IPCC Fourth Assessment Report: Climate Change 2007
Climate Change 2007: Working Group I: The Physical Science Basis Summary of ‘Inverse’ Estimates of Net Aerosol Forcing

Forward model approaches to estimating aerosol forcing are based on estimates of emissions and models of aerosol physics and chemistry. They directly resolve the separate contributions by various aerosol components and forcing mechanisms. This must be borne in mind when comparing results to those from inverse calculations (see Section 9.6 and Supplementary Material, Appendix 9.B for details), which, for example, infer the net aerosol forcing required to match climate model simulations with observations. These methods can be applied using a global average forcing and response, or using the spatial and temporal patterns of the climate response in order to increase the ability to distinguish between responses to different external forcings. Inverse methods have been used to constrain one or several uncertain radiative forcings (e.g., by aerosols), as well as climate sensitivity (Section 9.6) and other uncertain climate parameters (Wigley, 1989; Schlesinger and Ramankutty, 1992; Wigley et al., 1997; Andronova and Schlesinger, 2001; Forest et al., 2001, 2002; Harvey and Kaufmann, 2002; Knutti et al., 2002, 2003; Andronova et al., 2007; Forest et al., 2006; see Table 9.1 – Stott et al., 2006c). The reliability of the spatial and temporal patterns used is discussed in Sections and

In the past, forward calculations have been unable to rule out a total net negative radiative forcing over the 20th century (Boucher and Haywood, 2001). However, Section 2.9 updates the Boucher and Haywood analysis for current radiative forcing estimates since 1750 and shows that it is extemely likely that the combined anthropogenic RF is both positive and substantial (best estimate: +1.6 W m–2). A net forcing close to zero would imply a very high value of climate sensitivity, and would be very difficult to reconcile with the observed increase in temperature (Sections 9.6 and 9.7). Inverse calculations yield only the ‘net forcing’, which includes all forcings that project on the fingerprint of the forcing that is estimated. For example, the response to tropospheric ozone forcing could project onto that for sulphate aerosol forcing. Therefore, differences between forward estimates and inverse estimates may have one of several causes, including (1) the magnitude of the forward model calculation is incorrect due to inadequate physics and/or chemistry, (2) the forward calculation has not evaluated all forcings and feedbacks or (3) other forcings project on the fingerprint of the forcing that is estimated in the inverse calculation.

Studies providing inverse estimates of aerosol forcing are compared in Table 9.1. One type of inverse method uses the ranges of climate change fingerprint scaling factors derived from detection and attribution analyses that attempt to separate the climate response to greenhouse gas forcing from the response to aerosol forcing and often from natural forcing as well (Gregory et al., 2002a; Stott et al., 2006c; see also Section These provide the range of fingerprint magnitudes (e.g., for the combined temperature response to different aerosol forcings) that are consistent with observed climate change, and can therefore be used to infer the likely range of forcing that is consistent with the observed record. The separation between greenhouse gas and aerosol fingerprints exploits the fact that the forcing from well-mixed greenhouse gases is well known, and that errors in the model’s transient sensitivity can therefore be separated from errors in aerosol forcing in the model (assuming that there are similar errors in a model’s sensitivity to greenhouse gas and aerosol forcing; see Gregory et al., 2002a; Table 9.1). By scaling spatio-temporal patterns of response up or down, this technique takes account of gross model errors in climate sensitivity and net aerosol forcing but does not fully account for modelling uncertainty in the patterns of temperature response to uncertain forcings.

Another approach uses the response of climate models, most often simple climate models or Earth System Models of Intermediate Complexity (EMICs, Table 8.3) to explore the range of forcings and climate parameters that yield results consistent with observations (Andronova and Schlesinger, 2001; Forest et al., 2002; Harvey and Kaufmann, 2002; Knutti et al., 2002, 2003; Forest et al., 2006). Like detection methods, these approaches seek to fit the space-time patterns, or spatial means in time, of observed surface, atmospheric or ocean temperatures. They determine the probability of combinations of climate sensitivity and net aerosol forcing based on the fit between simulations and observations (see Section 9.6 and Supplementary Material, Appendix 9.B for further discussion). These are often based on Bayesian approaches, where prior assumptions about ranges of external forcing are used to constrain the estimated net aerosol forcing and climate sensitivity. Some of these studies use the difference between Northern and Southern Hemisphere mean temperature to separate the greenhouse gas and aerosol forcing effects (e.g., Andronova and Schlesinger, 2001; Harvey and Kaufmann, 2002). In these analyses, it is necessary to accurately account for hemispheric asymmetry in tropospheric ozone forcing in order to infer the hemispheric aerosol forcing. Additionally, aerosols from biomass burning could cause an important fraction of the total aerosol forcing although this forcing shows little hemispheric asymmetry. Since it therefore projects on the greenhouse gas forcing, it is difficult to separate in an inverse calculation. Overall, results will be only as good as the spatial or temporal pattern that is assumed in the analysis. Missing forcings or lack of knowledge about uncertainties, and the highly parametrized spatial distribution of response in some of these models may hamper the interpretation of results.

