Estimates of the Earth's equilibrium climate sensitivity (ECS) from twentieth century observations predict a lower ECS than estimates from climate models, paleoclimate data, and interannual variability. Here we show that estimates of ECS from the twentieth century observations are sensitive to the assumed efficacy of aerosol and ozone forcing (efficacy for a forcer is the amount of warming per unit global average forcing divided by the warming per unit forcing from CO 2 ). Previous estimates of ECS based on the twentieth century observations have assumed that the efficacy is unity, which in our study yields an ECS of 2.3 K (5%–95% confidence range of 1.6–4.1 K), near the bottom of the Intergovernmental Panel on Climate Change's likely range of 1.5–4.5 K. Increasing the aerosol and ozone efficacy to 1.33 increases the ECS to 3.0 K (1.9–6.8 K), a value in excellent agreement with other estimates. Forcing efficacy therefore provides a way to bridge the gap between the different estimates of ECS.

1 Introduction One of the most consequential but uncertain quantities in climate science is the equilibrium climate sensitivity (ECS), which is the equilibrium surface warming in response to a doubling of carbon dioxide. Estimates of the ECS can be obtained from observations of the warming over the twentieth century [Gregory et al., 2002; Annan and Hargreaves, 2006; Aldrin et al., 2012; Otto et al., 2013], climate models [Soden and Held, 2006; Andrews et al., 2012; Dalton and Shell, 2013], paleoclimate data [Hoffert and Covey, 1992; Crucifix, 2006; Lunt et al., 2010; Schmittner et al., 2011], or from analysis of interannual variations [Forster and Gregory, 2006; Dessler, 2013]. These various estimates often do not agree. In particular, estimates of ECS from the twentieth century observations generally imply most likely values less than 2.5 K, lower than from the other data sources (although the uncertainties in all estimates are large enough to overlap). These low ECS estimates were one of the main reasons that the most recent Intergovernmental Panel on Climate Change (IPCC) report extended the bottom end of the likely ECS range from 2.0 K to 1.5 K [Collins et al., 2013]. Understanding the differences in these estimates of ECS should therefore be a high priority.

2 Methodology and Data Sets (1) The Earth's top‐of‐atmosphere (TOA) energy balance can be written as N is the net energy imbalance for the Earth, F is the radiative forcing imposed upon the planet by, for example, an increase in greenhouse gases. ΔT Sfc is the resulting surface temperature change and λ is the feedback factor, the change in TOA net flux per unit surface temperature change. We will solve equation 1 for λ, from which an estimate of ECS can be obtained using the relation , where F 2 × CO2 is the forcing from doubled CO 2 (3.7 W/m2 [Collins et al., 2013]). λ (2) Murphy et al., 2009 λ. From this, we calculate the ECS range. In our calculations, we begin by integrating equation 1 and then solving forwith all integrals covering the period 1958–2010. The advantage of using an integral form is that it tends to reduce the impact of natural variability on the calculation []. For each term, we have a central value of the integral and an uncertainty, and we then use a Monte Carlo approach to estimate the probability distribution of. From this, we calculate the ECS range. The term ∫Ndt, the time integral of the TOA net flux, is equal to the change in heat content of the climate system over the integral period. Because the heat content of the climate system is mainly stored in the ocean, we estimate this term from ocean heat content (OHC) estimates from the European Centre for Medium‐Range Weather Forecasts' Ocean Reanalysis System 4 (ORAS4) [Balmaseda et al., 2013]. The advantage of this data set is that it uses a reanalysis system to estimate the change in heat content for the entire ocean, including the deep ocean, which most observational data sets exclude. To account for the heating of non‐ocean reservoirs (such as melting ice and land), we add an additional heat flux of 0.06 W/m2 [Hansen et al., 2011]. The ORAS4 contains five ensemble members, which sample plausible uncertainties in the wind forcing, observation coverage, and the deep ocean. We average them to come up with a single best‐estimate value and use the standard deviation as the 1σ uncertainty in the Monte Carlo calculation. Forcing comes from the IPCC's Fifth Assessment Report [Myhre et al., 2013, Table 8.6], which provides forcing broken down by component. For aerosols, we use the effective radiative forcing, which allows tropospheric adjustment. In the Monte Carlo calculation, we assume a 1σ uncertainty in the integrated forcing of 20%, consistent with the IPCC's uncertainty estimate. Monthly surface temperature anomalies come from the Goddard Institute for Space Studies (GISS) Global Land‐Ocean Index [Hansen et al., 2010], Hadley Climate Research Unit HadCRUT4 [Morice et al., 2012], and National Climatic Data Center (NCDC) Global Index [Smith et al., 2008]. The forcing time series is referenced to 1750, which means that the temperature anomaly time series must also be referenced to that same time. However, temperature data extend only back to the late nineteenth century, so we assume that there is little temperature change between 1750 and the end of the nineteenth century, and we offset each time series so that the 1880–1900 average is zero. We discuss the uncertainty from this assumption later. We then integrate the three anomaly time series and average them to come up with a single best‐estimate value and use the standard deviation as the 1σ uncertainty in the Monte Carlo calculation. In the Monte Carlo calculation, 107 values of ∫N, ∫F, and ∫ΔT sfc are randomly sampled from the normal distributions described above, and a value of λ is calculated for each one. From these 107 values of λ, an average value and confidence interval are calculated. ECS values are then calculated from the λ distribution.

