1. Introduction
A perturbation to the composition of Earth’s atmosphere can be quantified through the degree to which it disturbs the radiative balance at the top of the atmosphere, its radiative forcing. This radiative forcing is a motive force for climate change as (at least for small perturbations) Earth’s globally averaged surface temperature is expected to change proportionally with the forcing (e.g., Myhre et al. 2013a; Sherwood et al. 2015). More than 20 years ago Charlson et al. (1992) used simple physical arguments to raise the specter of a relatively large but negative (−2.3 W m−2) radiative forcing by tropospheric aerosols resulting from human activities. Although subsequent assessments (e.g., Boucher et al. 2013) have suggested that the present-day radiative forcing by the tropospheric aerosol (
One important implication of a strongly negative aerosol forcing is that Earth’s globally averaged surface temperature must be very sensitive to greenhouse gas forcing to have risen at all over the instrumental record. Another implication is that if 
The complexity of the processes leading to an aerosol forcing is daunting, and understanding remains rudimentary. The scale of the processes controlling the lifetime and composition of the aerosols and their interaction with clouds is far below what can be resolved by a large-scale model. So even if these processes were well understood, it would be far from trivial to represent with any quantitative fidelity their collective effects on the scales of motion representable by a global model. So it is not surprising that Earth system models constructed to estimate 
For these reasons, I believe there is little foundation for the expectation that comprehensive modeling alone can provide a basis for reducing uncertainty in estimates of 
My main arguments are developed in three parts. First, I develop and motivate a simple model designed to represent the time history of 
2. A simple model for the time history of aerosol forcing
The central idea developed in this paper is that if aerosol forcing arising from the interactions between aerosols and clouds increases sublinearly with emissions, for instance logarithmically as is suggested both by physical understanding and comprehensive modeling (Charlson et al. 1992; Carslaw et al. 2013), then a disproportionate amount of the forcing would be expected to arise early in the instrumental record. Put another way, one unit of emissions in a pristine atmosphere can be expected to introduce a larger radiative forcing than one unit of emissions in an atmosphere already burdened by substantial anthropogenic emissions. The implication is that during the early part of the industrial period aerosol forcing will have increased disproportionately compared to greenhouse gas forcing, and hence it might be informative to look to this period to help disentangle the effect of the radiative forcing of aerosols from other anthropogenic forcings.
To take advantage of this line of thought one requires a model capable of resolving the temporal evolution of aerosol forcing. In principle a climate–chemistry model could be used for this purpose. In practice the most comprehensive models are usually run for short time periods with preindustrial climate forcings, and again for the present day, with relatively little regard to what happens in between. Simulating the entire history of the industrial period with a comprehensive model is computationally expensive, but not prohibitively so; but assessing and sampling the uncertainty space of such a model is another story (cf. Carslaw et al. 2013). To circumvent this difficulty, I posit a functional form for the aerosol forcing whose time dependence is carried solely by the global emission history of sulfur dioxide (SO2), which I denote by 
Parameterizing 
Anthropogenic SO2 emissions 
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
In the remainder of this section the two main premises of the simple model for 
a. Scaling aerosol forcing by SO2 emissions
As a first approximation I simply assume that 
Different estimates of the aerosol forcing, normalized to the best estimate of the IPCC AR5, vs anthropogenic sulfate emissions taken from Smith et al. (2011). Estimates from comprehensive modeling are provided for recently published studies (Carslaw et al. 2013; Shindell et al. 2013) by large filled circles with 1σ uncertainty indicated by the vertical lines. For comparison to the AR5, all estimates are normalized to correspond to the AR5 best estimate, as in the AR5 Annex II (see text for further details). AR5 time series of aerosol forcing are shown by the closed gray circles. The solid line through the data is based on Eq. (1) with α = 0.001 875, β = 0.634, and 
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
To demonstrate the form of the relationship between 
A critical eye might complain that after 1980 and prior to 1900 the form of the relationship between 
Nonetheless, because 
To the extent that changing patterns of emissions are important for the global forcing, it would be more appropriate to express 
The statement that 
In summary, the idea that 
b. A simple model
The first term in Eq. (1) is derived formally in appendix A. It models the radiative forcing from aerosol–radiation interactions 
The second term in Eq. (1) is derived formally in appendix B. It models the radiative forcing from aerosol–cloud interactions 
Despite its simplicity, Fig. 2 demonstrates that with a suitable choice for the free parameters, Eq. (1) provides a satisfactory model of the time history of 
3. Implications of the simple model for aerosol forcing
Considerable benefit can be derived by expressing 
The period prior to 1950 is also interesting because there was marked warming in the early part of the century that appears difficult to reconcile with a very strong aerosol forcing. The median of 100 ensemble members from the HadCRUT4 dataset (Morice et al. 2012) suggest a 0.3-K warming. Indeed, it was this warming that motivated early speculation as to the role of rising concentrations of atmospheric carbon dioxide (Callendar 1938). As shown in Fig. 3, most of this warming occurred in a 30-yr period starting after the termination of a period of active volcanism and ending around 1950 when 
(a) Time series of hemispherically averaged surface temperatures plotted as anomalies relative to the average over the 1961–90 period and (b) their difference. Data are from the HadCRUT4.2 dataset. Also shown are gray-shaded bands indicating periods of more active volcanism.
