Separating the shortwave and longwave components of greenhouse gas radiative forcing

Many important greenhouse gases (including water vapour, carbon dioxide, methane and ozone) absorb solar radiation. When gas concentrations change, this absorption exerts a radiative forcing that modifies the thermal infrared (‘longwave’) radiative forcing which is predominant for most gases (ozone being a major exception). The nature of the solar forcing differs from the longwave forcing in several ways. For example, the sign of the instantaneous solar forcing can differ between the tropopause and top‐of‐atmosphere, and the sign can differ between gases. In addition, a significant part of the solar forcing can be manifested in the longwave, following stratospheric temperature adjustment, which can counteract or enhance the instantaneous solar forcing. Here the nature of solar forcing is examined via a mixture of idealised and more realistic calculations, which consider the effect of perturbations in carbon dioxide, methane and ozone. An apparent contradiction in the sign of the solar forcing of carbon dioxide is resolved; it is shown to be negative, reducing the net carbon dioxide forcing by about 2.3%. The relevance of this work to the effective radiative forcing concept is also discussed.


| INTRODUCTION
As well as absorbing thermal infrared radiation ('longwave [LW]' hereafter), greenhouse gases (hereafter GHGs, including H 2 O, CO 2 , O 3 and CH 4 ) absorb incoming solar radiation at near-infrared and sometimes visible and ultra-violet wavelengths (e.g., Gordon et al., 2017). We refer to this as shortwave (SW), often taken to be wavelengths less than 4 μm, acknowledging that some solar radiation is incident at longer wavelengths.
Many papers consider GHG LW radiative forcing in detail (e.g., Ramaswamy et al., 2018) and several explore mechanisms by which this forcing is manifested; Dufresne et al. (2020) presented an elegant demonstration of the relative contributions of increased atmospheric opacity, and the related change in emission height to CO 2 forcing. However, while GHG shortwave absorption, especially by H 2 O, CO 2 and O 3 , has long been included in climate model calculations (e.g., Manabe & Wetherald, 1967), its radiative forcing role has been relatively neglected, with the exception of O 3 . In addition, the radiative forcing literature indicates apparent contradictions in the sign of the SW forcing. An intercomparison of climate model radiative transfer codes (Collins et al., 2006) demonstrated that, at that time, many ignored GHG SW absorption beyond those mentioned above; Pincus et al. (2020) report progress in recent years.
This letter aims to resolve apparent contradictions in the nature of SW GHG radiative forcing. After reviewing current understanding, idealised and more realistic model calculations illustrate the SW processes in the framework of the instantaneous radiative forcing (IRF) and radiative forcing including stratospheric temperature adjustment (henceforth RF) (e.g., Myhre et al., 2013). The relevance to Effective Radiative Forcing (ERF) (e.g., Myhre et al., 2013) is also discussed.
2 | CURRENT UNDERSTANDING Hansen et al. (1981) presented calculations of top-ofatmosphere (TOA) LW and SW forcing due to a CO 2 doubling from 300 ppm. IRF SW was 0.1 WÁm À2 , compared to IRF LW of 2.4 WÁm À2 . The TOA RF SW (i.e., forcing including stratospheric temperature adjustment) of 0.1 WÁm À2 is unchanged from its IRF value; RF LW is 3.8 WÁm À2 , significantly higher than IRF LW . Hence, Hansen et al. (1981) found a positive SW forcing of 2.6% or 4% of the net (LW + SW) forcing, depending on whether RF or IRF is considered. The view that CO 2 IRF SW is positive re-emerged in the ERF framework, which takes a TOA perspective (e.g., fig. 14-6 of Ramaswamy et al., 2018).
By contrast, Cess et al. (1993) reported that CO 2 IRF SW was negative, and about 6% of IRF LW (for a doubling from 330 ppm). This view became established, although not all studies have found a negative CO 2 tropopause IRF SW (Forster et al., 2001). The apparent contradiction is because Cess et al. (1993) defined forcing at the tropopause; Hansen et al. (1981) chose TOA. This still leaves a question as to which perspective is of most value, and whether they can be reconciled. Myhre et al. (1998) also found a negative IRF SW for CO 2 of order 4% (À0.11 WÁm À2 ) of RF LW , for a doubling from 278 ppm. However, and of importance here, the additional SW absorption warms the stratosphere (relative to the LW-only case). In the RF framework, Myhre et al. (1998) calculated that this warming led to a positive tropopause RF LW (0.05 WÁm À2 ); thus, the net RF due to SW forcing (À0.06 WÁm À2 ) is about half IRF SW .
