Accounting for Aerosol Forcing in Pattern Scaling

Pattern scaling was invented by the first author of this paper, and first described in Santer et al. (1990).  The primary motive was to allow a limited number of GCM results to be generalized to cover a wider range of both emissions scenarios and climate model parameters in a computationally efficient way. The underlying assumption of pattern scaling is that the geographical patterns of climate change per unit of global-mean warming are similar, and largely independent of the amount of warming and the details of atmospheric composition changes that lead to this warming. If this assumption is reasonable, then the time-evolving pattern of change for variable “Y” will be given, to a high degree of approximation, by:

      ΔYb(x,t) = ΔTb(t) * [ΔYa(x,t0) / ΔTa(t0)]

 where ΔYa(x,t0) is the pattern of change and ΔTa(t0) is the global-mean temperature change for an experiment with emissions scenario ‘a’ at some time t0, and ΔYb(x,t) and ΔTb(t) are the corresponding terms for emissions scenario ‘b’ at time t. Essentially, emissions scenario ‘a’ is used to define a characteristic standardized pattern of change (i.e., the change per unit global-mean warming) and this is simply scaled up by ΔTb(t) to obtain the pattern at time t for scenario ‘b’. This method, which we call ‘naïve’ pattern scaling, has been used many times subsequent to our original paper. The method works well for forcing that is dominated by long-lived species, such as CO2, where the forcing pattern satisfies the underlying assumption of the method.

 For short-lived species, however, such as sulfate aerosols, the underlying assumption clearly fails. Forcing patterns for such species are closely related to the pattern of emissions, which have changed in the past and are projected to change markedly over space and time in the future. These changes in emissions and forcing lead to spatio-temporal changes in climate response patterns. This is particularly important for SO2 emissions and sulfate aerosol forcing. Over the past four decades, the pattern of SO2 emissions has shifted dramatically from peak emissions over North America and Europe to maximum emissions over eastern Asia. A method for accounting for these changes was developed in the mid 1990s, and has been implemented since then in various versions of the MAGICC/SCENGEN climate model software (  The method divides emissions into long-lived species with a single characteristic response pattern, and short-lived species with time-varying response patterns. The latter in turn are determined by dividing the globe into three primary emissions regions, each of which has a characteristic response pattern. The total response pattern is determined by a linear combination of the three regional patterns, with time-varying weights that are related to the time-varying emissions in the three regions. In this paper we describe the method in more detail and present illustrative results.


Santer, B.D., Wigley, T.M.L., Schlesinger, M.E. and Mitchell, J.F.B., 1990:  Developing Climate Scenarios from Equilibrium GCM Results. Max-Planck-Institut für Meteorologie Report No. 47, Hamburg, Germany, 29 pp.

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Tom Wigley

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Wednesday, April 23, 2014 - 6:30pm