First, define the ratio of the radiative forcing (RF) of CO2 to that of N2O, call it “R” for lack of a better name
R = RF(CO2)/RF(N2O) (1)
The forcing function is defined as the change in the balance of the radiation coming into the atmosphere to the radiation going out. (source
**broken link removed**) (reference 1) The Global Warming Potential (GWP) is defined as the time integrated radiative forcing from the release of 1kg of gas to that of 1kg of a reference gas, the reference gas being CO2, which has a GWP of 1. (source: see post #223) (reference 2)
GWP = RF(1kg N2O)/RF(1kgCO2)
The value for N2O is 30, so for an equal mass of N2O to CO2, the radiative forcing is 30 times more.
Thus, given the mass of the various gases, equation (1) can be used calculate the radiative forcing ratio of two gases, ie CO2 and NO
R = GWP(C02)*mass(CO2)/GWP(N2O)*mass(N2O)
Now, the total mass of the atmosphere is 4.41 million billion tons, or 4.41X10^15 tons. ( I can’t find my source any longer, but this figure is conservative compared to other sources, and significance of which will become more clear later )
The amount of CO2 in the atmosphere is 383ppm my volumn, or 582ppm by mass ( source:
Carbon dioxide - Wikipedia, the free encyclopedia) If the rise on CO2 is 17% as in reference 2, then the starting value is about 497ppm. And thus, the rise in the mass of CO2 during the interval is given as the difference is ppm times the total weight of the atmosphere:
M(CO2) = 4.41X10^15*/1X1-^6*85 = 3.75X10^11 tons.
During the interval, the rise on N2O was 9000 tons. (see reference 2)
Using these results, the relative forcing can be calculated from (1)
R = 3.75X10^11/9000*30 = 1,309. Thus, the radiative forcing for the rise in CO2 is more than 1000 times that of the lowering for N2O over the same period.
EDIT: Corrected symbols