For increased concentrations of stratospheric H 2 O, Forster and Shine (2002) (see also Forster et al., 2001;Myhre et al., 2007Myhre et al., , 2009 found a negative tropopause IRF SW , offsetting about 20% of RF LW. Etminan et al. (2016) presented IRF SW calculations for methane; the tropopause IRF SW (for a 750-1800 ppb perturbation) was positive and 6% of the total forcing; accounting for the effect of warming of the stratosphere due to the additional SW absorption on RF LW , methane's SW forcing enhanced the LW-only RF by 15%.
Ozone is a distinct GHG because of its strong absorption of ultraviolet (and, to some extent, visible) radiation. Its SW forcing has long been recognised (e.g., Ramaswamy et al., 1992;Ramaswamy and Bowen, 1994;Hauglustaine et al., 1994) but, to our knowledge, the specific role of SW absorption in modifying RF LW has not been isolated. The differing TOA and tropopause perspectives have been indicated, but not fully explained, by Michou et al. (2020); they found the signs of TOA ERF SW and ERF LW for stratospheric ozone depletion were opposite to the tropopause RF LW and RF SW calculations of Checa-Garcia et al. (2018).
Taken together, these studies show that the apparent SW forcing depends on whether a tropopause or TOA perspective is taken, and whether its impact on stratospheric temperature adjustment (and hence on RF LW ) is accounted for. They also show that the sign of SW forcing varies among gases, sometimes enhancing and sometimes opposing RF LW . This letter constructs a framework to better understand SW forcing and to resolve apparent contradictions. This stresses that judging the importance of SW forcing via IRF SW , RF SW or ERF SW alone gives a misleading impression.
The impact of SW forcing on the LW via stratospheric temperatures (in the RF framework) and rapid (tropospheric and stratospheric) temperature adjustments (in the ERF framework) must be accounted for to give a correct impression of the size and sometimes the sign of SW forcing. In the ERF framework, other adjustments (e.g., in clouds and water vapour) driven by SW processes can also impact on ERF LW ; similarly, changes driven by LW processes can impact on ERF SW (e.g., Donohoe et al., 2014).
TOA IRF SW must be positive (consistent with Hansen et al. (1981)) for GHG concentration increases. Additional shortwave absorption always decreases planetary albedo. At the tropopause, the situation is unclear, unless the gas perturbation is solely in the stratosphere. Stratospheric absorption deprives the troposphere of radiation giving a negative IRF SW . However, additional tropospheric absorption decreases the albedo of the troposphere-surface system giving a positive IRF SW . Hence the tropopause IRF SW can have either sign. Etminan et al. (2016) show that the sign of CO 2 and CH 4 tropopause IRF SW varies with wavelength. They also show that the sign depends on the intensity of absorption features (for strong absorption features, additional absorption is mostly in the stratosphere, leading to a negative IRF SW ), and overlap with strong near-IR water vapour bands; if these bands are saturated in the troposphere, additional absorbers exert little influence on the upwelling irradiance at the tropopause. By contrast, additional absorption in relatively transparent windows between these bands can lead to a positive IRF SW . This is especially so for cloudy skies, as tropospheric albedo is higher, and the importance of absorption of upwelling radiation by the gas is enhanced; Etminan et al. (2016) find the wavelength-integrated CH 4 IRF SW at the tropopause is negative for clear skies but positive when clouds are included (although Collins et al., 2018 found it to be positive in both cases). Etminan et al. (2016) found it was negative in both cases for CO 2 .
As noted above, IRF alone cannot constrain the effect of shortwave absorption; within the RF framework, the impact of increased stratospheric SW absorption on LW forcing must be considered. Section 3 uses idealised calculations to illustrate this.

| IDEALISED CALCULATIONS WITH NO INSTANTANEOUS LONGWAVE RADIATIVE FORCING
The idealised calculations of SW forcing employ the LW code of Shine and Myhre (2020) and the SW code of Slingo and Schrecker (1982) with updated gaseous absorption coefficients from Chagas et al. (2001). Calculations use a global-mean atmospheric profile (temperature, humidity, ozone and clouds) from Freckleton et al. (1998) with a global-mean tropopause of 128.6 hPa, global-mean insolation (solar zenith angle of 60 for 12 h) and a spectrally-constant surface albedo of 0.06 (representing a sea surface). The forcing due to a grey absorber which is added only to near-IR bands (wavelengths greater than 1 μm) is computed; that is, there is no IRF LW . The grey absorber has an absorption coefficient of 4 Â 10 À4 m 2 Ákg À1 and a constant mass mixing ratio of 0.0005 kgÁkg À1 , giving an optical depth of 0.003 when the absorber is in the stratosphere only and 0.024 when at all altitudes. RF is computed by a standard timestepping procedure that adjusts stratospheric temperature until the LW + SW heating rates return to global-mean radiative equilibrium.
