1. Introduction
Numerous studies using statistical and numerical methodologies have shown that historical trends in many features of the observed climate system during the last half of the twentieth century (1950–2000)—including global and regional temperature trends (e.g., Stott et al. 2006; Solomon et al. 2007); increased tropical sea level pressures (Gillett and Stott 2009) and tropopause heights (Santer et al. 2003); subsurface ocean temperatures (Barnett et al. 2001); mean and extreme precipitation (Zhang et al. 2007; Min et al. 2009); atmospheric humidity (Santer et al. 2007; Willett et al. 2010); and streamflow (Hidalgo et al. 2009)—are consistent with increased anthropogenic emissions of greenhouse gases and aerosols and inconsistent with other known forcing agents, including solar and volcanic activity (Barnett et al. 2005; Solomon et al. 2007).
However, such consistency does not preclude the possible influence of other unknown forcing agents (Stone et al. 2009). For instance, interannual to decadal changes in sea surface temperatures (SSTs) in the equatorial Pacific (Alexander et al. 2002; Swanson et al. 2009) and the North Atlantic (Rodwell et al. 2004; Kravtsov and Spannagle 2008) can produce hemispheric and global-scale climate variations that may have initiated a global-scale climate regime shift leading to subsequent long-lived tropospheric warming (Bratcher and Giese 2002; Giese et al. 2002; Levitus et al. 2005). Unfortunately, the influence of large-scale natural climate variability tends to be underestimated in most coupled ocean–atmosphere numerical models used for attribution studies (DelSole 2006; Compo and Sardeshmukh 2009; Swanson et al. 2009).
In addition, this consistency is dependent upon correct estimates of the radiative forcing associated with changing concentrations of atmospheric constituents (Forster and Taylor 2006; Collins et al. 2006; Solomon et al. 2007). Large uncertainties in historical radiative forcing arise from aerosols’ impact on the reflection (Penner et al. 1994; Boucher et al. 1998) and absorption (Ramanathan and Carmichael 2008) of solar radiation, as well as the indirect effects of aerosols upon cloud characteristics (Knutti et al. 2002; Quaas et al. 2006; Lohmann et al. 2007). More recently, uncertainties in the forcing of the climate system by increasing concentrations of CO2 and other greenhouse gases have been identified, even for the same prescribed changes in radiatively active concentrations (Forster and Taylor 2006; Collins et al. 2006; Solomon et al. 2007; Anderson et al. 2010).
Given these remaining uncertainties, we set out to investigate the validity of three competing hypotheses: 1) long-term historical changes in global-mean near-surface temperatures are being forced predominantly by natural climate variations; 2) long-term historical changes in global-mean near-surface temperatures have been influenced by changes in radiative forcing from unknown sources (either positive or negative) along with changes in radiative forcing from known sources; and 3) long-term historical changes in global-mean near-surface temperatures are being driven predominantly by changes in radiative forcing from known sources. While we do not know the nature of the unknown radiative forcings or of the possible natural climate variations, we can still test these hypotheses by examining how the climate system would have evolved over the last half of the twentieth century under each hypothesis. Here, our aim is to try to disprove those hypotheses that do not match the observations over the same time period. In this case, our interest is in the long-term (e.g., secular) changes over the period 1950–2000, not necessarily those occurring on interannual to decadal time scales.
2. Numerical simulations
For this study, we use output from atmosphere-only global climate model (AGCM) simulations produced by the National Center for Atmospheric Research Community Atmosphere Model, version 3.1 (CAM3.1) at T85 resolution (equivalent to 1.35° latitude × 1.35° longitude), which has been developed and evaluated over the course of the last two decades (Collins et al. 2006; Hack et al. 2006; Deser et al. 2006). Three separate simulations are examined, each with five ensemble members (Deser and Phillips 2009). In the first, simulations of the AGCM are forced only by historical changes in global SSTs during 1950–2000 [termed the Atmospheric Model Intercomparison Project (AMIP) simulation]. In the second, simulations are forced by historical changes in global SSTs, along with greenhouse gas (GHG) concentrations, sulfate aerosols, volcanic aerosols, stratospheric and tropospheric ozone, and solar activity [termed the combined AMIP and atmospheric forcing (AMIP-ATM) simulation]. In the third, simulations are forced only by historical changes in GHG concentrations, sulfate aerosols, volcanic aerosols, stratospheric and tropospheric ozone, and solar activity, while keeping the SSTs at their climatological values [termed the atmospheric forcing only (ATM) simulation]. Different initial conditions are used for each member of the ensemble. Table 1 provides a summary description of the atmosphere-only model simulations used in the study.
