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The globally averaged temperature change simulated by the Upwelling-Diffusion Climate Model (UDCM) needs to be scaled to obtain geographical implicit maps of temperature change and precipitation change. The models within the Terrestrial Environment System (TES) of IMAGE 2.2 require monthly climatic data on a two-dimensional 0.5 degree longitude and latitude grid. The standardized approach for pattern-scaling is described in detail by Carter et al. (1994). The approach used to combine the geographical pattern-scaling for the combined climate response to forcing by greenhouse gases and sulphate aerosols, as summarized here, is described in detail by Schlesinger et al. (2000). Its implementation in IMAGE 2.2 is presented by Eickhout et al. (2001).
The major model input and output of Geographical Pattern Scaling (GPS) are presented in the table below:
| Model input | Yearly, global mean surface temperature change |
| Model output | Monthly, regionalized temperature and precipitation changes, and daily temperatures (0.5 by 0.5 degree grid) |
The main assumption of the approach used in GPS is the linear climate response to greenhouse forcings is linear, while the response to aerosol (sulphate) forcings is non-linear. In this approach geographical patterns of reponse to greenhouse gases and to sulphate aerosols are combined by adding the appropriate weights to the patterns. The different geographical patterns are obtained as follows:
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with:
Tcell(m) = temperature of grid cell in year t relative to 1990 for GCM run m
TGCM,cell(m) = temperature change of grid cell from GCM run m
GCM,global = global mean surface temperature change from GCM run
UDCM,global = global mean surface temperature change from UDCM in year t
To take the linear effect of GHG and the non-linear effect of sulphate aerosols into account, this equation is applied eight times:
1. The first run of UDCM is based on the climate forcing after 1990 by greenhouse gases only. The corresponding temperature change is scaled with a GHG-only pattern from the selected GCM as explained in the above equation. The Hadley GCM run with greenhouse gases only (HADCM2) is used as default in IMAGE 2.2.
2. The second run of UDCM uses the climate forcing by sulphate only (other greenhouse gases held contant after 1990). The corresponding temperature change is scaled with a sulphate-only pattern from the UIUC-GCM (University of Illinois at Urbana-Champaign). The results of the first and second iteration are added (no weights) to obtain the combined pattern of radiative forcings by greenhouse gases and sulphate aerosols.
3-8. So far, only linear responses are taken into account. Runs 3-8 are made to account for the non-linear climate response to radiative forcing by sulphate aerosols. These runs are based on the relative change in radiative forcing since 1990 in six UIUC-regions (see table below for UIUC regions with the corresponding IMAGE 2.2 regions). The weights of the regional patterns are calculated as follows:
The result is a pattern in which the non-linear effect of sulphate is taken into account. This pattern is added to the 1990 observed climate (New et al., 1999) to obtain a total temperature pattern every five years for the 0.5 by 0.5 degree IMAGE grid cells.
The table below presents the 6 UIUC regions (Schlesinger et al., 2000) and the corresponding IMAGE 2.2 regions.
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