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
(a) Net forcing resulting from long-lived greenhouse gases (including CFCs) alone (dashed), with 
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
This line of argumentation can be developed to further bound the magnitude of an aerosol forcing whose historical evolution can be described by an equation of the form of Eq. (1). Supposing that, as is stated in the AR5 (IPCC 2013), it is extremely likely that most of the 0.5-K warming since 1950 can be attributed to anthropogenic activity, it seems equally unlikely that none of the 0.3-K warming between 1850 through 1950 can be attributed to anthropogenic forcing. Or put another way, it seems very unlikely that the natural contribution to the warming, generally thought to be due to a confluence of increased insolation during a quiescent period of volcanism (e.g., Suo et al. 2013), was so strong that it offset a negative anthropogenic forcing. This idea that the anthropogenic forcing was nonnegative at the end of the period of rapid warming in 1950 can then be used to provide tighter bounds on the present day magnitude of 
To estimate a lower bound for the present-day 
The value of the aerosol forcing associated with an emission source equivalent to that in the year 2005 is equated with the present-day aerosol forcing, and denoted 
Idealized experiments using several comprehensive climate models suggest that the hemispheric temperature response is expected to follow the sign of the hemispheric forcing. Voigt et al. (2014a) explored the effect of asymmetric hemispheric forcing by perturbing the surface albedos differently in the different hemispheres (zero mean) in four different general circulation models running in an aquaplanet configuration, all with a very different representations of the tropical climate. The asymmetric forcing, ΔF in Table 1, is measured as the difference between the dark and bright hemispherically averaged radiative forcing and is calculated in a way that accounts for changes in cloudiness (Voigt et al. 2014b). The calculations demonstrate that a pronounced temperature difference results from an asymmetric forcing, suggesting that shifts in the Hadley cell (which is the prime way in which the atmosphere transports heat across the equator) does not completely compensate hemispheric forcing asymmetries. Based on this result, and the evidence that the warming in the early part of the century is, if anything, stronger in the Northern Hemisphere, I argue that the magnitude of 
Summary of differences in surface temperatures between hemispheres asymmetrically forced by the indicated forcing ΔF. The sense of the temperature change follows that of the forcing. Calculations were performed for an aquaplanet with a mixed layer ocean whose depth is set to 30 m, and for which heat flux convergence is set to zero at each point. Experiments with a 50-m mixed layer ocean show a stronger response (5%–20%) but the forcing is unchanged. Model names follow the designation in Voigt et al. (2014a).
