# Calculate GWP over arbitrary time

The GWP (Global warming potential) is calculated over a given time scale $$T$$ (20 or 100 years usually), defined as the ratio between the energy absorbed by a pulse of 1Kg of gas during time $$T$$ compared to the energy absorbed by a pulse of 1Kg of CO2 during the same time.

The AR4 IPCC report gives a table of the GWP$$_{20}$$ and GWP$$_{100}$$ of most greenhouse gases. How can someone calculate the GWP of a given gas (say methane for instance) over another period of time GWP$$_T$$ ?

I understand from the AR4 that the calculations of GWP depend on several assumptions (among which how the carbon cycle is calculated and predictions in emissions to a lesser extent, due to the nonlinear increase of radiative forcing of CO2/methane with concentration). So let's put that problem aside and just focus on one scenario (the IPCC's for instance.)

What would be a concrete formula $$\mathop{GWP}(gas, T) = \dots$$ ?