A two box linear model has been fitted to the HadCM3 4xCO₂ run f or both global mean temperature (T) and thermal expansion (S) response. The data can be viewed from the links below. The equations and parameters are as follows:

Where T(t) is the transient global mean surface temperature change at time t, F(t) is the relative radiative forcing (expressed as a fraction of the equilibrium value) and R(t) is the climate response function. A similar expression can be written for sea level.

Note:- The forcing caused by a doubling of CO2 quoted in the IPCC TAR (page 358) is 3.71 Wm^-2. The value estimated for CO2 doubling in HadCM3 is 3.74 Wm^-2. The constants are given below.

The constants a₁, a₂, t₁,t₂ and T_final etc. were derived by fitting the temperature curve to a GCM stabilisation experiment in which the carbon dioxide was modified. The carbon dioxide concentration was increased from a pre-industrial value at 2% per year compounded until it reached 4 times the pre-industrial level. It was stabilised at this level for the remainder of the simulation.

CO2, CH₄, N₂O, CFC-11, CFC-12, CFC-113,
HCFC-22, HFC-125, HFC-134A, SO₄-- aerosol, O₃

Details of the experiment can be found in the Hadley Centre technical note

Notes on forcing:

1. the forcing values for the A2 experiment (which can be downloaded from the table below) are expressed relative to the 1880-1920 mean value. The forcing for the 1880-1920 period relative to pre-industrial times is estimated as being 0.36 Wm^-2
2. the values are slightly different and supersede those in Figure 6 of the Tech Note. The difference between the forcing estimates results from the way the contribution from ozone is determined. The new values will be used when the work appears as a paper.

Note: In the current work we are only planning to include the first three greenhouse gases and sulphate aerosol. There will be some differences between the results obtained using the simple parameterisations and the OAGCM (HadCM3) because:

1. if you don't use the concentrations for CO2, CH4 and N2O given below (as used in HadCM3) then this can be a source of difference.
2. the minor greenhouse gases used in the Hadley Centre experiment will have some effect.
3. the climate system is not really linear, so the linear model tuned to the 4xCO2 run will not exactly match the HadCM3 A2 simulation even if the same forcing were used.

* sea-level time-series 4xCO2_sl was originally incorrect. Updated May 14th. If you previously downloaded it, please collect it again.
‡ 4xCO2_temp and 4xCO2_sl diagrams updated May 16th.