The RF results for all 48 cases are presented in Table S1 and include the shortwave RF, the instantaneous clear‐sky and all‐sky longwave RF, the adjusted longwave RF (which includes the influence of the shortwave forcing on stratospheric temperature), and the net forcing. The row numbers in Table S1 will be used to refer to particular cases; forcing values for the cases where only one gas changes, and the impact of overlap, are shown in Figure 2 , wc 4 . The change, relative to the MHSS98 expressions, is also shown in Table S1. Updated expressions are discussed in section 4 . The new calculations are, for the most part, within about 5% of the old fits, but with a few notable exceptions. In particular, for cases where only methane changes (Table S1, rows 4, 7, and 10), the new calculations are 17–27% higher than the old fits—the reasons for this will be discussed in section 3.2 . For high CO 2 cases (2000 ppm—Table S1, rows 37–48) the new calculations are typically 10% higher than the old fits, indicating that the CO 2 forcing increases more rapidly than expected from a purely logarithmic dependence (as noted by others [e.g., Hansen et al ., 1988 ; Zhong and Haigh , 2013 ], and see section 4 ). Such high CO 2 amounts were outside the range considered by MHSS98. The ice age CO 2 concentrations (180 ppm—Table S1, rows 13–24) were also outside the range considered in MHSS98, but nevertheless, the old fits are within about 5% of the new calculations, which indicates that the pure logarithmic dependence was more appropriate for lower CO 2 levels. A few cases in Table S1 (rows 6, 8, and 12) have a high error (exceeding 50%) where the forcing is a small residual due to an increase in CH 4 and a decrease in N 2 O, or vice versa.

3.2 Explanation of Methane Forcing Changes

The most striking feature of the results is the enhancement of the methane RF by about 17–27% compared to the old expressions; this is beyond the nominal uncertainty estimates (about 10%) given in successive IPCC reports for WMGHG forcings. Two mechanisms are responsible–it is primarily due to the role of methane's shortwave bands, which were not included in MHSS98, with a secondary effect of an update to the water vapor continuum strength relative to that used in MHSS98.

Considering, as an example, the CH 4 change, from 750 to 1800 ppb (Table S1, row 4), the instantaneous shortwave forcing due to methane (0.03 W m−2) is about 6% of the total methane forcing (0.58 W m−2). This is further enhanced because the shortwave forcing affects stratospheric temperature adjustment; this effect is manifested by the change between the instantaneous and adjusted longwave forcings. Without the shortwave effect, the adjustment is found to be small and negative; the instantaneous RF of 0.516 W m−2 decreases by 2% to 0.504 W m−2 after adjustment for the 750–1800 ppb CH 4 change. Rind and Lacis [1993] report a 0.5% decrease after stratosphere temperature adjustment for a 280–560 ppb change in CH 4 , using a radiative‐convective model. When methane's shortwave absorption is included, the longwave adjustment is positive, increasing the longwave forcing from its instantaneous RF value of 0.516 to 0.548 W m−2 after adjustment, a 6% increase (or 9% relative to adjusted forcing without the shortwave effect). Hence, in total, the shortwave effect increases the methane forcing by 15% from its adjusted longwave‐only value of 0.504 to 0.582 W m−2.

The fact that the shortwave forcing for CH 4 is positive is notable, in the context of earlier work. For CO 2 , the shortwave bands cause a forcing that opposes and so acts to decrease the magnitude of the CO 2 longwave‐only forcing by about 5% (e.g., MHSS98 and Table S1, rows 13, 25, and 37); this is due to the combined effect of the direct absorption of the solar radiation in the stratosphere and its subsequent effect on temperature adjustment. For CH 4 , the instantaneous forcing calculations of Collins et al. [2006] and Forster et al. [2011] also imply a negative, rather than a positive shortwave forcing; in Collins et al. [2006] the shortwave forcing is 15% of, but the opposite sign to, the longwave irradiance change at 200 hPa for a doubling of CH 4 from preindustrial concentrations. However, these calculations were for an idealized clear‐sky case with a fixed solar zenith angle of 53° and a surface albedo of 0.1. The shortwave bands of N 2 O contribute less than 1% of the forcing; this forcing is included here but discussed no further.

The contrasting signs of the shortwave forcings of CH 4 and CO 2 can be explained by reference to Figure 1. This shows the spectral variation of global‐mean shortwave net forcing for the two gases (180 ppm to 389 ppm for CO 2 and 750 to 1800 ppb for CH 4 ). Supporting information Figure S1 shows the upward and downward forcing components. For both gases (Figures 1a and 1b), the sign of the forcing varies with wavelength, the net impact being the residual of these. In the case of CO 2 the negative forcing due to its 2.7 µm band dominates. For CH 4 , the positive forcing due to its 1.7 and 2.3 µm bands dominates. This contrasting behavior is driven by two processes. One is the stratospheric opacity of the gases, and the other is the degree of overlap of absorption bands with the near‐IR bands of water vapor. Figures 1c and 1d show the sum of line strengths for each 1 nm interval in the OLBL for water vapor (in both plots) and CO 2 and CH 4 .