The condition that 
The conditional probabilities from this further constraint, shown by the dashed line in Fig. 4b, suggest that 
In summary, a simple model of aerosol forcing [Eq. (1)], shown to be a good approximation of present-day understanding of aerosol processes, is used to revisit the lower bound on aerosol forcing. I use this model to interpret the time history of radiative forcing over the Northern Hemisphere prior to 1950. Based on this analysis I argue that an aerosol forcing less than −1.0 W m−2 is very unlikely. It seems likely that the 0.3-K rise of temperatures in the first half of the century likely has a naturally forced component, for instance from increasing insolation and the rebound from volcanic forcing. But a present-day aerosol forcing more negative than −1.0 W m−2 would imply that none of the rise in Northern Hemisphere surface temperatures during the 100-yr period from 1850 to 1950 could be attributed to anthropogenic forcing. This would imply a degree of natural variability that I find difficult to reconcile both with variability in comprehensive modeling (as discussed subsequently) and with the consensus that most of the post-1950 temperature rise can be attributed to anthropogenic causes.
4. Reconciling less negative aerosol forcing with physical understanding
In the AR5, the central estimate of 
a. Aerosol–radiation interactions
The interpretive framework implied by Eq. (2) is routinely used to understand differences in more complex models and shows that models arrive at similar estimates of 
Adjusting the sulfate-aerosol forcing to account for other components of the aerosol, or from physical adjustments, amounts to estimating η. This is challenging, as it requires piecing together contributions taken from a very inhomogeneous sampling of models, with widely divergent estimates of individual forcing components (Shindell et al. 2013; Myhre et al. 2013b). For instance, estimates of the radiative forcing by nitrate vary by more than a factor of 10 in the most recent model intercomparison (Shindell et al. 2013). Nonetheless, taken at face values, most models estimate a positive contribution to 
Observations of Earth’s energy budget suggest that even the less negative, −0.25 W m−2 estimate of 
For reasons elaborated on in the next section, it is assumed that, in regions where large asymmetries in the background natural aerosol are not expected, the asymmetry measures the anthropogenic aerosol burden. Consistent with this interpretation, Fig. 5 shows that the clear-sky albedo over the oceans in the Northern Hemisphere is, as expected, larger than that it is over the oceans in the Southern Hemisphere, although differences in the tropics likely reflect differences in the natural aerosol, for instance from mineral dust sources in North Africa. Averaging between 25° and 50° latitude, where anthropogenic sources are expected to be large but contributions from mineral dust should be less important, yields 
Asymmetry A(φ) in zonally and annually averaged albedo α over the oceans as a function of sine of latitude φ. CERES measurements (blue) and the multimodel mean (dotted), excluding one outlier model (MRI-CGCM3). The mean between 25° and 50° latitude of the individual models and of CERES is indicated by the minor tick marks on the ordinate axis.
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
AMIP simulations from the CMIP5 database (see also Table C1); tabulated are the analysis periods, the global surface and TOA albedo as well as the asymmetry of clear-sky ocean albedos (
It is possible that biases in measurements of 
A possible bias associated with hemispheric biases in the identification of clear-sky scenes could also cause 
Related to this issue of cloud clearing, because the models define clear sky differently than the observations, the model asymmetry may be amplified by the clear skies being systematically more humid (cf. Sohn et al. 2010; Boucher and Quaas 2012) in the model, which would amplify (through a humidification effect) any background asymmetry. However, the relatively small (1 km) clear-sky footprint of the CERES EBAF data should mitigate against such effects. Additionally, the tendency for the EBAF product, which uses the less conservative (than the SYN product) cloud clearing algorithm, to be less asymmetric argues against the sampling playing a major role.
A further indication that something is amiss in the models rather than in the data arises from a simple inspection of maps of the outgoing clear-sky shortwave irradiances from the models and from CERES. In Fig. 6 the 10-yr average of irradiances from two models are compared with CERES. The two models were selected for presentation because they formed the basis of the assertion by Shindell et al. (2013) that changes in the pattern of aerosol emissions have caused 
Zonal anomaly in top-of-atmosphere clear-sky radiation from two models, (top) GFDL-CM3 and (middle) GISS-E-R-CC, and (bottom) as observed by CERES EBAF (Ed2.8). The anomalies are calculated with respect to a baseline as described in the text. The global and Northern Hemisphere average of the fields are given on the upper right of each panel.
