Abstract

Global-scale variations in the climate system over the last half of the twentieth century, including long-term increases in global-mean near-surface temperatures, are consistent with concurrent human-induced emissions of radiatively active gases and aerosols. However, such consistency does not preclude the possible influence of other forcing agents, including internal modes of climate variability or unaccounted for aerosol effects. To test whether other unknown forcing agents may have contributed to multidecadal increases in global-mean near-surface temperatures from 1950 to 2000, data pertaining to observed changes in global-scale sea surface temperatures and observed changes in radiatively active atmospheric constituents are incorporated into numerical global climate models. Results indicate that the radiative forcing needed to produce the observed long-term trends in sea surface temperatures—and global-mean near-surface temperatures—is provided predominantly by known changes in greenhouse gases and aerosols. Further, results indicate that less than 10% of the long-term historical increase in global-mean near-surface temperatures over the last half of the twentieth century could have been the result of internal climate variability. In addition, they indicate that less than 25% of the total radiative forcing needed to produce the observed long-term trend in global-mean near-surface temperatures could have been provided by changes in net radiative forcing from unknown sources (either positive or negative). These results, which are derived from simple energy balance requirements, emphasize the important role humans have played in modifying the global climate over the last half of the twentieth century.

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.

Table 1.

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.

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.
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.

Fig. 1.

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.

Fig. 1.

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.

Next, we analyze changes (relative to the 1950–54 period) in the top-of-atmosphere (TOA) net incoming radiation (net incoming shortwave radiation minus outgoing longwave radiation ) from each model setup, which in turn provide estimates of important quantities related to changes in the planetary energy balance (Knutti and Hegerl 2008),

 
formula

where is the net radiative forcing of the system and represents the radiative response of the system, which is a function of the change in globally averaged near-surface temperatures and the climate feedback parameter .

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, ; hence , which quantifies the radiative response of the system to the historical evolution of SSTs. In addition, though, it also provides an estimate of the effective radiative forcing needed to produce these historical SSTs, such that (Cess et al. 1990; Ringer et al. 2006). In the ATM simulations, and hence and therefore (Hansen et al. 2002; Shine et al. 2003; Gregory and Webb 2008); for comparison with the effective radiative forcing, we use this equation to estimate the explicitly imposed total radiative forcing (associated predominantly with the changing composition of the atmosphere; Solomon et al. 2007; Murphy et al. 2009), such that . Finally, in the AMIP-ATM simulations , which provides an estimate of the radiative imbalance arising from the difference between the known total radiative forcing and the effective radiative forcing needed to produce the historical evolution of SSTs (see also Hansen et al. 2002; Anderson et al. 2010). This relationship is confirmed by comparing from the AMIP-ATM simulation with the combined values from the ATM and AMIP simulations (Fig. 3b).

Fig. 2.

Schematic of estimated (underlined) and derived quantities from the three different AGCM setups. (a) AMIP run. Variables are defined as follows: is change in globally averaged TOA net radiative fluxes from the AMIP simulation (blue arrow); is change in imposed surface heat flux associated with observed increase in SSTs; and is effective radiative forcing needed to produce the historical evolution of SSTs. (b) ATM run. Variables are defined as follows: is change in globally averaged TOA net radiative fluxes from the ATM simulation (green arrow); is change in imposed surface heat flux associated with known changes in radiative-forcing agents; and is explicitly imposed total radiative forcing. (c) AMIP-ATM run. Variables are defined as follows: is change in globally averaged TOA net radiative fluxes from the AMIP-ATM simulation (red arrow) and is change in imposed surface heat flux associated with the imbalance between known changes in total radiative forcing and the effective radiative forcing needed to produce the historical evolution of SSTs.

Fig. 2.