Figure 1 Open in figure viewer PowerPoint Spectral variation of near‐infrared tropopause forcing (global‐mean, all sky) for (a) CH 4 (750 to 1800 ppb) and (b) CO 2 (180 to 389 ppm). The sum of the absorption line strengths in each 1 nm spectral interval is shown for (c) CH 4 and (d) CO 2 , with H 2 O line strengths shown in blue in both frames.

For all bands, the downward shortwave flux at the tropopause is always decreased by the increased concentrations, due to increased absorption in the stratosphere (Figures S1a and S1b). The sign of the forcing depends on whether this negative contribution dominates over the increased absorption by these gases in the troposphere, which contributes a positive forcing. For CO 2 , the extremely strong band at 4.3 µm makes little contribution to forcing at band center; absorption is almost complete in the stratosphere at unperturbed concentrations, and it only starts to contribute to forcing at the band edges. The CO 2 2.7 µm band lies toward the center of a strong water vapor band (Figure 1d). The change in the downward forcing is strongly negative (Figure S1b), but there is not a compensating increase in tropospheric absorption because the heavy spectral overlap with water vapor strongly mutes the impact of CO 2 increases. By contrast, the weaker bands of CO 2 at 1.6 and 2.0 µm lie in, or toward the edges of, windows between the main water vapor bands (Figure 1d); hence, they are more able to increase tropospheric absorption causing a positive forcing that dominates over the negative stratospheric component.

Methane has a strong band at 3.3 µm (Figure 1a), which lies within a region of relatively strong water vapor absorption (Figure 1c), leading to a negative net forcing. The weaker bands at 1.6 and 2.3 µm lie toward the center of the windows in the water vapor spectrum. They cause a positive forcing which more than compensates for the 3.3 µm negative forcing. In summary, the magnitude and sign of the solar RF depend on band strength, gas concentration, and overlap with water vapor.

The contrast with the implied negative forcing in earlier work originates from clouds. For the Collins et al. [2006] clear‐sky case, there is little tropospheric upward scatter of radiation (no clouds and low surface albedo), so that photons largely take a single pass through the troposphere. When clouds are added, the added CH 4 absorbs not only downwelling radiation but also upward scattered radiation, greatly increasing the tropospheric absorption (see Table S2). For both the extratropical and tropical cases, the inclusion of clouds causes the shortwave RF to change from a negative to a positive forcing of almost the same size; the negative clear‐sky forcing of about −0.04 W m−2 is consistent with the Collins et al. [2006] value of −0.13 W m−2 (for approximately the same methane change) after accounting for the higher incoming solar irradiance for their (fixed‐Sun) case. The effect of clouds on the shortwave RF from CH 4 is similar to the effect of clouds on the shortwave RF of black carbon aerosols [Haywood and Shine, 1997].

In trying to reconcile the present (longwave) results with those in MHSS98, we identified a further influence on the forcing due to CH 4 (and, to a lesser extent, the N 2 O). MHSS98 used the Clough‐Kneizys‐Davies (CKD) water vapor continuum version 0 in the OLBL calculations. In the region of the CH 4 and N 2 O bands that are most responsible for the longwave forcing (around 1300 cm−1), the foreign continuum was weakened by about a factor of 3.5 in subsequent versions of CKD [e.g., Mlawer et al., 1998] and successor versions (the Mlawer‐Tobin‐CKD) [Mlawer et al., 2012]. This reduces the effect of water vapor overlap with CH 4 , increasing its RF. Changes in the self‐continuum in this spectral region were much smaller during these updates. To isolate the effect of the continuum changes, the instantaneous cloudy‐sky longwave forcings were examined when CKD version 0 is updated to version 2.4.1. The update caused the CH 4 forcing for a 1800 to 3500 ppb change to increase by 4.2%. For comparison, the N 2 O forcing increased by about 1.7% for a 323 to 525 ppb change; for CO 2 , RF changed by less than 0.2%.

In total, comparing the new RFs to those calculated with the MHSS98 expressions, the CH 4 forcing increases by 17–27% for cases 4, 7, and 10 shown in Table S1. This is mostly due to the shortwave forcing, with a smaller contribution from the decreased strength of the foreign continuum in the region of methane's longwave bands. We note that contemporary radiation codes used in climate models often neglect the shortwave band of methane (e.g., all those models participating in the Collins et al. [2006] and CCMval [Fomichev and Forster, 2010] intercomparisons); by contrast, it is likely that more recent versions of the water vapor continuum in the mid‐infrared are already in use in these codes, and so they will be less affected by this component of our update to the MHSS98 calculations.