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
The CERES data can be used to construct a rough estimate of 
In summary, the data provide no evidence that the models produce an insufficiently negative estimate of 
b. Aerosol–cloud interactions
In Eq. (1) the term representing 
The factor CE can be inferred from the literature. Storelvmo et al. (2009) used the ECMWF Integrated Forecasting System, which compared to many climate models has a relatively good representation of clouds, to explore the effect of different parameterizations of the cloud droplet concentrations on 
Sulfate radiative forcing efficiency, 
Inferences from an analysis of observed cloud-radiative effects provide further support for C ≈ 0.1. For a typical stratocumulus cloud with an insolation weighted solar zenith angle of 43.66°, radiative transfer calculations yield R = −115 W m−2 for N = 100 cm−3, or R = −100 W m−2 for N = 50 cm−3—a large value. As a reference, the globally averaged shortwave cloud radiative effect from CERES is −46 W m−2. Hence if one assumes that such stratiform clouds contributed a cloud fraction of 0.3 they would be responsible for roughly 75% of the globally averaged forcing. Given the very large shortwave cloud radiative effect arising from much deeper and ice containing clouds, such a large contribution to the global cloud radiative effect is unreasonable (i.e., the low cloud fraction should be substantially less than 0.3). An effective stratiform cloud fraction of 0.3 also appears large when one considers that the average cloud-radiative effect over the subsiding regions of the tropical oceans is closer to −20 W m−2 so that the equivalent stratocumulus cloud fraction in subsiding regions alone would be about 0.2. Given that subsiding air covers about 60% of the globe, and in regions of upward motion high clouds will increasingly mask changes to low cloud radiative effects, this implies an equivalent stratocumulus cloud fraction of 0.12, similar to Storelvmo et al. (2009). Even limiting oneself to a consideration of the climatological stratocumulus regions, defined as subsiding regions where the lower tropospheric stability is larger than 18 K (e.g., Klein and Hartmann 1993; Medeiros and Stevens 2011; Medeiros et al. 2015), and which cover about 30% of Earth’s ocean, the cloud radiative effect is still −45 W m−2. This implies an effective cloud fraction of 0.5 over these stratocumulus regions or about 0.15 overall. Using a different approach Wood (2012) arrives at a similar value. Because one does not expect every stratocumulus cloud on Earth to experience a change in its droplet concentrations on the order of the mean global change (which is mostly concentrated over land in the Northern Hemisphere) I find it difficult to make the case for a value of C > 0.1 and believe that C = 0.15 is a reasonable upper bound.
Estimates of C from comprehensive modeling, inferences from aerosol climatologies, and observations of cloud-radiative forcing are thus surprisingly consistent, indicating C < 0.1, more than a factor of 3 smaller than what was assumed by Charlson et al. (1992). In addition to suggesting that early estimates of 
To estimate 
Some sense of the susceptibility of droplet concentrations to large-aerosol perturbations in pristine environments is provided by ship-track data. Retrievals of droplet sizes by satellite show that in detectable ship plumes the effective radius is reduced by 20% on average, equivalently 
Even allowing for what I believe to be an unrealistically large (factor of 2) uncertainty in my estimate of 
c. New bounds on aerosol forcing
5. Reconciling less negative aerosol forcing with comprehensive modeling
The above analysis begs the question as to why comprehensive models are able to reasonably simulate the twentieth-century trends in globally averaged surface temperatures, despite values of 
My arguments would suggest that to judge whether the simulated values of 
(a) Decadal temperature anomalies with respect to the 1961–90 period for the CMIP5 historical simulations (box and whiskers) and from the HadCRUT4 dataset (red dots, median estimates). (b) Decadal trends (blue dots) for individual CMIP5 models during the 30-yr period 1920–50 overlain on the normal distribution of possible trends (with a standard deviation of 0.037 K decade−1 taken to be equal to the standard deviation of the regressed 1920–50 trends in a 100-member CMIP5 historical ensemble) for the case of no forcing. The 0.95 value of the cumulative distribution is shown by the black dashed line and the observed trend by the red dashed line. A naturally forced trend larger than the distance between the black line and the red line would make it impossible to rule out the possibility (at the 5% level) that the observed trend arose independently of anthropogenic forcing.
