Radiative Forcing

Changes in the concentration of greenhouse gases in the atmosphere induce warming by changing the solar energy balance. It is straight forward to calculate the change in radiative forcing from a change in atmospheric concentration, but there are some subtitles that need to be understood, particularly for methane. We discuss radiative forcing for CO2 and CH4 in this document.

Figure 1. Mole fractions of carbon dioxide and methane in the atmosphere since 1750 from the IPCC(2013).

Figure 1 shows how CO2 and methane concentration changes in the atmosphere from 1750 to 2011. Formulae for calculating radiative forcing from concentration are given in IPCC (2013, supplementary material for chapter 8, p 8SM-7). These formulae are reproduced in Figure 2 below.

Figure 2. Formulae for calculating radiative forcing (RF) from IPCC(2013, supplemental material for chapter 8). Note indirect impacts augment methane’s contribution by a factor of 1.65, so methane’s  becomes 0.0594 rather than 0036. See discussion in text.

Figure 1 shows that between 1750 and 2011 methane increased from 722±25 ppbv (parts per billion by volume, or mole fraction CH4) to 1803±2 ppbv, and the concentration of CO2 increased from 278±5 to 390.5 ppmv. These values cannot be read from the graph with this accuracy, but can be found in IPCC (2013, p. 676-677). Table 1 shows the radiative forcings computed for these changes in atmospheric methane and CO2 concentrations

The radiative forcing calculated from the 1750 to 2011 concentration changes are given in Table 1, and a plot of these forcings since 1850 is given in Figure 3. Table 1 shows that between these two principle greenhouse gases, the rise of atmospheric CO2 over the industrial era (1750 to 2011) provided 79% of the greenhouse forcing and the rise in methane 21%. Figure 3 shows how the CO2 and CH4 forcings developed from 1850 to present and compares their contribution to those of the other gree nhouse gases.

Table 1. The radiative forcing, F, produced by the rise in the atmospheric concentrations of CO2 and CH4 over the industrial era (1750 to 2011) as calculated by the IPCC(2013) formulae in Figure 2. Faug is the forcing augmented by indirect contributions as discussed in the text.

-2 -2 Greenhouse gas 1750 2011 F[W m ] percent Faug[W m ] percent

CO2[ppmv] 278±5 390.5±0.1 1.82 79% 1.82 70%

CH4[ppvb] 722±25 1803±2 0.48 21% 0.79 30%

N2O[ppvb] 270 324.1±.1

Total forcing by CO2 and CH4 2.3 100% 2.61 100%

Figure 3. Radiative forcings for all the greenhouse gases computed over the industrial era from 1750 to 2011 and shown here from 1850. From Figure 8.6 of IPCC (2013). The forcings in 2011 correspond exactly to the unaugmented values in Table 1.

A complication in this simple story is that an increase in the concentration of a greenhouse gas may cause chemical changes in the troposphere or stratosphere than leads to additional (positive or negative) greenhouse forcing. Specifically methane’s contribution to greenhouse forcing is augmented in this fashion by impacting ozone in the troposphere and stratosphere (ftsOZ) and by changing stratospheric H2O (fsH2O). The result is that the radiative forcing of methane computed by the formula in

Figure 2 is augmented by a factor of 1.65 = (1+ftsOZ+fsH2O), where ftsOZ=0.5 and fsH2O=0.15 (IPCC, 2013, supplemental material Chapter 8, p. 8SM-17). This augmentation, suggested by Shindell and others, has been emphasized by Howarth in his arguments on the global warming dangers of methane. With this indirect augmentation, methane contributes 30% of the combined CO2+CH4 forcing over the industrial era, rather than 21%.

We use the augmented radiative forcing for methane in our discussions (e.g., the radiative forcing of methane additions to the atmosphere that is augmented by methane’s impact on ozone and water in the troposphere and stratosphere.

Finally, including the N2O correction to methane forcing in the formula in Figure 2 for projections past

2011 AD decreases the forcing by ~17% over a very broad range of CH4 increases (10 to 3000 ppbv). In our spreadsheet calculations we take advantage of this observation and simplify the calculations by reducing the methane forcing by 17%.

References 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.