Forcing F is defined as the amount of the energy flux emitted by the Earth surface in the IR range and by the Sun in the UV–Vis–nearIR range that will be absorbed by components of the atmosphere and must be re-emitted at lower temperature to exit to the outer space.

Forcing by atmospheric CO₂ takes place mostly in bands around 4200 and 15000 nm

Myhre et al. have evaluated the radiative forcing caused by well mixed greenhouse gases by performing band by band calculations. They could establish the relationship for CO₂ as:

                     (eq. 6)

Where:

• F is the energy flux “forced” by CO₂ [W m^-2]
• C₀ and C₁ the initial and final CO₂ concentration

The magnitude of the parameter 5.35 is still disputed, and was reduced from publications to publications to lower values. However, it is now generally used by climate scientists and the IPCC. Il faut faire avec ce que l'on a.

Note the decreasing logarithmic relation: the forcing caused by a 1 ppm change at 800 ppm will be only 50% of the one caused by the same 1 ppm at a 400 ppm level.

Lapse rate shift

When added GHGs absorb more long-wave outgoing radiations the lapse rate in the troposphere will need to be shifted to higher temperatures to satisfy the necessary balance between incoming and outgoing energy.

Surface temperature increase as result of forcing and lapse rate. Forcing: transforming W m^-2 to °C.
Equilibrium: the upwelling heat flux, in the lower part of the troposphere in the form of convective and radiative transfer, will ultimately escape the Earth in the form of IR radiation.
Imbalance: when additional energy will be absorbed by GHGs, the corresponding “characteristic emission level” τ will be elevated to a cooler altitude.
Re-equilibration: the lapse rate (moist adiabatic) will shift towards higher temperatures.