Name and characteristics of model simulations used in this analysis, where “GHGs” refers to historic changes in greenhouse gas concentrations and “SSTs” refers to historic changes in sea surface temperatures.
We will evaluate our results using additional output from AGCM simulations taken from the Climate of the Twentieth Century Project (Folland et al. 2005), including the Hadley Centre atmospheric model (HadAM3; Pope et al. 2000); the atmospheric component of the Coupled-Atmosphere-Biosphere-Ocean model (CABO; Zeng et al. 2004); and the Euro-Mediterranean Centre for Climate Change model (CMCC), which is based upon the ECHAM4 AGCM (Roeckner et al. 1996). For these models, we analyze multiple simulations (five each) forced by historical changes in global SSTs, along with GHG concentrations, sulfate aerosols, volcanic aerosols (HadAM3 and CABO only), stratospheric and tropospheric ozone, and solar activity (again termed the AMIP-ATM simulations). See Anderson et al. (2010) for a more detailed description and evaluation of the simulations from these four models. It is important to note that none of the atmosphere-only models are explicitly “tuned” to reproduce observed changes in the state of the climate system.
For comparison, observational estimates of global near-surface temperatures are taken from the University of East Anglia Climate Research Unit (CRU; Jones et al. 1999; Brohan et al. 2006), the National Aeronautics and Space Administration (NASA) Goddard Institute for Space Studies (GISS; Hansen et al. 2010), and the National Oceanic and Atmospheric Administration/National Climatic Data Center (NOAA/NCDC; Smith et al. 2008). Observed global ocean heat content (OHC) data come from Levitus et al. (2009), Domingues et al. (2008), Ishii and Kimoto (2009), and Palmer et al. (2007). While additional OHC estimates are available (Willis et al. 2008; Lyman and Johnson 2008; Gouretski and Reseghetti 2010), most start in 1993, which only provides a 7-yr overlap with the simulated data.
3. Results
Figure 1 shows changes (relative to the 1950–54 period) in global-average surface temperatures from the CAM3.1 model experiments, along with changes in global-average surface temperatures taken from the observational products. Global temperature changes in both the AMIP and AMIP-ATM simulations approximate the observed global temperature changes, which is to be expected since the SST evolution is prescribed in these simulations (Hansen et al. 2002; Compo and Sardeshmukh 2009); it should be noted that for this plot no effort is taken to account for the changing network of historical observations, since our interest is in diagnosing the models’ responses to the changing SSTs (and atmospheric chemical constituents), not necessarily evaluating the global temperature changes against observed estimates (as in Folland et al. 1998; Sexton et al. 2001). In comparison, there is relatively little temperature change in the ATM simulation because the global ocean temperatures, which determine the global near-surface temperatures (Hansen et al. 2002; Shine et al. 2003), are fixed in this experiment.
Globally averaged surface temperature changes. Surface temperature data are taken from the CAM3.1 simulations and the CRU, GISS, and NOAA observations. For all data, time series are smoothed using a 12-month running mean. Data are plotted such that the 5-yr period at the beginning of the time series are centered on 0. Gray shading represents the spread between the maximum and minimum simulated values, based upon the five ensemble members from each simulation; black shading represents the spread between the maximum and minimum observed values. (a) AMIP simulations; (b) AMIP-ATM simulations; (c) and ATM simulations.