In Idealised Example 1 (Table 1), the grey absorber is in the stratosphere only. As expected from Section 2, IRF SW is positive at TOA, and negative at the tropopause.
This causes additional stratospheric absorption of solar radiation; in this case, the TOA forcing is +0.29 WÁm À2 , the tropopause forcing is À0.54 WÁm À2 , giving a convergence of 0.83 WÁm À2 . The consequent warming of the stratosphere increases LW emission to space and the troposphere. Increased upward TOA irradiance constitutes a negative LW forcing; increased downward tropopause irradiance constitutes a positive LW forcing. Thus, RF LW is opposite in sign and comparable in size to IRF SW at both TOA and tropopause (Table 1).
It is initially surprising that at TOA, RF LW (À0.4 WÁm À2 ) is larger in magnitude than IRF SW . However, increased LW emission from the stratosphere due to the adjustment (0.4 WÁm À2 upwards at TOA and 0.43 WÁm À2 downwards at the tropopause) is consistent, as it should be, with the 0.83 WÁm À2 convergence of SW radiation. In this case, RF LW is nearly equal at TOA and tropopause; the SW effect on RF LW could be estimated by partitioning the convergence of SW radiation in this way. This is because the grey absorber is at all stratospheric levels. When placed in the topmost layer only (at 1 hPa), TOA RF LW is about 6 times larger than the tropopause RF LW . When placed only in the layer closest to the tropopause, the tropopause RF LW is about double TOA RF LW .
The net forcing, RF NET , at TOA and tropopause is now equal (À0.11 WÁm À2 ), as is required following stratospheric temperature adjustment. In this example, because SW absorption deprives the surface-troposphere system of energy, RF NET is negative but, because of the compensatory effect of increased stratospheric LW emission, it is only 20% of the value inferred from the tropopause IRF SW .
This illustrates how IRF SW differs in sign between the TOA and tropopause perspectives (i.e., there is no contradiction in the literature) and also illustrates how SW absorption cannot be judged from IRF SW alone; the effect on RF LW must be considered. Once RF LW is included, there is no ambiguity in the sign of RF NET and it agrees at TOA and tropopause.
In Idealised Example 2 ( Table 2) the grey absorber is present at all altitudes. IRF SW is now positive at both TOA and tropopause, because of increased tropospheric absorption of solar radiation. Because stratospheric convergence of SW radiation is only slightly affected by T A B L E 1 Idealised example 1: Global and annual instantaneous and adjusted radiative forcing (WÁm À2 ) at the top-of-atmosphere and tropopause when including a weakly-absorbing grey shortwave-only absorber in the stratosphere only tropospheric absorption (i.e., 1.50-0.67 = 0.83 WÁm À2 as in Example 1), RF LW from stratospheric temperature adjustment is almost identical to Table 1. In this case, RF LW is a smaller proportion of IRF SW , and RF NET is positive. Again, this example illustrates that forcing due shortwave absorption cannot be judged by IRF SW alone, although in this case the sign of IRF SW is the same at TOA and tropopause and consistent with RF NET .

| MORE REALISTIC CALCULATIONS FOR CARBON DIOXIDE, METHANE AND OZONE
The role of SW forcing in more realistic cases is calculated using the more sophisticated configuration of Checa-Garcia et al. (2018). RF is calculated on a 5 Â 5 horizontal grid; stratospheric temperature adjustment is calculated using the fixed-dynamical heating method. It uses the SOCRATES radiative transfer code (Walters et al., 2019), using the Met Office Earth System Model configuration: 9 LW bands (wavenumbers 1-2995 cm À1 ) and 6 SW bands (wavenumbers 1-50,000 cm À1 ). Unlike Section 3, IRF has both LW and SW components. We perform calculations with both LW and SW components, and then repeat them with only the LW component active ('LW only' in the tables). The difference between these yields the total RF SW forcing, including its impact on RF LW via stratospheric temperature adjustment.
SOCRATES is regularly updated to reflect its performance in radiation code intercomparisons (e.g., Pincus et al., 2015) and updated spectral data. Walters et al.
(2019) (their sec. 3.2.1) document significant improvements in the version used here, relative to a high-spectral resolution code which was compared with other benchmark codes in Pincus et al. (2020).
