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The Upwelling-Diffusion Climate Model (UDCM) of IMAGE 2.2 represents the core-model of the Atmospheric Ocean System (AOS). UDCM converts the concentrations of the different greenhouse gases and SO2 emissions into radiative forcings and successively into temperature changes of the global-mean surface and the ocean. UDCM is based on the MAGICC-model of Climate Research Unit (CRU) (Hulme et al., 2000). The MAGICC model is the most widely used simple climate model within the IPCC (2001). More details on MAGICC can be found in Raper et al. (1996) and Hulme et al. (2000). The implementation of MAGICC in IMAGE 2.2 and the calculation of the radiative forcings is described by Eickhout et al. (2001).
The model input and output of UDCM are presented in the table below.
| Model input | Atmospheric concentrations of greenhouse gases and emissions of SO2 |
| Model output | Radiative forcings of greenhouse gases and aerosols |
| Global-mean surface temperature change and temperature change of the ocean |
The different chemical compounds, with the determination of their radiative forcing specified, are listed below. For an explanation of these compounds, see definitions - chemical compounds.
|
Chemical compounds |
Determination of radiative forcing |
| Greenhouse gases (CO2, CH4 and N2O) | Simplified expressions taken from Table 6.2 in TAR (IPPC, 2001). Both the CH4 and N2O forcing are corrected for the overlap in their radiative forcings |
| Chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), hydrofluorocarbons (HFCs), chlorocarbons (CCs), bromocarbons, perfluorocarbons (PFCs) sulphur hexafluoride (SF6) |
Conversion of the change in atmospheric concentration to radiative forcing with the radiative efficiency (W m-2 per ppbv) from Table 6.7 in TAR (IPCC, 2001) |
| Tropospheric and stratospheric ozone | Tropospheric ozone concentration from ACM is converted into radiative forcing with a radiative efficiency of 0.042 W m-2 per Dobson Unit (DU) (IPCC, 2001).
Stratospheric-ozone forcing is calculated by using the concentration of chlorine- and bromine-containing gases multiplied by the numbers of chlorine and bromine atoms of the halocarbon concerned (Harvey et al., 1997). |
| Stratospheric water vapour | Calculated as a fraction of the pure CH4 forcing (without correction for N2O overlap) accordig to Harvey et al. (1997). |
| Aerosols | Direct and indirect forcing of sulphate aerosols are calculated according to Harvey et al. (1997). Hence, the direct effect is scaled linearly with the energy and industry emissions of SO2 and the indirect effect varies with the logarithm of SO2 emissions from energy and industry.
The effect of fossil organic and black-carbon aerosol is calculated with an offset value of 0.1 W m-2 for 1990, and scaling after 1990 on the basis of SO2 emissions of energy and industry. Biomass-burning organic- and black-carbon aerosol effects are assumed to be -0.2 W m-2 in 1990 (IPCC, 2001). After 1990, these effects are scaled on the basis of SO2 emissions from biomass burning. |
UDCM is an upwelling-diffusion, energy-balance model of which the basis is presented by Wigley and Schlesinger (1985). The model consists of an atmosphere box, two land and two ocean boxes (representing the Northern and Southern Hemisphere). The two ocean boxes are divided into 40 layers each, with a mixed layer on top that absorbs the energy of solar radiation. It is assumed that no energy is adsorbed above land. The energy balance of the climate system can be described as follows:
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with:
Q = radiative forcing (J yr-1 m-2)
F = net heat flux into the ocean (J yr-1 m-2)
= feedback parameter (J yr-1 m-2 K-1)
Q and F are both averaged over the entire world area. The term 
T is the change in the rate of heat loss to space from the climate system. The feedback parameter is the inverse of the climate sensitivity parameter. The climate sensitivity parameter is defined as the global-mean surface temperature response to the radiative forcing. The climate sensitivity parameter is determined by the eventual global-mean temperature change for a CO2 doubling (T2x) divided by the radiative forcing that accompanies such a doubling (Q2x). T2x is the most uncertain input of UDCM. According to TAR (IPCC, 2001), three values are used: 1.5ºC as the lowest, 2.5ºC as best guess and 4.5ºC as the highest. Note that, instead of using a global mean value for the feedback parameter, UDCM uses a land/ocean sensitivity ratio of 1.2:1 to account for a difference in response of land and ocean to changes in CO2 concentrations (Raper et al., 1996).
On time scales relevant to climate change, the atmosphere may be assumed to be in equilibrium with the underlying oceanic mixed layer:
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with:
dT/dt = temperature change per year for the oceanic upper layer (K yr-1)
Cm = the effective bulk heat capacity of the oceanic mixed layer (J yr-1 m-2 K-1).
The absorbed heat is transported within each ocean box by diffusion and upwelling. The upwelling decreases at increasing temperatures of the ocean, with a maximum decrease of 1.2 m per year (from 4.0 to 2.8 m per year) to simulate the slowing down of the thermohaline circulation of the ocean (Raper et al., 2000).
The output of UDCM is the global-mean surface temperature change and the global temperature change of the 40 oceanic layers. The temperature change in the oceanic mixed layer is corrected to account for a slower response of the upper layer since large areas are ice-covered.
For geographical pattern-scaling (GPS) UDCM can be used in two ways to account for the nonlinearity of climate forcing by sulphate aerosols:
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