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
The slower warming during this period may be a consequence of internal variability, so that the average model warms less than what is observed. But the reduced warming simulated during this period is not simply a property of the multimodel mean. Only three or four of the 35 models (Fig. 7b) simulate as much warming as is observed during the period between 1920 and 1950, while six models show essentially no warming (or even cooling) during this 30-yr period. This result is consistent with the hypothesis that the aerosol forcing in the models is too negative. Nonetheless, to explore the role of natural variability more thoroughly I analyze a 100-member ensemble of the latest version of the MPI Earth System Model (MPI-ESM, version 1.1), which was run for the period between 1850 and 2005. The 30-yr trends from this ensemble have been calculated by regressing annually averaged global surface temperatures against time for the period between 1920 and 1950. The standard deviation of the regressed trends is 0.037 K decade−1. Assuming normally distributed trends, if the net forcing were negative the probability that the trend would be as large as observed (0.095 K decade−1) is less than 0.5% (2.6σ). Some of the warming prior to 1950 is likely to have a naturally forced component, as insolation is believed to have increased during this period (Suo et al. 2013). The 100-member MPI-ESM historical ensemble thus suggests that the naturally forced trend would have to have accounted for about half of the observed trend for it to be explainable at the 10% level without any contribution from anthropogenic forcing.
Based on these measures of variability and noting that not all of the CMIP5 models are likely to have excessive aerosol forcing, my analysis supports the argument that the aerosol forcing in the CMIP5 ensemble is too negative. It would be interesting to more systematically test these ideas by running large ensembles in more models, ideally with the same (or at least a well characterized) aerosol forcing. Another way to develop this line of argumentation further would be to contrast the temperature trends in the present period, for which there have also been no major volcanoes since the eruption of Mt. Pinatubo in 1991 and aerosol forcing has been relatively constant, with those between 1920 and 1950. Here again, however, comparisons among models require a good characterization of the aerosol forcing applied to the models for both periods.
As alluded to in the last paragraph, one difficulty with interpreting the CMIP models is their very different representations of non–greenhouse gas forcing, particularly associated with aerosols. Interpreting the simulations in terms of the observational record thus convolves differences in how individual model configurations are forced with differences in their climate response. Except for the small subset of the models that performed dedicated experiments (cf. Zelinka et al. 2014) designed to assess the aerosol forcing in models, it is not possible to diagnose differences in 
To circumvent this problem I estimate differences in the aerosol forcing across the CMIP5 ensemble by calculating the anthropogenic contribution to the asymmetry parameter, denoted Aa, as a function of time for the CMIP5 historical simulations. This is possible because for the historical simulations I can remove the contribution of the natural aerosol to A by subtracting the background asymmetry (not just the background clear sky) from a period late in the nineteenth century (1860–70) when aerosol forcing and volcanic activity were believed to be small. The results of this calculation are presented in Fig. 8. As a comparison, models submitting historical simulations with only natural forcing (historicalNat simulations) are also evaluated by calculating the change in total reflected clear-sky radiation over oceans (Fig. 9a) and the hemispheric asymmetry Aa (Fig. 9b). In these historicalNat simulations periods of volcanic activity are readily evident (Fig. 9a) but outside of these periods Aa is nearly zero, with little evidence of a trend, as one would expect as by definition Aa should be zero. This analysis thus supports the idea that Aa in the historical forcing experiments indeed measures the anthropogenic aerosol forcing. Figure 8 further shows that in the historical simulations Aa scales well with 
(a) Clear-sky ocean asymmetry A calculated from CMIP5 historical simulations for 4-yr intervals after removing the asymmetry from the background aerosol estimated as the mean for the period between 1850 and 1870. The solid red line shows the asymmetry parameter (including natural background aerosol) from CERES scaled backward in times using changes in emissions of SO2 relative to the present day. The dashed red line is the same as the solid, but multiplied by a factor of 2.2. (b) Clear-sky asymmetry parameter A for CMIP5 models (with the effects of natural aerosols removed) for the 10-yr period centered around 1975 vs the value for the 10-yr period centered around 1950. Models without aerosol–cloud interactions are denoted by red dots; models that include aerosol–cloud interactions are shown by blue dots. Also shown are estimates of A from CERES (without removing natural aerosols) for the present day. Because SO2 emissions double between 1950 and 1975 if the asymmetry were to follow the anthropogenic emissions of SO2 the models would be expected to scatter along the 2:1 line.
