GWP. Global warming potential

Global Warming Potential(GWP) is a relative measure of the heat a greenhouse gas traps inside the atmosphere, in reference to $CO_2$ . $\frac{\Phi_{RF,X}}{\Phi_{RF,CO_2}}=\frac{GWP_{X,y[yr]}}{GWP_{CO_2}}\frac{M_X}{M_{CO_2}}=GWP_{X,y[yr]}\frac{M_X}{M_{CO_2}}$ where $M_X$ and $M_{CO_2}$ are the total mass of gas $X$ and $CO_2$ in the atmosphere (not the mass of one molecule), respectively, and $GWP_{X,y[yr]}$ is the global warming potential of gas X over a time period of y years. And $GWP_{CO_2} = 1$ by definition (CO₂ is the reference, so the middle term simplifies).

Three levels of comparison ( $CH_4$ , 100 yr):

Per kg: GWP = 34
Per ppm: Same number of molecules, but a lighter molecule has less mass- less impact per molecule → $34\cdot\frac{16}{44} = 12.4$
Impact in real atmosphere: × ppm ratio → $12.4\cdot\frac{1.8}{400} = 0.055$

Why GWP depends on the time period: gases break down in the atmosphere at different rates. Methane has a half-life of ~12.4 yr, $CO_2$ ~350 yr. Over 20 years most of the methane is still present, so $GWP_{CH_4,20yr} = 86$ . Over 100 years most of it has already decayed while $CO_2$ remains, so $GWP_{CH_4,100yr} = 34$ .

Typical traps

$M_X/M_{CO_2} = \frac{\text{ppm}_X}{\text{ppm}_{CO_2}}\cdot\frac{M_{m,X}}{M_{m,CO_2}}$ . Don’t forget the ppm ratio (HW 4E).
$CO_2$ is given in ppm, the answer is often asked in ppb (1 ppm = 1000 ppb).
Check which time period the given GWP refers to (20, 25 or 100 yr). It changes between exams.

Related: Radiative forcing, Mole and Avogadro constant (ppm → mass ratio)