Citation: Journal of Climate 25, 20; 10.1175/JCLI-D-11-00645.1
A schematic of these terms, as derived from each simulation, is shown in Fig. 2; the time evolution of these terms is shown in Fig. 3. In the AMIP simulations, 
Schematic of estimated (underlined) and derived quantities from the three different AGCM setups. (a) AMIP run. Variables are defined as follows: 
Citation: Journal of Climate 25, 20; 10.1175/JCLI-D-11-00645.1
Globally averaged change in net incoming radiation at the TOA. (a) Data taken from the CAM3.1 AMIP, ATM, and AMIP-ATM simulations. Net incoming radiation calculated as the difference between the net incoming shortwave radiation and outgoing longwave radiation. All values are smoothed using a 12-month running mean. Data are plotted such that the 5-yr period at the beginning of the time series is centered on 0. All values have units of W m−2. Shading represents the spread between the maximum and minimum simulated value, based upon the five ensemble members from each simulation. (b) Data show the globally averaged radiative imbalance of the climate system based upon the net incoming radiation from the CAM3.1 AMIP-ATM simulation (black) and the sum of the ATM and AMIP simulations (gray). Shading represents the spread between the maximum and minimum simulated value, based upon the five ensemble members from each simulation.
Citation: Journal of Climate 25, 20; 10.1175/JCLI-D-11-00645.1
Assuming the time rate of change of the integrated atmospheric energy is small, 
Implied change in global-average OHC associated with changes in net incoming radiation at the TOA. Changes in OHC calculated by integrating the 12-month running-mean values of net incoming radiation at the TOA, taken from the CAM3.1 AMIP, AMIP-ATM, and ATM simulations and normalized by the area of the ocean (following Hansen et al. 2005). Shading represents the spread between the maximum and minimum simulated value, based upon the five ensemble members from each simulation. Observed OHC estimates derived from Levitus et al. (2005), Domingues et al. (2008), Palmer et al. (2007), and Ishii and Kimoto (2009); shading represents the spread between the maximum and minimum observed value. Observed OHC estimates from 0 to 3000 m (dashed green line) are derived from the mean of the four 0–700-m observational datasets divided by fraction of total heat content (70%; Solomon et al. 2007). Data are plotted such that the 5-yr period from 1955 to 1959 is centered on 0. Sensitivity of the OHC to reductions in the imposed radiative forcing (blue lines) is determined from the imbalance between the effective radiative forcing (AMIP) and fractional amounts of imposed total radiative forcing (0.25 × ATM through 0.90 × ATM); see text for details. Sensitivity of the OHC to the addition of alternate climate forcings (black lines) is determined from the imbalance between imposed total radiative forcing (ATM) and the fraction that contributes to the effective radiative forcing (0.25 × AMIP through 0.90 × AMIP); see text for details.
Citation: Journal of Climate 25, 20; 10.1175/JCLI-D-11-00645.1
Results from the AMIP-ATM simulation provide an estimate of the net heat flux into the oceans arising from the imbalance between the historical forcing associated with the changing chemical composition of the atmosphere and the effective radiative forcing needed to produce the observed response of the climate system. The estimated heat flux arising from this imbalance results in a change in OHC that agrees well with observations, indicating that known changes in the atmospheric composition can generate the radiative forcing needed to produce the observed evolution of SSTs and the observed evolution of ocean heat content. Similar results have been shown for other models as well (Hansen et al. 2002).
Using the additional model setups, we can further estimate how the climate system would have behaved if the actual radiative forcing associated with historical changes in the atmospheric composition were weaker than that found in the ATM model; for example, if the net heating were offset by underrepresented changes in radiative-forcing processes associated with aerosol direct and indirect effects (or, alternatively, if the observed global temperature increases were simply the result of internal climate variations associated with coupled ocean–atmosphere interactions). To investigate this possibility, we estimate the expected OHC changes for the given effective radiative forcing needed to produce the observed evolution of SSTs 
We can also estimate how the climate system would have behaved if only a fraction of the effective radiative forcing needed to produce the observed evolution of SSTs (0.25–0.90
Given the uncertainty in the observed OHC estimates, as well as the possible storage of heat in the deeper ocean, results suggest that there may be an additional positive radiative-forcing agent acting on the observed system that is unaccounted for in the model (as represented by the 0.90 × AMIP line in Fig. 4); however, it only represents about a 10% increase to the total changes in known radiative forcing. At the same time, given the uncertainty in implied OHC changes associated with the imbalance between the known changes in total radiative forcing and the effective radiative forcing needed to produce the historical evolution of SSTs (red shading), the observed OHC record is fully consistent with historical changes in the chemical composition of the atmosphere as well.