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
(a) Change in globally averaged reflected clear-sky shortwave radiation over the ocean relative to a reference period (1860–70) for CMIP5 historical simulations with natural forcing only (historicalNat). (b) Change in asymmetry A relative to the reference period for CMIP5 historical simulations with natural forcing only.
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
To more quantitatively compare the scaling of Aa with 
6. Findings and implications
A simple model of aerosol forcing, shown to be consistent with present-day understanding of aerosol processes, is used to revisit the lower bound on aerosol forcing. I use this model to interpret the time history of radiative forcing over the Northern Hemisphere prior to 1950. Based on this analysis I argue that an aerosol forcing less than −1.0 W m−2 is very unlikely. A more negative aerosol forcing would imply that none of the roughly 0.3-K rise in Northern Hemisphere surface temperatures during the 100-yr period from 1850 to 1950 could be attributed to anthropogenic forcing, which seems implausible. This lower bound is shown to be consistent with bottom-up estimates derived from physical understanding of aerosols and constraints from observations of Earth’s energy budget, the amplitude of cloud droplet concentration changes associated with strong local forcing (ship tracks), and patterns of aerosol perturbations taken from comprehensive modeling. The argument of a weaker (less negative) aerosol forcing is also consistent with the tendency of comprehensive modeling to underestimate the warming in the period between 1920 and 1950, even after accounting for natural variability. In conclusion: three different lines of evidence provide support for an aerosol forcing less negative than −1.0 W m−2. If one adopts an upper bound for the aerosol forcing of −0.3 W m−2, based on an analysis of Earth’s energy budget since 1950, this suggests that the radiative forcing from the anthropogenic aerosol is very likely (90%) to be between −0.3 and −1.0 W m−2.
This range for the present-day aerosol forcing is consistent with, but considerably narrower than, the estimate of that same forcing in the IPCC AR5. The central estimate from the AR5 (−0.9 W m−2) is also consistent with the present forcing range. Nonetheless, the arguments I adopt based on an analysis of the forcing prior to 1950 raises the question as to how the AR5 (e.g., Fig. 8.18 and Annex II therein) can so comfortably accommodate a very negative aerosol forcing without the appearance of a negative trend in the net anthropogenic forcing over the first 100 years (1850–1950) of the historical period. There are two explanations for this apparent inconsistency. The first is that my less negative forcing arises from my assertion that the Northern Hemisphere forcing must be positive between 1850 and 1950, and the AR5 shows global forcing. An argument that only considers the global forcing yields a somewhat more negative bound of −1.3 W m−2. The second explanation is that the time series of aerosol forcing provided in the AR5 is unusual, and I believe unrealistic. The AR5 forcing is estimated to have increased as much between 1750 and 1850 as it did between 1850 and 1940 despite the fact that anthropogenic emissions of SO2 increased elevenfold as much in the latter period as compared to the earlier period. One might be tempted to interpret this an extreme example of the nonlinearity in the forcing response to emissions expected from aerosol–cloud interactions, but this seems difficult to reconcile with a 30% increase in the forcing efficiency after 1940, even well before the pattern of global emissions began changing substantially.
