Removal of atmospheric GHGs and Global
Warming Potential Factors
Removal formulae
Computing the impact of greenhouse gas additions to the atmosphere is complicated by the fact that
these gases are removed by natural processes as they are added. Here we review the latest IPCC (2013)
approach to these removals and discuss why global warming potential factors (or the equivalent) are
useful and how they are computed.
The IPCC (2013) removes a sudden addition of methane or CO2 from the atmosphere by multiplying that
addition by the following function of time after the addition, t:
(1)
fCH 4 t   e
 t
 CH 4
fCO2 t   0.2173  0.224e
t
394.4
 0.2824e
t
36.54
 0.2763e
t
4.304
The previous IPCC report (AR4) removed methane in the same fashion, but removed CO2:
(2)
fCO2 t   0.217  0.259e
t
172.9
 0.338e
t
18.51
 0.186e
t
1.186
At t=1 all these factors =1, e.g., fCH4(t=0) = fCO2(t=0) = 1. Figure 1 compares the removal of CO2 in (1) and
(2) and to other suggested removal suggestions. They two most recent IPCC are not as different as they
might appear from the above formulae, but the range of removal suggestions (especially their 2
shaded spread) is quite broad.
Figure 1. fCO2(t) shown in text equations (1, black curve) and (2, blue curve) and other suggestions for the removal of a
sudden addition of CO2 to the atmosphere from other workers. Reproduced from IPCC (2013, Figure 8SM.4).
The proper method of calculation
The proper method of calculation is to:
1. adopt an emissions scenario, e.g., how much coal, oil, and gas is to be burned each year, how
much CO2 is released as a consequence, how much methane is released in the process of mining
the coal and producing, transporting, and delivering the gas, etc.,
2. determine the yearly additions of CO2 and CH4 (and other greenhouse gasses) to the
atmosphere from this scenario,
3. decay these yearly additions according to (1) above, and
4. sum all the yearly additions to obtain the increase in concentration of CO2 and CH4 (and other
GHGs) in the atmosphere as a result of the scenario.
This method was used by Cathles (2012) to compare the greenhouse impact of (1) converting electricity
generation and holding oil use steady by substituting gas and then converting to zero carbon energy
sources, compared to (2) converting to zero carbon energy sources immediately. This method is also
that used by Wigley in his MAGICC program (available at http://www.cgd.ucar.edu/cas/wigley/magicc/).
The Global Warming Potential (GWP) Approximation
Because the proper method requires considerable programming and data assembly, the GWP
approximation has become popular. This method expresses, over some stated time interval, the relative
greenhouse impact of another greenhouse gas to the same mass (or mole) addition of CO2. The
radiative efficiency of each gas (i.e., the forcing produced by the addition of 1ppbv of that gas to the
atmosphere) is multiplied by the average concentration of the gas over the time interval (e.g., the
integral of fCH4(t) or fCO2(t) in equation (1) above over the time interval divided by the time interval) and
the ratio of the two gases taken. The analytical expression for the GWP of methane is:
1 
(3)
GWP(t ) 
ftsOZ
 t