3 Analysis Using the data described above, we obtain an estimate for λ of 1.6 W/m2K, with a 5–95% confidence interval of 0.9–2.3 W/m2K; the PDF of λ is plotted in Figure 1. This corresponds to an ECS of 2.3 K, with a 5–95% confidence interval of 1.6–4.1 K. In agreement with other recent calculations (summarized in Table 1), this estimate tends toward the bottom of the IPCC's sensitivity range. Figure 1 Open in figure viewer PowerPoint Probability distributions for λ (W/m2/K) given two different efficacies, with units of fraction per W/m2/K. Table 1. Estimates of λ and ECS Based On the Twentieth Century Observations Analysis Central Value of λ (W/m2/K) 5–95% Confidence Interval of λ (W/m2/K) Central Value of ECS (K) 5–95% Confidence Interval of ECS (K) This analysis, efficacy = 1.0 1.6 0.9–2.3 2.3 1.6–4.1 This analysis, efficacy = 1.33 1.2 0.5–1.9 3.0 1.9–6.8 This analysis, efficacy = 1.5 1.1 0.4–1.8 3.5 2.1–10.2 Otto et al. [ 2013 1.8 N/A 1.9 0.9–5.0 Annan and Hargreaves [ 2006 1.3 N/A 2.9 1.7–4.9 Aldrin et al. [ 2012 1.9 N/A 2.0 1.2–3.5 Skeie et al. [ 2014 N/A N/A 1.8 0.9–3.2 Ring et al. [ 2012 N/A N/A ~1.8 N/A It has long been expected that forcings with the same global average magnitude but different spatial patterns could evoke different responses in global surface temperature [Hansen et al., 1997, 2005; Shindell and Faluvegi, 2009; Shindell et al., 2010]. For example, forcing concentrated at high latitudes, which are less strongly restored by infrared radiation to space, will lead to more warming than well‐mixed forcing agents. Certain forcing agents, particularly aerosols and tropospheric ozone, are indeed not uniformly distributed and impact the climate system differently than well‐mixed constituents [Shindell et al., 2003; Feichter et al., 2004; Chung and Seinfeld, 2005; Crook et al., 2011]. Different formalisms have been adopted in the literature to account for this process [e.g., Hansen et al., 2005; Winton et al., 2010; Armour et al., 2013]. One is to account for the effect using a so‐called forcing “efficacy” [Hansen et al., 1997, 2005], which is the amount of warming per unit of global average forcing divided by the amount of warming per unit of forcing from carbon dioxide. Most calculations of ECS based on the twentieth century observations assumed that the efficacy of different forcers is one, so this effect was ignored. Recently, Shindell [2014] analyzed transient model simulations to show that the combined ozone and aerosol efficacy is about 1.5. This high efficacy for ozone and aerosol forcing in Shindell′s analysis arises from two physical processes: different heat capacities in the two hemispheres and different values of λ for ozone/aerosols and well‐mixed greenhouse gases. For the ECS calculations in this paper, it is the efficacy arising from differing λ that is most relevant. To test the impact of efficacy on the inferred λ and ECS in our calculations, we multiply the aerosol and ozone forcing time series by an efficacy factor in the calculation of the total forcing. We find that increasing the efficacy shifts the PDF of λ to lower values (Figure 1), corresponding to increased climate sensitivity. Using Shindell's [2014] estimate of efficacy of 1.5 decreases λ to 1.1 W/m2K (0.4–1.7 W/m2K), corresponding to an ECS of 3.5 K (2.1–10.2 K). We can reasonably simulate the IPCC's climate sensitivity range using an efficacy of 1.33, which gives an ECS of 3.0 K (1.9–6.8 K). Assuming warming of ± 0.1°C between 1750 and the end of the nineteenth century would affect the ECS by 20% and would not affect our conclusions. Thus, an efficacy for aerosols and ozone of ≈ 1.33 would resolve the fundamental disagreement between estimates of climate sensitivity based on the twentieth century observational record and those based on climate models, the paleoclimate record, and interannual variations. It would also mean that the twentieth century observational record strongly supports the IPCC's canonical range. Clearly, better quantification of the forcing efficacy should be a high priority.

Acknowledgments The HadCRUT4, GISS, and NCDC temperature data can be found at http://www.cru.uea.ac.uk/cru/data/temperature/, http://data.giss.nasa.gov/gistemp/, and https://www.ncdc.noaa.gov/monitoring‐references/faq/anomalies.php, respectively. We thank Piers Forster for providing the forcing time series data. The ORAS4 ECMWF OHC data are from Balmaseda et al. [2013, Figure 1]. The secondary OHC data were obtained from http://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/index.html. This work was supported by NASA grant NNX13AK25G to Texas A&M University. We thank Alexander Otto and Troy Masters for helpful discussions. The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.