At this point it seems worthwhile to step back and adopt a different perspective, as the present work raises the question as to why we, in the first place, think that aerosol forcing might be more negative than about −1 W m−2. Just because we cannot model solar irradiance from first principles accurately is not a good basis for assuming that solar forcing before 1950 is hugely uncertain, so why should such an argument apply to estimates of aerosol forcing? Forcing estimates based on simple physical reasoning (Charlson et al. 1992) once motivated the consideration of a large and negative aerosol forcing, but these arguments are now shown to actually be consistent with forcing of a much smaller magnitude. Comprehensive modeling readily produces very negative estimates of aerosol forcing, but its quantitative representation of the distribution of important aerosol properties is not credible (e.g., Figs. 5 and 6) and is dependent on ever more speculative effects that are increasingly contradicted by finescale modeling (Stevens and Feingold 2009). In the present work it is shown that the models produce an anthropogenic aerosol signal that is distributed much more broadly over the World Ocean than is observed (e.g., Fig. 9.28 in Flato et al. 2013) and poorly represent what little we know about present-day droplet concentrations. Moreover, because 
One advantage of the simple approach adopted here is that, even if one does not accept my arguments, they help identify what would be required for an aerosol forcing to be considerably more negative than about −1.0 W m−2. If, for instance, SO2 emissions in 1950 relative to 1975 are too large in the estimates by Smith et al. (2011), or if the forcing from aerosol–cloud interactions is for some reason linear in global SO2, a more negative aerosol forcing becomes plausible. The latter could arise because emissions become increasingly distributed, as two widely separate sources each contributing 50% to the total emissions will, all things else being equal, contribute a greater forcing than a single source producing all of the emissions. The distributed source argument is however most effective in the case of entirely new sources. Emissions of SO2 by China in 1980, 35 years ago, were still 10% of the global mean. So although emissions there have increased threefold in the past 30 years, it may well be that additional forcing had reached the point of diminishing returns long ago. One way to explore these ideas would be to extend Eq. (1) to incorporate two sources, such that Qa = Qa,1 + Qa,2, where rather than interpreting the two sources physically, they are instead used to optimally decompose the spatiotemporal–compositional pattern of aerosol burdens worldwide. Such a model would still be simple enough to be tractable, something that is essential if the ideas are to be held accountable to physical reasoning, but would be able to account for the possibility that the present model [i.e., Eq. (1)] insufficiently considers the effects from changing patterns of emissions.
Irrespective of the ultimate strength of the aerosol forcing, evidence that it has changed over the part of the observational record (the last 30–50 years) most useful for constraining the major terms in Earth’s energy budget is scant. This finding alone lends credence to recent, somewhat lower, estimates of the transient climate response (Bengtsson and Schwartz 2013) and suggests that the limitations associated with an insufficiently detailed understanding of aerosol forcing may be less of an obstacle to progress than previously thought.
Acknowledgments
I thank the Max Planck Society for the Advancement of Science for its support for the freedom of scientific research. I also thank the Lorenz Center at MIT for hosting the author during a period of time when some of these ideas were developed, during which time discussions with Kerry Emanuel, Paul O’Gorman, Dan Rothman, and Susan Solomon are gratefully acknowledged. Additional support was provided through funding from the European Union Seventh Framework Programme (FP7/2007-2013) under Grant Agreement 244067. Sandrine Bony, Saskia Brose, Jean-Louis Dufresne, Andrew Gettleman, Stefan Kinne, Nic Lewis, Robert Pincus, Florian Rauser, Hauke Schmidt, Philip Stier, Robert Wood, and several anonymous reviewers are thanked for comments on draft versions of the manuscript. Anders Engström, Seiji Kato, Stefan Kinne, Norman Loeb, and Wenying Su are thanked for supplementary radiative transfer calculations (Kinne) and analysis of the CERES data (Loeb and Kato), and further analysis of the CMIP-CERES models (Engström) to double check the author’s work. Jobst Müße is thanked for sharing his analysis of droplet concentrations from the AEROCOM Phase II models. Luis Kornblueh is thanked for babysitting the hundred historical simulations, and Thomas Schulthess and the Swiss national supercomputing center (CSCS) are thanked for providing access to their facilities for these simulations. I acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and I thank the climate modeling groups (listed in Table A2 of this paper) for producing and making available their model output and the funding agencies and institutions who provided support for coordination and data distribution. The CERES data were obtained from the NASA Langley Research Center Atmospheric Science Data Center. Primary data and scripts used in the analysis and other supplementary information that may be useful in reproducing the author’s work are archived by the Max Planck Institute for Meteorology and can be obtained by contacting publications@mpimet.mpg.de.