FCH 4  C
 CH 4 




1

e
 f sH 2O 

 M 
CH 4 
CH 4  
ppbvCH 4 




.
3


t
FCO2  C


i 

ao t   i ai 1  e



ppbvCO2  M CO2 



i 1


The derivatives of the radiative forcings with respect to concentration are called the radiative
efficiencies (e.g., RE  FCH 4 ). They can be computed from formulae given in IPCC(2013,
CH 4
ppbvCH 4
supplemental material for chapter 8) as discussed here. The f factors in the numerator augment the
forcing of methane for troposphere and stratosphere changes in ozone and stratosphere changes in
water vapor that are induced by changes in CH4 in the atmosphere. The factor C/Mi (where i is the
species and C 
109 M air
matm
=5.6414 x 10-9, where Mair is the molecular weight of air 28.97 and matm is
the mass of the atmosphere 5.1352 x 1018 kg) converts the units of RE from W m-2 ppbv-1 to W m-2 kgi-1.
Values are given in Table 8.A.1 of IPCC (2013). C/Mi has the units of ppbv per kg of the gas. The values
of i and ai are given in equation (1) above and are: ao=0.2173, a1=0.224, 1=394.4, etc. t is the time
interval in years. CH4 is the perturbation lifetime of methane in the atmosphere (~12.4 years), which
differs from the lifetime of methane (8.75 years, see discussion here) for reasons apparently related to
methane’s indirect interactions. Currently, I do not understand the physical-chemical basis of this
distinction. Regardless, in the limit of t→0, the bracket expression →1 and thus GWP(0) is the ratio of
the radiative efficiencies (RE) of the two gases with the f factors included:
1.65 x (RECH4=3.63x10-4) /RECO2=1.37x10-5) = 120.4. Instantaneously methane is 120.4 times more
potent than CO2 on a mole for mole (or ppbv) basis.
The absolute radiative efficiency: ACH 4 [
W m-2
FCH 4  C
 , where A
]


CH 4 is the absolute
kg CH4
ppbvCH 4  M CH 4 
radiative efficiency of pure methane. The numerator and denominator in equation (3) are the absolute
GWP factors for the two species and equation (3) can be rewritten to reflect this:
(4)
GWP(t ) 
AGWPCH 4 (t )

AGWPCO2 (t )
1 
 t



ftsOZ  f sH 2O ACH 4 CH 4 1  e CH 4 

,
3
 t



ACO2  ao t   i ai 1  e  i  


i 1

AGWPCH4 is the absolute GWP factor of pure methane.
Table 8.A.1(at the end of IPCC chapter 8) lists the RE and AGWP for all greenhouse species for 20 and
100 years. From it and the expressions above one can easily verify that the 0, 20 and 100 year GWP for
methane are 120.4, 84 and 28 respectively. There is a lot of jargon, but what should be remembered is
that the GWP simply corrects the ratio of greenhouse forcing for the average concentration of the two
gases over some selected interval of time. The uses and pitfalls of GWP analysis are discussed here.
References
Cathles LM, Brown L, Taam M, and Hunter A (2012a) A commentary of “The greenhousegas footprint of natural gas in shale formations” by RW Howarth, R. Santoro, and A
Ingraffea, Climatic Change, DOI 10.1007/s10584-011-0333-0.
http://www.springerlink.com/content/x001g12t2332462p/
Cathles LM, Brown L, Taam M, and Hunter A: (2012b) Press Release: Response to Howarth
et al’s Reply (February 29, 2012).
http://www.geo.cornell.edu/eas/PeoplePlaces/Faculty/cathles/Natural%20Gas/Resp
onse%20to%20Howarth's%20Reply%20Distributed%20Feb%2030,%202012.pdf
Cathles, LM (2012) Assessing the greenhouse impact of natural gas, G3, 13(6), 18 p.
http://www.geo.cornell.edu/eas/PeoplePlaces/Faculty/cathles/Natural%20Gas/Cathles%20Assessing%20GH%20Impact%20Natural%20Gas.pdf
Howarth RW, Santoro R, and Ingraffea A (2012) Venting and leaking of methane from shale
gas development: Response to Cathles et al., Climatic Change. Doi: 10.1007/s10584012-0401-0: http://www.springerlink.com/content/c338g7j559580172/fulltext.pdf
Howarth RW, Santoro R, and Ingraffea A (2011) Methane and the greenhouse gas footprint
of natural gas from shale formations. Climatic Change Letters, doi: 10.1007/s10584011-0061-5. http://www.springerlink.com/content/e384226wr4160653/
IPCC (2013) Climate Change 2013: The Physical Science Basis. Contribution of Working
Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate
Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels,
Y. Xia, V. Bex and P.M. Midgley(eds.)]. Cambridge University Press, Cambridge, United
Kingdom and New York, NY, USA, 1535 pp.