Historical Aerosol Forcing

21 Mar 2018

Earth's climate over the past 150 or so years has been strongly affected by humans. The most well known, and important, human perturbation is the increased concentration of CO\(_2\) in the atmosphere, which is responsible for the global warming we have experienced, and will continue to experience in the future. But humans have also emitted large amounts of aerosols into the atmosphere. Aerosols actually cool the planet, counteracting the increased CO\(_2\) concentrations to some extent, and we don't know by how much they've cooled the planet.

This is a surprisingly important question. If the aerosol effect is large, say a -2Wm\(^{-2}\) forcing from pre-industrial to present, it would imply that Earth's surface temperature is very sensitive to greenhouse gas forcing. This would also be worrying since we expect the aerosol forcing to increase more slowly in the future (because of efforts to reduce pollution), so temperatures would rise more quickly in the future than they have in the past. On the other hand, a small aerosol effect would point to a lower climate sensitivity. (Note that there's been a lot of work recently on why it's deceptive to use historical records to estimate Earth's sensitivity, so the magnitude of the aerosol forcing isn't the only thing to consider).

Another reason to worry about the historical aerosol forcing is that climate models are often tuned by comparing with global-mean surface temperatures from the 20th century. As part of this, models have to be given estimates of how aerosol and greenhouse gas levels varied during this time, making the final parameter settings in models sensitive to our guesses of the historical aerosol forcing.

Why is the aerosol forcing poorly constrained? Because of the classic climate issues: we don't have long enough historical records of aerosol emissions, and even if we did, aerosol processes take place on scales that are much too small to resolve in climate models, so we have to parameterize them. Another issue is that there are natural aerosols (dust, sea-salt, etc.), so even a "clean" (human-free) atmosphere has an aerosol forcing but since we've only observed a polluted atmosphere we don't know the size of this background forcing.

In a study from 2015, Bjorn Stevens tried to get at the historical aerosol forcing indirectly, using several different approaches. This is an intriguing paper: tighter constrains on the aerosol forcing would be a big step forward, and I've been curious to read it for a while.

A Simple Model for Aerosol Forcing

The centerpiece of the paper is a simple model for the global aersol forcing \(F$, based on a paper by Carlson et al. (1992). The model parameterizes \(F\) using the emission of sulfur dioxide (SO\(_2\)), which is useful because we have estimates of SO\(_2\) emissions going back to 1750, and consists of a linear term and a logarithmic term: $$ F(t) = -\alpha SO_2(t) - \beta ln\left(\frac{SO_2(t)}{\overline{SO_2}} + 1\right), $$ where \(\alpha\) and \(\beta\) are coefficients and \(\overline{SO_2}\) is a natural source of SO\(_2\).

The first term is the direct radiative effect of sulfur emissions, and the assumption is that, although the factors that determine \(\alpha\) may have varied over time, their net effect is relatively constant when averaged over a long enough period. There is some discussion of the terms that go into \(\alpha\), as well as a general discussion of how big we should expect the aerosol direct effect to be. This is based on the fact that over oceans the clear-sky albedo should be larger in the Northern Hemisphere (where most aerosols are emitted) than over the Southern Hemisphere. Observations show that this asymmetry is quite small, and give a direct aerosol effect of -0.15 Wm\(^{-2}\). There are a lot of other details here, but the conclusion is that the aerosol direct effect should be relatively small (>-0.25Wm\(^{-2}\)), and so \(\alpha\) is small as well.

The second term is the aerosol indirect effect, the influence of aerosols on clouds. Here the assumption is that \(F\) depends on the cloud droplet number, \(N\), which is often related to \(SO_2\) via a power law: \(N \sim\) SO\(_2^x\). In fact, in the appendix \(F\) also seems to be related to \(N\) via a power law. Stevens approximates all this as a logarithm (I think \(x\) is assumed to be less than 1), with the constant \(\beta\) representing the conversion from droplet number to a radiative forcing and from \(SO_2\) concentration to \(N\). There is a lot of uncertainty in all of this, but somehow Stevens claims that the aerosol indirect effect should be \(>\)-0.75Wm\(^{-2}\). It is unclear to me where he gets this number from.

Stevens estimates \(\alpha\) and \(\beta\) by fitting SO\(_2\) to various estimates of what \(F\) was at different points in time. The uncertainty is large, but the mean estimate of \(F\) is then -0.5Wm\(^{-2}\). The results of the fitting suggest that the indirect effect has been the main driver of the changes in \(F\) (\(\beta\) is much larger than \(\alpha\)), and so \(F\) has increased logarithmically with SO\(_2\) concentrations. Next, Stevens combines the model with an estimate of the historical greenhouse gas forcing to show that \(F\) must be \(>\)-1Wm\(^{-2}\) for the total (aerosols plus greenhouse gases) forcing to be greater than zero between 1850 and 1950. If the total forcing was less than zero, then the 0.3K warming of the Northern Hemisphere over that time would be entirely due to natural variability, which seems implausible.

The end result is an estimate for the aerosol forcing of -0.3Wm\(^{-2}\) to -1Wm\(^{-2}\), where the upper bound (-0.3) comes from an obervational study by Murphy et al. The point of the paper is really the lower bound of -1Wm\(^{-2}\); previous estimates, like from the Carlson et al paper, got as high as -2.3Wm\(^{-2}\).

Comparisons with CMIP5 Models

This lower bound is supported by some comparisons of models to observations. First, Stevens looks at temperature trends from 1920 to 1950, a period of rapid warming (0.09K/dec), little volcanic activity and during which the aerosol forcing and the greenhouse gas forcing were probably comparable. The volcanic activity is important because different models treat volcanoes in different ways, which adds uncertainy.

Stevens shows that in the (unforced) pre-industrial control simulations trends this big are extremely rare, so the warming trend over this period is almost surely externally forced, but only four CMIP5 models produce a comparable trend over this period in their historical simulations. This implies that models generally overestimate the magnitude of the aerosol forcing, and Stevens references a study that gave a mean aerosol forcing of -1.4Wm\(^{-2}\) for an ensemble of nine CMIP5 models.

The other comparison is with the asymmetry in the clear-sky albedo, mentioned above. The ensemble-mean value is about 2.2 times larger than an observational estimate from CERES, with the asymmetry being more than five times larger in some models than the observations. This is more evidence that the aerosol forcing is too strong in models, though models in which the indirect effect is included tend to have a smaller asymmetry.


This is a compelling paper, though it is quite confusing in places. For example, Stevens is trying to constrain the magnitude of the aerosol forcing, but uses previously published estimates to fit the parameters of his model. It is also unclear where Stevens gets some of his numbers from, like the -0.75Wm\(^{-2}\) bound on the indirect effect.

For me, the strongest part of the paper is the comparison between the CMIP5 data and observations. Stevens makes a convincing case that the historical aerosol forcing is overestimated by most of the models (or else the models are way too sensitive to aerosol forcing). It is also intriguing that models which include the indirect effect seem to fit the observations better. The form of the conceptual model is nice, and gives an intuition for how aerosol forcing should behave, but I am not convinced that the parameters Stevens estimates for it are reliable. The logarithmic form for the indirect effect is also questionable, though on a conceptual level the model is probably fine.

Although the main point of the paper is that the aerosol forcing is probably \(>\)-1Wm\(^{-2}\), his value is still within the IPCC range, whose mean is -0.9Wm\(^{-2}\), and he's basically just saying \(F\) is probably on the low side of the IPCC range. This is suggestive of a relatively low (transient) climate sensitivity for Earth's climate, though other evidence is needed before we can say anything definitive.