The example GHGs (CO 2 , CH 4 , O 3 ) are the ones most widely discussed in earlier work (Section 2); their different behaviours should guide how other GHGs would behave. CO 2 has intense SW stratospheric absorption so that its tropopause IRF SW is negative; methane is weaker giving a positive tropopause IRF SW ; ozone is unusual as RF SW and RF LW are comparable. Etminan et al. (2016) demonstrate that nitrous oxide's RF SW is much smaller than gases considered here. The results presented here are highly relevant to the ERF framework. Stratospheric temperature adjustment is the largest adjustment in ERF calculations for CO 2 (Smith et al., 2018) and ozone (Skeie et al., 2020); for methane, adjustments are small when RF SW is neglected, but are more important when it is included (Etminan et al., 2016).
Calculations use multi-year (2000-2009) monthlymean averages of temperature, water vapour, clouds and surface albedo from ERA-Interim (Checa-Garcia et al., 2018). The source of ozone fields is described below. Calculations include the impact of tropospheric scattering of solar radiation by clouds and the surface on absorption of SW radiation in the stratosphere; this has been shown (Section 2) to be important in quantifying methane's IRF SW Etminan et al., 2016). To demonstrate the role of SW forcing, methane and CO 2 calculations are presented for January, as there is a relatively small seasonal dependence; for ozone, where seasonal variations larger, results are presented as annual-means derived from monthly-mean calculations. Table 3 (and Figure 1) shows the forcing for CO 2 increasing from 278 to 417 ppm; the IRF SW is +5.6% of IRF NET at TOA and À5.2% at the tropopause, consistent with earlier literature (Section 2). The effect of stratospheric temperature adjustment on RF NET is much larger at TOA (increasing it by 70%) than at the tropopause (decreasing it by 8%), consistent with earlier literature. This means that RF SW (which is unchanged from IRF SW because of the weak impact of stratospheric temperature change) is a smaller component of RF NET at TOA (3.3%) and a slightly larger tropopause component (À5.6%). As required, RF NET now agrees at TOA and tropopause but, as shown in Table 3 and Figure 1 (left), the apparent SW attribution differs in sign between these levels.
However, this does not account for the role of SW absorption in temperature adjustment. This can be assessed by calculating RF NET due to LW processes alone (Etminan et al., 2016;Myhre et al., 1998). The lower two rows in Table 3 shows this LW-only RF NET is 0.05 WÁm À2 greater than the full RF NET . This 0.05 WÁm À2 reduction in RF NET robustly indicates the T A B L E 2 Idealised example 2: Global and annual instantaneous and adjusted radiative forcing (WÁm À2 ) at the top-of-atmosphere and tropopause when including a weakly-absorbing shortwave-only grey absorber at all altitudes total impact of SW forcing, accounting for the direct effect via IRF SW , and its indirect impact on RF LW via stratospheric temperature change. RF NET decreases by 2.3% at both TOA and tropopause (see Figure 1 [right]). As in Section 2, the contribution of the direct IRF SW , and its impact on RF LW , differs depending on TOA and tropopause perspectives. In this case the positive TOA IRF SW gives an incorrect perception of the sign of SW absorption. Tropopause IRF SW significantly overemphasises the size of the (negative) SW forcing, as noted by Myhre et al. (1998). In the Section 3 idealised calculations, the RF LW due to SW absorption was approximately equal and opposite at TOA and tropopause. For CO 2 , the additional SW absorption is mostly in the upper stratosphere; the effect on RF LW is about 1.7 times higher at TOA than at the T A B L E 3 Global-mean instantaneous and adjusted radiative forcing (WÁm À2 ) for January at the top-of-atmosphere and tropopause for an increase in CO 2 from 278 to 417 ppm tropopause (compare the À0.12 and 0.07 WÁm À2 values in parentheses in the adjusted RF LW column of Table 3). Table 4 and Figure 1 show results for methane doubling from 725 ppb. We will show elsewhere that the low spectral-resolution version of SOCRATES underestimates methane's IRF SW ; the purpose here is to illustrate processes, rather than to present definitive values for methane RF. In this case, both TOA and tropopause IRF SW are positive, although TOA IRF SW is more strongly so. Stratospheric temperature adjustment is small in the LW-only case (Etminan et al., 2016); both IRF NET and RF NET are 0.37 WÁm À2 . When SW is included, convergence of SW radiation in the stratosphere (0.06 WÁm À2 ) drives a larger adjustment; IRF NET and RF NET differ by about 0.03 W m À2 at TOA and tropopause. Unlike the CO 2 case this is not sufficiently strong to reverse the sign of TOA RF SW (it decreases from +0.07 to +0.03 WÁm À2 ) but it significantly enhances tropopause RF NET (from 0.01 to 0.03 WÁm À2 ) compared to the IRF SW , consistent with Etminan et al. (2016). Figure 1 shows results for ozone perturbations, taking the CMIP6 case from Checa-Garcia et al. (2018) for stratospheric ozone change (Table 5) and stratospheric and tropospheric ozone change (Table 6) derived from multimodel averages. Forcing is calculated using decadal-mean ozone fields for 2000-2009, relative to 1850-1859. Ozone differs from CO 2 and CH 4 because of the perturbation's more complex morphology, and because SW forcing plays a larger relative role (Figure 1). For stratospheric ozone depletion (Table 5) IRF SW is negative at TOA (the decreased stratospheric absorption means more SW radiation is reflected). and positive at the tropopause (more radiation is transmitted through the stratosphere). In both cases IRF LW is negative. The instantaneous divergence of forcing across the stratosphere (≈0.07 WÁm À2 due to IRF LW and ≈0.22 WÁm À2 due to IRF SW ) drives strong stratospheric cooling. The reduced emission increases TOA RF LW relative to IRF LW , changing its sign from À0.045 to +0.088 WÁm À2 , and makes tropopause RF LW more negative (À0.02 to À0.13 WÁm À2 ). This reduces TOA RF NET and changes the sign of tropopause RF NET . Importantly, even though RF NET is identical at TOA and tropopause, the LW and SW components are of opposite signs, explaining the apparent discrepancy mentioned by Michou et al. (2020) (see Section 2). The TOA RF is most consistent with the ERF perspective.
