What is the real radiative forcing value of CO2?

IPCC has used as radiative forcing value for carbon dioxide (CO2) the equation introduced by Myhre et al. in 1998 even in its latest report AR5. The formula of this equation is:

(1) RF = 5.35*ln(C/280)

Where RF is radiative forcing in W/m2, and C is the CO2 concentration in ppm. Myhre et al. (1998) informs that “only the direct forcing to a change in WMGG (well mixed greenhouse gases) concentration is considered here” in calculating RF values.

There are two other studies referred in AR4. The RF values of 560 ppm CO2 concentrations in these three studies are: Myhre et. al. (1998) 3.71 W/m^2, Hansen et al. (1998) 3.63 W/m^2, and Shi (1992) 3.98 W/m^2. IPCC has regarded these three simplified expressions to be reliable and one can see the RF values are very close to each other. Only Shi specifies that he has used “fixed relative humidity”, which means positive water feedback. The other studies do not specify humidity conditions. The author’s conclusion is that also Myhre et al. and Hansen et al. have used the constant relative humidity conditions in the atmosphere. Otherwise Shi’s RF value for CO2 should be about twice as much as in the other studies. The exact water content has not been specified in any of these studies.

The author has carried out an analysis using the spectral analysis method for finding out, what is the RF value of CO2 utilizing the Spectral Calculator tool available through Internet. The atmospheric model has been one dimensional model (1D) combined from three climate zones published by Ellingson et al. (1991). The most important feature is that the water profile of 1D atmosphere is 2.6 TPW (total precibitable water). In this method the author has calculated the OLR (outgoing longwave radiation) changes for three different concentrations of CO2 (393 ppm, 560 ppm, 1370 ppm), when the reference value is 280 ppm. The OLR changes for these three different concentrations are 1.03 W/m^2, 2.16 W/m^2, and 5.04 W/m^2. The logarithmic formula is:

(2) RF = 3.12*ln(C/280)

The logarithmic relationship is a very good representation form but the coefficient is different from that of Myhre et al.

The RF value according to equation (2) for the CO2 concentration 560 ppm is 2.16 W/m^2 and it is 58.4 % of the RF value of 3.7 W/m^2 according to equation (1). The author carried out the same analysis using another spectral analysis tool MODTRAN. The RF value according to MODTRAN simulations is exactly 50 % smaller for the CO2 concentration 560 ppm. This is another evidence that equation (1) by Myhre et al. has been calculated in the constant RH conditions, because this RF value of CO2 is practically 100 % bigger than the value calculated without water increase.