Schematic of estimated (underlined) and derived quantities from the three different AGCM setups. (a) AMIP run. Variables are defined as follows: is change in globally averaged TOA net radiative fluxes from the AMIP simulation (blue arrow); is change in imposed surface heat flux associated with observed increase in SSTs; and is effective radiative forcing needed to produce the historical evolution of SSTs. (b) ATM run. Variables are defined as follows: is change in globally averaged TOA net radiative fluxes from the ATM simulation (green arrow); is change in imposed surface heat flux associated with known changes in radiative-forcing agents; and is explicitly imposed total radiative forcing. (c) AMIP-ATM run. Variables are defined as follows: is change in globally averaged TOA net radiative fluxes from the AMIP-ATM simulation (red arrow) and is change in imposed surface heat flux associated with the imbalance between known changes in total radiative forcing and the effective radiative forcing needed to produce the historical evolution of SSTs.

Fig. 3.

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.

Fig. 3.

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.

Assuming the time rate of change of the integrated atmospheric energy is small, in each experiment is balanced by energy fluxes from the atmosphere to the underlying surface (predominantly the ocean surface and to a lesser extent the land surface and cryosphere; Trenberth et al. 2002; Levitus et al. 2005). Integrating these fluxes with time (see  appendix A) provides an estimate of the implicit global OHC changes associated with the changes in TOA radiative fluxes in each of the simulations (Levitus et al. 2005; Hansen et al. 2005), which can be compared with observed OHC changes (Fig. 4), recognizing that the observed value may underestimate the total earth energy storage by 5%–15% (Levitus et al. 2005; Hansen et al. 2005; Church et al. 2011). In this study, we chose to use the OHC data as a proxy for observed globally averaged top-of-atmosphere net radiation estimates (Trenberth et al. 2002; Hansen et al. 2005) because satellite-based TOA radiation estimates have a relatively short period of overlap and relatively large uncertainties (e.g., Fasullo and Trenberth 2008; Loeb et al. 2009; Harries and Belotti 2010). Here we utilize both the standard observed OHC estimates, which represent changes in OHC from 0 to 700 m, as well as estimates that account for deep-ocean heat content changes, which are based on the assumption that the heat content changes from 0 to 700 m represent 70% of the total OHC change over this period (Solomon et al. 2007).

Fig. 4.

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.

Fig. 4.

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.

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 but with fractional amounts of imposed total radiative forcing (0.25–0.90ΔFtot; see  appendix B). With weaker , increasing SSTs (and global-mean temperatures) are maintained by energy drawn from the subsurface ocean, significantly reducing OHC. For example, if were only 50% of the estimated value (the 0.50 × ATM curve), the historical OHC would have had to drop by about 20 × 1022 J in order to sustain the observed global temperature increases.

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) is supplied by historical changes in the chemical composition of the atmosphere, with the rest supplied by changes in unknown (positive) radiative-forcing processes not represented in the model. In this scenario, there is a significant increase in OHC as the remainder of the known changes in total radiative forcing is redistributed into the subsurface ocean. As an example, if 50% of were supplied by , with the rest being supplied by changes in a heretofore unknown source (the 0.50 × AMIP curve), the remainder of would have produced an increase in the historical OHC of around 30 × 1022 J.

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 and within the multiple AMIP-ATM simulations produced by HadAM3, CABO, and CMCC, as represented by their respective estimates (see  appendix A). While there are differences between the observed estimates of historical OHC and the various simulated estimates (Fig. 5), by the end of the twentieth century there is clear separation between these estimates and what would be expected had there been any significant contribution from changes in unknown radiative-forcing agents (0.75 × AMIP line) or internal climate variations (0.75 × ATM line).

Fig. 5.

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.

Fig. 5.

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.