Aerosol forcing appears to have grown rapidly during the period from 1945 to 1980, while greenhouse gas forcing grew more slowly (Ramaswamy et al., 2001). Global sulphur emissions (and thus sulphate aerosol forcing) appear to have decreased after 1980 (Stern, 2005), further rendering the temporal evolution of aerosols and greenhouse gases distinct. As long as the temporal pattern of variation in aerosol forcing is approximately correct, the need to achieve a reasonable fit to the temporal variation in global mean temperature and the difference between Northern and Southern Hemisphere temperatures can provide a useful constraint on the net aerosol radiative forcing (as demonstrated, e.g., by Harvey and Kaufmann, 2002; Stott et al., 2006c).

The inverse estimates summarised in Table 9.1 suggest that to be consistent with observed warming, the net aerosol forcing over the 20th century should be negative with likely ranges between –1.7 and –0.1 W m–2. This assessment accounts for the probability of other forcings projecting onto the fingerprints. These results typically provide a somewhat smaller upper limit for the total aerosol forcing than the estimates given in Chapter 2, which are derived from forward calculations and range between –2.2 and –0.5 W m–2 (5 to 95% range, median –1.3 W m–2). Note that the uncertainty ranges from inverse and forward calculations are different due to the use of different information, and that they are affected by different uncertainties. Nevertheless, the similarity between results from inverse and forward estimates of aerosol forcing strengthens confidence in estimates of total aerosol forcing, despite remaining uncertainties. Harvey and Kaufmann (2002), who use an approach that focuses on the TAR range of climate sensitivity, further conclude that global mean forcing from fossil-fuel related aerosols was probably less than –1.0 W m–2 in 1990 and that global mean forcing from biomass burning and anthropogenically enhanced soil dust aerosols is ‘unlikely’ to have exceeded –0.5 W m–2 in 1990.

Table 9.1. Inverse estimates of aerosol forcing from detection and attribution studies and studies estimating equilibrium climate sensitivity (see Section 9.6 and Table 9.3 for details on studies). The 5 to 95% estimates for the range of aerosol forcing relate to total or net fossil-fuel related aerosol forcing (in W m–2).

 Forest et al. (2006) Andronova and Schlesinger (2001) Knutti et al. (2002, 2003) Gregory et al. (2002a) Stott et al. (2006c) Harvey and Kaufmann (2002) 
Observational data used to constrain aerosol forcing Upper air, surface and deep ocean space-time temperature, latter half of 20th century  Global mean and hemispheric difference in surface air temperature 1856 to 1997 Global mean ocean heat uptake 1955 to 1995, global mean surface air temperature increase 1860 to 2000 Surface air temperature space-time patterns, one AOGCM Surface air temperature space-time patterns, three AOGCMs Global mean and hemispheric difference in surface air temperature 1856 to 2000 
Forcings considereda G, Sul, Sol, Vol, OzS, land surface changes G, OzT, Sul, Sol, Vol G, Sul, Suli, OzT, OzS, BC+OM, stratospheric water vapour, Vol, Sol G, Sul, Suli, Sol, Vol G, Sul, Suli, OzT, OzS, Sol, Vol G, Sul, biomass aerosol, Sol, Vol 
Yearb 1980s 1990 2000 2000 2000 1990 
Aerosol forcing (W m–2)c  –0.14 to –0.74 –0.07 to –0.65 with expert prior  –0.54 to –1.3  0 to –1.2 indirect aerosol –0.6 to –1.7 total aerosol  –0.4 to –1.6 total aerosol –0.4 to –1.4 total aerosol Fossil fuel aerosol unlikely < –1, biomass plus dust unlikely < –0.5d 


a G: greenhouse gases; Sul: direct sulphate aerosol effect; Suli: (first) indirect sulphate aerosol effect; OzT: tropospheric ozone; OzS: stratospheric ozone; Vol: volcanic forcing; Sol: solar forcing; BC+OM: black carbon and organic matter from fossil fuel and biomass burning.

b Year(s) for which aerosol forcing is calculated, relative to pre-industrial conditions.

c 5 to 95% inverse estimate of the total aerosol forcing in the year given relative to pre-industrial forcing. The aerosol range refers to the net fossil-fuel related aerosol range, which tends to be all forcings not directly accounted for that project onto the pattern associated with fossil fuel aerosols, and includes all unknown forcings and those not explicitly considered (for example, OzT and BC+OM in several of the studies).

d Explores IPCC TAR range of climate sensitivity (i.e., 1.5°C to 4.5°C), while other studies explore wider ranges