Parameters for tuning a simple climate model (plus aerosol forcing)

Jason Lowe (Met Office, Hadley Centre for Climate Prediction and Research, UK) has provided some tuning data from HadCM3 for the first phase of the study, and aerosol forcing for the second. Parameters for a simple double exponential impulse response function model are given below. Parties do not have to use the IRF model if they have an alternative.

Impulse response climate model

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.

Temperature constants

 Tfinal = 7.3583 a1 = 0.59557 a2 = 0.40443 t1 = 8.4007 t2 = 409.54

Sea level constants

 Sfinal = 4.7395 a1 = 0.96677 a2 = 0.03323 t1 = 1700.2 t2 = 33.788

The constants a1, a2, t1,t2 and Tfinal 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.

A2 OAGCM simulation
This experiment used the HadCM3 model to simulate the climate between 1860 and 2100. Prior to 1990 historical concentrations, derived from historical emissions, were used. Beyond 1990 the concentrations were derived from the A2 emissions scenarios. The simulation included the following chemical species:

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.