APPENDIX A
Aerosol–Radiation Interactions (ARI)
The form for the expression of 
Key parameters in determining α in the expression for 
Because estimates of the effective yield and sulfate lifetime are available from relatively few model studies, α in Eq. (1) is estimated from the modeling as 
APPENDIX B
Aerosol–Cloud Interactions (ACI)
Charlson et al. (1992) and the subsequent literature often has focused on marine stratocumulus clouds, when considering the possible magnitude of 
Cloud radiative effect R for a solar zenith angle of 43.66° assuming a net downward shortwave radiation equal to the tropical (35°S–35°N) average. Shown are radiative transfer calculations (points) for a cloud with liquid water content of 0.35 g kg−1 (stronger forcing) and 0.10 g kg−1 (weaker forcing) for a cloud inhomogeneity factor of 0.75, as well as a homogeneous cloud with liquid water content of 0.32 g kg−1. Analytic fits to the points assuming a power-law or logarithmic dependence on N are illustrated by the lines.
Citation: Journal of Climate 28, 12; 10.1175/JCLI-D-14-00656.1
APPENDIX C
Models, Data, and Methods
For primary data the present study relies on simulations provided by many modeling centers as part of CMIP5 (Taylor et al. 2012). A complete list of the models and the experiments used in this study is provided in Table C1, along with a reference describing each model and its associated experiments (when available).
CMIP5 models and experiments used in this study.
Radiant energy budgets are taken from the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) and SYN products (Loeb et al. 2009). Note that Ed2.8 data were mostly used, but compared to Ed2.7 and Ed3.0 data. Different editions of the data did not influence the results. The albedo is constructed from the monthly climatology from 13 years (March 2000 through April 2013) of upward clear sky and downward shortwave irradiances at the top of the atmosphere. The data are processed on the native CERES 1° × 1° latitude–longitude grid, and monthly fluxes are weighted by days per month in forming the long-term average. Land values and monthly values without insolation are masked. The median surface temperature estimates are from the HadCRUT4.2.0.0 product (Morice et al. 2012). For the aerosol data, use is made of MAC-v1.0 (Kinne et al. 2013), which describes the optical properties of tropospheric aerosols on monthly time scales, discriminated partly by species so as to separate sulfate from other contributions, and with global coverage also on a 1° grid. The climatology is developed from locally sparse, but high-quality, data collected from the AERONET ground-based sun-photometer network, and merged onto complete background maps defined by central data from global aerosol models.
In calculating greenhouse gas forcing I used concentrations taken from the data provided by the representative concentration pathways, which were developed for CMIP5 (PRE2005_MIDYR_CONC.DAT). Concentrations for CO2, CH4, N2O, and all gases controlled under the Montreal Protocol (expressed as CFC-12 equivalent concentrations) are converted to a forcing using the simplified expressions provided in Ramaswamy et al. (2001). Stratospheric ozone (a negative forcing) and tropospheric ozone (a somewhat larger positive forcing) are not considered, and assumed to be offset by land-use changes, which are commensurate with the net ozone forcing, but of opposite sign (Myhre et al. 2013a). It is estimated that accounting for these forcings could influence the estimates of the lower bound on 
Radiative transfer calculations to estimate parameter values and assumptions in the model for 
In exploring the asymmetry of the albedo in the CERES measurements averages are taken over the region between 25° and 50°N. Over this latitude belt the averaged irradiance is 337.6 W m−2, and the averaged zenith angle is 49.6°. For calculations related to cloud forcing of tropical clouds, the tropical average for a broad tropical region, equatorward of 35°, was defined. In this region the irradiance weighted zenith angle reduces to 43.66°N and the averaged solar irradiance is 390 W m−2.
For the simulations with the MPI-ESM, version 1.1 of that model was used, with the 100 ensemble members starting from a preindustrial control simulation. Ensemble members were spawned every 48 years from the control simulation, with the first ensemble member starting from year 48 of the control.
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Here and throughout radiative forcing defined as a global quantity. Although there is clear evidence of regional changes in emissions of aerosols and aerosol precursors during the modern period, the available evidences suggests that these have at most a regional imprint (e.g., Murphy et al. 2009; Stevens and Schwartz 2012; Murphy 2013; Bengtsson and Schwartz 2013).
Carslaw et al. (2013) estimate that uncertainty in 
Zelinka et al. (2014) show that for the CMIP5 models performing aerosol only runs for forcing calculations, absorption makes 
Some modeling groups (e.g., Déandreis et al. 2012) are beginning to explore the role of temporal covariances in their models. In this respect critical comparisons between the modeling and data would help increase confidence that modeled signals are capturing something fundamental.
