I recently wrote a review and analysis of the methane atmospheric chemistry feedback (Holmes, 2018 JAMES). After it was published, a colleague asked me for some details about calculating the CH_{4} radiative forcing using output from the GEOS-Chem chemical transport model. Although the relevant equation can be derived from the JAMES paper, it doesn’t explicitly appear there.

The direct radiative forcing (RF) resulting from a change in methane burden (*δm*) in the atmosphere is*RF _{CH4}= E_{RF,CH4} δm*, (1)

where

*E*is the radiative forcing efficiency of CH

_{RF,CH4}_{4}. This efficiency can be calculated from an IPCC (Ramaswamy et al., 2001) formula originally developed by Myhre et al. (1998). For present-day levels of CH

_{4}and N

_{2}O,

*E*= 270 mW m

_{RF,CH4}^{-2}ppm(CH

_{4})

^{-1}.

Many atmospheric chemistry models prescribe CH_{4} concentrations so, by design, they can’t calculate *δm*. However, these models can and do simulate chemical loss of CH_{4} by reactions with tropospheric OH and other oxidants. As Eq. 10 in the JAMES paper shows, the mass change resulting from a steady state change in CH_{4} emissions (*δE*) or CH_{4} lifetime (*δτ*) is*δm/m _{0} = f δE/E_{0} = f δτ/τ_{0}*. (2)

The variables with subscript zero represent the present-day values and

*f*≈ 1.37 is the feedback factor.

From Eq. 2, we can derive

*δm = f m*(3)

_{0}δE/E_{0}and

*δm = f m*. (4)

_{0}δτ/τ_{0}As a result, for a change in CH_{4} emissions, the resulting steady-state CH_{4} RF is** RF_{CH4} = E_{RF,CH4} f τ_{0} δE/E_{0}**. (5)

For a change in CH

_{4}lifetime (e.g. due to changing NOx emissions), the steady-state CH

_{4}RF is

**. (6)**

*RF*_{CH4}= E_{RF,CH4}f m_{0}δτ/τ_{0}Atmospheric chemistry models that prescribe CH_{4} concentrations will also lack the tropospheric O_{3} change that is induced by CH_{4} changes. The CH_{4}-induced O_{3} provides an additional RF of** RF_{O3-from-CH4} = E_{RF,O3} f m_{0} δτ/τ_{0} d(O_{3})/d(CH_{4})**. (7)

Reasonable values are

*E*= 36 mW m

_{RF,O3}^{-2}DU(O

_{3})

^{-1}

*and*= 3.5 DU(O

*d(O*_{3})/d(CH_{4})_{3}) ppm(CH

_{4})

^{-1}(Holmes et al., 2011, PNAS). If the changes are driven by CH

_{4}emission changes then Eq. 7 still applies with δE/E

_{0}taking the place of δτ/τ

_{0}. Parameter values in the equations can be updated based on recent literature as needed.