To test the robustness of the results derived from the CAM3.1 model, we examine the implicit changes in OHC arising from the imbalance between 
Multimodel estimates of implied change in global-average OHC associated with changes in net incoming radiation at the TOA. Changes in OHC calculated by integrating the 12-month running-mean values of net incoming radiation at the TOA, taken from the ensemble-mean AMIP-ATM simulations of the CAM3, HAD3, CABO, and CMCC and normalized by the area of the ocean (following Hansen et al. 2005). Observed OHC estimates from 0 to 3000 m are derived from the 0–700-m observational datasets (Levitus et al. 2005; Domingues et al. 2008; Palmer et al. 2007; Ishii and Kimoto 2009) divided by fraction of total heat content (70%; Solomon et al. 2007). Gray shading represents the spread between the maximum and minimum simulated value; black shading represents the spread between the maximum and minimum observed value. Data are plotted such that the 5-yr period from 1955 to 1959 is centered on 0. For reference, the 0.75 × ATM line (dashed) and 0.75 × AMIP line (solid) from Fig. 4 are also shown.
Citation: Journal of Climate 25, 20; 10.1175/JCLI-D-11-00645.1
4. Discussion and summary
Overall, our research indicates that known changes in total radiative forcing (associated predominantly with GHGs and aerosols, as well as solar activity) over the last half of the twentieth century balance both the effective radiative forcing needed to produce the long-term observed changes in global-scale SSTs (and hence global-mean temperatures) and the observed change in ocean heat content. Further, our results, which are not sensitive to simulated estimates of internal climate variability or the specifics of numerical ocean models (Folland et al. 1998; Sexton et al. 2001; Sokolov et al. 2003), indicate that long-term historical variations in global-mean temperatures and ocean heat content are inconsistent with forcing by large-scale internal climate variations, which contributed less than 10% to the global-mean temperature increase over the last half of the twentieth century (as evidenced by the absence of overlap between the observations and the 0.90 × ATM line in Fig. 4). In addition, historical variations in global-mean temperatures and ocean heat content are inconsistent with changes in additional radiative forcing by unknown sources, which could not have contributed more than 25% of the total radiative forcing needed to generate the historical temperature and heat content changes (as evidenced by the absence of overlap by the end of the twentieth century between the observations and the 0.75 × AMIP line in Fig. 5). As such, our results confirm those derived from observationally based estimates of historical energy flux terms (Murphy et al. 2009) that indicate it is unlikely any unknown radiative-forcing agent has contributed significantly to an increase (or offset) of the earth’s energy budget over the period 1950–2000.
It should be noted that, in both of these analyses, there are two alternate, untested hypotheses. One is that the known change in total radiative forcing over the last half of the twentieth century 
Acknowledgments
Dr. Anderson’s research was supported by a Visiting Scientist appointment to the Grantham Institute for Climate Change, administered by Imperial College of Science, Technology, and Medicine. We thank Clara Deser and Adam S. Phillips from the National Center for Atmospheric Research for providing the CAM3.1 data. We also thank Sydney Levitus and John Antonov for supplying the Levitus et al. (2005), Domingues et al. (2008), and Ishii and Kimoto (2009) estimates of globally averaged ocean heat content; Palmer et al. (2007) estimates were obtained from the National Climatic Data Center Climate Services and Monitoring Division.
APPENDIX A
Calculation of Changes in Ocean Heat Content
To calculate the implied ocean heat content change associated with the surface heat fluxes from a given CAM3.1 model run, we calculate the change in heat content associated with the long-term trend by fitting a time-dependent linear trend across the 12-month running-mean values of 
When calculating the heat content changes for the different model systems, a slightly different procedure is performed since each model system adopts a slightly different set of forcing agents. In particular, to avoid end effects (associated with Pinatubo-related volcanic signatures near the end of the CAM3, CABO, and HadAM3 simulations but not the CMCC simulations). We calculate the change in heat content associated with the long-term trend by first calculating the difference between the 5-yr-mean values of 
APPENDIX B
Sensitivity of Ocean Heat Content to Changes in Radiative Forcing
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