, for example, the range of LW climate forcings shown in the top three panels of Fig. 6.

For the twenty-first century (Fig. 5), there is a much wider spread in the range of climate forcing estimates. Most models have an increasing SW climate forcing, presumably due to tropospheric aerosol reductions. The GISS models, however, have clear negative forcing trends that would partly offset the effect of their larger-than-average LW forcing. In the LW, the spread of the 2000–2100 climate forcing estimate is a factor of 2. There is also some inconsistency in the time evolution of twenty-first century LW forcing changes (Fig. 5). Particularly apparent is the relatively small increase in LW forcing in the latter part of the twenty-first century for the GFDL-CM2.1, L’Institut Pierre-Simon Laplace Coupled Model version 4 (IPSL-CM4), the National Center for Atmospheric Research Parallel Climate Model version 1 (NCAR-PCM1), and MRI-CGCM2.3.2 models; reasons for this remain undiscovered.

The range of model forcing estimates illustrated in Figs. 4, 5 and 6 is perhaps surprising given that most of the LW forcing would be expected to be due to carbon dioxide, and the LW carbon dioxide forcings agreed to within 25% for the models evaluated (Table 2 and section 4). Forcings from other well-mixed greenhouse gases and ozone would, however, also affect these time series. Furthermore, several models that did not evaluate their CO2 forcing are outliers on Fig. 6, thus the actual spread in model CO2 forcing could be greater than indicated by Table 1. Among 16 GCM radiation codes employing identically prescribed clear-sky vertical atmospheric profiles of temperature and water vapor, Collins et al. (2006) find spreads of up to 40% in their carbon dioxide forcing and 60% in their well-mixed greenhouse gas forcing.

7. Conclusions

This paper has introduced a simple way of retrieving global mean climate forcing from energy balance and surface temperature diagnostics in coupled climate models. This is done by first estimating a global climate feedback term from integrations where CO2 is increased by 1% yr−1. Then the climate feedback term is used to diagnose climate forcing time series in transient climate change experiments with unknown radiative forcings.

This methodology can be applied as a useful first step to aid understanding of AOGCM differences. Forcings are not routinely calculated by models, but without knowing them, differences in model response are hard to interpret. Our results provide several useful illustrations of this. Three examples are discussed below.

First, one might assume that, as all models followed the SRES A1B scenario, differences in model response would be more likely due to climate response, rather than forcing. Our results in Table 3 suggest, however, that forcing scenarios also account for a significant fraction of the differences in temperature change found at year 2100: the models with the smallest NET forcing in 2100 also tend to be the ones with the smallest surface temperature change. Second, comparison of the responses in two versions of the MIROC model leads to the unexpected result that at the end of the twenty-first century, the larger temperature change found in the “hires” model could be due to a stronger LW climate forcing, rather than a different climate response. Inspection of the Y–NET and Q–NET values in Table 3 supports this conclusion. Third, the technique also helps evaluate a single AOGCM’s forcing, which, for example, enabled us to determine that the volcanic forcing in MRI-CGCM2.3.2 is too small compared to previously published volcanic forcing estimates (see section 5).

Importantly, our paper suggests that several AOGCMs may not correctly model the forcing from well-mixed greenhouse gases. We found, across models, a large range in LW forcing and different time evolution of this forcing, which is surprising given that greenhouse gas changes should account for most of this forcing and that this forcing should be essentially the same in every model. These results support the findings of Collins et al. (2006) and suggest that in AOGCMs the radiative transfer of the well-mixed greenhouse gases should be examined as a matter of some urgency.

The diagnosed forcings are not designed to replace conventional radiative forcing calculations. The diagnosed climate forcings cannot be split into components associated with different forcing agents (unless multiple integrations with individual forcing agents are performed), nor can it diagnose spatial patterns of forcings, so our analysis is somewhat limited if a more detailed understanding of climate forcing and response is sought. The techniques themselves also employ several assumptions that are not necessarily always valid. These assumptions (see sections 5 and 6 for details) would suggest that the techniques are only likely to work well in ∼100-yr integrations that are slowly warming, largely as a response to CO2 increases. Furthermore, although the technique gives good results in current AOGCMs, the linear forcing response model may not be valid in future AOGCMs that will likely incorporate additional climate feedbacks, such as biogeochemical effects.

Despite these caveats it is hoped that the simple methodology presented in this paper will be routinely applied to diagnose coupled model integrations. Knowing the global climate forcing should be a first step in the quest to understand both an individual model’s response and the differences between models. Comparing this climate forcing diagnostic to conventionally calculated radiative forcing would also provide a useful estimate of the semidirect effect.

Acknowledgments

The radiative forcing data provided by Toshihiko Takemura and Jim Hansen is appreciated, and we thank Ben Santer for carefully compiling the information used in Table 1. Jonathan Gregory and Jim Haywood contributed to a helpful discussion regarding the ideas used in this paper. We also appreciate the helpful suggestions made by two anonymous reviewers. We gratefully acknowledge the international modeling groups for providing their data for analysis: the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modeling (WGCM) and their Coupled Model Intercomparison Project (CMIP) and Climate Simulation Panel for organizing the model data analysis activity, and the IPCC WG1 TSU for technical support. The IPCC data archive and work at the University of California, Lawrence Livermore National Laboratory is supported under the auspices of the U.S. Department of Energy Office of Science (Climate Change Prediction Program) under Contract W-7405-ENG-48.

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Footnotes

Corresponding author address: Piers Forster, School of Earth and Environment, University of Leeds, Leeds LS2 9JT, United Kingdom. Email: piers@env.leeds.ac.uk

1

In contrast to the other models, CCSM3, PCM, ECHO-G, and MRI-CGCM2.3.2 employed a present-day control integration as the starting point for its 1% yr−1 CO2 increase experiment.

2

We used PCM1 upwelling tropopause flux data from run 5 for 2001–2100, as these data were not available from run 1.