zankaon said:
One might keep in mind that equal quantities might be best considered in terms of effect of equal number of molecules; that is 1 mole. The respective gram molecular weights are 44 gm for CO2 and 16 gm for methane, giving the same number of molecules i.e. Avogadro number of ~6 x 10^23, even though the wt difference would be 44/16 = 2.75. http://en.wikipedia.org/wiki/Avagadro%27s_number"
Quite right. The factor 23 difference is per additional molecule, not per equal mass unit.
vanesch said:
I think the 23 more comes from equal QUANTITIES of gas added:
375 ppm CO2 and 1.7 ppm CH4 gives you (MODTRAN) 287.844 W/m2
add 10 ppm CO2: this gives you 287.75 W/m2 or a forcing of 0.094 W/m2 for 10 ppm CO2
add 10 ppm CH4: you get 285.143 W/m2 or a forcing of 2.7 W/m2
so here we find a factor of 28 more forcing for 10 ppm of CH4 added, than for 10 ppm of CO2 added.
Your value of 28 is actually more accurate for current conditions than the 23 quoted previously. But we can improve it further. The modtran calculator is a useful but simple tool intended for student use; and it doesn't actually work all that well for calculating forcings accurately. (See email from the author David Archer in [post=2324953]msg#26[/post] of thread "Rising Carbon Dioxide Levels Don’t Increase Earth’s Temperature", in response to some issues you uncovered earlier.)
A more accurate approach would be to use formulae for estimating forcings, and take derivatives. The equations in http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/212.htm of the third IPCC assessment report continue to be a good guide and are still applied in the more recent fourth assessment. Note that the methane forcing has a correction for N
2O, due to overlap in the absorption bands.
Here is a transcription of those formulae, followed by some algebraic manipulations to get the forcing per unit concentration. A "forcing" is a change in energy balance, measured in W/m
2, arising from a change (in this case) in concentrations of gases.
Variables used:
\begin{array}{ll}<br />
M_0, M & \text{Methane concentrations (ppbv) initial and final} \\<br />
N_0, N & N_2O \text{ concentrations (ppbv) initial and final} \\<br />
C_0, C & CO_2 \text{ concentrations (ppmv) initial and final} \\<br />
\Delta F_M, \Delta F_N, \Delta F_C & \text{Associated forcings}<br />
\end{array}
Formulae:
\begin{align*}<br />
\Delta F_C & = 5.35 \times \log_e \left[ C / C_0 \right] \\<br />
f(M, N) &= 0.47 \times \log_e \left[ 1 + 2.01 \times 10^{-5} (MN)^{0.75} + 5.31 \times 10^{-15} M(MN)^{1.52} \right] \\<br />
\Delta F_M & = 0.036 ( \sqrt{M} - \sqrt{M_0} ) - ( f(M, N_0) - f(M_0, N_0) ) \\<br />
\Delta F_N & = 0.12 ( \sqrt{N} - \sqrt{N_0} ) - ( f(M_0, N) - f(M_0, N_0) ) \\<br />
\intertext{Now get rates of change for forcing, per change concentrations}<br />
\frac{dF}{dC} &= \frac{5.35}{C} \\<br />
\frac{\partial f}{\partial M} & = 0.47 \frac{2.01 \times 10^{-5} \times 0.75 \times N^{0.75}M^{-0.25} + 5.31 \times 10^{-15} \times 2.52 \times (MN)^{1.52}}{1 + 2.01 \times 10^{-5} (MN)^{0.75} + 5.31 \times 10^{-15} M(MN)^{1.52}} \\<br />
\frac{dF}{dM} &= \frac{0.018}{\sqrt{M}} - \frac{\partial f}{\partial M}[M,N_0]<br />
\end{align*}
As we should expect, the rate of change of forcing is independent of initial values; although methane results depend on N
2O concentrations. Current values (accessed July 2009) are at
Recent Greenhouse Gas Concentrations, CDIAC. Note that methane varies significantly over the course of a year, so a range is given.
Values: C = 383.8 ppm. N = 320 .. 321 ppb. M = 1735 .. 1857 ppb.
Substituting in the formulae, and scaling the methane rate by 1000 to convert from ppb to ppm, gives:
\begin{align*}<br />
\frac{dF}{dC} &= 0.014 \\<br />
1000 \times \frac{dF}{dM} &= 0.36 \text{ to } 0.37 \\<br />
\text{ratio efficacy methane to } CO_2 &= 25.7 \text{ to } 26.6<br />
\end{align*}
Methane is currently about 26 times more potent in the forcing impact, molecule for molecule. The main reason for this is not because the molecules themselves are any better at thermal absorption, but because concentrations are so much lower, which means small additional changes have a larger effect.
After doing this calculation, I found that the results are available in the
fourth assessment report, table 2.14, as "radiative efficiency" given in W m
-2 ppb
-1. Scaling by 1000, they are 0.014 for CO
2 and 0.37 for methane; as obtained in the calculations shown here.
Cheers -- sylas