By comparing with the LW-only case, Table 5 and Figure 1 show the major effect of SW-induced stratospheric cooling on RF LW . Without SW-induced cooling, RF LW is À0.06 WÁm À2 at TOA and tropopause; with it, they are +0.09 and À0.13 WÁm À2 respectively.
The case with decreasing stratospheric and increasing tropospheric ozone (Table 6, Figure 1) is more complex than the stratosphere-only case. The biggest difference is the positive IRF LW at both TOA and tropopause, but IRF SW is also impacted via reduced SW reflection from the troposphere. The instantaneous divergence of forcing T A B L E 5 Annual-mean global-mean instantaneous and adjusted radiative forcing (WÁm À2 ) at the top-of-atmosphere and tropopause for the stratospheric ozone perturbation described in the text across the stratosphere (0.23 WÁm À2 due to LW and 0.24 WÁm À2 due to SW) still drives strong stratospheric cooling. The SW forcing, via its impact on stratospheric temperature, increases TOA RF LW by 85% (from 0.19 to 0.34 WÁm À2 ) and decreases tropopause RF LW by 45% (from 0.19 to 0.11 WÁm À2 ). Unlike Table 5, RF LW is positive at tropopause and TOA for both the full and LW-only case, as the forcing from tropospheric ozone increases dominates. As shown in Figure 1 (right), RF LW is the dominant contributor to RF NET , even when the impact of SW forcing on RF LW is accounted for.

| CONCLUSIONS
Via idealised and more realistic calculations, the nature of SW radiative forcing has been investigated. It has been shown that even the sign of the SW forcing can differ between topof-atmosphere and tropopause perspectives, even though, following stratospheric temperature adjustment, the net topof-atmosphere and tropopause forcings are identical. This indicates that, on its own, the shortwave forcing is not a consistent indicator of its importance in net forcing. A more consistent view is achieved by considering the impact of SW forcing on LW forcing via stratospheric temperature adjustment. This separation can be achieved by comparing calculations that include and exclude SW forcing.
In this perspective, not only do the top-of-atmosphere and tropopause perspectives agree in the net forcing, but also the partitioning between SW and LW agrees. In the specific case of increased CO 2 , SW processes decrease the net forcing at both the top of the atmosphere and tropopause by 2.3%; this resolves an apparent contradiction in the earlier literature that indicated that the sign of the SW forcing differs between these perspectives. For methane, the instantaneous SW tropopause forcing is smaller than the top-of-atmosphere because it is a residual of negative forcing due to increased stratospheric absorption and positive forcing due to decreased tropospheric reflection; including the effect of this SW absorption on stratospheric temperatures achieves a more nuanced but consistent view. For the ozone, again the top-ofatmosphere and tropopause views of the importance of SW and LW components differ significantly unless the SW influence on LW forcing is accounted for.
The most important conclusion here is that in both radiative forcing and effective radiative forcing frameworks, the role of SW forcing, when it arises from atmospheric absorption (rather than scattering), cannot be assessed by considering changes in SW irradiances alone; indeed, even the implied sign of the SW forcing may be incorrect. We have demonstrated that this is the case for stratospheric temperature adjustment. More detailed calculations with ESMs would be needed to understand how other LW rapid adjustments are affected by SW forcings to achieve a more complete view.