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 is systematically overestimated by the models and that the long-term observed changes in global-mean temperatures are instead being driven by an unknown radiative-forcing agent. The second hypothesis is that the global-scale radiative response of the system is systematically underestimated by the models (equivalently the climate sensitivity is systematically overestimated) and that the long-term observed changes in global-mean temperatures are instead being driven by an unknown radiative-forcing agent in combination with known changes in total radiative forcing over the last half of the twentieth century. However, for either of these two alternate hypotheses to supplant the current one (i.e., that known historical changes in total radiative forcing produced the observed evolution of global-mean SSTs and ocean heat content), the unknown forcing agent would need to be identified, changes in its magnitude would need to be quantified, and it would have to be demonstrated that either (i) changes in the magnitude of known forcing agents in the model systems are systematically overestimated by almost exactly the same amount or (ii) the radiative responses in the model systems are systematically underestimated by almost exactly the same amount. However, testing either of these two hypotheses given the current model systems is not feasible until a candidate unknown forcing agent is identified and its magnitude is quantified.

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 and then integrating with time to arrive at the low-frequency component of the ocean heat content. To arrive at the high-frequency component, the 12-month running-mean values of are detrended (by fitting and removing the time-dependent linear trend across the entire time series); the detrended 12-month running-mean values are then integrated with time to obtain the corresponding interannual change in ocean heat content (by construction the trend in implied heat content from the beginning of this integration to the end is identically 0). These two estimates are then added together to arrive at the overall change in ocean heat content as a function of time.

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 at the beginning and end of each model integration. The linear trend in heat fluxes associated with this difference is then integrated with time to arrive at the low-frequency component of the ocean heat content. As before, to arrive at the high-frequency component the 12-month running-mean values of from each model are detrended (by fitting and removing a time-dependent linear trend across the entire time series); the detrended 12-month running-mean values are then integrated with time to obtain the corresponding interannual change in ocean heat content (again by construction the trend in implied heat content from the beginning of this integration to the end is identically 0). These two estimates are then added together to arrive at the values shown in Fig. 5.

APPENDIX B

Sensitivity of Ocean Heat Content to Changes in Radiative Forcing

To calculate the sensitivity of the ocean heat content changes to imposed radiative forcing, the effective radiative forcing needed to produce the observed evolution of sea surface temperatures , as determined from the AMIP simulation, is kept constant. The imposed total forcing associated with the historical evolution of radiatively active chemical constituents , as determined from the ATM simulation, is systematically reduced from 0 (no forcing associated with the historical evolution of radiatively active chemical constituents is imposed) to 0.90 (90% of the estimated forcing associated with the historical evolution of radiatively active chemical constituents is imposed). The effective radiative forcing needed to produce the observed evolution of sea surface temperatures is then subtracted from this value, giving the implied heat flux to/from the underlying surface (predominantly the ocean surface, and to a lesser extent the land surface) needed to maintain the historical evolution of sea surface temperatures ,

 
formula

These implied heat fluxes are converted into an implied ocean heat content change by integrating the 12-month running-mean values as above.

To calculate the sensitivity of the ocean heat content to the addition of alternate climate forcings, the imposed total forcing associated with the historical evolution of radiatively active chemical constituents , as determined from the ATM simulation, is kept constant. However, its contribution to the effective radiative forcing needed to produce the observed evolution of sea surface temperatures , as determined from the AMIP simulation, is systematically reduced from 0 (no fraction of the effective radiative forcing needed to produce the observed evolution of sea surface temperatures is supplied by the historical evolution of radiatively active chemical constituents; e.g., all of it is assumed to be supplied by unknown radiative-forcing processes not represented in the model system) to 0.90 (90% of the effective radiative forcing needed to produce the observed evolution of sea surface temperatures is supplied by the historical evolution of radiatively active chemical constituents). The difference between the imposed total forcing associated with the historical evolution of radiatively active chemical constituents and the fraction that contributes to the effective radiative forcing needed to produce the observed evolution of sea surface temperatures gives the implied net heat flux to the underlying surface from the remaining imposed total forcing,

 
formula

Again, these implied heat fluxes are converted into an implied ocean heat content change by integrating the 12-month running-mean values as above.

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